Physical and numerical approximations of reactive distillation ...than models using the physical...

AN ABSTRACT OF THE THESIS OF

Varong Pavarajarn for the degree of Master of Science in Chemical Engineering

presented on January 3 1996 Title Physical and Numerical Approximations of

Reactive Distillation Dynamics

Abstract approved Keith L Levien

Two approaches to reduce computational requirements for solving reactive

distillation problems have been studied simplification of the model using physical

assumptions and numerical approximation using an orthogonal collocation technique

The results of a full-order model with time dependent stage molar holdups was

compared to published steady-state experimental data and was found to be more

accurate than previously published methods

Two example problems concerning reactive distillation columns with different

number of stages were investigated in order to find limitations of the order-reduction

technique The steady-state results obtained in both cases were remarkably accurate

even though the reduced-order model contained only 40 percent of the number of

equations However step and pulse responses indicated that very low order models did

not provide good approximations in the dynamic behavior of a column which contained

29 stages

Modeling errors introduced by either physical or numerical approximations were

compared for several example problems The results showed that the reduced-order

models with time-dependent holdups provided better steady-state and dynamic results

Redacted for Privacy

than models using the physical approximation of constant molar holdups in almost

every case The only case in which the reduced-order model failed was when the 40

order-reduction model was used to approximate dynamic responses of a column with a

significant pressure drop across each tray The effects of plate and weir geometries

were also studied The results obtained indicated that the volume holdup on the plate

was the dominant parameter columns with plates of different sizes but the same steady-

state holdup behaved similarly

Physical and Numerical Approximations of


by

Varong Pavarajarn

A THESIS

submitted to

Oregon State University

in partial fulfillment of the requirements for the

degree of

Master of Science

Completed January 3 1996 Commencement June 1996

Master of Science thesis of Varong Pavarajarn presented on January 3 1996

APPROVED

Major Professor representing Chemical Engineering

C

Dean of Gra to School

I understand that my thesis will become part of the permanent collection of Oregon

State University Library My signature below authorizes release of my thesis to any

reader upon request

Varong Pavarajarn Author





ACKNOWLEDGEMENTS

I would like to express my sincere appreciation to all of people who have helped

me make this dream come true

Royal Thai Government for full sponsorship through out the entire course of this work I would not have had the opportunity to be here without them

Dr Keith Levien my major professor who taught me precious lessons and gave me many valuable comments through out the research This work would not exist without his guide

Dr Terrence Beaumariage Dr Goran Jovanovic and Dr Michael Milota who were my committee members special thanks for their invaluable time

Rungsun Pianpucktr who was my counselor and taught me how to enjoy life I would be a working machine without his lessons

Udom Techakijkajorn who generously lent me his powerful computer Without his computer I might have needed other three months to complete all simulations

Rangsi Yokubol for his benevolence Every time when I was in deep trouble I got help from him

Charlie Chairatanatrai for all his computer tricks I would know nothing about UNIX without him

My parents for their support and encouragement I could face any problems because of them

Alisa Vangnai for her sincere love and understanding I could hardly live without her

TABLE OF CONTENTS

Page

1 INTRODUCTION 1

11 Computational Approach 2

12 Approach to the Problem 5 121 Process modeling 5 122 Solving system of differential and algebraic equations 6 123 Orthogonal collocation 7

13 Literature Survey 10

2 DEVELOPMENT OF THE MODELS 13

21 General Assumptions 13

22 Full-order Models 14 221 The constant molar holdup (CMH) model 19 222 The time-dependent molar holdup (TDMH) model 25

23 Reduced-order Model 29 231 Constant molar holdup model 33 232 Time-dependent molar holdup model 33

3 NUMERICAL IMPLEMENTATION 35

31 Thermodynamic Properties 35 311 Enthalpies 35 312 Equilibrium constants 39 313 Bubble point temperature 40 314 Fraction of feed vaporized 41 315 Liquid densities 42

32 Derivatives of Thermodynamic Properties 43

33 Rate of Reactions 47

34 Collocation Points 48

35 Integration Software 49

TABLE OF CONTENTS (Continued)

Page

4 MODEL VALIDATION AND DESIGN OF MODEL TESTING 51

41 Validation with Published Steady-state Experimental Data 51

42 Simulation Tests of Models 55

5 EXAMPLE PROBLEM 1 58



71 Example Problem 31 Non-uniform Pressure Effects 112

72 Example Problem 32 Plate Geometry Effects 140

8 CONCLUSIONS AND RECOMMENDATIONS 167

BIBLIOGRAPHY 169

APPENDICES 172

Appendix A Physical Properties Data 173

Appendix B Sequence of Computations 176

Appendix C Numerical Results of Model Validation 179

LIST OF FIGURES

Figure Page

11 Schematic diagram illustrating the continuous position variable s within a separation module 8

21 Schematic diagram and notation for a distillation column 16

22 Schematic diagram and notation for i-th equilibrium stage 17

23 Schematic diagram and notation for total condenser 17

24 Schematic diagram and notation for reboiler 17

25 Schematic diagram for end-around mass and energy balances 22

26 Mass and energy balance envelopes utilized in the derivation of the equations for calculating liquid and vapor flowrates 23

27 Geometry utilized for calculating liquid flowrates leaving an equilibrium stage using Francis weir formula 26

28 Schematic diagram and notation utilized for a reduced-order column model 30

411 Steady-state composition profiles for model validation 54

51 Steady-state temperature profiles for Example problem 1 61

52 Steady-state composition profiles of A for Example problem 1 62

53 Steady-state composition profiles of R for Example problem 1 63

54 Steady-state composition profiles of S for Example problem 1 64

55 Steady-state liquid and vapor flowrate profiles for Example problem 1 65

56 Step responses for A in bottom product for Example problem 1 69

57 Step responses for R in bottom product for Example problem 1 70

LIST OF FIGURES (Continued)

Figure Page

58 Step responses for S in bottom product for Example problem 1 71

59 Initial and final molar holdup profiles for step test of full-order TDMH model in Example problem 1 74

510 Pulse responses for A in bottom product for Example problem 1 75

511 Pulse responses for R in bottom product for Example problem 1 76

512 Pulse responses for S in bottom product for Example problem 1 77

513 Bode diagram for full-order pulse responses of A in Example problem 1 79

514 Bode diagram for the TDMH model pulse responses of A in Example problem 1 80

515 Bode diagram for the CMH model pulse responses of A in Example problem 1 81

61 Steady-state liquid composition profiles for Example problem 2 87

62 Steady-state profiles of parameters of the column for Example problem 2 88

63 Vapor pressure of each species over the temperature range in Example problem 2 89

64 Step responses for liquid composition of each species in reboiler for Example problem 2 92

65 Final steady-state liquid composition profiles for Example problem 2 after 20 step increasing in feed flowrate 93

66 Final steady-state profiles of column parameters for Example problem 2 after 20 step increasing in feed flowrate 94


Figure Page

67 Pulse responses for liquid composition of each species in reboiler for Example problem 2 96

68 Bode diagram for pulse responses of AcOEt in Example problem 2 97

71 Steady-state composition profiles for Example problem 3 103



74 Pulse responses for liquid composition of each species in the bottom product for Example problem 3 109


76 Bode diagram for pulse responses of water in Example problem 3 111

711 Pressure profile for various values of pressure drop 112

712 Steady-state temperature profiles for case 31a-31c 115

713 Steady-state composition profiles of AcOH for case 31a-31c 116

714 Steady-state composition profiles of EtOH for case 31a-31c 117

715 Steady-state composition profiles of water for case 31a-31c 118

716 Steady-state composition profiles of AcOEt for case 31a-31c 119

717 Steady-state flowrate profiles for case 31a-31c 120

718 Liquid molar holdup profiles for case 31a-31c 121


Figure Page

719 Profiles show rate of total consumption of AcOH (71AcoH) for case 31a-31c 122

7110 Vapor pressure of each species over the temperature range in Example problem 31a 124

7111 Full-order step responses for liquid composition of each species in reboiler at various value of pressure drop 126

7112 Step responses for composition of AcOH for case 31a-31c 127

7113 Step responses for composition of EtOH for case 31a-31c 128

7114 Step responses for composition of water for case 31a-31c 129

7115 Step responses for composition of AcOEt for case 31a-31c 130

7116 Pulse responses for composition of AcOH for case 31a-31c 132

7117 Pulse responses for composition of EtOH for case 31a-31c 133

7118 Pulse responses for composition of water for case 31a-31c 134

7119 Pulse responses for composition of AcOEt for case 31a-31c 135

7120 Bode diagram for pulse responses of AcOEt at various pressure drop 136

7121 Bode diagram for pulse responses of AcOEt when pressure drop in each tray = 005 atm 137



721 Steady-state temperature profiles for case 32a-32d 143


Figure Page

722 Steady-state composition profiles of AcOH for case 32a-32d 144

723 Steady-state composition profiles of EtOH for case 32a-32d 145

724 Steady-state composition profiles of water for case 32a-32d 146

725 Steady-state composition profiles of AcOEt for case 32a-32d 147

726 Steady-state flowrate profiles for case 32a-32d 148

727 Liquid molar holdup profiles for case 32a-32d 149

728 Profiles show rate of consumption of AcOH for case 32a-32d 150

729 Full-order step responses for liquid composition of each species in reboiler of various size of column 153

7210 Step responses for composition of AcOH for case 32a-32d 154

7211 Step responses for composition of EtOH for case 32a-32d 155

7212 Step responses for composition of water for case 32a-32d 156

7213 Step responses for composition of AcOEt for case 32a-32d 157

7214 Pulse responses for composition of AcOH for case 32a-32d 159

7215 Pulse responses for composition of EtOH for case 32a-32d 160

7216 Pulse responses for composition of water for case 32a-32d 161

7217 Pulse responses for composition of AcOEt for case 32a-32d 162

7218 Bode diagram for pulse responses of AcOEt from various plate dimension 163

7219 Bode diagram for pulse responses of AcOEt from case 32b 164


Figure Page

7220 Bode diagram for pulse responses of AcOEt from case 32c 165

7221 Bode diagram for pulse responses of AcOEt from case 32d 166

LIST OF TABLES

Table Page

411 Conditions for Komatsu (1976) experiment 52

412 Mean squared errors for steady-state profiles in the validation of the model 53

421 Summary of problems 56

51 Thermodynamic properties of species utilized in Example problem 1 58

52 Problem specifications for Example problem 1 59

53 Collocation points utilized in Example problem 1 60

54 Mean Squared Errors for steady-state profiles for Example problem 1 66

55 Initial and final value of composition of bottom product for step test in Example problem 1 72

56 Relative computing times for step tests in Example problem 1 72


62 Location of collocation points utilized in Example problem 2 84


64 Total rate of consumption of AcOH in the column for Example problem 2 86




73 Mean Squared Errors for steady-state profile for Example problem 3 102

LIST OF TABLES (Continued)

Table Page



711 Mean squared errors for full-order steady-state profiles for Example problem 31a 113

712 Mean squared errors for reduced-order steady-state profiles for Example problem 31 114

721 Plate dimension of the columns utilized in Example problem 32 140


LIST OF APPENDIX FIGURES

Figure Page

B1 Flowsheet diagram demonstrating the sequence of computations utilized for solving a reactive distillation problem using the CMH model 177

B2 Flowsheet diagram demonstrating the sequence of computations utilized for solving a reactive distillation problem using the TDMH model 178

LIST OF APPENDIX TABLES

Table Page

A1 Physical constants 173

A2 Enthalpy data 173

A3 Coefficient for the Benedict-Webb-Rubin (BWR) equation of state 174

A4 Constant for Antoine equation for vapor pressure (Pideg) 174

A5 Parameters for the Margules equation for activity coefficient (Eqn 3-15) 175

C1 Mole fraction of acetic acid obtained from the problem discussed in Sec41 179

C2 Mole fraction of ethanol obtained from the problem discussed in Sec41 179

C3 Mole fraction of water obtained from the problem discussed in Sec41 180

C4 Mole fraction of ethyl acetate obtained from the problem discussed in Sec41 180

LIST OF NOTATIONS

Unless otherwise stated in the text the definitions below express the intended

meaning for the following symbols

a b c d Stoichiometric constants

Ao Bo Co ao bo co oto yo Parameters in BWR equation of state

A1 A16 Parameters in Margules equation

AJO Bi0 C10 Parameters in Antoine equation

B Bottom product flowrate [gmolemin]

Concentration of species j in liquid phase [gmolem3]

D Distillate product flowrate [gmolemin]

41 Column diameter [m]

Ei Vaporization efficiency of species j (1 for calculation in this thesis)

F Feed stream flowrate [gmolemin]

f Feed stage

f Fugacity [atm]

F Flow constant for Francis weir formula (1 for calculation in this thesis) Eqn (2-24b)

hB Molar enthalpy of bottom product [calgmole]

ho Molar enthalpy of distillate product [calgmole]

HF Molar enthalpy of feed stream [calgmole]

hi Liquid molar enthalpy on stage i [calgmole]

Vapor molar enthalpy on stage i [calgmole]

how Height of vapor-free liquid over the weir on stage i [m]

Hw Molar enthalpy of withdrawal stream [calgmole]

11) Weir height [m]

k Rate constant for forward reaction

k Rate constant for backward reaction

ICi Phase equilibrium constant for species j on stage i

(s t) Generic variable related to the liquid phase

L Liquid flowrate leaving stage i [gmolemin]

1 Weir length [m]

M Number of actual stages in a module

m Number of collocation points in a module

M Total molar holdup on stage i [gmole]

N Total number of internal stages in the Column

tic Total number of components

Pe Critical pressure [atm]

P Pressure on stage i [atm]

pio Vapor pressure of species j [atm]

Qc Condenser duty [calmin]

q Liquid volumetric flowrate leaving stage i [m3min]

QR Reboiler duty [calmin]

R Gas constant [0082061atmgmoleK]

Rate of consumption of the base reactant A [gmole Am3min]

s Position variable (continuous)

t Time [min]

Tc Critical temperature [K]

T Temperature on stage i [K]

Ui Liquid volume holdup on stage i [m3]

v(st) Generic variable related to the vapor phase

Vc Critical volume [m3gmole]

Vapor flowrate leaving stage i [gmolemin]

W Withdrawal stream flowrate [gmolemin]

W(st) Lagrange interpolating polynomial for liquid phase variables

Wn v(S t) Lagrange interpolating polynomial for vapor phase variables

xtri Composition of species j in bottom product

xpi Composition of species j in distillate product

XFJ Composition of species j in feed stream

Liquid composition of species j on stage i

Composition of species j in withdrawal stream

Vapor composition of species j on stage i

Critical compressibility factor of species j

Composition of species j in feed stream

Greek symbols

a Parameters in orthogonality condition for Hahn polynomials

Activity coefficient for species j on stage i

IliA Moles of A consumed by reaction per unit time on stage i [gmolemin]

Latent heat of vaporization of species j [calgmole]

Normalized stoichiometric coefficient for species jvi Eqn (2-1)

Critical molar density [gmolem3] Pc

Molar liquid density on stage i [gmolem3]Pi

Molar density of liquid [gmolem3]Pi

Pv Molar density of vapor [gmolem3]

SZj Enthalpy departure of species j [calgmole]

Fraction of feed vaporized

Subscripts

B Bottom product

c Critical thermodynamic property

D Distillate product

F Feed stream

1 Liquid phase

r Reduced thermodynamic property

v

R Rectifying section

S Stripping section

Vapor phase

PHYSICAL AND NUMERICAL APPROXIMATIONS OF REACTIVE DISTILLATION DYNAMICS

I INTRODUCTION

Reactive distillation is a unit operation in which chemical reactions and

distillation take place simultaneously This combined system can be attractive for

processes involving an equilibrium-limited reaction such as the production of methyl-

acetate

acetic acid + methanol lt-gt water + methyl-acetate

The continual separation of products from reactants causes the reaction to shift

to the right following LeChateliers principle In some cases this effect causes a

remarkable payoff in simplifying the phase behavior by eliminating azeotropes This

has been claimed as the most important feature of reactive distillation (Doherty et al

1992) Reactive distillation can also lead to substantial savings in capital and operating

costs compared to a conventional scheme composed of separate reactor and distillation

vessels Because reactions and separation are carried out in the same vessel the cost

associated with major equipment pumps piping and instrumentation can often be

reduced Moreover the energy released in an exothermic reaction can be utilized

efficiently which results in energy savings Because reaction and separation occur

simultaneously recycle costs can be decreased

2

Although there are many advantages from the use of reactive distillation not

every process can be carried out in this combined system The candidate reactions

should be reversible reactions in which the products have significantly different

volatility than the reactants The desired reactions also have to have acceptable rates of

reaction at temperatures and pressures which are reasonable for separation Hence a

high pressure high temperature gas-phase reaction such as hydrogenation is unsuitable

for reactive distillation On the other hand the production of ethers such as methyl

tert-butyl ether (MTBE) and tert-amyl methyl ether (TAME) or the production of

esters such as methyl acetate can be done using reactive distillation

Because of the importance of reactive distillation methods to solve the reactive

distillation equations are of interest Several methods have been proposed Suzuki et al

(1971) Komatsu (1977) Izarraraz (1980) and Alejski et al (1988) However most

previous studies considered only steady-state simulation Furthermore only a few

rigorous dynamic simulations were done where the hydraulics of the column were

discussed In this thesis a program to simulate column dynamics which included

hydraulic effects was developed In addition orthogonal collocation techniques were

applied to reduce the computational demand by reducing the number of differential

equations in the model

11 Computational Approach

A rigorous model of an equilibrium-staged separation operation such as a

distillation column consists of a large number of non-linear material energy and

3

equilibrium relationships which must be simultaneously satisfied To solve this kind of

complex problem significant computational effort is required For reactive distillation

operations however the problem is even more complex due to kinetic expressions

which are normally non-linear

One obvious approach to reduce the computational requirements for multistage-

multicomponent separation problems is to somehow reduce the number of equations

Traditionally the number of equations needed has been reduced by simplifying the

model based on assumptions about physical properties material energy and equilibrium

relations Moreover some dynamic phenomena such as hydraulic effects are

neglected in order to decrease the complexity of the model Although the

computational effort for solving the problem is significantly reduced by these

assumptions substantial errors can arise Such physical approximations may be

suitable only for preliminary evaluation of designs

An alternative approach is to simplify the computations by solving the stage

equations only at certain locations within a column ie at collocation points Thus the

number of equations to be solved can be reduced however this approach also

introduces some accuracies The work reported in this thesis was done to make

quantitative comparisons of modeling errors introduced by physical or numerical

approximation methods in reactive distillation simulation The following physical

models were studied

1 Constant molar holdup model (CMH)

2 Time dependent molar holdup model (TDMH) either

4

TDMH with constant pressure in the column

TDMH with a pressure gradient in the column

In these studies a full-order model was compared to several reduced-order

models obtained by numerical approximations This full-order TDMH model was

treated as the true process which yields true dynamic and steady-state results The

accuracy of this full-order TDMH model was first examined by comparing its simulated

results with previously published experimental results The following aspects were

considered as criteria in comparisons of different models

1) Steady-state profiles

Steady-state profiles represent the initial and final states of dynamic simulations

The profiles for temperature compositions flowrate and holdup obtained from each

model were compared against steady-state profiles calculated from the reference model

2) Dynamic responses to step changes in input variables

This criterion is a common tool to demonstrate the ability of a model to predict

dynamics of a column or path from one steady state to another The required

computing times for each model were also compared

3) Dynamic pulse tests

The results from this test were used to present dynamic characteristics of each

model in the form of Bode plots of the frequency response

5

12 Approach to the Problem

121 Process modeling

The dynamic models were developed from a set of equations and assumptions

applying to each equilibrium stage in the column The equations required for

equilibrium-staged separation models are

1 Overall material balance

2 Material balance for each species

3 Overall energy balance

4 Equilibrium relationships

5 Kinetic expressions

Combining these relationships with thermodynamic properties and hydraulic

relationships yields a set of differential and algebraic equations which are the model

Algebraic relations included in a generalized model would include

- Multicomponent non-ideal thermodynamic properties

Non-adiabatic column heat transfer rates

Pressure dependent vapor flowrates

Plate geometry dependent liquid flowrates

Entrainment weeping and flooding effects

Bubble froth and wave formation

6

These algebraic relations increase the complexity of the model Thus some

assumptions are usually made in order to reduce or eliminate minor effects from the

model However the degree of complexity of the model must be sufficient to

accomplish the objectives of modeling such as process or control system design The

details of model development are presented in Chapter 2

122 Solving system of differential and algebraic equations

The set of differential and algebraic equations which make up the model can be

arranged into the general form

du = f (uv t)

dt

0 = g(u v t)

where u is the solution of vector of length k v is vector of dependent variables and g

represents a set of algebraic relations Several numerical techniques are available for

integrating systems of equations Two methods were examined by Gani et al (1986)

for solving sets of equations obtained from distillation system models were the

backward-differentiation method (BDF) and diagonally implicit Runge-Kutta method

(DIRK) The Jacobian matrix J is required in order to accomplish the calculation of

solution vector u

7

According to Gani et al BDF is preferable to DIRK for high accuracy The

BDF method as incorporated in the software package DASSL (Brenan et al 1989) was

chosen to be the integration method for solving the differential and algebraic equations

in this work

123 Orthogonal collocation

One major difficulty of staged separation models is the solution of the large

number of equations One procedure for reducing that number is the method of

orthogonal collocation The application of orthogonal collocation to staged separation

systems is based on the assumption that any stage variable can be represented by a

function of the position variable s within a section or module Variables at integer stage

locations can be found using interpolation polynomials based on values at non-integer

interior collocation points and boundary points of a module (Stewart et al1985)

Consider M stages in a separation module as shown in Figure 11 Let l(st) and

v(st) respectively represent a variable related to liquid or vapor phases at time t The m

interior grid points (m5M) are selected at sn (n=1m) The entry point for the liquid

so and the entry point for the vapor sm are chosen at s=0 and s=M+1 respectively

Consequently (st) and v(st) can be approximated by the following expressions

8

s=0

s=1

s=2

s=M-1

s=M

S=M+1

Figure 11 Schematic diagram illustrating the continuous position variable s within a separation module

T(s t) = (s)T(sn t) 0 lt s lt M (1-1) n=0

m+1

1)-(St)= (S)1(Snt) 1 ltslt M+1 (1-2) n=1

where the tilde (j-) represents a calculated volume of the variable of interest and the W-

functions are Lagrange interpolating polynomials defined by the following expressions

Sk n = 0m (1-3)Wnl(s)

kVn Sn Sk k

m +1 S k n = 1m+1 (1-4)Wnv(S)

k=1 Sn Sk ktn

The internal collocation points are selected as the roots of orthogonal

polynomials In order to avoid a poor choice of grid points Stewart et al (1985)

suggested Hahn orthogonal polynomials Qn(xaPN) as an appropriate basis for

9

collocation points for staged separation systems These polynomials satisfy the

following orthogonality criteria

N

WOC aj3 N)Q(x a(3N)Qn (xa13N) = 0 min (1-5) x=o

where cc 0 gt -1 and since

s= 1 --gt m and x = 0 gt N then x = s-1 and N = M-1

The weighting function w(xo4AV) is given by

(a+Dx(13+1)N-xw(x a 13 N) - (1-6)x(N x)

Selection of a and 3 determine the location of collocation points By choosing

a =3 the collocation points obtained are symmetrical within a module The choice

a=i3=0 gives uniform weighting in Eqs (1-5) and the choice a=11 results in

collocation points which are less concentrated near the ends than those for a =3=0 In

this work the simplest choice (a =3=0 w=1) was used When the number of collocation

points is equal to the number of actual stages the use of Hahn orthogonal polynomials

yields collocation points at the exact location of the actual stages ie the model

converges to the full-order model

Matandos (1991) reviewed alternatives to the Hahn polynomials and found that

the number of collocation points was the major factor in determining the accuracy and

10

efficiency of this method The examples in Chapter 5 6 and 7 demonstrate the results

of simulations for various numbers of collocation points

13 Literature Survey

The idea of combining the operations of multi-stage distillation and chemical

reactions has been recognized since 1921 when Backhaus obtained a patent describing

an esterification process carried out in a distillation column (Doherty and Buzad 1992)

Early efforts of modeling this combined system were carried out with manual plate-to-

plate calculations (Leyes and Othmer (1945) Belck (1955)) However very rough

approximations were made for phase equilibrium relations and reaction rates because of

the computational demands for solving problems using more detailed models

In the 1970s many numerical methods were developed and utilized in order to

obtain steady-state simulations of reactive distillation processes Some computational

methods for reactive distillation were modifications of the methods used for

conventional distillation columns Nelson (1971) used a Newton-Raphson technique to

solve matrix equations derived from material balances and then adjusted the flow rate

and temperature on each stage by using the method of damped least squares Suzuki et

al (1971) developed a tridiagonal matrix algorithm to solve linearized material balance

equations and used Mullers method for the convergence of the temperature profile

Komatsu (1977) proposed a relaxation method which consisted of normalization

between compositions computed at the n-th trial and the compositions resulting from

11

material balance at the hypothetical steady state He also conducted experiments to

confirm simulated behavior Komatsu and Holland (1977) proposed the multi-041

method to solve reactive distillation problems This method is based on the 0 method

of convergence which is a well-documented method applied to conventional distillation

columns (Holland and Liapus 1983)

More complicated procedures to find steady-state results were proposed during

the 1980s Izarraraz et al (1980) and Kinoshita et al (1983) combined the tridiagonal

matrix algorithm with the Newton-Raphson method for the calculations in the main

loop Izarraraz also utilized the 0 method for convergence in each iteration Although

the Newton-Raphson method yielded fast computation the results were dependent upon

the initial estimates of the variables Alternatives to the Newton-Raphson method were

also proposed Chang and Seader (1988) used a robust homotopy continuation method

for solving the simultaneous nonlinear equations resulting from the reactive distillation

model Alejski et al (1988) proposed a steady-state model which could be described as

a single function containing all the parameters and constraints together Then the model

was solved for composition and temperature profiles at steady state by minimization of

an error function He found that the results obtained did not depend upon initial

estimates like the Newton-Raphson method Bogacki et al (1989) utilized the Adams-

Moulton method for solving the set of differential equations in the model for reactive

distillation problems A review of calculation methods for simulation of reactive

distillation was reported by Doherty and Buzad (1992) They also pointed out

opportunities for further research in reactive distillation especially in dynamic

12

simulation More recently Doherty and Buzad (1994) presented a steady-state design

procedure for kinetically controlled reactive distillation columns by introducing a new

set of transformed composition variables into the model They demonstrated that liquid

holdup per stage had significant effects on the steady-state design

Only a few articles consider dynamic simulation of reactive distillation columns

An early article on dynamics was presented by Roat et al (1986) They reported that

control schemes based on accurate steady-state gain relationships frequently failed

under dynamic conditions Such failures were discovered only by using the full

nonlinear dynamic simulation A recent dynamic simulation method was proposed by

Ruiz et al (1995) They considered a detailed model which included the effect of plate

hydraulics The model was an extension of the model developed by Gani et al (1986)

and Cameron et al (1986) for conventional distillation columns

13

2 DEVELOPMENT OF THE MODELS

21 General Assumptions

In developing all models in this thesis the following assumptions were made

1 On each stage each phase is homogeneous and well mixed thus pressure and

temperature are uniform throughout each stage

2 Liquid and vapor leaving each stage are in equilibrium and the equilibrium

relationships between the compositions of these streams are defined

3 Mass and energy holdups in the vapor phase are negligible compared to those in

the liquid phase

4 The column is insulated therefore heat transfer to the surroundings is neglected

5 All reactions take place only in the liquid phase

6 Any required thermodynamic properties of mixtures are considered to be mole

fraction weighted averages of pure component properties

Additional assumptions made for each particular model will be discussed before

that models development

14

22 Full-order Models

A reactive distillation column containing N internal stages total condenser and

partial reboiler as shown in Figure 21 is considered in this thesis The detailed

schemes of each standard element (internal equilibrium stage condenser or reboiler) are

presented as Figures 22 23 and 24 respectively There can be chemical reactions

occurring in the liquid phase on every stage

For the case where a single reaction occurs in the following form

aA + bB H cC + dD

the stoichiometry can be expressed as

VAA + VBB + VCC + VDD = 0 (2-1)

where

vA = -1 vB = -ba vc = ca vD = dia

The mass and energy holdup of vapor are assumed to be negligible Thus the

application of material balances for species j (j=1n) overall material balance and

energy balance on each element yield the following equations

15

Condenser

dMo Loxo Dxaj +vjrkA (2-2a)

dt

dt dM0

nr

LOLo (2-2b) 1=1

dMoho 111-11 Lohdeg QC (2-2c)

dt

Internal Stages

dM + + FX

dt (2-3a) +

dM nc

V F Vi W + (2-3b)dt j=1

dM ihi Vi+Hi+ + Li_lhi_ + FHF ViHi Lihi WH (2-3c)

dt

Reboiler

dMN+1XN+1 LN X V N+y BXBi v inN+1A (2-4a)

dt

nc dMN+1

N VN+1 B +77N+1A (2-4b)LNdt

dM N+1hN+1 LNhN VN+111N+1 BhB + QB (2-4c)dt

16

D

Figure 21 Schematic diagram and notation for a distillation column

17

Hw Xwj

Figure 22 Schematic diagram and notation for i-th equilibrium stage

Figure 23 Schematic diagram and notation for total condenser

i=N VN+1 HN+1 YN+1j

QR LN hN XNj

B hB xBd i=N+1

Figure 24 Schematic diagram and notation for reboiler

18

The moles of base component A reacted per unit time on stage i iliA is defined by

(2-5)1iA =

where Ui is volume of liquid on stage i

The correlations for vapor-liquid equilibria and enthalpies of each phase are

defined differently depending on complexity of the thermodynamic properties model

Simplified thermodynamic model Liquid and vapor enthalpies are given respectively

by

h = h(Ti xi j) Hi = H(T yij) = set of mole fractions (2-6)

Vapor-liquid equilibrium relationships are expressed as

yij = Ei Kij(Ti) xij (2-7)

(2-8)

where i=01N+1 is the stage number Ei is a vaporization efficiency and Kid is the

phase equilibrium constant (y xi) on stage i

19

Rigorous thermodynamic model In the rigorous model the effects of pressure on

enthalpies and vapor-liquid equilibria are included in the model given by

h = h(T Pi H = H(Ti Pi Yi) (2-9)

The liquid mixture is no longer treated as an ideal solution Therefore the phase

equilibrium equations becomes

Id(TE (2-10)

n

(2-11)ij 1=1

221 The constant molar holdup (CMH) model

For this model it is assumed that the total number of moles present on any stage

is constant Thus the left hand sides of the total molar balances Eqn (2-2b) (2-3b)

and (2-4b) become zero while those of the energy balances Eqn (2-2c) (2-3c) and

(2-4c) can be written as

dMik dhi (2-12)

dt dt

20

As demonstrated by Howard (1970) and under the assumption of negligible mixing

effects by Cho and Joseph (1983) at constant pressure the term dhildt can be expressed

as

dhi ahi dT n` dh dx+y (2-13)dt aT dt dx dtJ= ij

For the simplified thermodynamic model as described in Matandos (1991 pg29) the

differential term dT dt can be derived by differentiating the bubble point relationship

The result is

nc dx EK

dTi 1=1 dt nc (2-14)

dt dK E x

1=1 dT

Eqn (2-13) then becomes

_ -nc di ci

idhi ah JI dt I dh clx + i

(2-15)dt dT -c dKi ax dt L E jxii

-di1=1

For the simple or rigorous thermodynamic model differentiating the bubble point

relation given by Eqn (2-10) and (2-11) yields

dvn` dki E iKi =1E xi (2-16)xi1 Kiidt dt0=1 1 1=1

21

Because Kij in the rigorous thermodynamic model is a function of activity coefficient

(which is a function of the liquid composition) as well as temperature the differential

term dKildt can be written as

At constant pressure

dkj dK dT n` ( di K1 m M (2-17)

dt aT dt axm dt

Substitution of Eqn (2-17) into Eqn (2-16) yields

n dK cbcii I M x

11 0 (2-18)j+Eic Edt m=t ax dt dt(11 1=1 m

which can be solved for dTIdt

n cbcij x-n`

+1E E L dt i=1 m=1 0Aim dt

(2-19)aKijEE xii i=i

From Eqn 2-19 it can be seen that the second term in the numerator will

disappear if KJ is a function of temperature only yielding the same expression as

derived in Eqn (2-14) for the simplified thermodynamic model

22

Figure 25 Schematic diagram for end-around mass and energy balances

23

F

Figure 26 Mass and energy balance envelopes utilized in the derivation of the equations for calculating liquid and vapor flowrates

24

The liquid and vapor flowrates along the column are obtained by applying mass

and energy balances around the bottom of the column and stage i+1 as shown in Figures

25 and 26 and for constant molar holdups the following expressions are found

i +1 n i+1 dhk

B(hB Hi+1)+ F Hi+ HF)- QR y rik1v k dtk =N +l j=1 k=N+1

Li (2-20) (h 11+1)

i+1 I n

= Li + Ft B+ (2-21) k =N +l j=1

i = NN-110

where B is obtained from a mass balance around the entire column for constant molar

holdups

n

B=F-D+E nkA vi (2-22) k=0

The differential term dhk dt is calculated by using Eqn (2-13) The feed related

variables F and HF are defined using the function of feed vaporized (v) as

0 HF = 0 when igtf below the feed stage

F = (1-ty)F HF = hF when i=f on the feed stage

F = F HF = HF+ hF when iltf above the feed stage

25

Finally all of the variables calculated (M Li 171 B h H dhidt) are then placed

in the material and energy balances (Eqn 2-2 2-3 and 2-4) As a result a system matrix

defined by a set of differentialalgebraic equations is obtained The mole fractions in

the liquid phase fxJI are used as state variables

222 The time-dependent molar holdup (TDMH) model

This model incorporates a hydraulic model of the dependence of liquid flowrate

on liquid holdup thus molar holdups are functions of time Therefore the left-hand

sides of Eqns (2-2c) (2-3c) and (2-4c) can be rewritten as

dM h dh dM (2-23)dt dt dt

The term dhildt can still be calculated by using the same expression Eqn (2-13) as

described in Sec221

Unlike the CMH model the liquid flowrates leaving an internal stage as shown

in Figure 27 depend upon the height of liquid on that stage The modified Francis weir

formula as described in Holland (1981) was utilized for these calculations

qi =lk owi

(2-24a)

A hat (A) indicates that a variable has a unit as defined in the reference

26

how Eqn (2-25) vi h

Li

A

1

Figure 27 Geometry utilized for calculating liquid flowrates leaving an equilibrium stage using Francis weir formula

27

where q is the volumetric flowrate of liquid leaving the stage [gallonsmin]

iw is length of weir [inch]

P is a weir constant

how is the height of vapor-free liquid over the weir [inch]

Since all variables in this thesis are described in SI units Eqn (2-24a) was converted

for variables in SI units

how jY2qt = 36815 (2-24b)t

048F

how is defined by

(

M (2-25)

r7r Ceol4)Pi

For condenser and reboiler liquid volumes in both drums are assumed to be constant

due to perfect level control Thus the derivatives on the left hand sides of Eqn (2-2b)

and (2-4b) become

dM d(Ui pi) dpU (2-26)dt dt dt

For negligible liquid compressibility the term dp dt can be written as

dpi dp dT dp = + (2-27)dt dT dt J1 dx dt

28

The appropriate expression for dTdt from Sec 221 is used depending on the type of

model (simplified or rigorous)

To find the leaving liquid and vapor flowrates from the reboiler total mass and

energy balances around the reboiler were made to yield

n dhN+1

LN(hN hB)plusmn QR +1A I v AiN+1 dt

VN+1 (2-28)(Hi+ h8)

n t N +1B = LN 17N+I 76+LAIV dt

(2-29) J=1

For internal stages application of energy balances around the bottom of the

column and stage i (end-around energy balances) yields

dMkhk BhB F QR dtk=N+I (2-30)

H1

i = (NN-12)

Application of a mass balance around stage N+1 to stage 1 together with energy

balance around the condenser leads to the following expressions for streams leaving and

entering the condenser

I ndM0 vi dMkhkF H BhB ho D + 110o AIV + QR 1dt dtk=N+I

171 (2-31)(H1 ho

where F and ItF follow the same criteria as described in Sec221

29

n dM LN =VI D 710AIV (2-32)

=1 dt

Finally the model is defined by substituting these calculated variables (L B

hi II dhdt) into material and energy balances as in Sec221 However the molar

holdups for internal stages are required to be the additional state variables together with

x according to the introduction of independent equations for liquid flowrates Eqn

(2-24)

23 Reduced-order Model

The diagram shown in Figure 28 will be used to describe the order reduction

technique In Figure 28 a tilde (-) represents a variable entering a collocation point

location which is calculated by interpolation According to Matandos (1991) the stages

above and below the feed should be treated separately in order to provide the necessary

boundary conditions for the reduced-order models in the rectifying and stripping

modules A single column with m1 collocation points in the rectifying module and m2

points in the stripping module is considered in this thesis Application of species

material balance overall mass and energy balances around each collocation point yield

the following expressions

30

i=0

D

V1 Hr

hi

1

VF YFI HE

(1-OF xF

i=mi+m2+3

Rectifying module (m1 collocation pts)

Stripping module (m2 collocation pts)

B

Figure 28 Schematic diagram and notation utilized for a reduced-order column model

31

Condenser

dM0x0 1703-10i Loxoi DX + V irkAdt

dM0 -dt

- Vo Lo D + j =1

dM oho 170i4 - Loho - phi)dt

Stage within a module

dM dt

dM n

-v + dt 1=1

dM ihi + L h L hdt

Stage above feed location

dM Vrni+2 Ymi+2j Ltni+1imi+1 j lifFYFjdt

Ymi +1 j Lmi+1 Xmi +1 j Vi ILI +1A

dM n = 2 + Lm +1 plusmn iliF Vm + 11mi+1A Vdt

dM +ihi - 17i+2H + jimi+1 + tifFHF

dt -Vi+11 +1 Lh+lh+1

(2-33a)

(2-33b)

(2-33c)

(2 -34 a)

(2-34b)

(2-34c)

(2-35a)

(2-35b)

(2-35c)

32

Stage below feed location

dMmo2xn+2 7 ty)FxFidt (2-36a)

V +2 Ym +2 j Lmi +2Xmi + VA +2A

na 1 V Lmi+ + (1 Vm1+2 411+2 plusmn nmi +2A Ey (2-36b)

dt J=1

dM mi+2hni+2 V mi+2H + L+Ihm1+1 + (1 lif)FhF

dt (2-36c) V mi+2H L02hmi+2

Reboiler

a 1 mo-m2+3xm+m2+3 Lmi+m2+3-7m1+m2+3j Vmo-m2+3 Ymi +m2+3 j dt (2-37a)

BXB Vi rimi +3 A

dM n morm2+3

LMl +M2 + 3 VM I +M2 + 3 B + nmi+m2 +3A vi (2-37b)dt j =1

dMm1-1n2 +3 hm +m2 +3 Lm +m2+3ilmi+m2 +3 Vini-Fm2 +3 Hmi+m2+3 dt (2-37c)

BhB QR

In the development of the reduced-order model the stages above and below the

feed location are treated individually in order to guarantee closure of the mass and

energy balances at any quality of feed stream (Matandos 1991) The model can be

obtained by the same approaches as described in Sec22 The full-order balances

including species and energy balance equations are simply replaced by their reduced-

33

order counterparts while all assumptions algebraic relations and design variables

remain unchanged

231 Constant molar holdup model

In this model the molar holdup on each stage is required to be specified In

order to compare the results with the TDMH model the molar holdup in each stage has

to agree with the capacity of the stage in TDMH model The molar holdup for CMH

model is calculated by multiplying volume holdup of plate (h=0) in TDMH model by

the molar density of the feed contents Since all plates studied in TDMH model are

uniform through out the column the molar holdups in CMH model have to be uniform

through out the column as well

In order to set the material and energy balances around the collocation point it

is necessary to determine compositions enthalpies and flowrates of streams entering the

collocation point The compositions and enthalpies for both liquid and vapor streams

are calculated by interpolation as described in Chapter 1 Liquid and vapor flowrates

are calculated using end-around material and energy balances as presented in Sec221

232 Time-dependent molar holdup model

For this model the molar holdups are also state variables in the system matrix

Thus interpolation of molar holdups is not necessary However interpolations for

composition and enthalpy for liquid and vapor streams are required The liquid

flowrates have to be found by interpolation as well

34

The vapor flowrates leaving each stage and the liquid flowrates leaving

condenser and reboiler are calculated by using end-around material and energy

balances as described in Sec222

35

3 NUMERICAL IMPLEMENTATION

This chapter presents the mathematical details of the models developed in

Chapter Two

31 Thermodynamic Properties

The correlations for thermodynamic properties of liquid and vapor phases have

been considered as two different models the simplified and the rigorous model In the

simplified model it was assumed that there is no pressure variation along a column All

thermodynamic correlations used for this model are used to calculate thermodynamic

properties at a particular fixed pressure On the other hand the rigorous model can

incorporate a pressure change within the column Thus the effects of pressure are

included in the thermodynamic expressions used for the rigorous model

311 Enthalpies

Simplified model Liquid and vapor enthalpies of mixtures are given by

n

hi =Ix h j(Ti) (3-1a)

n

Hi =I yi H(7) (3-1b) i=1

36

Molar enthalpies of pure species h for liquid and 1-1 for vapor are specified as

polynomial functions of temperature

(TO =ai+117+c1Ti2 +cljTi3 + ejTi4 (3-2a)

H (TO = Ai + B + C + D + E iTi4 (3-2b)

Rigorous model Liquid and vapor enthalpies of mixtures are given by

= x (To Pi) (3-3a)

Hi =1 i(Ti Pi) (3-3b) J=1

The pure species molar enthalpies in each phase are calculated by the following

procedures

Enthalpies of Vapor

Molar enthalpies of pure component vapors Hi are calculated by

=Hjdeg(T)+Cli(TiP) (3-4)

37

The enthalpies of pure species j (j=1nc) at a standard state HdegJ are given by a

polynomial of temperature as shown in Eqn (3-2b) The term SI is the deviation of a

gas from the standard state called the enthalpy departure This term is defined by

_RT2( din f (3-5) aT )p

This term can be obtained by using an equation of state In this thesis the Benedict-

Webb-Rubin (BWR) equation of state is used All parameters used in BWR equation of

state are listed in Appendix A Eqn (3-5) then becomes

40 p 6aoa 35v 2v2SI = (BoRT-2A0 H p +(21yoRT3a0) +

T2 (3-6)

cop [31 exP( 704 ex13(-- YoPv2 ) 2 + YO Pv exP(--Y0P2)]T2 2YoPv2

The molar density of vapor pv is a function of pressure and temperature which

can be evaluated by using the BWR equation of state as well At a specified pressure

and temperature the BWR equation of state can be rewritten as

F(p)=[RTp +(BORT Ao CZ pv +(boRTao)p +aoaop +

cop y p2)exp(yop1] P =0 (3-7)

T2 deg v

38

The solution of this equation can be found by using Newtons method

F (Pvk) (3-8)Pvk+1 = P

vk F(pvk)

where the subscript k indicates the trial number and the derivative TApv) is calculated as

F(pv)= RT+2(BoRT Ac )pv +3(boRT ao)pv2 +6a0a0p +T2

72 [(p + yo p )(-2y0 pv ) exp( yo )+(3p2 + 570 pi) exP( P2 )] (3-9)

Because of the complexity of Eqn(3-9) Newtons method requires a reasonably good

initial estimate of pv In this thesis the molar density calculated from the ideal gas law

was used as the initial estimate The calculation continued until the difference of these

two iterations was less than 10-6 which was the desired convergence tolerance for this

thesis

Enthalpies of Liquid

The molar enthalpy of a pure species for liquid ej is calculated from the enthalpy of

the vapor and the latent heat of vaporization

= Hsi(Ti) A1(T) (3-10)

The latent heat of vaporization j is assumed to be function of temperature only

39

and can be calculated from Izarraraz (1980)

038 1 T T

where Tr = (3-11)A(7`)=7 A 1Tr

The superscript indicates a reference state which is the normal bubble point

312 Equilibrium constants

Simplified model Equilibrium constants can be calculated using a simple expression

such as

Ki(T)=Oi + AT+ of T2 -F ei T3 (3-12)

The coefficients ei pi S E have to be specified for the given pressure

Rigorous model The liquid mixture is no longer assumed to be an ideal solution in the

rigorous model and an activity coefficient is used to model the nonideality Moreover

this model is generalized to account for pressure effects The equilibrium constant can

then be expressed by the following function

j0

(3-13)

The vapor pressure of a pure liquid was calculated by using the Antoine equation with

values for coefficients are reported by Suzuki et al (1970) and listed in Table A4 of

Appendix A

40

Bcit

log P3deg = (3-14)T + cdeg

To calculate the activity coefficient there are a number of equations available

for a particular mixture In this thesis the Margules equation as rearranged by Suzuki

et al (1970) was used for the problems which contained four species

logy = A1xz + A24 + A34 + A4x2x3 + A5x2x4 + A6x3x4 +

A x14 + A8x14 + A9 Xi Jet (3-15)Al0X1X2X3 + Al 1 X2X3X4

X3X4X1 Al3 X4 X 1X 2 +A14 x2 x32+A15 x2 x42 +A16 x3 x4

The activity coefficient for the remaining species were obtained by rotating the

subscripts on the xs 1--gt2gt3gt4gt1

313 Bubble point temperature

The bubble point temperature of a liquid mixture of known composition can be

calculated by combining the vapor-liquid equilibrium relation Eqn (2-7) or Eqn (2-10)

together with the summation relation Eqn (2-8) Considering the liquid mixture on

stage i where the pressure is known combination of Eqn (2-10) with Eqn (2-8) yields

F(T)=[Ixi jE1Ki(TP)]-1= 0 (3-16) i=1

41

The root of Eqn (3-16) can be determined by Newtons method

F(Tk) (3-17)Tk+1 = Tk PAK)

where the derivative is

nc dK j(T P)F AT) =1 x E (3-18)dTj=1

Starting with an initial estimate of Tk the bubble point temperature a new value

Tk+] is calculated and used to revise the estimate The calculation continues until the

difference of these two iterations is less than the desired convergence tolerance which

was 10-6 in this thesis

314 Fraction of feed vaporized

The fraction of feed vaporized by flash vaporization of the feed stream when

temperature pressure and composition zi are known can be found by using the

following function (Walas 1985)

Z (1 K (TF PF ))F(1)= L o (3-19)

=1 + ty(K (TF PF ) 1)

42

The root of this function can also be obtained by using Newtons method The initial

estimate for this calculation was 05 The phase compositions are then obtained by

using the following criteria

xJ zJ and yi = 0 if ty= 0

zi

X - and yi = Kixi if 0 lt tylt 1 (3-20) 1+ vf(K 1)

y = zi and xi = 0 if ty= 1

315 Liquid densities

The molar density of the liquid mixture on stage i is calculated by

=ExiJP(Ti) (3-21)

Because pressure has a negligible effect on the molar density of liquid the molar

density of each pure species is considered to be a function of temperature only The

following expression is used to calculate the pure component molar densities at a given

temperature (Smith and Van Ness 1987)

where r = T (3-22)T

43

where subscript c indicates a critical property of the species which are reported in

Table A1 of Appendix A

32 Derivatives of Thermodynamic Properties

There are many derivatives of thermodynamic properties which appear in the

models such as ahiaT ahiaxii dKild xJ (913(37 and apidxjj In this section

the differential terms in the simplified or rigorous model are discussed separately

Simplified model

Liquid enthalpy

The enthalpy of a liquid mixture is defined as described in Eqn (3-1a) Hence

the derivatives ahaT and ahaxid are

dh dh = x (3-23)

dT

dT

dh where = b +2c iT +3d iT2 + 4ei T3 (3-24)

(3-25)

44

- Equilibrium constant

For the simplified model the equilibrium constant is a simple function only of

temperature as shown in Eqn (3-12) thus

dki +28T + 3E 72 (3-26)

dT dT

Density of liquid mixture

The density of a liquid mixture (pi) is given by Eqn (3-21) Differentiation of

Eqn (3-21) with respect to Ti or xi yields respectively

apo dpij (3-27)

dpi 2 Ki ln(Zci)where (3-28)

dT dT 7 j(i_Trf

n axik 1i (3-29)

aXij k=1 j

45

Rigorous model

Liquid enthalpy

The enthalpy of a liquid mixture for the rigorous model is obtained from molar

enthalpies of pure components as shown in Eqn (3-3a) After differentiation it can be

shown that the results are the same as Eqn (3-23) and (3-25) However the pure

component term ahaT in this model is different than in the simplified model

Considering Eqn (3-10) and Eqn (3-4) the value of the molar enthalpy for a

pure component can be calculated as

(3-30)

Thus

ah - + (3-31)dT dT dT dT

First from Eqn(3-2b) the derivative of is

0

B + T +3D T2 +4E T3 (3-32)

Next the derivative of can be found from Eqn (3-6)

46

=(130R+13-Cijp +bRo2aT T3 v

2cpv2 [1 exp( exp( ) + yp exp(--yp) (3-33)

T3 YPv

Then the term da7 is derived from Eqn (3-11)

dA 038 A (3-34)

dT (T T)

Finally the results from Eqn (3-32) (3-33) and (3-34) are replaced in Eqn (3-

31) to evaluate the partial derivative of enthalpy with respect to temperature

Equilibrium constant

The equilibrium constant is defined by Eqn (3-13) and (3-14) Differentiation

with respect to T or x yields the following expressions

ln(10) kJ (3-35) aT (T + C

9K1 Po1I (3-36)

dx dx


In the rigorous model the equations for calculating the density of a liquid are

the same as those for the simplified model Thus the derivatives of liquid density are

the same as derived for the simplified model

47

33 Rate of Reactions

The rate of reaction used in this thesis follows a separable form of a rate law

(-rA) = [k(7)][ fn( CA CB )1 (3-23)

where the rate constant (k) is assumed to be a function of temperature only and to

follow the Arrhenius equation

Combining Eqn (2-5) and Eqn (3-23) the number of moles of the base component A

reacted per unit time on stage i rhA can be derived in terms of the state variables

M j as follows

For a first-order irreversible reaction A -3 products

= [k(T)C = k(T)MiX (3-24)

For a second-order irreverisible reaction A + B H products

niA = ik(T)CiACiddUi = puMik(T)xiAxiB (3-25)

48

For a second-order reversible reaction A+ B H C+ D

=[k(T)CACB k(T)C1iA JUj

(3-26)

= [k(T)xAxB k(T)xcxD1

34 Collocation Points

The optimal collocation points used in this thesis are selected as the roots of

Hahn orthogonal polynomials The following recursive expression is used to find the

desired location of collocation points s=12M

AnQn+ (x a 13 N) = ( x + + B)- Q(x a 13 N) B Q_1(x a P N) (3-24)

x=s-1 N=M-1

(N n)(n +a+1)(n+a+ 3+1)An (3-27)

(2n + a + 13 + 1)2

n(n+ I3)(N + n+ a + 3 +1) B (3-28)(2n + a + 11)2

where

(a)k = 0 k = 0

(a)k = (a)(a+1)(a+k-1) kgt 0

49

The initial values for this recursive relationship are

Q0(xa P N) =1 (3-29)

(a+ 0+2)xQi(xa P N) 1 (3-30)Ma +1)

The zeroes of Qn+i(xaAN) can be successfully found from a combination of

Newtons method with suppression of previously determined roots using a scheme

similar to that proposed by Villadsen and Michelsen (1978) for determining the zeros of

the Jacobi polynomials

35 Integration Software

The models discussed previously consist of a set of ordinary differential

equations which incorporate some algebraic equations The various methods to solve

these models are discussed next Gani et al (1986) suggested a set of requirements for

numerical methods to solve dynamic simulation models of distillation processes

According to Gani et al a successful numerical methods should satisfy the following

requirements

Robustness The method should be able to solve a wide range of

problems and ensure the success of the simulation

50

Appropriateness The method should suit the underlying mathematical

set of equations

Efficiency The computational method should be efficient in terms of

the CPU time dependence on the problem size and the

required accuracy

One of the methods that satisfies these requirements with high accuracy is the

backward-differentiation method In this thesis all simulations have been done by

using the package DASSL (Differential Algebraic System SoLver Petzold 1983)

which uses this method to solve the general mathematical model in the form of

g(tuu)=0 The vector u generally is the desired solution of the model while u is the

vector of derivatives of u with respect to the variable t For distillation models treated

here the vector u represents a vector of state variables xij (and M in case of TDMH

model) and u is the vector of derivatives of those state variables with respect to time

51

4 MODEL VALIDATION AND DESIGN OF MODEL TESTING

41 Validation with Published Steady-state Experimental Data

In this thesis the full-order TDMH model is expected to yield true dynamic and

steady-state results In order to validate this expectation experimental results were

needed However only one experimental set of data for a reactive distillation column

could be found in the literature This work of Komatsu (1976) studied the production

of ethyl acetate

A + B H C + D

CH3COOH + C2H5OH lt--gt H2O + C3H7COOH

(AcOH) (EtOH) (water) (AcOEt)

The conditions for his experiment are shown in Table 411 however only steady-state

results were reported The steady-state profiles are contained in Appendix C

Several authors have proposed various methods in order to solve the reactive

distillation equations Some of them compared their computed results with this

experimental data For instance Komatsu (1976) used a relaxation method to simulate

the results of this experiment Alejski et al (1988) utilized this problem to demonstrate

a method for minimization of an error function to compute the steady-state profiles of

the reactive distillation system This experiment was also chosen as a numerical

example by Bogacki et al (1989) who presented an Adam-Moulton method for solving

the reactive distillation problem

52

Table 411 Conditions for Komatsu (1976) experiment

Design Variables

Total number of stages 6

Location of feed stage 1 (top stage)

Feed flowrate [gmolemin] 02584

Status of feed Liquid at bubble point

Composition of feed [mole fraction]

AcOH zA 02559

Et0H zs 06159

Water zc 00743

- AcOEt zD 00539

Distillate rate [gmolmin] 00425

Reboiler duty [calmin] 10737

Column diameter [m] 014

Weir length [m] 006

Weir height [m] 002645

Volumetric holdup of liquid

in reboiler [m3] 06x10-3

The rigorous TDMH model was utilized for this simulation in order to avoid

inaccuracies due to simplified thermodynamic expressions However Komatsu did not

report the pressure in the column Thus the pressure was assumed to be constant at 1

atm corresponding to the assumption made by other authors

The steady-state profiles for each composition in the liquid phase are shown in

Figure 411 The deviation from the experimental data of each obtained profile was

derived by using the mean squared error norm (MSE) proposed by Stewart et al (1985)

53

N+1

(Ai )2

MSE I=deg (4-1)N + 2

The generic variable A represents the reference solution which in this case is the

experimental result and the variable A with a tilde () is the solution obtained via

simulation Table 412 shows the values of MSE for each calculation method

Table 412 Mean squared errors for steady-state profiles in the validation of the model

MSE TDMH Komatsu Alej ski Bogacki

xitcoH 11893E-03 66924E-03 28242E-03 16359E-03

xEtolf 61785E-03 98927E-03 16722E-02 18820E-02

xwater 92009E-03 94784E-03 53772E-03 49359E-03

XAcOEt 13209E-03 47090E-03 12271E-02 11779E-02

The computed steady-state profiles demonstrated the good performance of the

full-order TDMH model compared to the results from other methods The profiles

obtained by this model are closer to the experimental results than the others The mean

squared error norms also confirm the accuracy of the TDMH model MSE values for

AcOH EtOH and AcOEt were lower than those values obtained from other methods

Although the MSE value for water from the TDMH model was higher than Alejski and

Bogacki the composition profile for water in Figure 411 shows that 7 out of 8 data

points calculated from the TDMH model were closer to the data than those previous

results

Composition profile of AcOH 1

09 0 Experiment 08 4- --TDMH 07 AKomatsu 06 Alejski 05 04 03 02 01

0 1 2 3 4 5

Stage number

Composition profile of EtOH

0 1 2 3 4 5 6 7

Stage number

Composition profile of water 1

09 --B--Experiment 08 --- 4- - -TDMH 07 A Komatsu 06 0 Alejski05 x---Bogacki04 03 02 01

0 0 1 2 3 4 5 6 7

Stage number

Composition profile of AcOEt 1

09 eExperiment 08 - -TDMH 07 A--Komatsu 06 0 Alejski05 xBogacki04 tit- 03 02 Q 01

0 0 1 2 3 4 5 6 7

Stage number

Figure 411 Steady-state composition profiles for model validation

55

Although the TDMH model performs well there were some deviations from the

experimental data These might have been caused by inaccurate vapor-liquid equilibria

data thermodynamic correlations for enthalpies and kinetic data as well as the

assumption of pressure in the column On the other hand some experimental errors

must exist in the experimental data

As mentioned no dynamic results from experiments were found in the

literature Thus based on steady-state performance the full-order TDMH model was

used as the reference model in other numerical examples

42 Simulation Tests of Models

The objective of this thesis was to make quantitative comparisons of modeling

errors introduced by physical and numerical approximation methods in reactive

distillation simulation Several example problems shown in detail in Table 421 were

studied in order to achieve this objective In each problem both the steady-state and

dynamic behaviors of numerical and physical models were compared with the true

results obtained from a full-order reference model It was expected that reduced-order

models would perform more accurate prediction of full-order dynamic and steady-state

behavior of reactive distillation column than models using simple physical

approximations if the number of collocation points were nearly the number of physical

stages According to Matandos (1991) a reduced-order model with a small number of

collocation points however can yield unreasonable results when the steady-state

profiles in a nonreactive distillation column are steep Thus for reactive distillation

Table 421 Summary of problems

Topic of studies

Physical

approximation

Numerical

approximation

Number of stages

Type of reaction

Thermodynamic

model

Pressure in the

column

Example 1

advantages of reduced-

order model over the

model assuming

constant molar holdup

full-order CMH model

reduced-order TDMH

model

8

irreversible

( 2A ---gt R + S )

simple

uniform (1 atm)

Example 2

efficiency of reduced-

order model in a

column with many

stages

reduced-order TDMH

model

29

rigorous

uniform (1 atm)

Example 30


order model in a

column with fewer

stages

-

reduced-order TDMH

model

11

Example 31


order model in a

column with pressure

gradient over the model

assuming uniform

pressure

full-order TDMH

model assuming that

pressure in the column

is uniform

reduced-order TDMH

model

11

reversible

( AcOH + Et0H lt---gt Water + AcOEt )

rigorous rigorous

uniform (1 atm) linear through the

column

Example 32

effect of plate geometry

on steady-state and

dynamic behaviors

full-order TDMH

model using various

plate geometries

-

11

rigorous

uniform (1 atm)

57

simulation it was expected that a lower limit to the number of collocation points would

be observed

58

5 EXAMPLE PROBLEM 1

This problem is presented in order to demonstrate the comparison between the

CMH and TDMH model The problem is modified from the example in Izarraraz

(1980) in order to be able to apply the reduced order technique The simplified CMH

and simplified TDMH model were used to solve the problems

In this problem the following reaction takes place on every stage

2A gt R + S

with the rate equation

(-17A) = kACA

where

kA = exp(56 270007) [hil] and T is in degR

Correlations for vapor and liquid enthalpies and the equilibrium constant are listed in

Table 51 and the specifications of the problem are listed in Table 52

Table 51 Thermodynamic properties of species utilized in Example problem 1

Component hij z [Btulbmol] [Btulbmol] [ degR] [ft3lbmol]

A 11000 + 30T 4000 + 30T 001Ts 10699 275 02

R 20000 + 20T 15000 + 20T 002T 11651 090 0229

S 25300 + 10T 25000 + 10T 003T 9418 459 0252

T is in degF

59

Table 52 Problem specifications for Example problem 1

Design Variables


Location of feed stage 5

Feed flowrate [lbmolemin] 100



A 08

R 01

S 01

Distillate rate D [lbmolmin] 90

Reboiler duty QR [kcalmin] 3006866

Column diameter ckor [m] 20

Weir length lw [m] 080

Weir height hi [m] 050

Liquid volume in condenser and

reboiler drums [m3] 0471

The molar holdup for the CMH model is calculated by multiplying each volume

holdup within the column in the TDMH model by the molar density of the initial

contents which is equal to the feed compositions

Steady-state results The notation mR x ms designates the number of collocation

points in the rectifying and stripping sections respectively Two reduced-order models

2x2 and 1 x 1 were used in order to demonstrate the accuracy of different levels of

reduction For this example with 10 holdups (including condenser and reboiler) the

60

2x2 model provides roughly a 20 reduction in the number of required differential

equations (from 38 to 30 for the TDMH model from 30 to 24 for the CMH model)

while the 1x1 model provides approximately a 40 reduction (from 38 to 22 for the

TDMH model from 30 to 18 for the CMH model) Collocation points utilized in this

example are shown in Table 53

Table 53 Collocation points utilized in Example problem 1

2x2 lx1

Rectifying Module 00000 00000

11835 20000

0 = condenser 28165 40000

4 = vapor feed stage 40000

Stripping Module 50000 50000

61835 70000

5 = liquid feed stage 78165 90000

9 = reboiler 90000

Figures 51 to 55 contain the steady-state profiles obtained from the

simulations The profiles obtained from reduced-order models were then interpolated

for the value of parameters at the actual stages by using Lagrange polynomials After

that the MSE as described in Eqn (4-1) for each model could be calculated For full-

order CMH models the results from full-order TDMH models were used as reference

solutions

61

60

55

50

45

40

35

30 0

60

55 C Of 41) 50

I a 45 m ei n 40 I i 35

30 0

60

55 ii Oi a) 50 73

12a 45 co

isoo 40 i

35

30 0

Temperature profiles

1 2 3 4 5 6

Stage number

(a)

1 2 3 4 5 6 Stage number

(b)

i I i i i 1


(c)

B TDMH - - -0- - CM H

7 8

B TDMH gt 2x2

O 1x1

7 8

--B CM H 2x2 o 1x1

I

7 8

9

9

9

Figure 51 Steady-state temperature profiles for Example problem 1 (a) - Full-order models (b) - TDMH full and reduced order (c) - CMH full and reduced order

62

Composition profiles of A 1

09 -08 07 --e-- TDMH 06 -0- CMH 05 04 03 02 01

0 Ulf

0 1 2 3 4 5 6 7 8 9

Stage number

(a)

1

09 08 07 06 05 04 03 02 01

0 0 1 2 3 4 5 6 7 8 9

Stage number

(b)

1

09 08 8 CM H 07 2x2 06 - 0 1x1 05 04 03 02 01

0 111 microf i I I I

0 1 2 3 4 5 6 7 8 9

Stage number

(c)

Figure 52 Steady-state composition profiles of A for Example problem 1 (a) - Full-order models (b) TDMH full and reduced order (c) CMH full and reduced order

63

1

09 -08-07 06 05 04 -03-02 -01

0 0

1

09 08 07 -06 -05 04 03 02 01 -

0 0

1

09 08 07 06 05 04 03 02 01

0 0

Composition profiles of R

1I I I I I

1 2 3 4 5 6

Stage number

(a)

1 2 3 4 5 6

Stage number

(b)

t 1 I 1

1 2 3 4 5 6

Stage number

(c)

$ TDMH CMH

1 1

7 8 9

--e TDM H o 2x2

0 1x1

7 8 9

9-- CM H 2x2

0 1x1

7 8 9

Figure 53 Steady-state composition profiles of R for Example problem 1 (a) - Full-order models (b) TDMH full and reduced order (c) CMH full and reduced order

64

Composition profile of S

09 08 07 06 05 04 03 02 01

0 0

I

1

i

2 3

I

4 I

5 6

p TDMH

CMH

7 8 9

Stage number

(a)

1

09 08 07 06 05 04 03 02 01

0 0

I

1

I

2 3 4 5 6

e TDMH 2x2

O 1x1

7 8 9

Stage number

(b)

1

09 08 07 06 05 04-03 02 01

0 0

I

1 2 3 4 5 6

--eCMH 2x2

O 1x1

7 8 9

Stage number

(c)

Figure 54 Steady-state composition profiles of S for Example problem 1 (a) Full-order models (b) TDMH full and reduced order (c) CMH full and reduced order

65

Flowrate profiles 800

700

600

500

400

300

$ TDMH CMH

200

100

0 0 1 2 3 4 5

Stage number 6 7 8 9

(a)

800

700

600 Vapor

500

400

300

200

Liquid

9 TDM H 2x2

O 1x1

100

0


6 7 8 9

(b)

800

700

600 Vapor

500

400

300

200

Liquid 8CMH

2x2

O 1x1

100

0 0

F

1

f

2 I

3 I I

4 5 Stage number

i

6 I

7 i

8 9

(c)

Figure 55 Steady-state liquid and vapor flowrate profiles for Example problem 1 (a) Full-order models (b) TDMH full and reduced order (c) CMH full and reduced order

66

The errors for reduced-order models are computed relatively to the full-order model for

the same holdup assumption (CMH and TDMH) The MSE values for steady-state

profiles are shown in Table 54

Table 54 Mean Squared Errors for steady-state profiles for Example problem 1

TDMH CMH

(2x2) (1x1) Full (3x3) (2x2) (1x1)

T (degF)2 75654E-05 32486E-02 64722E-02 59785E-05 18506E-02

XA 18871E-07 28772E-05 97558E-05 20379E-07 29484E-05

XR 37528E-07 18061E-04 90993E-05 45029E-07 90603E-05

xs 90549E-08 11304E-04 22755E-06 99641E-08 44224E-05

L (lbmolmin)2 16683 3641945 317355 23006 2405854

V (lbmolmin)2 16822 3058993 317355 34804 2278430

For this mixture of compounds A is the heaviest (least volatile) component

while S is the lightest (most volatile) The steady-state profiles show that the mole

fraction of S was higher in the top of the column than the bottom while the

composition of R was highest in the bottom The presence of A was low everywhere

because A was converted into R and S by an irreversible reaction

In this problem a relatively large amount of heat was applied to the reboiler

which resulted in a high reflux ratio Figure 55 indicates that the flowrates inside the

column were much higher than flowrates of products leaving the column

67

Although a steep change existed in the liquid flowrate profile as shown in

Figure 55 both steady-state profiles and MSE values indicate that the higher-order 2x2

TDMH model yielded much more accurate profiles than the full-order CMH model did

The errors from the full-order CMH model were higher than those from 2x2 TDMH

model by an order of magnitude However the lower order 1 xl model did not work

very well on this problem because a single collocation point in the stripping module

was unable to predict the profile Since there are errors in the prediction of liquid

flowrate the lx1 model was unable to match the composition on each stage correctly

and possibly resulted in calculated negative mole fractions and poor temperature

predictions This problem was observed in both the lx1 TDMH and lx1 CMH models

Comparing the deviation of each reduced-order model from its full-order model

(TDMH and CMH) it was obvious that TDMH and CMH with the same order of

reduction yield errors of the same order of magnitude Nevertheless the errors from the

reduced-order TDMH model were higher than those from the CMH model especially

from the 1 xl model These errors were caused because the TDMH model allows liquid

molar holdup on each plate to change with time The molar holdup on each tray was

calculated from the net liquid flowrate entering the tray and the geometry of plate

Thus errors in liquid flowrate calculations caused errors in calculated molar holdups

which consequently affected the reaction rate and final composition of each component

The reduced TDMH model yielded more precise steady-state profiles with less

computational efforts than the full-order model with the physical assumption of

constant molar holdups

68

Step test This section deals with the accuracy of predicted transient responses to the

introduction of a step increase in feed flowrate A 20 step increase in feed flowrate

(from 100 to 120 lbmolmin) was introduced to the system at steady state The time

required to simulate 50 minutes of column operation and the response of bottom

product mole fractions were considered as criteria for the performance of a given

model

Because different models may produce different steady-state results the starting

point for a step test can vary To compensate for this the deviation from the initial

steady -state result of each model was considered when comparing the transient

responses between different models All tests in this thesis are carried out on a

486DX2-66 MHz machine using the Microsoft FORTRAN Powerstation 10 coding

compiler The initial and final values obtained in each test are reported in Table 55

while the changes with respect to time are shown in Figures 56 through 58 The

required computing times (relative to full-order TDMH model) to obtain these

responses are shown in Table 56

69

0035 Step responses for A

003

0025

002 0015

001

0005

TDMH

CMH

0 0 10 20 30

time (min)

40 50

(a)

0035

003

0025

002

0015

001

0005

TDMH

2x2 1x1

0 0 10 20 30

time (min)

40 50

(b)

0035

003

0025

002-0015

001

0005

0 0 10 20 30 40

CMH 2x2 1x1

50

time (min)

(C)

Figure 56 Step responses for A in bottom product for Example problem 1 (a) Full-order models (b) TDMH full and reduced order (c) - CMH full and reduced order

70

Step responses for R

-001

-002

TDMH

CMH

-003

-004 _ _ _

-005

-006 0 10 20 30

time (min)

40 50

(a)

I I I I

-001

-002

-003

TDMH

2x2 1x1

-004

-005

-006 0 10 20 30

time (min)

40 50

(b)

-001

-002

CMH

2x2 1x1

-003

-004

-005

-006 0 10 20 30

time (min)

40 50

(c)

Figure 57 Step responses for R in bottom product for Example problem 1 (a) - Full-order models (b) - TDMH full and reduced order (c) - CMH full and reduced order

71

0025 Step responses for S

002 _-____

0015

001

0005 TDMH

CMH

0 10 20 30

time (min)

40 50

(a)

0025

002

0015

001

0005

TDMH

2x2 lx1

0 10 20 30

time (min)

40 50

(b)

0025

002

0015

001

0005

CMH

2x2 1x1

0 10 20 30

time (min)

40 50

(c)

Figure 58 Step responses for S in bottom product for Example problem 1 (a) Full-order models (b) TDMH full and reduced order (c) - CMH full and reduced order

72

Table 55 Initial and final value of composition of bottom product for step test in Example problem 1

Composition of TDMH CMH

liquid in reboiler full (3x3) 2x2 1x1 full (3x3) 2x2 1x1

xA initial 00858 00859 00829 01041 01042 01009

final 01160 01160 01138 01248 01248 01212

XR initial 08237 08237 08257 08040 08040 08077

final 07706 07706 07705 07614 07614 07647

xs initial 00905 00905 00914 00919 00918 00915

final 01135 01134 01158 01138 01138 01141

Table 56 Relative computing times for step tests in Example problem 1

Model Relative time

TDMH Full (3x3) 1

2x2 08972

lx1 06576

CMH Full (3x3) 07157

2x2 06150

lx1 04706

Note Computing time required for full-order TDMH model was 1 minute 298 seconds

Because A is the least volatile component the fraction of A in the bottom

product should increase after introducing a step in the feed flowrate since the feed is 80

mole percent A As expected Figure 56 shows an increase in mole fraction of A for

either model However the CMH model did not predict the transient response well

73

Some offset from the final true solution was also observed On the other hand the

2x2 TDMH model worked very well No deviation the from the full-order results

appears in Figure 56 (b) Moreover the results shown in Table 55 indicate that

solutions from the 2x2 TDMH and the full-order TDMH models agree to at least three

figures Although some deviations took place when the 1x1 TDMH model was used

these errors were two to four times smaller than errors from the full-order CMH model

During a step test the amount of feed flow to the column is increased while the

heat duty applied to reboiler remains unchanged This corresponds to a decrease in the

intensity of separation and a decrease in the purity of R in the bottom product would be

expected In other words the final mole fraction of R should be less than the initial

value while the final mole fraction of S should be higher The simulation results from

both TDMH and CMH model agree with this expectation However even the 1 xl

TDMH model shows better performance in the prediction of transient responses than

the full-order CMH model and with a shorter computing time

One source of errors in the CMH model can be found by inspection of Figure

59 where the initial and final liquid holdup profiles for the full-order TDMH model are

presented Since the CMH model utilizes a constant molar holdup assumption the

variation in molar holdup is neglected which causes errors in the prediction of dynamic

behavior

74

420 390 0 initial TWIN 360 330 final RAC 300 270 240 210 180 150 120 90

0 1 2 3 4 5 6 7 8 9

stage number

Figure 59 Initial and final molar holdup profiles for step test of full-order TDMH model in Example problem 1

Pulse test As a second dynamic test the feed rate was pulsed in order to determine

the frequency response which is a characteristic of each model The input and output

signals were numerically transformed and presented as a Bode diagram which is an

important tool for designing linear controllers Although the reactive distillation

systems are not linear the controller design is usually based on a linear dynamic model

Thus this test was conducted in order to examine the suitability of a reduced-order

model for the purpose of controller design

A rectangular pulse in feed flowrate (from 100 to 120 lbmolmin) was

introduced to the model at the same steady-state conditions as in the previous section

The higher flowrate was sustained for 25 minutes after which the feed flowrate was

returned to its initial value

75

Pulse responses for A 0012

001

0008

0006

0004

0002

0 0 10 20 30 40 50 60

time (m in)

(a)

0012

001- MAC 2x2

0008 1x1

0006

0004

0002

0 0 10 20 30 40 50 60

time (min)

(b)

0012

001

0008

0006

0004

0002

0 0 10 20 30 40 50 60

time (m in)

(C)

Figure 510 Pulse responses for A in bottom product for Example problem 1 (a) Full-order models (b) - TDMH full and reduced order (c) - CMH full and reduced order

76

Pulse responses for R 0

-0002 -0004 -0006 -0008 -001

-0012 -0014 -0016 -0018 -002

0 10 20 30 40 50 60

time (m in)

(a)

0 -0002 -0004 -0006 -0008

-001 -0012 -0014 -0016 -0018

-002 0 10 20 30 40 50 60

time (min)

(b)

0 -0002 -0004 -0006 -0008

-001 -0012 -0014 -0016 -0018

-002 0 10 20 30 40 50 60

time (m in)

(C)

Figure 511 Pulse responses for R in bottom product for Example problem 1 (a) - Full-order models (b) - TDMH full and reduced order (c) CMH full and reduced order

77

Pulse responses for S 0008

0007 0006 TUC 0005 CM-I 0004

0003

0002

0001

0 0 10 20 30 40 50 60

time (min)

(a)

0008

0007 0006

0005 0004

0003 0002

0001

0 0 10 20 30 40 50 60

time (min)

(b)

0008

0007 0006

0005 0004

0003 0002

0001

0 0 10 20 30 40 50 60

time (m in)

(c)

Figure 512 Pulse responses for S in bottom product for Example problem 1 (a) Full-order models (b) - TDMH full and reduced order (c) CMH full and reduced order

78

The responses for the bottom product are shown in Figure 510 to 512 As in the step

responses deviations from initial steady-state values were used instead of actual mole

fractions

The results from the pulse tests were similar to the results from step tests The

responses in Figure 510 to 512 indicate that the CMH model should not be used to

simulate the dynamic behavior of the full-order TDMH model Again even the 1 xl

TDMH yielded better prediction than the full-order CMH model and all reduced-order

models fit their respective full-order model very well

Bode diagrams were generated from the inputoutput data of each pulse test

Then the residual amplitude ratio and residual phase angle were calculated in order to

compare the dynamic behavior of a model relative to true behavior For a reduced-order

model the results from the full-order of the same model were used as the reference At

each frequency the residual amplitude ratio (AR) was defined as the ratio between the

AR of the approximate model and true model while the residual phase angle (PA) was

defined as the difference between the PA of the approximate and true model For a

perfect approximation the residual AR and residual PA should thus be equal to 10 and

00 respectively for all frequencies

The Bode diagrams comparing the dynamic response of component A in the

bottom product for the full-order CMH and TDMH models are shown in Figure 513 (a)

and the residual-type Bode diagrams are shown in Figure 513 (b) The similar sets of

Bode diagrams which contain results from reduced-order models and full-order models

are shown in Figures 514 and 515 for the TDMH and CMH models respectively

001 10

0

v 0001 0 E

TDMH

CMH

00001 000001 00001 0001 001

Frequency (radmin) 01 1

01

000001 00001 0001 001

Frequency ( radmin) 01 1

20

10

-90 TDMH

CMH

-180 000001 00001 0001 001 01 1

Frequency ( radmin)

0

-10

CMH

000001 00001

(a)

Fig 513 (a) Bode diagram for full-order pulse responses of A in Example problem 1 (b) physical simplification of the model

0001 001

Frequency (radmin)

01

(b)

Residual dynamics resulting from the

10

2x2 1x1

1

01

00001 0001 001 01 000001 00001 0001 001 01

Frequency (radmin) Frequency (radmin)

90 10

2x2 1x1

0

-90 TDMH

2x2 1x1

-180 -10 000001 00001 0001 001 01 000001 00001 0001 001 01 1


(a) (b)

Fig 514 (a) Bode diagram for the TDMH model pulse responses of A in Example problem 1 (b) Residual dynamics resulting from the collocation approximation

001 10

CMH

2x2

1x1

00001 01

000001 00001 0001 001 01 1 000001 00001 0001 001 01


10

0

-90 CMH

2x2 1x1

-180 -10 000001 00001 0001 001 01 1 000001 00001 0001 001 01 1


(a) (b)

Fig 515 (a) Bode diagram for the CMH model pulse responses of A in Example problem 1 (b) - Residual dynamics resulting from the collocation approximation

82

The Bode diagrams show that at higher frequencies amplitude ratios are

nearly straight lines with slopes of approximately -1 but that the phase angle is

unbounded The amplitude ratio thus indicates that the numerator of a process transfer

function model would be one order lower than the denominator The unbounded phase

angle indicates the presence of time delay term in the transfer function or additional

fast process poles In addition the responses to step inputs in the previous section

also appeared to be nearly first-order with time delay Thus the distillation column in

this example could be approximated by a first-order system with time delay

In Figure 513 the Bode plots show Similar patterns for full-order CMH and

TDMH models The residual AR of the CMH model was nearly constant for the range

of frequencies analyzed However the value of the residual AR was not 10 Both the

CMH and TDMH models yield similar forms of transfer functions but the gains are

different On the other hand inspection of Figure 514 demonstrates the exceptional

ability of the reduced-order TDMH models in preserving the dynamic characteristics of

the full-order system The residual AR was almost equal to 10 and the residual PA was

almost equal to 00 through all frequencies even when the 1 xl model was used

Consequently it can be concluded that the reduced-order TDMH model offered better

dynamic simulation than the model using the constant molar holdup assumption

83

6 EXAMPLE PROBLEM 2

This problem was constructed to demonstrate the usefulness of reduced-order

models More stages were used in the column and a more complex (reversible) reaction

was used The problem is a modification of a problem presented by Suzuki et al

(1971) which involved the production of ethyl acetate as described in Section 41 The

problem specifications are shown in Table 61


Design Variables

Pressure in the column uniform at 1 atm



Feed flowrate [gmole min] 01076



AcOH zA 04962

EtOH zs 04808

water zc 00229

AcOEt zD 0

Distillate rate D [gmolmin] 00208

Reboiler duty QR [calmin] 186093

Column diameter dm [m] 012

Weir length 1 [m] 009

Weir height h [m] 003

Liquid volume in condenser [m3] 3393x10-4

Liquid volume in reboiler [m3] 1018x10-3

84

In order to determine the effects caused by the numerical approximation a

minimum number of physical assumptions were made and only the rigorous TDMH

model was utilized All constants involved such as constants for the BWR equation of

state and the Margules activity coefficient equation are listed in Appendix A

Steady-state results The column consisted of 9 stages in the rectifying module and

18 stages in the stripping module Many combinations of collocation points can be

made The reduced-order models utilized in this problem were 8x16 7x14 6x12 4x9

and 3x6 TDMH models which roughly provided 9 20 29 46 and 59 reductions in

the number of differential equations (from 153 to 138 123 108 83 and 63

respectively) Table 62 shows the locations of collocation points for each model

Table 62 Location of collocation points utilized in Example problem 2

8x16 7x14 6x12 4x9 3x6

Rectifying Module 00000 00000 00000 00000 00000

10003 10036 10209 12230 15649

0 = condenser 20129 20873 22952 35293 50000

10 = vapor feed stage 31068 34290 40295 64707 84351

43453 50000 59705 87770 100000

56547 65710 77048 100000

68932 79127 89791

79871 89964 100000

89997 100000

100000

85

Table 62 (continued)

8x16 7x14 6x12 4x9 3x6

Stripping Module 110000 110000 110000 110000 110000

120000 120000 120005 120210 122214

11 = liquid feed stage 130000 130016 130258 133250 146709

30 = reboiler 140008 140282 142129 152490 183980

150112 151682 157096 177252 226020

160676 165036 174991 205000 263291

172205 180226 194781 232748 287786

184815 196607 215219 257510 300000

198183 213393 235009 276750

211817 229774 252904 289790

225185 244964 267871 300000

237795 258318 279742

249324 269718 289995

259888 279984 300000

269992 290000

280000 300000

290000

300000

The steady-state profiles shown in Figure 61 and 62 indicate the very good

capability of the order reduction technique The profiles obtained from the reduced-

order models were very close to true profiles Because the results obtained from each

model are very close together it is very difficult to distinguish the data points when the

results from all models are displayed Thus only the profiles from the 6x12 4x9 and

3x6 models are displayed However the mean squared errors for every model (relative

86

to the results from full-order TDMH model) and the total rate of consumption of AcOH

(A) were computed and are shown in Table 63 and 64 respectively


8x16 7x14 6x12 4x9 3x6

T (K)2 34681E-06 61907E-06 99419E-06 78225E-05 77447E-03

XAcOH 40090E-11 25666E-10 10937E-09 52778E-08 79956E-06

xEioll 34920E-09 56707E-09 89310E-09 47621E-08 40108E-06

Xwater 18735E-09 37718E-09 63574E-09 26774E-08 86463E-07

XAcOEt 86031E-09 13058E-08 16382E-08 53505E-08 85873E-07

YAcoH 29980E-11 14345E-10 58830E-10 11738E-07 18645E-05

YEt0H 67593E-09 96737E-09 12643E-08 76121E-08 80113E-06

Ywater 24000E-09 47672E-09 80790E-09 45331E-08 19307E-06

YAcOEt 15738E-08 22710E-08 27523E-08 82866E-08 16307E-06

L (gmolmin)2 14936E-10 24385E-10 60968E-10 25848E-09 13842E-07

V (gmolmin)2 43025E-09 40383E-09 60686E-09 70445E-09 14962E-07

M (gmol)2 42749E-07 31854E-06 25227E-05 61481E-04 21716E-03

imam (gmolmin)2 33790E-14 68526E-14 14397E-13 10055E-12 83704E-11

Table 64 Total rate of consumption of AcOH in the column for Example problem 2

Total rate of consumption of Order of model AcOH (A) in the column

(gmolmin)

Full (9x18) 0014071

8x16 0014071

7x14 0014069

6x12 0014067

4x9 0014063

3x6 0014038

Composition profiles of AcOH (A) 1

09 - full A 6x1208 -07 - o 4x9 x 3x6 06 -05 -04 -03 -02 01 iiiiliiloilli0 II liKei Ct )1( MY A

0 3 6 9 12 15 18 21 24 27 30

Stage number

Composition profiles of EtOH (B) 1

09 08 07 -06 05 04 - full A 6x1203 02 o 4x9 x 3x6 01 If tif IIIIiiit i 11110 1 1

0 3 6 9 12 15 18 21 24 27 30

Stage number

1

09 c 08 ot 07 E 06 e 05 oE 04 a 03 3 02

01 0

0

1

09 08 07 06 05 04 03 02 01

0 0

Composition profiles of water (C)

- full A 6x12

o 4x9 x 3x6

iiiii isii 1 3 6 9 12 15 18 21 24 27 30

Stage number

Composition profiles of AcOEt (D)

3 6 9 12 15 18 21 24 27 30

Stage number

Figure 61 Steady-state liquid composition profiles for Example problem 2

370 Temperature profile

30 Rate of consumption of AcOH (-rAx10 5

o) 365

E 25

20

a)

L

360

355 -

E o E

15

10

sect 350I-

0 E

5

0

345 5 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(a) (b)

035 Flowrate profile

21 Molar holdup profile

03

025

02

vapor 19 17 -15 -13 -

0 4x9

p

x

6x12

3x6

015

01

005

0

liquid

4-1 I I I

full

o 4x9

I it N 1 4 I

p

x 6x12

3x6

11 -9-7-5 ilitiltr_erfpsmarriaitsesah_os_latriKeieitIerE418

s1 1 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(c) (d)

Figure 62 Steady-state profiles of parameters of the column for Example problem 2 (a) temperature (b) rate of consumption of AcOH (A) (c) flowrate (d) liquid molar holdup

89

There were however some limitations for the low-order model For this

system as shown in Figure 63 the vapor pressure of AcOH (A) is much lower than the

vapor pressure of other species and also lower than the operating pressure for the entire

range of temperature in the column On the other hand the vapor pressures of EtOH

(B) and AcOEt (D) are higher than the operating pressure for almost the entire

temperature range This implies that only a concentration of AcOH (A) and water (C)

should exist in the rectifying section due to low vapor transfer up the column Thus the

reaction would mostly occur in the liquid in the stripping section

25

AcOH

EtOH

-

- - water_

1 05 _ - -- AcOEt

0 1

345 350 355 360 365 370

Temperature (K)

Figure 63 Vapor pressure of each species over the temperature range in Example problem 2

The steady-state composition profiles show a high level of AcOH (A) in the

reboiler and a high level of EtOH (B) and AcOEt (D) in the condenser as expected

Figure 62(b) shows that the rate of AcOH consumed by reaction is nearly zero in the

rectifying section Both the forward reaction and reverse reaction rates are low because

90

both AcOH (A) and water (C) are at low concentrations in the rectifying section Thus

as expected most of the reaction occurs in the stripping section

Since the feed was introduced as a liquid at stage 11 and the feed had a high

composition of AcOH a steep change in the composition profile of AcOH occured

which was a problem for the lowest order model Because the true mole fraction of

AcOH in the condenser was nearly zero negative mole fractions in the condenser were

calculated when using the 3x6 model The problem was avoided by using higher order

reduced models

Step test A step in feed flowrate from 01076 to 01291 gmolmin (20 increase) was

introduced to the column as done in the prior example Because of the complexity of

this problem a longer process time was required for the column to reach a new steady

state The simulation times from each model were recorded for 80 hours of process

time and the relative computing times for each model are shown in Table 65 The

dynamic responses of liquid bottom product determined from each model are displayed

in Figure 64

Because the feed stream consisted mainly of AcOH and EtOH an increase in

feed rate was expected to result in higher mole fractions of EtOH through out the

column

91


Order of model Relative time

Full (9x18) 1

8x16 09715

7x14 08797

6x12 07190

4x9 05733

3x6 04794

Note Computing time required for full-order TDMH model

was 9 minutes 4149 seconds

Although the feed flowrate was increased the reboiler duty and flowrate of

distillate were the same The increase in feed flowrate thus caused an increase in the

flowrate of bottom products and the mole fraction of heavy components (AcOH and

water) in the reboiler were expected to decrease However this decrease of AcOH mole

fraction should be compensated by an offsetting increase due to more AcOH in the feed

stream

As described in the previous example the heat duty of the column remains the

same while the feed rate is increased This reduces the intensity of separation As

displayed in Figure 63 in the reboiler the vapor pressure of AcOEt is less than that of

EtOH Thus the fraction of AcOEt in the reboiler should increase

Step responses for AcOH Step responses for water

048

2 046

to - 044

E 042V 04

TEM 7x14 4x9

8x16 6x12 3x6

018

0175

017

0165

016

0155

IDVH 7x14 4x9

8x16 6x12 3x6

038 0 10 20 30 40 50 60 70 80

015 0 10 20 30 40 50 60 70 80

time (hr) time (hr)

042 Step responses for EtOH

0035 Step responses for AcOEt

04

038

036

0 034 3 7 032

TDM-I 7x14 4x9

8x16 6x12 3x6

g 0033 ra co 1- 0031

Edeg 0029

yor 0027

TDMI-1

7x14 4x9

8x16 6x12 3x6

03 0 10 20 30 40 50 60 70 80

0025 0 10 20 30 40 50 60 70 80

time (hr) time (hr)

Figure 64 Step responses for liquid composition of each species in reboiler for Example problem 2

Composition profiles of AcOH 1

09 - full p 6x12 08 07 o 4x9 x 3x6 06 05 04 03 02 01

0 it AKA lap DI ti iiiiislitit 0 3 6 9 12 15 18 21 24 27 30

Stage number

Composition profiles of EtOH

09 08 07 06 05

6x1204 - full p03 02 o 4x9 x 3x6 01

0 i I I I I I I I

0 3 6 9 12 15 18 21 24 27 30

Stage number

Composition profiles of water-1

09 -08

full p 6x12

07 o 4x9 x 3x6 06 05 04 03 02 -01

0 T 0 3 6 9 12 15 18 21 24 27 30

Stage number

1 -Composition profiles of AcOEt

09 08 full A 6x12 07 06 0 4x9 x 3x6

05 04 03 02 01

0 I I I

0 3 6 9 12 15 18 21 24 27 30

Stage number

Figure 65 Final steady-state liquid composition profiles for Example problem 2 after 20 step increasing in feed flowrate

46

370

365

360

355

- full

Temperature profile

p 6x12

o 4x9 x 3x6

E

E 5 E

Rate of consumption of AcOH (-rAx105) 30

25 -20 -15-10 -

- full A 6x12

o 4x9 x 3x6

sect 350

345

-6 E cr)

5 -0 if ----4r-aiamp

5 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(a) (b)



03 19

025

02

vapor 17 15 13

015

01

005

0 1-

liquid

I 4 4 I

full o 4x9

I i l I III I

A

x 6x12

3x6

I I

11

9-7-5-3

0 3 6 9 12 15 18 Stage number

21 24 27 30 0 3 6 9 12 15 18 Stage number

21 24 27 30

(c) (d)

Figure 66 Final steady-state profiles of column parameters for Example problem 2 after 20 step increasing in feed flowrate (a) temperature (b) rate of consumption of AcOH (c) flowrate (d) liquid molar holdup

95

The responses shown in Figure 64 indicate that only the high order 8x16 model

yielded dynamic responses close to the full-order results and larger deviations were

observed when fewer collocation points were utilized Large oscillations were observed

with the lowest order model even though the full-order model exhibited almost no

oscillation Thus a small number of collocation points were insufficient for the

approximation of steep profiles However for all models displayed the final steady-

state results predicted from the reduced-order models were nearly identical to the final

results for the full model The new steady-state profiles for selected models are shown

in Figure 65 and 66 Because of shorter computing time a reduced-order model might

be useful for estimation of final steady-state conditions but further work would be

required to improve the dynamic modeling

Pulse test A rectangular pulse in feed flowrate from 01076 to 01291 gmolmin and

sustained for 25 minutes was simulated The pulse responses for liquid bottom product

composition obtained from each model are displayed in Figure 67 Bode diagrams for

composition of AcOEt in the bottom product were generated and are shown in Figure

68

It is obvious that the dynamic response of this complex system was much slower

than for the simple system of Example problem 1 Many factors such as number of

stages and the reaction kinetic influence the dynamic behavior of the system

00004

00002 0

-00002 -00004 -00006 -00008 -0001

-00012 -00014

00012

0001

00008

00006

00004

00002

0

-00002

-00004

Pulse responses for AcOH

time (hr)

Pulse responses for EtOH

time (hr)

000015

00001

000005

0

-000005

-00001

-000015

-00002

000006

000005

000004

000003

000002

0

000001 -0

-000001 0

Pulse responses for water

10 20 30 40 50

time (hr)

Pulse responses for AcOEt

10 20 30 40 50

time (hr)

Figure 67 Pulse responses for liquid composition of each species in reboiler for Example problem 2

10 10

1

01

13 001 1

c E 0001 TDIVI-1 8x16 8x16 7x14

00001 7x14 4x9

6x12 3x6

6x12 3x6

4x9

000001 01

000001 00001 0001 001 Frequency (radm in)

01 000001 00001 0001 001 Frequency (radm in)

01

90 60 IDN1-1 8x16 50

407x 14 6x12 30

4x9 3x6 T 20 20 5 10

0 2 -10 0

-20 8x16 7x14o -30 6x12 4x9-40 3x6cc -50

-180 -60 000001 00001 0001 001 01 000001 00001 0001 001 01 1

Frequency (radm in) Frequency (radm in)

(a) (b)

Figure 68 (a) - Bode diagram for pulse responses of AcOEt in Example problem 2 (b) Residual dynamic resulting from the collocation approximation

98

According to Figure 67 only the 8x16 model which is nearly a full-order

model provided good predictions of the dynamic responses to the pulse input Lower

order models such as 6x12 and 4x9 models did not represent the dynamic behavior of

this complex system These results agree with results from the step test

The Bode diagram of AcOEt shows a highly complex frequency response It

should be noted that all models yielded good prediction at very low frequencies The

residual AR is very close to 10 and the residual PA is very close to 00 due to the good

performance of these models at steady state At frequencies higher than 00001

radianmin deviations from the full-order solution were observed Thus accordingto

both step and pulse tests reduced-order models using this collocation technique are not

as suitable for prediction of the dynamic behavior of complicated columns as they are

for simpler columns

99

7 EXAMPLE PROBLEM 3

The capability and efficiency of reduced-order models were discussed in

previous examples In this example comparisons of the accuracy between the model

using numerical approximation (reduced-order model) and models using physical

assumptions are investigated

Two case studies are employed for two different physical approximations The

first case is used to study the efficiency of the models when there is a pressure drop

through the column Often a column is approximated by assuming that pressure drop

on each tray is negligible This assumption might cause deviations from true

solutions Thus the model using numerical approximation is proposed to solve this

problem

The second case deals with liquid holdup on each plate Doherty and Buzad

(1994) mentioned the importance of liquid holdup on reactive distillation design In

this work the effect of plate geometry on the dynamic behavior of a reactive distillation

column was studied

The same esterification reaction as discussed in example problem 2 was used

however using a column with fewer stages for simplification Other operating

conditions including plate geometry were the same This system is the same system

demonstrated by Suzuki et al (1971) Ruiz et al (1995) also picked this problem as an

example for dynamic simulation using a rigorous model where hydraulic effects were

considered Problem specifications are shown in Table 71 The simulations were done

by using the rigorous TDMH model

100


Design Variables







AcOH za 04962

EtOH zB 04808

water zc 00229

AcOEt zD 0




Weir length [m] 009

Weir height [m] 003



Steady-state results In this problem there were 3 stages in the rectifying module and

6 stages in the stripping module Therefore the maximum numbers of collocation

points in each module for a reduced-order model were 2 and 5 points respectively

Consequently 2x5 2x4 and 1x3 reduced-order models which roughly provided a 16

24 or 40 reduction in the number of differential equations (from 63 to 53 48 and 38

101

respectively) were considered Table 72 shows the locations of collocation points for

each model


2x5 2x4 1x3 Rectifying Module 00000 00000 00000

11835 11835 20000 0 = condenser 28165 28165 40000 4 = vapor feed stage 40000 40000

Stripping Module 50000 50000 50000 60087 60644 62528

5 = liquid feed stage 71403 75762 85000 12 = reboiler 85000 94238 107472

98597 109356 120000 109913 120000 120000

The only difference between the system in this problem and the system in

Example problem 2 was the number of stages in the column Thus the same patterns in

steady-state profiles were expected For the same plate geometry fewer stages meant a

lower amount of total liquid holdup in the column which consequently affected the

amount of products generated from chemical reactions Hence the average amounts of

products (water and AcOEt) were expected to be lower than the results shown in

Example problem 2 while the average amounts of reactants (AcOH and EtOH) whould

be higher Furthermore since the vapor pressure of AcOEt is higher than other

components AcOEt generated by reaction would tend to move to the rectifying section

102

The liquid composition profiles exhibited in Figure 71 indicate good agreement

with the above expectations The mole fraction of AcOEt (D) is obviously lower in

Figure 71 than the results in Example problem 2 (Figure 61) especially in the

rectifying module On the contrary mole fractions of water obtained in this example

(Figure 71) were slightly more than in Figure 61 except in the bottom product of the

column

An overview of Figures 71 and 72 reveals the good steady-state performance

for reduced-order models The MSEs relative to the full-order solution and total rate of

consumption of AcOH are shown in Table 73 and 74 respectively

Table 73 Mean Squared Errors for steady-state profile for Example problem 3

(2x5) (2x4) (1x3)

T (K)2 60609E-05 13436E-03 29741E-02

XAeOH 35046E-08 10320E-06 17373E-05

XEtOH 73801E-07 12009E-06 16073E-05

xwater 23561E-08 13345E-07 46047E-06

Xite0Et 78982E-07 78798E-07 17033E-05

Y AcOH 53545E-08 23869E-06 40598E-05

Y Et0H 60827E-07 15434E-06 26427E-05

Ywater 25369E-08 30654E-07 59017E-06

YAcOEt 64649E-07 64980E-07 16455E-05

L (gmolmin)2 16799E-09 26341E-08 35570E-07

V (gmolmin)2 18206E-09 33777E-08 48041E-07

M (gmol)2 11613E-03 11617E-03 10803E-02

rlacoll (gmolmin)2 56152E-13 18139E-11 26727E-10

Composition profiles of AcOH Composition profiles of water 1 1

09 09-s- TDVH08 08 -s-TDVH 07 x 2x5 07 x 2x5 06 06o 2x4 o 2x4 05 05o 1x3 0 1x304 04 03 03 02 02 01 01

10 EMI Cl 0111111 1111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number Stage number

Composition profiles of EtOH Composition profiles of AcOEt 1 1

09 09 -a- MAC08 08 07 07 x 2x5 06 06 4 2x4 05 -s- TEAM 05

0 1x304 04x 2x503 03

o 2x402 02 01 O 1x3 01

0 011111111 1411 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


Figure 71 Steady-state composition profiles for Example problem 3

Temperature profiles Rate of consumption of AcOH (-rAx1 05)370 35

TDM-I aTow 30 Y 365 x 2x5 25 x 2x5

360 2x4 20 2x4 E 070o 1x3 15 0 1x3

11 355 E10 IP EX

a 0 5g 350

1- rn 0 i

345 i i -51111 E

1

0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12 Stage number Stage number

(a) (b) Flowrate profiles Molar holdup profiles

035 21

03 19 6 TDMH 17VaporE 025 x 2x5

8 15-2x402 13E

12) TDVH 11 - O 1x3015 Liquid 2x5 is 9-

01 2x4 7-=005- 5o 1x3

0 3 il 111111 1 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)

Figure 72 Steady-state profiles of parameters of the column for Example problem 3 (a) temperature (b) rate of consumption of AcOH (c) flowrate (d) liquid molar holdup

105



(gmolmin) Full (3x6) 0011346

2x5 0011345

2x4 0011343

lx3 0011364

From Table 73 it can be seen that the MSE values were higher than in Example

problem 2 when computed for models which provide roughly the same order of

reduction This is because the absolute number of collocation points can be very

important especially for low-order models Although the models in this example and

previous example provide the same relative order of reduction in the number of

differential equations the models in this example utilized fewer collocation points

Thus the models in this example were less capable of good prediction

Step test The same step test as done in Example problem 2 was conducted for this

system The responses are displayed in Figure 73 Since the number of stages in this

problem was less than in the previous problem this system responded to the step

change more quickly and reached a new steady state faster than the column in Example

problem 2 The required computing times for this problem relative to the full-order

model are listed in Table 75

106



Full (3x6) 1

2x5 09313

2x4 08556

1x3 06608

Note Computing time required for full-order TDMH model was 4 minutes 1156 seconds

Considering the responses from the full-order model the responses obtained

from this system and the responses from the system in Example 2 have similar

characteristics because the set of components and operating conditions in these two

problem were the same However for the same percentage of reduction in differential

equations the reduced-order models in the column with fewer stages yielded more

accurate dynamic results

As described in Chapter 2 the entry points for vapor and liquid streams to each

module are treated as grid points in addition to the interior collocation points calculated

from Hahn orthogonal polynomials All columns studied in this thesis consisted of two

modules rectifying and stripping Consequently there are 4 positions which are always

included in a reduced-order model condenser reboiler stages above and below feed

position In this problem the column consisted of 13 actual stages therefore the

reduction technique applied to 9 stages which occupy only 692 of the column On

the other hand there were 31 stages in the column in Example problem 2 Thus 27

stages which take up 871 of the column were utilized by the reduction technique

Step responses for AcOH Step responses for water 049 015

0485 - 0145C TDVH0048 0475 1 014 2x5

IMF 2x4 047 0 0135

2x5 o lx3E0465 0132x4 733 lx3 5r 0125

046

0455 I I I045 012

0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

Step responses for EtOH Step responses for AcOEt 038 003

0375 00295 037 -

00290365 -036 00285 TDVHTDVH

0355 2x52x5 0028 035 2x42x4

002750345 1x3lx3 034 0027 4 I I I

0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)


0

108

Because the smaller section is utilized for numerical approximation less errors built up

in this Example problem

Pulse test A pulse in feed flowrate with the same magnitude and duration as done in

Example problem 2 was introduced into the column at steady state The responses and

Bode diagram of liquid bottom product compositions are shown in Figures 74 and 75

respectively

As discussed for the step test this system responded to the change in input faster

and reached a new steady state faster than the column with more stages The results

from pulse test also indicate this faster dynamic behavior

The Bode diagram for AcOEt shows the same pattern of dynamic behavior as

the system in Example problem 2 The residual plot indicates that the reduced-order

models worked better in this simple problem The residual AR and residual PA values

are nearly 10 and 00 at low frequency However at intermediate frequencies where

the complicated behavior occurs the reduced-order model yielded errors On the

contrary for water which had a more simple dynamic behavior the results from

reduced-order models were very close to the solutions from the full-order model Thus

it might be concluded that the reduced-order model has less capability to predict a

dynamic behavior of a system with more complicated characteristics

Pulse responses for AcOH 00002 00001

0 -00001 -00002 -00003 -- 00004 -00005 2x5 -00006 -00007

2x4

-00008 lx3 -00009

0 10 20 30 40 50

time (hr)

Pulse responses for EtOH 00008 00007 00006 00005 00004 00003 00002 00001

0 -00001

0 10 20 30 40 50

time (hr)

Pulse responses for water 00001

000008 000006 TDMr1 2x5

000004 2x4 1x3 000002

0 -000002 -000004 -000006 -000008

-00001 0 10 20 30 40 50

time (hr)

Pulse responses for AcOEt 0000035

000003

0000025

000002

0000015 000001

0000005

0

-0000005 0 10 20 30 40 50

time (hr)

Figure 74 Pulse responses for liquid composition of each species in the bottom product for Example problem

10 10

1

01

1

001 full

2x5

0001 2x4

lx3 00001 01

000001 00001 0001 001 01 000001 00001 0001 001 01 1


90

0

full -90 2x5

2x4 1x3

-180 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)

Fig 75 (a) Bode diagram for pulse responses of AcOEt in Example problem 3 (b) Residual dynamics resulting from the collocation approximation

10 10

2x5 1 2x4

0 1x3 0 s 01 0is c= 001 full Tx E4 2x5

0001 2x4

lx3 00001 01

000001 00001 0001 001 01 000001 00001 0001 001 01 Frequency (radm in) Frequency (radm in)

90 10

clii0 ii 13

w 0 0to

la -90 c co coco c co

co full co - 180 c co 2x5

c- 1 0 2x5

co iic c 2x42x4 0cs -270 H co lx31x3 cc

-360 -20 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)

Fig 76 (a) Bode diagram for pulse responses of water in Example problem 3 (b) Residual dynamics resulting from the collocation approximation

112

71 Example Problem 31 Non-uniform Pressure Effects

One of the common assumptions made when solving a distillation problem is

that the pressure drop over each tray is negligible Thus pressure is assumed to be

uniform within the column This assumption reduces the computational effort required

to solve the problem however it is likely that some pressure drop occurs in real

operations

In this case study a linear pressure drop through the column was assumed where

the average pressure in the column was kept at one atmosphere The pressure drop

across each tray was assumed to be 005 01 and 015 atm for simulation in case study

31a 31b and 31c respectively Figure 711 shows the variation of pressure along the

column in each case

pressure atm) 2

18

16

14

12

1

08

06

0--AP=005 X--AP=OA

AP= 015

04

02

0 I I I l iti 0 1 2 3 4 5 6 7 8 9 10 11 12

stage number

Figure 711 Pressure profile for various values of pressure drop

The simulations were made in order to demonstrate the results of neglecting a pressure

gradient in the column on both static and dynamic behaviors of the system Moreover

113

the simulation results also show the accuracy of applying the reduced-order technique

on a column with nonuniform pressure

Steady-state results The steady-state results are plotted in Figures 712 to 719

Table 711 shows the MSE value for full-order results for different value of pressure

drop compared to the full-order result for uniform pressure The MSE values computed

for reduced-order models relative to full-order model results for each case are shown in

Table 712

Table 711 Mean squared errors for full-order steady-state profiles for Example Problem 31a

AP=005 atm AP=010 atm AP=015 atm

T (K)2 250357 1175582 4137036

xAcoH 61711E-05 21799E-04 45062E-04

xEroll 86611E-04 23323E-03 33668E-03

Xwater 10578E-04 35052E-04 71882E-04

XAcOEt 10156E-03 25721E-03 34075E-03

YAcOH 36414E-05 12001E-04 22977E-04

YEt0H 14054E-03 41997E-03 76426E-03

Ywater 10252E-04 32920E-04 67493E-04

YAcoEt 15273E-03 43664E-03 77664E-03

L (gmolmin) 2 33027E-06 19272E-05 80700E-05

V (gmolmin)2 32945E-06 19270E-05 80678E-05

M (gmol) 2 77791E-03 17231E-02 16933E-02

11AcOH (gmolmin)2 23729E-07 81195E-07 15842E-06

Table 712 Mean squared errors for reduced-order steady-state profiles for Example Problem 31

Case 31a AP=005 atm Case 31b AP=010 atm Case 31c AP=015 atm

(2x5) (2x4) (1x3) (2x5) (2x4) (1x3) (2x5) (2x4) (1x3)

T 1035E-04 1426E-03 2166E-02 6500E-04 1982E-03 7342E-02 1339E-01 1352E-01 4376E+00

xAcoH 3449E-08 9791E-07 1516E-05 3483E-08 9113E-07 1324E-05 4424E-08 8416E-07 1161E-05

XEt0H 4048E-07 7949E-07 1783E-05 3143E-07 6492E-07 1769E-05 4013E-06 4320E-06 2098E-04

xwate 1055E-08 1436E-07 5492E-06 9188E-09 1514E-07 5428E-06 2914E-07 4453E-07 1212E-05

XAr0Et 3785E-07 3776E-07 2799E-05 2746E-07 2758E-07 2852E-05 5805E-06 5805E-06 2511E-04

YACOH 5878E-08 2296E-06 3546E-05 6219E-08 2153E-06 3092E-05 6902E-08 1982E-06 2702E-05

Y DOH 3397E-07 1107E-06 2434E-05 2647E-07 9055E-07 2223E-05 3398E-06 3928E-06 1891E-04

Ywater 1769E-08 3608E-07 6662E-06 1902E-08 3893E-07 6484E-06 3001E-07 6846E-07 1419E-05

YAcOEt 3125E-07 3179E-07 2400E-05 2263E-07 2349E-07 2424E-05 4911E-06 4918E-06 2227E-04

L 1259E-09 2441E-08 2874E-07 1710E-09 2253E-08 2670E-07 8557E-08 1044E-07 4197E-06

V 1283E-09 2963E-08 3925E-07 1497E-09 2656E-08 3329E-07 1008E-07 1231E-07 5191E-06

M 1064E-03 1064E-03 1077E-02 1052E-03 1053E-03 1086E-02 1306E-03 1308E-03 1878E-02

17awn 9882E-13 3055E-11 3667E-10 1565E-12 4471E-11 4994E-10 1379E-11 7137E-11 1149E-09

Temperature profiles390 380 370 360 350 340 p P =O330 cr

320 -4 310 300 -- 290 CI

CY

I t f

A

1 flAP=010

0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)

Pressure drop at each tray = 010 atm390 380 370 360 350 340 9 TDMH 330 x 2x5 320 310

1x3300 290 tIllli11111

2x4

0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(c)

390 380 370 360 350 340 330 320 310 300 290

0 f III-1111111 1 2 3 4 5 6 7 8 9 10 11

Stage number

Pressure drop at each tray = 005 atm

9-- TDMH x 2x5 o 2x4 o 1x3

12

(b)

390 380 370 360 350 340 330 320 310 300 290

0 1111f-1-11111

2 3 4 5 6 7 8 9 10 11

Stage number


9 TDMH 2x5

o 2x4 o 1x3

1 12

(d)

Figure 712 Steady-state temperature profiles (a) Full-order models for case 31a-31c (b) Full and reduced order for case 31a (c) - Full and reduced order for case 31b (d) Full and reduced order for case 31c

- --

09 -08 07 -06 -05 -04 03 -02 -01

0 II 0

1

09 -08 07 06 05 -04 -03 02 01 -

0 0

Composition profile of AcOH

--B--AP=0 - -AP= 005

A AP= 010 ---G---AP= 015

1111111 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


-B-TDMH 2x5

o 2x4 o 1x3

i BM El i I I I

1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(c)

1

09 -08 -07 -06 05 -04 -03 -02 01 -

0 0

1

09 08 07 06 05 04 03 02 01

0 0


-13-TDMH x 2x5

2x4

O 1x3

1111111 OE U 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)

Pressure dro at each tra = 015 atm

1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(d)

Figure 713 Steady-state composition profiles of AcOH (a) - Full-order models for case 31a-31c (b) Full and reduced order for case 31a (c) - Full and reduced order for case 31b (d) Full and reduced order for case 31c

Composition profile of EtOH 09 -08 -07 -06 05 04 --B--AP=0

AP = 00503 02 fi AP - 010 01 - - -G - -AP= 015

0 11111111111 O 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)

Pressure drop at each tray = 010 atm 1

09 08 07 06 05 -8- TDM H04 x 2x503

O 2x4 02 01 0 1x3

0 O 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(c)

Figure 714 Steady-state composition profiles of EtOH (a)


09 -08 -07 -06 -05 - -9- TDM H04 - x 2x503 -

O 2x402 -01-

0 loi1x3i i I f iiii0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)

Pressure drop at each tray = 015 atm1

09 -08 07 06 05 -04 -9- TDMH 03 - x 2x5 02 - p 2x4 01 - 0 1x3

0 0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(d)

Full-order models for case 31a-31c (b) - Full and reduced order for case 31a (c) - Full and reduced order for case 31b (d) Full and reduced order for case 31c

Composition profile of water Pressure drop at each tray = 005 atm 11

09 -09 - --B--AP=0 -e-TDMH0808 07 07 - x 2x5

A AP=01006 06 2x4 05 05 O 1x3 04 - 04 -03 - 03 02 - 02 -01 01 -

0 0 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)

Pressure drop at each tray = 010 atm Pressure dro at each tra = 015 atm 11

0909 -08 - TDMH 08

07 x 2x5 07

06 o 2x4 06 0505 o 1x3

04 - 04

03 - 03 02 - 02 01 01111111110 0


(c) (d)

Figure 715 Steady-state composition profiles of water (a) - Full-order models for case 31a-31c (b) Full and reduced order for case 31a (c) Full and reduced order for case 31b (d) Full and reduced order for case 31c

Composition profile of AcOEt Pressure drop at each tray = 005 atm 1 1

09 09--B--AP=0 -B- TDMH08 - 08 -07 - 07 2x5

A AP= 01006- 06 - 2x4 ---0---AP= 01505 05 O 1x3

04 04 -03 - 03 -02 02 01 01lilt0 0I


(a) (b)


09 - 09 08 - -9- TDMH 08 07 x 2x5 07 06 - 06o 2x4

0505 o 1x3 04 - 04 03 - 03 02 02 01 - 01

0 0Iflit 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)

Figure 716 Steady-state composition profiles of AcOEt (a) Full-order models for case 31a-31c (b) Full and reduced order for case 31a (c) Full and reduced order for case 31b (d) Full and reduced order for case 31c

035 035 035 Pressure drop at each tray = 005 atm

035

2r

03

025

02

015

01

005

-13-- AP = 0 AP = 005

A AP= 010 --0---4P= 015

03

025

02

015

01

005

0

03

025

02

015

01

005

Vapor

- 2-- TDMH Liquid 2x5

2x4 o 1x3111114-11111

03

025 B

02 g0

015 8 0

01

005

0 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12

(a) (b)

035 Pressure drop at each tray = 010 atm

035 035 Pressure drop at each tray = 015 atm

035

03

025

02

015

01 -

005

Vapor

c CI 113 Liquid

NION101 -B-TDMH

X 2x5 2x4

II 1x3 t I 0

03

025

02

015

01

005

03 -

025 -

02

015

01

005

O NID Liquid x 2x5

O 2x4 O 1x3

I I 114111+1-f

Vapor

- 8- TDMH

03

025

02

015

01

005

0 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(c) (d)

Figure 717 Steady-state flowrate profiles (a) Full-order models for case 31a-31c (b) Full and reduced order for case 31a (c) Full and reduced order for case 31b (d) Full and reduced order for case 31c

Molar holdup profiles21 Pressure drop at each tray = 005 atm

21

1919 --B--AP=0 El-- TEM17 17 x 2x515 15A AP=010 o 2x413 13 11 o 1x311

9 9 7 7 5

3 3111111111 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)

Pressure drop at each tray = 010 atm Pressure drop at each tray = 015 atm21 21

19 - 19 8 TDMH-8 TCM-I 17

g 15 x 2x5 -6 17 rA 15

2x5

a 13 o 2x4 cl 13 o 2x4

31- 11 - 0 1x3 12 11 1x3 c

9 c

9 co 03 75 E

7 5 111--0K 3 1 i 111111111

7 5 3 i i 111111111


(c) (d)

Figure 718 Liquid molar holdup profiles (a) Full-order models for case 31a-31c (b) Full and reduced order for case 31a (c) Full and reduced order for case 31b (d) Full and reduced order for case 31c

Rate of consumption of AcOH Pressure drop at each tray = 005 atm0011 0011

0009 --18HAP0 0009 a TDVH x 2x50007 0007A AP=010 o 2x4

E0005o 0005 o 1x3E E 9 0003 0) 0003

0001 0001 III

-0001 -0001 i


(a) (b) Pressure drop at each tray = 010 atm Pressure drop at each tray = 015 atm

0011 0011

e TDVH0009 0009 -x 2x5

0007 s 0007 o 2x4

t 0005 t 0005o 1x3 E E a) 0003 0)0003

0001

-0001 El OK 0 4 I I I

0001

-0001 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(c) (d)

Figure 719 Profiles show rate of total consumption of AcOH (Nam) (a) Full-order models for case 31a-31c (b) - Full and reduced order for case 31a (c) - Full and reduced order for case 31b (d) Full and reduced order for case 31c

123

The variables expected to be most influenced by different pressure differences

is temperature Figure 712 (a) and the MSE values from Table 711 support this

expectation A larger pressure drop on each tray resulted in a larger deviation in the

temperature profile The error from the model using a constant pressure assumption to

approximate the system with the largest pressure drop was noticeably higher

(MSE=4137) than the results from the lowest order reduced-order model

(MSE=4376)

Composition profiles for each component are shown in Figures 713 to 716

Both the profiles and MSE value in Table 712 indicate that models using the reduction

technique yielded better results than the full-order constant pressure model Even at the

lowest order 1x3 approximation the MSE values from constant pressure model are

larger by about an order of magnitude then the errors from the reduced order model for

the Example Problem 31c

The deviation of the constant pressure model from the full-order model with

pressure gradient was larger for the lighter components (ethanol and ethyl-acetate)

Deviation for the heavy components (water and ethyl acetate) were noticeable only in

the stripping section Moreover Table 711 also shows that the MSE values for light

components were much higher than those for heavy components For the constant

pressure model the pressure at the bottom of the column was lower than the actual

pressure especially when the value of the pressure drop on each tray was high

Consequently temperature calculated in the stripping section was lower than in the true

model According to Figure 7110 the vapor pressure of light components (AcOEt and

124

EtOH) increases rapidly at high temperature Thus the vapor pressure predicted in the

constant pressure model was much lower than the true solution which caused errors in

the calculations of the composition in each phase

3

25

2 MOH

15 EtOH

1 - - water

05 Ac0Et

0

290 310 330 350 370

Temperature (K)

Figure 7110 Vapor pressure of each species over the temperature range

in Example Problem 31a

Furthermore as discussed in the last example most of the reactions occurred at the

bottom of the column and the rate of reaction depended on temperature Thus the

errors in the computing temperatures in the stripping module caused large effects on

product generation rates As shown in Figure 719(a) the consumption of AcOH in

the reboiler when the pressure drop in each tray equaled 015 atm was almost twice the

value calculated from the constant pressure model This factor causes the mole fraction

of reactants calculated using the constant pressure model to be higher than the true

solution while the calculated product mole fractions were lower

125

Another variable obviously influenced by pressure is the vapor flowrate which

consequently affects the liquid flowrate Considering liquid and vapor flowrate profiles

shown in Figure 717 the largest deviations obtained with the constant pressure model

were in the rectifying section Again based on MSE values the reduced-order models

clearly yielded better steady-state results than the full-order constant pressure model

Inspection of Figure 718 shows a sudden change in the molar holdup profiles

from condenser to the first stage The one point collocation in the rectifying module did

not correctly predict this profile however the 2x4 model obtained noticeably better

results

Step test The same step test as the other example was applied to this example As

shown in the previous section the full order TDMH models for different values of

pressure drop yield different steady-state results which are the initial points for each

step test Thus the raw results shown in Figure 7111 are difficult to use for dynamic

behavior analysis The deviations from each initial steady-state results were calculated

and plotted to compare the transient responses among different models in Figures 7112

to 7115 in each figure section (a) demonstrates the efficiency in the prediction of

transient responses at various values of pressure drop using physical approximations

while section (b) (c) and (d) show the results from numerical approximations in each

case

049 Step responses for AcOH

022 Step responses for water

048 047

02 - AP - 0 AP= 010

AP - 005 AP- 015

046 018 -045 044

016

043 014 042 AP = 0 AP= 005 012 -041 AP = 010 AP= 015 04 01

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

Step responses for EtOH Step responses for AcOEt037 007

036 006 035 005 --034 004 -033

003032 DP =0 AP = 005 AP - 0 AP= 005002031 AP = 010 AP= 015 AP= 010 AP- 015

03 001 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

Figure 7111 Full-order step responses for liquid composition of each species in reboiler at various value of pressure drop

Step responses for AcOH 001

0005 0

-0005 -001

-0015 -002 APdeg AP=005

-0025 AP=010 AP=015

-003 0 10 20 30 40 50

time (hr)

(a)


0005 0

-0005 -001

-0015 -002 TDVH 2x5

-0025 2x4 1x3

-003 0 10 20 30 40 50

time (hr)

(c)


0005 0

-0005 -001

-0015 -002 TDAH 2x5

-0025 2x4 1x3

-003 0 10 20 30 40 50

time (hr)

(b)


0005 0

-0005 -001

-0015 TEM 2x5-002

-0025 2x4

-003 0 10 20 30 40

time (hr)

(d)

Figure 7112 Step responses for composition of AcOH (a) Full-order models for case 31a-31c (b) Full and reduced order for case 31a (c) Full and reduced order for case 31b (d) Full and reduced order for case 31c

50



003 003

0025 0025

002 002

0015 0015

001 AP-0 AP- 005

001 IDA4-1 2x5

0005 itP =010 AP-015 0005 1 2x4 1x3

0 i I I i 0 i 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)



003 003

0025 0025

002 002

0015 0015

001 -MINH 2x5 001

0005 2x4 1x3 0005

0 1 1 1 0

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)

Figure 7113 Step responses for composition of EtOH (a) Full-order models for case 31a-31c (b) Full and reduced order for case 31a (c) - Full and reduced order for case 31b (d) Full and reduced order for case 31c



0 0

-0005 APdeg AP= 005 -0005 TDVH 2x5

-001 AP- 010 AP- 015 -001 2x4 1x3

-0015 -0015

-002 -002

-0025 -0025

-003 -003 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(a) (b)



0 0

-0005 TDM- 2x5 -0005 MAC 2x5

-001 2x4 1x3 -001 2x4

-0015 -0015

-002 -002

-0025 -0025

-003 -003 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)

Figure 7114 Step responses for composition of water (a) Full-order models for case 31a-31c (b) Full and reduced order for case 31a (c) Full and reduced order for case 31b (d) Full and reduced order for case 31c



00035 - 00035 -0003 - 0003

00025 00025 -0002

00015 0001 TCMI 2x5

00005 2x4 1x3

0 50 0 10 20 30 40 50

time (hr)

(a) (b)



00035 00035 0003 0003

00025 00025 0002 0002

00015 00015 0001 0001

00005 00005 0 0

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)

Figure 7115 Step responses for composition of AcOEt (a) Full-order models for case 31a-31c (b) Full and reduced order for case 31a (c) Full and reduced order for case 31b (d) Full and reduced order for case 31c

131

The results in Figures 7112 to 7115 show that the results from collocation

approximations were better than the results from physical approximations in most cases

Although some deviations occurred especially when the lowest order 1x3 model was

utilized the results from the reduced-order models converged to the same new steady

state as the solutions from the full-order model

Pulse test The pulse responses of liquid composition of the bottom product for the

same pulse in feed flowrate as used in previous examples are shown in Figures 7116 to

7119 The plots show that the results from reduced -order models represent true

solutions obtained from full-order models better than the results from constant pressure

models in most cases Like the outcomes from the step test the pulse test results also

show that the 1x3 model did not produce reasonable responses for the case when the

pressure drop in each tray equaled 015 atm

According to the Bode plot and residual plots shown in Figure 7120 the

constant pressure model did not produce good prediction of the dynamic characteristics

of the system with pressure drop The residual ARs obtained were not equal to 10 for

the entire frequency range The residual PAs show that the constant pressure model

provided good phase angle prediction only at both extremes of the frequency range

Large errors occurred at intermediate frequencies where the system showed complex

behavior Moreover the deviation from the true characteristics increased when the

value of pressure drop in each tray increased

Pulse responses for AcOH 00003 00002 00001

0 -00001 -00002 -00003 A- AP = 0 -0 0004 AP= 005 -00005 AP= 010 -00006 -00007 AP=015 -00008

0 500 1000 1500 2000 2500 3000 time (min)

(a)

Pressure drop at each tray = 010 atm 00003 00002 00001

0 -00001 -00002 -00003 -00004 -00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)


0 -00001 --00002 T -00003 -00004 --00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)

(b)

Pressure drop at each tray = 015 atm00003 00002 00001

0 -00001 1--00002 + -00003 4 -00004 -t--00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)

Figure 7116 Pulse responses for composition of AcOH (a) - Full-order models for case 31a-31c (b) Full and reduced order for case 31a (c) Full and reduced order for case 31b (d) - Full and reduced order for case 31c

Pulse responses for EtOH00008 00007 00006 AP - 0 00005 AP - 005 00004 AP- 010 00003 AP- 015 00002 00001

0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)

(a)

Pressure drop at each tray = 010 atm 00008 00007 00006 00005 00004 00003 00002 00001 1

0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)

Pressure drop at each tray = 005 atm00008 00007 00006 TDMH 00005 2x5 00004

2x400003 J-lx300002 4-

00001 0

-00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)

(b)

Pressure drop at each tray = 015 atm00008 00007 00006 00005 00004 00003 --00002 00001 -

0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)

Figure 7117 Pulse responses for composition of EtOH (a) Full-order models for case 31a-31c (b) Full and reduced order for case 31a (c) Full and reduced order for case 31b (d) Full and reduced order for case 31c


000005

0

-000005 AP = 0 AP = 005-00001 AP= 010

-000015 AP= 015

-00002 0 500 1000 1500 2000 2500 3000

time (min)

(a)


000005

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)


000005

0

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)

(b)


000005

0

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)

Figure 7118 Pulse responses for composition of water (a) - Full-order models for case 31a-31c (b) Full and reduced order for case 31a (c) Full and reduced order for case 31b (d) Full and reduced order for case 31c


500 1000 1500 2000 2500 3000 time (min)

(a)

Pressure drop at each tray = 010 atm000007 000006 000005 000004 000003 000002 000001

0 -000001

0 500 1000 1500 2000 2500 3000 time (min)

Figure 7119 Pulse responses for composition of AcOEt (a)

Pressure drop at each tray = 005 atm000007 000006 000005 000004 000003 000002 000001 a-

0

-000001 0 500 1000 1500 2000 2500 3000

time (min)

(b)

Pressure drop at each tray = 015 atm000007 000006

000005 000004

000003 000002 -r 000001 VI

0

-000001 0 500 1000 1500 2000 2500 3000

time (min)

Full-order models for case 31a-31c (b) Full and reduced order for case 31a (c) Full and reduced order for case 31b (d) - Full and reduced order for case 31c

10

0001

00001 000001

90

-90

-180 000001

OP -0 4P =005 AP- 010 AP= 015

00001 0001 001

Frequency (radm in) 01

4P =0 AP= 005 AP- 010 AP= 015

00001 0001 001

Frequency (radmin)

(a)

01

10

0

0V

ac 1

0 O 0 0

CC

01

000001

20

10

O 0 0 S -10 0 c a -20 0

w -30 flo cc

-40 000001

AP- 005 AP= 010 AP= 015

00001 0001 001

Frequency (radmin) 01

AP= 005 AP= 010 AP= 015

00001 0001 001

Frequency (radm in)

(b)

01

Figure 7120 (a) - Bode diagram for pulse responses of AcOEt at various pressure drop (b) - Residual dynamics resulting from the physical simplification of the model

10 10

01 =0I0

GI

1 01 1774) a= 3 iTDMI-10010 E 2x5 rozQ 0

0001 2x4 el a)

lx3 cc

00001 01

000001 00001 0001 001 01 000001 00001 0001 001 01 1

Frequency (radmin) Frequency (radm in)

90 50

of 40 a)a

---tu 30 co cco 20 a)

RAC fa al 10c02x5 To 002x4 0 4411 - 1 0 1x3 CC

-180 -20 000001 00001 0001 001 01 1 000001 00001 0001 001 01


(a) (b)

Figure 7121 (a) - Bode diagram for pulse responses of AcOEt when pressure drop in each tray = 005 atm (b) Residual dynamics resulting from the numerical simplification

10 10

1

0

01 a)

a 001 E 2x5

2x4 0001

lx3

00001 01



01

90 50

S40 2x5

30 rn

2x4

1x3 20

210 0 -g 0

X10 cc

-180 -20 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)

Figure 7122 (a) Bode diagram for pulse responses of AcOEt when pressure drop in each tray = 010 atm (b) Residual dynamics resulting from the numerical simplification

10

1

0

01 0

ma a fi 001

0001

00001 000001

90

rn

a)

a) -90

a

-180 000001

TDM-I

2x5

2x4

lx3

00001 0001 001 Frequency (radm in)

TDIVH

2x5

2x4

1x3


(a)

10

1

01 01

000001 00001

01

90 80

O 70 60

40 50

40 30

c 0 20 713 10

2 00 cca) - 1 0

-20 000001 00001

0001 001 Frequency (radm in)

01


(b)

01


140

For the model using numerical approximations the deviation from the true

solution was almost independent of magnitude of pressure drop on each stage For all

values of pressure drop studied reduced order models provided good prediction for

amplitude ratio especially at low frequency However reduced-order models were not

able to predict reasonable phase angles at intermediate frequencies as well as the

constant pressure model As expected the errors in PA prediction were much larger for

the 1x3 model

72 Example Problem 32 Plate Geometry Effects

Very little previous work has addressed the effects of plate geometry on the

performance of reactive distillation columns In this section four cases were utilized in

order to study these effects A thirteen-stage column with the same operating

conditions as described in Table 71 was utilized However the dimension of the plates

were changed to the values shown in Table 721 The problem depicted in Example

problem 3 is assigned as case 32a

Table 721 Plate dimension of the columns utilized in Example Problem 32

case 32a case 32b case 32c case 32d

Column diameter [m] 012 010 018 008

Weir length [m] 009 009 009 002

Weir height [m] 003 003 003 006

Volume holdup [1] 0301 0181 0741 0301

141

Cases 32a 32b and 32c were conducted and compared in order to determine the

results from columns with different diameters which resulted in different volume

holdup on each plate The effects of dimension changes of the plate itself can be

observed from comparisons of the results between case 32a and 32d where the volume

holdup of liquid on each plate was the same

Steady-state and dynamic results for each case were determined by using the

rigorous TDMH model The reduced-order models were also utilized in order to

evaluate the efficiency of this numerical technique on various sizes of column stages

Steady-state results Considering case 32a to 32c different column diameters and

different liquid volumes certainly affected the generation of products by chemical

reaction The more liquid on each plate the closer the reaction approaches equilibrium

The profiles in Figure 728 show that the amount of AcOH reacted in case 32c was

higher than the other two cases The difference can be easily observed in the stripping

module where most of the reaction took place Thus it could be expected that the

overall composition of water and AcOEt in case 32c would be higher than in cases 32a

and 32b A larger change in the mole fraction of AcOEt should be observed in the

rectifying section because AcOEt was the lightest species Most AcOEt produced in the

stripping section was vaporized and moved into the rectifying section while water

which is a heavy product stayed in the bottom part of the column According to the

same reasoning the levels of AcOH and EtOH which are reactants would become

lower in case 32c

Table 722 Mean squared errors for reduced-order steady-state profiles for Example problem 32

Case 32b Case 32c Case 32d

(2x5) (2x4) (1x3) (2x5) (2x4) (1x3) (2x5) (2x4) (1x3)

T 24206E-04 15413E-03 35626E-02 56883E-05 11573E-03 14283E-02 46403E-05 13594E-03 31742E-02

xAccui 41506E-08 10257E-06 20122E-05 29278E-08 91570E-07 12481E-05 36518E-08 10579E-06 18048E-05

XEOH 61717E-07 11827E-06 72673E-05 25819E-08 38742E-07 16468E-05 92104E-07 14047E-06 17848E-05

xwater 62745E-08 12803E-07 20718E-06 73871E-09 14184E-07 41030E-06 34528E-08 14213E-07 41997E-06

xAcoEt 74983E-07 76236E-07 67248E-05 45924E-08 53904E-08 25289E-05 10331E-06 10328E-06 14748E-05

YAcOH 47334E-08 22850E-06 46167E-05 64134E-08 22165E-06 29649E-05 54052E-08 24397E-06 42173E-05

YEt0H 48963E-07 16300E-06 78916E-05 26729E-08 70829E-07 20844E-05 75289E-07 17309E-06 29040E-05



L 86334E-10 27762E-08 48216E-07 12360E-09 21860E-08 26573E-07 17252E-09 27603E-08 36756E-07

V 18824E-09 43611E-08 60301E-07 11625E-09 21731E-08 27373E-07 19103E-09 36782E-08 49566E-07

M 28172E-03 28172E-03 19939E-02 19775E-04 20413E-04 48878E-03 38266E-06 42605E-06 18753E-04

1Acoll 26856E-13 83250E-12 14633E-10 20313E-12 52102E-11 57418E-10 53902E-13 19199E41 28894E40

370 Temperature profiles

370 Case 32b

365 9 case 32a - -o- - case 32b

365 a TDVH

A case 32c -1- case 32d 52 x 2x5

360 360 o 2x4

355

350

345

14

A AAA g 355

) 350

345

O 1x3

Ii 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)

370 Case 32c

370 Case 32d

365 TDVH

365 a TDVH

x 2x5 x 2x5

360 o 2x4 360 o 2x4

17a 355 o 1x3

a co 355 O 1x3

350

345 I I

350

345 i III ill ill 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)

Figure 721 Steady-state temperature profiles (a) - Full-order model for case 32a-32d (b) Full and reduced order for case 32b (c) Full and reduced order for case 32c (d) - Full and reduced order for case 32d

Composition profile of AcOH Case 32b 1

09

08 13- case 32a - - - - case 32b

09 -

08 --a- TDVH

07 A case 32c case 32d 07 - x 2x5

06 06 - o 2x4

05 05 - 0 1x3 04 04 -

03 03 -

02 02 -

01 01

0 0 ml( a 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)

Case 32c Case 32d 1

09 -a- TDMH 09 -e-1DtVH 08 08

07 x 2x5 07

$ 2x5

06 2x4 06 2x4 05 O 1x3 05 o 1x3 04 04

03 03

02 02

01 01

0 MK 0 al a 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)

Figure 722 Steady-state composition profiles of AcOH (a) Full-order model for case 32a-32d (b) Full and reduced order for case 32b (c) Full and reduced order for case 32c (d) Full and reduced order for case 32d

Composition profile of EtOH Case 32b 11

09 09 08 08 07 - 07 06 e 06

-8- TDM-I 05 05 04 A 04 - x 2x5 03 - 03-a- case 32a case 32b 2x4 02 02 -

6 case 32c + case 32d o 1x3 01 01 00- -4-411111Illf


(a) (b)

Case 32c Case 32d 1

09 09 08 08 07 07 06 06 05 05 Or -111r-f-13-----aNH11-119-8E-ee4449CNTIV 04 04 x 2x5 03 -a- TDVH x 2x5

2x4 02 02o 2x4 0 1x301 01 0 1x3

0 0 Iiili11111 03

441 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)

Figure 723 Steady-state composition profiles of EtOH (a) Full-order model for case 32a-32d (b) - Full and reduced order for case 32b (c) Full and reduced order for case 32c (d) Full and reduced order for case 32d

Composition profile of water Case 32b 1 1

09 - 09-El-- case 32a - - - - case 32b -a- TDM-108 - OA 07 - A case 32c + case 32d 07 X 2x5 06 - 06 2x4 05 - 05 0 1x304 - 04 03 - 03 02 - 02 01 - 01

0 ilf111 0 S- 1111111


(a) (b)

Case 32c Case 32d 1 1

09 09 08 -8- TCM-I -9-11)Virl08 07 x 2x5 07- x 2x5 06 062x4 2x4 05 05

O 1x3 0 1x304 04 03 03 02 02 01 01

0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)

Figure 724 Steady-state composition profiles of water (a) Full-order model for case 32a-32d (b) - Full and reduced order for case 32b (c) Full and reduced order for case 32c (d) Full and reduced order for case 32d

Composition profile of AcOEt Case 32b 1 1

09 - 09El- case 32a - - - case 32b -a- TEIVH08 - 08 07 - A case 32c + case 32d 07 x 2x5 06 - 06 o 2x4 05 05

o 1x3 04 E 04 03 03 02 - 7 02 01 - A- 01

-0- -0 01111


(a) (b)


09 - 09-a- TDVH08 08

07- x 2x5 07 06 - 06p 2x4 05 S 05

0 1x304 - 04 03 - 03 02 - 02 01 - 01

0 0 11111111111 1


(c) (d)

Figure 725 Steady-state composition profiles of AcOEt (a) - Full-order model for case 32a-32d (b) - Full and reduced order for case 32b (c) - Full and reduced order for case 32c (d) Full and reduced order for case 32d

035

03

025

02

015

01

005

0 0

035

03

025

Flowrate profile (gm olm in)

Vapor

Liquid -El- case 32a 0 case 32b

a case 32c + case 32d11111111111 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a) Case 32c

Vapor

02 III fit 015 Liquid

01 TDM-I x 2x5

005

0 0

2x4 o 1x311111111111 1 2 3 4 5 6 7 8 9 10 11

Stage number 12

(c)

Case 32b 035

03 Vapor 025 -

02 IF_

015

01

005 -

0 0

035

03

025

02

015

01

005

0 0

Liquid

11111111 1 2 3 4 5 6 7 8

Stage number

(b) Case 32d

1 2 3 4 5 6 7 8 Stage number

(d)

-9- TUC x 2x5

2x4

0 1x3

9 10 11 12

9 10 11 12

Figure 726 Steady-state flowrate profiles (a) Full-order model for case 32a-32d (b) Full and reduced order for case 32b (c) Full and reduced order for case 32c (d) Full and reduced order for case 32d

Molar holdup profiles

40 35 30

El case 32a A case 32c

- -0- - - case 32b

+ case 32d

25

20 15

10 a A A A A A A A A A

5

0 1 2 3 4 5 6 7 Stage number

8 12

(a)

45 40 35 30 25 20

a IDNI-1 x 2x5

o 2x4

o 1x3

Case 32c

15

10

5 0

0 1 2 3 4 5 6 7 Stage number

8 9 10 11 12

(c)

45 Case 32b

40 35 30 25 20 15 10

5

0 0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)

45 Case 32d

40 35 30 25

20 15 10

5 0

0 1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(d)

Figure 727 Liquid molar holdup profiles (a) - Full-order model for case 32a-32d (b) Full and reduced order for case 32b (c) Full and reduced order for case 32c (d) Full and reduced order for case 32d

Rate of consumption of AcOH Case 32b0011 0011

8 case 32a - - - - case 32b0009 - 0009 8 TDMI-1 case 32c + case 32d x 2x5-E 0007 -E 0007

t 0005 - g 0005 2x4

O 1x3E SI 0003 - Cn 0003

0001 - 0001 TT El 19

-0001 -0001


(a) (b) Case 32c Case 32d

0011 0011

0009 B-- MAC 0009

0007 - x 2x5 -2- 0007

E 0005 -0 o

o

2x4

1x3 0005

EDI 0003 - c7) 0003

0001 - 0001 III En CI

-0001 -0001


(c) (d)

Figure 728 Profiles show rate of consumption of AcOH (a) Full-order model for case 32a-32d (b) - Full and reduced order for case 32b (c) - Full and reduced order for case 32c (d) Full and reduced order for case 32d

151

The results from the model in case 32a and 32d showed that the volume holdup

was the major factor for the steady-state results The profiles obtained from both cases

were almost identical for the same volume holdup even though the dimensions of the

plates in both cases were different

The reduced-order models still gave steady-state results which were very close

to the true solution obtained from the full-order model An inspection of Table 722

indicates that applying the reduction technique to the system in case 32c yielded less

error than in other cases In case 32c most of the profiles obtained from the full-order

model did not have steep changes Thus the prediction by the collocation method

would be expected to be good

Step test The full-order results from the same step test as done before are displayed in

Figure 729 However because each case yields different steady-state results it would

be difficult to compare transient responses for each case from the direct results shown

in Figure 729 Therefore deviation variables from initial steady states were again

used

The comparisons of the results from case 32a 32b and 32c indicate that as

expected dynamic responses of the largest column (case 32c) were slower than the

responses of the smaller columns and a longer process time was needed to reach the

new steady state From Figure 729 it can be seen that mole fraction levels of both

reactants in the largest column were lower than in the smallest column while the levels

of products were higher This resulted from higher conversion of reactants into

152

products in the largest column due to a larger quantity of liquid holdup However

according to Figure 7210 to 13 the change in mole fraction of reactants in the largest

column was less than in the smallest column while the change in mole fraction of

products was larger

Because the main components of the feed stream were AcOH and EtOH the

mole fractions of these reactants should increase after the introduction of the step in

feed flowrate if there were no reaction However some of these reactants are consumed

when the reaction occurs which consequently reduces the increase of reactants levels

More reaction occurring causes a smaller increase in reactants than without reaction

Hence for the largest column in which more reaction takes place the change in mole

fraction of reactants was less than in the smallest column On the other hand more

reaction in the largest column caused large increases in product mole fractions

Nevertheless the results obtained show that the mole fraction of water decreased after

the introduction of the step in feed flowrate and the decrease was largest in the largest

column According to the reasoning discussed in Example problem 2 the mole fraction

of water in the bottom product should decrease after the increase of feed flowrate

because water would be purged along with the increased bottom product rate In this

example the steady-state result in previous section shows that the mole fraction of

water in the reboiler in the largest column was higher than in the smallest column

Thus for the largest column more water comes out of the column due to the increased

bottom flowrate which consequently results in a larger change in decreased mole

fraction of water in the reboiler



051

049 c 02 -

047 045 015

043 E 01

041 039 037

- case 32a

case 32c

case 32b

case 32d z 2 005 case 32a

case 32c

case 32b

case 32d 035 0

0 10 20 30 time (hr)

40 50 0 10 20 30 time (hr)

40 50

(a) (b)



037 006 c 035 -0 005

033 1 004 o deg 031 cd 003 _

12= 029 - case 32a case 32b 002

12- 027 case 32c case 32d a

001 case 32a case 32c

case 32b case 32d

025 0 L

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)

Figure 729 Full-order step responses for liquid composition of each species in reboiler of various size of column


001 Case 32b

0005 0

c 0005 0

0 -0005 k b -0005 -001 o -001

-0015 E -0015 -002 case 32a case 32b o -002

-0025 case 32c case 32d o -0025 TDVH 2x5

-003 v -003 2x4 1x3

-0035 -0035 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(a) (b)


0005 0005 o 0 0

-0005 -0005

o -001 -001 E -0015 -0015 o o -002

- 0025 TDVH 2x5

-002 -0025

1DM-I 2x5

s -003 - 2x4 1x3 -003 2x4 1x3

-0035 -0035 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)

Figure 7210 Step responses for composition of AcOH (a) Full-order models for case 32a-32d (b) Full and reduced order for case 32b (c) Full and reduced order for case 32c (d) Full and reduced order for case 32d


0035 Case 32b

003 g 003 TDA11 2x5 0025 I 0025 2x4 1x3

002

0015 ----___--- _____ -- ebe 0020 E 0015

001 case 32a case 32b Tc0 001

0005 case 32c case 32d gt0 0005 13

0 f I I 0 1 1 1 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)

Case 32c Case 32d 0035 0035

g 003 TDM-1 2x5 003 TEM-I 2x5

a 0025 2x4 1x3 0025 2x4 1x3

m 0020 002

E 0015 0015 cG1 001 001 gt0 0005 0005 13

0 I I t 1 0 1 1 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)

Figure 7211 Step responses for composition of EtOH (a) Full-order models for case 32a-32d (b) Full and reduced order for case 32b (c) Full and reduced order for case 32c (d) - Full and reduced order for case 32d


0005 Case 32b

0 0 z 0-0005 - case 32a case 32b 1 -0005 - TIlvti 2x5

o -001 case 32c case 32d

O -001 - 2x4 1x3

0-0015 ro

-002

-0025 -0025

0 10 20 30 time (hr)

40 50 0 10 20 30 time (hr)

40 50

(a) (b)

Case 32c Case 32d 0005 0005

0 0 0

-0005 TDIVI-1 2x5 -0005 111vH 2x5

O -001 2x4 1x3 -001 2x4 1x3

o -0015 -0015

-002 -002

-0025 -0025 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)

Figure 7212 Step responses for composition of water (a) Full-order models for case 32a-32d (b) - Full and reduced order for case 32b (c) Full and reduced order for case 32c (d) Full and reduced order for case 32d


0007 Case 32b

0006 case 32a case 32b g 0006 TDM-I 2x5 0005 case 32c case 32d I 0005 2x4 1x3 0004 0 0004

o 0003 E 0003 _

c 0002 o

laquo- 0002 W

0001 gt0 0001 11

0 r-411egel7 I I I

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)

Case 32c Case 32d 0007 0007

5 0006 0006 TIM-I 2x5 V 0005 0005 2x4 1x3 w 00040 0004

E 0003 C

0003

0002 TI341-1 2x5 0002 es

0001 2x4 1x3 0001

0 i 1 i

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)

Figure 7213 Step responses for composition of AcOEt (a) - Full-order models for case 32a-32d (b) Full and reduced order for case 32b (c) Full and reduced order for case 32c (d) Full and reduced order for case 32d

158

The inspection of case 32a and 32d indicated that there are small differences

between the responses of these two columns However these differences are so small

that they might be caused from tiny differences in volume holdup between these two

columns Further study was done by using a pulse test

Pulse test A pulse in feed flowrate with the same magnitude and duration as in

Example problem 2 was introduced to the column in each case The comparisons of the

responses of the columns with different plate geometry are displayed in the following

figures The same characteristics of dynamic behavior as discussed in the step tests

were also found in this test The column with small plates responded to feed

disturbances more quickly and went back to the initial state faster than the column with

large plates

The Bode plot in Figure 7218 shows that the columns with different volume

holdup have different dynamic characteristics The complex behavior at intermediate

frequencies disappeared in the column with large volume holdup (32c) The Bode plot

also shows that columns in case 32a and 32d which have almost the same volume

holdup have very similar dynamic characteristics The deviations which occurred might

have been caused by small differences in volume holdup between these two columns

Thus it can be concluded that the volume holdup on each plate was a major factor for

dynamic behavior of reactive distillation columns and that the individual dimensions of

each plate or weir are of lesser importance

00002 Pulse responses for AcOH

00002 Case 32b

0 0

-00002 -00002 -- 00004 case 32a m -00004 -

0 TINH -00006 case 32c -00006 - 2x5 - 00008 case 32c r -00008 2x4 -0001 case 32d y -0001 lx3

-00012 -00012 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

00002 Case 32c

00002 Case 32d

0 0

-00002 -00002

-00004 -00004 TEM -00006 -00006 2x5 -00008 -00008 2x4

-0001 -0001 lx3 -00012 -00012

0 10 20 30 40 0 10 20 30 40 50 time (hr) time (hr)

(C) (d)

Figure 7214 Pulse responses for composition of AcOH (a) Full-order models for case 32a-32d (b) - Full and reduced order for case 32b (c) Full and reduced order for case 32c (d) - Full and reduced order for case 32d

00012 Pulse responses for EtOH

00012 Case 32b

0001 - case 32a 0001

00008 case 32b 00008

00006 case 32c 00006

00004 - case 32d 00004

00002 00002

0 -4 0

-00002 -00002 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

Case 32c Case 32d 00012 00012

0001 0001 TUC 00008 00008 2x5 00006 00006 2x4 00004 00004 lx3 00002 00002

0 0

-00002 -00002 0 10 20 30 40 0 10 20 30 40 50

time (hr) time (hr)

(C) (d)

Figure 7215 Pulse responses for composition of EtOH (a) - Full-order models for case 32a-32d (b) Full and reduced order for case 32b (c) Full and reduced order for case 32c (d) Full and reduced order for case 32d


case 32a case 32b 00001 case 32c case 32d

000005

0

-000005

-00001

-000015 0 10 20 30 40

time (hr)

(a)

Case 32c 000015

00001

000005

0

-000005

-00001

-000015 0 10 20 30 40

time (hr)

(C)

000015

00001

000005

Case 32b

TDAH

2x4

2x5

1x3

0 i 1 impoomponn

-000005

-00001

-000015 0 10 20

time (hr) 30 40

(b)

000015 Case 32d

00001 -

000005

TDIVH

2x4

2x5

1x3

0

-000005 -

00001 -

-000015 0 10 20 30

time (hr) 40 50

(d)

Figure 7216 Pulse responses for composition of water (a) Full-order models for case 32a-32d (b) - Full and reduced order for case 32b (c) Full and reduced order for case 32c (d) Full and reduced order for case 32d

Pulse responses for AcOEt] Case 32b 000007 000007 000006 000006case 32a 000005 000005case 32b 000004 000004

case 32c 000003 000003

case 32d 000002 000002 000001 000001

0 0

-000001 -000001 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

000007 Case 32c

000007 Case 32d

000006 TDIVH 000006 000005 2x5 000005 000004 2x4 000004 000003 lx3 000003 000002 000002 000001

000001 0

0 -000001

0 10 20 30 40 -000001

time (hr) 0 10 20 30

time (hr) 40 50

(C) (d)

Figure 7217 Pulse responses for composition of AcOEt (a) - Full-order models for case 32a-32d (b) - Full and reduced order for case 32b (c) Full and reduced order for case 32c (d) - Full and reduced order for case 32d

10

0001

00001 000001

90

-180 000001

case 32a

case 32b

case 32c

case 32d

00001 Frequency (raSiiril in)

case 32a

case 32b

case 32c

case 32d

00001 001 001 Fre0quency (radmin)

(a)

01 1

01

10

0

V ac 1

a)

cc

01

000001 00001

80

60 cn 4140

SI 20

63 0

120 o--40 0-60

1E)-80

-100 000001 00001

FreliEqlency (ragFriin)

case 32b

case 32c

case 32d

01

001 001 Fr0equency (radmin)

(b)

01 1

Figure 7218 (a) Bode diagram for pulse responses of AcOEt from various plate dimension (b) - Residual dynamics resulting from the physical simplification of the model

10 10

1 0

0

01 V

o 001

E

0001

TD 1-i

2x5

2x4

lx3

113

V

CC

00001 000001 00001 0001 001


01


01

90 250

200 2x5

V Ilk 150

ca) 100

2x4

lx3

a) -90 C)

a=-180

TDA1-1

2x5

2x4

lx3

S 50 c a 0 To

-50

m-100

-270 000001 00001 0001 001


-150 000001 00001 0001 001


(a) (b)

Figure 7219 (a) Bode diagram for pulse responses of AcOEt from case 32b (b) Residual dynamics resulting from the numerical simplification of the model

10 10

2x5 1 2x4

1x3

TDVH E4

0001

2x5

2x4

00001 lx3

01

000001 00001 0001 001 Frequency (radmin)


01

90 20

Si0 013 0 m c0 0 -90 c a

-180 000001

TDMI 2x5

2x4

lx3

00001 0001 001 Frequency (radmin)

01 1

s 15 as0 10 0 1n 5 c0 0 o c so -5as

deg -10-10 co =

-13 -15 0 0 -20 CE

-25 000001 00001 0001 001


(a) (b)

Figure 7220 (a) - Bode diagram for pulse responses of AcOEt from case 32c (b) - Residual dynamics resulting from the numerical simplification of the model

10 10

0

0

01

-enV

V 001 TUC E

ao

E

0001

2x5

2x4

lx3

V 0 cc

00001 01 000001 00001 0001 001

Frequency (radmin) 01 1 000001 00001 0001 001


90 80

rn 0

TDV1-1

2x5

2x4 1x3

rn 70

43 60 O 50 of g 40 S 30

o c 20 To 10 13 00

-10

2x5

2x4

1x3

-270 -20 000001 00001 0001 001

Frequency (radm in) 01 000001 00001 0001 001


(a) (b)

Figure 7221 (a) Bode diagram for pulse responses of AcOEt from case 32d (b) Residual dynamics resulting from the numerical simplification of the model

167

8 CONCLUSIONS AND RECOMMENDATIONS

The results from all example problems indicated that the orthogonal collocation

technique was remarkably accurate for the approximation of steady-state results of

reactive distillation column even when the number of equations was reduced by 60

The steady-state results from reduced-order models were closer to the full-order exact

results than were the results obtained from the full-order model with constant molar

holdups (CMH)

The dynamic behavior of a reactive distillation column can be very well

approximated by a reduced-order model when the behavior is not complicated The

errors in dynamic behavior prediction especially for phase angle appeared when

complex dynamic behavior occurred However at higher order approximations the

numerical approximation model yielded better dynamic prediction than the full-order

constant holdup model

Example problem 32 demonstrated that both the steady-state and dynamic

behaviors of a reactive distillation column were highly dependent on liquid volume

holdup The results for different plate dimensions were quite similar unless the volume

holdup on the plate was changed The results from example 1 showed that the molar

holdup on each plate in the column was different even though each plate in the column

had the same plate geometry Thus the reduced-order TDMH model yielded better

approximation in the behavior of a reactive distillation column than did the CMH

model

168

For future work the interpolation algorithm (for L ) used in total material end-

around balance equation should be improved for better dynamic prediction of reduced-

order model Then other aspects in comparisons of physical and numerical

approximations such as the responses from control scheme (open-loop and close-loop

control schemes) should be studied Finally the application of collocation technique

might be considered for a packed reactive distillation column

169

BIBLIOGRAPHY

Alejski K J Szymanowski and M Bogacki The Application of a Minimization Method for Solving Reactive Distillation Problems Computers amp Chemical Engineering 12 833-839 (1988)

Belck L H Continuous Reactions in Distillation Equipment AIChE Journal 1 467-470 (1955)

Bogacki M B K Alejski and J Szymanowski The Fast Method of the Solution of a Reacting Distillation Problem Computers amp Chemical Engineering 13 1081-1085 (1989)

Brenan K E S L Campbell and L R Petzold Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations Elsevier Science Publishing Co Inc New York (1989)

Cameron I T C A Ruiz and R Gani A Generalized Model for Distillation Columns H Numerical and Computational Aspects Computer amp Chemical Engineering 10 199-211 (1986 )

Chang Y A and J D Seader Simulation of Continuous Reactive Distillation by a Homotopy-Continuation Method Computer amp Chemical Engineering 12 1243-1255 (1988)

Cho Y S and B Joseph Reduced-Order Steady-State and Dynamic Models for Separation Process II Application to Nonlinear Multicomponent Systems AIChE Journal 29 270 (1983)

Doherty M F and G Buzad Reactive Distillation by Design Trans IChemE 70 Part A 448-458 (1992)

Doherty M F and G Buzad New Tools for the Design of Kinetically Controlled Reactive Distillation Columns Computer amp Chemical Engineering 18 Supplement S 1-S 13 (1994)

Finlayson B A Nonlinear Analysis in Chemical Engineering McGraw-Hill Book Co New York (1980)

Gani R C A Ruiz and I T Cameron A Generalized Model for Distillation Columns Model Description and Applications Computer amp Chemical Engineering 10 181-198 (1986)

170

Holland C D Fundamentals of Multicomponent Distillation McGraw-Hill Book Co New York (1981)

Holland C D and A I Liapis Computer Methods for Solving Dynamic Separation Problems McGraw-Hill Book Co New York (1983)

Howard G M Unsteady State Behavior of Multicomponent Distillation Columns AIChE Journal 16 1023 (1970)

Izarraraz A G W Bentzen R G Anthony and C D Holland Solve More Distillation Problems Part 9 When Chemical Reaction Occur Hydrocarbon Processing 59 195-203 (1980)

Kinoshita M I Hashimoto and T Takamatsu A New Simulation Procedure for Multicomponent Distillation Column Processing Nonideal Solutions or Reactive Solutions Journal of Chemical Engineering of Japan 16 370-377 (1983)

Komatsu H Application of the Relaxation Method for Solving Reacting Distillation Problems Journal of Chemical Engineering of Japan 10 200-205 (1977)

Komatsu H and C D Holland A New Method of Convergence for Solving Reacting Distillation Problems Journal of Chemical Engineering of Japan 10 292-297 (1977)

Leyes C E and D F Othmer Continuous Esterification of Butanol and Acetic Acid Kinetic and Distillation Considerations Trans AIChE 41 157-196 (1945)

Luyben W L Process Modeling Simulation and Control for Chemical Engineers McGraw-Hill Book Co New York (1973)

Matandos M Use of Orthogonal Collocation in the Dynamic Simulation of Staged Separation Processes MS Thesis Oregon State University Corvallis OR (1991)

Nelson P A Countercurrent Equilibrium Stage Separation with Reaction AIChE Journal 17 1043-1049 (1971)

Reid R C J M Prausnitz and T K Sherwood The Properties of Gases and Liquids McGraw-Hill Book Co New York (1977)

Roat S D J J Downs E F Vogel and J E Doss The Integration of Rigorous Dynamic Modeling and Control System Synthesis for Distillation Columns An Industrial Approach Chemical Process Control-CPC III (1986)

171

Ruiz C A M S Basualdo and N J Scenna Reactive Distillation Dynamic Simulation Trans IChemE 73 Part A 363-378 (1995)

Sawistowski H and PA Pilavakis Performance of Esterification in a Reactive Distillation Column Chemical Engineering Science 43 355-360 (1988)

Seborg D E T F Edgar and D A Mellichamp Process Dynamics and Control John Wiley amp Sons Inc New York (1989)

Smith JM and H C Van Ness Introduction to Chemical Engineering Thermodynamics McGraw-Hill Book Co New York (1987)

Stewart W E K L Levien and M Morari Simulation of Fractionation by Orthogonal Collocation Chemical Engineering Science 40 409-421 (1985)

Suzuki I H Komatsu and M Hirata Formulation and Prediction Quaternary Vapor Liquid Equilibria Accompanied by Esterification Journal of Chemical Engineering of Japan 3 152-157 (1970)

Suzuki I H Yagi H Komatsu and M Hirata Calculation of Multicomponent Distillation Accompaned by Chemical Reaction Journal of Chemical Engineering of Japan 4 26-32 (1971)

Villadsen J and M Michelsen Solution of Differential Equation Models by Polynomial Approximation Prentice-Hall Inc New Jersey (1978)

Walas S M Phase Equilibria in Chemical Engineering Butterworth Publishers (1985)

172

APPENDICES

173

APPENDIX A

Physical Properties Data

Table A1 Physical constants

Species Tc V Z

[K] [cm3gmol]

AcOH 5944 171 02

EtOH 5162 167 0248

Water 6473 56 0229

AcOEt 5232 286 0252

(Reported by Reid et al (1977))

Table A2 Enthalpy data

Enthalpy of vapor at 1 atm is give by

Hideg = Ai + BJT + CiT2 + DjT3 + E j74

Species Aj 13j

AcOH -242129 20142

EtOH -300324 475

Water 0 04077

AcOEt -498159 1031

(Reported by Suzuki et al (1971))

Normal Heat of

Pc boiling point vaporization (TB) at TB

[atm] [K] [calgmole]

571 3911 5660

63 3515 9260

2176 3732 9717

378 3503 7700

(Hideg in calgmole T in K)

Cj Dj EJ

28033x10-2 -01136x10-4 00020x10-6

25030x10-2 -08263x10-5 11975x10-9

36657x10-3 00615x10-4 0

30495x102 -53900x106 0

174

Table A3 Coefficient for the Benedict-Webb-Rubin (BWR) equation of state

P = RTp +[BoRT Ao -(Mp2 plusmn [bRT

3

1-

[cp]-1plusmnyple_p2 T2

+ aap6

AcOH EtOH

Ao (1gmol)2atm 1004538 686619

Bo lgmol 006519 005087

Co (1gmo1)2K2atm 3121503 1605577

ao (1gmo1)3atm 15616 084012

bo (1gmo1)2 002703 001674

Co (1gmo1)3K2atm 8087892 3279836

ao (1gmo1)3 0001601 0000781

yo (1gmo1)2 004365 002704

(Based on data taken from Izarraraz et al (1980))

Water

1175617

008668

2828098

242981

004778

9748118

0003763

007717

AcOEt

311069

001856

1141020

013766

000219

8428061

369E-05

000354

Table A4 Constant for Antoine equation for vapor pressure (Pjdeg)

log = A + C

(P3deg in mmHg T in degC)

Species Adeg Bdeg

AcOH 75596 164405

EtOH 783124 144052

Water 796681 166821

AcOEt 709808 123871


Cdeg

233524

21271

228

217

175

Table A5 Parameters for the Margules equation for activity coefficient (Eqn 3-15)

Acetic acid Ethanol Water Ethly acetate

A -05543 0581778 0688636 -006014

A2 -032436 0209245 0024303 0229575

A3 -010369 -025733 0375534 186575

A4 -070546 -056264 127548 0355191

A5 -201335 -031485 177863 0468416

A6 -225362 0451732 0696279 15111

A7 0837926 -011541 0936722 -005997

A8 052376 0069531 0449357 0067399

A9 0434061 0074053 071779 -315997

A10 -053406 018701 144979 0941858

A -325231 -036999 -211099 -192225

Al2 590329 -008234 0746905 -075573

A13 3354 -040947 112914 103791

A14 0197296 109247 0120436 0365254

A15 -045266 0192416 -164268 -136587

A16 0014715 -017257 0330018 -213818


176

APPENDIX B

Sequence of Computations

Figure B1 and B2 present the basic sequence of computations utilized by the

FORTRAN programs for solving the example problems discussed in this thesis The

program code for each model was written separately Copies of the source codes of

these programs may be obtained by writing to

Dr Keith L Levien Chemical Engineering Department Oregon State University Gleeson Hall 103 Corvallis OR 97331-2702

177

Start

Read inputs from data files

Calculate feed conditions

Set initial liquid composition on each plate

Calculate buble point temperatures vapor compositions at each plate

Calculate liquid and vapor enthalpies at each stage

Calculate differential term for energy balances

Calculate generation term from kinetic correlations

educed-order solu ion

Interpolate liquid and vapor compositions - liquid and vapor enthalpies

for stream entering collocationpoints

Read change in manipulated variable

Calculate liquid and vapor flowrates

Reset ODEs and call integrating package

Has integrator conve ged

as steady state been reached

Continue simulation

Figure B1 Flowsheet diagram demonstrating the sequence of computations utilized for solving a reactive distillation problem using the CMH model

178


educed-order Interpolate for pressure at solution collocation point


Set initial liquid composition and molar holdups on each plate


Calculate buble point temperatures vapor compositions and liquid flowrates

at each plate

Calculate vapor and liquid enthalpies at each stage



Calculate differential term for mass balance for condenser and reboiler


No

Interpolate liquid and vapor compositions

liquid and vapor enthalpies - liquid flowrates


C Stop

Figure B2 - Flowsheet diagram demonstrating the sequence of computations utilized for solving a reactive distillation problem using the TDMH model

179

APPENDIX C

Numerical Results of Model Validation

Tables C1 C2 C3 and C4 present the numerical results of the problem

discussed in Section 41

Table C1 Mole fraction of acetic acid obtained from the problem discussed in Sec41

Stage Experiment TDMH Komatsu Alejski Bogacki model

0 0000 0003 0017 0001 0003 1 0032 0046 0041 0006 0024 2 0159 0205 0258 0172 0174 3 0167 0203 0261 0146 0156 4 0169 0201 0267 0129 014 5 0173 0200 0267 0119 0128 6 0188 0206 0267 0103 0119 7 0216 0278 0314 0118 0145

Table C2 Mole fraction of ethanol obtained from the problem discussed in Sec41


0 0649 0693 0752 0543 0539 1 0741 0734 0755 0633 0617 2 0649 0638 0583 0579 0576 3 0653 0634 0579 0551 0545 4 0677 0631 0573 0529 0521 5 0723 0630 0572 0516 0504 6 0659 0626 0572 0512 0496 7 0386 0573 0518 0482 0471

180

Table C3 Mole fraction of water obtained from the problem discussed in Sec41


0 0067 0090 0115 0043 0048 1 0067 0100 0100 0076 0077 2 0070 0084 0089 0100 0100 3 0070 0088 0089 0121 0121 4 0075 0092 0090 0138 0138 5 0079 0096 0090 0156 0155 6 0077 0102 0087 0191 0179 7 0364 0099 0097 0238 0240

Table C4 Mole fraction of ethyl acetate obtained from the problem discussed in Sec41


0 0284 0214 0116 0413 0411 1 0160 0121 0104 0289 0282 2 0122 0073 0070 0149 0150 3 0110 0076 0070 0183 0179 4 0089 0077 0071 0204 0201 5 0086 0074 0071 0208 0213 6 0076 0066 0071 0194 0206 7 0034 0050 0070 0162 0144

than models using the physical approximation of constant molar holdups in almost

every case The only case in which the reduced-order model failed was when the 40

order-reduction model was used to approximate dynamic responses of a column with a

significant pressure drop across each tray The effects of plate and weir geometries

were also studied The results obtained indicated that the volume holdup on the plate

was the dominant parameter columns with plates of different sizes but the same steady-

state holdup behaved similarly



by

Varong Pavarajarn

A THESIS

submitted to



degree of

Master of Science



APPROVED


C




reader upon request






ACKNOWLEDGEMENTS












TABLE OF CONTENTS

Page

1 INTRODUCTION 1















Page










BIBLIOGRAPHY 169

APPENDICES 172




LIST OF FIGURES

Figure Page



















Figure Page
















Figure Page


















Figure Page


















Figure Page




















Figure Page



LIST OF TABLES

Table Page



















Table Page








Figure Page




Table Page










LIST OF NOTATIONS













f Feed stage

f Fugacity [atm]









11) Weir height [m]






1 Weir length [m]















t Time [min]


















Greek symbols












Subscripts

B Bottom product



F Feed stream

1 Liquid phase


v


S Stripping section

Vapor phase


I INTRODUCTION




acetate













2






















3




















models were studied



4




















5




















6









du = f (uv t)

dt

0 = g(u v t)







solution vector u

7




in this work














8

s=0

s=1

s=2

s=M-1

s=M

S=M+1



m+1

1)-(St)= (S)1(Snt) 1 ltslt M+1 (1-2) n=1



Sk n = 0m (1-3)Wnl(s)

kVn Sn Sk k

m +1 S k n = 1m+1 (1-4)Wnv(S)

k=1 Sn Sk ktn




9



N





(a+Dx(13+1)N-xw(x a 13 N) - (1-6)x(N x)











10





















11























12













13









the liquid phase







14








aA + bB H cC + dD


VAA + VBB + VCC + VDD = 0 (2-1)

where





15

Condenser


dt

dt dM0

nr

LOLo (2-2b) 1=1


dt

Internal Stages

dM + + FX

dt (2-3a) +

dM nc

V F Vi W + (2-3b)dt j=1


dt

Reboiler


dt

nc dMN+1



16

D


17

Hw Xwj



i=N VN+1 HN+1 YN+1j

QR LN hN XNj

B hB xBd i=N+1


18


(2-5)1iA =





by




(2-8)



19






Id(TE (2-10)

n

(2-11)ij 1=1






dMik dhi (2-12)

dt dt

20



as




The result is

nc dx EK

dTi 1=1 dt nc (2-14)

dt dK E x

1=1 dT


_ -nc di ci



-di1=1




21






dt aT dt axm dt


n dK cbcii I M x



n cbcij x-n`






22


23

F


24




i +1 n i+1 dhk


Li (2-20) (h 11+1)

i+1 I n

= Li + Ft B+ (2-21) k =N +l j=1

i = NN-110


holdups

n







25











described in Sec221




qi =lk owi

(2-24a)


26

how Eqn (2-25) vi h

Li

A

1


27







how jY2qt = 36815 (2-24b)t

048F

how is defined by

(

M (2-25)

r7r Ceol4)Pi



and (2-4b) become




28





n dhN+1


VN+1 (2-28)(Hi+ h8)


(2-29) J=1




H1

i = (NN-12)





171 (2-31)(H1 ho


29


=1 dt





(2-24)











30

i=0

D

V1 Hr

hi

1

VF YFI HE

(1-OF xF

i=mi+m2+3



B


31

Condenser


dM0 -dt

- Vo Lo D + j =1



dM dt

dM n

-v + dt 1=1

dM ihi + L h L hdt







(2-33a)

(2-33b)

(2-33c)

(2 -34 a)

(2-34b)

(2-34c)

(2-35a)

(2-35b)

(2-35c)

32





dt J=1



Reboiler


BXB Vi rimi +3 A

dM n morm2+3



BhB QR






33


remain unchanged



















34




35



Chapter Two









311 Enthalpies


n


n

Hi =I yi H(7) (3-1b) i=1

36




H (TO = Ai + B + C + D + E iTi4 (3-2b)


= x (To Pi) (3-3a)

Hi =1 i(Ti Pi) (3-3b) J=1


procedures

Enthalpies of Vapor



37




_RT2( din f (3-5) aT )p





T2 (3-6)







T2 deg v

38


F (Pvk) (3-8)Pvk+1 = P

vk F(pvk)








thesis




= Hsi(Ti) A1(T) (3-10)


39


038 1 T T

where Tr = (3-11)A(7`)=7 A 1Tr




such as

Ki(T)=Oi + AT+ of T2 -F ei T3 (3-12)






j0

(3-13)



Appendix A

40

Bcit















F(T)=[Ixi jE1Ki(TP)]-1= 0 (3-16) i=1

41


F(Tk) (3-17)Tk+1 = Tk PAK)











Z (1 K (TF PF ))F(1)= L o (3-19)

=1 + ty(K (TF PF ) 1)

42





zi





=ExiJP(Ti) (3-21)





where r = T (3-22)T

43







Simplified model

Liquid enthalpy



dh dh = x (3-23)

dT

dT


(3-25)

44




dki +28T + 3E 72 (3-26)

dT dT




apo dpij (3-27)


dT dT 7 j(i_Trf

n axik 1i (3-29)

aXij k=1 j

45

Rigorous model

Liquid enthalpy







(3-30)

Thus



0

B + T +3D T2 +4E T3 (3-32)


46



T3 YPv


dA 038 A (3-34)

dT (T T)






ln(10) kJ (3-35) aT (T + C

9K1 Po1I (3-36)

dx dx





47



(-rA) = [k(7)][ fn( CA CB )1 (3-23)





M j as follows


= [k(T)C = k(T)MiX (3-24)



48



(3-26)







x=s-1 N=M-1

(N n)(n +a+1)(n+a+ 3+1)An (3-27)

(2n + a + 13 + 1)2

n(n+ I3)(N + n+ a + 3 +1) B (3-28)(2n + a + 11)2

where

(a)k = 0 k = 0

(a)k = (a)(a+1)(a+k-1) kgt 0

49


Q0(xa P N) =1 (3-29)

(a+ 0+2)xQi(xa P N) 1 (3-30)Ma +1)











requirements



50


set of equations



required accuracy









51







of ethyl acetate

A + B H C + D













52


Design Variables






AcOH zA 02559

Et0H zs 06159

Water zc 00743

- AcOEt zD 00539




Weir length [m] 006











53

N+1

(Ai )2







xitcoH 11893E-03 66924E-03 28242E-03 16359E-03

xEtolf 61785E-03 98927E-03 16722E-02 18820E-02

xwater 92009E-03 94784E-03 53772E-03 49359E-03

XAcOEt 13209E-03 47090E-03 12271E-02 11779E-02









results



0 1 2 3 4 5

Stage number


0 1 2 3 4 5 6 7

Stage number



0 0 1 2 3 4 5 6 7

Stage number



0 0 1 2 3 4 5 6 7

Stage number


55























Topic of studies

Physical

approximation

Numerical

approximation

Number of stages

Type of reaction

Thermodynamic

model

Pressure in the

column

Example 1



model assuming



reduced-order TDMH

model

8

irreversible

( 2A ---gt R + S )

simple

uniform (1 atm)

Example 2


order model in a

column with many

stages

reduced-order TDMH

model

29

rigorous

uniform (1 atm)

Example 30


order model in a

column with fewer

stages

-

reduced-order TDMH

model

11

Example 31


order model in a



assuming uniform

pressure

full-order TDMH

model assuming that


is uniform

reduced-order TDMH

model

11

reversible


rigorous rigorous


column

Example 32


on steady-state and

dynamic behaviors

full-order TDMH

model using various

plate geometries

-

11

rigorous

uniform (1 atm)

57


be observed

58

5 EXAMPLE PROBLEM 1






2A gt R + S


(-17A) = kACA

where






A 11000 + 30T 4000 + 30T 001Ts 10699 275 02

R 20000 + 20T 15000 + 20T 002T 11651 090 0229

S 25300 + 10T 25000 + 10T 003T 9418 459 0252

T is in degF

59


Design Variables






A 08

R 01

S 01















60







2x2 lx1


11835 20000

0 = condenser 28165 40000



61835 70000


9 = reboiler 90000






solutions

61

60

55

50

45

40

35

30 0

60

55 C Of 41) 50

I a 45 m ei n 40 I i 35

30 0

60

55 ii Oi a) 50 73

12a 45 co

isoo 40 i

35

30 0


1 2 3 4 5 6

Stage number

(a)


(b)

i I i i i 1


(c)

B TDMH - - -0- - CM H

7 8

B TDMH gt 2x2

O 1x1

7 8

--B CM H 2x2 o 1x1

I

7 8

9

9

9


62


09 -08 07 --e-- TDMH 06 -0- CMH 05 04 03 02 01

0 Ulf

0 1 2 3 4 5 6 7 8 9

Stage number

(a)

1

09 08 07 06 05 04 03 02 01

0 0 1 2 3 4 5 6 7 8 9

Stage number

(b)

1

09 08 8 CM H 07 2x2 06 - 0 1x1 05 04 03 02 01


0 1 2 3 4 5 6 7 8 9

Stage number

(c)


63

1

09 -08-07 06 05 04 -03-02 -01

0 0

1

09 08 07 -06 -05 04 03 02 01 -

0 0

1

09 08 07 06 05 04 03 02 01

0 0


1I I I I I

1 2 3 4 5 6

Stage number

(a)

1 2 3 4 5 6

Stage number

(b)

t 1 I 1

1 2 3 4 5 6

Stage number

(c)

$ TDMH CMH

1 1

7 8 9

--e TDM H o 2x2

0 1x1

7 8 9

9-- CM H 2x2

0 1x1

7 8 9


64


09 08 07 06 05 04 03 02 01

0 0

I

1

i

2 3

I

4 I

5 6

p TDMH

CMH

7 8 9

Stage number

(a)

1

09 08 07 06 05 04 03 02 01

0 0

I

1

I

2 3 4 5 6

e TDMH 2x2

O 1x1

7 8 9

Stage number

(b)

1

09 08 07 06 05 04-03 02 01

0 0

I

1 2 3 4 5 6

--eCMH 2x2

O 1x1

7 8 9

Stage number

(c)


65


700

600

500

400

300

$ TDMH CMH

200

100

0 0 1 2 3 4 5


(a)

800

700

600 Vapor

500

400

300

200

Liquid

9 TDM H 2x2

O 1x1

100

0


6 7 8 9

(b)

800

700

600 Vapor

500

400

300

200

Liquid 8CMH

2x2

O 1x1

100

0 0

F

1

f

2 I

3 I I

4 5 Stage number

i

6 I

7 i

8 9

(c)


66





TDMH CMH

(2x2) (1x1) Full (3x3) (2x2) (1x1)

T (degF)2 75654E-05 32486E-02 64722E-02 59785E-05 18506E-02

XA 18871E-07 28772E-05 97558E-05 20379E-07 29484E-05

XR 37528E-07 18061E-04 90993E-05 45029E-07 90603E-05

xs 90549E-08 11304E-04 22755E-06 99641E-08 44224E-05

L (lbmolmin)2 16683 3641945 317355 23006 2405854

V (lbmolmin)2 16822 3058993 317355 34804 2278430









67























68






model










69


003

0025

002 0015

001

0005

TDMH

CMH

0 0 10 20 30

time (min)

40 50

(a)

0035

003

0025

002

0015

001

0005

TDMH

2x2 1x1

0 0 10 20 30

time (min)

40 50

(b)

0035

003

0025

002-0015

001

0005

0 0 10 20 30 40

CMH 2x2 1x1

50

time (min)

(C)


70


-001

-002

TDMH

CMH

-003

-004 _ _ _

-005

-006 0 10 20 30

time (min)

40 50

(a)

I I I I

-001

-002

-003

TDMH

2x2 1x1

-004

-005

-006 0 10 20 30

time (min)

40 50

(b)

-001

-002

CMH

2x2 1x1

-003

-004

-005

-006 0 10 20 30

time (min)

40 50

(c)


71


002 _-____

0015

001

0005 TDMH

CMH

0 10 20 30

time (min)

40 50

(a)

0025

002

0015

001

0005

TDMH

2x2 lx1

0 10 20 30

time (min)

40 50

(b)

0025

002

0015

001

0005

CMH

2x2 1x1

0 10 20 30

time (min)

40 50

(c)


72




xA initial 00858 00859 00829 01041 01042 01009

final 01160 01160 01138 01248 01248 01212

XR initial 08237 08237 08257 08040 08040 08077

final 07706 07706 07705 07614 07614 07647

xs initial 00905 00905 00914 00919 00918 00915

final 01135 01134 01158 01138 01138 01141


Model Relative time

TDMH Full (3x3) 1

2x2 08972

lx1 06576


2x2 06150

lx1 04706






73



















behavior

74


0 1 2 3 4 5 6 7 8 9

stage number













75


001

0008

0006

0004

0002

0 0 10 20 30 40 50 60

time (m in)

(a)

0012

001- MAC 2x2

0008 1x1

0006

0004

0002

0 0 10 20 30 40 50 60

time (min)

(b)

0012

001

0008

0006

0004

0002

0 0 10 20 30 40 50 60

time (m in)

(C)


76


-0002 -0004 -0006 -0008 -001

-0012 -0014 -0016 -0018 -002

0 10 20 30 40 50 60

time (m in)

(a)

0 -0002 -0004 -0006 -0008

-001 -0012 -0014 -0016 -0018

-002 0 10 20 30 40 50 60

time (min)

(b)

0 -0002 -0004 -0006 -0008

-001 -0012 -0014 -0016 -0018

-002 0 10 20 30 40 50 60

time (m in)

(C)


77


0007 0006 TUC 0005 CM-I 0004

0003

0002

0001

0 0 10 20 30 40 50 60

time (min)

(a)

0008

0007 0006

0005 0004

0003 0002

0001

0 0 10 20 30 40 50 60

time (min)

(b)

0008

0007 0006

0005 0004

0003 0002

0001

0 0 10 20 30 40 50 60

time (m in)

(c)


78



fractions




















001 10

0

v 0001 0 E

TDMH

CMH

00001 000001 00001 0001 001


01

000001 00001 0001 001


20

10

-90 TDMH

CMH

-180 000001 00001 0001 001 01 1

Frequency ( radmin)

0

-10

CMH

000001 00001

(a)


0001 001

Frequency (radmin)

01

(b)


10

2x2 1x1

1

01

00001 0001 001 01 000001 00001 0001 001 01


90 10

2x2 1x1

0

-90 TDMH

2x2 1x1

-180 -10 000001 00001 0001 001 01 000001 00001 0001 001 01 1


(a) (b)


001 10

CMH

2x2

1x1

00001 01

000001 00001 0001 001 01 1 000001 00001 0001 001 01


10

0

-90 CMH

2x2 1x1

-180 -10 000001 00001 0001 001 01 1 000001 00001 0001 001 01 1


(a) (b)


82



















83

6 EXAMPLE PROBLEM 2







Design Variables







AcOH zA 04962

EtOH zs 04808

water zc 00229

AcOEt zD 0








84












8x16 7x14 6x12 4x9 3x6


10003 10036 10209 12230 15649

0 = condenser 20129 20873 22952 35293 50000

10 = vapor feed stage 31068 34290 40295 64707 84351

43453 50000 59705 87770 100000

56547 65710 77048 100000

68932 79127 89791

79871 89964 100000

89997 100000

100000

85


8x16 7x14 6x12 4x9 3x6


120000 120000 120005 120210 122214


30 = reboiler 140008 140282 142129 152490 183980

150112 151682 157096 177252 226020

160676 165036 174991 205000 263291

172205 180226 194781 232748 287786

184815 196607 215219 257510 300000

198183 213393 235009 276750

211817 229774 252904 289790

225185 244964 267871 300000

237795 258318 279742

249324 269718 289995

259888 279984 300000

269992 290000

280000 300000

290000

300000







86




8x16 7x14 6x12 4x9 3x6

T (K)2 34681E-06 61907E-06 99419E-06 78225E-05 77447E-03

XAcOH 40090E-11 25666E-10 10937E-09 52778E-08 79956E-06

xEioll 34920E-09 56707E-09 89310E-09 47621E-08 40108E-06

Xwater 18735E-09 37718E-09 63574E-09 26774E-08 86463E-07

XAcOEt 86031E-09 13058E-08 16382E-08 53505E-08 85873E-07

YAcoH 29980E-11 14345E-10 58830E-10 11738E-07 18645E-05

YEt0H 67593E-09 96737E-09 12643E-08 76121E-08 80113E-06

Ywater 24000E-09 47672E-09 80790E-09 45331E-08 19307E-06

YAcOEt 15738E-08 22710E-08 27523E-08 82866E-08 16307E-06

L (gmolmin)2 14936E-10 24385E-10 60968E-10 25848E-09 13842E-07

V (gmolmin)2 43025E-09 40383E-09 60686E-09 70445E-09 14962E-07

M (gmol)2 42749E-07 31854E-06 25227E-05 61481E-04 21716E-03




(gmolmin)

Full (9x18) 0014071

8x16 0014071

7x14 0014069

6x12 0014067

4x9 0014063

3x6 0014038



0 3 6 9 12 15 18 21 24 27 30

Stage number



0 3 6 9 12 15 18 21 24 27 30

Stage number

1

09 c 08 ot 07 E 06 e 05 oE 04 a 03 3 02

01 0

0

1

09 08 07 06 05 04 03 02 01

0 0


- full A 6x12

o 4x9 x 3x6

iiiii isii 1 3 6 9 12 15 18 21 24 27 30

Stage number


3 6 9 12 15 18 21 24 27 30

Stage number




o) 365

E 25

20

a)

L

360

355 -

E o E

15

10

sect 350I-

0 E

5

0

345 5 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(a) (b)



03

025

02

vapor 19 17 -15 -13 -

0 4x9

p

x

6x12

3x6

015

01

005

0

liquid

4-1 I I I

full

o 4x9

I it N 1 4 I

p

x 6x12

3x6


s1 1 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(c) (d)


89









25

AcOH

EtOH

-

- - water_

1 05 _ - -- AcOEt

0 1

345 350 355 360 365 370

Temperature (K)






90








reduced models







in Figure 64



column

91



Full (9x18) 1

8x16 09715

7x14 08797

6x12 07190

4x9 05733

3x6 04794








stream






048

2 046

to - 044

E 042V 04

TEM 7x14 4x9

8x16 6x12 3x6

018

0175

017

0165

016

0155

IDVH 7x14 4x9

8x16 6x12 3x6

038 0 10 20 30 40 50 60 70 80

015 0 10 20 30 40 50 60 70 80

time (hr) time (hr)



04

038

036

0 034 3 7 032

TDM-I 7x14 4x9

8x16 6x12 3x6

g 0033 ra co 1- 0031

Edeg 0029

yor 0027

TDMI-1

7x14 4x9

8x16 6x12 3x6

03 0 10 20 30 40 50 60 70 80

0025 0 10 20 30 40 50 60 70 80

time (hr) time (hr)



09 - full p 6x12 08 07 o 4x9 x 3x6 06 05 04 03 02 01


Stage number


09 08 07 06 05

6x1204 - full p03 02 o 4x9 x 3x6 01

0 i I I I I I I I

0 3 6 9 12 15 18 21 24 27 30

Stage number


09 -08

full p 6x12

07 o 4x9 x 3x6 06 05 04 03 02 -01

0 T 0 3 6 9 12 15 18 21 24 27 30

Stage number


09 08 full A 6x12 07 06 0 4x9 x 3x6

05 04 03 02 01

0 I I I

0 3 6 9 12 15 18 21 24 27 30

Stage number


46

370

365

360

355

- full

Temperature profile

p 6x12

o 4x9 x 3x6

E

E 5 E


25 -20 -15-10 -

- full A 6x12

o 4x9 x 3x6

sect 350

345

-6 E cr)


5 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(a) (b)



03 19

025

02

vapor 17 15 13

015

01

005

0 1-

liquid

I 4 4 I

full o 4x9

I i l I III I

A

x 6x12

3x6

I I

11

9-7-5-3

0 3 6 9 12 15 18 Stage number

21 24 27 30 0 3 6 9 12 15 18 Stage number

21 24 27 30

(c) (d)


95
















68




00004

00002 0

-00002 -00004 -00006 -00008 -0001

-00012 -00014

00012

0001

00008

00006

00004

00002

0

-00002

-00004


time (hr)


time (hr)

000015

00001

000005

0

-000005

-00001

-000015

-00002

000006

000005

000004

000003

000002

0

000001 -0

-000001 0


10 20 30 40 50

time (hr)


10 20 30 40 50

time (hr)


10 10

1

01

13 001 1

c E 0001 TDIVI-1 8x16 8x16 7x14

00001 7x14 4x9

6x12 3x6

6x12 3x6

4x9

000001 01



01

90 60 IDN1-1 8x16 50

407x 14 6x12 30

4x9 3x6 T 20 20 5 10

0 2 -10 0

-20 8x16 7x14o -30 6x12 4x9-40 3x6cc -50

-180 -60 000001 00001 0001 001 01 000001 00001 0001 001 01 1


(a) (b)


98












for simpler columns

99

7 EXAMPLE PROBLEM 3










problem




column was studied








100


Design Variables







AcOH za 04962

EtOH zB 04808

water zc 00229

AcOEt zD 0




Weir length [m] 009

Weir height [m] 003








101


each model






98597 109356 120000 109913 120000 120000










102






column





(2x5) (2x4) (1x3)

T (K)2 60609E-05 13436E-03 29741E-02

XAeOH 35046E-08 10320E-06 17373E-05

XEtOH 73801E-07 12009E-06 16073E-05

xwater 23561E-08 13345E-07 46047E-06

Xite0Et 78982E-07 78798E-07 17033E-05

Y AcOH 53545E-08 23869E-06 40598E-05

Y Et0H 60827E-07 15434E-06 26427E-05

Ywater 25369E-08 30654E-07 59017E-06

YAcOEt 64649E-07 64980E-07 16455E-05

L (gmolmin)2 16799E-09 26341E-08 35570E-07

V (gmolmin)2 18206E-09 33777E-08 48041E-07

M (gmol)2 11613E-03 11617E-03 10803E-02




10 EMI Cl 0111111 1111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12



09 09 -a- MAC08 08 07 07 x 2x5 06 06 4 2x4 05 -s- TEAM 05

0 1x304 04x 2x503 03

o 2x402 02 01 O 1x3 01

0 011111111 1411 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12




TDM-I aTow 30 Y 365 x 2x5 25 x 2x5

360 2x4 20 2x4 E 070o 1x3 15 0 1x3

11 355 E10 IP EX

a 0 5g 350

1- rn 0 i

345 i i -51111 E

1



035 21

03 19 6 TDMH 17VaporE 025 x 2x5

8 15-2x402 13E


01 2x4 7-=005- 5o 1x3

0 3 il 111111 1 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)


105




2x5 0011345

2x4 0011343

lx3 0011364














106



Full (3x6) 1

2x5 09313

2x4 08556

1x3 06608


















0485 - 0145C TDVH0048 0475 1 014 2x5

IMF 2x4 047 0 0135

2x5 o lx3E0465 0132x4 733 lx3 5r 0125

046

0455 I I I045 012

0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)


0375 00295 037 -

00290365 -036 00285 TDVHTDVH

0355 2x52x5 0028 035 2x42x4

002750345 1x3lx3 034 0027 4 I I I

0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)


0

108






respectively














0 -00001 -00002 -00003 -- 00004 -00005 2x5 -00006 -00007

2x4

-00008 lx3 -00009

0 10 20 30 40 50

time (hr)


0 -00001

0 10 20 30 40 50

time (hr)


000008 000006 TDMr1 2x5

000004 2x4 1x3 000002

0 -000002 -000004 -000006 -000008

-00001 0 10 20 30 40 50

time (hr)


000003

0000025

000002

0000015 000001

0000005

0

-0000005 0 10 20 30 40 50

time (hr)


10 10

1

01

1

001 full

2x5

0001 2x4

lx3 00001 01

000001 00001 0001 001 01 000001 00001 0001 001 01 1


90

0

full -90 2x5

2x4 1x3

-180 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


10 10

2x5 1 2x4

0 1x3 0 s 01 0is c= 001 full Tx E4 2x5

0001 2x4

lx3 00001 01


90 10

clii0 ii 13

w 0 0to



c- 1 0 2x5


-360 -20 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


112






operations





column in each case

pressure atm) 2

18

16

14

12

1

08

06

0--AP=005 X--AP=OA

AP= 015

04

02

0 I I I l iti 0 1 2 3 4 5 6 7 8 9 10 11 12

stage number




113







Table 712



T (K)2 250357 1175582 4137036

xAcoH 61711E-05 21799E-04 45062E-04

xEroll 86611E-04 23323E-03 33668E-03

Xwater 10578E-04 35052E-04 71882E-04

XAcOEt 10156E-03 25721E-03 34075E-03

YAcOH 36414E-05 12001E-04 22977E-04

YEt0H 14054E-03 41997E-03 76426E-03

Ywater 10252E-04 32920E-04 67493E-04

YAcoEt 15273E-03 43664E-03 77664E-03

L (gmolmin) 2 33027E-06 19272E-05 80700E-05

V (gmolmin)2 32945E-06 19270E-05 80678E-05

M (gmol) 2 77791E-03 17231E-02 16933E-02

11AcOH (gmolmin)2 23729E-07 81195E-07 15842E-06



(2x5) (2x4) (1x3) (2x5) (2x4) (1x3) (2x5) (2x4) (1x3)

T 1035E-04 1426E-03 2166E-02 6500E-04 1982E-03 7342E-02 1339E-01 1352E-01 4376E+00

xAcoH 3449E-08 9791E-07 1516E-05 3483E-08 9113E-07 1324E-05 4424E-08 8416E-07 1161E-05

XEt0H 4048E-07 7949E-07 1783E-05 3143E-07 6492E-07 1769E-05 4013E-06 4320E-06 2098E-04

xwate 1055E-08 1436E-07 5492E-06 9188E-09 1514E-07 5428E-06 2914E-07 4453E-07 1212E-05

XAr0Et 3785E-07 3776E-07 2799E-05 2746E-07 2758E-07 2852E-05 5805E-06 5805E-06 2511E-04

YACOH 5878E-08 2296E-06 3546E-05 6219E-08 2153E-06 3092E-05 6902E-08 1982E-06 2702E-05

Y DOH 3397E-07 1107E-06 2434E-05 2647E-07 9055E-07 2223E-05 3398E-06 3928E-06 1891E-04



L 1259E-09 2441E-08 2874E-07 1710E-09 2253E-08 2670E-07 8557E-08 1044E-07 4197E-06

V 1283E-09 2963E-08 3925E-07 1497E-09 2656E-08 3329E-07 1008E-07 1231E-07 5191E-06

M 1064E-03 1064E-03 1077E-02 1052E-03 1053E-03 1086E-02 1306E-03 1308E-03 1878E-02

17awn 9882E-13 3055E-11 3667E-10 1565E-12 4471E-11 4994E-10 1379E-11 7137E-11 1149E-09


320 -4 310 300 -- 290 CI

CY

I t f

A

1 flAP=010

0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


1x3300 290 tIllli11111

2x4

0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(c)

390 380 370 360 350 340 330 320 310 300 290

0 f III-1111111 1 2 3 4 5 6 7 8 9 10 11

Stage number


9-- TDMH x 2x5 o 2x4 o 1x3

12

(b)

390 380 370 360 350 340 330 320 310 300 290

0 1111f-1-11111

2 3 4 5 6 7 8 9 10 11

Stage number


9 TDMH 2x5

o 2x4 o 1x3

1 12

(d)


- --

09 -08 07 -06 -05 -04 03 -02 -01

0 II 0

1

09 -08 07 06 05 -04 -03 02 01 -

0 0


--B--AP=0 - -AP= 005

A AP= 010 ---G---AP= 015

1111111 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


-B-TDMH 2x5

o 2x4 o 1x3

i BM El i I I I

1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(c)

1

09 -08 -07 -06 05 -04 -03 -02 01 -

0 0

1

09 08 07 06 05 04 03 02 01

0 0


-13-TDMH x 2x5

2x4

O 1x3

1111111 OE U 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)


1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(d)



AP = 00503 02 fi AP - 010 01 - - -G - -AP= 015

0 11111111111 O 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


09 08 07 06 05 -8- TDM H04 x 2x503

O 2x4 02 01 0 1x3

0 O 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(c)



09 -08 -07 -06 -05 - -9- TDM H04 - x 2x503 -

O 2x402 -01-

0 loi1x3i i I f iiii0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)


09 -08 07 06 05 -04 -9- TDMH 03 - x 2x5 02 - p 2x4 01 - 0 1x3

0 0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(d)



09 -09 - --B--AP=0 -e-TDMH0808 07 07 - x 2x5

A AP=01006 06 2x4 05 05 O 1x3 04 - 04 -03 - 03 02 - 02 -01 01 -

0 0 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)


0909 -08 - TDMH 08

07 x 2x5 07

06 o 2x4 06 0505 o 1x3

04 - 04

03 - 03 02 - 02 01 01111111110 0


(c) (d)



09 09--B--AP=0 -B- TDMH08 - 08 -07 - 07 2x5

A AP= 01006- 06 - 2x4 ---0---AP= 01505 05 O 1x3

04 04 -03 - 03 -02 02 01 01lilt0 0I


(a) (b)


09 - 09 08 - -9- TDMH 08 07 x 2x5 07 06 - 06o 2x4

0505 o 1x3 04 - 04 03 - 03 02 02 01 - 01

0 0Iflit 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



035

2r

03

025

02

015

01

005

-13-- AP = 0 AP = 005

A AP= 010 --0---4P= 015

03

025

02

015

01

005

0

03

025

02

015

01

005

Vapor


2x4 o 1x3111114-11111

03

025 B

02 g0

015 8 0

01

005

0 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(a) (b)



035

03

025

02

015

01 -

005

Vapor

c CI 113 Liquid

NION101 -B-TDMH

X 2x5 2x4

II 1x3 t I 0

03

025

02

015

01

005

03 -

025 -

02

015

01

005

O NID Liquid x 2x5

O 2x4 O 1x3

I I 114111+1-f

Vapor

- 8- TDMH

03

025

02

015

01

005

0 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(c) (d)



21


9 9 7 7 5

3 3111111111 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)


19 - 19 8 TDMH-8 TCM-I 17

g 15 x 2x5 -6 17 rA 15

2x5

a 13 o 2x4 cl 13 o 2x4

31- 11 - 0 1x3 12 11 1x3 c

9 c

9 co 03 75 E

7 5 111--0K 3 1 i 111111111

7 5 3 i i 111111111


(c) (d)




E0005o 0005 o 1x3E E 9 0003 0) 0003

0001 0001 III

-0001 -0001 i



0011 0011

e TDVH0009 0009 -x 2x5

0007 s 0007 o 2x4

t 0005 t 0005o 1x3 E E a) 0003 0)0003

0001

-0001 El OK 0 4 I I I

0001

-0001 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(c) (d)


123







(MSE=4376)
















124




3

25

2 MOH

15 EtOH

1 - - water

05 Ac0Et

0

290 310 330 350 370

Temperature (K)











125









results










case



048 047

02 - AP - 0 AP= 010

AP - 005 AP- 015

046 018 -045 044

016

043 014 042 AP = 0 AP= 005 012 -041 AP = 010 AP= 015 04 01

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)


036 006 035 005 --034 004 -033


03 001 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)



0005 0

-0005 -001

-0015 -002 APdeg AP=005

-0025 AP=010 AP=015

-003 0 10 20 30 40 50

time (hr)

(a)


0005 0

-0005 -001

-0015 -002 TDVH 2x5

-0025 2x4 1x3

-003 0 10 20 30 40 50

time (hr)

(c)


0005 0

-0005 -001

-0015 -002 TDAH 2x5

-0025 2x4 1x3

-003 0 10 20 30 40 50

time (hr)

(b)


0005 0

-0005 -001

-0015 TEM 2x5-002

-0025 2x4

-003 0 10 20 30 40

time (hr)

(d)


50



003 003

0025 0025

002 002

0015 0015

001 AP-0 AP- 005

001 IDA4-1 2x5

0005 itP =010 AP-015 0005 1 2x4 1x3

0 i I I i 0 i 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)



003 003

0025 0025

002 002

0015 0015

001 -MINH 2x5 001

0005 2x4 1x3 0005

0 1 1 1 0

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)




0 0

-0005 APdeg AP= 005 -0005 TDVH 2x5

-001 AP- 010 AP- 015 -001 2x4 1x3

-0015 -0015

-002 -002

-0025 -0025

-003 -003 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(a) (b)



0 0

-0005 TDM- 2x5 -0005 MAC 2x5

-001 2x4 1x3 -001 2x4

-0015 -0015

-002 -002

-0025 -0025

-003 -003 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)




00035 - 00035 -0003 - 0003

00025 00025 -0002

00015 0001 TCMI 2x5

00005 2x4 1x3

0 50 0 10 20 30 40 50

time (hr)

(a) (b)



00035 00035 0003 0003

00025 00025 0002 0002

00015 00015 0001 0001

00005 00005 0 0

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)


131






















0 -00001 -00002 -00003 A- AP = 0 -0 0004 AP= 005 -00005 AP= 010 -00006 -00007 AP=015 -00008

0 500 1000 1500 2000 2500 3000 time (min)

(a)


0 -00001 -00002 -00003 -00004 -00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)


0 -00001 --00002 T -00003 -00004 --00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)

(b)


0 -00001 1--00002 + -00003 4 -00004 -t--00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)



0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)

(a)


0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)


2x400003 J-lx300002 4-

00001 0

-00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)

(b)


0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)



000005

0

-000005 AP = 0 AP = 005-00001 AP= 010

-000015 AP= 015

-00002 0 500 1000 1500 2000 2500 3000

time (min)

(a)


000005

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)


000005

0

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)

(b)


000005

0

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)



500 1000 1500 2000 2500 3000 time (min)

(a)


0 -000001

0 500 1000 1500 2000 2500 3000 time (min)



0

-000001 0 500 1000 1500 2000 2500 3000

time (min)

(b)


000005 000004

000003 000002 -r 000001 VI

0

-000001 0 500 1000 1500 2000 2500 3000

time (min)


10

0001

00001 000001

90

-90

-180 000001

OP -0 4P =005 AP- 010 AP= 015

00001 0001 001


4P =0 AP= 005 AP- 010 AP= 015

00001 0001 001

Frequency (radmin)

(a)

01

10

0

0V

ac 1

0 O 0 0

CC

01

000001

20

10

O 0 0 S -10 0 c a -20 0

w -30 flo cc

-40 000001

AP- 005 AP= 010 AP= 015

00001 0001 001


AP= 005 AP= 010 AP= 015

00001 0001 001

Frequency (radm in)

(b)

01


10 10

01 =0I0

GI

1 01 1774) a= 3 iTDMI-10010 E 2x5 rozQ 0

0001 2x4 el a)

lx3 cc

00001 01

000001 00001 0001 001 01 000001 00001 0001 001 01 1


90 50

of 40 a)a

---tu 30 co cco 20 a)


-180 -20 000001 00001 0001 001 01 1 000001 00001 0001 001 01


(a) (b)


10 10

1

0

01 a)

a 001 E 2x5

2x4 0001

lx3

00001 01



01

90 50

S40 2x5

30 rn

2x4

1x3 20

210 0 -g 0

X10 cc

-180 -20 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


10

1

0

01 0

ma a fi 001

0001

00001 000001

90

rn

a)

a) -90

a

-180 000001

TDM-I

2x5

2x4

lx3


TDIVH

2x5

2x4

1x3


(a)

10

1

01 01

000001 00001

01

90 80

O 70 60

40 50

40 30

c 0 20 713 10

2 00 cca) - 1 0

-20 000001 00001


01


(b)

01


140







the 1x3 model











Weir length [m] 009 009 009 002

Weir height [m] 003 003 003 006

Volume holdup [1] 0301 0181 0741 0301

141





















lower in case 32c



(2x5) (2x4) (1x3) (2x5) (2x4) (1x3) (2x5) (2x4) (1x3)

T 24206E-04 15413E-03 35626E-02 56883E-05 11573E-03 14283E-02 46403E-05 13594E-03 31742E-02


XEOH 61717E-07 11827E-06 72673E-05 25819E-08 38742E-07 16468E-05 92104E-07 14047E-06 17848E-05



YAcOH 47334E-08 22850E-06 46167E-05 64134E-08 22165E-06 29649E-05 54052E-08 24397E-06 42173E-05

YEt0H 48963E-07 16300E-06 78916E-05 26729E-08 70829E-07 20844E-05 75289E-07 17309E-06 29040E-05



L 86334E-10 27762E-08 48216E-07 12360E-09 21860E-08 26573E-07 17252E-09 27603E-08 36756E-07

V 18824E-09 43611E-08 60301E-07 11625E-09 21731E-08 27373E-07 19103E-09 36782E-08 49566E-07

M 28172E-03 28172E-03 19939E-02 19775E-04 20413E-04 48878E-03 38266E-06 42605E-06 18753E-04

1Acoll 26856E-13 83250E-12 14633E-10 20313E-12 52102E-11 57418E-10 53902E-13 19199E41 28894E40


370 Case 32b

365 9 case 32a - -o- - case 32b

365 a TDVH


360 360 o 2x4

355

350

345

14

A AAA g 355

) 350

345

O 1x3

Ii 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)

370 Case 32c

370 Case 32d

365 TDVH

365 a TDVH

x 2x5 x 2x5

360 o 2x4 360 o 2x4

17a 355 o 1x3

a co 355 O 1x3

350

345 I I

350

345 i III ill ill 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



09

08 13- case 32a - - - - case 32b

09 -

08 --a- TDVH

07 A case 32c case 32d 07 - x 2x5

06 06 - o 2x4

05 05 - 0 1x3 04 04 -

03 03 -

02 02 -

01 01

0 0 ml( a 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)

Case 32c Case 32d 1

09 -a- TDMH 09 -e-1DtVH 08 08

07 x 2x5 07

$ 2x5

06 2x4 06 2x4 05 O 1x3 05 o 1x3 04 04

03 03

02 02

01 01

0 MK 0 al a 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



09 09 08 08 07 - 07 06 e 06




(a) (b)

Case 32c Case 32d 1


2x4 02 02o 2x4 0 1x301 01 0 1x3

0 0 Iiili11111 03

441 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)




0 ilf111 0 S- 1111111


(a) (b)


09 09 08 -8- TCM-I -9-11)Virl08 07 x 2x5 07- x 2x5 06 062x4 2x4 05 05

O 1x3 0 1x304 04 03 03 02 02 01 01

0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)




o 1x3 04 E 04 03 03 02 - 7 02 01 - A- 01

-0- -0 01111


(a) (b)


09 - 09-a- TDVH08 08

07- x 2x5 07 06 - 06p 2x4 05 S 05

0 1x304 - 04 03 - 03 02 - 02 01 - 01

0 0 11111111111 1


(c) (d)


035

03

025

02

015

01

005

0 0

035

03

025


Vapor


a case 32c + case 32d11111111111 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a) Case 32c

Vapor


01 TDM-I x 2x5

005

0 0

2x4 o 1x311111111111 1 2 3 4 5 6 7 8 9 10 11

Stage number 12

(c)

Case 32b 035

03 Vapor 025 -

02 IF_

015

01

005 -

0 0

035

03

025

02

015

01

005

0 0

Liquid

11111111 1 2 3 4 5 6 7 8

Stage number

(b) Case 32d

1 2 3 4 5 6 7 8 Stage number

(d)

-9- TUC x 2x5

2x4

0 1x3

9 10 11 12

9 10 11 12



40 35 30


- -0- - - case 32b

+ case 32d

25

20 15


5

0 1 2 3 4 5 6 7 Stage number

8 12

(a)

45 40 35 30 25 20

a IDNI-1 x 2x5

o 2x4

o 1x3

Case 32c

15

10

5 0

0 1 2 3 4 5 6 7 Stage number

8 9 10 11 12

(c)

45 Case 32b

40 35 30 25 20 15 10

5

0 0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)

45 Case 32d

40 35 30 25

20 15 10

5 0

0 1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(d)




t 0005 - g 0005 2x4

O 1x3E SI 0003 - Cn 0003

0001 - 0001 TT El 19

-0001 -0001



0011 0011

0009 B-- MAC 0009

0007 - x 2x5 -2- 0007

E 0005 -0 o

o

2x4

1x3 0005

EDI 0003 - c7) 0003

0001 - 0001 III En CI

-0001 -0001


(c) (d)


151















used







152




products was larger





















051

049 c 02 -

047 045 015

043 E 01

041 039 037

- case 32a

case 32c

case 32b


case 32c

case 32b

case 32d 035 0

0 10 20 30 time (hr)

40 50 0 10 20 30 time (hr)

40 50

(a) (b)



037 006 c 035 -0 005

033 1 004 o deg 031 cd 003 _

12= 029 - case 32a case 32b 002



case 32b case 32d

025 0 L

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)



001 Case 32b

0005 0

c 0005 0

0 -0005 k b -0005 -001 o -001

-0015 E -0015 -002 case 32a case 32b o -002


-003 v -003 2x4 1x3

-0035 -0035 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(a) (b)


0005 0005 o 0 0

-0005 -0005

o -001 -001 E -0015 -0015 o o -002

- 0025 TDVH 2x5

-002 -0025

1DM-I 2x5

s -003 - 2x4 1x3 -003 2x4 1x3

-0035 -0035 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)



0035 Case 32b

003 g 003 TDA11 2x5 0025 I 0025 2x4 1x3

002

0015 ----___--- _____ -- ebe 0020 E 0015


0005 case 32c case 32d gt0 0005 13

0 f I I 0 1 1 1 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)

Case 32c Case 32d 0035 0035

g 003 TDM-1 2x5 003 TEM-I 2x5

a 0025 2x4 1x3 0025 2x4 1x3

m 0020 002

E 0015 0015 cG1 001 001 gt0 0005 0005 13

0 I I t 1 0 1 1 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)



0005 Case 32b



O -001 - 2x4 1x3

0-0015 ro

-002

-0025 -0025

0 10 20 30 time (hr)

40 50 0 10 20 30 time (hr)

40 50

(a) (b)

Case 32c Case 32d 0005 0005

0 0 0

-0005 TDIVI-1 2x5 -0005 111vH 2x5

O -001 2x4 1x3 -001 2x4 1x3

o -0015 -0015

-002 -002

-0025 -0025 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)



0007 Case 32b


o 0003 E 0003 _

c 0002 o

laquo- 0002 W

0001 gt0 0001 11

0 r-411egel7 I I I

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)

Case 32c Case 32d 0007 0007

5 0006 0006 TIM-I 2x5 V 0005 0005 2x4 1x3 w 00040 0004

E 0003 C

0003

0002 TI341-1 2x5 0002 es

0001 2x4 1x3 0001

0 i 1 i

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)


158











large plates











00002 Case 32b

0 0

-00002 -00002 -- 00004 case 32a m -00004 -


-00012 -00012 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

00002 Case 32c

00002 Case 32d

0 0

-00002 -00002

-00004 -00004 TEM -00006 -00006 2x5 -00008 -00008 2x4

-0001 -0001 lx3 -00012 -00012

0 10 20 30 40 0 10 20 30 40 50 time (hr) time (hr)

(C) (d)



00012 Case 32b

0001 - case 32a 0001

00008 case 32b 00008

00006 case 32c 00006

00004 - case 32d 00004

00002 00002

0 -4 0

-00002 -00002 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

Case 32c Case 32d 00012 00012

0001 0001 TUC 00008 00008 2x5 00006 00006 2x4 00004 00004 lx3 00002 00002

0 0

-00002 -00002 0 10 20 30 40 0 10 20 30 40 50

time (hr) time (hr)

(C) (d)




000005

0

-000005

-00001

-000015 0 10 20 30 40

time (hr)

(a)

Case 32c 000015

00001

000005

0

-000005

-00001

-000015 0 10 20 30 40

time (hr)

(C)

000015

00001

000005

Case 32b

TDAH

2x4

2x5

1x3

0 i 1 impoomponn

-000005

-00001

-000015 0 10 20

time (hr) 30 40

(b)

000015 Case 32d

00001 -

000005

TDIVH

2x4

2x5

1x3

0

-000005 -

00001 -

-000015 0 10 20 30

time (hr) 40 50

(d)



case 32c 000003 000003

case 32d 000002 000002 000001 000001

0 0

-000001 -000001 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

000007 Case 32c

000007 Case 32d

000006 TDIVH 000006 000005 2x5 000005 000004 2x4 000004 000003 lx3 000003 000002 000002 000001

000001 0

0 -000001

0 10 20 30 40 -000001

time (hr) 0 10 20 30

time (hr) 40 50

(C) (d)


10

0001

00001 000001

90

-180 000001

case 32a

case 32b

case 32c

case 32d


case 32a

case 32b

case 32c

case 32d


(a)

01 1

01

10

0

V ac 1

a)

cc

01

000001 00001

80

60 cn 4140

SI 20

63 0

120 o--40 0-60

1E)-80

-100 000001 00001


case 32b

case 32c

case 32d

01


(b)

01 1


10 10

1 0

0

01 V

o 001

E

0001

TD 1-i

2x5

2x4

lx3

113

V

CC

00001 000001 00001 0001 001


01


01

90 250

200 2x5

V Ilk 150

ca) 100

2x4

lx3

a) -90 C)

a=-180

TDA1-1

2x5

2x4

lx3

S 50 c a 0 To

-50

m-100

-270 000001 00001 0001 001


-150 000001 00001 0001 001


(a) (b)


10 10

2x5 1 2x4

1x3

TDVH E4

0001

2x5

2x4

00001 lx3

01



01

90 20

Si0 013 0 m c0 0 -90 c a

-180 000001

TDMI 2x5

2x4

lx3


01 1

s 15 as0 10 0 1n 5 c0 0 o c so -5as

deg -10-10 co =

-13 -15 0 0 -20 CE

-25 000001 00001 0001 001


(a) (b)


10 10

0

0

01

-enV

V 001 TUC E

ao

E

0001

2x5

2x4

lx3

V 0 cc

00001 01 000001 00001 0001 001



90 80

rn 0

TDV1-1

2x5

2x4 1x3

rn 70

43 60 O 50 of g 40 S 30

o c 20 To 10 13 00

-10

2x5

2x4

1x3

-270 -20 000001 00001 0001 001



(a) (b)


167







holdups (CMH)














model

168







169

BIBLIOGRAPHY












170














171










172

APPENDICES

173

APPENDIX A



Species Tc V Z

[K] [cm3gmol]

AcOH 5944 171 02

EtOH 5162 167 0248

Water 6473 56 0229

AcOEt 5232 286 0252





Species Aj 13j

AcOH -242129 20142

EtOH -300324 475

Water 0 04077

AcOEt -498159 1031


Normal Heat of



571 3911 5660

63 3515 9260

2176 3732 9717

378 3503 7700


Cj Dj EJ

28033x10-2 -01136x10-4 00020x10-6

25030x10-2 -08263x10-5 11975x10-9

36657x10-3 00615x10-4 0

30495x102 -53900x106 0

174



3

1-


+ aap6

AcOH EtOH

Ao (1gmol)2atm 1004538 686619

Bo lgmol 006519 005087

Co (1gmo1)2K2atm 3121503 1605577

ao (1gmo1)3atm 15616 084012

bo (1gmo1)2 002703 001674

Co (1gmo1)3K2atm 8087892 3279836

ao (1gmo1)3 0001601 0000781

yo (1gmo1)2 004365 002704


Water

1175617

008668

2828098

242981

004778

9748118

0003763

007717

AcOEt

311069

001856

1141020

013766

000219

8428061

369E-05

000354


log = A + C


Species Adeg Bdeg

AcOH 75596 164405

EtOH 783124 144052

Water 796681 166821

AcOEt 709808 123871


Cdeg

233524

21271

228

217

175



A -05543 0581778 0688636 -006014

A2 -032436 0209245 0024303 0229575

A3 -010369 -025733 0375534 186575

A4 -070546 -056264 127548 0355191

A5 -201335 -031485 177863 0468416

A6 -225362 0451732 0696279 15111

A7 0837926 -011541 0936722 -005997

A8 052376 0069531 0449357 0067399

A9 0434061 0074053 071779 -315997

A10 -053406 018701 144979 0941858

A -325231 -036999 -211099 -192225

Al2 590329 -008234 0746905 -075573

A13 3354 -040947 112914 103791

A14 0197296 109247 0120436 0365254

A15 -045266 0192416 -164268 -136587

A16 0014715 -017257 0330018 -213818


176

APPENDIX B







177

Start
















Continue simulation


178







at each plate






No




C Stop


179

APPENDIX C






0 0000 0003 0017 0001 0003 1 0032 0046 0041 0006 0024 2 0159 0205 0258 0172 0174 3 0167 0203 0261 0146 0156 4 0169 0201 0267 0129 014 5 0173 0200 0267 0119 0128 6 0188 0206 0267 0103 0119 7 0216 0278 0314 0118 0145



0 0649 0693 0752 0543 0539 1 0741 0734 0755 0633 0617 2 0649 0638 0583 0579 0576 3 0653 0634 0579 0551 0545 4 0677 0631 0573 0529 0521 5 0723 0630 0572 0516 0504 6 0659 0626 0572 0512 0496 7 0386 0573 0518 0482 0471

180



0 0067 0090 0115 0043 0048 1 0067 0100 0100 0076 0077 2 0070 0084 0089 0100 0100 3 0070 0088 0089 0121 0121 4 0075 0092 0090 0138 0138 5 0079 0096 0090 0156 0155 6 0077 0102 0087 0191 0179 7 0364 0099 0097 0238 0240



0 0284 0214 0116 0413 0411 1 0160 0121 0104 0289 0282 2 0122 0073 0070 0149 0150 3 0110 0076 0070 0183 0179 4 0089 0077 0071 0204 0201 5 0086 0074 0071 0208 0213 6 0076 0066 0071 0194 0206 7 0034 0050 0070 0162 0144



by

Varong Pavarajarn

A THESIS

submitted to



degree of

Master of Science



APPROVED


C




reader upon request






ACKNOWLEDGEMENTS












TABLE OF CONTENTS

Page

1 INTRODUCTION 1















Page










BIBLIOGRAPHY 169

APPENDICES 172




LIST OF FIGURES

Figure Page



















Figure Page
















Figure Page


















Figure Page


















Figure Page




















Figure Page



LIST OF TABLES

Table Page



















Table Page








Figure Page




Table Page










LIST OF NOTATIONS













f Feed stage

f Fugacity [atm]









11) Weir height [m]






1 Weir length [m]















t Time [min]


















Greek symbols












Subscripts

B Bottom product



F Feed stream

1 Liquid phase


v


S Stripping section

Vapor phase


I INTRODUCTION




acetate













2






















3




















models were studied



4




















5




















6









du = f (uv t)

dt

0 = g(u v t)







solution vector u

7




in this work














8

s=0

s=1

s=2

s=M-1

s=M

S=M+1



m+1

1)-(St)= (S)1(Snt) 1 ltslt M+1 (1-2) n=1



Sk n = 0m (1-3)Wnl(s)

kVn Sn Sk k

m +1 S k n = 1m+1 (1-4)Wnv(S)

k=1 Sn Sk ktn




9



N





(a+Dx(13+1)N-xw(x a 13 N) - (1-6)x(N x)











10





















11























12













13









the liquid phase







14








aA + bB H cC + dD


VAA + VBB + VCC + VDD = 0 (2-1)

where





15

Condenser


dt

dt dM0

nr

LOLo (2-2b) 1=1


dt

Internal Stages

dM + + FX

dt (2-3a) +

dM nc

V F Vi W + (2-3b)dt j=1


dt

Reboiler


dt

nc dMN+1



16

D


17

Hw Xwj



i=N VN+1 HN+1 YN+1j

QR LN hN XNj

B hB xBd i=N+1


18


(2-5)1iA =





by




(2-8)



19






Id(TE (2-10)

n

(2-11)ij 1=1






dMik dhi (2-12)

dt dt

20



as




The result is

nc dx EK

dTi 1=1 dt nc (2-14)

dt dK E x

1=1 dT


_ -nc di ci



-di1=1




21






dt aT dt axm dt


n dK cbcii I M x



n cbcij x-n`






22


23

F


24




i +1 n i+1 dhk


Li (2-20) (h 11+1)

i+1 I n

= Li + Ft B+ (2-21) k =N +l j=1

i = NN-110


holdups

n







25











described in Sec221




qi =lk owi

(2-24a)


26

how Eqn (2-25) vi h

Li

A

1


27







how jY2qt = 36815 (2-24b)t

048F

how is defined by

(

M (2-25)

r7r Ceol4)Pi



and (2-4b) become




28





n dhN+1


VN+1 (2-28)(Hi+ h8)


(2-29) J=1




H1

i = (NN-12)





171 (2-31)(H1 ho


29


=1 dt





(2-24)











30

i=0

D

V1 Hr

hi

1

VF YFI HE

(1-OF xF

i=mi+m2+3



B


31

Condenser


dM0 -dt

- Vo Lo D + j =1



dM dt

dM n

-v + dt 1=1

dM ihi + L h L hdt







(2-33a)

(2-33b)

(2-33c)

(2 -34 a)

(2-34b)

(2-34c)

(2-35a)

(2-35b)

(2-35c)

32





dt J=1



Reboiler


BXB Vi rimi +3 A

dM n morm2+3



BhB QR






33


remain unchanged



















34




35



Chapter Two









311 Enthalpies


n


n

Hi =I yi H(7) (3-1b) i=1

36




H (TO = Ai + B + C + D + E iTi4 (3-2b)


= x (To Pi) (3-3a)

Hi =1 i(Ti Pi) (3-3b) J=1


procedures

Enthalpies of Vapor



37




_RT2( din f (3-5) aT )p





T2 (3-6)







T2 deg v

38


F (Pvk) (3-8)Pvk+1 = P

vk F(pvk)








thesis




= Hsi(Ti) A1(T) (3-10)


39


038 1 T T

where Tr = (3-11)A(7`)=7 A 1Tr




such as

Ki(T)=Oi + AT+ of T2 -F ei T3 (3-12)






j0

(3-13)



Appendix A

40

Bcit















F(T)=[Ixi jE1Ki(TP)]-1= 0 (3-16) i=1

41


F(Tk) (3-17)Tk+1 = Tk PAK)











Z (1 K (TF PF ))F(1)= L o (3-19)

=1 + ty(K (TF PF ) 1)

42





zi





=ExiJP(Ti) (3-21)





where r = T (3-22)T

43







Simplified model

Liquid enthalpy



dh dh = x (3-23)

dT

dT


(3-25)

44




dki +28T + 3E 72 (3-26)

dT dT




apo dpij (3-27)


dT dT 7 j(i_Trf

n axik 1i (3-29)

aXij k=1 j

45

Rigorous model

Liquid enthalpy







(3-30)

Thus



0

B + T +3D T2 +4E T3 (3-32)


46



T3 YPv


dA 038 A (3-34)

dT (T T)






ln(10) kJ (3-35) aT (T + C

9K1 Po1I (3-36)

dx dx





47



(-rA) = [k(7)][ fn( CA CB )1 (3-23)





M j as follows


= [k(T)C = k(T)MiX (3-24)



48



(3-26)







x=s-1 N=M-1

(N n)(n +a+1)(n+a+ 3+1)An (3-27)

(2n + a + 13 + 1)2

n(n+ I3)(N + n+ a + 3 +1) B (3-28)(2n + a + 11)2

where

(a)k = 0 k = 0

(a)k = (a)(a+1)(a+k-1) kgt 0

49


Q0(xa P N) =1 (3-29)

(a+ 0+2)xQi(xa P N) 1 (3-30)Ma +1)











requirements



50


set of equations



required accuracy









51







of ethyl acetate

A + B H C + D













52


Design Variables






AcOH zA 02559

Et0H zs 06159

Water zc 00743

- AcOEt zD 00539




Weir length [m] 006











53

N+1

(Ai )2







xitcoH 11893E-03 66924E-03 28242E-03 16359E-03

xEtolf 61785E-03 98927E-03 16722E-02 18820E-02

xwater 92009E-03 94784E-03 53772E-03 49359E-03

XAcOEt 13209E-03 47090E-03 12271E-02 11779E-02









results



0 1 2 3 4 5

Stage number


0 1 2 3 4 5 6 7

Stage number



0 0 1 2 3 4 5 6 7

Stage number



0 0 1 2 3 4 5 6 7

Stage number


55























Topic of studies

Physical

approximation

Numerical

approximation

Number of stages

Type of reaction

Thermodynamic

model

Pressure in the

column

Example 1



model assuming



reduced-order TDMH

model

8

irreversible

( 2A ---gt R + S )

simple

uniform (1 atm)

Example 2


order model in a

column with many

stages

reduced-order TDMH

model

29

rigorous

uniform (1 atm)

Example 30


order model in a

column with fewer

stages

-

reduced-order TDMH

model

11

Example 31


order model in a



assuming uniform

pressure

full-order TDMH

model assuming that


is uniform

reduced-order TDMH

model

11

reversible


rigorous rigorous


column

Example 32


on steady-state and

dynamic behaviors

full-order TDMH

model using various

plate geometries

-

11

rigorous

uniform (1 atm)

57


be observed

58

5 EXAMPLE PROBLEM 1






2A gt R + S


(-17A) = kACA

where






A 11000 + 30T 4000 + 30T 001Ts 10699 275 02

R 20000 + 20T 15000 + 20T 002T 11651 090 0229

S 25300 + 10T 25000 + 10T 003T 9418 459 0252

T is in degF

59


Design Variables






A 08

R 01

S 01















60







2x2 lx1


11835 20000

0 = condenser 28165 40000



61835 70000


9 = reboiler 90000






solutions

61

60

55

50

45

40

35

30 0

60

55 C Of 41) 50

I a 45 m ei n 40 I i 35

30 0

60

55 ii Oi a) 50 73

12a 45 co

isoo 40 i

35

30 0


1 2 3 4 5 6

Stage number

(a)


(b)

i I i i i 1


(c)

B TDMH - - -0- - CM H

7 8

B TDMH gt 2x2

O 1x1

7 8

--B CM H 2x2 o 1x1

I

7 8

9

9

9


62


09 -08 07 --e-- TDMH 06 -0- CMH 05 04 03 02 01

0 Ulf

0 1 2 3 4 5 6 7 8 9

Stage number

(a)

1

09 08 07 06 05 04 03 02 01

0 0 1 2 3 4 5 6 7 8 9

Stage number

(b)

1

09 08 8 CM H 07 2x2 06 - 0 1x1 05 04 03 02 01


0 1 2 3 4 5 6 7 8 9

Stage number

(c)


63

1

09 -08-07 06 05 04 -03-02 -01

0 0

1

09 08 07 -06 -05 04 03 02 01 -

0 0

1

09 08 07 06 05 04 03 02 01

0 0


1I I I I I

1 2 3 4 5 6

Stage number

(a)

1 2 3 4 5 6

Stage number

(b)

t 1 I 1

1 2 3 4 5 6

Stage number

(c)

$ TDMH CMH

1 1

7 8 9

--e TDM H o 2x2

0 1x1

7 8 9

9-- CM H 2x2

0 1x1

7 8 9


64


09 08 07 06 05 04 03 02 01

0 0

I

1

i

2 3

I

4 I

5 6

p TDMH

CMH

7 8 9

Stage number

(a)

1

09 08 07 06 05 04 03 02 01

0 0

I

1

I

2 3 4 5 6

e TDMH 2x2

O 1x1

7 8 9

Stage number

(b)

1

09 08 07 06 05 04-03 02 01

0 0

I

1 2 3 4 5 6

--eCMH 2x2

O 1x1

7 8 9

Stage number

(c)


65


700

600

500

400

300

$ TDMH CMH

200

100

0 0 1 2 3 4 5


(a)

800

700

600 Vapor

500

400

300

200

Liquid

9 TDM H 2x2

O 1x1

100

0


6 7 8 9

(b)

800

700

600 Vapor

500

400

300

200

Liquid 8CMH

2x2

O 1x1

100

0 0

F

1

f

2 I

3 I I

4 5 Stage number

i

6 I

7 i

8 9

(c)


66





TDMH CMH

(2x2) (1x1) Full (3x3) (2x2) (1x1)

T (degF)2 75654E-05 32486E-02 64722E-02 59785E-05 18506E-02

XA 18871E-07 28772E-05 97558E-05 20379E-07 29484E-05

XR 37528E-07 18061E-04 90993E-05 45029E-07 90603E-05

xs 90549E-08 11304E-04 22755E-06 99641E-08 44224E-05

L (lbmolmin)2 16683 3641945 317355 23006 2405854

V (lbmolmin)2 16822 3058993 317355 34804 2278430









67























68






model










69


003

0025

002 0015

001

0005

TDMH

CMH

0 0 10 20 30

time (min)

40 50

(a)

0035

003

0025

002

0015

001

0005

TDMH

2x2 1x1

0 0 10 20 30

time (min)

40 50

(b)

0035

003

0025

002-0015

001

0005

0 0 10 20 30 40

CMH 2x2 1x1

50

time (min)

(C)


70


-001

-002

TDMH

CMH

-003

-004 _ _ _

-005

-006 0 10 20 30

time (min)

40 50

(a)

I I I I

-001

-002

-003

TDMH

2x2 1x1

-004

-005

-006 0 10 20 30

time (min)

40 50

(b)

-001

-002

CMH

2x2 1x1

-003

-004

-005

-006 0 10 20 30

time (min)

40 50

(c)


71


002 _-____

0015

001

0005 TDMH

CMH

0 10 20 30

time (min)

40 50

(a)

0025

002

0015

001

0005

TDMH

2x2 lx1

0 10 20 30

time (min)

40 50

(b)

0025

002

0015

001

0005

CMH

2x2 1x1

0 10 20 30

time (min)

40 50

(c)


72




xA initial 00858 00859 00829 01041 01042 01009

final 01160 01160 01138 01248 01248 01212

XR initial 08237 08237 08257 08040 08040 08077

final 07706 07706 07705 07614 07614 07647

xs initial 00905 00905 00914 00919 00918 00915

final 01135 01134 01158 01138 01138 01141


Model Relative time

TDMH Full (3x3) 1

2x2 08972

lx1 06576


2x2 06150

lx1 04706






73



















behavior

74


0 1 2 3 4 5 6 7 8 9

stage number













75


001

0008

0006

0004

0002

0 0 10 20 30 40 50 60

time (m in)

(a)

0012

001- MAC 2x2

0008 1x1

0006

0004

0002

0 0 10 20 30 40 50 60

time (min)

(b)

0012

001

0008

0006

0004

0002

0 0 10 20 30 40 50 60

time (m in)

(C)


76


-0002 -0004 -0006 -0008 -001

-0012 -0014 -0016 -0018 -002

0 10 20 30 40 50 60

time (m in)

(a)

0 -0002 -0004 -0006 -0008

-001 -0012 -0014 -0016 -0018

-002 0 10 20 30 40 50 60

time (min)

(b)

0 -0002 -0004 -0006 -0008

-001 -0012 -0014 -0016 -0018

-002 0 10 20 30 40 50 60

time (m in)

(C)


77


0007 0006 TUC 0005 CM-I 0004

0003

0002

0001

0 0 10 20 30 40 50 60

time (min)

(a)

0008

0007 0006

0005 0004

0003 0002

0001

0 0 10 20 30 40 50 60

time (min)

(b)

0008

0007 0006

0005 0004

0003 0002

0001

0 0 10 20 30 40 50 60

time (m in)

(c)


78



fractions




















001 10

0

v 0001 0 E

TDMH

CMH

00001 000001 00001 0001 001


01

000001 00001 0001 001


20

10

-90 TDMH

CMH

-180 000001 00001 0001 001 01 1

Frequency ( radmin)

0

-10

CMH

000001 00001

(a)


0001 001

Frequency (radmin)

01

(b)


10

2x2 1x1

1

01

00001 0001 001 01 000001 00001 0001 001 01


90 10

2x2 1x1

0

-90 TDMH

2x2 1x1

-180 -10 000001 00001 0001 001 01 000001 00001 0001 001 01 1


(a) (b)


001 10

CMH

2x2

1x1

00001 01

000001 00001 0001 001 01 1 000001 00001 0001 001 01


10

0

-90 CMH

2x2 1x1

-180 -10 000001 00001 0001 001 01 1 000001 00001 0001 001 01 1


(a) (b)


82



















83

6 EXAMPLE PROBLEM 2







Design Variables







AcOH zA 04962

EtOH zs 04808

water zc 00229

AcOEt zD 0








84












8x16 7x14 6x12 4x9 3x6


10003 10036 10209 12230 15649

0 = condenser 20129 20873 22952 35293 50000

10 = vapor feed stage 31068 34290 40295 64707 84351

43453 50000 59705 87770 100000

56547 65710 77048 100000

68932 79127 89791

79871 89964 100000

89997 100000

100000

85


8x16 7x14 6x12 4x9 3x6


120000 120000 120005 120210 122214


30 = reboiler 140008 140282 142129 152490 183980

150112 151682 157096 177252 226020

160676 165036 174991 205000 263291

172205 180226 194781 232748 287786

184815 196607 215219 257510 300000

198183 213393 235009 276750

211817 229774 252904 289790

225185 244964 267871 300000

237795 258318 279742

249324 269718 289995

259888 279984 300000

269992 290000

280000 300000

290000

300000







86




8x16 7x14 6x12 4x9 3x6

T (K)2 34681E-06 61907E-06 99419E-06 78225E-05 77447E-03

XAcOH 40090E-11 25666E-10 10937E-09 52778E-08 79956E-06

xEioll 34920E-09 56707E-09 89310E-09 47621E-08 40108E-06

Xwater 18735E-09 37718E-09 63574E-09 26774E-08 86463E-07

XAcOEt 86031E-09 13058E-08 16382E-08 53505E-08 85873E-07

YAcoH 29980E-11 14345E-10 58830E-10 11738E-07 18645E-05

YEt0H 67593E-09 96737E-09 12643E-08 76121E-08 80113E-06

Ywater 24000E-09 47672E-09 80790E-09 45331E-08 19307E-06

YAcOEt 15738E-08 22710E-08 27523E-08 82866E-08 16307E-06

L (gmolmin)2 14936E-10 24385E-10 60968E-10 25848E-09 13842E-07

V (gmolmin)2 43025E-09 40383E-09 60686E-09 70445E-09 14962E-07

M (gmol)2 42749E-07 31854E-06 25227E-05 61481E-04 21716E-03




(gmolmin)

Full (9x18) 0014071

8x16 0014071

7x14 0014069

6x12 0014067

4x9 0014063

3x6 0014038



0 3 6 9 12 15 18 21 24 27 30

Stage number



0 3 6 9 12 15 18 21 24 27 30

Stage number

1

09 c 08 ot 07 E 06 e 05 oE 04 a 03 3 02

01 0

0

1

09 08 07 06 05 04 03 02 01

0 0


- full A 6x12

o 4x9 x 3x6

iiiii isii 1 3 6 9 12 15 18 21 24 27 30

Stage number


3 6 9 12 15 18 21 24 27 30

Stage number




o) 365

E 25

20

a)

L

360

355 -

E o E

15

10

sect 350I-

0 E

5

0

345 5 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(a) (b)



03

025

02

vapor 19 17 -15 -13 -

0 4x9

p

x

6x12

3x6

015

01

005

0

liquid

4-1 I I I

full

o 4x9

I it N 1 4 I

p

x 6x12

3x6


s1 1 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(c) (d)


89









25

AcOH

EtOH

-

- - water_

1 05 _ - -- AcOEt

0 1

345 350 355 360 365 370

Temperature (K)






90








reduced models







in Figure 64



column

91



Full (9x18) 1

8x16 09715

7x14 08797

6x12 07190

4x9 05733

3x6 04794








stream






048

2 046

to - 044

E 042V 04

TEM 7x14 4x9

8x16 6x12 3x6

018

0175

017

0165

016

0155

IDVH 7x14 4x9

8x16 6x12 3x6

038 0 10 20 30 40 50 60 70 80

015 0 10 20 30 40 50 60 70 80

time (hr) time (hr)



04

038

036

0 034 3 7 032

TDM-I 7x14 4x9

8x16 6x12 3x6

g 0033 ra co 1- 0031

Edeg 0029

yor 0027

TDMI-1

7x14 4x9

8x16 6x12 3x6

03 0 10 20 30 40 50 60 70 80

0025 0 10 20 30 40 50 60 70 80

time (hr) time (hr)



09 - full p 6x12 08 07 o 4x9 x 3x6 06 05 04 03 02 01


Stage number


09 08 07 06 05

6x1204 - full p03 02 o 4x9 x 3x6 01

0 i I I I I I I I

0 3 6 9 12 15 18 21 24 27 30

Stage number


09 -08

full p 6x12

07 o 4x9 x 3x6 06 05 04 03 02 -01

0 T 0 3 6 9 12 15 18 21 24 27 30

Stage number


09 08 full A 6x12 07 06 0 4x9 x 3x6

05 04 03 02 01

0 I I I

0 3 6 9 12 15 18 21 24 27 30

Stage number


46

370

365

360

355

- full

Temperature profile

p 6x12

o 4x9 x 3x6

E

E 5 E


25 -20 -15-10 -

- full A 6x12

o 4x9 x 3x6

sect 350

345

-6 E cr)


5 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(a) (b)



03 19

025

02

vapor 17 15 13

015

01

005

0 1-

liquid

I 4 4 I

full o 4x9

I i l I III I

A

x 6x12

3x6

I I

11

9-7-5-3

0 3 6 9 12 15 18 Stage number

21 24 27 30 0 3 6 9 12 15 18 Stage number

21 24 27 30

(c) (d)


95
















68




00004

00002 0

-00002 -00004 -00006 -00008 -0001

-00012 -00014

00012

0001

00008

00006

00004

00002

0

-00002

-00004


time (hr)


time (hr)

000015

00001

000005

0

-000005

-00001

-000015

-00002

000006

000005

000004

000003

000002

0

000001 -0

-000001 0


10 20 30 40 50

time (hr)


10 20 30 40 50

time (hr)


10 10

1

01

13 001 1

c E 0001 TDIVI-1 8x16 8x16 7x14

00001 7x14 4x9

6x12 3x6

6x12 3x6

4x9

000001 01



01

90 60 IDN1-1 8x16 50

407x 14 6x12 30

4x9 3x6 T 20 20 5 10

0 2 -10 0

-20 8x16 7x14o -30 6x12 4x9-40 3x6cc -50

-180 -60 000001 00001 0001 001 01 000001 00001 0001 001 01 1


(a) (b)


98












for simpler columns

99

7 EXAMPLE PROBLEM 3










problem




column was studied








100


Design Variables







AcOH za 04962

EtOH zB 04808

water zc 00229

AcOEt zD 0




Weir length [m] 009

Weir height [m] 003








101


each model






98597 109356 120000 109913 120000 120000










102






column





(2x5) (2x4) (1x3)

T (K)2 60609E-05 13436E-03 29741E-02

XAeOH 35046E-08 10320E-06 17373E-05

XEtOH 73801E-07 12009E-06 16073E-05

xwater 23561E-08 13345E-07 46047E-06

Xite0Et 78982E-07 78798E-07 17033E-05

Y AcOH 53545E-08 23869E-06 40598E-05

Y Et0H 60827E-07 15434E-06 26427E-05

Ywater 25369E-08 30654E-07 59017E-06

YAcOEt 64649E-07 64980E-07 16455E-05

L (gmolmin)2 16799E-09 26341E-08 35570E-07

V (gmolmin)2 18206E-09 33777E-08 48041E-07

M (gmol)2 11613E-03 11617E-03 10803E-02




10 EMI Cl 0111111 1111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12



09 09 -a- MAC08 08 07 07 x 2x5 06 06 4 2x4 05 -s- TEAM 05

0 1x304 04x 2x503 03

o 2x402 02 01 O 1x3 01

0 011111111 1411 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12




TDM-I aTow 30 Y 365 x 2x5 25 x 2x5

360 2x4 20 2x4 E 070o 1x3 15 0 1x3

11 355 E10 IP EX

a 0 5g 350

1- rn 0 i

345 i i -51111 E

1



035 21

03 19 6 TDMH 17VaporE 025 x 2x5

8 15-2x402 13E


01 2x4 7-=005- 5o 1x3

0 3 il 111111 1 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)


105




2x5 0011345

2x4 0011343

lx3 0011364














106



Full (3x6) 1

2x5 09313

2x4 08556

1x3 06608


















0485 - 0145C TDVH0048 0475 1 014 2x5

IMF 2x4 047 0 0135

2x5 o lx3E0465 0132x4 733 lx3 5r 0125

046

0455 I I I045 012

0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)


0375 00295 037 -

00290365 -036 00285 TDVHTDVH

0355 2x52x5 0028 035 2x42x4

002750345 1x3lx3 034 0027 4 I I I

0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)


0

108






respectively














0 -00001 -00002 -00003 -- 00004 -00005 2x5 -00006 -00007

2x4

-00008 lx3 -00009

0 10 20 30 40 50

time (hr)


0 -00001

0 10 20 30 40 50

time (hr)


000008 000006 TDMr1 2x5

000004 2x4 1x3 000002

0 -000002 -000004 -000006 -000008

-00001 0 10 20 30 40 50

time (hr)


000003

0000025

000002

0000015 000001

0000005

0

-0000005 0 10 20 30 40 50

time (hr)


10 10

1

01

1

001 full

2x5

0001 2x4

lx3 00001 01

000001 00001 0001 001 01 000001 00001 0001 001 01 1


90

0

full -90 2x5

2x4 1x3

-180 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


10 10

2x5 1 2x4

0 1x3 0 s 01 0is c= 001 full Tx E4 2x5

0001 2x4

lx3 00001 01


90 10

clii0 ii 13

w 0 0to



c- 1 0 2x5


-360 -20 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


112






operations





column in each case

pressure atm) 2

18

16

14

12

1

08

06

0--AP=005 X--AP=OA

AP= 015

04

02

0 I I I l iti 0 1 2 3 4 5 6 7 8 9 10 11 12

stage number




113







Table 712



T (K)2 250357 1175582 4137036

xAcoH 61711E-05 21799E-04 45062E-04

xEroll 86611E-04 23323E-03 33668E-03

Xwater 10578E-04 35052E-04 71882E-04

XAcOEt 10156E-03 25721E-03 34075E-03

YAcOH 36414E-05 12001E-04 22977E-04

YEt0H 14054E-03 41997E-03 76426E-03

Ywater 10252E-04 32920E-04 67493E-04

YAcoEt 15273E-03 43664E-03 77664E-03

L (gmolmin) 2 33027E-06 19272E-05 80700E-05

V (gmolmin)2 32945E-06 19270E-05 80678E-05

M (gmol) 2 77791E-03 17231E-02 16933E-02

11AcOH (gmolmin)2 23729E-07 81195E-07 15842E-06



(2x5) (2x4) (1x3) (2x5) (2x4) (1x3) (2x5) (2x4) (1x3)

T 1035E-04 1426E-03 2166E-02 6500E-04 1982E-03 7342E-02 1339E-01 1352E-01 4376E+00

xAcoH 3449E-08 9791E-07 1516E-05 3483E-08 9113E-07 1324E-05 4424E-08 8416E-07 1161E-05

XEt0H 4048E-07 7949E-07 1783E-05 3143E-07 6492E-07 1769E-05 4013E-06 4320E-06 2098E-04

xwate 1055E-08 1436E-07 5492E-06 9188E-09 1514E-07 5428E-06 2914E-07 4453E-07 1212E-05

XAr0Et 3785E-07 3776E-07 2799E-05 2746E-07 2758E-07 2852E-05 5805E-06 5805E-06 2511E-04

YACOH 5878E-08 2296E-06 3546E-05 6219E-08 2153E-06 3092E-05 6902E-08 1982E-06 2702E-05

Y DOH 3397E-07 1107E-06 2434E-05 2647E-07 9055E-07 2223E-05 3398E-06 3928E-06 1891E-04



L 1259E-09 2441E-08 2874E-07 1710E-09 2253E-08 2670E-07 8557E-08 1044E-07 4197E-06

V 1283E-09 2963E-08 3925E-07 1497E-09 2656E-08 3329E-07 1008E-07 1231E-07 5191E-06

M 1064E-03 1064E-03 1077E-02 1052E-03 1053E-03 1086E-02 1306E-03 1308E-03 1878E-02

17awn 9882E-13 3055E-11 3667E-10 1565E-12 4471E-11 4994E-10 1379E-11 7137E-11 1149E-09


320 -4 310 300 -- 290 CI

CY

I t f

A

1 flAP=010

0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


1x3300 290 tIllli11111

2x4

0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(c)

390 380 370 360 350 340 330 320 310 300 290

0 f III-1111111 1 2 3 4 5 6 7 8 9 10 11

Stage number


9-- TDMH x 2x5 o 2x4 o 1x3

12

(b)

390 380 370 360 350 340 330 320 310 300 290

0 1111f-1-11111

2 3 4 5 6 7 8 9 10 11

Stage number


9 TDMH 2x5

o 2x4 o 1x3

1 12

(d)


- --

09 -08 07 -06 -05 -04 03 -02 -01

0 II 0

1

09 -08 07 06 05 -04 -03 02 01 -

0 0


--B--AP=0 - -AP= 005

A AP= 010 ---G---AP= 015

1111111 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


-B-TDMH 2x5

o 2x4 o 1x3

i BM El i I I I

1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(c)

1

09 -08 -07 -06 05 -04 -03 -02 01 -

0 0

1

09 08 07 06 05 04 03 02 01

0 0


-13-TDMH x 2x5

2x4

O 1x3

1111111 OE U 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)


1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(d)



AP = 00503 02 fi AP - 010 01 - - -G - -AP= 015

0 11111111111 O 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


09 08 07 06 05 -8- TDM H04 x 2x503

O 2x4 02 01 0 1x3

0 O 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(c)



09 -08 -07 -06 -05 - -9- TDM H04 - x 2x503 -

O 2x402 -01-

0 loi1x3i i I f iiii0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)


09 -08 07 06 05 -04 -9- TDMH 03 - x 2x5 02 - p 2x4 01 - 0 1x3

0 0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(d)



09 -09 - --B--AP=0 -e-TDMH0808 07 07 - x 2x5

A AP=01006 06 2x4 05 05 O 1x3 04 - 04 -03 - 03 02 - 02 -01 01 -

0 0 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)


0909 -08 - TDMH 08

07 x 2x5 07

06 o 2x4 06 0505 o 1x3

04 - 04

03 - 03 02 - 02 01 01111111110 0


(c) (d)



09 09--B--AP=0 -B- TDMH08 - 08 -07 - 07 2x5

A AP= 01006- 06 - 2x4 ---0---AP= 01505 05 O 1x3

04 04 -03 - 03 -02 02 01 01lilt0 0I


(a) (b)


09 - 09 08 - -9- TDMH 08 07 x 2x5 07 06 - 06o 2x4

0505 o 1x3 04 - 04 03 - 03 02 02 01 - 01

0 0Iflit 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



035

2r

03

025

02

015

01

005

-13-- AP = 0 AP = 005

A AP= 010 --0---4P= 015

03

025

02

015

01

005

0

03

025

02

015

01

005

Vapor


2x4 o 1x3111114-11111

03

025 B

02 g0

015 8 0

01

005

0 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(a) (b)



035

03

025

02

015

01 -

005

Vapor

c CI 113 Liquid

NION101 -B-TDMH

X 2x5 2x4

II 1x3 t I 0

03

025

02

015

01

005

03 -

025 -

02

015

01

005

O NID Liquid x 2x5

O 2x4 O 1x3

I I 114111+1-f

Vapor

- 8- TDMH

03

025

02

015

01

005

0 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(c) (d)



21


9 9 7 7 5

3 3111111111 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)


19 - 19 8 TDMH-8 TCM-I 17

g 15 x 2x5 -6 17 rA 15

2x5

a 13 o 2x4 cl 13 o 2x4

31- 11 - 0 1x3 12 11 1x3 c

9 c

9 co 03 75 E

7 5 111--0K 3 1 i 111111111

7 5 3 i i 111111111


(c) (d)




E0005o 0005 o 1x3E E 9 0003 0) 0003

0001 0001 III

-0001 -0001 i



0011 0011

e TDVH0009 0009 -x 2x5

0007 s 0007 o 2x4

t 0005 t 0005o 1x3 E E a) 0003 0)0003

0001

-0001 El OK 0 4 I I I

0001

-0001 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(c) (d)


123







(MSE=4376)
















124




3

25

2 MOH

15 EtOH

1 - - water

05 Ac0Et

0

290 310 330 350 370

Temperature (K)











125









results










case



048 047

02 - AP - 0 AP= 010

AP - 005 AP- 015

046 018 -045 044

016

043 014 042 AP = 0 AP= 005 012 -041 AP = 010 AP= 015 04 01

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)


036 006 035 005 --034 004 -033


03 001 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)



0005 0

-0005 -001

-0015 -002 APdeg AP=005

-0025 AP=010 AP=015

-003 0 10 20 30 40 50

time (hr)

(a)


0005 0

-0005 -001

-0015 -002 TDVH 2x5

-0025 2x4 1x3

-003 0 10 20 30 40 50

time (hr)

(c)


0005 0

-0005 -001

-0015 -002 TDAH 2x5

-0025 2x4 1x3

-003 0 10 20 30 40 50

time (hr)

(b)


0005 0

-0005 -001

-0015 TEM 2x5-002

-0025 2x4

-003 0 10 20 30 40

time (hr)

(d)


50



003 003

0025 0025

002 002

0015 0015

001 AP-0 AP- 005

001 IDA4-1 2x5

0005 itP =010 AP-015 0005 1 2x4 1x3

0 i I I i 0 i 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)



003 003

0025 0025

002 002

0015 0015

001 -MINH 2x5 001

0005 2x4 1x3 0005

0 1 1 1 0

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)




0 0

-0005 APdeg AP= 005 -0005 TDVH 2x5

-001 AP- 010 AP- 015 -001 2x4 1x3

-0015 -0015

-002 -002

-0025 -0025

-003 -003 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(a) (b)



0 0

-0005 TDM- 2x5 -0005 MAC 2x5

-001 2x4 1x3 -001 2x4

-0015 -0015

-002 -002

-0025 -0025

-003 -003 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)




00035 - 00035 -0003 - 0003

00025 00025 -0002

00015 0001 TCMI 2x5

00005 2x4 1x3

0 50 0 10 20 30 40 50

time (hr)

(a) (b)



00035 00035 0003 0003

00025 00025 0002 0002

00015 00015 0001 0001

00005 00005 0 0

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)


131






















0 -00001 -00002 -00003 A- AP = 0 -0 0004 AP= 005 -00005 AP= 010 -00006 -00007 AP=015 -00008

0 500 1000 1500 2000 2500 3000 time (min)

(a)


0 -00001 -00002 -00003 -00004 -00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)


0 -00001 --00002 T -00003 -00004 --00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)

(b)


0 -00001 1--00002 + -00003 4 -00004 -t--00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)



0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)

(a)


0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)


2x400003 J-lx300002 4-

00001 0

-00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)

(b)


0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)



000005

0

-000005 AP = 0 AP = 005-00001 AP= 010

-000015 AP= 015

-00002 0 500 1000 1500 2000 2500 3000

time (min)

(a)


000005

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)


000005

0

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)

(b)


000005

0

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)



500 1000 1500 2000 2500 3000 time (min)

(a)


0 -000001

0 500 1000 1500 2000 2500 3000 time (min)



0

-000001 0 500 1000 1500 2000 2500 3000

time (min)

(b)


000005 000004

000003 000002 -r 000001 VI

0

-000001 0 500 1000 1500 2000 2500 3000

time (min)


10

0001

00001 000001

90

-90

-180 000001

OP -0 4P =005 AP- 010 AP= 015

00001 0001 001


4P =0 AP= 005 AP- 010 AP= 015

00001 0001 001

Frequency (radmin)

(a)

01

10

0

0V

ac 1

0 O 0 0

CC

01

000001

20

10

O 0 0 S -10 0 c a -20 0

w -30 flo cc

-40 000001

AP- 005 AP= 010 AP= 015

00001 0001 001


AP= 005 AP= 010 AP= 015

00001 0001 001

Frequency (radm in)

(b)

01


10 10

01 =0I0

GI

1 01 1774) a= 3 iTDMI-10010 E 2x5 rozQ 0

0001 2x4 el a)

lx3 cc

00001 01

000001 00001 0001 001 01 000001 00001 0001 001 01 1


90 50

of 40 a)a

---tu 30 co cco 20 a)


-180 -20 000001 00001 0001 001 01 1 000001 00001 0001 001 01


(a) (b)


10 10

1

0

01 a)

a 001 E 2x5

2x4 0001

lx3

00001 01



01

90 50

S40 2x5

30 rn

2x4

1x3 20

210 0 -g 0

X10 cc

-180 -20 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


10

1

0

01 0

ma a fi 001

0001

00001 000001

90

rn

a)

a) -90

a

-180 000001

TDM-I

2x5

2x4

lx3


TDIVH

2x5

2x4

1x3


(a)

10

1

01 01

000001 00001

01

90 80

O 70 60

40 50

40 30

c 0 20 713 10

2 00 cca) - 1 0

-20 000001 00001


01


(b)

01


140







the 1x3 model











Weir length [m] 009 009 009 002

Weir height [m] 003 003 003 006

Volume holdup [1] 0301 0181 0741 0301

141





















lower in case 32c



(2x5) (2x4) (1x3) (2x5) (2x4) (1x3) (2x5) (2x4) (1x3)

T 24206E-04 15413E-03 35626E-02 56883E-05 11573E-03 14283E-02 46403E-05 13594E-03 31742E-02


XEOH 61717E-07 11827E-06 72673E-05 25819E-08 38742E-07 16468E-05 92104E-07 14047E-06 17848E-05



YAcOH 47334E-08 22850E-06 46167E-05 64134E-08 22165E-06 29649E-05 54052E-08 24397E-06 42173E-05

YEt0H 48963E-07 16300E-06 78916E-05 26729E-08 70829E-07 20844E-05 75289E-07 17309E-06 29040E-05



L 86334E-10 27762E-08 48216E-07 12360E-09 21860E-08 26573E-07 17252E-09 27603E-08 36756E-07

V 18824E-09 43611E-08 60301E-07 11625E-09 21731E-08 27373E-07 19103E-09 36782E-08 49566E-07

M 28172E-03 28172E-03 19939E-02 19775E-04 20413E-04 48878E-03 38266E-06 42605E-06 18753E-04

1Acoll 26856E-13 83250E-12 14633E-10 20313E-12 52102E-11 57418E-10 53902E-13 19199E41 28894E40


370 Case 32b

365 9 case 32a - -o- - case 32b

365 a TDVH


360 360 o 2x4

355

350

345

14

A AAA g 355

) 350

345

O 1x3

Ii 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)

370 Case 32c

370 Case 32d

365 TDVH

365 a TDVH

x 2x5 x 2x5

360 o 2x4 360 o 2x4

17a 355 o 1x3

a co 355 O 1x3

350

345 I I

350

345 i III ill ill 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



09

08 13- case 32a - - - - case 32b

09 -

08 --a- TDVH

07 A case 32c case 32d 07 - x 2x5

06 06 - o 2x4

05 05 - 0 1x3 04 04 -

03 03 -

02 02 -

01 01

0 0 ml( a 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)

Case 32c Case 32d 1

09 -a- TDMH 09 -e-1DtVH 08 08

07 x 2x5 07

$ 2x5

06 2x4 06 2x4 05 O 1x3 05 o 1x3 04 04

03 03

02 02

01 01

0 MK 0 al a 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



09 09 08 08 07 - 07 06 e 06




(a) (b)

Case 32c Case 32d 1


2x4 02 02o 2x4 0 1x301 01 0 1x3

0 0 Iiili11111 03

441 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)




0 ilf111 0 S- 1111111


(a) (b)


09 09 08 -8- TCM-I -9-11)Virl08 07 x 2x5 07- x 2x5 06 062x4 2x4 05 05

O 1x3 0 1x304 04 03 03 02 02 01 01

0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)




o 1x3 04 E 04 03 03 02 - 7 02 01 - A- 01

-0- -0 01111


(a) (b)


09 - 09-a- TDVH08 08

07- x 2x5 07 06 - 06p 2x4 05 S 05

0 1x304 - 04 03 - 03 02 - 02 01 - 01

0 0 11111111111 1


(c) (d)


035

03

025

02

015

01

005

0 0

035

03

025


Vapor


a case 32c + case 32d11111111111 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a) Case 32c

Vapor


01 TDM-I x 2x5

005

0 0

2x4 o 1x311111111111 1 2 3 4 5 6 7 8 9 10 11

Stage number 12

(c)

Case 32b 035

03 Vapor 025 -

02 IF_

015

01

005 -

0 0

035

03

025

02

015

01

005

0 0

Liquid

11111111 1 2 3 4 5 6 7 8

Stage number

(b) Case 32d

1 2 3 4 5 6 7 8 Stage number

(d)

-9- TUC x 2x5

2x4

0 1x3

9 10 11 12

9 10 11 12



40 35 30


- -0- - - case 32b

+ case 32d

25

20 15


5

0 1 2 3 4 5 6 7 Stage number

8 12

(a)

45 40 35 30 25 20

a IDNI-1 x 2x5

o 2x4

o 1x3

Case 32c

15

10

5 0

0 1 2 3 4 5 6 7 Stage number

8 9 10 11 12

(c)

45 Case 32b

40 35 30 25 20 15 10

5

0 0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)

45 Case 32d

40 35 30 25

20 15 10

5 0

0 1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(d)




t 0005 - g 0005 2x4

O 1x3E SI 0003 - Cn 0003

0001 - 0001 TT El 19

-0001 -0001



0011 0011

0009 B-- MAC 0009

0007 - x 2x5 -2- 0007

E 0005 -0 o

o

2x4

1x3 0005

EDI 0003 - c7) 0003

0001 - 0001 III En CI

-0001 -0001


(c) (d)


151















used







152




products was larger





















051

049 c 02 -

047 045 015

043 E 01

041 039 037

- case 32a

case 32c

case 32b


case 32c

case 32b

case 32d 035 0

0 10 20 30 time (hr)

40 50 0 10 20 30 time (hr)

40 50

(a) (b)



037 006 c 035 -0 005

033 1 004 o deg 031 cd 003 _

12= 029 - case 32a case 32b 002



case 32b case 32d

025 0 L

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)



001 Case 32b

0005 0

c 0005 0

0 -0005 k b -0005 -001 o -001

-0015 E -0015 -002 case 32a case 32b o -002


-003 v -003 2x4 1x3

-0035 -0035 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(a) (b)


0005 0005 o 0 0

-0005 -0005

o -001 -001 E -0015 -0015 o o -002

- 0025 TDVH 2x5

-002 -0025

1DM-I 2x5

s -003 - 2x4 1x3 -003 2x4 1x3

-0035 -0035 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)



0035 Case 32b

003 g 003 TDA11 2x5 0025 I 0025 2x4 1x3

002

0015 ----___--- _____ -- ebe 0020 E 0015


0005 case 32c case 32d gt0 0005 13

0 f I I 0 1 1 1 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)

Case 32c Case 32d 0035 0035

g 003 TDM-1 2x5 003 TEM-I 2x5

a 0025 2x4 1x3 0025 2x4 1x3

m 0020 002

E 0015 0015 cG1 001 001 gt0 0005 0005 13

0 I I t 1 0 1 1 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)



0005 Case 32b



O -001 - 2x4 1x3

0-0015 ro

-002

-0025 -0025

0 10 20 30 time (hr)

40 50 0 10 20 30 time (hr)

40 50

(a) (b)

Case 32c Case 32d 0005 0005

0 0 0

-0005 TDIVI-1 2x5 -0005 111vH 2x5

O -001 2x4 1x3 -001 2x4 1x3

o -0015 -0015

-002 -002

-0025 -0025 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)



0007 Case 32b


o 0003 E 0003 _

c 0002 o

laquo- 0002 W

0001 gt0 0001 11

0 r-411egel7 I I I

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)

Case 32c Case 32d 0007 0007

5 0006 0006 TIM-I 2x5 V 0005 0005 2x4 1x3 w 00040 0004

E 0003 C

0003

0002 TI341-1 2x5 0002 es

0001 2x4 1x3 0001

0 i 1 i

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)


158











large plates











00002 Case 32b

0 0

-00002 -00002 -- 00004 case 32a m -00004 -


-00012 -00012 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

00002 Case 32c

00002 Case 32d

0 0

-00002 -00002

-00004 -00004 TEM -00006 -00006 2x5 -00008 -00008 2x4

-0001 -0001 lx3 -00012 -00012

0 10 20 30 40 0 10 20 30 40 50 time (hr) time (hr)

(C) (d)



00012 Case 32b

0001 - case 32a 0001

00008 case 32b 00008

00006 case 32c 00006

00004 - case 32d 00004

00002 00002

0 -4 0

-00002 -00002 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

Case 32c Case 32d 00012 00012

0001 0001 TUC 00008 00008 2x5 00006 00006 2x4 00004 00004 lx3 00002 00002

0 0

-00002 -00002 0 10 20 30 40 0 10 20 30 40 50

time (hr) time (hr)

(C) (d)




000005

0

-000005

-00001

-000015 0 10 20 30 40

time (hr)

(a)

Case 32c 000015

00001

000005

0

-000005

-00001

-000015 0 10 20 30 40

time (hr)

(C)

000015

00001

000005

Case 32b

TDAH

2x4

2x5

1x3

0 i 1 impoomponn

-000005

-00001

-000015 0 10 20

time (hr) 30 40

(b)

000015 Case 32d

00001 -

000005

TDIVH

2x4

2x5

1x3

0

-000005 -

00001 -

-000015 0 10 20 30

time (hr) 40 50

(d)



case 32c 000003 000003

case 32d 000002 000002 000001 000001

0 0

-000001 -000001 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

000007 Case 32c

000007 Case 32d

000006 TDIVH 000006 000005 2x5 000005 000004 2x4 000004 000003 lx3 000003 000002 000002 000001

000001 0

0 -000001

0 10 20 30 40 -000001

time (hr) 0 10 20 30

time (hr) 40 50

(C) (d)


10

0001

00001 000001

90

-180 000001

case 32a

case 32b

case 32c

case 32d


case 32a

case 32b

case 32c

case 32d


(a)

01 1

01

10

0

V ac 1

a)

cc

01

000001 00001

80

60 cn 4140

SI 20

63 0

120 o--40 0-60

1E)-80

-100 000001 00001


case 32b

case 32c

case 32d

01


(b)

01 1


10 10

1 0

0

01 V

o 001

E

0001

TD 1-i

2x5

2x4

lx3

113

V

CC

00001 000001 00001 0001 001


01


01

90 250

200 2x5

V Ilk 150

ca) 100

2x4

lx3

a) -90 C)

a=-180

TDA1-1

2x5

2x4

lx3

S 50 c a 0 To

-50

m-100

-270 000001 00001 0001 001


-150 000001 00001 0001 001


(a) (b)


10 10

2x5 1 2x4

1x3

TDVH E4

0001

2x5

2x4

00001 lx3

01



01

90 20

Si0 013 0 m c0 0 -90 c a

-180 000001

TDMI 2x5

2x4

lx3


01 1

s 15 as0 10 0 1n 5 c0 0 o c so -5as

deg -10-10 co =

-13 -15 0 0 -20 CE

-25 000001 00001 0001 001


(a) (b)


10 10

0

0

01

-enV

V 001 TUC E

ao

E

0001

2x5

2x4

lx3

V 0 cc

00001 01 000001 00001 0001 001



90 80

rn 0

TDV1-1

2x5

2x4 1x3

rn 70

43 60 O 50 of g 40 S 30

o c 20 To 10 13 00

-10

2x5

2x4

1x3

-270 -20 000001 00001 0001 001



(a) (b)


167







holdups (CMH)














model

168







169

BIBLIOGRAPHY












170














171










172

APPENDICES

173

APPENDIX A



Species Tc V Z

[K] [cm3gmol]

AcOH 5944 171 02

EtOH 5162 167 0248

Water 6473 56 0229

AcOEt 5232 286 0252





Species Aj 13j

AcOH -242129 20142

EtOH -300324 475

Water 0 04077

AcOEt -498159 1031


Normal Heat of



571 3911 5660

63 3515 9260

2176 3732 9717

378 3503 7700


Cj Dj EJ

28033x10-2 -01136x10-4 00020x10-6

25030x10-2 -08263x10-5 11975x10-9

36657x10-3 00615x10-4 0

30495x102 -53900x106 0

174



3

1-


+ aap6

AcOH EtOH

Ao (1gmol)2atm 1004538 686619

Bo lgmol 006519 005087

Co (1gmo1)2K2atm 3121503 1605577

ao (1gmo1)3atm 15616 084012

bo (1gmo1)2 002703 001674

Co (1gmo1)3K2atm 8087892 3279836

ao (1gmo1)3 0001601 0000781

yo (1gmo1)2 004365 002704


Water

1175617

008668

2828098

242981

004778

9748118

0003763

007717

AcOEt

311069

001856

1141020

013766

000219

8428061

369E-05

000354


log = A + C


Species Adeg Bdeg

AcOH 75596 164405

EtOH 783124 144052

Water 796681 166821

AcOEt 709808 123871


Cdeg

233524

21271

228

217

175



A -05543 0581778 0688636 -006014

A2 -032436 0209245 0024303 0229575

A3 -010369 -025733 0375534 186575

A4 -070546 -056264 127548 0355191

A5 -201335 -031485 177863 0468416

A6 -225362 0451732 0696279 15111

A7 0837926 -011541 0936722 -005997

A8 052376 0069531 0449357 0067399

A9 0434061 0074053 071779 -315997

A10 -053406 018701 144979 0941858

A -325231 -036999 -211099 -192225

Al2 590329 -008234 0746905 -075573

A13 3354 -040947 112914 103791

A14 0197296 109247 0120436 0365254

A15 -045266 0192416 -164268 -136587

A16 0014715 -017257 0330018 -213818


176

APPENDIX B







177

Start
















Continue simulation


178







at each plate






No




C Stop


179

APPENDIX C






0 0000 0003 0017 0001 0003 1 0032 0046 0041 0006 0024 2 0159 0205 0258 0172 0174 3 0167 0203 0261 0146 0156 4 0169 0201 0267 0129 014 5 0173 0200 0267 0119 0128 6 0188 0206 0267 0103 0119 7 0216 0278 0314 0118 0145



0 0649 0693 0752 0543 0539 1 0741 0734 0755 0633 0617 2 0649 0638 0583 0579 0576 3 0653 0634 0579 0551 0545 4 0677 0631 0573 0529 0521 5 0723 0630 0572 0516 0504 6 0659 0626 0572 0512 0496 7 0386 0573 0518 0482 0471

180



0 0067 0090 0115 0043 0048 1 0067 0100 0100 0076 0077 2 0070 0084 0089 0100 0100 3 0070 0088 0089 0121 0121 4 0075 0092 0090 0138 0138 5 0079 0096 0090 0156 0155 6 0077 0102 0087 0191 0179 7 0364 0099 0097 0238 0240



0 0284 0214 0116 0413 0411 1 0160 0121 0104 0289 0282 2 0122 0073 0070 0149 0150 3 0110 0076 0070 0183 0179 4 0089 0077 0071 0204 0201 5 0086 0074 0071 0208 0213 6 0076 0066 0071 0194 0206 7 0034 0050 0070 0162 0144


APPROVED


C




reader upon request






ACKNOWLEDGEMENTS












TABLE OF CONTENTS

Page

1 INTRODUCTION 1















Page










BIBLIOGRAPHY 169

APPENDICES 172




LIST OF FIGURES

Figure Page



















Figure Page
















Figure Page


















Figure Page


















Figure Page




















Figure Page



LIST OF TABLES

Table Page



















Table Page








Figure Page




Table Page










LIST OF NOTATIONS













f Feed stage

f Fugacity [atm]









11) Weir height [m]






1 Weir length [m]















t Time [min]


















Greek symbols












Subscripts

B Bottom product



F Feed stream

1 Liquid phase


v


S Stripping section

Vapor phase


I INTRODUCTION




acetate













2






















3




















models were studied



4




















5




















6









du = f (uv t)

dt

0 = g(u v t)







solution vector u

7




in this work














8

s=0

s=1

s=2

s=M-1

s=M

S=M+1



m+1

1)-(St)= (S)1(Snt) 1 ltslt M+1 (1-2) n=1



Sk n = 0m (1-3)Wnl(s)

kVn Sn Sk k

m +1 S k n = 1m+1 (1-4)Wnv(S)

k=1 Sn Sk ktn




9



N





(a+Dx(13+1)N-xw(x a 13 N) - (1-6)x(N x)











10





















11























12













13









the liquid phase







14








aA + bB H cC + dD


VAA + VBB + VCC + VDD = 0 (2-1)

where





15

Condenser


dt

dt dM0

nr

LOLo (2-2b) 1=1


dt

Internal Stages

dM + + FX

dt (2-3a) +

dM nc

V F Vi W + (2-3b)dt j=1


dt

Reboiler


dt

nc dMN+1



16

D


17

Hw Xwj



i=N VN+1 HN+1 YN+1j

QR LN hN XNj

B hB xBd i=N+1


18


(2-5)1iA =





by




(2-8)



19






Id(TE (2-10)

n

(2-11)ij 1=1






dMik dhi (2-12)

dt dt

20



as




The result is

nc dx EK

dTi 1=1 dt nc (2-14)

dt dK E x

1=1 dT


_ -nc di ci



-di1=1




21






dt aT dt axm dt


n dK cbcii I M x



n cbcij x-n`






22


23

F


24




i +1 n i+1 dhk


Li (2-20) (h 11+1)

i+1 I n

= Li + Ft B+ (2-21) k =N +l j=1

i = NN-110


holdups

n







25











described in Sec221




qi =lk owi

(2-24a)


26

how Eqn (2-25) vi h

Li

A

1


27







how jY2qt = 36815 (2-24b)t

048F

how is defined by

(

M (2-25)

r7r Ceol4)Pi



and (2-4b) become




28





n dhN+1


VN+1 (2-28)(Hi+ h8)


(2-29) J=1




H1

i = (NN-12)





171 (2-31)(H1 ho


29


=1 dt





(2-24)











30

i=0

D

V1 Hr

hi

1

VF YFI HE

(1-OF xF

i=mi+m2+3



B


31

Condenser


dM0 -dt

- Vo Lo D + j =1



dM dt

dM n

-v + dt 1=1

dM ihi + L h L hdt







(2-33a)

(2-33b)

(2-33c)

(2 -34 a)

(2-34b)

(2-34c)

(2-35a)

(2-35b)

(2-35c)

32





dt J=1



Reboiler


BXB Vi rimi +3 A

dM n morm2+3



BhB QR






33


remain unchanged



















34




35



Chapter Two









311 Enthalpies


n


n

Hi =I yi H(7) (3-1b) i=1

36




H (TO = Ai + B + C + D + E iTi4 (3-2b)


= x (To Pi) (3-3a)

Hi =1 i(Ti Pi) (3-3b) J=1


procedures

Enthalpies of Vapor



37




_RT2( din f (3-5) aT )p





T2 (3-6)







T2 deg v

38


F (Pvk) (3-8)Pvk+1 = P

vk F(pvk)








thesis




= Hsi(Ti) A1(T) (3-10)


39


038 1 T T

where Tr = (3-11)A(7`)=7 A 1Tr




such as

Ki(T)=Oi + AT+ of T2 -F ei T3 (3-12)






j0

(3-13)



Appendix A

40

Bcit















F(T)=[Ixi jE1Ki(TP)]-1= 0 (3-16) i=1

41


F(Tk) (3-17)Tk+1 = Tk PAK)











Z (1 K (TF PF ))F(1)= L o (3-19)

=1 + ty(K (TF PF ) 1)

42





zi





=ExiJP(Ti) (3-21)





where r = T (3-22)T

43







Simplified model

Liquid enthalpy



dh dh = x (3-23)

dT

dT


(3-25)

44




dki +28T + 3E 72 (3-26)

dT dT




apo dpij (3-27)


dT dT 7 j(i_Trf

n axik 1i (3-29)

aXij k=1 j

45

Rigorous model

Liquid enthalpy







(3-30)

Thus



0

B + T +3D T2 +4E T3 (3-32)


46



T3 YPv


dA 038 A (3-34)

dT (T T)






ln(10) kJ (3-35) aT (T + C

9K1 Po1I (3-36)

dx dx





47



(-rA) = [k(7)][ fn( CA CB )1 (3-23)





M j as follows


= [k(T)C = k(T)MiX (3-24)



48



(3-26)







x=s-1 N=M-1

(N n)(n +a+1)(n+a+ 3+1)An (3-27)

(2n + a + 13 + 1)2

n(n+ I3)(N + n+ a + 3 +1) B (3-28)(2n + a + 11)2

where

(a)k = 0 k = 0

(a)k = (a)(a+1)(a+k-1) kgt 0

49


Q0(xa P N) =1 (3-29)

(a+ 0+2)xQi(xa P N) 1 (3-30)Ma +1)











requirements



50


set of equations



required accuracy









51







of ethyl acetate

A + B H C + D













52


Design Variables






AcOH zA 02559

Et0H zs 06159

Water zc 00743

- AcOEt zD 00539




Weir length [m] 006











53

N+1

(Ai )2







xitcoH 11893E-03 66924E-03 28242E-03 16359E-03

xEtolf 61785E-03 98927E-03 16722E-02 18820E-02

xwater 92009E-03 94784E-03 53772E-03 49359E-03

XAcOEt 13209E-03 47090E-03 12271E-02 11779E-02









results



0 1 2 3 4 5

Stage number


0 1 2 3 4 5 6 7

Stage number



0 0 1 2 3 4 5 6 7

Stage number



0 0 1 2 3 4 5 6 7

Stage number


55























Topic of studies

Physical

approximation

Numerical

approximation

Number of stages

Type of reaction

Thermodynamic

model

Pressure in the

column

Example 1



model assuming



reduced-order TDMH

model

8

irreversible

( 2A ---gt R + S )

simple

uniform (1 atm)

Example 2


order model in a

column with many

stages

reduced-order TDMH

model

29

rigorous

uniform (1 atm)

Example 30


order model in a

column with fewer

stages

-

reduced-order TDMH

model

11

Example 31


order model in a



assuming uniform

pressure

full-order TDMH

model assuming that


is uniform

reduced-order TDMH

model

11

reversible


rigorous rigorous


column

Example 32


on steady-state and

dynamic behaviors

full-order TDMH

model using various

plate geometries

-

11

rigorous

uniform (1 atm)

57


be observed

58

5 EXAMPLE PROBLEM 1






2A gt R + S


(-17A) = kACA

where






A 11000 + 30T 4000 + 30T 001Ts 10699 275 02

R 20000 + 20T 15000 + 20T 002T 11651 090 0229

S 25300 + 10T 25000 + 10T 003T 9418 459 0252

T is in degF

59


Design Variables






A 08

R 01

S 01















60







2x2 lx1


11835 20000

0 = condenser 28165 40000



61835 70000


9 = reboiler 90000






solutions

61

60

55

50

45

40

35

30 0

60

55 C Of 41) 50

I a 45 m ei n 40 I i 35

30 0

60

55 ii Oi a) 50 73

12a 45 co

isoo 40 i

35

30 0


1 2 3 4 5 6

Stage number

(a)


(b)

i I i i i 1


(c)

B TDMH - - -0- - CM H

7 8

B TDMH gt 2x2

O 1x1

7 8

--B CM H 2x2 o 1x1

I

7 8

9

9

9


62


09 -08 07 --e-- TDMH 06 -0- CMH 05 04 03 02 01

0 Ulf

0 1 2 3 4 5 6 7 8 9

Stage number

(a)

1

09 08 07 06 05 04 03 02 01

0 0 1 2 3 4 5 6 7 8 9

Stage number

(b)

1

09 08 8 CM H 07 2x2 06 - 0 1x1 05 04 03 02 01


0 1 2 3 4 5 6 7 8 9

Stage number

(c)


63

1

09 -08-07 06 05 04 -03-02 -01

0 0

1

09 08 07 -06 -05 04 03 02 01 -

0 0

1

09 08 07 06 05 04 03 02 01

0 0


1I I I I I

1 2 3 4 5 6

Stage number

(a)

1 2 3 4 5 6

Stage number

(b)

t 1 I 1

1 2 3 4 5 6

Stage number

(c)

$ TDMH CMH

1 1

7 8 9

--e TDM H o 2x2

0 1x1

7 8 9

9-- CM H 2x2

0 1x1

7 8 9


64


09 08 07 06 05 04 03 02 01

0 0

I

1

i

2 3

I

4 I

5 6

p TDMH

CMH

7 8 9

Stage number

(a)

1

09 08 07 06 05 04 03 02 01

0 0

I

1

I

2 3 4 5 6

e TDMH 2x2

O 1x1

7 8 9

Stage number

(b)

1

09 08 07 06 05 04-03 02 01

0 0

I

1 2 3 4 5 6

--eCMH 2x2

O 1x1

7 8 9

Stage number

(c)


65


700

600

500

400

300

$ TDMH CMH

200

100

0 0 1 2 3 4 5


(a)

800

700

600 Vapor

500

400

300

200

Liquid

9 TDM H 2x2

O 1x1

100

0


6 7 8 9

(b)

800

700

600 Vapor

500

400

300

200

Liquid 8CMH

2x2

O 1x1

100

0 0

F

1

f

2 I

3 I I

4 5 Stage number

i

6 I

7 i

8 9

(c)


66





TDMH CMH

(2x2) (1x1) Full (3x3) (2x2) (1x1)

T (degF)2 75654E-05 32486E-02 64722E-02 59785E-05 18506E-02

XA 18871E-07 28772E-05 97558E-05 20379E-07 29484E-05

XR 37528E-07 18061E-04 90993E-05 45029E-07 90603E-05

xs 90549E-08 11304E-04 22755E-06 99641E-08 44224E-05

L (lbmolmin)2 16683 3641945 317355 23006 2405854

V (lbmolmin)2 16822 3058993 317355 34804 2278430









67























68






model










69


003

0025

002 0015

001

0005

TDMH

CMH

0 0 10 20 30

time (min)

40 50

(a)

0035

003

0025

002

0015

001

0005

TDMH

2x2 1x1

0 0 10 20 30

time (min)

40 50

(b)

0035

003

0025

002-0015

001

0005

0 0 10 20 30 40

CMH 2x2 1x1

50

time (min)

(C)


70


-001

-002

TDMH

CMH

-003

-004 _ _ _

-005

-006 0 10 20 30

time (min)

40 50

(a)

I I I I

-001

-002

-003

TDMH

2x2 1x1

-004

-005

-006 0 10 20 30

time (min)

40 50

(b)

-001

-002

CMH

2x2 1x1

-003

-004

-005

-006 0 10 20 30

time (min)

40 50

(c)


71


002 _-____

0015

001

0005 TDMH

CMH

0 10 20 30

time (min)

40 50

(a)

0025

002

0015

001

0005

TDMH

2x2 lx1

0 10 20 30

time (min)

40 50

(b)

0025

002

0015

001

0005

CMH

2x2 1x1

0 10 20 30

time (min)

40 50

(c)


72




xA initial 00858 00859 00829 01041 01042 01009

final 01160 01160 01138 01248 01248 01212

XR initial 08237 08237 08257 08040 08040 08077

final 07706 07706 07705 07614 07614 07647

xs initial 00905 00905 00914 00919 00918 00915

final 01135 01134 01158 01138 01138 01141


Model Relative time

TDMH Full (3x3) 1

2x2 08972

lx1 06576


2x2 06150

lx1 04706






73



















behavior

74


0 1 2 3 4 5 6 7 8 9

stage number













75


001

0008

0006

0004

0002

0 0 10 20 30 40 50 60

time (m in)

(a)

0012

001- MAC 2x2

0008 1x1

0006

0004

0002

0 0 10 20 30 40 50 60

time (min)

(b)

0012

001

0008

0006

0004

0002

0 0 10 20 30 40 50 60

time (m in)

(C)


76


-0002 -0004 -0006 -0008 -001

-0012 -0014 -0016 -0018 -002

0 10 20 30 40 50 60

time (m in)

(a)

0 -0002 -0004 -0006 -0008

-001 -0012 -0014 -0016 -0018

-002 0 10 20 30 40 50 60

time (min)

(b)

0 -0002 -0004 -0006 -0008

-001 -0012 -0014 -0016 -0018

-002 0 10 20 30 40 50 60

time (m in)

(C)


77


0007 0006 TUC 0005 CM-I 0004

0003

0002

0001

0 0 10 20 30 40 50 60

time (min)

(a)

0008

0007 0006

0005 0004

0003 0002

0001

0 0 10 20 30 40 50 60

time (min)

(b)

0008

0007 0006

0005 0004

0003 0002

0001

0 0 10 20 30 40 50 60

time (m in)

(c)


78



fractions




















001 10

0

v 0001 0 E

TDMH

CMH

00001 000001 00001 0001 001


01

000001 00001 0001 001


20

10

-90 TDMH

CMH

-180 000001 00001 0001 001 01 1

Frequency ( radmin)

0

-10

CMH

000001 00001

(a)


0001 001

Frequency (radmin)

01

(b)


10

2x2 1x1

1

01

00001 0001 001 01 000001 00001 0001 001 01


90 10

2x2 1x1

0

-90 TDMH

2x2 1x1

-180 -10 000001 00001 0001 001 01 000001 00001 0001 001 01 1


(a) (b)


001 10

CMH

2x2

1x1

00001 01

000001 00001 0001 001 01 1 000001 00001 0001 001 01


10

0

-90 CMH

2x2 1x1

-180 -10 000001 00001 0001 001 01 1 000001 00001 0001 001 01 1


(a) (b)


82



















83

6 EXAMPLE PROBLEM 2







Design Variables







AcOH zA 04962

EtOH zs 04808

water zc 00229

AcOEt zD 0








84












8x16 7x14 6x12 4x9 3x6


10003 10036 10209 12230 15649

0 = condenser 20129 20873 22952 35293 50000

10 = vapor feed stage 31068 34290 40295 64707 84351

43453 50000 59705 87770 100000

56547 65710 77048 100000

68932 79127 89791

79871 89964 100000

89997 100000

100000

85


8x16 7x14 6x12 4x9 3x6


120000 120000 120005 120210 122214


30 = reboiler 140008 140282 142129 152490 183980

150112 151682 157096 177252 226020

160676 165036 174991 205000 263291

172205 180226 194781 232748 287786

184815 196607 215219 257510 300000

198183 213393 235009 276750

211817 229774 252904 289790

225185 244964 267871 300000

237795 258318 279742

249324 269718 289995

259888 279984 300000

269992 290000

280000 300000

290000

300000







86




8x16 7x14 6x12 4x9 3x6

T (K)2 34681E-06 61907E-06 99419E-06 78225E-05 77447E-03

XAcOH 40090E-11 25666E-10 10937E-09 52778E-08 79956E-06

xEioll 34920E-09 56707E-09 89310E-09 47621E-08 40108E-06

Xwater 18735E-09 37718E-09 63574E-09 26774E-08 86463E-07

XAcOEt 86031E-09 13058E-08 16382E-08 53505E-08 85873E-07

YAcoH 29980E-11 14345E-10 58830E-10 11738E-07 18645E-05

YEt0H 67593E-09 96737E-09 12643E-08 76121E-08 80113E-06

Ywater 24000E-09 47672E-09 80790E-09 45331E-08 19307E-06

YAcOEt 15738E-08 22710E-08 27523E-08 82866E-08 16307E-06

L (gmolmin)2 14936E-10 24385E-10 60968E-10 25848E-09 13842E-07

V (gmolmin)2 43025E-09 40383E-09 60686E-09 70445E-09 14962E-07

M (gmol)2 42749E-07 31854E-06 25227E-05 61481E-04 21716E-03




(gmolmin)

Full (9x18) 0014071

8x16 0014071

7x14 0014069

6x12 0014067

4x9 0014063

3x6 0014038



0 3 6 9 12 15 18 21 24 27 30

Stage number



0 3 6 9 12 15 18 21 24 27 30

Stage number

1

09 c 08 ot 07 E 06 e 05 oE 04 a 03 3 02

01 0

0

1

09 08 07 06 05 04 03 02 01

0 0


- full A 6x12

o 4x9 x 3x6

iiiii isii 1 3 6 9 12 15 18 21 24 27 30

Stage number


3 6 9 12 15 18 21 24 27 30

Stage number




o) 365

E 25

20

a)

L

360

355 -

E o E

15

10

sect 350I-

0 E

5

0

345 5 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(a) (b)



03

025

02

vapor 19 17 -15 -13 -

0 4x9

p

x

6x12

3x6

015

01

005

0

liquid

4-1 I I I

full

o 4x9

I it N 1 4 I

p

x 6x12

3x6


s1 1 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(c) (d)


89









25

AcOH

EtOH

-

- - water_

1 05 _ - -- AcOEt

0 1

345 350 355 360 365 370

Temperature (K)






90








reduced models







in Figure 64



column

91



Full (9x18) 1

8x16 09715

7x14 08797

6x12 07190

4x9 05733

3x6 04794








stream






048

2 046

to - 044

E 042V 04

TEM 7x14 4x9

8x16 6x12 3x6

018

0175

017

0165

016

0155

IDVH 7x14 4x9

8x16 6x12 3x6

038 0 10 20 30 40 50 60 70 80

015 0 10 20 30 40 50 60 70 80

time (hr) time (hr)



04

038

036

0 034 3 7 032

TDM-I 7x14 4x9

8x16 6x12 3x6

g 0033 ra co 1- 0031

Edeg 0029

yor 0027

TDMI-1

7x14 4x9

8x16 6x12 3x6

03 0 10 20 30 40 50 60 70 80

0025 0 10 20 30 40 50 60 70 80

time (hr) time (hr)



09 - full p 6x12 08 07 o 4x9 x 3x6 06 05 04 03 02 01


Stage number


09 08 07 06 05

6x1204 - full p03 02 o 4x9 x 3x6 01

0 i I I I I I I I

0 3 6 9 12 15 18 21 24 27 30

Stage number


09 -08

full p 6x12

07 o 4x9 x 3x6 06 05 04 03 02 -01

0 T 0 3 6 9 12 15 18 21 24 27 30

Stage number


09 08 full A 6x12 07 06 0 4x9 x 3x6

05 04 03 02 01

0 I I I

0 3 6 9 12 15 18 21 24 27 30

Stage number


46

370

365

360

355

- full

Temperature profile

p 6x12

o 4x9 x 3x6

E

E 5 E


25 -20 -15-10 -

- full A 6x12

o 4x9 x 3x6

sect 350

345

-6 E cr)


5 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(a) (b)



03 19

025

02

vapor 17 15 13

015

01

005

0 1-

liquid

I 4 4 I

full o 4x9

I i l I III I

A

x 6x12

3x6

I I

11

9-7-5-3

0 3 6 9 12 15 18 Stage number

21 24 27 30 0 3 6 9 12 15 18 Stage number

21 24 27 30

(c) (d)


95
















68




00004

00002 0

-00002 -00004 -00006 -00008 -0001

-00012 -00014

00012

0001

00008

00006

00004

00002

0

-00002

-00004


time (hr)


time (hr)

000015

00001

000005

0

-000005

-00001

-000015

-00002

000006

000005

000004

000003

000002

0

000001 -0

-000001 0


10 20 30 40 50

time (hr)


10 20 30 40 50

time (hr)


10 10

1

01

13 001 1

c E 0001 TDIVI-1 8x16 8x16 7x14

00001 7x14 4x9

6x12 3x6

6x12 3x6

4x9

000001 01



01

90 60 IDN1-1 8x16 50

407x 14 6x12 30

4x9 3x6 T 20 20 5 10

0 2 -10 0

-20 8x16 7x14o -30 6x12 4x9-40 3x6cc -50

-180 -60 000001 00001 0001 001 01 000001 00001 0001 001 01 1


(a) (b)


98












for simpler columns

99

7 EXAMPLE PROBLEM 3










problem




column was studied








100


Design Variables







AcOH za 04962

EtOH zB 04808

water zc 00229

AcOEt zD 0




Weir length [m] 009

Weir height [m] 003








101


each model






98597 109356 120000 109913 120000 120000










102






column





(2x5) (2x4) (1x3)

T (K)2 60609E-05 13436E-03 29741E-02

XAeOH 35046E-08 10320E-06 17373E-05

XEtOH 73801E-07 12009E-06 16073E-05

xwater 23561E-08 13345E-07 46047E-06

Xite0Et 78982E-07 78798E-07 17033E-05

Y AcOH 53545E-08 23869E-06 40598E-05

Y Et0H 60827E-07 15434E-06 26427E-05

Ywater 25369E-08 30654E-07 59017E-06

YAcOEt 64649E-07 64980E-07 16455E-05

L (gmolmin)2 16799E-09 26341E-08 35570E-07

V (gmolmin)2 18206E-09 33777E-08 48041E-07

M (gmol)2 11613E-03 11617E-03 10803E-02




10 EMI Cl 0111111 1111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12



09 09 -a- MAC08 08 07 07 x 2x5 06 06 4 2x4 05 -s- TEAM 05

0 1x304 04x 2x503 03

o 2x402 02 01 O 1x3 01

0 011111111 1411 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12




TDM-I aTow 30 Y 365 x 2x5 25 x 2x5

360 2x4 20 2x4 E 070o 1x3 15 0 1x3

11 355 E10 IP EX

a 0 5g 350

1- rn 0 i

345 i i -51111 E

1



035 21

03 19 6 TDMH 17VaporE 025 x 2x5

8 15-2x402 13E


01 2x4 7-=005- 5o 1x3

0 3 il 111111 1 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)


105




2x5 0011345

2x4 0011343

lx3 0011364














106



Full (3x6) 1

2x5 09313

2x4 08556

1x3 06608


















0485 - 0145C TDVH0048 0475 1 014 2x5

IMF 2x4 047 0 0135

2x5 o lx3E0465 0132x4 733 lx3 5r 0125

046

0455 I I I045 012

0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)


0375 00295 037 -

00290365 -036 00285 TDVHTDVH

0355 2x52x5 0028 035 2x42x4

002750345 1x3lx3 034 0027 4 I I I

0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)


0

108






respectively














0 -00001 -00002 -00003 -- 00004 -00005 2x5 -00006 -00007

2x4

-00008 lx3 -00009

0 10 20 30 40 50

time (hr)


0 -00001

0 10 20 30 40 50

time (hr)


000008 000006 TDMr1 2x5

000004 2x4 1x3 000002

0 -000002 -000004 -000006 -000008

-00001 0 10 20 30 40 50

time (hr)


000003

0000025

000002

0000015 000001

0000005

0

-0000005 0 10 20 30 40 50

time (hr)


10 10

1

01

1

001 full

2x5

0001 2x4

lx3 00001 01

000001 00001 0001 001 01 000001 00001 0001 001 01 1


90

0

full -90 2x5

2x4 1x3

-180 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


10 10

2x5 1 2x4

0 1x3 0 s 01 0is c= 001 full Tx E4 2x5

0001 2x4

lx3 00001 01


90 10

clii0 ii 13

w 0 0to



c- 1 0 2x5


-360 -20 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


112






operations





column in each case

pressure atm) 2

18

16

14

12

1

08

06

0--AP=005 X--AP=OA

AP= 015

04

02

0 I I I l iti 0 1 2 3 4 5 6 7 8 9 10 11 12

stage number




113







Table 712



T (K)2 250357 1175582 4137036

xAcoH 61711E-05 21799E-04 45062E-04

xEroll 86611E-04 23323E-03 33668E-03

Xwater 10578E-04 35052E-04 71882E-04

XAcOEt 10156E-03 25721E-03 34075E-03

YAcOH 36414E-05 12001E-04 22977E-04

YEt0H 14054E-03 41997E-03 76426E-03

Ywater 10252E-04 32920E-04 67493E-04

YAcoEt 15273E-03 43664E-03 77664E-03

L (gmolmin) 2 33027E-06 19272E-05 80700E-05

V (gmolmin)2 32945E-06 19270E-05 80678E-05

M (gmol) 2 77791E-03 17231E-02 16933E-02

11AcOH (gmolmin)2 23729E-07 81195E-07 15842E-06



(2x5) (2x4) (1x3) (2x5) (2x4) (1x3) (2x5) (2x4) (1x3)

T 1035E-04 1426E-03 2166E-02 6500E-04 1982E-03 7342E-02 1339E-01 1352E-01 4376E+00

xAcoH 3449E-08 9791E-07 1516E-05 3483E-08 9113E-07 1324E-05 4424E-08 8416E-07 1161E-05

XEt0H 4048E-07 7949E-07 1783E-05 3143E-07 6492E-07 1769E-05 4013E-06 4320E-06 2098E-04

xwate 1055E-08 1436E-07 5492E-06 9188E-09 1514E-07 5428E-06 2914E-07 4453E-07 1212E-05

XAr0Et 3785E-07 3776E-07 2799E-05 2746E-07 2758E-07 2852E-05 5805E-06 5805E-06 2511E-04

YACOH 5878E-08 2296E-06 3546E-05 6219E-08 2153E-06 3092E-05 6902E-08 1982E-06 2702E-05

Y DOH 3397E-07 1107E-06 2434E-05 2647E-07 9055E-07 2223E-05 3398E-06 3928E-06 1891E-04



L 1259E-09 2441E-08 2874E-07 1710E-09 2253E-08 2670E-07 8557E-08 1044E-07 4197E-06

V 1283E-09 2963E-08 3925E-07 1497E-09 2656E-08 3329E-07 1008E-07 1231E-07 5191E-06

M 1064E-03 1064E-03 1077E-02 1052E-03 1053E-03 1086E-02 1306E-03 1308E-03 1878E-02

17awn 9882E-13 3055E-11 3667E-10 1565E-12 4471E-11 4994E-10 1379E-11 7137E-11 1149E-09


320 -4 310 300 -- 290 CI

CY

I t f

A

1 flAP=010

0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


1x3300 290 tIllli11111

2x4

0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(c)

390 380 370 360 350 340 330 320 310 300 290

0 f III-1111111 1 2 3 4 5 6 7 8 9 10 11

Stage number


9-- TDMH x 2x5 o 2x4 o 1x3

12

(b)

390 380 370 360 350 340 330 320 310 300 290

0 1111f-1-11111

2 3 4 5 6 7 8 9 10 11

Stage number


9 TDMH 2x5

o 2x4 o 1x3

1 12

(d)


- --

09 -08 07 -06 -05 -04 03 -02 -01

0 II 0

1

09 -08 07 06 05 -04 -03 02 01 -

0 0


--B--AP=0 - -AP= 005

A AP= 010 ---G---AP= 015

1111111 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


-B-TDMH 2x5

o 2x4 o 1x3

i BM El i I I I

1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(c)

1

09 -08 -07 -06 05 -04 -03 -02 01 -

0 0

1

09 08 07 06 05 04 03 02 01

0 0


-13-TDMH x 2x5

2x4

O 1x3

1111111 OE U 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)


1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(d)



AP = 00503 02 fi AP - 010 01 - - -G - -AP= 015

0 11111111111 O 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


09 08 07 06 05 -8- TDM H04 x 2x503

O 2x4 02 01 0 1x3

0 O 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(c)



09 -08 -07 -06 -05 - -9- TDM H04 - x 2x503 -

O 2x402 -01-

0 loi1x3i i I f iiii0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)


09 -08 07 06 05 -04 -9- TDMH 03 - x 2x5 02 - p 2x4 01 - 0 1x3

0 0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(d)



09 -09 - --B--AP=0 -e-TDMH0808 07 07 - x 2x5

A AP=01006 06 2x4 05 05 O 1x3 04 - 04 -03 - 03 02 - 02 -01 01 -

0 0 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)


0909 -08 - TDMH 08

07 x 2x5 07

06 o 2x4 06 0505 o 1x3

04 - 04

03 - 03 02 - 02 01 01111111110 0


(c) (d)



09 09--B--AP=0 -B- TDMH08 - 08 -07 - 07 2x5

A AP= 01006- 06 - 2x4 ---0---AP= 01505 05 O 1x3

04 04 -03 - 03 -02 02 01 01lilt0 0I


(a) (b)


09 - 09 08 - -9- TDMH 08 07 x 2x5 07 06 - 06o 2x4

0505 o 1x3 04 - 04 03 - 03 02 02 01 - 01

0 0Iflit 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



035

2r

03

025

02

015

01

005

-13-- AP = 0 AP = 005

A AP= 010 --0---4P= 015

03

025

02

015

01

005

0

03

025

02

015

01

005

Vapor


2x4 o 1x3111114-11111

03

025 B

02 g0

015 8 0

01

005

0 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(a) (b)



035

03

025

02

015

01 -

005

Vapor

c CI 113 Liquid

NION101 -B-TDMH

X 2x5 2x4

II 1x3 t I 0

03

025

02

015

01

005

03 -

025 -

02

015

01

005

O NID Liquid x 2x5

O 2x4 O 1x3

I I 114111+1-f

Vapor

- 8- TDMH

03

025

02

015

01

005

0 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(c) (d)



21


9 9 7 7 5

3 3111111111 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)


19 - 19 8 TDMH-8 TCM-I 17

g 15 x 2x5 -6 17 rA 15

2x5

a 13 o 2x4 cl 13 o 2x4

31- 11 - 0 1x3 12 11 1x3 c

9 c

9 co 03 75 E

7 5 111--0K 3 1 i 111111111

7 5 3 i i 111111111


(c) (d)




E0005o 0005 o 1x3E E 9 0003 0) 0003

0001 0001 III

-0001 -0001 i



0011 0011

e TDVH0009 0009 -x 2x5

0007 s 0007 o 2x4

t 0005 t 0005o 1x3 E E a) 0003 0)0003

0001

-0001 El OK 0 4 I I I

0001

-0001 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(c) (d)


123







(MSE=4376)
















124




3

25

2 MOH

15 EtOH

1 - - water

05 Ac0Et

0

290 310 330 350 370

Temperature (K)











125









results










case



048 047

02 - AP - 0 AP= 010

AP - 005 AP- 015

046 018 -045 044

016

043 014 042 AP = 0 AP= 005 012 -041 AP = 010 AP= 015 04 01

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)


036 006 035 005 --034 004 -033


03 001 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)



0005 0

-0005 -001

-0015 -002 APdeg AP=005

-0025 AP=010 AP=015

-003 0 10 20 30 40 50

time (hr)

(a)


0005 0

-0005 -001

-0015 -002 TDVH 2x5

-0025 2x4 1x3

-003 0 10 20 30 40 50

time (hr)

(c)


0005 0

-0005 -001

-0015 -002 TDAH 2x5

-0025 2x4 1x3

-003 0 10 20 30 40 50

time (hr)

(b)


0005 0

-0005 -001

-0015 TEM 2x5-002

-0025 2x4

-003 0 10 20 30 40

time (hr)

(d)


50



003 003

0025 0025

002 002

0015 0015

001 AP-0 AP- 005

001 IDA4-1 2x5

0005 itP =010 AP-015 0005 1 2x4 1x3

0 i I I i 0 i 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)



003 003

0025 0025

002 002

0015 0015

001 -MINH 2x5 001

0005 2x4 1x3 0005

0 1 1 1 0

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)




0 0

-0005 APdeg AP= 005 -0005 TDVH 2x5

-001 AP- 010 AP- 015 -001 2x4 1x3

-0015 -0015

-002 -002

-0025 -0025

-003 -003 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(a) (b)



0 0

-0005 TDM- 2x5 -0005 MAC 2x5

-001 2x4 1x3 -001 2x4

-0015 -0015

-002 -002

-0025 -0025

-003 -003 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)




00035 - 00035 -0003 - 0003

00025 00025 -0002

00015 0001 TCMI 2x5

00005 2x4 1x3

0 50 0 10 20 30 40 50

time (hr)

(a) (b)



00035 00035 0003 0003

00025 00025 0002 0002

00015 00015 0001 0001

00005 00005 0 0

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)


131






















0 -00001 -00002 -00003 A- AP = 0 -0 0004 AP= 005 -00005 AP= 010 -00006 -00007 AP=015 -00008

0 500 1000 1500 2000 2500 3000 time (min)

(a)


0 -00001 -00002 -00003 -00004 -00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)


0 -00001 --00002 T -00003 -00004 --00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)

(b)


0 -00001 1--00002 + -00003 4 -00004 -t--00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)



0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)

(a)


0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)


2x400003 J-lx300002 4-

00001 0

-00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)

(b)


0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)



000005

0

-000005 AP = 0 AP = 005-00001 AP= 010

-000015 AP= 015

-00002 0 500 1000 1500 2000 2500 3000

time (min)

(a)


000005

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)


000005

0

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)

(b)


000005

0

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)



500 1000 1500 2000 2500 3000 time (min)

(a)


0 -000001

0 500 1000 1500 2000 2500 3000 time (min)



0

-000001 0 500 1000 1500 2000 2500 3000

time (min)

(b)


000005 000004

000003 000002 -r 000001 VI

0

-000001 0 500 1000 1500 2000 2500 3000

time (min)


10

0001

00001 000001

90

-90

-180 000001

OP -0 4P =005 AP- 010 AP= 015

00001 0001 001


4P =0 AP= 005 AP- 010 AP= 015

00001 0001 001

Frequency (radmin)

(a)

01

10

0

0V

ac 1

0 O 0 0

CC

01

000001

20

10

O 0 0 S -10 0 c a -20 0

w -30 flo cc

-40 000001

AP- 005 AP= 010 AP= 015

00001 0001 001


AP= 005 AP= 010 AP= 015

00001 0001 001

Frequency (radm in)

(b)

01


10 10

01 =0I0

GI

1 01 1774) a= 3 iTDMI-10010 E 2x5 rozQ 0

0001 2x4 el a)

lx3 cc

00001 01

000001 00001 0001 001 01 000001 00001 0001 001 01 1


90 50

of 40 a)a

---tu 30 co cco 20 a)


-180 -20 000001 00001 0001 001 01 1 000001 00001 0001 001 01


(a) (b)


10 10

1

0

01 a)

a 001 E 2x5

2x4 0001

lx3

00001 01



01

90 50

S40 2x5

30 rn

2x4

1x3 20

210 0 -g 0

X10 cc

-180 -20 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


10

1

0

01 0

ma a fi 001

0001

00001 000001

90

rn

a)

a) -90

a

-180 000001

TDM-I

2x5

2x4

lx3


TDIVH

2x5

2x4

1x3


(a)

10

1

01 01

000001 00001

01

90 80

O 70 60

40 50

40 30

c 0 20 713 10

2 00 cca) - 1 0

-20 000001 00001


01


(b)

01


140







the 1x3 model











Weir length [m] 009 009 009 002

Weir height [m] 003 003 003 006

Volume holdup [1] 0301 0181 0741 0301

141





















lower in case 32c



(2x5) (2x4) (1x3) (2x5) (2x4) (1x3) (2x5) (2x4) (1x3)

T 24206E-04 15413E-03 35626E-02 56883E-05 11573E-03 14283E-02 46403E-05 13594E-03 31742E-02


XEOH 61717E-07 11827E-06 72673E-05 25819E-08 38742E-07 16468E-05 92104E-07 14047E-06 17848E-05



YAcOH 47334E-08 22850E-06 46167E-05 64134E-08 22165E-06 29649E-05 54052E-08 24397E-06 42173E-05

YEt0H 48963E-07 16300E-06 78916E-05 26729E-08 70829E-07 20844E-05 75289E-07 17309E-06 29040E-05



L 86334E-10 27762E-08 48216E-07 12360E-09 21860E-08 26573E-07 17252E-09 27603E-08 36756E-07

V 18824E-09 43611E-08 60301E-07 11625E-09 21731E-08 27373E-07 19103E-09 36782E-08 49566E-07

M 28172E-03 28172E-03 19939E-02 19775E-04 20413E-04 48878E-03 38266E-06 42605E-06 18753E-04

1Acoll 26856E-13 83250E-12 14633E-10 20313E-12 52102E-11 57418E-10 53902E-13 19199E41 28894E40


370 Case 32b

365 9 case 32a - -o- - case 32b

365 a TDVH


360 360 o 2x4

355

350

345

14

A AAA g 355

) 350

345

O 1x3

Ii 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)

370 Case 32c

370 Case 32d

365 TDVH

365 a TDVH

x 2x5 x 2x5

360 o 2x4 360 o 2x4

17a 355 o 1x3

a co 355 O 1x3

350

345 I I

350

345 i III ill ill 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



09

08 13- case 32a - - - - case 32b

09 -

08 --a- TDVH

07 A case 32c case 32d 07 - x 2x5

06 06 - o 2x4

05 05 - 0 1x3 04 04 -

03 03 -

02 02 -

01 01

0 0 ml( a 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)

Case 32c Case 32d 1

09 -a- TDMH 09 -e-1DtVH 08 08

07 x 2x5 07

$ 2x5

06 2x4 06 2x4 05 O 1x3 05 o 1x3 04 04

03 03

02 02

01 01

0 MK 0 al a 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



09 09 08 08 07 - 07 06 e 06




(a) (b)

Case 32c Case 32d 1


2x4 02 02o 2x4 0 1x301 01 0 1x3

0 0 Iiili11111 03

441 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)




0 ilf111 0 S- 1111111


(a) (b)


09 09 08 -8- TCM-I -9-11)Virl08 07 x 2x5 07- x 2x5 06 062x4 2x4 05 05

O 1x3 0 1x304 04 03 03 02 02 01 01

0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)




o 1x3 04 E 04 03 03 02 - 7 02 01 - A- 01

-0- -0 01111


(a) (b)


09 - 09-a- TDVH08 08

07- x 2x5 07 06 - 06p 2x4 05 S 05

0 1x304 - 04 03 - 03 02 - 02 01 - 01

0 0 11111111111 1


(c) (d)


035

03

025

02

015

01

005

0 0

035

03

025


Vapor


a case 32c + case 32d11111111111 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a) Case 32c

Vapor


01 TDM-I x 2x5

005

0 0

2x4 o 1x311111111111 1 2 3 4 5 6 7 8 9 10 11

Stage number 12

(c)

Case 32b 035

03 Vapor 025 -

02 IF_

015

01

005 -

0 0

035

03

025

02

015

01

005

0 0

Liquid

11111111 1 2 3 4 5 6 7 8

Stage number

(b) Case 32d

1 2 3 4 5 6 7 8 Stage number

(d)

-9- TUC x 2x5

2x4

0 1x3

9 10 11 12

9 10 11 12



40 35 30


- -0- - - case 32b

+ case 32d

25

20 15


5

0 1 2 3 4 5 6 7 Stage number

8 12

(a)

45 40 35 30 25 20

a IDNI-1 x 2x5

o 2x4

o 1x3

Case 32c

15

10

5 0

0 1 2 3 4 5 6 7 Stage number

8 9 10 11 12

(c)

45 Case 32b

40 35 30 25 20 15 10

5

0 0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)

45 Case 32d

40 35 30 25

20 15 10

5 0

0 1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(d)




t 0005 - g 0005 2x4

O 1x3E SI 0003 - Cn 0003

0001 - 0001 TT El 19

-0001 -0001



0011 0011

0009 B-- MAC 0009

0007 - x 2x5 -2- 0007

E 0005 -0 o

o

2x4

1x3 0005

EDI 0003 - c7) 0003

0001 - 0001 III En CI

-0001 -0001


(c) (d)


151















used







152




products was larger





















051

049 c 02 -

047 045 015

043 E 01

041 039 037

- case 32a

case 32c

case 32b


case 32c

case 32b

case 32d 035 0

0 10 20 30 time (hr)

40 50 0 10 20 30 time (hr)

40 50

(a) (b)



037 006 c 035 -0 005

033 1 004 o deg 031 cd 003 _

12= 029 - case 32a case 32b 002



case 32b case 32d

025 0 L

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)



001 Case 32b

0005 0

c 0005 0

0 -0005 k b -0005 -001 o -001

-0015 E -0015 -002 case 32a case 32b o -002


-003 v -003 2x4 1x3

-0035 -0035 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(a) (b)


0005 0005 o 0 0

-0005 -0005

o -001 -001 E -0015 -0015 o o -002

- 0025 TDVH 2x5

-002 -0025

1DM-I 2x5

s -003 - 2x4 1x3 -003 2x4 1x3

-0035 -0035 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)



0035 Case 32b

003 g 003 TDA11 2x5 0025 I 0025 2x4 1x3

002

0015 ----___--- _____ -- ebe 0020 E 0015


0005 case 32c case 32d gt0 0005 13

0 f I I 0 1 1 1 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)

Case 32c Case 32d 0035 0035

g 003 TDM-1 2x5 003 TEM-I 2x5

a 0025 2x4 1x3 0025 2x4 1x3

m 0020 002

E 0015 0015 cG1 001 001 gt0 0005 0005 13

0 I I t 1 0 1 1 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)



0005 Case 32b



O -001 - 2x4 1x3

0-0015 ro

-002

-0025 -0025

0 10 20 30 time (hr)

40 50 0 10 20 30 time (hr)

40 50

(a) (b)

Case 32c Case 32d 0005 0005

0 0 0

-0005 TDIVI-1 2x5 -0005 111vH 2x5

O -001 2x4 1x3 -001 2x4 1x3

o -0015 -0015

-002 -002

-0025 -0025 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)



0007 Case 32b


o 0003 E 0003 _

c 0002 o

laquo- 0002 W

0001 gt0 0001 11

0 r-411egel7 I I I

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)

Case 32c Case 32d 0007 0007

5 0006 0006 TIM-I 2x5 V 0005 0005 2x4 1x3 w 00040 0004

E 0003 C

0003

0002 TI341-1 2x5 0002 es

0001 2x4 1x3 0001

0 i 1 i

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)


158











large plates











00002 Case 32b

0 0

-00002 -00002 -- 00004 case 32a m -00004 -


-00012 -00012 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

00002 Case 32c

00002 Case 32d

0 0

-00002 -00002

-00004 -00004 TEM -00006 -00006 2x5 -00008 -00008 2x4

-0001 -0001 lx3 -00012 -00012

0 10 20 30 40 0 10 20 30 40 50 time (hr) time (hr)

(C) (d)



00012 Case 32b

0001 - case 32a 0001

00008 case 32b 00008

00006 case 32c 00006

00004 - case 32d 00004

00002 00002

0 -4 0

-00002 -00002 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

Case 32c Case 32d 00012 00012

0001 0001 TUC 00008 00008 2x5 00006 00006 2x4 00004 00004 lx3 00002 00002

0 0

-00002 -00002 0 10 20 30 40 0 10 20 30 40 50

time (hr) time (hr)

(C) (d)




000005

0

-000005

-00001

-000015 0 10 20 30 40

time (hr)

(a)

Case 32c 000015

00001

000005

0

-000005

-00001

-000015 0 10 20 30 40

time (hr)

(C)

000015

00001

000005

Case 32b

TDAH

2x4

2x5

1x3

0 i 1 impoomponn

-000005

-00001

-000015 0 10 20

time (hr) 30 40

(b)

000015 Case 32d

00001 -

000005

TDIVH

2x4

2x5

1x3

0

-000005 -

00001 -

-000015 0 10 20 30

time (hr) 40 50

(d)



case 32c 000003 000003

case 32d 000002 000002 000001 000001

0 0

-000001 -000001 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

000007 Case 32c

000007 Case 32d

000006 TDIVH 000006 000005 2x5 000005 000004 2x4 000004 000003 lx3 000003 000002 000002 000001

000001 0

0 -000001

0 10 20 30 40 -000001

time (hr) 0 10 20 30

time (hr) 40 50

(C) (d)


10

0001

00001 000001

90

-180 000001

case 32a

case 32b

case 32c

case 32d


case 32a

case 32b

case 32c

case 32d


(a)

01 1

01

10

0

V ac 1

a)

cc

01

000001 00001

80

60 cn 4140

SI 20

63 0

120 o--40 0-60

1E)-80

-100 000001 00001


case 32b

case 32c

case 32d

01


(b)

01 1


10 10

1 0

0

01 V

o 001

E

0001

TD 1-i

2x5

2x4

lx3

113

V

CC

00001 000001 00001 0001 001


01


01

90 250

200 2x5

V Ilk 150

ca) 100

2x4

lx3

a) -90 C)

a=-180

TDA1-1

2x5

2x4

lx3

S 50 c a 0 To

-50

m-100

-270 000001 00001 0001 001


-150 000001 00001 0001 001


(a) (b)


10 10

2x5 1 2x4

1x3

TDVH E4

0001

2x5

2x4

00001 lx3

01



01

90 20

Si0 013 0 m c0 0 -90 c a

-180 000001

TDMI 2x5

2x4

lx3


01 1

s 15 as0 10 0 1n 5 c0 0 o c so -5as

deg -10-10 co =

-13 -15 0 0 -20 CE

-25 000001 00001 0001 001


(a) (b)


10 10

0

0

01

-enV

V 001 TUC E

ao

E

0001

2x5

2x4

lx3

V 0 cc

00001 01 000001 00001 0001 001



90 80

rn 0

TDV1-1

2x5

2x4 1x3

rn 70

43 60 O 50 of g 40 S 30

o c 20 To 10 13 00

-10

2x5

2x4

1x3

-270 -20 000001 00001 0001 001



(a) (b)


167







holdups (CMH)














model

168







169

BIBLIOGRAPHY












170














171










172

APPENDICES

173

APPENDIX A



Species Tc V Z

[K] [cm3gmol]

AcOH 5944 171 02

EtOH 5162 167 0248

Water 6473 56 0229

AcOEt 5232 286 0252





Species Aj 13j

AcOH -242129 20142

EtOH -300324 475

Water 0 04077

AcOEt -498159 1031


Normal Heat of



571 3911 5660

63 3515 9260

2176 3732 9717

378 3503 7700


Cj Dj EJ

28033x10-2 -01136x10-4 00020x10-6

25030x10-2 -08263x10-5 11975x10-9

36657x10-3 00615x10-4 0

30495x102 -53900x106 0

174



3

1-


+ aap6

AcOH EtOH

Ao (1gmol)2atm 1004538 686619

Bo lgmol 006519 005087

Co (1gmo1)2K2atm 3121503 1605577

ao (1gmo1)3atm 15616 084012

bo (1gmo1)2 002703 001674

Co (1gmo1)3K2atm 8087892 3279836

ao (1gmo1)3 0001601 0000781

yo (1gmo1)2 004365 002704


Water

1175617

008668

2828098

242981

004778

9748118

0003763

007717

AcOEt

311069

001856

1141020

013766

000219

8428061

369E-05

000354


log = A + C


Species Adeg Bdeg

AcOH 75596 164405

EtOH 783124 144052

Water 796681 166821

AcOEt 709808 123871


Cdeg

233524

21271

228

217

175



A -05543 0581778 0688636 -006014

A2 -032436 0209245 0024303 0229575

A3 -010369 -025733 0375534 186575

A4 -070546 -056264 127548 0355191

A5 -201335 -031485 177863 0468416

A6 -225362 0451732 0696279 15111

A7 0837926 -011541 0936722 -005997

A8 052376 0069531 0449357 0067399

A9 0434061 0074053 071779 -315997

A10 -053406 018701 144979 0941858

A -325231 -036999 -211099 -192225

Al2 590329 -008234 0746905 -075573

A13 3354 -040947 112914 103791

A14 0197296 109247 0120436 0365254

A15 -045266 0192416 -164268 -136587

A16 0014715 -017257 0330018 -213818


176

APPENDIX B







177

Start
















Continue simulation


178







at each plate






No




C Stop


179

APPENDIX C






0 0000 0003 0017 0001 0003 1 0032 0046 0041 0006 0024 2 0159 0205 0258 0172 0174 3 0167 0203 0261 0146 0156 4 0169 0201 0267 0129 014 5 0173 0200 0267 0119 0128 6 0188 0206 0267 0103 0119 7 0216 0278 0314 0118 0145



0 0649 0693 0752 0543 0539 1 0741 0734 0755 0633 0617 2 0649 0638 0583 0579 0576 3 0653 0634 0579 0551 0545 4 0677 0631 0573 0529 0521 5 0723 0630 0572 0516 0504 6 0659 0626 0572 0512 0496 7 0386 0573 0518 0482 0471

180



0 0067 0090 0115 0043 0048 1 0067 0100 0100 0076 0077 2 0070 0084 0089 0100 0100 3 0070 0088 0089 0121 0121 4 0075 0092 0090 0138 0138 5 0079 0096 0090 0156 0155 6 0077 0102 0087 0191 0179 7 0364 0099 0097 0238 0240



0 0284 0214 0116 0413 0411 1 0160 0121 0104 0289 0282 2 0122 0073 0070 0149 0150 3 0110 0076 0070 0183 0179 4 0089 0077 0071 0204 0201 5 0086 0074 0071 0208 0213 6 0076 0066 0071 0194 0206 7 0034 0050 0070 0162 0144

ACKNOWLEDGEMENTS












TABLE OF CONTENTS

Page

1 INTRODUCTION 1















Page










BIBLIOGRAPHY 169

APPENDICES 172




LIST OF FIGURES

Figure Page



















Figure Page
















Figure Page


















Figure Page


















Figure Page




















Figure Page



LIST OF TABLES

Table Page



















Table Page








Figure Page




Table Page










LIST OF NOTATIONS













f Feed stage

f Fugacity [atm]









11) Weir height [m]






1 Weir length [m]















t Time [min]


















Greek symbols












Subscripts

B Bottom product



F Feed stream

1 Liquid phase


v


S Stripping section

Vapor phase


I INTRODUCTION




acetate













2






















3




















models were studied



4




















5




















6









du = f (uv t)

dt

0 = g(u v t)







solution vector u

7




in this work














8

s=0

s=1

s=2

s=M-1

s=M

S=M+1



m+1

1)-(St)= (S)1(Snt) 1 ltslt M+1 (1-2) n=1



Sk n = 0m (1-3)Wnl(s)

kVn Sn Sk k

m +1 S k n = 1m+1 (1-4)Wnv(S)

k=1 Sn Sk ktn




9



N





(a+Dx(13+1)N-xw(x a 13 N) - (1-6)x(N x)











10





















11























12













13









the liquid phase







14








aA + bB H cC + dD


VAA + VBB + VCC + VDD = 0 (2-1)

where





15

Condenser


dt

dt dM0

nr

LOLo (2-2b) 1=1


dt

Internal Stages

dM + + FX

dt (2-3a) +

dM nc

V F Vi W + (2-3b)dt j=1


dt

Reboiler


dt

nc dMN+1



16

D


17

Hw Xwj



i=N VN+1 HN+1 YN+1j

QR LN hN XNj

B hB xBd i=N+1


18


(2-5)1iA =





by




(2-8)



19






Id(TE (2-10)

n

(2-11)ij 1=1






dMik dhi (2-12)

dt dt

20



as




The result is

nc dx EK

dTi 1=1 dt nc (2-14)

dt dK E x

1=1 dT


_ -nc di ci



-di1=1




21






dt aT dt axm dt


n dK cbcii I M x



n cbcij x-n`






22


23

F


24




i +1 n i+1 dhk


Li (2-20) (h 11+1)

i+1 I n

= Li + Ft B+ (2-21) k =N +l j=1

i = NN-110


holdups

n







25











described in Sec221




qi =lk owi

(2-24a)


26

how Eqn (2-25) vi h

Li

A

1


27







how jY2qt = 36815 (2-24b)t

048F

how is defined by

(

M (2-25)

r7r Ceol4)Pi



and (2-4b) become




28





n dhN+1


VN+1 (2-28)(Hi+ h8)


(2-29) J=1




H1

i = (NN-12)





171 (2-31)(H1 ho


29


=1 dt





(2-24)











30

i=0

D

V1 Hr

hi

1

VF YFI HE

(1-OF xF

i=mi+m2+3



B


31

Condenser


dM0 -dt

- Vo Lo D + j =1



dM dt

dM n

-v + dt 1=1

dM ihi + L h L hdt







(2-33a)

(2-33b)

(2-33c)

(2 -34 a)

(2-34b)

(2-34c)

(2-35a)

(2-35b)

(2-35c)

32





dt J=1



Reboiler


BXB Vi rimi +3 A

dM n morm2+3



BhB QR






33


remain unchanged



















34




35



Chapter Two









311 Enthalpies


n


n

Hi =I yi H(7) (3-1b) i=1

36




H (TO = Ai + B + C + D + E iTi4 (3-2b)


= x (To Pi) (3-3a)

Hi =1 i(Ti Pi) (3-3b) J=1


procedures

Enthalpies of Vapor



37




_RT2( din f (3-5) aT )p





T2 (3-6)







T2 deg v

38


F (Pvk) (3-8)Pvk+1 = P

vk F(pvk)








thesis




= Hsi(Ti) A1(T) (3-10)


39


038 1 T T

where Tr = (3-11)A(7`)=7 A 1Tr




such as

Ki(T)=Oi + AT+ of T2 -F ei T3 (3-12)






j0

(3-13)



Appendix A

40

Bcit















F(T)=[Ixi jE1Ki(TP)]-1= 0 (3-16) i=1

41


F(Tk) (3-17)Tk+1 = Tk PAK)











Z (1 K (TF PF ))F(1)= L o (3-19)

=1 + ty(K (TF PF ) 1)

42





zi





=ExiJP(Ti) (3-21)





where r = T (3-22)T

43







Simplified model

Liquid enthalpy



dh dh = x (3-23)

dT

dT


(3-25)

44




dki +28T + 3E 72 (3-26)

dT dT




apo dpij (3-27)


dT dT 7 j(i_Trf

n axik 1i (3-29)

aXij k=1 j

45

Rigorous model

Liquid enthalpy







(3-30)

Thus



0

B + T +3D T2 +4E T3 (3-32)


46



T3 YPv


dA 038 A (3-34)

dT (T T)






ln(10) kJ (3-35) aT (T + C

9K1 Po1I (3-36)

dx dx





47



(-rA) = [k(7)][ fn( CA CB )1 (3-23)





M j as follows


= [k(T)C = k(T)MiX (3-24)



48



(3-26)







x=s-1 N=M-1

(N n)(n +a+1)(n+a+ 3+1)An (3-27)

(2n + a + 13 + 1)2

n(n+ I3)(N + n+ a + 3 +1) B (3-28)(2n + a + 11)2

where

(a)k = 0 k = 0

(a)k = (a)(a+1)(a+k-1) kgt 0

49


Q0(xa P N) =1 (3-29)

(a+ 0+2)xQi(xa P N) 1 (3-30)Ma +1)











requirements



50


set of equations



required accuracy









51







of ethyl acetate

A + B H C + D













52


Design Variables






AcOH zA 02559

Et0H zs 06159

Water zc 00743

- AcOEt zD 00539




Weir length [m] 006











53

N+1

(Ai )2







xitcoH 11893E-03 66924E-03 28242E-03 16359E-03

xEtolf 61785E-03 98927E-03 16722E-02 18820E-02

xwater 92009E-03 94784E-03 53772E-03 49359E-03

XAcOEt 13209E-03 47090E-03 12271E-02 11779E-02









results



0 1 2 3 4 5

Stage number


0 1 2 3 4 5 6 7

Stage number



0 0 1 2 3 4 5 6 7

Stage number



0 0 1 2 3 4 5 6 7

Stage number


55























Topic of studies

Physical

approximation

Numerical

approximation

Number of stages

Type of reaction

Thermodynamic

model

Pressure in the

column

Example 1



model assuming



reduced-order TDMH

model

8

irreversible

( 2A ---gt R + S )

simple

uniform (1 atm)

Example 2


order model in a

column with many

stages

reduced-order TDMH

model

29

rigorous

uniform (1 atm)

Example 30


order model in a

column with fewer

stages

-

reduced-order TDMH

model

11

Example 31


order model in a



assuming uniform

pressure

full-order TDMH

model assuming that


is uniform

reduced-order TDMH

model

11

reversible


rigorous rigorous


column

Example 32


on steady-state and

dynamic behaviors

full-order TDMH

model using various

plate geometries

-

11

rigorous

uniform (1 atm)

57


be observed

58

5 EXAMPLE PROBLEM 1






2A gt R + S


(-17A) = kACA

where






A 11000 + 30T 4000 + 30T 001Ts 10699 275 02

R 20000 + 20T 15000 + 20T 002T 11651 090 0229

S 25300 + 10T 25000 + 10T 003T 9418 459 0252

T is in degF

59


Design Variables






A 08

R 01

S 01















60







2x2 lx1


11835 20000

0 = condenser 28165 40000



61835 70000


9 = reboiler 90000






solutions

61

60

55

50

45

40

35

30 0

60

55 C Of 41) 50

I a 45 m ei n 40 I i 35

30 0

60

55 ii Oi a) 50 73

12a 45 co

isoo 40 i

35

30 0


1 2 3 4 5 6

Stage number

(a)


(b)

i I i i i 1


(c)

B TDMH - - -0- - CM H

7 8

B TDMH gt 2x2

O 1x1

7 8

--B CM H 2x2 o 1x1

I

7 8

9

9

9


62


09 -08 07 --e-- TDMH 06 -0- CMH 05 04 03 02 01

0 Ulf

0 1 2 3 4 5 6 7 8 9

Stage number

(a)

1

09 08 07 06 05 04 03 02 01

0 0 1 2 3 4 5 6 7 8 9

Stage number

(b)

1

09 08 8 CM H 07 2x2 06 - 0 1x1 05 04 03 02 01


0 1 2 3 4 5 6 7 8 9

Stage number

(c)


63

1

09 -08-07 06 05 04 -03-02 -01

0 0

1

09 08 07 -06 -05 04 03 02 01 -

0 0

1

09 08 07 06 05 04 03 02 01

0 0


1I I I I I

1 2 3 4 5 6

Stage number

(a)

1 2 3 4 5 6

Stage number

(b)

t 1 I 1

1 2 3 4 5 6

Stage number

(c)

$ TDMH CMH

1 1

7 8 9

--e TDM H o 2x2

0 1x1

7 8 9

9-- CM H 2x2

0 1x1

7 8 9


64


09 08 07 06 05 04 03 02 01

0 0

I

1

i

2 3

I

4 I

5 6

p TDMH

CMH

7 8 9

Stage number

(a)

1

09 08 07 06 05 04 03 02 01

0 0

I

1

I

2 3 4 5 6

e TDMH 2x2

O 1x1

7 8 9

Stage number

(b)

1

09 08 07 06 05 04-03 02 01

0 0

I

1 2 3 4 5 6

--eCMH 2x2

O 1x1

7 8 9

Stage number

(c)


65


700

600

500

400

300

$ TDMH CMH

200

100

0 0 1 2 3 4 5


(a)

800

700

600 Vapor

500

400

300

200

Liquid

9 TDM H 2x2

O 1x1

100

0


6 7 8 9

(b)

800

700

600 Vapor

500

400

300

200

Liquid 8CMH

2x2

O 1x1

100

0 0

F

1

f

2 I

3 I I

4 5 Stage number

i

6 I

7 i

8 9

(c)


66





TDMH CMH

(2x2) (1x1) Full (3x3) (2x2) (1x1)

T (degF)2 75654E-05 32486E-02 64722E-02 59785E-05 18506E-02

XA 18871E-07 28772E-05 97558E-05 20379E-07 29484E-05

XR 37528E-07 18061E-04 90993E-05 45029E-07 90603E-05

xs 90549E-08 11304E-04 22755E-06 99641E-08 44224E-05

L (lbmolmin)2 16683 3641945 317355 23006 2405854

V (lbmolmin)2 16822 3058993 317355 34804 2278430









67























68






model










69


003

0025

002 0015

001

0005

TDMH

CMH

0 0 10 20 30

time (min)

40 50

(a)

0035

003

0025

002

0015

001

0005

TDMH

2x2 1x1

0 0 10 20 30

time (min)

40 50

(b)

0035

003

0025

002-0015

001

0005

0 0 10 20 30 40

CMH 2x2 1x1

50

time (min)

(C)


70


-001

-002

TDMH

CMH

-003

-004 _ _ _

-005

-006 0 10 20 30

time (min)

40 50

(a)

I I I I

-001

-002

-003

TDMH

2x2 1x1

-004

-005

-006 0 10 20 30

time (min)

40 50

(b)

-001

-002

CMH

2x2 1x1

-003

-004

-005

-006 0 10 20 30

time (min)

40 50

(c)


71


002 _-____

0015

001

0005 TDMH

CMH

0 10 20 30

time (min)

40 50

(a)

0025

002

0015

001

0005

TDMH

2x2 lx1

0 10 20 30

time (min)

40 50

(b)

0025

002

0015

001

0005

CMH

2x2 1x1

0 10 20 30

time (min)

40 50

(c)


72




xA initial 00858 00859 00829 01041 01042 01009

final 01160 01160 01138 01248 01248 01212

XR initial 08237 08237 08257 08040 08040 08077

final 07706 07706 07705 07614 07614 07647

xs initial 00905 00905 00914 00919 00918 00915

final 01135 01134 01158 01138 01138 01141


Model Relative time

TDMH Full (3x3) 1

2x2 08972

lx1 06576


2x2 06150

lx1 04706






73



















behavior

74


0 1 2 3 4 5 6 7 8 9

stage number













75


001

0008

0006

0004

0002

0 0 10 20 30 40 50 60

time (m in)

(a)

0012

001- MAC 2x2

0008 1x1

0006

0004

0002

0 0 10 20 30 40 50 60

time (min)

(b)

0012

001

0008

0006

0004

0002

0 0 10 20 30 40 50 60

time (m in)

(C)


76


-0002 -0004 -0006 -0008 -001

-0012 -0014 -0016 -0018 -002

0 10 20 30 40 50 60

time (m in)

(a)

0 -0002 -0004 -0006 -0008

-001 -0012 -0014 -0016 -0018

-002 0 10 20 30 40 50 60

time (min)

(b)

0 -0002 -0004 -0006 -0008

-001 -0012 -0014 -0016 -0018

-002 0 10 20 30 40 50 60

time (m in)

(C)


77


0007 0006 TUC 0005 CM-I 0004

0003

0002

0001

0 0 10 20 30 40 50 60

time (min)

(a)

0008

0007 0006

0005 0004

0003 0002

0001

0 0 10 20 30 40 50 60

time (min)

(b)

0008

0007 0006

0005 0004

0003 0002

0001

0 0 10 20 30 40 50 60

time (m in)

(c)


78



fractions




















001 10

0

v 0001 0 E

TDMH

CMH

00001 000001 00001 0001 001


01

000001 00001 0001 001


20

10

-90 TDMH

CMH

-180 000001 00001 0001 001 01 1

Frequency ( radmin)

0

-10

CMH

000001 00001

(a)


0001 001

Frequency (radmin)

01

(b)


10

2x2 1x1

1

01

00001 0001 001 01 000001 00001 0001 001 01


90 10

2x2 1x1

0

-90 TDMH

2x2 1x1

-180 -10 000001 00001 0001 001 01 000001 00001 0001 001 01 1


(a) (b)


001 10

CMH

2x2

1x1

00001 01

000001 00001 0001 001 01 1 000001 00001 0001 001 01


10

0

-90 CMH

2x2 1x1

-180 -10 000001 00001 0001 001 01 1 000001 00001 0001 001 01 1


(a) (b)


82



















83

6 EXAMPLE PROBLEM 2







Design Variables







AcOH zA 04962

EtOH zs 04808

water zc 00229

AcOEt zD 0








84












8x16 7x14 6x12 4x9 3x6


10003 10036 10209 12230 15649

0 = condenser 20129 20873 22952 35293 50000

10 = vapor feed stage 31068 34290 40295 64707 84351

43453 50000 59705 87770 100000

56547 65710 77048 100000

68932 79127 89791

79871 89964 100000

89997 100000

100000

85


8x16 7x14 6x12 4x9 3x6


120000 120000 120005 120210 122214


30 = reboiler 140008 140282 142129 152490 183980

150112 151682 157096 177252 226020

160676 165036 174991 205000 263291

172205 180226 194781 232748 287786

184815 196607 215219 257510 300000

198183 213393 235009 276750

211817 229774 252904 289790

225185 244964 267871 300000

237795 258318 279742

249324 269718 289995

259888 279984 300000

269992 290000

280000 300000

290000

300000







86




8x16 7x14 6x12 4x9 3x6

T (K)2 34681E-06 61907E-06 99419E-06 78225E-05 77447E-03

XAcOH 40090E-11 25666E-10 10937E-09 52778E-08 79956E-06

xEioll 34920E-09 56707E-09 89310E-09 47621E-08 40108E-06

Xwater 18735E-09 37718E-09 63574E-09 26774E-08 86463E-07

XAcOEt 86031E-09 13058E-08 16382E-08 53505E-08 85873E-07

YAcoH 29980E-11 14345E-10 58830E-10 11738E-07 18645E-05

YEt0H 67593E-09 96737E-09 12643E-08 76121E-08 80113E-06

Ywater 24000E-09 47672E-09 80790E-09 45331E-08 19307E-06

YAcOEt 15738E-08 22710E-08 27523E-08 82866E-08 16307E-06

L (gmolmin)2 14936E-10 24385E-10 60968E-10 25848E-09 13842E-07

V (gmolmin)2 43025E-09 40383E-09 60686E-09 70445E-09 14962E-07

M (gmol)2 42749E-07 31854E-06 25227E-05 61481E-04 21716E-03




(gmolmin)

Full (9x18) 0014071

8x16 0014071

7x14 0014069

6x12 0014067

4x9 0014063

3x6 0014038



0 3 6 9 12 15 18 21 24 27 30

Stage number



0 3 6 9 12 15 18 21 24 27 30

Stage number

1

09 c 08 ot 07 E 06 e 05 oE 04 a 03 3 02

01 0

0

1

09 08 07 06 05 04 03 02 01

0 0


- full A 6x12

o 4x9 x 3x6

iiiii isii 1 3 6 9 12 15 18 21 24 27 30

Stage number


3 6 9 12 15 18 21 24 27 30

Stage number




o) 365

E 25

20

a)

L

360

355 -

E o E

15

10

sect 350I-

0 E

5

0

345 5 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(a) (b)



03

025

02

vapor 19 17 -15 -13 -

0 4x9

p

x

6x12

3x6

015

01

005

0

liquid

4-1 I I I

full

o 4x9

I it N 1 4 I

p

x 6x12

3x6


s1 1 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(c) (d)


89









25

AcOH

EtOH

-

- - water_

1 05 _ - -- AcOEt

0 1

345 350 355 360 365 370

Temperature (K)






90








reduced models







in Figure 64



column

91



Full (9x18) 1

8x16 09715

7x14 08797

6x12 07190

4x9 05733

3x6 04794








stream






048

2 046

to - 044

E 042V 04

TEM 7x14 4x9

8x16 6x12 3x6

018

0175

017

0165

016

0155

IDVH 7x14 4x9

8x16 6x12 3x6

038 0 10 20 30 40 50 60 70 80

015 0 10 20 30 40 50 60 70 80

time (hr) time (hr)



04

038

036

0 034 3 7 032

TDM-I 7x14 4x9

8x16 6x12 3x6

g 0033 ra co 1- 0031

Edeg 0029

yor 0027

TDMI-1

7x14 4x9

8x16 6x12 3x6

03 0 10 20 30 40 50 60 70 80

0025 0 10 20 30 40 50 60 70 80

time (hr) time (hr)



09 - full p 6x12 08 07 o 4x9 x 3x6 06 05 04 03 02 01


Stage number


09 08 07 06 05

6x1204 - full p03 02 o 4x9 x 3x6 01

0 i I I I I I I I

0 3 6 9 12 15 18 21 24 27 30

Stage number


09 -08

full p 6x12

07 o 4x9 x 3x6 06 05 04 03 02 -01

0 T 0 3 6 9 12 15 18 21 24 27 30

Stage number


09 08 full A 6x12 07 06 0 4x9 x 3x6

05 04 03 02 01

0 I I I

0 3 6 9 12 15 18 21 24 27 30

Stage number


46

370

365

360

355

- full

Temperature profile

p 6x12

o 4x9 x 3x6

E

E 5 E


25 -20 -15-10 -

- full A 6x12

o 4x9 x 3x6

sect 350

345

-6 E cr)


5 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(a) (b)



03 19

025

02

vapor 17 15 13

015

01

005

0 1-

liquid

I 4 4 I

full o 4x9

I i l I III I

A

x 6x12

3x6

I I

11

9-7-5-3

0 3 6 9 12 15 18 Stage number

21 24 27 30 0 3 6 9 12 15 18 Stage number

21 24 27 30

(c) (d)


95
















68




00004

00002 0

-00002 -00004 -00006 -00008 -0001

-00012 -00014

00012

0001

00008

00006

00004

00002

0

-00002

-00004


time (hr)


time (hr)

000015

00001

000005

0

-000005

-00001

-000015

-00002

000006

000005

000004

000003

000002

0

000001 -0

-000001 0


10 20 30 40 50

time (hr)


10 20 30 40 50

time (hr)


10 10

1

01

13 001 1

c E 0001 TDIVI-1 8x16 8x16 7x14

00001 7x14 4x9

6x12 3x6

6x12 3x6

4x9

000001 01



01

90 60 IDN1-1 8x16 50

407x 14 6x12 30

4x9 3x6 T 20 20 5 10

0 2 -10 0

-20 8x16 7x14o -30 6x12 4x9-40 3x6cc -50

-180 -60 000001 00001 0001 001 01 000001 00001 0001 001 01 1


(a) (b)


98












for simpler columns

99

7 EXAMPLE PROBLEM 3










problem




column was studied








100


Design Variables







AcOH za 04962

EtOH zB 04808

water zc 00229

AcOEt zD 0




Weir length [m] 009

Weir height [m] 003








101


each model






98597 109356 120000 109913 120000 120000










102






column





(2x5) (2x4) (1x3)

T (K)2 60609E-05 13436E-03 29741E-02

XAeOH 35046E-08 10320E-06 17373E-05

XEtOH 73801E-07 12009E-06 16073E-05

xwater 23561E-08 13345E-07 46047E-06

Xite0Et 78982E-07 78798E-07 17033E-05

Y AcOH 53545E-08 23869E-06 40598E-05

Y Et0H 60827E-07 15434E-06 26427E-05

Ywater 25369E-08 30654E-07 59017E-06

YAcOEt 64649E-07 64980E-07 16455E-05

L (gmolmin)2 16799E-09 26341E-08 35570E-07

V (gmolmin)2 18206E-09 33777E-08 48041E-07

M (gmol)2 11613E-03 11617E-03 10803E-02




10 EMI Cl 0111111 1111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12



09 09 -a- MAC08 08 07 07 x 2x5 06 06 4 2x4 05 -s- TEAM 05

0 1x304 04x 2x503 03

o 2x402 02 01 O 1x3 01

0 011111111 1411 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12




TDM-I aTow 30 Y 365 x 2x5 25 x 2x5

360 2x4 20 2x4 E 070o 1x3 15 0 1x3

11 355 E10 IP EX

a 0 5g 350

1- rn 0 i

345 i i -51111 E

1



035 21

03 19 6 TDMH 17VaporE 025 x 2x5

8 15-2x402 13E


01 2x4 7-=005- 5o 1x3

0 3 il 111111 1 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)


105




2x5 0011345

2x4 0011343

lx3 0011364














106



Full (3x6) 1

2x5 09313

2x4 08556

1x3 06608


















0485 - 0145C TDVH0048 0475 1 014 2x5

IMF 2x4 047 0 0135

2x5 o lx3E0465 0132x4 733 lx3 5r 0125

046

0455 I I I045 012

0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)


0375 00295 037 -

00290365 -036 00285 TDVHTDVH

0355 2x52x5 0028 035 2x42x4

002750345 1x3lx3 034 0027 4 I I I

0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)


0

108






respectively














0 -00001 -00002 -00003 -- 00004 -00005 2x5 -00006 -00007

2x4

-00008 lx3 -00009

0 10 20 30 40 50

time (hr)


0 -00001

0 10 20 30 40 50

time (hr)


000008 000006 TDMr1 2x5

000004 2x4 1x3 000002

0 -000002 -000004 -000006 -000008

-00001 0 10 20 30 40 50

time (hr)


000003

0000025

000002

0000015 000001

0000005

0

-0000005 0 10 20 30 40 50

time (hr)


10 10

1

01

1

001 full

2x5

0001 2x4

lx3 00001 01

000001 00001 0001 001 01 000001 00001 0001 001 01 1


90

0

full -90 2x5

2x4 1x3

-180 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


10 10

2x5 1 2x4

0 1x3 0 s 01 0is c= 001 full Tx E4 2x5

0001 2x4

lx3 00001 01


90 10

clii0 ii 13

w 0 0to



c- 1 0 2x5


-360 -20 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


112






operations





column in each case

pressure atm) 2

18

16

14

12

1

08

06

0--AP=005 X--AP=OA

AP= 015

04

02

0 I I I l iti 0 1 2 3 4 5 6 7 8 9 10 11 12

stage number




113







Table 712



T (K)2 250357 1175582 4137036

xAcoH 61711E-05 21799E-04 45062E-04

xEroll 86611E-04 23323E-03 33668E-03

Xwater 10578E-04 35052E-04 71882E-04

XAcOEt 10156E-03 25721E-03 34075E-03

YAcOH 36414E-05 12001E-04 22977E-04

YEt0H 14054E-03 41997E-03 76426E-03

Ywater 10252E-04 32920E-04 67493E-04

YAcoEt 15273E-03 43664E-03 77664E-03

L (gmolmin) 2 33027E-06 19272E-05 80700E-05

V (gmolmin)2 32945E-06 19270E-05 80678E-05

M (gmol) 2 77791E-03 17231E-02 16933E-02

11AcOH (gmolmin)2 23729E-07 81195E-07 15842E-06



(2x5) (2x4) (1x3) (2x5) (2x4) (1x3) (2x5) (2x4) (1x3)

T 1035E-04 1426E-03 2166E-02 6500E-04 1982E-03 7342E-02 1339E-01 1352E-01 4376E+00

xAcoH 3449E-08 9791E-07 1516E-05 3483E-08 9113E-07 1324E-05 4424E-08 8416E-07 1161E-05

XEt0H 4048E-07 7949E-07 1783E-05 3143E-07 6492E-07 1769E-05 4013E-06 4320E-06 2098E-04

xwate 1055E-08 1436E-07 5492E-06 9188E-09 1514E-07 5428E-06 2914E-07 4453E-07 1212E-05

XAr0Et 3785E-07 3776E-07 2799E-05 2746E-07 2758E-07 2852E-05 5805E-06 5805E-06 2511E-04

YACOH 5878E-08 2296E-06 3546E-05 6219E-08 2153E-06 3092E-05 6902E-08 1982E-06 2702E-05

Y DOH 3397E-07 1107E-06 2434E-05 2647E-07 9055E-07 2223E-05 3398E-06 3928E-06 1891E-04



L 1259E-09 2441E-08 2874E-07 1710E-09 2253E-08 2670E-07 8557E-08 1044E-07 4197E-06

V 1283E-09 2963E-08 3925E-07 1497E-09 2656E-08 3329E-07 1008E-07 1231E-07 5191E-06

M 1064E-03 1064E-03 1077E-02 1052E-03 1053E-03 1086E-02 1306E-03 1308E-03 1878E-02

17awn 9882E-13 3055E-11 3667E-10 1565E-12 4471E-11 4994E-10 1379E-11 7137E-11 1149E-09


320 -4 310 300 -- 290 CI

CY

I t f

A

1 flAP=010

0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


1x3300 290 tIllli11111

2x4

0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(c)

390 380 370 360 350 340 330 320 310 300 290

0 f III-1111111 1 2 3 4 5 6 7 8 9 10 11

Stage number


9-- TDMH x 2x5 o 2x4 o 1x3

12

(b)

390 380 370 360 350 340 330 320 310 300 290

0 1111f-1-11111

2 3 4 5 6 7 8 9 10 11

Stage number


9 TDMH 2x5

o 2x4 o 1x3

1 12

(d)


- --

09 -08 07 -06 -05 -04 03 -02 -01

0 II 0

1

09 -08 07 06 05 -04 -03 02 01 -

0 0


--B--AP=0 - -AP= 005

A AP= 010 ---G---AP= 015

1111111 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


-B-TDMH 2x5

o 2x4 o 1x3

i BM El i I I I

1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(c)

1

09 -08 -07 -06 05 -04 -03 -02 01 -

0 0

1

09 08 07 06 05 04 03 02 01

0 0


-13-TDMH x 2x5

2x4

O 1x3

1111111 OE U 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)


1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(d)



AP = 00503 02 fi AP - 010 01 - - -G - -AP= 015

0 11111111111 O 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


09 08 07 06 05 -8- TDM H04 x 2x503

O 2x4 02 01 0 1x3

0 O 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(c)



09 -08 -07 -06 -05 - -9- TDM H04 - x 2x503 -

O 2x402 -01-

0 loi1x3i i I f iiii0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)


09 -08 07 06 05 -04 -9- TDMH 03 - x 2x5 02 - p 2x4 01 - 0 1x3

0 0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(d)



09 -09 - --B--AP=0 -e-TDMH0808 07 07 - x 2x5

A AP=01006 06 2x4 05 05 O 1x3 04 - 04 -03 - 03 02 - 02 -01 01 -

0 0 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)


0909 -08 - TDMH 08

07 x 2x5 07

06 o 2x4 06 0505 o 1x3

04 - 04

03 - 03 02 - 02 01 01111111110 0


(c) (d)



09 09--B--AP=0 -B- TDMH08 - 08 -07 - 07 2x5

A AP= 01006- 06 - 2x4 ---0---AP= 01505 05 O 1x3

04 04 -03 - 03 -02 02 01 01lilt0 0I


(a) (b)


09 - 09 08 - -9- TDMH 08 07 x 2x5 07 06 - 06o 2x4

0505 o 1x3 04 - 04 03 - 03 02 02 01 - 01

0 0Iflit 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



035

2r

03

025

02

015

01

005

-13-- AP = 0 AP = 005

A AP= 010 --0---4P= 015

03

025

02

015

01

005

0

03

025

02

015

01

005

Vapor


2x4 o 1x3111114-11111

03

025 B

02 g0

015 8 0

01

005

0 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(a) (b)



035

03

025

02

015

01 -

005

Vapor

c CI 113 Liquid

NION101 -B-TDMH

X 2x5 2x4

II 1x3 t I 0

03

025

02

015

01

005

03 -

025 -

02

015

01

005

O NID Liquid x 2x5

O 2x4 O 1x3

I I 114111+1-f

Vapor

- 8- TDMH

03

025

02

015

01

005

0 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(c) (d)



21


9 9 7 7 5

3 3111111111 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)


19 - 19 8 TDMH-8 TCM-I 17

g 15 x 2x5 -6 17 rA 15

2x5

a 13 o 2x4 cl 13 o 2x4

31- 11 - 0 1x3 12 11 1x3 c

9 c

9 co 03 75 E

7 5 111--0K 3 1 i 111111111

7 5 3 i i 111111111


(c) (d)




E0005o 0005 o 1x3E E 9 0003 0) 0003

0001 0001 III

-0001 -0001 i



0011 0011

e TDVH0009 0009 -x 2x5

0007 s 0007 o 2x4

t 0005 t 0005o 1x3 E E a) 0003 0)0003

0001

-0001 El OK 0 4 I I I

0001

-0001 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(c) (d)


123







(MSE=4376)
















124




3

25

2 MOH

15 EtOH

1 - - water

05 Ac0Et

0

290 310 330 350 370

Temperature (K)











125









results










case



048 047

02 - AP - 0 AP= 010

AP - 005 AP- 015

046 018 -045 044

016

043 014 042 AP = 0 AP= 005 012 -041 AP = 010 AP= 015 04 01

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)


036 006 035 005 --034 004 -033


03 001 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)



0005 0

-0005 -001

-0015 -002 APdeg AP=005

-0025 AP=010 AP=015

-003 0 10 20 30 40 50

time (hr)

(a)


0005 0

-0005 -001

-0015 -002 TDVH 2x5

-0025 2x4 1x3

-003 0 10 20 30 40 50

time (hr)

(c)


0005 0

-0005 -001

-0015 -002 TDAH 2x5

-0025 2x4 1x3

-003 0 10 20 30 40 50

time (hr)

(b)


0005 0

-0005 -001

-0015 TEM 2x5-002

-0025 2x4

-003 0 10 20 30 40

time (hr)

(d)


50



003 003

0025 0025

002 002

0015 0015

001 AP-0 AP- 005

001 IDA4-1 2x5

0005 itP =010 AP-015 0005 1 2x4 1x3

0 i I I i 0 i 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)



003 003

0025 0025

002 002

0015 0015

001 -MINH 2x5 001

0005 2x4 1x3 0005

0 1 1 1 0

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)




0 0

-0005 APdeg AP= 005 -0005 TDVH 2x5

-001 AP- 010 AP- 015 -001 2x4 1x3

-0015 -0015

-002 -002

-0025 -0025

-003 -003 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(a) (b)



0 0

-0005 TDM- 2x5 -0005 MAC 2x5

-001 2x4 1x3 -001 2x4

-0015 -0015

-002 -002

-0025 -0025

-003 -003 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)




00035 - 00035 -0003 - 0003

00025 00025 -0002

00015 0001 TCMI 2x5

00005 2x4 1x3

0 50 0 10 20 30 40 50

time (hr)

(a) (b)



00035 00035 0003 0003

00025 00025 0002 0002

00015 00015 0001 0001

00005 00005 0 0

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)


131






















0 -00001 -00002 -00003 A- AP = 0 -0 0004 AP= 005 -00005 AP= 010 -00006 -00007 AP=015 -00008

0 500 1000 1500 2000 2500 3000 time (min)

(a)


0 -00001 -00002 -00003 -00004 -00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)


0 -00001 --00002 T -00003 -00004 --00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)

(b)


0 -00001 1--00002 + -00003 4 -00004 -t--00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)



0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)

(a)


0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)


2x400003 J-lx300002 4-

00001 0

-00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)

(b)


0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)



000005

0

-000005 AP = 0 AP = 005-00001 AP= 010

-000015 AP= 015

-00002 0 500 1000 1500 2000 2500 3000

time (min)

(a)


000005

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)


000005

0

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)

(b)


000005

0

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)



500 1000 1500 2000 2500 3000 time (min)

(a)


0 -000001

0 500 1000 1500 2000 2500 3000 time (min)



0

-000001 0 500 1000 1500 2000 2500 3000

time (min)

(b)


000005 000004

000003 000002 -r 000001 VI

0

-000001 0 500 1000 1500 2000 2500 3000

time (min)


10

0001

00001 000001

90

-90

-180 000001

OP -0 4P =005 AP- 010 AP= 015

00001 0001 001


4P =0 AP= 005 AP- 010 AP= 015

00001 0001 001

Frequency (radmin)

(a)

01

10

0

0V

ac 1

0 O 0 0

CC

01

000001

20

10

O 0 0 S -10 0 c a -20 0

w -30 flo cc

-40 000001

AP- 005 AP= 010 AP= 015

00001 0001 001


AP= 005 AP= 010 AP= 015

00001 0001 001

Frequency (radm in)

(b)

01


10 10

01 =0I0

GI

1 01 1774) a= 3 iTDMI-10010 E 2x5 rozQ 0

0001 2x4 el a)

lx3 cc

00001 01

000001 00001 0001 001 01 000001 00001 0001 001 01 1


90 50

of 40 a)a

---tu 30 co cco 20 a)


-180 -20 000001 00001 0001 001 01 1 000001 00001 0001 001 01


(a) (b)


10 10

1

0

01 a)

a 001 E 2x5

2x4 0001

lx3

00001 01



01

90 50

S40 2x5

30 rn

2x4

1x3 20

210 0 -g 0

X10 cc

-180 -20 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


10

1

0

01 0

ma a fi 001

0001

00001 000001

90

rn

a)

a) -90

a

-180 000001

TDM-I

2x5

2x4

lx3


TDIVH

2x5

2x4

1x3


(a)

10

1

01 01

000001 00001

01

90 80

O 70 60

40 50

40 30

c 0 20 713 10

2 00 cca) - 1 0

-20 000001 00001


01


(b)

01


140







the 1x3 model











Weir length [m] 009 009 009 002

Weir height [m] 003 003 003 006

Volume holdup [1] 0301 0181 0741 0301

141





















lower in case 32c



(2x5) (2x4) (1x3) (2x5) (2x4) (1x3) (2x5) (2x4) (1x3)

T 24206E-04 15413E-03 35626E-02 56883E-05 11573E-03 14283E-02 46403E-05 13594E-03 31742E-02


XEOH 61717E-07 11827E-06 72673E-05 25819E-08 38742E-07 16468E-05 92104E-07 14047E-06 17848E-05



YAcOH 47334E-08 22850E-06 46167E-05 64134E-08 22165E-06 29649E-05 54052E-08 24397E-06 42173E-05

YEt0H 48963E-07 16300E-06 78916E-05 26729E-08 70829E-07 20844E-05 75289E-07 17309E-06 29040E-05



L 86334E-10 27762E-08 48216E-07 12360E-09 21860E-08 26573E-07 17252E-09 27603E-08 36756E-07

V 18824E-09 43611E-08 60301E-07 11625E-09 21731E-08 27373E-07 19103E-09 36782E-08 49566E-07

M 28172E-03 28172E-03 19939E-02 19775E-04 20413E-04 48878E-03 38266E-06 42605E-06 18753E-04

1Acoll 26856E-13 83250E-12 14633E-10 20313E-12 52102E-11 57418E-10 53902E-13 19199E41 28894E40


370 Case 32b

365 9 case 32a - -o- - case 32b

365 a TDVH


360 360 o 2x4

355

350

345

14

A AAA g 355

) 350

345

O 1x3

Ii 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)

370 Case 32c

370 Case 32d

365 TDVH

365 a TDVH

x 2x5 x 2x5

360 o 2x4 360 o 2x4

17a 355 o 1x3

a co 355 O 1x3

350

345 I I

350

345 i III ill ill 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



09

08 13- case 32a - - - - case 32b

09 -

08 --a- TDVH

07 A case 32c case 32d 07 - x 2x5

06 06 - o 2x4

05 05 - 0 1x3 04 04 -

03 03 -

02 02 -

01 01

0 0 ml( a 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)

Case 32c Case 32d 1

09 -a- TDMH 09 -e-1DtVH 08 08

07 x 2x5 07

$ 2x5

06 2x4 06 2x4 05 O 1x3 05 o 1x3 04 04

03 03

02 02

01 01

0 MK 0 al a 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



09 09 08 08 07 - 07 06 e 06




(a) (b)

Case 32c Case 32d 1


2x4 02 02o 2x4 0 1x301 01 0 1x3

0 0 Iiili11111 03

441 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)




0 ilf111 0 S- 1111111


(a) (b)


09 09 08 -8- TCM-I -9-11)Virl08 07 x 2x5 07- x 2x5 06 062x4 2x4 05 05

O 1x3 0 1x304 04 03 03 02 02 01 01

0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)




o 1x3 04 E 04 03 03 02 - 7 02 01 - A- 01

-0- -0 01111


(a) (b)


09 - 09-a- TDVH08 08

07- x 2x5 07 06 - 06p 2x4 05 S 05

0 1x304 - 04 03 - 03 02 - 02 01 - 01

0 0 11111111111 1


(c) (d)


035

03

025

02

015

01

005

0 0

035

03

025


Vapor


a case 32c + case 32d11111111111 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a) Case 32c

Vapor


01 TDM-I x 2x5

005

0 0

2x4 o 1x311111111111 1 2 3 4 5 6 7 8 9 10 11

Stage number 12

(c)

Case 32b 035

03 Vapor 025 -

02 IF_

015

01

005 -

0 0

035

03

025

02

015

01

005

0 0

Liquid

11111111 1 2 3 4 5 6 7 8

Stage number

(b) Case 32d

1 2 3 4 5 6 7 8 Stage number

(d)

-9- TUC x 2x5

2x4

0 1x3

9 10 11 12

9 10 11 12



40 35 30


- -0- - - case 32b

+ case 32d

25

20 15


5

0 1 2 3 4 5 6 7 Stage number

8 12

(a)

45 40 35 30 25 20

a IDNI-1 x 2x5

o 2x4

o 1x3

Case 32c

15

10

5 0

0 1 2 3 4 5 6 7 Stage number

8 9 10 11 12

(c)

45 Case 32b

40 35 30 25 20 15 10

5

0 0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)

45 Case 32d

40 35 30 25

20 15 10

5 0

0 1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(d)




t 0005 - g 0005 2x4

O 1x3E SI 0003 - Cn 0003

0001 - 0001 TT El 19

-0001 -0001



0011 0011

0009 B-- MAC 0009

0007 - x 2x5 -2- 0007

E 0005 -0 o

o

2x4

1x3 0005

EDI 0003 - c7) 0003

0001 - 0001 III En CI

-0001 -0001


(c) (d)


151















used







152




products was larger





















051

049 c 02 -

047 045 015

043 E 01

041 039 037

- case 32a

case 32c

case 32b


case 32c

case 32b

case 32d 035 0

0 10 20 30 time (hr)

40 50 0 10 20 30 time (hr)

40 50

(a) (b)



037 006 c 035 -0 005

033 1 004 o deg 031 cd 003 _

12= 029 - case 32a case 32b 002



case 32b case 32d

025 0 L

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)



001 Case 32b

0005 0

c 0005 0

0 -0005 k b -0005 -001 o -001

-0015 E -0015 -002 case 32a case 32b o -002


-003 v -003 2x4 1x3

-0035 -0035 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(a) (b)


0005 0005 o 0 0

-0005 -0005

o -001 -001 E -0015 -0015 o o -002

- 0025 TDVH 2x5

-002 -0025

1DM-I 2x5

s -003 - 2x4 1x3 -003 2x4 1x3

-0035 -0035 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)



0035 Case 32b

003 g 003 TDA11 2x5 0025 I 0025 2x4 1x3

002

0015 ----___--- _____ -- ebe 0020 E 0015


0005 case 32c case 32d gt0 0005 13

0 f I I 0 1 1 1 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)

Case 32c Case 32d 0035 0035

g 003 TDM-1 2x5 003 TEM-I 2x5

a 0025 2x4 1x3 0025 2x4 1x3

m 0020 002

E 0015 0015 cG1 001 001 gt0 0005 0005 13

0 I I t 1 0 1 1 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)



0005 Case 32b



O -001 - 2x4 1x3

0-0015 ro

-002

-0025 -0025

0 10 20 30 time (hr)

40 50 0 10 20 30 time (hr)

40 50

(a) (b)

Case 32c Case 32d 0005 0005

0 0 0

-0005 TDIVI-1 2x5 -0005 111vH 2x5

O -001 2x4 1x3 -001 2x4 1x3

o -0015 -0015

-002 -002

-0025 -0025 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)



0007 Case 32b


o 0003 E 0003 _

c 0002 o

laquo- 0002 W

0001 gt0 0001 11

0 r-411egel7 I I I

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)

Case 32c Case 32d 0007 0007

5 0006 0006 TIM-I 2x5 V 0005 0005 2x4 1x3 w 00040 0004

E 0003 C

0003

0002 TI341-1 2x5 0002 es

0001 2x4 1x3 0001

0 i 1 i

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)


158











large plates











00002 Case 32b

0 0

-00002 -00002 -- 00004 case 32a m -00004 -


-00012 -00012 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

00002 Case 32c

00002 Case 32d

0 0

-00002 -00002

-00004 -00004 TEM -00006 -00006 2x5 -00008 -00008 2x4

-0001 -0001 lx3 -00012 -00012

0 10 20 30 40 0 10 20 30 40 50 time (hr) time (hr)

(C) (d)



00012 Case 32b

0001 - case 32a 0001

00008 case 32b 00008

00006 case 32c 00006

00004 - case 32d 00004

00002 00002

0 -4 0

-00002 -00002 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

Case 32c Case 32d 00012 00012

0001 0001 TUC 00008 00008 2x5 00006 00006 2x4 00004 00004 lx3 00002 00002

0 0

-00002 -00002 0 10 20 30 40 0 10 20 30 40 50

time (hr) time (hr)

(C) (d)




000005

0

-000005

-00001

-000015 0 10 20 30 40

time (hr)

(a)

Case 32c 000015

00001

000005

0

-000005

-00001

-000015 0 10 20 30 40

time (hr)

(C)

000015

00001

000005

Case 32b

TDAH

2x4

2x5

1x3

0 i 1 impoomponn

-000005

-00001

-000015 0 10 20

time (hr) 30 40

(b)

000015 Case 32d

00001 -

000005

TDIVH

2x4

2x5

1x3

0

-000005 -

00001 -

-000015 0 10 20 30

time (hr) 40 50

(d)



case 32c 000003 000003

case 32d 000002 000002 000001 000001

0 0

-000001 -000001 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

000007 Case 32c

000007 Case 32d

000006 TDIVH 000006 000005 2x5 000005 000004 2x4 000004 000003 lx3 000003 000002 000002 000001

000001 0

0 -000001

0 10 20 30 40 -000001

time (hr) 0 10 20 30

time (hr) 40 50

(C) (d)


10

0001

00001 000001

90

-180 000001

case 32a

case 32b

case 32c

case 32d


case 32a

case 32b

case 32c

case 32d


(a)

01 1

01

10

0

V ac 1

a)

cc

01

000001 00001

80

60 cn 4140

SI 20

63 0

120 o--40 0-60

1E)-80

-100 000001 00001


case 32b

case 32c

case 32d

01


(b)

01 1


10 10

1 0

0

01 V

o 001

E

0001

TD 1-i

2x5

2x4

lx3

113

V

CC

00001 000001 00001 0001 001


01


01

90 250

200 2x5

V Ilk 150

ca) 100

2x4

lx3

a) -90 C)

a=-180

TDA1-1

2x5

2x4

lx3

S 50 c a 0 To

-50

m-100

-270 000001 00001 0001 001


-150 000001 00001 0001 001


(a) (b)


10 10

2x5 1 2x4

1x3

TDVH E4

0001

2x5

2x4

00001 lx3

01



01

90 20

Si0 013 0 m c0 0 -90 c a

-180 000001

TDMI 2x5

2x4

lx3


01 1

s 15 as0 10 0 1n 5 c0 0 o c so -5as

deg -10-10 co =

-13 -15 0 0 -20 CE

-25 000001 00001 0001 001


(a) (b)


10 10

0

0

01

-enV

V 001 TUC E

ao

E

0001

2x5

2x4

lx3

V 0 cc

00001 01 000001 00001 0001 001



90 80

rn 0

TDV1-1

2x5

2x4 1x3

rn 70

43 60 O 50 of g 40 S 30

o c 20 To 10 13 00

-10

2x5

2x4

1x3

-270 -20 000001 00001 0001 001



(a) (b)


167







holdups (CMH)














model

168







169

BIBLIOGRAPHY












170














171










172

APPENDICES

173

APPENDIX A



Species Tc V Z

[K] [cm3gmol]

AcOH 5944 171 02

EtOH 5162 167 0248

Water 6473 56 0229

AcOEt 5232 286 0252





Species Aj 13j

AcOH -242129 20142

EtOH -300324 475

Water 0 04077

AcOEt -498159 1031


Normal Heat of



571 3911 5660

63 3515 9260

2176 3732 9717

378 3503 7700


Cj Dj EJ

28033x10-2 -01136x10-4 00020x10-6

25030x10-2 -08263x10-5 11975x10-9

36657x10-3 00615x10-4 0

30495x102 -53900x106 0

174



3

1-


+ aap6

AcOH EtOH

Ao (1gmol)2atm 1004538 686619

Bo lgmol 006519 005087

Co (1gmo1)2K2atm 3121503 1605577

ao (1gmo1)3atm 15616 084012

bo (1gmo1)2 002703 001674

Co (1gmo1)3K2atm 8087892 3279836

ao (1gmo1)3 0001601 0000781

yo (1gmo1)2 004365 002704


Water

1175617

008668

2828098

242981

004778

9748118

0003763

007717

AcOEt

311069

001856

1141020

013766

000219

8428061

369E-05

000354


log = A + C


Species Adeg Bdeg

AcOH 75596 164405

EtOH 783124 144052

Water 796681 166821

AcOEt 709808 123871


Cdeg

233524

21271

228

217

175



A -05543 0581778 0688636 -006014

A2 -032436 0209245 0024303 0229575

A3 -010369 -025733 0375534 186575

A4 -070546 -056264 127548 0355191

A5 -201335 -031485 177863 0468416

A6 -225362 0451732 0696279 15111

A7 0837926 -011541 0936722 -005997

A8 052376 0069531 0449357 0067399

A9 0434061 0074053 071779 -315997

A10 -053406 018701 144979 0941858

A -325231 -036999 -211099 -192225

Al2 590329 -008234 0746905 -075573

A13 3354 -040947 112914 103791

A14 0197296 109247 0120436 0365254

A15 -045266 0192416 -164268 -136587

A16 0014715 -017257 0330018 -213818


176

APPENDIX B







177

Start
















Continue simulation


178







at each plate






No




C Stop


179

APPENDIX C






0 0000 0003 0017 0001 0003 1 0032 0046 0041 0006 0024 2 0159 0205 0258 0172 0174 3 0167 0203 0261 0146 0156 4 0169 0201 0267 0129 014 5 0173 0200 0267 0119 0128 6 0188 0206 0267 0103 0119 7 0216 0278 0314 0118 0145



0 0649 0693 0752 0543 0539 1 0741 0734 0755 0633 0617 2 0649 0638 0583 0579 0576 3 0653 0634 0579 0551 0545 4 0677 0631 0573 0529 0521 5 0723 0630 0572 0516 0504 6 0659 0626 0572 0512 0496 7 0386 0573 0518 0482 0471

180



0 0067 0090 0115 0043 0048 1 0067 0100 0100 0076 0077 2 0070 0084 0089 0100 0100 3 0070 0088 0089 0121 0121 4 0075 0092 0090 0138 0138 5 0079 0096 0090 0156 0155 6 0077 0102 0087 0191 0179 7 0364 0099 0097 0238 0240



0 0284 0214 0116 0413 0411 1 0160 0121 0104 0289 0282 2 0122 0073 0070 0149 0150 3 0110 0076 0070 0183 0179 4 0089 0077 0071 0204 0201 5 0086 0074 0071 0208 0213 6 0076 0066 0071 0194 0206 7 0034 0050 0070 0162 0144

TABLE OF CONTENTS

Page

1 INTRODUCTION 1















Page










BIBLIOGRAPHY 169

APPENDICES 172




LIST OF FIGURES

Figure Page



















Figure Page
















Figure Page


















Figure Page


















Figure Page




















Figure Page



LIST OF TABLES

Table Page



















Table Page








Figure Page




Table Page










LIST OF NOTATIONS













f Feed stage

f Fugacity [atm]









11) Weir height [m]






1 Weir length [m]















t Time [min]


















Greek symbols












Subscripts

B Bottom product



F Feed stream

1 Liquid phase


v


S Stripping section

Vapor phase


I INTRODUCTION




acetate













2






















3




















models were studied



4




















5




















6









du = f (uv t)

dt

0 = g(u v t)







solution vector u

7




in this work














8

s=0

s=1

s=2

s=M-1

s=M

S=M+1



m+1

1)-(St)= (S)1(Snt) 1 ltslt M+1 (1-2) n=1



Sk n = 0m (1-3)Wnl(s)

kVn Sn Sk k

m +1 S k n = 1m+1 (1-4)Wnv(S)

k=1 Sn Sk ktn




9



N





(a+Dx(13+1)N-xw(x a 13 N) - (1-6)x(N x)











10





















11























12













13









the liquid phase







14








aA + bB H cC + dD


VAA + VBB + VCC + VDD = 0 (2-1)

where





15

Condenser


dt

dt dM0

nr

LOLo (2-2b) 1=1


dt

Internal Stages

dM + + FX

dt (2-3a) +

dM nc

V F Vi W + (2-3b)dt j=1


dt

Reboiler


dt

nc dMN+1



16

D


17

Hw Xwj



i=N VN+1 HN+1 YN+1j

QR LN hN XNj

B hB xBd i=N+1


18


(2-5)1iA =





by




(2-8)



19






Id(TE (2-10)

n

(2-11)ij 1=1






dMik dhi (2-12)

dt dt

20



as




The result is

nc dx EK

dTi 1=1 dt nc (2-14)

dt dK E x

1=1 dT


_ -nc di ci



-di1=1




21






dt aT dt axm dt


n dK cbcii I M x



n cbcij x-n`






22


23

F


24




i +1 n i+1 dhk


Li (2-20) (h 11+1)

i+1 I n

= Li + Ft B+ (2-21) k =N +l j=1

i = NN-110


holdups

n







25











described in Sec221




qi =lk owi

(2-24a)


26

how Eqn (2-25) vi h

Li

A

1


27







how jY2qt = 36815 (2-24b)t

048F

how is defined by

(

M (2-25)

r7r Ceol4)Pi



and (2-4b) become




28





n dhN+1


VN+1 (2-28)(Hi+ h8)


(2-29) J=1




H1

i = (NN-12)





171 (2-31)(H1 ho


29


=1 dt





(2-24)











30

i=0

D

V1 Hr

hi

1

VF YFI HE

(1-OF xF

i=mi+m2+3



B


31

Condenser


dM0 -dt

- Vo Lo D + j =1



dM dt

dM n

-v + dt 1=1

dM ihi + L h L hdt







(2-33a)

(2-33b)

(2-33c)

(2 -34 a)

(2-34b)

(2-34c)

(2-35a)

(2-35b)

(2-35c)

32





dt J=1



Reboiler


BXB Vi rimi +3 A

dM n morm2+3



BhB QR






33


remain unchanged



















34




35



Chapter Two









311 Enthalpies


n


n

Hi =I yi H(7) (3-1b) i=1

36




H (TO = Ai + B + C + D + E iTi4 (3-2b)


= x (To Pi) (3-3a)

Hi =1 i(Ti Pi) (3-3b) J=1


procedures

Enthalpies of Vapor



37




_RT2( din f (3-5) aT )p





T2 (3-6)







T2 deg v

38


F (Pvk) (3-8)Pvk+1 = P

vk F(pvk)








thesis




= Hsi(Ti) A1(T) (3-10)


39


038 1 T T

where Tr = (3-11)A(7`)=7 A 1Tr




such as

Ki(T)=Oi + AT+ of T2 -F ei T3 (3-12)






j0

(3-13)



Appendix A

40

Bcit















F(T)=[Ixi jE1Ki(TP)]-1= 0 (3-16) i=1

41


F(Tk) (3-17)Tk+1 = Tk PAK)











Z (1 K (TF PF ))F(1)= L o (3-19)

=1 + ty(K (TF PF ) 1)

42





zi





=ExiJP(Ti) (3-21)





where r = T (3-22)T

43







Simplified model

Liquid enthalpy



dh dh = x (3-23)

dT

dT


(3-25)

44




dki +28T + 3E 72 (3-26)

dT dT




apo dpij (3-27)


dT dT 7 j(i_Trf

n axik 1i (3-29)

aXij k=1 j

45

Rigorous model

Liquid enthalpy







(3-30)

Thus



0

B + T +3D T2 +4E T3 (3-32)


46



T3 YPv


dA 038 A (3-34)

dT (T T)






ln(10) kJ (3-35) aT (T + C

9K1 Po1I (3-36)

dx dx





47



(-rA) = [k(7)][ fn( CA CB )1 (3-23)





M j as follows


= [k(T)C = k(T)MiX (3-24)



48



(3-26)







x=s-1 N=M-1

(N n)(n +a+1)(n+a+ 3+1)An (3-27)

(2n + a + 13 + 1)2

n(n+ I3)(N + n+ a + 3 +1) B (3-28)(2n + a + 11)2

where

(a)k = 0 k = 0

(a)k = (a)(a+1)(a+k-1) kgt 0

49


Q0(xa P N) =1 (3-29)

(a+ 0+2)xQi(xa P N) 1 (3-30)Ma +1)











requirements



50


set of equations



required accuracy









51







of ethyl acetate

A + B H C + D













52


Design Variables






AcOH zA 02559

Et0H zs 06159

Water zc 00743

- AcOEt zD 00539




Weir length [m] 006











53

N+1

(Ai )2







xitcoH 11893E-03 66924E-03 28242E-03 16359E-03

xEtolf 61785E-03 98927E-03 16722E-02 18820E-02

xwater 92009E-03 94784E-03 53772E-03 49359E-03

XAcOEt 13209E-03 47090E-03 12271E-02 11779E-02









results



0 1 2 3 4 5

Stage number


0 1 2 3 4 5 6 7

Stage number



0 0 1 2 3 4 5 6 7

Stage number



0 0 1 2 3 4 5 6 7

Stage number


55























Topic of studies

Physical

approximation

Numerical

approximation

Number of stages

Type of reaction

Thermodynamic

model

Pressure in the

column

Example 1



model assuming



reduced-order TDMH

model

8

irreversible

( 2A ---gt R + S )

simple

uniform (1 atm)

Example 2


order model in a

column with many

stages

reduced-order TDMH

model

29

rigorous

uniform (1 atm)

Example 30


order model in a

column with fewer

stages

-

reduced-order TDMH

model

11

Example 31


order model in a



assuming uniform

pressure

full-order TDMH

model assuming that


is uniform

reduced-order TDMH

model

11

reversible


rigorous rigorous


column

Example 32


on steady-state and

dynamic behaviors

full-order TDMH

model using various

plate geometries

-

11

rigorous

uniform (1 atm)

57


be observed

58

5 EXAMPLE PROBLEM 1






2A gt R + S


(-17A) = kACA

where






A 11000 + 30T 4000 + 30T 001Ts 10699 275 02

R 20000 + 20T 15000 + 20T 002T 11651 090 0229

S 25300 + 10T 25000 + 10T 003T 9418 459 0252

T is in degF

59


Design Variables






A 08

R 01

S 01















60







2x2 lx1


11835 20000

0 = condenser 28165 40000



61835 70000


9 = reboiler 90000






solutions

61

60

55

50

45

40

35

30 0

60

55 C Of 41) 50

I a 45 m ei n 40 I i 35

30 0

60

55 ii Oi a) 50 73

12a 45 co

isoo 40 i

35

30 0


1 2 3 4 5 6

Stage number

(a)


(b)

i I i i i 1


(c)

B TDMH - - -0- - CM H

7 8

B TDMH gt 2x2

O 1x1

7 8

--B CM H 2x2 o 1x1

I

7 8

9

9

9


62


09 -08 07 --e-- TDMH 06 -0- CMH 05 04 03 02 01

0 Ulf

0 1 2 3 4 5 6 7 8 9

Stage number

(a)

1

09 08 07 06 05 04 03 02 01

0 0 1 2 3 4 5 6 7 8 9

Stage number

(b)

1

09 08 8 CM H 07 2x2 06 - 0 1x1 05 04 03 02 01


0 1 2 3 4 5 6 7 8 9

Stage number

(c)


63

1

09 -08-07 06 05 04 -03-02 -01

0 0

1

09 08 07 -06 -05 04 03 02 01 -

0 0

1

09 08 07 06 05 04 03 02 01

0 0


1I I I I I

1 2 3 4 5 6

Stage number

(a)

1 2 3 4 5 6

Stage number

(b)

t 1 I 1

1 2 3 4 5 6

Stage number

(c)

$ TDMH CMH

1 1

7 8 9

--e TDM H o 2x2

0 1x1

7 8 9

9-- CM H 2x2

0 1x1

7 8 9


64


09 08 07 06 05 04 03 02 01

0 0

I

1

i

2 3

I

4 I

5 6

p TDMH

CMH

7 8 9

Stage number

(a)

1

09 08 07 06 05 04 03 02 01

0 0

I

1

I

2 3 4 5 6

e TDMH 2x2

O 1x1

7 8 9

Stage number

(b)

1

09 08 07 06 05 04-03 02 01

0 0

I

1 2 3 4 5 6

--eCMH 2x2

O 1x1

7 8 9

Stage number

(c)


65


700

600

500

400

300

$ TDMH CMH

200

100

0 0 1 2 3 4 5


(a)

800

700

600 Vapor

500

400

300

200

Liquid

9 TDM H 2x2

O 1x1

100

0


6 7 8 9

(b)

800

700

600 Vapor

500

400

300

200

Liquid 8CMH

2x2

O 1x1

100

0 0

F

1

f

2 I

3 I I

4 5 Stage number

i

6 I

7 i

8 9

(c)


66





TDMH CMH

(2x2) (1x1) Full (3x3) (2x2) (1x1)

T (degF)2 75654E-05 32486E-02 64722E-02 59785E-05 18506E-02

XA 18871E-07 28772E-05 97558E-05 20379E-07 29484E-05

XR 37528E-07 18061E-04 90993E-05 45029E-07 90603E-05

xs 90549E-08 11304E-04 22755E-06 99641E-08 44224E-05

L (lbmolmin)2 16683 3641945 317355 23006 2405854

V (lbmolmin)2 16822 3058993 317355 34804 2278430









67























68






model










69


003

0025

002 0015

001

0005

TDMH

CMH

0 0 10 20 30

time (min)

40 50

(a)

0035

003

0025

002

0015

001

0005

TDMH

2x2 1x1

0 0 10 20 30

time (min)

40 50

(b)

0035

003

0025

002-0015

001

0005

0 0 10 20 30 40

CMH 2x2 1x1

50

time (min)

(C)


70


-001

-002

TDMH

CMH

-003

-004 _ _ _

-005

-006 0 10 20 30

time (min)

40 50

(a)

I I I I

-001

-002

-003

TDMH

2x2 1x1

-004

-005

-006 0 10 20 30

time (min)

40 50

(b)

-001

-002

CMH

2x2 1x1

-003

-004

-005

-006 0 10 20 30

time (min)

40 50

(c)


71


002 _-____

0015

001

0005 TDMH

CMH

0 10 20 30

time (min)

40 50

(a)

0025

002

0015

001

0005

TDMH

2x2 lx1

0 10 20 30

time (min)

40 50

(b)

0025

002

0015

001

0005

CMH

2x2 1x1

0 10 20 30

time (min)

40 50

(c)


72




xA initial 00858 00859 00829 01041 01042 01009

final 01160 01160 01138 01248 01248 01212

XR initial 08237 08237 08257 08040 08040 08077

final 07706 07706 07705 07614 07614 07647

xs initial 00905 00905 00914 00919 00918 00915

final 01135 01134 01158 01138 01138 01141


Model Relative time

TDMH Full (3x3) 1

2x2 08972

lx1 06576


2x2 06150

lx1 04706






73



















behavior

74


0 1 2 3 4 5 6 7 8 9

stage number













75


001

0008

0006

0004

0002

0 0 10 20 30 40 50 60

time (m in)

(a)

0012

001- MAC 2x2

0008 1x1

0006

0004

0002

0 0 10 20 30 40 50 60

time (min)

(b)

0012

001

0008

0006

0004

0002

0 0 10 20 30 40 50 60

time (m in)

(C)


76


-0002 -0004 -0006 -0008 -001

-0012 -0014 -0016 -0018 -002

0 10 20 30 40 50 60

time (m in)

(a)

0 -0002 -0004 -0006 -0008

-001 -0012 -0014 -0016 -0018

-002 0 10 20 30 40 50 60

time (min)

(b)

0 -0002 -0004 -0006 -0008

-001 -0012 -0014 -0016 -0018

-002 0 10 20 30 40 50 60

time (m in)

(C)


77


0007 0006 TUC 0005 CM-I 0004

0003

0002

0001

0 0 10 20 30 40 50 60

time (min)

(a)

0008

0007 0006

0005 0004

0003 0002

0001

0 0 10 20 30 40 50 60

time (min)

(b)

0008

0007 0006

0005 0004

0003 0002

0001

0 0 10 20 30 40 50 60

time (m in)

(c)


78



fractions




















001 10

0

v 0001 0 E

TDMH

CMH

00001 000001 00001 0001 001


01

000001 00001 0001 001


20

10

-90 TDMH

CMH

-180 000001 00001 0001 001 01 1

Frequency ( radmin)

0

-10

CMH

000001 00001

(a)


0001 001

Frequency (radmin)

01

(b)


10

2x2 1x1

1

01

00001 0001 001 01 000001 00001 0001 001 01


90 10

2x2 1x1

0

-90 TDMH

2x2 1x1

-180 -10 000001 00001 0001 001 01 000001 00001 0001 001 01 1


(a) (b)


001 10

CMH

2x2

1x1

00001 01

000001 00001 0001 001 01 1 000001 00001 0001 001 01


10

0

-90 CMH

2x2 1x1

-180 -10 000001 00001 0001 001 01 1 000001 00001 0001 001 01 1


(a) (b)


82



















83

6 EXAMPLE PROBLEM 2







Design Variables







AcOH zA 04962

EtOH zs 04808

water zc 00229

AcOEt zD 0








84












8x16 7x14 6x12 4x9 3x6


10003 10036 10209 12230 15649

0 = condenser 20129 20873 22952 35293 50000

10 = vapor feed stage 31068 34290 40295 64707 84351

43453 50000 59705 87770 100000

56547 65710 77048 100000

68932 79127 89791

79871 89964 100000

89997 100000

100000

85


8x16 7x14 6x12 4x9 3x6


120000 120000 120005 120210 122214


30 = reboiler 140008 140282 142129 152490 183980

150112 151682 157096 177252 226020

160676 165036 174991 205000 263291

172205 180226 194781 232748 287786

184815 196607 215219 257510 300000

198183 213393 235009 276750

211817 229774 252904 289790

225185 244964 267871 300000

237795 258318 279742

249324 269718 289995

259888 279984 300000

269992 290000

280000 300000

290000

300000







86




8x16 7x14 6x12 4x9 3x6

T (K)2 34681E-06 61907E-06 99419E-06 78225E-05 77447E-03

XAcOH 40090E-11 25666E-10 10937E-09 52778E-08 79956E-06

xEioll 34920E-09 56707E-09 89310E-09 47621E-08 40108E-06

Xwater 18735E-09 37718E-09 63574E-09 26774E-08 86463E-07

XAcOEt 86031E-09 13058E-08 16382E-08 53505E-08 85873E-07

YAcoH 29980E-11 14345E-10 58830E-10 11738E-07 18645E-05

YEt0H 67593E-09 96737E-09 12643E-08 76121E-08 80113E-06

Ywater 24000E-09 47672E-09 80790E-09 45331E-08 19307E-06

YAcOEt 15738E-08 22710E-08 27523E-08 82866E-08 16307E-06

L (gmolmin)2 14936E-10 24385E-10 60968E-10 25848E-09 13842E-07

V (gmolmin)2 43025E-09 40383E-09 60686E-09 70445E-09 14962E-07

M (gmol)2 42749E-07 31854E-06 25227E-05 61481E-04 21716E-03




(gmolmin)

Full (9x18) 0014071

8x16 0014071

7x14 0014069

6x12 0014067

4x9 0014063

3x6 0014038



0 3 6 9 12 15 18 21 24 27 30

Stage number



0 3 6 9 12 15 18 21 24 27 30

Stage number

1

09 c 08 ot 07 E 06 e 05 oE 04 a 03 3 02

01 0

0

1

09 08 07 06 05 04 03 02 01

0 0


- full A 6x12

o 4x9 x 3x6

iiiii isii 1 3 6 9 12 15 18 21 24 27 30

Stage number


3 6 9 12 15 18 21 24 27 30

Stage number




o) 365

E 25

20

a)

L

360

355 -

E o E

15

10

sect 350I-

0 E

5

0

345 5 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(a) (b)



03

025

02

vapor 19 17 -15 -13 -

0 4x9

p

x

6x12

3x6

015

01

005

0

liquid

4-1 I I I

full

o 4x9

I it N 1 4 I

p

x 6x12

3x6


s1 1 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(c) (d)


89









25

AcOH

EtOH

-

- - water_

1 05 _ - -- AcOEt

0 1

345 350 355 360 365 370

Temperature (K)






90








reduced models







in Figure 64



column

91



Full (9x18) 1

8x16 09715

7x14 08797

6x12 07190

4x9 05733

3x6 04794








stream






048

2 046

to - 044

E 042V 04

TEM 7x14 4x9

8x16 6x12 3x6

018

0175

017

0165

016

0155

IDVH 7x14 4x9

8x16 6x12 3x6

038 0 10 20 30 40 50 60 70 80

015 0 10 20 30 40 50 60 70 80

time (hr) time (hr)



04

038

036

0 034 3 7 032

TDM-I 7x14 4x9

8x16 6x12 3x6

g 0033 ra co 1- 0031

Edeg 0029

yor 0027

TDMI-1

7x14 4x9

8x16 6x12 3x6

03 0 10 20 30 40 50 60 70 80

0025 0 10 20 30 40 50 60 70 80

time (hr) time (hr)



09 - full p 6x12 08 07 o 4x9 x 3x6 06 05 04 03 02 01


Stage number


09 08 07 06 05

6x1204 - full p03 02 o 4x9 x 3x6 01

0 i I I I I I I I

0 3 6 9 12 15 18 21 24 27 30

Stage number


09 -08

full p 6x12

07 o 4x9 x 3x6 06 05 04 03 02 -01

0 T 0 3 6 9 12 15 18 21 24 27 30

Stage number


09 08 full A 6x12 07 06 0 4x9 x 3x6

05 04 03 02 01

0 I I I

0 3 6 9 12 15 18 21 24 27 30

Stage number


46

370

365

360

355

- full

Temperature profile

p 6x12

o 4x9 x 3x6

E

E 5 E


25 -20 -15-10 -

- full A 6x12

o 4x9 x 3x6

sect 350

345

-6 E cr)


5 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(a) (b)



03 19

025

02

vapor 17 15 13

015

01

005

0 1-

liquid

I 4 4 I

full o 4x9

I i l I III I

A

x 6x12

3x6

I I

11

9-7-5-3

0 3 6 9 12 15 18 Stage number

21 24 27 30 0 3 6 9 12 15 18 Stage number

21 24 27 30

(c) (d)


95
















68




00004

00002 0

-00002 -00004 -00006 -00008 -0001

-00012 -00014

00012

0001

00008

00006

00004

00002

0

-00002

-00004


time (hr)


time (hr)

000015

00001

000005

0

-000005

-00001

-000015

-00002

000006

000005

000004

000003

000002

0

000001 -0

-000001 0


10 20 30 40 50

time (hr)


10 20 30 40 50

time (hr)


10 10

1

01

13 001 1

c E 0001 TDIVI-1 8x16 8x16 7x14

00001 7x14 4x9

6x12 3x6

6x12 3x6

4x9

000001 01



01

90 60 IDN1-1 8x16 50

407x 14 6x12 30

4x9 3x6 T 20 20 5 10

0 2 -10 0

-20 8x16 7x14o -30 6x12 4x9-40 3x6cc -50

-180 -60 000001 00001 0001 001 01 000001 00001 0001 001 01 1


(a) (b)


98












for simpler columns

99

7 EXAMPLE PROBLEM 3










problem




column was studied








100


Design Variables







AcOH za 04962

EtOH zB 04808

water zc 00229

AcOEt zD 0




Weir length [m] 009

Weir height [m] 003








101


each model






98597 109356 120000 109913 120000 120000










102






column





(2x5) (2x4) (1x3)

T (K)2 60609E-05 13436E-03 29741E-02

XAeOH 35046E-08 10320E-06 17373E-05

XEtOH 73801E-07 12009E-06 16073E-05

xwater 23561E-08 13345E-07 46047E-06

Xite0Et 78982E-07 78798E-07 17033E-05

Y AcOH 53545E-08 23869E-06 40598E-05

Y Et0H 60827E-07 15434E-06 26427E-05

Ywater 25369E-08 30654E-07 59017E-06

YAcOEt 64649E-07 64980E-07 16455E-05

L (gmolmin)2 16799E-09 26341E-08 35570E-07

V (gmolmin)2 18206E-09 33777E-08 48041E-07

M (gmol)2 11613E-03 11617E-03 10803E-02




10 EMI Cl 0111111 1111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12



09 09 -a- MAC08 08 07 07 x 2x5 06 06 4 2x4 05 -s- TEAM 05

0 1x304 04x 2x503 03

o 2x402 02 01 O 1x3 01

0 011111111 1411 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12




TDM-I aTow 30 Y 365 x 2x5 25 x 2x5

360 2x4 20 2x4 E 070o 1x3 15 0 1x3

11 355 E10 IP EX

a 0 5g 350

1- rn 0 i

345 i i -51111 E

1



035 21

03 19 6 TDMH 17VaporE 025 x 2x5

8 15-2x402 13E


01 2x4 7-=005- 5o 1x3

0 3 il 111111 1 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)


105




2x5 0011345

2x4 0011343

lx3 0011364














106



Full (3x6) 1

2x5 09313

2x4 08556

1x3 06608


















0485 - 0145C TDVH0048 0475 1 014 2x5

IMF 2x4 047 0 0135

2x5 o lx3E0465 0132x4 733 lx3 5r 0125

046

0455 I I I045 012

0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)


0375 00295 037 -

00290365 -036 00285 TDVHTDVH

0355 2x52x5 0028 035 2x42x4

002750345 1x3lx3 034 0027 4 I I I

0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)


0

108






respectively














0 -00001 -00002 -00003 -- 00004 -00005 2x5 -00006 -00007

2x4

-00008 lx3 -00009

0 10 20 30 40 50

time (hr)


0 -00001

0 10 20 30 40 50

time (hr)


000008 000006 TDMr1 2x5

000004 2x4 1x3 000002

0 -000002 -000004 -000006 -000008

-00001 0 10 20 30 40 50

time (hr)


000003

0000025

000002

0000015 000001

0000005

0

-0000005 0 10 20 30 40 50

time (hr)


10 10

1

01

1

001 full

2x5

0001 2x4

lx3 00001 01

000001 00001 0001 001 01 000001 00001 0001 001 01 1


90

0

full -90 2x5

2x4 1x3

-180 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


10 10

2x5 1 2x4

0 1x3 0 s 01 0is c= 001 full Tx E4 2x5

0001 2x4

lx3 00001 01


90 10

clii0 ii 13

w 0 0to



c- 1 0 2x5


-360 -20 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


112






operations





column in each case

pressure atm) 2

18

16

14

12

1

08

06

0--AP=005 X--AP=OA

AP= 015

04

02

0 I I I l iti 0 1 2 3 4 5 6 7 8 9 10 11 12

stage number




113







Table 712



T (K)2 250357 1175582 4137036

xAcoH 61711E-05 21799E-04 45062E-04

xEroll 86611E-04 23323E-03 33668E-03

Xwater 10578E-04 35052E-04 71882E-04

XAcOEt 10156E-03 25721E-03 34075E-03

YAcOH 36414E-05 12001E-04 22977E-04

YEt0H 14054E-03 41997E-03 76426E-03

Ywater 10252E-04 32920E-04 67493E-04

YAcoEt 15273E-03 43664E-03 77664E-03

L (gmolmin) 2 33027E-06 19272E-05 80700E-05

V (gmolmin)2 32945E-06 19270E-05 80678E-05

M (gmol) 2 77791E-03 17231E-02 16933E-02

11AcOH (gmolmin)2 23729E-07 81195E-07 15842E-06



(2x5) (2x4) (1x3) (2x5) (2x4) (1x3) (2x5) (2x4) (1x3)

T 1035E-04 1426E-03 2166E-02 6500E-04 1982E-03 7342E-02 1339E-01 1352E-01 4376E+00

xAcoH 3449E-08 9791E-07 1516E-05 3483E-08 9113E-07 1324E-05 4424E-08 8416E-07 1161E-05

XEt0H 4048E-07 7949E-07 1783E-05 3143E-07 6492E-07 1769E-05 4013E-06 4320E-06 2098E-04

xwate 1055E-08 1436E-07 5492E-06 9188E-09 1514E-07 5428E-06 2914E-07 4453E-07 1212E-05

XAr0Et 3785E-07 3776E-07 2799E-05 2746E-07 2758E-07 2852E-05 5805E-06 5805E-06 2511E-04

YACOH 5878E-08 2296E-06 3546E-05 6219E-08 2153E-06 3092E-05 6902E-08 1982E-06 2702E-05

Y DOH 3397E-07 1107E-06 2434E-05 2647E-07 9055E-07 2223E-05 3398E-06 3928E-06 1891E-04



L 1259E-09 2441E-08 2874E-07 1710E-09 2253E-08 2670E-07 8557E-08 1044E-07 4197E-06

V 1283E-09 2963E-08 3925E-07 1497E-09 2656E-08 3329E-07 1008E-07 1231E-07 5191E-06

M 1064E-03 1064E-03 1077E-02 1052E-03 1053E-03 1086E-02 1306E-03 1308E-03 1878E-02

17awn 9882E-13 3055E-11 3667E-10 1565E-12 4471E-11 4994E-10 1379E-11 7137E-11 1149E-09


320 -4 310 300 -- 290 CI

CY

I t f

A

1 flAP=010

0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


1x3300 290 tIllli11111

2x4

0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(c)

390 380 370 360 350 340 330 320 310 300 290

0 f III-1111111 1 2 3 4 5 6 7 8 9 10 11

Stage number


9-- TDMH x 2x5 o 2x4 o 1x3

12

(b)

390 380 370 360 350 340 330 320 310 300 290

0 1111f-1-11111

2 3 4 5 6 7 8 9 10 11

Stage number


9 TDMH 2x5

o 2x4 o 1x3

1 12

(d)


- --

09 -08 07 -06 -05 -04 03 -02 -01

0 II 0

1

09 -08 07 06 05 -04 -03 02 01 -

0 0


--B--AP=0 - -AP= 005

A AP= 010 ---G---AP= 015

1111111 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


-B-TDMH 2x5

o 2x4 o 1x3

i BM El i I I I

1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(c)

1

09 -08 -07 -06 05 -04 -03 -02 01 -

0 0

1

09 08 07 06 05 04 03 02 01

0 0


-13-TDMH x 2x5

2x4

O 1x3

1111111 OE U 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)


1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(d)



AP = 00503 02 fi AP - 010 01 - - -G - -AP= 015

0 11111111111 O 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


09 08 07 06 05 -8- TDM H04 x 2x503

O 2x4 02 01 0 1x3

0 O 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(c)



09 -08 -07 -06 -05 - -9- TDM H04 - x 2x503 -

O 2x402 -01-

0 loi1x3i i I f iiii0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)


09 -08 07 06 05 -04 -9- TDMH 03 - x 2x5 02 - p 2x4 01 - 0 1x3

0 0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(d)



09 -09 - --B--AP=0 -e-TDMH0808 07 07 - x 2x5

A AP=01006 06 2x4 05 05 O 1x3 04 - 04 -03 - 03 02 - 02 -01 01 -

0 0 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)


0909 -08 - TDMH 08

07 x 2x5 07

06 o 2x4 06 0505 o 1x3

04 - 04

03 - 03 02 - 02 01 01111111110 0


(c) (d)



09 09--B--AP=0 -B- TDMH08 - 08 -07 - 07 2x5

A AP= 01006- 06 - 2x4 ---0---AP= 01505 05 O 1x3

04 04 -03 - 03 -02 02 01 01lilt0 0I


(a) (b)


09 - 09 08 - -9- TDMH 08 07 x 2x5 07 06 - 06o 2x4

0505 o 1x3 04 - 04 03 - 03 02 02 01 - 01

0 0Iflit 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



035

2r

03

025

02

015

01

005

-13-- AP = 0 AP = 005

A AP= 010 --0---4P= 015

03

025

02

015

01

005

0

03

025

02

015

01

005

Vapor


2x4 o 1x3111114-11111

03

025 B

02 g0

015 8 0

01

005

0 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(a) (b)



035

03

025

02

015

01 -

005

Vapor

c CI 113 Liquid

NION101 -B-TDMH

X 2x5 2x4

II 1x3 t I 0

03

025

02

015

01

005

03 -

025 -

02

015

01

005

O NID Liquid x 2x5

O 2x4 O 1x3

I I 114111+1-f

Vapor

- 8- TDMH

03

025

02

015

01

005

0 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(c) (d)



21


9 9 7 7 5

3 3111111111 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)


19 - 19 8 TDMH-8 TCM-I 17

g 15 x 2x5 -6 17 rA 15

2x5

a 13 o 2x4 cl 13 o 2x4

31- 11 - 0 1x3 12 11 1x3 c

9 c

9 co 03 75 E

7 5 111--0K 3 1 i 111111111

7 5 3 i i 111111111


(c) (d)




E0005o 0005 o 1x3E E 9 0003 0) 0003

0001 0001 III

-0001 -0001 i



0011 0011

e TDVH0009 0009 -x 2x5

0007 s 0007 o 2x4

t 0005 t 0005o 1x3 E E a) 0003 0)0003

0001

-0001 El OK 0 4 I I I

0001

-0001 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(c) (d)


123







(MSE=4376)
















124




3

25

2 MOH

15 EtOH

1 - - water

05 Ac0Et

0

290 310 330 350 370

Temperature (K)











125









results










case



048 047

02 - AP - 0 AP= 010

AP - 005 AP- 015

046 018 -045 044

016

043 014 042 AP = 0 AP= 005 012 -041 AP = 010 AP= 015 04 01

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)


036 006 035 005 --034 004 -033


03 001 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)



0005 0

-0005 -001

-0015 -002 APdeg AP=005

-0025 AP=010 AP=015

-003 0 10 20 30 40 50

time (hr)

(a)


0005 0

-0005 -001

-0015 -002 TDVH 2x5

-0025 2x4 1x3

-003 0 10 20 30 40 50

time (hr)

(c)


0005 0

-0005 -001

-0015 -002 TDAH 2x5

-0025 2x4 1x3

-003 0 10 20 30 40 50

time (hr)

(b)


0005 0

-0005 -001

-0015 TEM 2x5-002

-0025 2x4

-003 0 10 20 30 40

time (hr)

(d)


50



003 003

0025 0025

002 002

0015 0015

001 AP-0 AP- 005

001 IDA4-1 2x5

0005 itP =010 AP-015 0005 1 2x4 1x3

0 i I I i 0 i 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)



003 003

0025 0025

002 002

0015 0015

001 -MINH 2x5 001

0005 2x4 1x3 0005

0 1 1 1 0

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)




0 0

-0005 APdeg AP= 005 -0005 TDVH 2x5

-001 AP- 010 AP- 015 -001 2x4 1x3

-0015 -0015

-002 -002

-0025 -0025

-003 -003 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(a) (b)



0 0

-0005 TDM- 2x5 -0005 MAC 2x5

-001 2x4 1x3 -001 2x4

-0015 -0015

-002 -002

-0025 -0025

-003 -003 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)




00035 - 00035 -0003 - 0003

00025 00025 -0002

00015 0001 TCMI 2x5

00005 2x4 1x3

0 50 0 10 20 30 40 50

time (hr)

(a) (b)



00035 00035 0003 0003

00025 00025 0002 0002

00015 00015 0001 0001

00005 00005 0 0

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)


131






















0 -00001 -00002 -00003 A- AP = 0 -0 0004 AP= 005 -00005 AP= 010 -00006 -00007 AP=015 -00008

0 500 1000 1500 2000 2500 3000 time (min)

(a)


0 -00001 -00002 -00003 -00004 -00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)


0 -00001 --00002 T -00003 -00004 --00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)

(b)


0 -00001 1--00002 + -00003 4 -00004 -t--00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)



0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)

(a)


0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)


2x400003 J-lx300002 4-

00001 0

-00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)

(b)


0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)



000005

0

-000005 AP = 0 AP = 005-00001 AP= 010

-000015 AP= 015

-00002 0 500 1000 1500 2000 2500 3000

time (min)

(a)


000005

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)


000005

0

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)

(b)


000005

0

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)



500 1000 1500 2000 2500 3000 time (min)

(a)


0 -000001

0 500 1000 1500 2000 2500 3000 time (min)



0

-000001 0 500 1000 1500 2000 2500 3000

time (min)

(b)


000005 000004

000003 000002 -r 000001 VI

0

-000001 0 500 1000 1500 2000 2500 3000

time (min)


10

0001

00001 000001

90

-90

-180 000001

OP -0 4P =005 AP- 010 AP= 015

00001 0001 001


4P =0 AP= 005 AP- 010 AP= 015

00001 0001 001

Frequency (radmin)

(a)

01

10

0

0V

ac 1

0 O 0 0

CC

01

000001

20

10

O 0 0 S -10 0 c a -20 0

w -30 flo cc

-40 000001

AP- 005 AP= 010 AP= 015

00001 0001 001


AP= 005 AP= 010 AP= 015

00001 0001 001

Frequency (radm in)

(b)

01


10 10

01 =0I0

GI

1 01 1774) a= 3 iTDMI-10010 E 2x5 rozQ 0

0001 2x4 el a)

lx3 cc

00001 01

000001 00001 0001 001 01 000001 00001 0001 001 01 1


90 50

of 40 a)a

---tu 30 co cco 20 a)


-180 -20 000001 00001 0001 001 01 1 000001 00001 0001 001 01


(a) (b)


10 10

1

0

01 a)

a 001 E 2x5

2x4 0001

lx3

00001 01



01

90 50

S40 2x5

30 rn

2x4

1x3 20

210 0 -g 0

X10 cc

-180 -20 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


10

1

0

01 0

ma a fi 001

0001

00001 000001

90

rn

a)

a) -90

a

-180 000001

TDM-I

2x5

2x4

lx3


TDIVH

2x5

2x4

1x3


(a)

10

1

01 01

000001 00001

01

90 80

O 70 60

40 50

40 30

c 0 20 713 10

2 00 cca) - 1 0

-20 000001 00001


01


(b)

01


140







the 1x3 model











Weir length [m] 009 009 009 002

Weir height [m] 003 003 003 006

Volume holdup [1] 0301 0181 0741 0301

141





















lower in case 32c



(2x5) (2x4) (1x3) (2x5) (2x4) (1x3) (2x5) (2x4) (1x3)

T 24206E-04 15413E-03 35626E-02 56883E-05 11573E-03 14283E-02 46403E-05 13594E-03 31742E-02


XEOH 61717E-07 11827E-06 72673E-05 25819E-08 38742E-07 16468E-05 92104E-07 14047E-06 17848E-05



YAcOH 47334E-08 22850E-06 46167E-05 64134E-08 22165E-06 29649E-05 54052E-08 24397E-06 42173E-05

YEt0H 48963E-07 16300E-06 78916E-05 26729E-08 70829E-07 20844E-05 75289E-07 17309E-06 29040E-05



L 86334E-10 27762E-08 48216E-07 12360E-09 21860E-08 26573E-07 17252E-09 27603E-08 36756E-07

V 18824E-09 43611E-08 60301E-07 11625E-09 21731E-08 27373E-07 19103E-09 36782E-08 49566E-07

M 28172E-03 28172E-03 19939E-02 19775E-04 20413E-04 48878E-03 38266E-06 42605E-06 18753E-04

1Acoll 26856E-13 83250E-12 14633E-10 20313E-12 52102E-11 57418E-10 53902E-13 19199E41 28894E40


370 Case 32b

365 9 case 32a - -o- - case 32b

365 a TDVH


360 360 o 2x4

355

350

345

14

A AAA g 355

) 350

345

O 1x3

Ii 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)

370 Case 32c

370 Case 32d

365 TDVH

365 a TDVH

x 2x5 x 2x5

360 o 2x4 360 o 2x4

17a 355 o 1x3

a co 355 O 1x3

350

345 I I

350

345 i III ill ill 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



09

08 13- case 32a - - - - case 32b

09 -

08 --a- TDVH

07 A case 32c case 32d 07 - x 2x5

06 06 - o 2x4

05 05 - 0 1x3 04 04 -

03 03 -

02 02 -

01 01

0 0 ml( a 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)

Case 32c Case 32d 1

09 -a- TDMH 09 -e-1DtVH 08 08

07 x 2x5 07

$ 2x5

06 2x4 06 2x4 05 O 1x3 05 o 1x3 04 04

03 03

02 02

01 01

0 MK 0 al a 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



09 09 08 08 07 - 07 06 e 06




(a) (b)

Case 32c Case 32d 1


2x4 02 02o 2x4 0 1x301 01 0 1x3

0 0 Iiili11111 03

441 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)




0 ilf111 0 S- 1111111


(a) (b)


09 09 08 -8- TCM-I -9-11)Virl08 07 x 2x5 07- x 2x5 06 062x4 2x4 05 05

O 1x3 0 1x304 04 03 03 02 02 01 01

0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)




o 1x3 04 E 04 03 03 02 - 7 02 01 - A- 01

-0- -0 01111


(a) (b)


09 - 09-a- TDVH08 08

07- x 2x5 07 06 - 06p 2x4 05 S 05

0 1x304 - 04 03 - 03 02 - 02 01 - 01

0 0 11111111111 1


(c) (d)


035

03

025

02

015

01

005

0 0

035

03

025


Vapor


a case 32c + case 32d11111111111 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a) Case 32c

Vapor


01 TDM-I x 2x5

005

0 0

2x4 o 1x311111111111 1 2 3 4 5 6 7 8 9 10 11

Stage number 12

(c)

Case 32b 035

03 Vapor 025 -

02 IF_

015

01

005 -

0 0

035

03

025

02

015

01

005

0 0

Liquid

11111111 1 2 3 4 5 6 7 8

Stage number

(b) Case 32d

1 2 3 4 5 6 7 8 Stage number

(d)

-9- TUC x 2x5

2x4

0 1x3

9 10 11 12

9 10 11 12



40 35 30


- -0- - - case 32b

+ case 32d

25

20 15


5

0 1 2 3 4 5 6 7 Stage number

8 12

(a)

45 40 35 30 25 20

a IDNI-1 x 2x5

o 2x4

o 1x3

Case 32c

15

10

5 0

0 1 2 3 4 5 6 7 Stage number

8 9 10 11 12

(c)

45 Case 32b

40 35 30 25 20 15 10

5

0 0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)

45 Case 32d

40 35 30 25

20 15 10

5 0

0 1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(d)




t 0005 - g 0005 2x4

O 1x3E SI 0003 - Cn 0003

0001 - 0001 TT El 19

-0001 -0001



0011 0011

0009 B-- MAC 0009

0007 - x 2x5 -2- 0007

E 0005 -0 o

o

2x4

1x3 0005

EDI 0003 - c7) 0003

0001 - 0001 III En CI

-0001 -0001


(c) (d)


151















used







152




products was larger





















051

049 c 02 -

047 045 015

043 E 01

041 039 037

- case 32a

case 32c

case 32b


case 32c

case 32b

case 32d 035 0

0 10 20 30 time (hr)

40 50 0 10 20 30 time (hr)

40 50

(a) (b)



037 006 c 035 -0 005

033 1 004 o deg 031 cd 003 _

12= 029 - case 32a case 32b 002



case 32b case 32d

025 0 L

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)



001 Case 32b

0005 0

c 0005 0

0 -0005 k b -0005 -001 o -001

-0015 E -0015 -002 case 32a case 32b o -002


-003 v -003 2x4 1x3

-0035 -0035 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(a) (b)


0005 0005 o 0 0

-0005 -0005

o -001 -001 E -0015 -0015 o o -002

- 0025 TDVH 2x5

-002 -0025

1DM-I 2x5

s -003 - 2x4 1x3 -003 2x4 1x3

-0035 -0035 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)



0035 Case 32b

003 g 003 TDA11 2x5 0025 I 0025 2x4 1x3

002

0015 ----___--- _____ -- ebe 0020 E 0015


0005 case 32c case 32d gt0 0005 13

0 f I I 0 1 1 1 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)

Case 32c Case 32d 0035 0035

g 003 TDM-1 2x5 003 TEM-I 2x5

a 0025 2x4 1x3 0025 2x4 1x3

m 0020 002

E 0015 0015 cG1 001 001 gt0 0005 0005 13

0 I I t 1 0 1 1 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)



0005 Case 32b



O -001 - 2x4 1x3

0-0015 ro

-002

-0025 -0025

0 10 20 30 time (hr)

40 50 0 10 20 30 time (hr)

40 50

(a) (b)

Case 32c Case 32d 0005 0005

0 0 0

-0005 TDIVI-1 2x5 -0005 111vH 2x5

O -001 2x4 1x3 -001 2x4 1x3

o -0015 -0015

-002 -002

-0025 -0025 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)



0007 Case 32b


o 0003 E 0003 _

c 0002 o

laquo- 0002 W

0001 gt0 0001 11

0 r-411egel7 I I I

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)

Case 32c Case 32d 0007 0007

5 0006 0006 TIM-I 2x5 V 0005 0005 2x4 1x3 w 00040 0004

E 0003 C

0003

0002 TI341-1 2x5 0002 es

0001 2x4 1x3 0001

0 i 1 i

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)


158











large plates











00002 Case 32b

0 0

-00002 -00002 -- 00004 case 32a m -00004 -


-00012 -00012 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

00002 Case 32c

00002 Case 32d

0 0

-00002 -00002

-00004 -00004 TEM -00006 -00006 2x5 -00008 -00008 2x4

-0001 -0001 lx3 -00012 -00012

0 10 20 30 40 0 10 20 30 40 50 time (hr) time (hr)

(C) (d)



00012 Case 32b

0001 - case 32a 0001

00008 case 32b 00008

00006 case 32c 00006

00004 - case 32d 00004

00002 00002

0 -4 0

-00002 -00002 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

Case 32c Case 32d 00012 00012

0001 0001 TUC 00008 00008 2x5 00006 00006 2x4 00004 00004 lx3 00002 00002

0 0

-00002 -00002 0 10 20 30 40 0 10 20 30 40 50

time (hr) time (hr)

(C) (d)




000005

0

-000005

-00001

-000015 0 10 20 30 40

time (hr)

(a)

Case 32c 000015

00001

000005

0

-000005

-00001

-000015 0 10 20 30 40

time (hr)

(C)

000015

00001

000005

Case 32b

TDAH

2x4

2x5

1x3

0 i 1 impoomponn

-000005

-00001

-000015 0 10 20

time (hr) 30 40

(b)

000015 Case 32d

00001 -

000005

TDIVH

2x4

2x5

1x3

0

-000005 -

00001 -

-000015 0 10 20 30

time (hr) 40 50

(d)



case 32c 000003 000003

case 32d 000002 000002 000001 000001

0 0

-000001 -000001 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

000007 Case 32c

000007 Case 32d

000006 TDIVH 000006 000005 2x5 000005 000004 2x4 000004 000003 lx3 000003 000002 000002 000001

000001 0

0 -000001

0 10 20 30 40 -000001

time (hr) 0 10 20 30

time (hr) 40 50

(C) (d)


10

0001

00001 000001

90

-180 000001

case 32a

case 32b

case 32c

case 32d


case 32a

case 32b

case 32c

case 32d


(a)

01 1

01

10

0

V ac 1

a)

cc

01

000001 00001

80

60 cn 4140

SI 20

63 0

120 o--40 0-60

1E)-80

-100 000001 00001


case 32b

case 32c

case 32d

01


(b)

01 1


10 10

1 0

0

01 V

o 001

E

0001

TD 1-i

2x5

2x4

lx3

113

V

CC

00001 000001 00001 0001 001


01


01

90 250

200 2x5

V Ilk 150

ca) 100

2x4

lx3

a) -90 C)

a=-180

TDA1-1

2x5

2x4

lx3

S 50 c a 0 To

-50

m-100

-270 000001 00001 0001 001


-150 000001 00001 0001 001


(a) (b)


10 10

2x5 1 2x4

1x3

TDVH E4

0001

2x5

2x4

00001 lx3

01



01

90 20

Si0 013 0 m c0 0 -90 c a

-180 000001

TDMI 2x5

2x4

lx3


01 1

s 15 as0 10 0 1n 5 c0 0 o c so -5as

deg -10-10 co =

-13 -15 0 0 -20 CE

-25 000001 00001 0001 001


(a) (b)


10 10

0

0

01

-enV

V 001 TUC E

ao

E

0001

2x5

2x4

lx3

V 0 cc

00001 01 000001 00001 0001 001



90 80

rn 0

TDV1-1

2x5

2x4 1x3

rn 70

43 60 O 50 of g 40 S 30

o c 20 To 10 13 00

-10

2x5

2x4

1x3

-270 -20 000001 00001 0001 001



(a) (b)


167







holdups (CMH)














model

168







169

BIBLIOGRAPHY












170














171










172

APPENDICES

173

APPENDIX A



Species Tc V Z

[K] [cm3gmol]

AcOH 5944 171 02

EtOH 5162 167 0248

Water 6473 56 0229

AcOEt 5232 286 0252





Species Aj 13j

AcOH -242129 20142

EtOH -300324 475

Water 0 04077

AcOEt -498159 1031


Normal Heat of



571 3911 5660

63 3515 9260

2176 3732 9717

378 3503 7700


Cj Dj EJ

28033x10-2 -01136x10-4 00020x10-6

25030x10-2 -08263x10-5 11975x10-9

36657x10-3 00615x10-4 0

30495x102 -53900x106 0

174



3

1-


+ aap6

AcOH EtOH

Ao (1gmol)2atm 1004538 686619

Bo lgmol 006519 005087

Co (1gmo1)2K2atm 3121503 1605577

ao (1gmo1)3atm 15616 084012

bo (1gmo1)2 002703 001674

Co (1gmo1)3K2atm 8087892 3279836

ao (1gmo1)3 0001601 0000781

yo (1gmo1)2 004365 002704


Water

1175617

008668

2828098

242981

004778

9748118

0003763

007717

AcOEt

311069

001856

1141020

013766

000219

8428061

369E-05

000354


log = A + C


Species Adeg Bdeg

AcOH 75596 164405

EtOH 783124 144052

Water 796681 166821

AcOEt 709808 123871


Cdeg

233524

21271

228

217

175



A -05543 0581778 0688636 -006014

A2 -032436 0209245 0024303 0229575

A3 -010369 -025733 0375534 186575

A4 -070546 -056264 127548 0355191

A5 -201335 -031485 177863 0468416

A6 -225362 0451732 0696279 15111

A7 0837926 -011541 0936722 -005997

A8 052376 0069531 0449357 0067399

A9 0434061 0074053 071779 -315997

A10 -053406 018701 144979 0941858

A -325231 -036999 -211099 -192225

Al2 590329 -008234 0746905 -075573

A13 3354 -040947 112914 103791

A14 0197296 109247 0120436 0365254

A15 -045266 0192416 -164268 -136587

A16 0014715 -017257 0330018 -213818


176

APPENDIX B







177

Start
















Continue simulation


178







at each plate






No




C Stop


179

APPENDIX C






0 0000 0003 0017 0001 0003 1 0032 0046 0041 0006 0024 2 0159 0205 0258 0172 0174 3 0167 0203 0261 0146 0156 4 0169 0201 0267 0129 014 5 0173 0200 0267 0119 0128 6 0188 0206 0267 0103 0119 7 0216 0278 0314 0118 0145



0 0649 0693 0752 0543 0539 1 0741 0734 0755 0633 0617 2 0649 0638 0583 0579 0576 3 0653 0634 0579 0551 0545 4 0677 0631 0573 0529 0521 5 0723 0630 0572 0516 0504 6 0659 0626 0572 0512 0496 7 0386 0573 0518 0482 0471

180



0 0067 0090 0115 0043 0048 1 0067 0100 0100 0076 0077 2 0070 0084 0089 0100 0100 3 0070 0088 0089 0121 0121 4 0075 0092 0090 0138 0138 5 0079 0096 0090 0156 0155 6 0077 0102 0087 0191 0179 7 0364 0099 0097 0238 0240



0 0284 0214 0116 0413 0411 1 0160 0121 0104 0289 0282 2 0122 0073 0070 0149 0150 3 0110 0076 0070 0183 0179 4 0089 0077 0071 0204 0201 5 0086 0074 0071 0208 0213 6 0076 0066 0071 0194 0206 7 0034 0050 0070 0162 0144


Page










BIBLIOGRAPHY 169

APPENDICES 172




LIST OF FIGURES

Figure Page



















Figure Page
















Figure Page


















Figure Page


















Figure Page




















Figure Page



LIST OF TABLES

Table Page



















Table Page








Figure Page




Table Page










LIST OF NOTATIONS













f Feed stage

f Fugacity [atm]









11) Weir height [m]






1 Weir length [m]















t Time [min]


















Greek symbols












Subscripts

B Bottom product



F Feed stream

1 Liquid phase


v


S Stripping section

Vapor phase


I INTRODUCTION




acetate













2






















3




















models were studied



4




















5




















6









du = f (uv t)

dt

0 = g(u v t)







solution vector u

7




in this work














8

s=0

s=1

s=2

s=M-1

s=M

S=M+1



m+1

1)-(St)= (S)1(Snt) 1 ltslt M+1 (1-2) n=1



Sk n = 0m (1-3)Wnl(s)

kVn Sn Sk k

m +1 S k n = 1m+1 (1-4)Wnv(S)

k=1 Sn Sk ktn




9



N





(a+Dx(13+1)N-xw(x a 13 N) - (1-6)x(N x)











10





















11























12













13









the liquid phase







14








aA + bB H cC + dD


VAA + VBB + VCC + VDD = 0 (2-1)

where





15

Condenser


dt

dt dM0

nr

LOLo (2-2b) 1=1


dt

Internal Stages

dM + + FX

dt (2-3a) +

dM nc

V F Vi W + (2-3b)dt j=1


dt

Reboiler


dt

nc dMN+1



16

D


17

Hw Xwj



i=N VN+1 HN+1 YN+1j

QR LN hN XNj

B hB xBd i=N+1


18


(2-5)1iA =





by




(2-8)



19






Id(TE (2-10)

n

(2-11)ij 1=1






dMik dhi (2-12)

dt dt

20



as




The result is

nc dx EK

dTi 1=1 dt nc (2-14)

dt dK E x

1=1 dT


_ -nc di ci



-di1=1




21






dt aT dt axm dt


n dK cbcii I M x



n cbcij x-n`






22


23

F


24




i +1 n i+1 dhk


Li (2-20) (h 11+1)

i+1 I n

= Li + Ft B+ (2-21) k =N +l j=1

i = NN-110


holdups

n







25











described in Sec221




qi =lk owi

(2-24a)


26

how Eqn (2-25) vi h

Li

A

1


27







how jY2qt = 36815 (2-24b)t

048F

how is defined by

(

M (2-25)

r7r Ceol4)Pi



and (2-4b) become




28





n dhN+1


VN+1 (2-28)(Hi+ h8)


(2-29) J=1




H1

i = (NN-12)





171 (2-31)(H1 ho


29


=1 dt





(2-24)











30

i=0

D

V1 Hr

hi

1

VF YFI HE

(1-OF xF

i=mi+m2+3



B


31

Condenser


dM0 -dt

- Vo Lo D + j =1



dM dt

dM n

-v + dt 1=1

dM ihi + L h L hdt







(2-33a)

(2-33b)

(2-33c)

(2 -34 a)

(2-34b)

(2-34c)

(2-35a)

(2-35b)

(2-35c)

32





dt J=1



Reboiler


BXB Vi rimi +3 A

dM n morm2+3



BhB QR






33


remain unchanged



















34




35



Chapter Two









311 Enthalpies


n


n

Hi =I yi H(7) (3-1b) i=1

36




H (TO = Ai + B + C + D + E iTi4 (3-2b)


= x (To Pi) (3-3a)

Hi =1 i(Ti Pi) (3-3b) J=1


procedures

Enthalpies of Vapor



37




_RT2( din f (3-5) aT )p





T2 (3-6)







T2 deg v

38


F (Pvk) (3-8)Pvk+1 = P

vk F(pvk)








thesis




= Hsi(Ti) A1(T) (3-10)


39


038 1 T T

where Tr = (3-11)A(7`)=7 A 1Tr




such as

Ki(T)=Oi + AT+ of T2 -F ei T3 (3-12)






j0

(3-13)



Appendix A

40

Bcit















F(T)=[Ixi jE1Ki(TP)]-1= 0 (3-16) i=1

41


F(Tk) (3-17)Tk+1 = Tk PAK)











Z (1 K (TF PF ))F(1)= L o (3-19)

=1 + ty(K (TF PF ) 1)

42





zi





=ExiJP(Ti) (3-21)





where r = T (3-22)T

43







Simplified model

Liquid enthalpy



dh dh = x (3-23)

dT

dT


(3-25)

44




dki +28T + 3E 72 (3-26)

dT dT




apo dpij (3-27)


dT dT 7 j(i_Trf

n axik 1i (3-29)

aXij k=1 j

45

Rigorous model

Liquid enthalpy







(3-30)

Thus



0

B + T +3D T2 +4E T3 (3-32)


46



T3 YPv


dA 038 A (3-34)

dT (T T)






ln(10) kJ (3-35) aT (T + C

9K1 Po1I (3-36)

dx dx





47



(-rA) = [k(7)][ fn( CA CB )1 (3-23)





M j as follows


= [k(T)C = k(T)MiX (3-24)



48



(3-26)







x=s-1 N=M-1

(N n)(n +a+1)(n+a+ 3+1)An (3-27)

(2n + a + 13 + 1)2

n(n+ I3)(N + n+ a + 3 +1) B (3-28)(2n + a + 11)2

where

(a)k = 0 k = 0

(a)k = (a)(a+1)(a+k-1) kgt 0

49


Q0(xa P N) =1 (3-29)

(a+ 0+2)xQi(xa P N) 1 (3-30)Ma +1)











requirements



50


set of equations



required accuracy









51







of ethyl acetate

A + B H C + D













52


Design Variables






AcOH zA 02559

Et0H zs 06159

Water zc 00743

- AcOEt zD 00539




Weir length [m] 006











53

N+1

(Ai )2







xitcoH 11893E-03 66924E-03 28242E-03 16359E-03

xEtolf 61785E-03 98927E-03 16722E-02 18820E-02

xwater 92009E-03 94784E-03 53772E-03 49359E-03

XAcOEt 13209E-03 47090E-03 12271E-02 11779E-02









results



0 1 2 3 4 5

Stage number


0 1 2 3 4 5 6 7

Stage number



0 0 1 2 3 4 5 6 7

Stage number



0 0 1 2 3 4 5 6 7

Stage number


55























Topic of studies

Physical

approximation

Numerical

approximation

Number of stages

Type of reaction

Thermodynamic

model

Pressure in the

column

Example 1



model assuming



reduced-order TDMH

model

8

irreversible

( 2A ---gt R + S )

simple

uniform (1 atm)

Example 2


order model in a

column with many

stages

reduced-order TDMH

model

29

rigorous

uniform (1 atm)

Example 30


order model in a

column with fewer

stages

-

reduced-order TDMH

model

11

Example 31


order model in a



assuming uniform

pressure

full-order TDMH

model assuming that


is uniform

reduced-order TDMH

model

11

reversible


rigorous rigorous


column

Example 32


on steady-state and

dynamic behaviors

full-order TDMH

model using various

plate geometries

-

11

rigorous

uniform (1 atm)

57


be observed

58

5 EXAMPLE PROBLEM 1






2A gt R + S


(-17A) = kACA

where






A 11000 + 30T 4000 + 30T 001Ts 10699 275 02

R 20000 + 20T 15000 + 20T 002T 11651 090 0229

S 25300 + 10T 25000 + 10T 003T 9418 459 0252

T is in degF

59


Design Variables






A 08

R 01

S 01















60







2x2 lx1


11835 20000

0 = condenser 28165 40000



61835 70000


9 = reboiler 90000






solutions

61

60

55

50

45

40

35

30 0

60

55 C Of 41) 50

I a 45 m ei n 40 I i 35

30 0

60

55 ii Oi a) 50 73

12a 45 co

isoo 40 i

35

30 0


1 2 3 4 5 6

Stage number

(a)


(b)

i I i i i 1


(c)

B TDMH - - -0- - CM H

7 8

B TDMH gt 2x2

O 1x1

7 8

--B CM H 2x2 o 1x1

I

7 8

9

9

9


62


09 -08 07 --e-- TDMH 06 -0- CMH 05 04 03 02 01

0 Ulf

0 1 2 3 4 5 6 7 8 9

Stage number

(a)

1

09 08 07 06 05 04 03 02 01

0 0 1 2 3 4 5 6 7 8 9

Stage number

(b)

1

09 08 8 CM H 07 2x2 06 - 0 1x1 05 04 03 02 01


0 1 2 3 4 5 6 7 8 9

Stage number

(c)


63

1

09 -08-07 06 05 04 -03-02 -01

0 0

1

09 08 07 -06 -05 04 03 02 01 -

0 0

1

09 08 07 06 05 04 03 02 01

0 0


1I I I I I

1 2 3 4 5 6

Stage number

(a)

1 2 3 4 5 6

Stage number

(b)

t 1 I 1

1 2 3 4 5 6

Stage number

(c)

$ TDMH CMH

1 1

7 8 9

--e TDM H o 2x2

0 1x1

7 8 9

9-- CM H 2x2

0 1x1

7 8 9


64


09 08 07 06 05 04 03 02 01

0 0

I

1

i

2 3

I

4 I

5 6

p TDMH

CMH

7 8 9

Stage number

(a)

1

09 08 07 06 05 04 03 02 01

0 0

I

1

I

2 3 4 5 6

e TDMH 2x2

O 1x1

7 8 9

Stage number

(b)

1

09 08 07 06 05 04-03 02 01

0 0

I

1 2 3 4 5 6

--eCMH 2x2

O 1x1

7 8 9

Stage number

(c)


65


700

600

500

400

300

$ TDMH CMH

200

100

0 0 1 2 3 4 5


(a)

800

700

600 Vapor

500

400

300

200

Liquid

9 TDM H 2x2

O 1x1

100

0


6 7 8 9

(b)

800

700

600 Vapor

500

400

300

200

Liquid 8CMH

2x2

O 1x1

100

0 0

F

1

f

2 I

3 I I

4 5 Stage number

i

6 I

7 i

8 9

(c)


66





TDMH CMH

(2x2) (1x1) Full (3x3) (2x2) (1x1)

T (degF)2 75654E-05 32486E-02 64722E-02 59785E-05 18506E-02

XA 18871E-07 28772E-05 97558E-05 20379E-07 29484E-05

XR 37528E-07 18061E-04 90993E-05 45029E-07 90603E-05

xs 90549E-08 11304E-04 22755E-06 99641E-08 44224E-05

L (lbmolmin)2 16683 3641945 317355 23006 2405854

V (lbmolmin)2 16822 3058993 317355 34804 2278430









67























68






model










69


003

0025

002 0015

001

0005

TDMH

CMH

0 0 10 20 30

time (min)

40 50

(a)

0035

003

0025

002

0015

001

0005

TDMH

2x2 1x1

0 0 10 20 30

time (min)

40 50

(b)

0035

003

0025

002-0015

001

0005

0 0 10 20 30 40

CMH 2x2 1x1

50

time (min)

(C)


70


-001

-002

TDMH

CMH

-003

-004 _ _ _

-005

-006 0 10 20 30

time (min)

40 50

(a)

I I I I

-001

-002

-003

TDMH

2x2 1x1

-004

-005

-006 0 10 20 30

time (min)

40 50

(b)

-001

-002

CMH

2x2 1x1

-003

-004

-005

-006 0 10 20 30

time (min)

40 50

(c)


71


002 _-____

0015

001

0005 TDMH

CMH

0 10 20 30

time (min)

40 50

(a)

0025

002

0015

001

0005

TDMH

2x2 lx1

0 10 20 30

time (min)

40 50

(b)

0025

002

0015

001

0005

CMH

2x2 1x1

0 10 20 30

time (min)

40 50

(c)


72




xA initial 00858 00859 00829 01041 01042 01009

final 01160 01160 01138 01248 01248 01212

XR initial 08237 08237 08257 08040 08040 08077

final 07706 07706 07705 07614 07614 07647

xs initial 00905 00905 00914 00919 00918 00915

final 01135 01134 01158 01138 01138 01141


Model Relative time

TDMH Full (3x3) 1

2x2 08972

lx1 06576


2x2 06150

lx1 04706






73



















behavior

74


0 1 2 3 4 5 6 7 8 9

stage number













75


001

0008

0006

0004

0002

0 0 10 20 30 40 50 60

time (m in)

(a)

0012

001- MAC 2x2

0008 1x1

0006

0004

0002

0 0 10 20 30 40 50 60

time (min)

(b)

0012

001

0008

0006

0004

0002

0 0 10 20 30 40 50 60

time (m in)

(C)


76


-0002 -0004 -0006 -0008 -001

-0012 -0014 -0016 -0018 -002

0 10 20 30 40 50 60

time (m in)

(a)

0 -0002 -0004 -0006 -0008

-001 -0012 -0014 -0016 -0018

-002 0 10 20 30 40 50 60

time (min)

(b)

0 -0002 -0004 -0006 -0008

-001 -0012 -0014 -0016 -0018

-002 0 10 20 30 40 50 60

time (m in)

(C)


77


0007 0006 TUC 0005 CM-I 0004

0003

0002

0001

0 0 10 20 30 40 50 60

time (min)

(a)

0008

0007 0006

0005 0004

0003 0002

0001

0 0 10 20 30 40 50 60

time (min)

(b)

0008

0007 0006

0005 0004

0003 0002

0001

0 0 10 20 30 40 50 60

time (m in)

(c)


78



fractions




















001 10

0

v 0001 0 E

TDMH

CMH

00001 000001 00001 0001 001


01

000001 00001 0001 001


20

10

-90 TDMH

CMH

-180 000001 00001 0001 001 01 1

Frequency ( radmin)

0

-10

CMH

000001 00001

(a)


0001 001

Frequency (radmin)

01

(b)


10

2x2 1x1

1

01

00001 0001 001 01 000001 00001 0001 001 01


90 10

2x2 1x1

0

-90 TDMH

2x2 1x1

-180 -10 000001 00001 0001 001 01 000001 00001 0001 001 01 1


(a) (b)


001 10

CMH

2x2

1x1

00001 01

000001 00001 0001 001 01 1 000001 00001 0001 001 01


10

0

-90 CMH

2x2 1x1

-180 -10 000001 00001 0001 001 01 1 000001 00001 0001 001 01 1


(a) (b)


82



















83

6 EXAMPLE PROBLEM 2







Design Variables







AcOH zA 04962

EtOH zs 04808

water zc 00229

AcOEt zD 0








84












8x16 7x14 6x12 4x9 3x6


10003 10036 10209 12230 15649

0 = condenser 20129 20873 22952 35293 50000

10 = vapor feed stage 31068 34290 40295 64707 84351

43453 50000 59705 87770 100000

56547 65710 77048 100000

68932 79127 89791

79871 89964 100000

89997 100000

100000

85


8x16 7x14 6x12 4x9 3x6


120000 120000 120005 120210 122214


30 = reboiler 140008 140282 142129 152490 183980

150112 151682 157096 177252 226020

160676 165036 174991 205000 263291

172205 180226 194781 232748 287786

184815 196607 215219 257510 300000

198183 213393 235009 276750

211817 229774 252904 289790

225185 244964 267871 300000

237795 258318 279742

249324 269718 289995

259888 279984 300000

269992 290000

280000 300000

290000

300000







86




8x16 7x14 6x12 4x9 3x6

T (K)2 34681E-06 61907E-06 99419E-06 78225E-05 77447E-03

XAcOH 40090E-11 25666E-10 10937E-09 52778E-08 79956E-06

xEioll 34920E-09 56707E-09 89310E-09 47621E-08 40108E-06

Xwater 18735E-09 37718E-09 63574E-09 26774E-08 86463E-07

XAcOEt 86031E-09 13058E-08 16382E-08 53505E-08 85873E-07

YAcoH 29980E-11 14345E-10 58830E-10 11738E-07 18645E-05

YEt0H 67593E-09 96737E-09 12643E-08 76121E-08 80113E-06

Ywater 24000E-09 47672E-09 80790E-09 45331E-08 19307E-06

YAcOEt 15738E-08 22710E-08 27523E-08 82866E-08 16307E-06

L (gmolmin)2 14936E-10 24385E-10 60968E-10 25848E-09 13842E-07

V (gmolmin)2 43025E-09 40383E-09 60686E-09 70445E-09 14962E-07

M (gmol)2 42749E-07 31854E-06 25227E-05 61481E-04 21716E-03




(gmolmin)

Full (9x18) 0014071

8x16 0014071

7x14 0014069

6x12 0014067

4x9 0014063

3x6 0014038



0 3 6 9 12 15 18 21 24 27 30

Stage number



0 3 6 9 12 15 18 21 24 27 30

Stage number

1

09 c 08 ot 07 E 06 e 05 oE 04 a 03 3 02

01 0

0

1

09 08 07 06 05 04 03 02 01

0 0


- full A 6x12

o 4x9 x 3x6

iiiii isii 1 3 6 9 12 15 18 21 24 27 30

Stage number


3 6 9 12 15 18 21 24 27 30

Stage number




o) 365

E 25

20

a)

L

360

355 -

E o E

15

10

sect 350I-

0 E

5

0

345 5 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(a) (b)



03

025

02

vapor 19 17 -15 -13 -

0 4x9

p

x

6x12

3x6

015

01

005

0

liquid

4-1 I I I

full

o 4x9

I it N 1 4 I

p

x 6x12

3x6


s1 1 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(c) (d)


89









25

AcOH

EtOH

-

- - water_

1 05 _ - -- AcOEt

0 1

345 350 355 360 365 370

Temperature (K)






90








reduced models







in Figure 64



column

91



Full (9x18) 1

8x16 09715

7x14 08797

6x12 07190

4x9 05733

3x6 04794








stream






048

2 046

to - 044

E 042V 04

TEM 7x14 4x9

8x16 6x12 3x6

018

0175

017

0165

016

0155

IDVH 7x14 4x9

8x16 6x12 3x6

038 0 10 20 30 40 50 60 70 80

015 0 10 20 30 40 50 60 70 80

time (hr) time (hr)



04

038

036

0 034 3 7 032

TDM-I 7x14 4x9

8x16 6x12 3x6

g 0033 ra co 1- 0031

Edeg 0029

yor 0027

TDMI-1

7x14 4x9

8x16 6x12 3x6

03 0 10 20 30 40 50 60 70 80

0025 0 10 20 30 40 50 60 70 80

time (hr) time (hr)



09 - full p 6x12 08 07 o 4x9 x 3x6 06 05 04 03 02 01


Stage number


09 08 07 06 05

6x1204 - full p03 02 o 4x9 x 3x6 01

0 i I I I I I I I

0 3 6 9 12 15 18 21 24 27 30

Stage number


09 -08

full p 6x12

07 o 4x9 x 3x6 06 05 04 03 02 -01

0 T 0 3 6 9 12 15 18 21 24 27 30

Stage number


09 08 full A 6x12 07 06 0 4x9 x 3x6

05 04 03 02 01

0 I I I

0 3 6 9 12 15 18 21 24 27 30

Stage number


46

370

365

360

355

- full

Temperature profile

p 6x12

o 4x9 x 3x6

E

E 5 E


25 -20 -15-10 -

- full A 6x12

o 4x9 x 3x6

sect 350

345

-6 E cr)


5 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(a) (b)



03 19

025

02

vapor 17 15 13

015

01

005

0 1-

liquid

I 4 4 I

full o 4x9

I i l I III I

A

x 6x12

3x6

I I

11

9-7-5-3

0 3 6 9 12 15 18 Stage number

21 24 27 30 0 3 6 9 12 15 18 Stage number

21 24 27 30

(c) (d)


95
















68




00004

00002 0

-00002 -00004 -00006 -00008 -0001

-00012 -00014

00012

0001

00008

00006

00004

00002

0

-00002

-00004


time (hr)


time (hr)

000015

00001

000005

0

-000005

-00001

-000015

-00002

000006

000005

000004

000003

000002

0

000001 -0

-000001 0


10 20 30 40 50

time (hr)


10 20 30 40 50

time (hr)


10 10

1

01

13 001 1

c E 0001 TDIVI-1 8x16 8x16 7x14

00001 7x14 4x9

6x12 3x6

6x12 3x6

4x9

000001 01



01

90 60 IDN1-1 8x16 50

407x 14 6x12 30

4x9 3x6 T 20 20 5 10

0 2 -10 0

-20 8x16 7x14o -30 6x12 4x9-40 3x6cc -50

-180 -60 000001 00001 0001 001 01 000001 00001 0001 001 01 1


(a) (b)


98












for simpler columns

99

7 EXAMPLE PROBLEM 3










problem




column was studied








100


Design Variables







AcOH za 04962

EtOH zB 04808

water zc 00229

AcOEt zD 0




Weir length [m] 009

Weir height [m] 003








101


each model






98597 109356 120000 109913 120000 120000










102






column





(2x5) (2x4) (1x3)

T (K)2 60609E-05 13436E-03 29741E-02

XAeOH 35046E-08 10320E-06 17373E-05

XEtOH 73801E-07 12009E-06 16073E-05

xwater 23561E-08 13345E-07 46047E-06

Xite0Et 78982E-07 78798E-07 17033E-05

Y AcOH 53545E-08 23869E-06 40598E-05

Y Et0H 60827E-07 15434E-06 26427E-05

Ywater 25369E-08 30654E-07 59017E-06

YAcOEt 64649E-07 64980E-07 16455E-05

L (gmolmin)2 16799E-09 26341E-08 35570E-07

V (gmolmin)2 18206E-09 33777E-08 48041E-07

M (gmol)2 11613E-03 11617E-03 10803E-02




10 EMI Cl 0111111 1111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12



09 09 -a- MAC08 08 07 07 x 2x5 06 06 4 2x4 05 -s- TEAM 05

0 1x304 04x 2x503 03

o 2x402 02 01 O 1x3 01

0 011111111 1411 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12




TDM-I aTow 30 Y 365 x 2x5 25 x 2x5

360 2x4 20 2x4 E 070o 1x3 15 0 1x3

11 355 E10 IP EX

a 0 5g 350

1- rn 0 i

345 i i -51111 E

1



035 21

03 19 6 TDMH 17VaporE 025 x 2x5

8 15-2x402 13E


01 2x4 7-=005- 5o 1x3

0 3 il 111111 1 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)


105




2x5 0011345

2x4 0011343

lx3 0011364














106



Full (3x6) 1

2x5 09313

2x4 08556

1x3 06608


















0485 - 0145C TDVH0048 0475 1 014 2x5

IMF 2x4 047 0 0135

2x5 o lx3E0465 0132x4 733 lx3 5r 0125

046

0455 I I I045 012

0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)


0375 00295 037 -

00290365 -036 00285 TDVHTDVH

0355 2x52x5 0028 035 2x42x4

002750345 1x3lx3 034 0027 4 I I I

0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)


0

108






respectively














0 -00001 -00002 -00003 -- 00004 -00005 2x5 -00006 -00007

2x4

-00008 lx3 -00009

0 10 20 30 40 50

time (hr)


0 -00001

0 10 20 30 40 50

time (hr)


000008 000006 TDMr1 2x5

000004 2x4 1x3 000002

0 -000002 -000004 -000006 -000008

-00001 0 10 20 30 40 50

time (hr)


000003

0000025

000002

0000015 000001

0000005

0

-0000005 0 10 20 30 40 50

time (hr)


10 10

1

01

1

001 full

2x5

0001 2x4

lx3 00001 01

000001 00001 0001 001 01 000001 00001 0001 001 01 1


90

0

full -90 2x5

2x4 1x3

-180 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


10 10

2x5 1 2x4

0 1x3 0 s 01 0is c= 001 full Tx E4 2x5

0001 2x4

lx3 00001 01


90 10

clii0 ii 13

w 0 0to



c- 1 0 2x5


-360 -20 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


112






operations





column in each case

pressure atm) 2

18

16

14

12

1

08

06

0--AP=005 X--AP=OA

AP= 015

04

02

0 I I I l iti 0 1 2 3 4 5 6 7 8 9 10 11 12

stage number




113







Table 712



T (K)2 250357 1175582 4137036

xAcoH 61711E-05 21799E-04 45062E-04

xEroll 86611E-04 23323E-03 33668E-03

Xwater 10578E-04 35052E-04 71882E-04

XAcOEt 10156E-03 25721E-03 34075E-03

YAcOH 36414E-05 12001E-04 22977E-04

YEt0H 14054E-03 41997E-03 76426E-03

Ywater 10252E-04 32920E-04 67493E-04

YAcoEt 15273E-03 43664E-03 77664E-03

L (gmolmin) 2 33027E-06 19272E-05 80700E-05

V (gmolmin)2 32945E-06 19270E-05 80678E-05

M (gmol) 2 77791E-03 17231E-02 16933E-02

11AcOH (gmolmin)2 23729E-07 81195E-07 15842E-06



(2x5) (2x4) (1x3) (2x5) (2x4) (1x3) (2x5) (2x4) (1x3)

T 1035E-04 1426E-03 2166E-02 6500E-04 1982E-03 7342E-02 1339E-01 1352E-01 4376E+00

xAcoH 3449E-08 9791E-07 1516E-05 3483E-08 9113E-07 1324E-05 4424E-08 8416E-07 1161E-05

XEt0H 4048E-07 7949E-07 1783E-05 3143E-07 6492E-07 1769E-05 4013E-06 4320E-06 2098E-04

xwate 1055E-08 1436E-07 5492E-06 9188E-09 1514E-07 5428E-06 2914E-07 4453E-07 1212E-05

XAr0Et 3785E-07 3776E-07 2799E-05 2746E-07 2758E-07 2852E-05 5805E-06 5805E-06 2511E-04

YACOH 5878E-08 2296E-06 3546E-05 6219E-08 2153E-06 3092E-05 6902E-08 1982E-06 2702E-05

Y DOH 3397E-07 1107E-06 2434E-05 2647E-07 9055E-07 2223E-05 3398E-06 3928E-06 1891E-04



L 1259E-09 2441E-08 2874E-07 1710E-09 2253E-08 2670E-07 8557E-08 1044E-07 4197E-06

V 1283E-09 2963E-08 3925E-07 1497E-09 2656E-08 3329E-07 1008E-07 1231E-07 5191E-06

M 1064E-03 1064E-03 1077E-02 1052E-03 1053E-03 1086E-02 1306E-03 1308E-03 1878E-02

17awn 9882E-13 3055E-11 3667E-10 1565E-12 4471E-11 4994E-10 1379E-11 7137E-11 1149E-09


320 -4 310 300 -- 290 CI

CY

I t f

A

1 flAP=010

0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


1x3300 290 tIllli11111

2x4

0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(c)

390 380 370 360 350 340 330 320 310 300 290

0 f III-1111111 1 2 3 4 5 6 7 8 9 10 11

Stage number


9-- TDMH x 2x5 o 2x4 o 1x3

12

(b)

390 380 370 360 350 340 330 320 310 300 290

0 1111f-1-11111

2 3 4 5 6 7 8 9 10 11

Stage number


9 TDMH 2x5

o 2x4 o 1x3

1 12

(d)


- --

09 -08 07 -06 -05 -04 03 -02 -01

0 II 0

1

09 -08 07 06 05 -04 -03 02 01 -

0 0


--B--AP=0 - -AP= 005

A AP= 010 ---G---AP= 015

1111111 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


-B-TDMH 2x5

o 2x4 o 1x3

i BM El i I I I

1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(c)

1

09 -08 -07 -06 05 -04 -03 -02 01 -

0 0

1

09 08 07 06 05 04 03 02 01

0 0


-13-TDMH x 2x5

2x4

O 1x3

1111111 OE U 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)


1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(d)



AP = 00503 02 fi AP - 010 01 - - -G - -AP= 015

0 11111111111 O 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


09 08 07 06 05 -8- TDM H04 x 2x503

O 2x4 02 01 0 1x3

0 O 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(c)



09 -08 -07 -06 -05 - -9- TDM H04 - x 2x503 -

O 2x402 -01-

0 loi1x3i i I f iiii0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)


09 -08 07 06 05 -04 -9- TDMH 03 - x 2x5 02 - p 2x4 01 - 0 1x3

0 0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(d)



09 -09 - --B--AP=0 -e-TDMH0808 07 07 - x 2x5

A AP=01006 06 2x4 05 05 O 1x3 04 - 04 -03 - 03 02 - 02 -01 01 -

0 0 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)


0909 -08 - TDMH 08

07 x 2x5 07

06 o 2x4 06 0505 o 1x3

04 - 04

03 - 03 02 - 02 01 01111111110 0


(c) (d)



09 09--B--AP=0 -B- TDMH08 - 08 -07 - 07 2x5

A AP= 01006- 06 - 2x4 ---0---AP= 01505 05 O 1x3

04 04 -03 - 03 -02 02 01 01lilt0 0I


(a) (b)


09 - 09 08 - -9- TDMH 08 07 x 2x5 07 06 - 06o 2x4

0505 o 1x3 04 - 04 03 - 03 02 02 01 - 01

0 0Iflit 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



035

2r

03

025

02

015

01

005

-13-- AP = 0 AP = 005

A AP= 010 --0---4P= 015

03

025

02

015

01

005

0

03

025

02

015

01

005

Vapor


2x4 o 1x3111114-11111

03

025 B

02 g0

015 8 0

01

005

0 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(a) (b)



035

03

025

02

015

01 -

005

Vapor

c CI 113 Liquid

NION101 -B-TDMH

X 2x5 2x4

II 1x3 t I 0

03

025

02

015

01

005

03 -

025 -

02

015

01

005

O NID Liquid x 2x5

O 2x4 O 1x3

I I 114111+1-f

Vapor

- 8- TDMH

03

025

02

015

01

005

0 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(c) (d)



21


9 9 7 7 5

3 3111111111 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)


19 - 19 8 TDMH-8 TCM-I 17

g 15 x 2x5 -6 17 rA 15

2x5

a 13 o 2x4 cl 13 o 2x4

31- 11 - 0 1x3 12 11 1x3 c

9 c

9 co 03 75 E

7 5 111--0K 3 1 i 111111111

7 5 3 i i 111111111


(c) (d)




E0005o 0005 o 1x3E E 9 0003 0) 0003

0001 0001 III

-0001 -0001 i



0011 0011

e TDVH0009 0009 -x 2x5

0007 s 0007 o 2x4

t 0005 t 0005o 1x3 E E a) 0003 0)0003

0001

-0001 El OK 0 4 I I I

0001

-0001 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(c) (d)


123







(MSE=4376)
















124




3

25

2 MOH

15 EtOH

1 - - water

05 Ac0Et

0

290 310 330 350 370

Temperature (K)











125









results










case



048 047

02 - AP - 0 AP= 010

AP - 005 AP- 015

046 018 -045 044

016

043 014 042 AP = 0 AP= 005 012 -041 AP = 010 AP= 015 04 01

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)


036 006 035 005 --034 004 -033


03 001 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)



0005 0

-0005 -001

-0015 -002 APdeg AP=005

-0025 AP=010 AP=015

-003 0 10 20 30 40 50

time (hr)

(a)


0005 0

-0005 -001

-0015 -002 TDVH 2x5

-0025 2x4 1x3

-003 0 10 20 30 40 50

time (hr)

(c)


0005 0

-0005 -001

-0015 -002 TDAH 2x5

-0025 2x4 1x3

-003 0 10 20 30 40 50

time (hr)

(b)


0005 0

-0005 -001

-0015 TEM 2x5-002

-0025 2x4

-003 0 10 20 30 40

time (hr)

(d)


50



003 003

0025 0025

002 002

0015 0015

001 AP-0 AP- 005

001 IDA4-1 2x5

0005 itP =010 AP-015 0005 1 2x4 1x3

0 i I I i 0 i 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)



003 003

0025 0025

002 002

0015 0015

001 -MINH 2x5 001

0005 2x4 1x3 0005

0 1 1 1 0

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)




0 0

-0005 APdeg AP= 005 -0005 TDVH 2x5

-001 AP- 010 AP- 015 -001 2x4 1x3

-0015 -0015

-002 -002

-0025 -0025

-003 -003 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(a) (b)



0 0

-0005 TDM- 2x5 -0005 MAC 2x5

-001 2x4 1x3 -001 2x4

-0015 -0015

-002 -002

-0025 -0025

-003 -003 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)




00035 - 00035 -0003 - 0003

00025 00025 -0002

00015 0001 TCMI 2x5

00005 2x4 1x3

0 50 0 10 20 30 40 50

time (hr)

(a) (b)



00035 00035 0003 0003

00025 00025 0002 0002

00015 00015 0001 0001

00005 00005 0 0

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)


131






















0 -00001 -00002 -00003 A- AP = 0 -0 0004 AP= 005 -00005 AP= 010 -00006 -00007 AP=015 -00008

0 500 1000 1500 2000 2500 3000 time (min)

(a)


0 -00001 -00002 -00003 -00004 -00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)


0 -00001 --00002 T -00003 -00004 --00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)

(b)


0 -00001 1--00002 + -00003 4 -00004 -t--00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)



0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)

(a)


0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)


2x400003 J-lx300002 4-

00001 0

-00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)

(b)


0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)



000005

0

-000005 AP = 0 AP = 005-00001 AP= 010

-000015 AP= 015

-00002 0 500 1000 1500 2000 2500 3000

time (min)

(a)


000005

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)


000005

0

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)

(b)


000005

0

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)



500 1000 1500 2000 2500 3000 time (min)

(a)


0 -000001

0 500 1000 1500 2000 2500 3000 time (min)



0

-000001 0 500 1000 1500 2000 2500 3000

time (min)

(b)


000005 000004

000003 000002 -r 000001 VI

0

-000001 0 500 1000 1500 2000 2500 3000

time (min)


10

0001

00001 000001

90

-90

-180 000001

OP -0 4P =005 AP- 010 AP= 015

00001 0001 001


4P =0 AP= 005 AP- 010 AP= 015

00001 0001 001

Frequency (radmin)

(a)

01

10

0

0V

ac 1

0 O 0 0

CC

01

000001

20

10

O 0 0 S -10 0 c a -20 0

w -30 flo cc

-40 000001

AP- 005 AP= 010 AP= 015

00001 0001 001


AP= 005 AP= 010 AP= 015

00001 0001 001

Frequency (radm in)

(b)

01


10 10

01 =0I0

GI

1 01 1774) a= 3 iTDMI-10010 E 2x5 rozQ 0

0001 2x4 el a)

lx3 cc

00001 01

000001 00001 0001 001 01 000001 00001 0001 001 01 1


90 50

of 40 a)a

---tu 30 co cco 20 a)


-180 -20 000001 00001 0001 001 01 1 000001 00001 0001 001 01


(a) (b)


10 10

1

0

01 a)

a 001 E 2x5

2x4 0001

lx3

00001 01



01

90 50

S40 2x5

30 rn

2x4

1x3 20

210 0 -g 0

X10 cc

-180 -20 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


10

1

0

01 0

ma a fi 001

0001

00001 000001

90

rn

a)

a) -90

a

-180 000001

TDM-I

2x5

2x4

lx3


TDIVH

2x5

2x4

1x3


(a)

10

1

01 01

000001 00001

01

90 80

O 70 60

40 50

40 30

c 0 20 713 10

2 00 cca) - 1 0

-20 000001 00001


01


(b)

01


140







the 1x3 model











Weir length [m] 009 009 009 002

Weir height [m] 003 003 003 006

Volume holdup [1] 0301 0181 0741 0301

141





















lower in case 32c



(2x5) (2x4) (1x3) (2x5) (2x4) (1x3) (2x5) (2x4) (1x3)

T 24206E-04 15413E-03 35626E-02 56883E-05 11573E-03 14283E-02 46403E-05 13594E-03 31742E-02


XEOH 61717E-07 11827E-06 72673E-05 25819E-08 38742E-07 16468E-05 92104E-07 14047E-06 17848E-05



YAcOH 47334E-08 22850E-06 46167E-05 64134E-08 22165E-06 29649E-05 54052E-08 24397E-06 42173E-05

YEt0H 48963E-07 16300E-06 78916E-05 26729E-08 70829E-07 20844E-05 75289E-07 17309E-06 29040E-05



L 86334E-10 27762E-08 48216E-07 12360E-09 21860E-08 26573E-07 17252E-09 27603E-08 36756E-07

V 18824E-09 43611E-08 60301E-07 11625E-09 21731E-08 27373E-07 19103E-09 36782E-08 49566E-07

M 28172E-03 28172E-03 19939E-02 19775E-04 20413E-04 48878E-03 38266E-06 42605E-06 18753E-04

1Acoll 26856E-13 83250E-12 14633E-10 20313E-12 52102E-11 57418E-10 53902E-13 19199E41 28894E40


370 Case 32b

365 9 case 32a - -o- - case 32b

365 a TDVH


360 360 o 2x4

355

350

345

14

A AAA g 355

) 350

345

O 1x3

Ii 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)

370 Case 32c

370 Case 32d

365 TDVH

365 a TDVH

x 2x5 x 2x5

360 o 2x4 360 o 2x4

17a 355 o 1x3

a co 355 O 1x3

350

345 I I

350

345 i III ill ill 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



09

08 13- case 32a - - - - case 32b

09 -

08 --a- TDVH

07 A case 32c case 32d 07 - x 2x5

06 06 - o 2x4

05 05 - 0 1x3 04 04 -

03 03 -

02 02 -

01 01

0 0 ml( a 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)

Case 32c Case 32d 1

09 -a- TDMH 09 -e-1DtVH 08 08

07 x 2x5 07

$ 2x5

06 2x4 06 2x4 05 O 1x3 05 o 1x3 04 04

03 03

02 02

01 01

0 MK 0 al a 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



09 09 08 08 07 - 07 06 e 06




(a) (b)

Case 32c Case 32d 1


2x4 02 02o 2x4 0 1x301 01 0 1x3

0 0 Iiili11111 03

441 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)




0 ilf111 0 S- 1111111


(a) (b)


09 09 08 -8- TCM-I -9-11)Virl08 07 x 2x5 07- x 2x5 06 062x4 2x4 05 05

O 1x3 0 1x304 04 03 03 02 02 01 01

0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)




o 1x3 04 E 04 03 03 02 - 7 02 01 - A- 01

-0- -0 01111


(a) (b)


09 - 09-a- TDVH08 08

07- x 2x5 07 06 - 06p 2x4 05 S 05

0 1x304 - 04 03 - 03 02 - 02 01 - 01

0 0 11111111111 1


(c) (d)


035

03

025

02

015

01

005

0 0

035

03

025


Vapor


a case 32c + case 32d11111111111 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a) Case 32c

Vapor


01 TDM-I x 2x5

005

0 0

2x4 o 1x311111111111 1 2 3 4 5 6 7 8 9 10 11

Stage number 12

(c)

Case 32b 035

03 Vapor 025 -

02 IF_

015

01

005 -

0 0

035

03

025

02

015

01

005

0 0

Liquid

11111111 1 2 3 4 5 6 7 8

Stage number

(b) Case 32d

1 2 3 4 5 6 7 8 Stage number

(d)

-9- TUC x 2x5

2x4

0 1x3

9 10 11 12

9 10 11 12



40 35 30


- -0- - - case 32b

+ case 32d

25

20 15


5

0 1 2 3 4 5 6 7 Stage number

8 12

(a)

45 40 35 30 25 20

a IDNI-1 x 2x5

o 2x4

o 1x3

Case 32c

15

10

5 0

0 1 2 3 4 5 6 7 Stage number

8 9 10 11 12

(c)

45 Case 32b

40 35 30 25 20 15 10

5

0 0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)

45 Case 32d

40 35 30 25

20 15 10

5 0

0 1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(d)




t 0005 - g 0005 2x4

O 1x3E SI 0003 - Cn 0003

0001 - 0001 TT El 19

-0001 -0001



0011 0011

0009 B-- MAC 0009

0007 - x 2x5 -2- 0007

E 0005 -0 o

o

2x4

1x3 0005

EDI 0003 - c7) 0003

0001 - 0001 III En CI

-0001 -0001


(c) (d)


151















used







152




products was larger





















051

049 c 02 -

047 045 015

043 E 01

041 039 037

- case 32a

case 32c

case 32b


case 32c

case 32b

case 32d 035 0

0 10 20 30 time (hr)

40 50 0 10 20 30 time (hr)

40 50

(a) (b)



037 006 c 035 -0 005

033 1 004 o deg 031 cd 003 _

12= 029 - case 32a case 32b 002



case 32b case 32d

025 0 L

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)



001 Case 32b

0005 0

c 0005 0

0 -0005 k b -0005 -001 o -001

-0015 E -0015 -002 case 32a case 32b o -002


-003 v -003 2x4 1x3

-0035 -0035 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(a) (b)


0005 0005 o 0 0

-0005 -0005

o -001 -001 E -0015 -0015 o o -002

- 0025 TDVH 2x5

-002 -0025

1DM-I 2x5

s -003 - 2x4 1x3 -003 2x4 1x3

-0035 -0035 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)



0035 Case 32b

003 g 003 TDA11 2x5 0025 I 0025 2x4 1x3

002

0015 ----___--- _____ -- ebe 0020 E 0015


0005 case 32c case 32d gt0 0005 13

0 f I I 0 1 1 1 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)

Case 32c Case 32d 0035 0035

g 003 TDM-1 2x5 003 TEM-I 2x5

a 0025 2x4 1x3 0025 2x4 1x3

m 0020 002

E 0015 0015 cG1 001 001 gt0 0005 0005 13

0 I I t 1 0 1 1 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)



0005 Case 32b



O -001 - 2x4 1x3

0-0015 ro

-002

-0025 -0025

0 10 20 30 time (hr)

40 50 0 10 20 30 time (hr)

40 50

(a) (b)

Case 32c Case 32d 0005 0005

0 0 0

-0005 TDIVI-1 2x5 -0005 111vH 2x5

O -001 2x4 1x3 -001 2x4 1x3

o -0015 -0015

-002 -002

-0025 -0025 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)



0007 Case 32b


o 0003 E 0003 _

c 0002 o

laquo- 0002 W

0001 gt0 0001 11

0 r-411egel7 I I I

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)

Case 32c Case 32d 0007 0007

5 0006 0006 TIM-I 2x5 V 0005 0005 2x4 1x3 w 00040 0004

E 0003 C

0003

0002 TI341-1 2x5 0002 es

0001 2x4 1x3 0001

0 i 1 i

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)


158











large plates











00002 Case 32b

0 0

-00002 -00002 -- 00004 case 32a m -00004 -


-00012 -00012 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

00002 Case 32c

00002 Case 32d

0 0

-00002 -00002

-00004 -00004 TEM -00006 -00006 2x5 -00008 -00008 2x4

-0001 -0001 lx3 -00012 -00012

0 10 20 30 40 0 10 20 30 40 50 time (hr) time (hr)

(C) (d)



00012 Case 32b

0001 - case 32a 0001

00008 case 32b 00008

00006 case 32c 00006

00004 - case 32d 00004

00002 00002

0 -4 0

-00002 -00002 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

Case 32c Case 32d 00012 00012

0001 0001 TUC 00008 00008 2x5 00006 00006 2x4 00004 00004 lx3 00002 00002

0 0

-00002 -00002 0 10 20 30 40 0 10 20 30 40 50

time (hr) time (hr)

(C) (d)




000005

0

-000005

-00001

-000015 0 10 20 30 40

time (hr)

(a)

Case 32c 000015

00001

000005

0

-000005

-00001

-000015 0 10 20 30 40

time (hr)

(C)

000015

00001

000005

Case 32b

TDAH

2x4

2x5

1x3

0 i 1 impoomponn

-000005

-00001

-000015 0 10 20

time (hr) 30 40

(b)

000015 Case 32d

00001 -

000005

TDIVH

2x4

2x5

1x3

0

-000005 -

00001 -

-000015 0 10 20 30

time (hr) 40 50

(d)



case 32c 000003 000003

case 32d 000002 000002 000001 000001

0 0

-000001 -000001 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

000007 Case 32c

000007 Case 32d

000006 TDIVH 000006 000005 2x5 000005 000004 2x4 000004 000003 lx3 000003 000002 000002 000001

000001 0

0 -000001

0 10 20 30 40 -000001

time (hr) 0 10 20 30

time (hr) 40 50

(C) (d)


10

0001

00001 000001

90

-180 000001

case 32a

case 32b

case 32c

case 32d


case 32a

case 32b

case 32c

case 32d


(a)

01 1

01

10

0

V ac 1

a)

cc

01

000001 00001

80

60 cn 4140

SI 20

63 0

120 o--40 0-60

1E)-80

-100 000001 00001


case 32b

case 32c

case 32d

01


(b)

01 1


10 10

1 0

0

01 V

o 001

E

0001

TD 1-i

2x5

2x4

lx3

113

V

CC

00001 000001 00001 0001 001


01


01

90 250

200 2x5

V Ilk 150

ca) 100

2x4

lx3

a) -90 C)

a=-180

TDA1-1

2x5

2x4

lx3

S 50 c a 0 To

-50

m-100

-270 000001 00001 0001 001


-150 000001 00001 0001 001


(a) (b)


10 10

2x5 1 2x4

1x3

TDVH E4

0001

2x5

2x4

00001 lx3

01



01

90 20

Si0 013 0 m c0 0 -90 c a

-180 000001

TDMI 2x5

2x4

lx3


01 1

s 15 as0 10 0 1n 5 c0 0 o c so -5as

deg -10-10 co =

-13 -15 0 0 -20 CE

-25 000001 00001 0001 001


(a) (b)


10 10

0

0

01

-enV

V 001 TUC E

ao

E

0001

2x5

2x4

lx3

V 0 cc

00001 01 000001 00001 0001 001



90 80

rn 0

TDV1-1

2x5

2x4 1x3

rn 70

43 60 O 50 of g 40 S 30

o c 20 To 10 13 00

-10

2x5

2x4

1x3

-270 -20 000001 00001 0001 001



(a) (b)


167







holdups (CMH)














model

168







169

BIBLIOGRAPHY












170














171










172

APPENDICES

173

APPENDIX A



Species Tc V Z

[K] [cm3gmol]

AcOH 5944 171 02

EtOH 5162 167 0248

Water 6473 56 0229

AcOEt 5232 286 0252





Species Aj 13j

AcOH -242129 20142

EtOH -300324 475

Water 0 04077

AcOEt -498159 1031


Normal Heat of



571 3911 5660

63 3515 9260

2176 3732 9717

378 3503 7700


Cj Dj EJ

28033x10-2 -01136x10-4 00020x10-6

25030x10-2 -08263x10-5 11975x10-9

36657x10-3 00615x10-4 0

30495x102 -53900x106 0

174



3

1-


+ aap6

AcOH EtOH

Ao (1gmol)2atm 1004538 686619

Bo lgmol 006519 005087

Co (1gmo1)2K2atm 3121503 1605577

ao (1gmo1)3atm 15616 084012

bo (1gmo1)2 002703 001674

Co (1gmo1)3K2atm 8087892 3279836

ao (1gmo1)3 0001601 0000781

yo (1gmo1)2 004365 002704


Water

1175617

008668

2828098

242981

004778

9748118

0003763

007717

AcOEt

311069

001856

1141020

013766

000219

8428061

369E-05

000354


log = A + C


Species Adeg Bdeg

AcOH 75596 164405

EtOH 783124 144052

Water 796681 166821

AcOEt 709808 123871


Cdeg

233524

21271

228

217

175



A -05543 0581778 0688636 -006014

A2 -032436 0209245 0024303 0229575

A3 -010369 -025733 0375534 186575

A4 -070546 -056264 127548 0355191

A5 -201335 -031485 177863 0468416

A6 -225362 0451732 0696279 15111

A7 0837926 -011541 0936722 -005997

A8 052376 0069531 0449357 0067399

A9 0434061 0074053 071779 -315997

A10 -053406 018701 144979 0941858

A -325231 -036999 -211099 -192225

Al2 590329 -008234 0746905 -075573

A13 3354 -040947 112914 103791

A14 0197296 109247 0120436 0365254

A15 -045266 0192416 -164268 -136587

A16 0014715 -017257 0330018 -213818


176

APPENDIX B







177

Start
















Continue simulation


178







at each plate






No




C Stop


179

APPENDIX C






0 0000 0003 0017 0001 0003 1 0032 0046 0041 0006 0024 2 0159 0205 0258 0172 0174 3 0167 0203 0261 0146 0156 4 0169 0201 0267 0129 014 5 0173 0200 0267 0119 0128 6 0188 0206 0267 0103 0119 7 0216 0278 0314 0118 0145



0 0649 0693 0752 0543 0539 1 0741 0734 0755 0633 0617 2 0649 0638 0583 0579 0576 3 0653 0634 0579 0551 0545 4 0677 0631 0573 0529 0521 5 0723 0630 0572 0516 0504 6 0659 0626 0572 0512 0496 7 0386 0573 0518 0482 0471

180



0 0067 0090 0115 0043 0048 1 0067 0100 0100 0076 0077 2 0070 0084 0089 0100 0100 3 0070 0088 0089 0121 0121 4 0075 0092 0090 0138 0138 5 0079 0096 0090 0156 0155 6 0077 0102 0087 0191 0179 7 0364 0099 0097 0238 0240



0 0284 0214 0116 0413 0411 1 0160 0121 0104 0289 0282 2 0122 0073 0070 0149 0150 3 0110 0076 0070 0183 0179 4 0089 0077 0071 0204 0201 5 0086 0074 0071 0208 0213 6 0076 0066 0071 0194 0206 7 0034 0050 0070 0162 0144

LIST OF FIGURES

Figure Page



















Figure Page
















Figure Page


















Figure Page


















Figure Page




















Figure Page



LIST OF TABLES

Table Page



















Table Page








Figure Page




Table Page










LIST OF NOTATIONS













f Feed stage

f Fugacity [atm]









11) Weir height [m]






1 Weir length [m]















t Time [min]


















Greek symbols












Subscripts

B Bottom product



F Feed stream

1 Liquid phase


v


S Stripping section

Vapor phase


I INTRODUCTION




acetate













2






















3




















models were studied



4




















5




















6









du = f (uv t)

dt

0 = g(u v t)







solution vector u

7




in this work














8

s=0

s=1

s=2

s=M-1

s=M

S=M+1



m+1

1)-(St)= (S)1(Snt) 1 ltslt M+1 (1-2) n=1



Sk n = 0m (1-3)Wnl(s)

kVn Sn Sk k

m +1 S k n = 1m+1 (1-4)Wnv(S)

k=1 Sn Sk ktn




9



N





(a+Dx(13+1)N-xw(x a 13 N) - (1-6)x(N x)











10





















11























12













13









the liquid phase







14








aA + bB H cC + dD


VAA + VBB + VCC + VDD = 0 (2-1)

where





15

Condenser


dt

dt dM0

nr

LOLo (2-2b) 1=1


dt

Internal Stages

dM + + FX

dt (2-3a) +

dM nc

V F Vi W + (2-3b)dt j=1


dt

Reboiler


dt

nc dMN+1



16

D


17

Hw Xwj



i=N VN+1 HN+1 YN+1j

QR LN hN XNj

B hB xBd i=N+1


18


(2-5)1iA =





by




(2-8)



19






Id(TE (2-10)

n

(2-11)ij 1=1






dMik dhi (2-12)

dt dt

20



as




The result is

nc dx EK

dTi 1=1 dt nc (2-14)

dt dK E x

1=1 dT


_ -nc di ci



-di1=1




21






dt aT dt axm dt


n dK cbcii I M x



n cbcij x-n`






22


23

F


24




i +1 n i+1 dhk


Li (2-20) (h 11+1)

i+1 I n

= Li + Ft B+ (2-21) k =N +l j=1

i = NN-110


holdups

n







25











described in Sec221




qi =lk owi

(2-24a)


26

how Eqn (2-25) vi h

Li

A

1


27







how jY2qt = 36815 (2-24b)t

048F

how is defined by

(

M (2-25)

r7r Ceol4)Pi



and (2-4b) become




28





n dhN+1


VN+1 (2-28)(Hi+ h8)


(2-29) J=1




H1

i = (NN-12)





171 (2-31)(H1 ho


29


=1 dt





(2-24)











30

i=0

D

V1 Hr

hi

1

VF YFI HE

(1-OF xF

i=mi+m2+3



B


31

Condenser


dM0 -dt

- Vo Lo D + j =1



dM dt

dM n

-v + dt 1=1

dM ihi + L h L hdt







(2-33a)

(2-33b)

(2-33c)

(2 -34 a)

(2-34b)

(2-34c)

(2-35a)

(2-35b)

(2-35c)

32





dt J=1



Reboiler


BXB Vi rimi +3 A

dM n morm2+3



BhB QR






33


remain unchanged



















34




35



Chapter Two









311 Enthalpies


n


n

Hi =I yi H(7) (3-1b) i=1

36




H (TO = Ai + B + C + D + E iTi4 (3-2b)


= x (To Pi) (3-3a)

Hi =1 i(Ti Pi) (3-3b) J=1


procedures

Enthalpies of Vapor



37




_RT2( din f (3-5) aT )p





T2 (3-6)







T2 deg v

38


F (Pvk) (3-8)Pvk+1 = P

vk F(pvk)








thesis




= Hsi(Ti) A1(T) (3-10)


39


038 1 T T

where Tr = (3-11)A(7`)=7 A 1Tr




such as

Ki(T)=Oi + AT+ of T2 -F ei T3 (3-12)






j0

(3-13)



Appendix A

40

Bcit















F(T)=[Ixi jE1Ki(TP)]-1= 0 (3-16) i=1

41


F(Tk) (3-17)Tk+1 = Tk PAK)











Z (1 K (TF PF ))F(1)= L o (3-19)

=1 + ty(K (TF PF ) 1)

42





zi





=ExiJP(Ti) (3-21)





where r = T (3-22)T

43







Simplified model

Liquid enthalpy



dh dh = x (3-23)

dT

dT


(3-25)

44




dki +28T + 3E 72 (3-26)

dT dT




apo dpij (3-27)


dT dT 7 j(i_Trf

n axik 1i (3-29)

aXij k=1 j

45

Rigorous model

Liquid enthalpy







(3-30)

Thus



0

B + T +3D T2 +4E T3 (3-32)


46



T3 YPv


dA 038 A (3-34)

dT (T T)






ln(10) kJ (3-35) aT (T + C

9K1 Po1I (3-36)

dx dx





47



(-rA) = [k(7)][ fn( CA CB )1 (3-23)





M j as follows


= [k(T)C = k(T)MiX (3-24)



48



(3-26)







x=s-1 N=M-1

(N n)(n +a+1)(n+a+ 3+1)An (3-27)

(2n + a + 13 + 1)2

n(n+ I3)(N + n+ a + 3 +1) B (3-28)(2n + a + 11)2

where

(a)k = 0 k = 0

(a)k = (a)(a+1)(a+k-1) kgt 0

49


Q0(xa P N) =1 (3-29)

(a+ 0+2)xQi(xa P N) 1 (3-30)Ma +1)











requirements



50


set of equations



required accuracy









51







of ethyl acetate

A + B H C + D













52


Design Variables






AcOH zA 02559

Et0H zs 06159

Water zc 00743

- AcOEt zD 00539




Weir length [m] 006











53

N+1

(Ai )2







xitcoH 11893E-03 66924E-03 28242E-03 16359E-03

xEtolf 61785E-03 98927E-03 16722E-02 18820E-02

xwater 92009E-03 94784E-03 53772E-03 49359E-03

XAcOEt 13209E-03 47090E-03 12271E-02 11779E-02









results



0 1 2 3 4 5

Stage number


0 1 2 3 4 5 6 7

Stage number



0 0 1 2 3 4 5 6 7

Stage number



0 0 1 2 3 4 5 6 7

Stage number


55























Topic of studies

Physical

approximation

Numerical

approximation

Number of stages

Type of reaction

Thermodynamic

model

Pressure in the

column

Example 1



model assuming



reduced-order TDMH

model

8

irreversible

( 2A ---gt R + S )

simple

uniform (1 atm)

Example 2


order model in a

column with many

stages

reduced-order TDMH

model

29

rigorous

uniform (1 atm)

Example 30


order model in a

column with fewer

stages

-

reduced-order TDMH

model

11

Example 31


order model in a



assuming uniform

pressure

full-order TDMH

model assuming that


is uniform

reduced-order TDMH

model

11

reversible


rigorous rigorous


column

Example 32


on steady-state and

dynamic behaviors

full-order TDMH

model using various

plate geometries

-

11

rigorous

uniform (1 atm)

57


be observed

58

5 EXAMPLE PROBLEM 1






2A gt R + S


(-17A) = kACA

where






A 11000 + 30T 4000 + 30T 001Ts 10699 275 02

R 20000 + 20T 15000 + 20T 002T 11651 090 0229

S 25300 + 10T 25000 + 10T 003T 9418 459 0252

T is in degF

59


Design Variables






A 08

R 01

S 01















60







2x2 lx1


11835 20000

0 = condenser 28165 40000



61835 70000


9 = reboiler 90000






solutions

61

60

55

50

45

40

35

30 0

60

55 C Of 41) 50

I a 45 m ei n 40 I i 35

30 0

60

55 ii Oi a) 50 73

12a 45 co

isoo 40 i

35

30 0


1 2 3 4 5 6

Stage number

(a)


(b)

i I i i i 1


(c)

B TDMH - - -0- - CM H

7 8

B TDMH gt 2x2

O 1x1

7 8

--B CM H 2x2 o 1x1

I

7 8

9

9

9


62


09 -08 07 --e-- TDMH 06 -0- CMH 05 04 03 02 01

0 Ulf

0 1 2 3 4 5 6 7 8 9

Stage number

(a)

1

09 08 07 06 05 04 03 02 01

0 0 1 2 3 4 5 6 7 8 9

Stage number

(b)

1

09 08 8 CM H 07 2x2 06 - 0 1x1 05 04 03 02 01


0 1 2 3 4 5 6 7 8 9

Stage number

(c)


63

1

09 -08-07 06 05 04 -03-02 -01

0 0

1

09 08 07 -06 -05 04 03 02 01 -

0 0

1

09 08 07 06 05 04 03 02 01

0 0


1I I I I I

1 2 3 4 5 6

Stage number

(a)

1 2 3 4 5 6

Stage number

(b)

t 1 I 1

1 2 3 4 5 6

Stage number

(c)

$ TDMH CMH

1 1

7 8 9

--e TDM H o 2x2

0 1x1

7 8 9

9-- CM H 2x2

0 1x1

7 8 9


64


09 08 07 06 05 04 03 02 01

0 0

I

1

i

2 3

I

4 I

5 6

p TDMH

CMH

7 8 9

Stage number

(a)

1

09 08 07 06 05 04 03 02 01

0 0

I

1

I

2 3 4 5 6

e TDMH 2x2

O 1x1

7 8 9

Stage number

(b)

1

09 08 07 06 05 04-03 02 01

0 0

I

1 2 3 4 5 6

--eCMH 2x2

O 1x1

7 8 9

Stage number

(c)


65


700

600

500

400

300

$ TDMH CMH

200

100

0 0 1 2 3 4 5


(a)

800

700

600 Vapor

500

400

300

200

Liquid

9 TDM H 2x2

O 1x1

100

0


6 7 8 9

(b)

800

700

600 Vapor

500

400

300

200

Liquid 8CMH

2x2

O 1x1

100

0 0

F

1

f

2 I

3 I I

4 5 Stage number

i

6 I

7 i

8 9

(c)


66





TDMH CMH

(2x2) (1x1) Full (3x3) (2x2) (1x1)

T (degF)2 75654E-05 32486E-02 64722E-02 59785E-05 18506E-02

XA 18871E-07 28772E-05 97558E-05 20379E-07 29484E-05

XR 37528E-07 18061E-04 90993E-05 45029E-07 90603E-05

xs 90549E-08 11304E-04 22755E-06 99641E-08 44224E-05

L (lbmolmin)2 16683 3641945 317355 23006 2405854

V (lbmolmin)2 16822 3058993 317355 34804 2278430









67























68






model










69


003

0025

002 0015

001

0005

TDMH

CMH

0 0 10 20 30

time (min)

40 50

(a)

0035

003

0025

002

0015

001

0005

TDMH

2x2 1x1

0 0 10 20 30

time (min)

40 50

(b)

0035

003

0025

002-0015

001

0005

0 0 10 20 30 40

CMH 2x2 1x1

50

time (min)

(C)


70


-001

-002

TDMH

CMH

-003

-004 _ _ _

-005

-006 0 10 20 30

time (min)

40 50

(a)

I I I I

-001

-002

-003

TDMH

2x2 1x1

-004

-005

-006 0 10 20 30

time (min)

40 50

(b)

-001

-002

CMH

2x2 1x1

-003

-004

-005

-006 0 10 20 30

time (min)

40 50

(c)


71


002 _-____

0015

001

0005 TDMH

CMH

0 10 20 30

time (min)

40 50

(a)

0025

002

0015

001

0005

TDMH

2x2 lx1

0 10 20 30

time (min)

40 50

(b)

0025

002

0015

001

0005

CMH

2x2 1x1

0 10 20 30

time (min)

40 50

(c)


72




xA initial 00858 00859 00829 01041 01042 01009

final 01160 01160 01138 01248 01248 01212

XR initial 08237 08237 08257 08040 08040 08077

final 07706 07706 07705 07614 07614 07647

xs initial 00905 00905 00914 00919 00918 00915

final 01135 01134 01158 01138 01138 01141


Model Relative time

TDMH Full (3x3) 1

2x2 08972

lx1 06576


2x2 06150

lx1 04706






73



















behavior

74


0 1 2 3 4 5 6 7 8 9

stage number













75


001

0008

0006

0004

0002

0 0 10 20 30 40 50 60

time (m in)

(a)

0012

001- MAC 2x2

0008 1x1

0006

0004

0002

0 0 10 20 30 40 50 60

time (min)

(b)

0012

001

0008

0006

0004

0002

0 0 10 20 30 40 50 60

time (m in)

(C)


76


-0002 -0004 -0006 -0008 -001

-0012 -0014 -0016 -0018 -002

0 10 20 30 40 50 60

time (m in)

(a)

0 -0002 -0004 -0006 -0008

-001 -0012 -0014 -0016 -0018

-002 0 10 20 30 40 50 60

time (min)

(b)

0 -0002 -0004 -0006 -0008

-001 -0012 -0014 -0016 -0018

-002 0 10 20 30 40 50 60

time (m in)

(C)


77


0007 0006 TUC 0005 CM-I 0004

0003

0002

0001

0 0 10 20 30 40 50 60

time (min)

(a)

0008

0007 0006

0005 0004

0003 0002

0001

0 0 10 20 30 40 50 60

time (min)

(b)

0008

0007 0006

0005 0004

0003 0002

0001

0 0 10 20 30 40 50 60

time (m in)

(c)


78



fractions




















001 10

0

v 0001 0 E

TDMH

CMH

00001 000001 00001 0001 001


01

000001 00001 0001 001


20

10

-90 TDMH

CMH

-180 000001 00001 0001 001 01 1

Frequency ( radmin)

0

-10

CMH

000001 00001

(a)


0001 001

Frequency (radmin)

01

(b)


10

2x2 1x1

1

01

00001 0001 001 01 000001 00001 0001 001 01


90 10

2x2 1x1

0

-90 TDMH

2x2 1x1

-180 -10 000001 00001 0001 001 01 000001 00001 0001 001 01 1


(a) (b)


001 10

CMH

2x2

1x1

00001 01

000001 00001 0001 001 01 1 000001 00001 0001 001 01


10

0

-90 CMH

2x2 1x1

-180 -10 000001 00001 0001 001 01 1 000001 00001 0001 001 01 1


(a) (b)


82



















83

6 EXAMPLE PROBLEM 2







Design Variables







AcOH zA 04962

EtOH zs 04808

water zc 00229

AcOEt zD 0








84












8x16 7x14 6x12 4x9 3x6


10003 10036 10209 12230 15649

0 = condenser 20129 20873 22952 35293 50000

10 = vapor feed stage 31068 34290 40295 64707 84351

43453 50000 59705 87770 100000

56547 65710 77048 100000

68932 79127 89791

79871 89964 100000

89997 100000

100000

85


8x16 7x14 6x12 4x9 3x6


120000 120000 120005 120210 122214


30 = reboiler 140008 140282 142129 152490 183980

150112 151682 157096 177252 226020

160676 165036 174991 205000 263291

172205 180226 194781 232748 287786

184815 196607 215219 257510 300000

198183 213393 235009 276750

211817 229774 252904 289790

225185 244964 267871 300000

237795 258318 279742

249324 269718 289995

259888 279984 300000

269992 290000

280000 300000

290000

300000







86




8x16 7x14 6x12 4x9 3x6

T (K)2 34681E-06 61907E-06 99419E-06 78225E-05 77447E-03

XAcOH 40090E-11 25666E-10 10937E-09 52778E-08 79956E-06

xEioll 34920E-09 56707E-09 89310E-09 47621E-08 40108E-06

Xwater 18735E-09 37718E-09 63574E-09 26774E-08 86463E-07

XAcOEt 86031E-09 13058E-08 16382E-08 53505E-08 85873E-07

YAcoH 29980E-11 14345E-10 58830E-10 11738E-07 18645E-05

YEt0H 67593E-09 96737E-09 12643E-08 76121E-08 80113E-06

Ywater 24000E-09 47672E-09 80790E-09 45331E-08 19307E-06

YAcOEt 15738E-08 22710E-08 27523E-08 82866E-08 16307E-06

L (gmolmin)2 14936E-10 24385E-10 60968E-10 25848E-09 13842E-07

V (gmolmin)2 43025E-09 40383E-09 60686E-09 70445E-09 14962E-07

M (gmol)2 42749E-07 31854E-06 25227E-05 61481E-04 21716E-03




(gmolmin)

Full (9x18) 0014071

8x16 0014071

7x14 0014069

6x12 0014067

4x9 0014063

3x6 0014038



0 3 6 9 12 15 18 21 24 27 30

Stage number



0 3 6 9 12 15 18 21 24 27 30

Stage number

1

09 c 08 ot 07 E 06 e 05 oE 04 a 03 3 02

01 0

0

1

09 08 07 06 05 04 03 02 01

0 0


- full A 6x12

o 4x9 x 3x6

iiiii isii 1 3 6 9 12 15 18 21 24 27 30

Stage number


3 6 9 12 15 18 21 24 27 30

Stage number




o) 365

E 25

20

a)

L

360

355 -

E o E

15

10

sect 350I-

0 E

5

0

345 5 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(a) (b)



03

025

02

vapor 19 17 -15 -13 -

0 4x9

p

x

6x12

3x6

015

01

005

0

liquid

4-1 I I I

full

o 4x9

I it N 1 4 I

p

x 6x12

3x6


s1 1 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(c) (d)


89









25

AcOH

EtOH

-

- - water_

1 05 _ - -- AcOEt

0 1

345 350 355 360 365 370

Temperature (K)






90








reduced models







in Figure 64



column

91



Full (9x18) 1

8x16 09715

7x14 08797

6x12 07190

4x9 05733

3x6 04794








stream






048

2 046

to - 044

E 042V 04

TEM 7x14 4x9

8x16 6x12 3x6

018

0175

017

0165

016

0155

IDVH 7x14 4x9

8x16 6x12 3x6

038 0 10 20 30 40 50 60 70 80

015 0 10 20 30 40 50 60 70 80

time (hr) time (hr)



04

038

036

0 034 3 7 032

TDM-I 7x14 4x9

8x16 6x12 3x6

g 0033 ra co 1- 0031

Edeg 0029

yor 0027

TDMI-1

7x14 4x9

8x16 6x12 3x6

03 0 10 20 30 40 50 60 70 80

0025 0 10 20 30 40 50 60 70 80

time (hr) time (hr)



09 - full p 6x12 08 07 o 4x9 x 3x6 06 05 04 03 02 01


Stage number


09 08 07 06 05

6x1204 - full p03 02 o 4x9 x 3x6 01

0 i I I I I I I I

0 3 6 9 12 15 18 21 24 27 30

Stage number


09 -08

full p 6x12

07 o 4x9 x 3x6 06 05 04 03 02 -01

0 T 0 3 6 9 12 15 18 21 24 27 30

Stage number


09 08 full A 6x12 07 06 0 4x9 x 3x6

05 04 03 02 01

0 I I I

0 3 6 9 12 15 18 21 24 27 30

Stage number


46

370

365

360

355

- full

Temperature profile

p 6x12

o 4x9 x 3x6

E

E 5 E


25 -20 -15-10 -

- full A 6x12

o 4x9 x 3x6

sect 350

345

-6 E cr)


5 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(a) (b)



03 19

025

02

vapor 17 15 13

015

01

005

0 1-

liquid

I 4 4 I

full o 4x9

I i l I III I

A

x 6x12

3x6

I I

11

9-7-5-3

0 3 6 9 12 15 18 Stage number

21 24 27 30 0 3 6 9 12 15 18 Stage number

21 24 27 30

(c) (d)


95
















68




00004

00002 0

-00002 -00004 -00006 -00008 -0001

-00012 -00014

00012

0001

00008

00006

00004

00002

0

-00002

-00004


time (hr)


time (hr)

000015

00001

000005

0

-000005

-00001

-000015

-00002

000006

000005

000004

000003

000002

0

000001 -0

-000001 0


10 20 30 40 50

time (hr)


10 20 30 40 50

time (hr)


10 10

1

01

13 001 1

c E 0001 TDIVI-1 8x16 8x16 7x14

00001 7x14 4x9

6x12 3x6

6x12 3x6

4x9

000001 01



01

90 60 IDN1-1 8x16 50

407x 14 6x12 30

4x9 3x6 T 20 20 5 10

0 2 -10 0

-20 8x16 7x14o -30 6x12 4x9-40 3x6cc -50

-180 -60 000001 00001 0001 001 01 000001 00001 0001 001 01 1


(a) (b)


98












for simpler columns

99

7 EXAMPLE PROBLEM 3










problem




column was studied








100


Design Variables







AcOH za 04962

EtOH zB 04808

water zc 00229

AcOEt zD 0




Weir length [m] 009

Weir height [m] 003








101


each model






98597 109356 120000 109913 120000 120000










102






column





(2x5) (2x4) (1x3)

T (K)2 60609E-05 13436E-03 29741E-02

XAeOH 35046E-08 10320E-06 17373E-05

XEtOH 73801E-07 12009E-06 16073E-05

xwater 23561E-08 13345E-07 46047E-06

Xite0Et 78982E-07 78798E-07 17033E-05

Y AcOH 53545E-08 23869E-06 40598E-05

Y Et0H 60827E-07 15434E-06 26427E-05

Ywater 25369E-08 30654E-07 59017E-06

YAcOEt 64649E-07 64980E-07 16455E-05

L (gmolmin)2 16799E-09 26341E-08 35570E-07

V (gmolmin)2 18206E-09 33777E-08 48041E-07

M (gmol)2 11613E-03 11617E-03 10803E-02




10 EMI Cl 0111111 1111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12



09 09 -a- MAC08 08 07 07 x 2x5 06 06 4 2x4 05 -s- TEAM 05

0 1x304 04x 2x503 03

o 2x402 02 01 O 1x3 01

0 011111111 1411 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12




TDM-I aTow 30 Y 365 x 2x5 25 x 2x5

360 2x4 20 2x4 E 070o 1x3 15 0 1x3

11 355 E10 IP EX

a 0 5g 350

1- rn 0 i

345 i i -51111 E

1



035 21

03 19 6 TDMH 17VaporE 025 x 2x5

8 15-2x402 13E


01 2x4 7-=005- 5o 1x3

0 3 il 111111 1 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)


105




2x5 0011345

2x4 0011343

lx3 0011364














106



Full (3x6) 1

2x5 09313

2x4 08556

1x3 06608


















0485 - 0145C TDVH0048 0475 1 014 2x5

IMF 2x4 047 0 0135

2x5 o lx3E0465 0132x4 733 lx3 5r 0125

046

0455 I I I045 012

0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)


0375 00295 037 -

00290365 -036 00285 TDVHTDVH

0355 2x52x5 0028 035 2x42x4

002750345 1x3lx3 034 0027 4 I I I

0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)


0

108






respectively














0 -00001 -00002 -00003 -- 00004 -00005 2x5 -00006 -00007

2x4

-00008 lx3 -00009

0 10 20 30 40 50

time (hr)


0 -00001

0 10 20 30 40 50

time (hr)


000008 000006 TDMr1 2x5

000004 2x4 1x3 000002

0 -000002 -000004 -000006 -000008

-00001 0 10 20 30 40 50

time (hr)


000003

0000025

000002

0000015 000001

0000005

0

-0000005 0 10 20 30 40 50

time (hr)


10 10

1

01

1

001 full

2x5

0001 2x4

lx3 00001 01

000001 00001 0001 001 01 000001 00001 0001 001 01 1


90

0

full -90 2x5

2x4 1x3

-180 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


10 10

2x5 1 2x4

0 1x3 0 s 01 0is c= 001 full Tx E4 2x5

0001 2x4

lx3 00001 01


90 10

clii0 ii 13

w 0 0to



c- 1 0 2x5


-360 -20 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


112






operations





column in each case

pressure atm) 2

18

16

14

12

1

08

06

0--AP=005 X--AP=OA

AP= 015

04

02

0 I I I l iti 0 1 2 3 4 5 6 7 8 9 10 11 12

stage number




113







Table 712



T (K)2 250357 1175582 4137036

xAcoH 61711E-05 21799E-04 45062E-04

xEroll 86611E-04 23323E-03 33668E-03

Xwater 10578E-04 35052E-04 71882E-04

XAcOEt 10156E-03 25721E-03 34075E-03

YAcOH 36414E-05 12001E-04 22977E-04

YEt0H 14054E-03 41997E-03 76426E-03

Ywater 10252E-04 32920E-04 67493E-04

YAcoEt 15273E-03 43664E-03 77664E-03

L (gmolmin) 2 33027E-06 19272E-05 80700E-05

V (gmolmin)2 32945E-06 19270E-05 80678E-05

M (gmol) 2 77791E-03 17231E-02 16933E-02

11AcOH (gmolmin)2 23729E-07 81195E-07 15842E-06



(2x5) (2x4) (1x3) (2x5) (2x4) (1x3) (2x5) (2x4) (1x3)

T 1035E-04 1426E-03 2166E-02 6500E-04 1982E-03 7342E-02 1339E-01 1352E-01 4376E+00

xAcoH 3449E-08 9791E-07 1516E-05 3483E-08 9113E-07 1324E-05 4424E-08 8416E-07 1161E-05

XEt0H 4048E-07 7949E-07 1783E-05 3143E-07 6492E-07 1769E-05 4013E-06 4320E-06 2098E-04

xwate 1055E-08 1436E-07 5492E-06 9188E-09 1514E-07 5428E-06 2914E-07 4453E-07 1212E-05

XAr0Et 3785E-07 3776E-07 2799E-05 2746E-07 2758E-07 2852E-05 5805E-06 5805E-06 2511E-04

YACOH 5878E-08 2296E-06 3546E-05 6219E-08 2153E-06 3092E-05 6902E-08 1982E-06 2702E-05

Y DOH 3397E-07 1107E-06 2434E-05 2647E-07 9055E-07 2223E-05 3398E-06 3928E-06 1891E-04



L 1259E-09 2441E-08 2874E-07 1710E-09 2253E-08 2670E-07 8557E-08 1044E-07 4197E-06

V 1283E-09 2963E-08 3925E-07 1497E-09 2656E-08 3329E-07 1008E-07 1231E-07 5191E-06

M 1064E-03 1064E-03 1077E-02 1052E-03 1053E-03 1086E-02 1306E-03 1308E-03 1878E-02

17awn 9882E-13 3055E-11 3667E-10 1565E-12 4471E-11 4994E-10 1379E-11 7137E-11 1149E-09


320 -4 310 300 -- 290 CI

CY

I t f

A

1 flAP=010

0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


1x3300 290 tIllli11111

2x4

0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(c)

390 380 370 360 350 340 330 320 310 300 290

0 f III-1111111 1 2 3 4 5 6 7 8 9 10 11

Stage number


9-- TDMH x 2x5 o 2x4 o 1x3

12

(b)

390 380 370 360 350 340 330 320 310 300 290

0 1111f-1-11111

2 3 4 5 6 7 8 9 10 11

Stage number


9 TDMH 2x5

o 2x4 o 1x3

1 12

(d)


- --

09 -08 07 -06 -05 -04 03 -02 -01

0 II 0

1

09 -08 07 06 05 -04 -03 02 01 -

0 0


--B--AP=0 - -AP= 005

A AP= 010 ---G---AP= 015

1111111 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


-B-TDMH 2x5

o 2x4 o 1x3

i BM El i I I I

1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(c)

1

09 -08 -07 -06 05 -04 -03 -02 01 -

0 0

1

09 08 07 06 05 04 03 02 01

0 0


-13-TDMH x 2x5

2x4

O 1x3

1111111 OE U 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)


1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(d)



AP = 00503 02 fi AP - 010 01 - - -G - -AP= 015

0 11111111111 O 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


09 08 07 06 05 -8- TDM H04 x 2x503

O 2x4 02 01 0 1x3

0 O 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(c)



09 -08 -07 -06 -05 - -9- TDM H04 - x 2x503 -

O 2x402 -01-

0 loi1x3i i I f iiii0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)


09 -08 07 06 05 -04 -9- TDMH 03 - x 2x5 02 - p 2x4 01 - 0 1x3

0 0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(d)



09 -09 - --B--AP=0 -e-TDMH0808 07 07 - x 2x5

A AP=01006 06 2x4 05 05 O 1x3 04 - 04 -03 - 03 02 - 02 -01 01 -

0 0 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)


0909 -08 - TDMH 08

07 x 2x5 07

06 o 2x4 06 0505 o 1x3

04 - 04

03 - 03 02 - 02 01 01111111110 0


(c) (d)



09 09--B--AP=0 -B- TDMH08 - 08 -07 - 07 2x5

A AP= 01006- 06 - 2x4 ---0---AP= 01505 05 O 1x3

04 04 -03 - 03 -02 02 01 01lilt0 0I


(a) (b)


09 - 09 08 - -9- TDMH 08 07 x 2x5 07 06 - 06o 2x4

0505 o 1x3 04 - 04 03 - 03 02 02 01 - 01

0 0Iflit 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



035

2r

03

025

02

015

01

005

-13-- AP = 0 AP = 005

A AP= 010 --0---4P= 015

03

025

02

015

01

005

0

03

025

02

015

01

005

Vapor


2x4 o 1x3111114-11111

03

025 B

02 g0

015 8 0

01

005

0 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(a) (b)



035

03

025

02

015

01 -

005

Vapor

c CI 113 Liquid

NION101 -B-TDMH

X 2x5 2x4

II 1x3 t I 0

03

025

02

015

01

005

03 -

025 -

02

015

01

005

O NID Liquid x 2x5

O 2x4 O 1x3

I I 114111+1-f

Vapor

- 8- TDMH

03

025

02

015

01

005

0 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(c) (d)



21


9 9 7 7 5

3 3111111111 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)


19 - 19 8 TDMH-8 TCM-I 17

g 15 x 2x5 -6 17 rA 15

2x5

a 13 o 2x4 cl 13 o 2x4

31- 11 - 0 1x3 12 11 1x3 c

9 c

9 co 03 75 E

7 5 111--0K 3 1 i 111111111

7 5 3 i i 111111111


(c) (d)




E0005o 0005 o 1x3E E 9 0003 0) 0003

0001 0001 III

-0001 -0001 i



0011 0011

e TDVH0009 0009 -x 2x5

0007 s 0007 o 2x4

t 0005 t 0005o 1x3 E E a) 0003 0)0003

0001

-0001 El OK 0 4 I I I

0001

-0001 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(c) (d)


123







(MSE=4376)
















124




3

25

2 MOH

15 EtOH

1 - - water

05 Ac0Et

0

290 310 330 350 370

Temperature (K)











125









results










case



048 047

02 - AP - 0 AP= 010

AP - 005 AP- 015

046 018 -045 044

016

043 014 042 AP = 0 AP= 005 012 -041 AP = 010 AP= 015 04 01

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)


036 006 035 005 --034 004 -033


03 001 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)



0005 0

-0005 -001

-0015 -002 APdeg AP=005

-0025 AP=010 AP=015

-003 0 10 20 30 40 50

time (hr)

(a)


0005 0

-0005 -001

-0015 -002 TDVH 2x5

-0025 2x4 1x3

-003 0 10 20 30 40 50

time (hr)

(c)


0005 0

-0005 -001

-0015 -002 TDAH 2x5

-0025 2x4 1x3

-003 0 10 20 30 40 50

time (hr)

(b)


0005 0

-0005 -001

-0015 TEM 2x5-002

-0025 2x4

-003 0 10 20 30 40

time (hr)

(d)


50



003 003

0025 0025

002 002

0015 0015

001 AP-0 AP- 005

001 IDA4-1 2x5

0005 itP =010 AP-015 0005 1 2x4 1x3

0 i I I i 0 i 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)



003 003

0025 0025

002 002

0015 0015

001 -MINH 2x5 001

0005 2x4 1x3 0005

0 1 1 1 0

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)




0 0

-0005 APdeg AP= 005 -0005 TDVH 2x5

-001 AP- 010 AP- 015 -001 2x4 1x3

-0015 -0015

-002 -002

-0025 -0025

-003 -003 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(a) (b)



0 0

-0005 TDM- 2x5 -0005 MAC 2x5

-001 2x4 1x3 -001 2x4

-0015 -0015

-002 -002

-0025 -0025

-003 -003 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)




00035 - 00035 -0003 - 0003

00025 00025 -0002

00015 0001 TCMI 2x5

00005 2x4 1x3

0 50 0 10 20 30 40 50

time (hr)

(a) (b)



00035 00035 0003 0003

00025 00025 0002 0002

00015 00015 0001 0001

00005 00005 0 0

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)


131






















0 -00001 -00002 -00003 A- AP = 0 -0 0004 AP= 005 -00005 AP= 010 -00006 -00007 AP=015 -00008

0 500 1000 1500 2000 2500 3000 time (min)

(a)


0 -00001 -00002 -00003 -00004 -00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)


0 -00001 --00002 T -00003 -00004 --00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)

(b)


0 -00001 1--00002 + -00003 4 -00004 -t--00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)



0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)

(a)


0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)


2x400003 J-lx300002 4-

00001 0

-00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)

(b)


0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)



000005

0

-000005 AP = 0 AP = 005-00001 AP= 010

-000015 AP= 015

-00002 0 500 1000 1500 2000 2500 3000

time (min)

(a)


000005

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)


000005

0

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)

(b)


000005

0

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)



500 1000 1500 2000 2500 3000 time (min)

(a)


0 -000001

0 500 1000 1500 2000 2500 3000 time (min)



0

-000001 0 500 1000 1500 2000 2500 3000

time (min)

(b)


000005 000004

000003 000002 -r 000001 VI

0

-000001 0 500 1000 1500 2000 2500 3000

time (min)


10

0001

00001 000001

90

-90

-180 000001

OP -0 4P =005 AP- 010 AP= 015

00001 0001 001


4P =0 AP= 005 AP- 010 AP= 015

00001 0001 001

Frequency (radmin)

(a)

01

10

0

0V

ac 1

0 O 0 0

CC

01

000001

20

10

O 0 0 S -10 0 c a -20 0

w -30 flo cc

-40 000001

AP- 005 AP= 010 AP= 015

00001 0001 001


AP= 005 AP= 010 AP= 015

00001 0001 001

Frequency (radm in)

(b)

01


10 10

01 =0I0

GI

1 01 1774) a= 3 iTDMI-10010 E 2x5 rozQ 0

0001 2x4 el a)

lx3 cc

00001 01

000001 00001 0001 001 01 000001 00001 0001 001 01 1


90 50

of 40 a)a

---tu 30 co cco 20 a)


-180 -20 000001 00001 0001 001 01 1 000001 00001 0001 001 01


(a) (b)


10 10

1

0

01 a)

a 001 E 2x5

2x4 0001

lx3

00001 01



01

90 50

S40 2x5

30 rn

2x4

1x3 20

210 0 -g 0

X10 cc

-180 -20 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


10

1

0

01 0

ma a fi 001

0001

00001 000001

90

rn

a)

a) -90

a

-180 000001

TDM-I

2x5

2x4

lx3


TDIVH

2x5

2x4

1x3


(a)

10

1

01 01

000001 00001

01

90 80

O 70 60

40 50

40 30

c 0 20 713 10

2 00 cca) - 1 0

-20 000001 00001


01


(b)

01


140







the 1x3 model











Weir length [m] 009 009 009 002

Weir height [m] 003 003 003 006

Volume holdup [1] 0301 0181 0741 0301

141





















lower in case 32c



(2x5) (2x4) (1x3) (2x5) (2x4) (1x3) (2x5) (2x4) (1x3)

T 24206E-04 15413E-03 35626E-02 56883E-05 11573E-03 14283E-02 46403E-05 13594E-03 31742E-02


XEOH 61717E-07 11827E-06 72673E-05 25819E-08 38742E-07 16468E-05 92104E-07 14047E-06 17848E-05



YAcOH 47334E-08 22850E-06 46167E-05 64134E-08 22165E-06 29649E-05 54052E-08 24397E-06 42173E-05

YEt0H 48963E-07 16300E-06 78916E-05 26729E-08 70829E-07 20844E-05 75289E-07 17309E-06 29040E-05



L 86334E-10 27762E-08 48216E-07 12360E-09 21860E-08 26573E-07 17252E-09 27603E-08 36756E-07

V 18824E-09 43611E-08 60301E-07 11625E-09 21731E-08 27373E-07 19103E-09 36782E-08 49566E-07

M 28172E-03 28172E-03 19939E-02 19775E-04 20413E-04 48878E-03 38266E-06 42605E-06 18753E-04

1Acoll 26856E-13 83250E-12 14633E-10 20313E-12 52102E-11 57418E-10 53902E-13 19199E41 28894E40


370 Case 32b

365 9 case 32a - -o- - case 32b

365 a TDVH


360 360 o 2x4

355

350

345

14

A AAA g 355

) 350

345

O 1x3

Ii 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)

370 Case 32c

370 Case 32d

365 TDVH

365 a TDVH

x 2x5 x 2x5

360 o 2x4 360 o 2x4

17a 355 o 1x3

a co 355 O 1x3

350

345 I I

350

345 i III ill ill 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



09

08 13- case 32a - - - - case 32b

09 -

08 --a- TDVH

07 A case 32c case 32d 07 - x 2x5

06 06 - o 2x4

05 05 - 0 1x3 04 04 -

03 03 -

02 02 -

01 01

0 0 ml( a 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)

Case 32c Case 32d 1

09 -a- TDMH 09 -e-1DtVH 08 08

07 x 2x5 07

$ 2x5

06 2x4 06 2x4 05 O 1x3 05 o 1x3 04 04

03 03

02 02

01 01

0 MK 0 al a 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



09 09 08 08 07 - 07 06 e 06




(a) (b)

Case 32c Case 32d 1


2x4 02 02o 2x4 0 1x301 01 0 1x3

0 0 Iiili11111 03

441 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)




0 ilf111 0 S- 1111111


(a) (b)


09 09 08 -8- TCM-I -9-11)Virl08 07 x 2x5 07- x 2x5 06 062x4 2x4 05 05

O 1x3 0 1x304 04 03 03 02 02 01 01

0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)




o 1x3 04 E 04 03 03 02 - 7 02 01 - A- 01

-0- -0 01111


(a) (b)


09 - 09-a- TDVH08 08

07- x 2x5 07 06 - 06p 2x4 05 S 05

0 1x304 - 04 03 - 03 02 - 02 01 - 01

0 0 11111111111 1


(c) (d)


035

03

025

02

015

01

005

0 0

035

03

025


Vapor


a case 32c + case 32d11111111111 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a) Case 32c

Vapor


01 TDM-I x 2x5

005

0 0

2x4 o 1x311111111111 1 2 3 4 5 6 7 8 9 10 11

Stage number 12

(c)

Case 32b 035

03 Vapor 025 -

02 IF_

015

01

005 -

0 0

035

03

025

02

015

01

005

0 0

Liquid

11111111 1 2 3 4 5 6 7 8

Stage number

(b) Case 32d

1 2 3 4 5 6 7 8 Stage number

(d)

-9- TUC x 2x5

2x4

0 1x3

9 10 11 12

9 10 11 12



40 35 30


- -0- - - case 32b

+ case 32d

25

20 15


5

0 1 2 3 4 5 6 7 Stage number

8 12

(a)

45 40 35 30 25 20

a IDNI-1 x 2x5

o 2x4

o 1x3

Case 32c

15

10

5 0

0 1 2 3 4 5 6 7 Stage number

8 9 10 11 12

(c)

45 Case 32b

40 35 30 25 20 15 10

5

0 0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)

45 Case 32d

40 35 30 25

20 15 10

5 0

0 1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(d)




t 0005 - g 0005 2x4

O 1x3E SI 0003 - Cn 0003

0001 - 0001 TT El 19

-0001 -0001



0011 0011

0009 B-- MAC 0009

0007 - x 2x5 -2- 0007

E 0005 -0 o

o

2x4

1x3 0005

EDI 0003 - c7) 0003

0001 - 0001 III En CI

-0001 -0001


(c) (d)


151















used







152




products was larger





















051

049 c 02 -

047 045 015

043 E 01

041 039 037

- case 32a

case 32c

case 32b


case 32c

case 32b

case 32d 035 0

0 10 20 30 time (hr)

40 50 0 10 20 30 time (hr)

40 50

(a) (b)



037 006 c 035 -0 005

033 1 004 o deg 031 cd 003 _

12= 029 - case 32a case 32b 002



case 32b case 32d

025 0 L

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)



001 Case 32b

0005 0

c 0005 0

0 -0005 k b -0005 -001 o -001

-0015 E -0015 -002 case 32a case 32b o -002


-003 v -003 2x4 1x3

-0035 -0035 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(a) (b)


0005 0005 o 0 0

-0005 -0005

o -001 -001 E -0015 -0015 o o -002

- 0025 TDVH 2x5

-002 -0025

1DM-I 2x5

s -003 - 2x4 1x3 -003 2x4 1x3

-0035 -0035 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)



0035 Case 32b

003 g 003 TDA11 2x5 0025 I 0025 2x4 1x3

002

0015 ----___--- _____ -- ebe 0020 E 0015


0005 case 32c case 32d gt0 0005 13

0 f I I 0 1 1 1 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)

Case 32c Case 32d 0035 0035

g 003 TDM-1 2x5 003 TEM-I 2x5

a 0025 2x4 1x3 0025 2x4 1x3

m 0020 002

E 0015 0015 cG1 001 001 gt0 0005 0005 13

0 I I t 1 0 1 1 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)



0005 Case 32b



O -001 - 2x4 1x3

0-0015 ro

-002

-0025 -0025

0 10 20 30 time (hr)

40 50 0 10 20 30 time (hr)

40 50

(a) (b)

Case 32c Case 32d 0005 0005

0 0 0

-0005 TDIVI-1 2x5 -0005 111vH 2x5

O -001 2x4 1x3 -001 2x4 1x3

o -0015 -0015

-002 -002

-0025 -0025 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)



0007 Case 32b


o 0003 E 0003 _

c 0002 o

laquo- 0002 W

0001 gt0 0001 11

0 r-411egel7 I I I

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)

Case 32c Case 32d 0007 0007

5 0006 0006 TIM-I 2x5 V 0005 0005 2x4 1x3 w 00040 0004

E 0003 C

0003

0002 TI341-1 2x5 0002 es

0001 2x4 1x3 0001

0 i 1 i

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)


158











large plates











00002 Case 32b

0 0

-00002 -00002 -- 00004 case 32a m -00004 -


-00012 -00012 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

00002 Case 32c

00002 Case 32d

0 0

-00002 -00002

-00004 -00004 TEM -00006 -00006 2x5 -00008 -00008 2x4

-0001 -0001 lx3 -00012 -00012

0 10 20 30 40 0 10 20 30 40 50 time (hr) time (hr)

(C) (d)



00012 Case 32b

0001 - case 32a 0001

00008 case 32b 00008

00006 case 32c 00006

00004 - case 32d 00004

00002 00002

0 -4 0

-00002 -00002 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

Case 32c Case 32d 00012 00012

0001 0001 TUC 00008 00008 2x5 00006 00006 2x4 00004 00004 lx3 00002 00002

0 0

-00002 -00002 0 10 20 30 40 0 10 20 30 40 50

time (hr) time (hr)

(C) (d)




000005

0

-000005

-00001

-000015 0 10 20 30 40

time (hr)

(a)

Case 32c 000015

00001

000005

0

-000005

-00001

-000015 0 10 20 30 40

time (hr)

(C)

000015

00001

000005

Case 32b

TDAH

2x4

2x5

1x3

0 i 1 impoomponn

-000005

-00001

-000015 0 10 20

time (hr) 30 40

(b)

000015 Case 32d

00001 -

000005

TDIVH

2x4

2x5

1x3

0

-000005 -

00001 -

-000015 0 10 20 30

time (hr) 40 50

(d)



case 32c 000003 000003

case 32d 000002 000002 000001 000001

0 0

-000001 -000001 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

000007 Case 32c

000007 Case 32d

000006 TDIVH 000006 000005 2x5 000005 000004 2x4 000004 000003 lx3 000003 000002 000002 000001

000001 0

0 -000001

0 10 20 30 40 -000001

time (hr) 0 10 20 30

time (hr) 40 50

(C) (d)


10

0001

00001 000001

90

-180 000001

case 32a

case 32b

case 32c

case 32d


case 32a

case 32b

case 32c

case 32d


(a)

01 1

01

10

0

V ac 1

a)

cc

01

000001 00001

80

60 cn 4140

SI 20

63 0

120 o--40 0-60

1E)-80

-100 000001 00001


case 32b

case 32c

case 32d

01


(b)

01 1


10 10

1 0

0

01 V

o 001

E

0001

TD 1-i

2x5

2x4

lx3

113

V

CC

00001 000001 00001 0001 001


01


01

90 250

200 2x5

V Ilk 150

ca) 100

2x4

lx3

a) -90 C)

a=-180

TDA1-1

2x5

2x4

lx3

S 50 c a 0 To

-50

m-100

-270 000001 00001 0001 001


-150 000001 00001 0001 001


(a) (b)


10 10

2x5 1 2x4

1x3

TDVH E4

0001

2x5

2x4

00001 lx3

01



01

90 20

Si0 013 0 m c0 0 -90 c a

-180 000001

TDMI 2x5

2x4

lx3


01 1

s 15 as0 10 0 1n 5 c0 0 o c so -5as

deg -10-10 co =

-13 -15 0 0 -20 CE

-25 000001 00001 0001 001


(a) (b)


10 10

0

0

01

-enV

V 001 TUC E

ao

E

0001

2x5

2x4

lx3

V 0 cc

00001 01 000001 00001 0001 001



90 80

rn 0

TDV1-1

2x5

2x4 1x3

rn 70

43 60 O 50 of g 40 S 30

o c 20 To 10 13 00

-10

2x5

2x4

1x3

-270 -20 000001 00001 0001 001



(a) (b)


167







holdups (CMH)














model

168







169

BIBLIOGRAPHY












170














171










172

APPENDICES

173

APPENDIX A



Species Tc V Z

[K] [cm3gmol]

AcOH 5944 171 02

EtOH 5162 167 0248

Water 6473 56 0229

AcOEt 5232 286 0252





Species Aj 13j

AcOH -242129 20142

EtOH -300324 475

Water 0 04077

AcOEt -498159 1031


Normal Heat of



571 3911 5660

63 3515 9260

2176 3732 9717

378 3503 7700


Cj Dj EJ

28033x10-2 -01136x10-4 00020x10-6

25030x10-2 -08263x10-5 11975x10-9

36657x10-3 00615x10-4 0

30495x102 -53900x106 0

174



3

1-


+ aap6

AcOH EtOH

Ao (1gmol)2atm 1004538 686619

Bo lgmol 006519 005087

Co (1gmo1)2K2atm 3121503 1605577

ao (1gmo1)3atm 15616 084012

bo (1gmo1)2 002703 001674

Co (1gmo1)3K2atm 8087892 3279836

ao (1gmo1)3 0001601 0000781

yo (1gmo1)2 004365 002704


Water

1175617

008668

2828098

242981

004778

9748118

0003763

007717

AcOEt

311069

001856

1141020

013766

000219

8428061

369E-05

000354


log = A + C


Species Adeg Bdeg

AcOH 75596 164405

EtOH 783124 144052

Water 796681 166821

AcOEt 709808 123871


Cdeg

233524

21271

228

217

175



A -05543 0581778 0688636 -006014

A2 -032436 0209245 0024303 0229575

A3 -010369 -025733 0375534 186575

A4 -070546 -056264 127548 0355191

A5 -201335 -031485 177863 0468416

A6 -225362 0451732 0696279 15111

A7 0837926 -011541 0936722 -005997

A8 052376 0069531 0449357 0067399

A9 0434061 0074053 071779 -315997

A10 -053406 018701 144979 0941858

A -325231 -036999 -211099 -192225

Al2 590329 -008234 0746905 -075573

A13 3354 -040947 112914 103791

A14 0197296 109247 0120436 0365254

A15 -045266 0192416 -164268 -136587

A16 0014715 -017257 0330018 -213818


176

APPENDIX B







177

Start
















Continue simulation


178







at each plate






No




C Stop


179

APPENDIX C






0 0000 0003 0017 0001 0003 1 0032 0046 0041 0006 0024 2 0159 0205 0258 0172 0174 3 0167 0203 0261 0146 0156 4 0169 0201 0267 0129 014 5 0173 0200 0267 0119 0128 6 0188 0206 0267 0103 0119 7 0216 0278 0314 0118 0145



0 0649 0693 0752 0543 0539 1 0741 0734 0755 0633 0617 2 0649 0638 0583 0579 0576 3 0653 0634 0579 0551 0545 4 0677 0631 0573 0529 0521 5 0723 0630 0572 0516 0504 6 0659 0626 0572 0512 0496 7 0386 0573 0518 0482 0471

180



0 0067 0090 0115 0043 0048 1 0067 0100 0100 0076 0077 2 0070 0084 0089 0100 0100 3 0070 0088 0089 0121 0121 4 0075 0092 0090 0138 0138 5 0079 0096 0090 0156 0155 6 0077 0102 0087 0191 0179 7 0364 0099 0097 0238 0240



0 0284 0214 0116 0413 0411 1 0160 0121 0104 0289 0282 2 0122 0073 0070 0149 0150 3 0110 0076 0070 0183 0179 4 0089 0077 0071 0204 0201 5 0086 0074 0071 0208 0213 6 0076 0066 0071 0194 0206 7 0034 0050 0070 0162 0144


Figure Page
















Figure Page


















Figure Page


















Figure Page




















Figure Page



LIST OF TABLES

Table Page



















Table Page








Figure Page




Table Page










LIST OF NOTATIONS













f Feed stage

f Fugacity [atm]









11) Weir height [m]






1 Weir length [m]















t Time [min]


















Greek symbols












Subscripts

B Bottom product



F Feed stream

1 Liquid phase


v


S Stripping section

Vapor phase


I INTRODUCTION




acetate













2






















3




















models were studied



4




















5




















6









du = f (uv t)

dt

0 = g(u v t)







solution vector u

7




in this work














8

s=0

s=1

s=2

s=M-1

s=M

S=M+1



m+1

1)-(St)= (S)1(Snt) 1 ltslt M+1 (1-2) n=1



Sk n = 0m (1-3)Wnl(s)

kVn Sn Sk k

m +1 S k n = 1m+1 (1-4)Wnv(S)

k=1 Sn Sk ktn




9



N





(a+Dx(13+1)N-xw(x a 13 N) - (1-6)x(N x)











10





















11























12













13









the liquid phase







14








aA + bB H cC + dD


VAA + VBB + VCC + VDD = 0 (2-1)

where





15

Condenser


dt

dt dM0

nr

LOLo (2-2b) 1=1


dt

Internal Stages

dM + + FX

dt (2-3a) +

dM nc

V F Vi W + (2-3b)dt j=1


dt

Reboiler


dt

nc dMN+1



16

D


17

Hw Xwj



i=N VN+1 HN+1 YN+1j

QR LN hN XNj

B hB xBd i=N+1


18


(2-5)1iA =





by




(2-8)



19






Id(TE (2-10)

n

(2-11)ij 1=1






dMik dhi (2-12)

dt dt

20



as




The result is

nc dx EK

dTi 1=1 dt nc (2-14)

dt dK E x

1=1 dT


_ -nc di ci



-di1=1




21






dt aT dt axm dt


n dK cbcii I M x



n cbcij x-n`






22


23

F


24




i +1 n i+1 dhk


Li (2-20) (h 11+1)

i+1 I n

= Li + Ft B+ (2-21) k =N +l j=1

i = NN-110


holdups

n







25











described in Sec221




qi =lk owi

(2-24a)


26

how Eqn (2-25) vi h

Li

A

1


27







how jY2qt = 36815 (2-24b)t

048F

how is defined by

(

M (2-25)

r7r Ceol4)Pi



and (2-4b) become




28





n dhN+1


VN+1 (2-28)(Hi+ h8)


(2-29) J=1




H1

i = (NN-12)





171 (2-31)(H1 ho


29


=1 dt





(2-24)











30

i=0

D

V1 Hr

hi

1

VF YFI HE

(1-OF xF

i=mi+m2+3



B


31

Condenser


dM0 -dt

- Vo Lo D + j =1



dM dt

dM n

-v + dt 1=1

dM ihi + L h L hdt







(2-33a)

(2-33b)

(2-33c)

(2 -34 a)

(2-34b)

(2-34c)

(2-35a)

(2-35b)

(2-35c)

32





dt J=1



Reboiler


BXB Vi rimi +3 A

dM n morm2+3



BhB QR






33


remain unchanged



















34




35



Chapter Two









311 Enthalpies


n


n

Hi =I yi H(7) (3-1b) i=1

36




H (TO = Ai + B + C + D + E iTi4 (3-2b)


= x (To Pi) (3-3a)

Hi =1 i(Ti Pi) (3-3b) J=1


procedures

Enthalpies of Vapor



37




_RT2( din f (3-5) aT )p





T2 (3-6)







T2 deg v

38


F (Pvk) (3-8)Pvk+1 = P

vk F(pvk)








thesis




= Hsi(Ti) A1(T) (3-10)


39


038 1 T T

where Tr = (3-11)A(7`)=7 A 1Tr




such as

Ki(T)=Oi + AT+ of T2 -F ei T3 (3-12)






j0

(3-13)



Appendix A

40

Bcit















F(T)=[Ixi jE1Ki(TP)]-1= 0 (3-16) i=1

41


F(Tk) (3-17)Tk+1 = Tk PAK)











Z (1 K (TF PF ))F(1)= L o (3-19)

=1 + ty(K (TF PF ) 1)

42





zi





=ExiJP(Ti) (3-21)





where r = T (3-22)T

43







Simplified model

Liquid enthalpy



dh dh = x (3-23)

dT

dT


(3-25)

44




dki +28T + 3E 72 (3-26)

dT dT




apo dpij (3-27)


dT dT 7 j(i_Trf

n axik 1i (3-29)

aXij k=1 j

45

Rigorous model

Liquid enthalpy







(3-30)

Thus



0

B + T +3D T2 +4E T3 (3-32)


46



T3 YPv


dA 038 A (3-34)

dT (T T)






ln(10) kJ (3-35) aT (T + C

9K1 Po1I (3-36)

dx dx





47



(-rA) = [k(7)][ fn( CA CB )1 (3-23)





M j as follows


= [k(T)C = k(T)MiX (3-24)



48



(3-26)







x=s-1 N=M-1

(N n)(n +a+1)(n+a+ 3+1)An (3-27)

(2n + a + 13 + 1)2

n(n+ I3)(N + n+ a + 3 +1) B (3-28)(2n + a + 11)2

where

(a)k = 0 k = 0

(a)k = (a)(a+1)(a+k-1) kgt 0

49


Q0(xa P N) =1 (3-29)

(a+ 0+2)xQi(xa P N) 1 (3-30)Ma +1)











requirements



50


set of equations



required accuracy









51







of ethyl acetate

A + B H C + D













52


Design Variables






AcOH zA 02559

Et0H zs 06159

Water zc 00743

- AcOEt zD 00539




Weir length [m] 006











53

N+1

(Ai )2







xitcoH 11893E-03 66924E-03 28242E-03 16359E-03

xEtolf 61785E-03 98927E-03 16722E-02 18820E-02

xwater 92009E-03 94784E-03 53772E-03 49359E-03

XAcOEt 13209E-03 47090E-03 12271E-02 11779E-02









results



0 1 2 3 4 5

Stage number


0 1 2 3 4 5 6 7

Stage number



0 0 1 2 3 4 5 6 7

Stage number



0 0 1 2 3 4 5 6 7

Stage number


55























Topic of studies

Physical

approximation

Numerical

approximation

Number of stages

Type of reaction

Thermodynamic

model

Pressure in the

column

Example 1



model assuming



reduced-order TDMH

model

8

irreversible

( 2A ---gt R + S )

simple

uniform (1 atm)

Example 2


order model in a

column with many

stages

reduced-order TDMH

model

29

rigorous

uniform (1 atm)

Example 30


order model in a

column with fewer

stages

-

reduced-order TDMH

model

11

Example 31


order model in a



assuming uniform

pressure

full-order TDMH

model assuming that


is uniform

reduced-order TDMH

model

11

reversible


rigorous rigorous


column

Example 32


on steady-state and

dynamic behaviors

full-order TDMH

model using various

plate geometries

-

11

rigorous

uniform (1 atm)

57


be observed

58

5 EXAMPLE PROBLEM 1






2A gt R + S


(-17A) = kACA

where






A 11000 + 30T 4000 + 30T 001Ts 10699 275 02

R 20000 + 20T 15000 + 20T 002T 11651 090 0229

S 25300 + 10T 25000 + 10T 003T 9418 459 0252

T is in degF

59


Design Variables






A 08

R 01

S 01















60







2x2 lx1


11835 20000

0 = condenser 28165 40000



61835 70000


9 = reboiler 90000






solutions

61

60

55

50

45

40

35

30 0

60

55 C Of 41) 50

I a 45 m ei n 40 I i 35

30 0

60

55 ii Oi a) 50 73

12a 45 co

isoo 40 i

35

30 0


1 2 3 4 5 6

Stage number

(a)


(b)

i I i i i 1


(c)

B TDMH - - -0- - CM H

7 8

B TDMH gt 2x2

O 1x1

7 8

--B CM H 2x2 o 1x1

I

7 8

9

9

9


62


09 -08 07 --e-- TDMH 06 -0- CMH 05 04 03 02 01

0 Ulf

0 1 2 3 4 5 6 7 8 9

Stage number

(a)

1

09 08 07 06 05 04 03 02 01

0 0 1 2 3 4 5 6 7 8 9

Stage number

(b)

1

09 08 8 CM H 07 2x2 06 - 0 1x1 05 04 03 02 01


0 1 2 3 4 5 6 7 8 9

Stage number

(c)


63

1

09 -08-07 06 05 04 -03-02 -01

0 0

1

09 08 07 -06 -05 04 03 02 01 -

0 0

1

09 08 07 06 05 04 03 02 01

0 0


1I I I I I

1 2 3 4 5 6

Stage number

(a)

1 2 3 4 5 6

Stage number

(b)

t 1 I 1

1 2 3 4 5 6

Stage number

(c)

$ TDMH CMH

1 1

7 8 9

--e TDM H o 2x2

0 1x1

7 8 9

9-- CM H 2x2

0 1x1

7 8 9


64


09 08 07 06 05 04 03 02 01

0 0

I

1

i

2 3

I

4 I

5 6

p TDMH

CMH

7 8 9

Stage number

(a)

1

09 08 07 06 05 04 03 02 01

0 0

I

1

I

2 3 4 5 6

e TDMH 2x2

O 1x1

7 8 9

Stage number

(b)

1

09 08 07 06 05 04-03 02 01

0 0

I

1 2 3 4 5 6

--eCMH 2x2

O 1x1

7 8 9

Stage number

(c)


65


700

600

500

400

300

$ TDMH CMH

200

100

0 0 1 2 3 4 5


(a)

800

700

600 Vapor

500

400

300

200

Liquid

9 TDM H 2x2

O 1x1

100

0


6 7 8 9

(b)

800

700

600 Vapor

500

400

300

200

Liquid 8CMH

2x2

O 1x1

100

0 0

F

1

f

2 I

3 I I

4 5 Stage number

i

6 I

7 i

8 9

(c)


66





TDMH CMH

(2x2) (1x1) Full (3x3) (2x2) (1x1)

T (degF)2 75654E-05 32486E-02 64722E-02 59785E-05 18506E-02

XA 18871E-07 28772E-05 97558E-05 20379E-07 29484E-05

XR 37528E-07 18061E-04 90993E-05 45029E-07 90603E-05

xs 90549E-08 11304E-04 22755E-06 99641E-08 44224E-05

L (lbmolmin)2 16683 3641945 317355 23006 2405854

V (lbmolmin)2 16822 3058993 317355 34804 2278430









67























68






model










69


003

0025

002 0015

001

0005

TDMH

CMH

0 0 10 20 30

time (min)

40 50

(a)

0035

003

0025

002

0015

001

0005

TDMH

2x2 1x1

0 0 10 20 30

time (min)

40 50

(b)

0035

003

0025

002-0015

001

0005

0 0 10 20 30 40

CMH 2x2 1x1

50

time (min)

(C)


70


-001

-002

TDMH

CMH

-003

-004 _ _ _

-005

-006 0 10 20 30

time (min)

40 50

(a)

I I I I

-001

-002

-003

TDMH

2x2 1x1

-004

-005

-006 0 10 20 30

time (min)

40 50

(b)

-001

-002

CMH

2x2 1x1

-003

-004

-005

-006 0 10 20 30

time (min)

40 50

(c)


71


002 _-____

0015

001

0005 TDMH

CMH

0 10 20 30

time (min)

40 50

(a)

0025

002

0015

001

0005

TDMH

2x2 lx1

0 10 20 30

time (min)

40 50

(b)

0025

002

0015

001

0005

CMH

2x2 1x1

0 10 20 30

time (min)

40 50

(c)


72




xA initial 00858 00859 00829 01041 01042 01009

final 01160 01160 01138 01248 01248 01212

XR initial 08237 08237 08257 08040 08040 08077

final 07706 07706 07705 07614 07614 07647

xs initial 00905 00905 00914 00919 00918 00915

final 01135 01134 01158 01138 01138 01141


Model Relative time

TDMH Full (3x3) 1

2x2 08972

lx1 06576


2x2 06150

lx1 04706






73



















behavior

74


0 1 2 3 4 5 6 7 8 9

stage number













75


001

0008

0006

0004

0002

0 0 10 20 30 40 50 60

time (m in)

(a)

0012

001- MAC 2x2

0008 1x1

0006

0004

0002

0 0 10 20 30 40 50 60

time (min)

(b)

0012

001

0008

0006

0004

0002

0 0 10 20 30 40 50 60

time (m in)

(C)


76


-0002 -0004 -0006 -0008 -001

-0012 -0014 -0016 -0018 -002

0 10 20 30 40 50 60

time (m in)

(a)

0 -0002 -0004 -0006 -0008

-001 -0012 -0014 -0016 -0018

-002 0 10 20 30 40 50 60

time (min)

(b)

0 -0002 -0004 -0006 -0008

-001 -0012 -0014 -0016 -0018

-002 0 10 20 30 40 50 60

time (m in)

(C)


77


0007 0006 TUC 0005 CM-I 0004

0003

0002

0001

0 0 10 20 30 40 50 60

time (min)

(a)

0008

0007 0006

0005 0004

0003 0002

0001

0 0 10 20 30 40 50 60

time (min)

(b)

0008

0007 0006

0005 0004

0003 0002

0001

0 0 10 20 30 40 50 60

time (m in)

(c)


78



fractions




















001 10

0

v 0001 0 E

TDMH

CMH

00001 000001 00001 0001 001


01

000001 00001 0001 001


20

10

-90 TDMH

CMH

-180 000001 00001 0001 001 01 1

Frequency ( radmin)

0

-10

CMH

000001 00001

(a)


0001 001

Frequency (radmin)

01

(b)


10

2x2 1x1

1

01

00001 0001 001 01 000001 00001 0001 001 01


90 10

2x2 1x1

0

-90 TDMH

2x2 1x1

-180 -10 000001 00001 0001 001 01 000001 00001 0001 001 01 1


(a) (b)


001 10

CMH

2x2

1x1

00001 01

000001 00001 0001 001 01 1 000001 00001 0001 001 01


10

0

-90 CMH

2x2 1x1

-180 -10 000001 00001 0001 001 01 1 000001 00001 0001 001 01 1


(a) (b)


82



















83

6 EXAMPLE PROBLEM 2







Design Variables







AcOH zA 04962

EtOH zs 04808

water zc 00229

AcOEt zD 0








84












8x16 7x14 6x12 4x9 3x6


10003 10036 10209 12230 15649

0 = condenser 20129 20873 22952 35293 50000

10 = vapor feed stage 31068 34290 40295 64707 84351

43453 50000 59705 87770 100000

56547 65710 77048 100000

68932 79127 89791

79871 89964 100000

89997 100000

100000

85


8x16 7x14 6x12 4x9 3x6


120000 120000 120005 120210 122214


30 = reboiler 140008 140282 142129 152490 183980

150112 151682 157096 177252 226020

160676 165036 174991 205000 263291

172205 180226 194781 232748 287786

184815 196607 215219 257510 300000

198183 213393 235009 276750

211817 229774 252904 289790

225185 244964 267871 300000

237795 258318 279742

249324 269718 289995

259888 279984 300000

269992 290000

280000 300000

290000

300000







86




8x16 7x14 6x12 4x9 3x6

T (K)2 34681E-06 61907E-06 99419E-06 78225E-05 77447E-03

XAcOH 40090E-11 25666E-10 10937E-09 52778E-08 79956E-06

xEioll 34920E-09 56707E-09 89310E-09 47621E-08 40108E-06

Xwater 18735E-09 37718E-09 63574E-09 26774E-08 86463E-07

XAcOEt 86031E-09 13058E-08 16382E-08 53505E-08 85873E-07

YAcoH 29980E-11 14345E-10 58830E-10 11738E-07 18645E-05

YEt0H 67593E-09 96737E-09 12643E-08 76121E-08 80113E-06

Ywater 24000E-09 47672E-09 80790E-09 45331E-08 19307E-06

YAcOEt 15738E-08 22710E-08 27523E-08 82866E-08 16307E-06

L (gmolmin)2 14936E-10 24385E-10 60968E-10 25848E-09 13842E-07

V (gmolmin)2 43025E-09 40383E-09 60686E-09 70445E-09 14962E-07

M (gmol)2 42749E-07 31854E-06 25227E-05 61481E-04 21716E-03




(gmolmin)

Full (9x18) 0014071

8x16 0014071

7x14 0014069

6x12 0014067

4x9 0014063

3x6 0014038



0 3 6 9 12 15 18 21 24 27 30

Stage number



0 3 6 9 12 15 18 21 24 27 30

Stage number

1

09 c 08 ot 07 E 06 e 05 oE 04 a 03 3 02

01 0

0

1

09 08 07 06 05 04 03 02 01

0 0


- full A 6x12

o 4x9 x 3x6

iiiii isii 1 3 6 9 12 15 18 21 24 27 30

Stage number


3 6 9 12 15 18 21 24 27 30

Stage number




o) 365

E 25

20

a)

L

360

355 -

E o E

15

10

sect 350I-

0 E

5

0

345 5 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(a) (b)



03

025

02

vapor 19 17 -15 -13 -

0 4x9

p

x

6x12

3x6

015

01

005

0

liquid

4-1 I I I

full

o 4x9

I it N 1 4 I

p

x 6x12

3x6


s1 1 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(c) (d)


89









25

AcOH

EtOH

-

- - water_

1 05 _ - -- AcOEt

0 1

345 350 355 360 365 370

Temperature (K)






90








reduced models







in Figure 64



column

91



Full (9x18) 1

8x16 09715

7x14 08797

6x12 07190

4x9 05733

3x6 04794








stream






048

2 046

to - 044

E 042V 04

TEM 7x14 4x9

8x16 6x12 3x6

018

0175

017

0165

016

0155

IDVH 7x14 4x9

8x16 6x12 3x6

038 0 10 20 30 40 50 60 70 80

015 0 10 20 30 40 50 60 70 80

time (hr) time (hr)



04

038

036

0 034 3 7 032

TDM-I 7x14 4x9

8x16 6x12 3x6

g 0033 ra co 1- 0031

Edeg 0029

yor 0027

TDMI-1

7x14 4x9

8x16 6x12 3x6

03 0 10 20 30 40 50 60 70 80

0025 0 10 20 30 40 50 60 70 80

time (hr) time (hr)



09 - full p 6x12 08 07 o 4x9 x 3x6 06 05 04 03 02 01


Stage number


09 08 07 06 05

6x1204 - full p03 02 o 4x9 x 3x6 01

0 i I I I I I I I

0 3 6 9 12 15 18 21 24 27 30

Stage number


09 -08

full p 6x12

07 o 4x9 x 3x6 06 05 04 03 02 -01

0 T 0 3 6 9 12 15 18 21 24 27 30

Stage number


09 08 full A 6x12 07 06 0 4x9 x 3x6

05 04 03 02 01

0 I I I

0 3 6 9 12 15 18 21 24 27 30

Stage number


46

370

365

360

355

- full

Temperature profile

p 6x12

o 4x9 x 3x6

E

E 5 E


25 -20 -15-10 -

- full A 6x12

o 4x9 x 3x6

sect 350

345

-6 E cr)


5 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(a) (b)



03 19

025

02

vapor 17 15 13

015

01

005

0 1-

liquid

I 4 4 I

full o 4x9

I i l I III I

A

x 6x12

3x6

I I

11

9-7-5-3

0 3 6 9 12 15 18 Stage number

21 24 27 30 0 3 6 9 12 15 18 Stage number

21 24 27 30

(c) (d)


95
















68




00004

00002 0

-00002 -00004 -00006 -00008 -0001

-00012 -00014

00012

0001

00008

00006

00004

00002

0

-00002

-00004


time (hr)


time (hr)

000015

00001

000005

0

-000005

-00001

-000015

-00002

000006

000005

000004

000003

000002

0

000001 -0

-000001 0


10 20 30 40 50

time (hr)


10 20 30 40 50

time (hr)


10 10

1

01

13 001 1

c E 0001 TDIVI-1 8x16 8x16 7x14

00001 7x14 4x9

6x12 3x6

6x12 3x6

4x9

000001 01



01

90 60 IDN1-1 8x16 50

407x 14 6x12 30

4x9 3x6 T 20 20 5 10

0 2 -10 0

-20 8x16 7x14o -30 6x12 4x9-40 3x6cc -50

-180 -60 000001 00001 0001 001 01 000001 00001 0001 001 01 1


(a) (b)


98












for simpler columns

99

7 EXAMPLE PROBLEM 3










problem




column was studied








100


Design Variables







AcOH za 04962

EtOH zB 04808

water zc 00229

AcOEt zD 0




Weir length [m] 009

Weir height [m] 003








101


each model






98597 109356 120000 109913 120000 120000










102






column





(2x5) (2x4) (1x3)

T (K)2 60609E-05 13436E-03 29741E-02

XAeOH 35046E-08 10320E-06 17373E-05

XEtOH 73801E-07 12009E-06 16073E-05

xwater 23561E-08 13345E-07 46047E-06

Xite0Et 78982E-07 78798E-07 17033E-05

Y AcOH 53545E-08 23869E-06 40598E-05

Y Et0H 60827E-07 15434E-06 26427E-05

Ywater 25369E-08 30654E-07 59017E-06

YAcOEt 64649E-07 64980E-07 16455E-05

L (gmolmin)2 16799E-09 26341E-08 35570E-07

V (gmolmin)2 18206E-09 33777E-08 48041E-07

M (gmol)2 11613E-03 11617E-03 10803E-02




10 EMI Cl 0111111 1111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12



09 09 -a- MAC08 08 07 07 x 2x5 06 06 4 2x4 05 -s- TEAM 05

0 1x304 04x 2x503 03

o 2x402 02 01 O 1x3 01

0 011111111 1411 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12




TDM-I aTow 30 Y 365 x 2x5 25 x 2x5

360 2x4 20 2x4 E 070o 1x3 15 0 1x3

11 355 E10 IP EX

a 0 5g 350

1- rn 0 i

345 i i -51111 E

1



035 21

03 19 6 TDMH 17VaporE 025 x 2x5

8 15-2x402 13E


01 2x4 7-=005- 5o 1x3

0 3 il 111111 1 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)


105




2x5 0011345

2x4 0011343

lx3 0011364














106



Full (3x6) 1

2x5 09313

2x4 08556

1x3 06608


















0485 - 0145C TDVH0048 0475 1 014 2x5

IMF 2x4 047 0 0135

2x5 o lx3E0465 0132x4 733 lx3 5r 0125

046

0455 I I I045 012

0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)


0375 00295 037 -

00290365 -036 00285 TDVHTDVH

0355 2x52x5 0028 035 2x42x4

002750345 1x3lx3 034 0027 4 I I I

0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)


0

108






respectively














0 -00001 -00002 -00003 -- 00004 -00005 2x5 -00006 -00007

2x4

-00008 lx3 -00009

0 10 20 30 40 50

time (hr)


0 -00001

0 10 20 30 40 50

time (hr)


000008 000006 TDMr1 2x5

000004 2x4 1x3 000002

0 -000002 -000004 -000006 -000008

-00001 0 10 20 30 40 50

time (hr)


000003

0000025

000002

0000015 000001

0000005

0

-0000005 0 10 20 30 40 50

time (hr)


10 10

1

01

1

001 full

2x5

0001 2x4

lx3 00001 01

000001 00001 0001 001 01 000001 00001 0001 001 01 1


90

0

full -90 2x5

2x4 1x3

-180 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


10 10

2x5 1 2x4

0 1x3 0 s 01 0is c= 001 full Tx E4 2x5

0001 2x4

lx3 00001 01


90 10

clii0 ii 13

w 0 0to



c- 1 0 2x5


-360 -20 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


112






operations





column in each case

pressure atm) 2

18

16

14

12

1

08

06

0--AP=005 X--AP=OA

AP= 015

04

02

0 I I I l iti 0 1 2 3 4 5 6 7 8 9 10 11 12

stage number




113







Table 712



T (K)2 250357 1175582 4137036

xAcoH 61711E-05 21799E-04 45062E-04

xEroll 86611E-04 23323E-03 33668E-03

Xwater 10578E-04 35052E-04 71882E-04

XAcOEt 10156E-03 25721E-03 34075E-03

YAcOH 36414E-05 12001E-04 22977E-04

YEt0H 14054E-03 41997E-03 76426E-03

Ywater 10252E-04 32920E-04 67493E-04

YAcoEt 15273E-03 43664E-03 77664E-03

L (gmolmin) 2 33027E-06 19272E-05 80700E-05

V (gmolmin)2 32945E-06 19270E-05 80678E-05

M (gmol) 2 77791E-03 17231E-02 16933E-02

11AcOH (gmolmin)2 23729E-07 81195E-07 15842E-06



(2x5) (2x4) (1x3) (2x5) (2x4) (1x3) (2x5) (2x4) (1x3)

T 1035E-04 1426E-03 2166E-02 6500E-04 1982E-03 7342E-02 1339E-01 1352E-01 4376E+00

xAcoH 3449E-08 9791E-07 1516E-05 3483E-08 9113E-07 1324E-05 4424E-08 8416E-07 1161E-05

XEt0H 4048E-07 7949E-07 1783E-05 3143E-07 6492E-07 1769E-05 4013E-06 4320E-06 2098E-04

xwate 1055E-08 1436E-07 5492E-06 9188E-09 1514E-07 5428E-06 2914E-07 4453E-07 1212E-05

XAr0Et 3785E-07 3776E-07 2799E-05 2746E-07 2758E-07 2852E-05 5805E-06 5805E-06 2511E-04

YACOH 5878E-08 2296E-06 3546E-05 6219E-08 2153E-06 3092E-05 6902E-08 1982E-06 2702E-05

Y DOH 3397E-07 1107E-06 2434E-05 2647E-07 9055E-07 2223E-05 3398E-06 3928E-06 1891E-04



L 1259E-09 2441E-08 2874E-07 1710E-09 2253E-08 2670E-07 8557E-08 1044E-07 4197E-06

V 1283E-09 2963E-08 3925E-07 1497E-09 2656E-08 3329E-07 1008E-07 1231E-07 5191E-06

M 1064E-03 1064E-03 1077E-02 1052E-03 1053E-03 1086E-02 1306E-03 1308E-03 1878E-02

17awn 9882E-13 3055E-11 3667E-10 1565E-12 4471E-11 4994E-10 1379E-11 7137E-11 1149E-09


320 -4 310 300 -- 290 CI

CY

I t f

A

1 flAP=010

0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


1x3300 290 tIllli11111

2x4

0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(c)

390 380 370 360 350 340 330 320 310 300 290

0 f III-1111111 1 2 3 4 5 6 7 8 9 10 11

Stage number


9-- TDMH x 2x5 o 2x4 o 1x3

12

(b)

390 380 370 360 350 340 330 320 310 300 290

0 1111f-1-11111

2 3 4 5 6 7 8 9 10 11

Stage number


9 TDMH 2x5

o 2x4 o 1x3

1 12

(d)


- --

09 -08 07 -06 -05 -04 03 -02 -01

0 II 0

1

09 -08 07 06 05 -04 -03 02 01 -

0 0


--B--AP=0 - -AP= 005

A AP= 010 ---G---AP= 015

1111111 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


-B-TDMH 2x5

o 2x4 o 1x3

i BM El i I I I

1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(c)

1

09 -08 -07 -06 05 -04 -03 -02 01 -

0 0

1

09 08 07 06 05 04 03 02 01

0 0


-13-TDMH x 2x5

2x4

O 1x3

1111111 OE U 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)


1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(d)



AP = 00503 02 fi AP - 010 01 - - -G - -AP= 015

0 11111111111 O 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


09 08 07 06 05 -8- TDM H04 x 2x503

O 2x4 02 01 0 1x3

0 O 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(c)



09 -08 -07 -06 -05 - -9- TDM H04 - x 2x503 -

O 2x402 -01-

0 loi1x3i i I f iiii0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)


09 -08 07 06 05 -04 -9- TDMH 03 - x 2x5 02 - p 2x4 01 - 0 1x3

0 0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(d)



09 -09 - --B--AP=0 -e-TDMH0808 07 07 - x 2x5

A AP=01006 06 2x4 05 05 O 1x3 04 - 04 -03 - 03 02 - 02 -01 01 -

0 0 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)


0909 -08 - TDMH 08

07 x 2x5 07

06 o 2x4 06 0505 o 1x3

04 - 04

03 - 03 02 - 02 01 01111111110 0


(c) (d)



09 09--B--AP=0 -B- TDMH08 - 08 -07 - 07 2x5

A AP= 01006- 06 - 2x4 ---0---AP= 01505 05 O 1x3

04 04 -03 - 03 -02 02 01 01lilt0 0I


(a) (b)


09 - 09 08 - -9- TDMH 08 07 x 2x5 07 06 - 06o 2x4

0505 o 1x3 04 - 04 03 - 03 02 02 01 - 01

0 0Iflit 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



035

2r

03

025

02

015

01

005

-13-- AP = 0 AP = 005

A AP= 010 --0---4P= 015

03

025

02

015

01

005

0

03

025

02

015

01

005

Vapor


2x4 o 1x3111114-11111

03

025 B

02 g0

015 8 0

01

005

0 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(a) (b)



035

03

025

02

015

01 -

005

Vapor

c CI 113 Liquid

NION101 -B-TDMH

X 2x5 2x4

II 1x3 t I 0

03

025

02

015

01

005

03 -

025 -

02

015

01

005

O NID Liquid x 2x5

O 2x4 O 1x3

I I 114111+1-f

Vapor

- 8- TDMH

03

025

02

015

01

005

0 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(c) (d)



21


9 9 7 7 5

3 3111111111 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)


19 - 19 8 TDMH-8 TCM-I 17

g 15 x 2x5 -6 17 rA 15

2x5

a 13 o 2x4 cl 13 o 2x4

31- 11 - 0 1x3 12 11 1x3 c

9 c

9 co 03 75 E

7 5 111--0K 3 1 i 111111111

7 5 3 i i 111111111


(c) (d)




E0005o 0005 o 1x3E E 9 0003 0) 0003

0001 0001 III

-0001 -0001 i



0011 0011

e TDVH0009 0009 -x 2x5

0007 s 0007 o 2x4

t 0005 t 0005o 1x3 E E a) 0003 0)0003

0001

-0001 El OK 0 4 I I I

0001

-0001 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(c) (d)


123







(MSE=4376)
















124




3

25

2 MOH

15 EtOH

1 - - water

05 Ac0Et

0

290 310 330 350 370

Temperature (K)











125









results










case



048 047

02 - AP - 0 AP= 010

AP - 005 AP- 015

046 018 -045 044

016

043 014 042 AP = 0 AP= 005 012 -041 AP = 010 AP= 015 04 01

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)


036 006 035 005 --034 004 -033


03 001 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)



0005 0

-0005 -001

-0015 -002 APdeg AP=005

-0025 AP=010 AP=015

-003 0 10 20 30 40 50

time (hr)

(a)


0005 0

-0005 -001

-0015 -002 TDVH 2x5

-0025 2x4 1x3

-003 0 10 20 30 40 50

time (hr)

(c)


0005 0

-0005 -001

-0015 -002 TDAH 2x5

-0025 2x4 1x3

-003 0 10 20 30 40 50

time (hr)

(b)


0005 0

-0005 -001

-0015 TEM 2x5-002

-0025 2x4

-003 0 10 20 30 40

time (hr)

(d)


50



003 003

0025 0025

002 002

0015 0015

001 AP-0 AP- 005

001 IDA4-1 2x5

0005 itP =010 AP-015 0005 1 2x4 1x3

0 i I I i 0 i 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)



003 003

0025 0025

002 002

0015 0015

001 -MINH 2x5 001

0005 2x4 1x3 0005

0 1 1 1 0

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)




0 0

-0005 APdeg AP= 005 -0005 TDVH 2x5

-001 AP- 010 AP- 015 -001 2x4 1x3

-0015 -0015

-002 -002

-0025 -0025

-003 -003 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(a) (b)



0 0

-0005 TDM- 2x5 -0005 MAC 2x5

-001 2x4 1x3 -001 2x4

-0015 -0015

-002 -002

-0025 -0025

-003 -003 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)




00035 - 00035 -0003 - 0003

00025 00025 -0002

00015 0001 TCMI 2x5

00005 2x4 1x3

0 50 0 10 20 30 40 50

time (hr)

(a) (b)



00035 00035 0003 0003

00025 00025 0002 0002

00015 00015 0001 0001

00005 00005 0 0

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)


131






















0 -00001 -00002 -00003 A- AP = 0 -0 0004 AP= 005 -00005 AP= 010 -00006 -00007 AP=015 -00008

0 500 1000 1500 2000 2500 3000 time (min)

(a)


0 -00001 -00002 -00003 -00004 -00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)


0 -00001 --00002 T -00003 -00004 --00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)

(b)


0 -00001 1--00002 + -00003 4 -00004 -t--00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)



0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)

(a)


0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)


2x400003 J-lx300002 4-

00001 0

-00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)

(b)


0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)



000005

0

-000005 AP = 0 AP = 005-00001 AP= 010

-000015 AP= 015

-00002 0 500 1000 1500 2000 2500 3000

time (min)

(a)


000005

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)


000005

0

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)

(b)


000005

0

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)



500 1000 1500 2000 2500 3000 time (min)

(a)


0 -000001

0 500 1000 1500 2000 2500 3000 time (min)



0

-000001 0 500 1000 1500 2000 2500 3000

time (min)

(b)


000005 000004

000003 000002 -r 000001 VI

0

-000001 0 500 1000 1500 2000 2500 3000

time (min)


10

0001

00001 000001

90

-90

-180 000001

OP -0 4P =005 AP- 010 AP= 015

00001 0001 001


4P =0 AP= 005 AP- 010 AP= 015

00001 0001 001

Frequency (radmin)

(a)

01

10

0

0V

ac 1

0 O 0 0

CC

01

000001

20

10

O 0 0 S -10 0 c a -20 0

w -30 flo cc

-40 000001

AP- 005 AP= 010 AP= 015

00001 0001 001


AP= 005 AP= 010 AP= 015

00001 0001 001

Frequency (radm in)

(b)

01


10 10

01 =0I0

GI

1 01 1774) a= 3 iTDMI-10010 E 2x5 rozQ 0

0001 2x4 el a)

lx3 cc

00001 01

000001 00001 0001 001 01 000001 00001 0001 001 01 1


90 50

of 40 a)a

---tu 30 co cco 20 a)


-180 -20 000001 00001 0001 001 01 1 000001 00001 0001 001 01


(a) (b)


10 10

1

0

01 a)

a 001 E 2x5

2x4 0001

lx3

00001 01



01

90 50

S40 2x5

30 rn

2x4

1x3 20

210 0 -g 0

X10 cc

-180 -20 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


10

1

0

01 0

ma a fi 001

0001

00001 000001

90

rn

a)

a) -90

a

-180 000001

TDM-I

2x5

2x4

lx3


TDIVH

2x5

2x4

1x3


(a)

10

1

01 01

000001 00001

01

90 80

O 70 60

40 50

40 30

c 0 20 713 10

2 00 cca) - 1 0

-20 000001 00001


01


(b)

01


140







the 1x3 model











Weir length [m] 009 009 009 002

Weir height [m] 003 003 003 006

Volume holdup [1] 0301 0181 0741 0301

141





















lower in case 32c



(2x5) (2x4) (1x3) (2x5) (2x4) (1x3) (2x5) (2x4) (1x3)

T 24206E-04 15413E-03 35626E-02 56883E-05 11573E-03 14283E-02 46403E-05 13594E-03 31742E-02


XEOH 61717E-07 11827E-06 72673E-05 25819E-08 38742E-07 16468E-05 92104E-07 14047E-06 17848E-05



YAcOH 47334E-08 22850E-06 46167E-05 64134E-08 22165E-06 29649E-05 54052E-08 24397E-06 42173E-05

YEt0H 48963E-07 16300E-06 78916E-05 26729E-08 70829E-07 20844E-05 75289E-07 17309E-06 29040E-05



L 86334E-10 27762E-08 48216E-07 12360E-09 21860E-08 26573E-07 17252E-09 27603E-08 36756E-07

V 18824E-09 43611E-08 60301E-07 11625E-09 21731E-08 27373E-07 19103E-09 36782E-08 49566E-07

M 28172E-03 28172E-03 19939E-02 19775E-04 20413E-04 48878E-03 38266E-06 42605E-06 18753E-04

1Acoll 26856E-13 83250E-12 14633E-10 20313E-12 52102E-11 57418E-10 53902E-13 19199E41 28894E40


370 Case 32b

365 9 case 32a - -o- - case 32b

365 a TDVH


360 360 o 2x4

355

350

345

14

A AAA g 355

) 350

345

O 1x3

Ii 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)

370 Case 32c

370 Case 32d

365 TDVH

365 a TDVH

x 2x5 x 2x5

360 o 2x4 360 o 2x4

17a 355 o 1x3

a co 355 O 1x3

350

345 I I

350

345 i III ill ill 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



09

08 13- case 32a - - - - case 32b

09 -

08 --a- TDVH

07 A case 32c case 32d 07 - x 2x5

06 06 - o 2x4

05 05 - 0 1x3 04 04 -

03 03 -

02 02 -

01 01

0 0 ml( a 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)

Case 32c Case 32d 1

09 -a- TDMH 09 -e-1DtVH 08 08

07 x 2x5 07

$ 2x5

06 2x4 06 2x4 05 O 1x3 05 o 1x3 04 04

03 03

02 02

01 01

0 MK 0 al a 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



09 09 08 08 07 - 07 06 e 06




(a) (b)

Case 32c Case 32d 1


2x4 02 02o 2x4 0 1x301 01 0 1x3

0 0 Iiili11111 03

441 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)




0 ilf111 0 S- 1111111


(a) (b)


09 09 08 -8- TCM-I -9-11)Virl08 07 x 2x5 07- x 2x5 06 062x4 2x4 05 05

O 1x3 0 1x304 04 03 03 02 02 01 01

0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)




o 1x3 04 E 04 03 03 02 - 7 02 01 - A- 01

-0- -0 01111


(a) (b)


09 - 09-a- TDVH08 08

07- x 2x5 07 06 - 06p 2x4 05 S 05

0 1x304 - 04 03 - 03 02 - 02 01 - 01

0 0 11111111111 1


(c) (d)


035

03

025

02

015

01

005

0 0

035

03

025


Vapor


a case 32c + case 32d11111111111 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a) Case 32c

Vapor


01 TDM-I x 2x5

005

0 0

2x4 o 1x311111111111 1 2 3 4 5 6 7 8 9 10 11

Stage number 12

(c)

Case 32b 035

03 Vapor 025 -

02 IF_

015

01

005 -

0 0

035

03

025

02

015

01

005

0 0

Liquid

11111111 1 2 3 4 5 6 7 8

Stage number

(b) Case 32d

1 2 3 4 5 6 7 8 Stage number

(d)

-9- TUC x 2x5

2x4

0 1x3

9 10 11 12

9 10 11 12



40 35 30


- -0- - - case 32b

+ case 32d

25

20 15


5

0 1 2 3 4 5 6 7 Stage number

8 12

(a)

45 40 35 30 25 20

a IDNI-1 x 2x5

o 2x4

o 1x3

Case 32c

15

10

5 0

0 1 2 3 4 5 6 7 Stage number

8 9 10 11 12

(c)

45 Case 32b

40 35 30 25 20 15 10

5

0 0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)

45 Case 32d

40 35 30 25

20 15 10

5 0

0 1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(d)




t 0005 - g 0005 2x4

O 1x3E SI 0003 - Cn 0003

0001 - 0001 TT El 19

-0001 -0001



0011 0011

0009 B-- MAC 0009

0007 - x 2x5 -2- 0007

E 0005 -0 o

o

2x4

1x3 0005

EDI 0003 - c7) 0003

0001 - 0001 III En CI

-0001 -0001


(c) (d)


151















used







152




products was larger





















051

049 c 02 -

047 045 015

043 E 01

041 039 037

- case 32a

case 32c

case 32b


case 32c

case 32b

case 32d 035 0

0 10 20 30 time (hr)

40 50 0 10 20 30 time (hr)

40 50

(a) (b)



037 006 c 035 -0 005

033 1 004 o deg 031 cd 003 _

12= 029 - case 32a case 32b 002



case 32b case 32d

025 0 L

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)



001 Case 32b

0005 0

c 0005 0

0 -0005 k b -0005 -001 o -001

-0015 E -0015 -002 case 32a case 32b o -002


-003 v -003 2x4 1x3

-0035 -0035 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(a) (b)


0005 0005 o 0 0

-0005 -0005

o -001 -001 E -0015 -0015 o o -002

- 0025 TDVH 2x5

-002 -0025

1DM-I 2x5

s -003 - 2x4 1x3 -003 2x4 1x3

-0035 -0035 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)



0035 Case 32b

003 g 003 TDA11 2x5 0025 I 0025 2x4 1x3

002

0015 ----___--- _____ -- ebe 0020 E 0015


0005 case 32c case 32d gt0 0005 13

0 f I I 0 1 1 1 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)

Case 32c Case 32d 0035 0035

g 003 TDM-1 2x5 003 TEM-I 2x5

a 0025 2x4 1x3 0025 2x4 1x3

m 0020 002

E 0015 0015 cG1 001 001 gt0 0005 0005 13

0 I I t 1 0 1 1 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)



0005 Case 32b



O -001 - 2x4 1x3

0-0015 ro

-002

-0025 -0025

0 10 20 30 time (hr)

40 50 0 10 20 30 time (hr)

40 50

(a) (b)

Case 32c Case 32d 0005 0005

0 0 0

-0005 TDIVI-1 2x5 -0005 111vH 2x5

O -001 2x4 1x3 -001 2x4 1x3

o -0015 -0015

-002 -002

-0025 -0025 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)



0007 Case 32b


o 0003 E 0003 _

c 0002 o

laquo- 0002 W

0001 gt0 0001 11

0 r-411egel7 I I I

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)

Case 32c Case 32d 0007 0007

5 0006 0006 TIM-I 2x5 V 0005 0005 2x4 1x3 w 00040 0004

E 0003 C

0003

0002 TI341-1 2x5 0002 es

0001 2x4 1x3 0001

0 i 1 i

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)


158











large plates











00002 Case 32b

0 0

-00002 -00002 -- 00004 case 32a m -00004 -


-00012 -00012 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

00002 Case 32c

00002 Case 32d

0 0

-00002 -00002

-00004 -00004 TEM -00006 -00006 2x5 -00008 -00008 2x4

-0001 -0001 lx3 -00012 -00012

0 10 20 30 40 0 10 20 30 40 50 time (hr) time (hr)

(C) (d)



00012 Case 32b

0001 - case 32a 0001

00008 case 32b 00008

00006 case 32c 00006

00004 - case 32d 00004

00002 00002

0 -4 0

-00002 -00002 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

Case 32c Case 32d 00012 00012

0001 0001 TUC 00008 00008 2x5 00006 00006 2x4 00004 00004 lx3 00002 00002

0 0

-00002 -00002 0 10 20 30 40 0 10 20 30 40 50

time (hr) time (hr)

(C) (d)




000005

0

-000005

-00001

-000015 0 10 20 30 40

time (hr)

(a)

Case 32c 000015

00001

000005

0

-000005

-00001

-000015 0 10 20 30 40

time (hr)

(C)

000015

00001

000005

Case 32b

TDAH

2x4

2x5

1x3

0 i 1 impoomponn

-000005

-00001

-000015 0 10 20

time (hr) 30 40

(b)

000015 Case 32d

00001 -

000005

TDIVH

2x4

2x5

1x3

0

-000005 -

00001 -

-000015 0 10 20 30

time (hr) 40 50

(d)



case 32c 000003 000003

case 32d 000002 000002 000001 000001

0 0

-000001 -000001 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

000007 Case 32c

000007 Case 32d

000006 TDIVH 000006 000005 2x5 000005 000004 2x4 000004 000003 lx3 000003 000002 000002 000001

000001 0

0 -000001

0 10 20 30 40 -000001

time (hr) 0 10 20 30

time (hr) 40 50

(C) (d)


10

0001

00001 000001

90

-180 000001

case 32a

case 32b

case 32c

case 32d


case 32a

case 32b

case 32c

case 32d


(a)

01 1

01

10

0

V ac 1

a)

cc

01

000001 00001

80

60 cn 4140

SI 20

63 0

120 o--40 0-60

1E)-80

-100 000001 00001


case 32b

case 32c

case 32d

01


(b)

01 1


10 10

1 0

0

01 V

o 001

E

0001

TD 1-i

2x5

2x4

lx3

113

V

CC

00001 000001 00001 0001 001


01


01

90 250

200 2x5

V Ilk 150

ca) 100

2x4

lx3

a) -90 C)

a=-180

TDA1-1

2x5

2x4

lx3

S 50 c a 0 To

-50

m-100

-270 000001 00001 0001 001


-150 000001 00001 0001 001


(a) (b)


10 10

2x5 1 2x4

1x3

TDVH E4

0001

2x5

2x4

00001 lx3

01



01

90 20

Si0 013 0 m c0 0 -90 c a

-180 000001

TDMI 2x5

2x4

lx3


01 1

s 15 as0 10 0 1n 5 c0 0 o c so -5as

deg -10-10 co =

-13 -15 0 0 -20 CE

-25 000001 00001 0001 001


(a) (b)


10 10

0

0

01

-enV

V 001 TUC E

ao

E

0001

2x5

2x4

lx3

V 0 cc

00001 01 000001 00001 0001 001



90 80

rn 0

TDV1-1

2x5

2x4 1x3

rn 70

43 60 O 50 of g 40 S 30

o c 20 To 10 13 00

-10

2x5

2x4

1x3

-270 -20 000001 00001 0001 001



(a) (b)


167







holdups (CMH)














model

168







169

BIBLIOGRAPHY












170














171










172

APPENDICES

173

APPENDIX A



Species Tc V Z

[K] [cm3gmol]

AcOH 5944 171 02

EtOH 5162 167 0248

Water 6473 56 0229

AcOEt 5232 286 0252





Species Aj 13j

AcOH -242129 20142

EtOH -300324 475

Water 0 04077

AcOEt -498159 1031


Normal Heat of



571 3911 5660

63 3515 9260

2176 3732 9717

378 3503 7700


Cj Dj EJ

28033x10-2 -01136x10-4 00020x10-6

25030x10-2 -08263x10-5 11975x10-9

36657x10-3 00615x10-4 0

30495x102 -53900x106 0

174



3

1-


+ aap6

AcOH EtOH

Ao (1gmol)2atm 1004538 686619

Bo lgmol 006519 005087

Co (1gmo1)2K2atm 3121503 1605577

ao (1gmo1)3atm 15616 084012

bo (1gmo1)2 002703 001674

Co (1gmo1)3K2atm 8087892 3279836

ao (1gmo1)3 0001601 0000781

yo (1gmo1)2 004365 002704


Water

1175617

008668

2828098

242981

004778

9748118

0003763

007717

AcOEt

311069

001856

1141020

013766

000219

8428061

369E-05

000354


log = A + C


Species Adeg Bdeg

AcOH 75596 164405

EtOH 783124 144052

Water 796681 166821

AcOEt 709808 123871


Cdeg

233524

21271

228

217

175



A -05543 0581778 0688636 -006014

A2 -032436 0209245 0024303 0229575

A3 -010369 -025733 0375534 186575

A4 -070546 -056264 127548 0355191

A5 -201335 -031485 177863 0468416

A6 -225362 0451732 0696279 15111

A7 0837926 -011541 0936722 -005997

A8 052376 0069531 0449357 0067399

A9 0434061 0074053 071779 -315997

A10 -053406 018701 144979 0941858

A -325231 -036999 -211099 -192225

Al2 590329 -008234 0746905 -075573

A13 3354 -040947 112914 103791

A14 0197296 109247 0120436 0365254

A15 -045266 0192416 -164268 -136587

A16 0014715 -017257 0330018 -213818


176

APPENDIX B







177

Start
















Continue simulation


178







at each plate






No




C Stop


179

APPENDIX C






0 0000 0003 0017 0001 0003 1 0032 0046 0041 0006 0024 2 0159 0205 0258 0172 0174 3 0167 0203 0261 0146 0156 4 0169 0201 0267 0129 014 5 0173 0200 0267 0119 0128 6 0188 0206 0267 0103 0119 7 0216 0278 0314 0118 0145



0 0649 0693 0752 0543 0539 1 0741 0734 0755 0633 0617 2 0649 0638 0583 0579 0576 3 0653 0634 0579 0551 0545 4 0677 0631 0573 0529 0521 5 0723 0630 0572 0516 0504 6 0659 0626 0572 0512 0496 7 0386 0573 0518 0482 0471

180



0 0067 0090 0115 0043 0048 1 0067 0100 0100 0076 0077 2 0070 0084 0089 0100 0100 3 0070 0088 0089 0121 0121 4 0075 0092 0090 0138 0138 5 0079 0096 0090 0156 0155 6 0077 0102 0087 0191 0179 7 0364 0099 0097 0238 0240



0 0284 0214 0116 0413 0411 1 0160 0121 0104 0289 0282 2 0122 0073 0070 0149 0150 3 0110 0076 0070 0183 0179 4 0089 0077 0071 0204 0201 5 0086 0074 0071 0208 0213 6 0076 0066 0071 0194 0206 7 0034 0050 0070 0162 0144


Figure Page


















Figure Page


















Figure Page




















Figure Page



LIST OF TABLES

Table Page



















Table Page








Figure Page




Table Page










LIST OF NOTATIONS













f Feed stage

f Fugacity [atm]









11) Weir height [m]






1 Weir length [m]















t Time [min]


















Greek symbols












Subscripts

B Bottom product



F Feed stream

1 Liquid phase


v


S Stripping section

Vapor phase


I INTRODUCTION




acetate













2






















3




















models were studied



4




















5




















6









du = f (uv t)

dt

0 = g(u v t)







solution vector u

7




in this work














8

s=0

s=1

s=2

s=M-1

s=M

S=M+1



m+1

1)-(St)= (S)1(Snt) 1 ltslt M+1 (1-2) n=1



Sk n = 0m (1-3)Wnl(s)

kVn Sn Sk k

m +1 S k n = 1m+1 (1-4)Wnv(S)

k=1 Sn Sk ktn




9



N





(a+Dx(13+1)N-xw(x a 13 N) - (1-6)x(N x)











10





















11























12













13









the liquid phase







14








aA + bB H cC + dD


VAA + VBB + VCC + VDD = 0 (2-1)

where





15

Condenser


dt

dt dM0

nr

LOLo (2-2b) 1=1


dt

Internal Stages

dM + + FX

dt (2-3a) +

dM nc

V F Vi W + (2-3b)dt j=1


dt

Reboiler


dt

nc dMN+1



16

D


17

Hw Xwj



i=N VN+1 HN+1 YN+1j

QR LN hN XNj

B hB xBd i=N+1


18


(2-5)1iA =





by




(2-8)



19






Id(TE (2-10)

n

(2-11)ij 1=1






dMik dhi (2-12)

dt dt

20



as




The result is

nc dx EK

dTi 1=1 dt nc (2-14)

dt dK E x

1=1 dT


_ -nc di ci



-di1=1




21






dt aT dt axm dt


n dK cbcii I M x



n cbcij x-n`






22


23

F


24




i +1 n i+1 dhk


Li (2-20) (h 11+1)

i+1 I n

= Li + Ft B+ (2-21) k =N +l j=1

i = NN-110


holdups

n







25











described in Sec221




qi =lk owi

(2-24a)


26

how Eqn (2-25) vi h

Li

A

1


27







how jY2qt = 36815 (2-24b)t

048F

how is defined by

(

M (2-25)

r7r Ceol4)Pi



and (2-4b) become




28





n dhN+1


VN+1 (2-28)(Hi+ h8)


(2-29) J=1




H1

i = (NN-12)





171 (2-31)(H1 ho


29


=1 dt





(2-24)











30

i=0

D

V1 Hr

hi

1

VF YFI HE

(1-OF xF

i=mi+m2+3



B


31

Condenser


dM0 -dt

- Vo Lo D + j =1



dM dt

dM n

-v + dt 1=1

dM ihi + L h L hdt







(2-33a)

(2-33b)

(2-33c)

(2 -34 a)

(2-34b)

(2-34c)

(2-35a)

(2-35b)

(2-35c)

32





dt J=1



Reboiler


BXB Vi rimi +3 A

dM n morm2+3



BhB QR






33


remain unchanged



















34




35



Chapter Two









311 Enthalpies


n


n

Hi =I yi H(7) (3-1b) i=1

36




H (TO = Ai + B + C + D + E iTi4 (3-2b)


= x (To Pi) (3-3a)

Hi =1 i(Ti Pi) (3-3b) J=1


procedures

Enthalpies of Vapor



37




_RT2( din f (3-5) aT )p





T2 (3-6)







T2 deg v

38


F (Pvk) (3-8)Pvk+1 = P

vk F(pvk)








thesis




= Hsi(Ti) A1(T) (3-10)


39


038 1 T T

where Tr = (3-11)A(7`)=7 A 1Tr




such as

Ki(T)=Oi + AT+ of T2 -F ei T3 (3-12)






j0

(3-13)



Appendix A

40

Bcit















F(T)=[Ixi jE1Ki(TP)]-1= 0 (3-16) i=1

41


F(Tk) (3-17)Tk+1 = Tk PAK)











Z (1 K (TF PF ))F(1)= L o (3-19)

=1 + ty(K (TF PF ) 1)

42





zi





=ExiJP(Ti) (3-21)





where r = T (3-22)T

43







Simplified model

Liquid enthalpy



dh dh = x (3-23)

dT

dT


(3-25)

44




dki +28T + 3E 72 (3-26)

dT dT




apo dpij (3-27)


dT dT 7 j(i_Trf

n axik 1i (3-29)

aXij k=1 j

45

Rigorous model

Liquid enthalpy







(3-30)

Thus



0

B + T +3D T2 +4E T3 (3-32)


46



T3 YPv


dA 038 A (3-34)

dT (T T)






ln(10) kJ (3-35) aT (T + C

9K1 Po1I (3-36)

dx dx





47



(-rA) = [k(7)][ fn( CA CB )1 (3-23)





M j as follows


= [k(T)C = k(T)MiX (3-24)



48



(3-26)







x=s-1 N=M-1

(N n)(n +a+1)(n+a+ 3+1)An (3-27)

(2n + a + 13 + 1)2

n(n+ I3)(N + n+ a + 3 +1) B (3-28)(2n + a + 11)2

where

(a)k = 0 k = 0

(a)k = (a)(a+1)(a+k-1) kgt 0

49


Q0(xa P N) =1 (3-29)

(a+ 0+2)xQi(xa P N) 1 (3-30)Ma +1)











requirements



50


set of equations



required accuracy









51







of ethyl acetate

A + B H C + D













52


Design Variables






AcOH zA 02559

Et0H zs 06159

Water zc 00743

- AcOEt zD 00539




Weir length [m] 006











53

N+1

(Ai )2







xitcoH 11893E-03 66924E-03 28242E-03 16359E-03

xEtolf 61785E-03 98927E-03 16722E-02 18820E-02

xwater 92009E-03 94784E-03 53772E-03 49359E-03

XAcOEt 13209E-03 47090E-03 12271E-02 11779E-02









results



0 1 2 3 4 5

Stage number


0 1 2 3 4 5 6 7

Stage number



0 0 1 2 3 4 5 6 7

Stage number



0 0 1 2 3 4 5 6 7

Stage number


55























Topic of studies

Physical

approximation

Numerical

approximation

Number of stages

Type of reaction

Thermodynamic

model

Pressure in the

column

Example 1



model assuming



reduced-order TDMH

model

8

irreversible

( 2A ---gt R + S )

simple

uniform (1 atm)

Example 2


order model in a

column with many

stages

reduced-order TDMH

model

29

rigorous

uniform (1 atm)

Example 30


order model in a

column with fewer

stages

-

reduced-order TDMH

model

11

Example 31


order model in a



assuming uniform

pressure

full-order TDMH

model assuming that


is uniform

reduced-order TDMH

model

11

reversible


rigorous rigorous


column

Example 32


on steady-state and

dynamic behaviors

full-order TDMH

model using various

plate geometries

-

11

rigorous

uniform (1 atm)

57


be observed

58

5 EXAMPLE PROBLEM 1






2A gt R + S


(-17A) = kACA

where






A 11000 + 30T 4000 + 30T 001Ts 10699 275 02

R 20000 + 20T 15000 + 20T 002T 11651 090 0229

S 25300 + 10T 25000 + 10T 003T 9418 459 0252

T is in degF

59


Design Variables






A 08

R 01

S 01















60







2x2 lx1


11835 20000

0 = condenser 28165 40000



61835 70000


9 = reboiler 90000






solutions

61

60

55

50

45

40

35

30 0

60

55 C Of 41) 50

I a 45 m ei n 40 I i 35

30 0

60

55 ii Oi a) 50 73

12a 45 co

isoo 40 i

35

30 0


1 2 3 4 5 6

Stage number

(a)


(b)

i I i i i 1


(c)

B TDMH - - -0- - CM H

7 8

B TDMH gt 2x2

O 1x1

7 8

--B CM H 2x2 o 1x1

I

7 8

9

9

9


62


09 -08 07 --e-- TDMH 06 -0- CMH 05 04 03 02 01

0 Ulf

0 1 2 3 4 5 6 7 8 9

Stage number

(a)

1

09 08 07 06 05 04 03 02 01

0 0 1 2 3 4 5 6 7 8 9

Stage number

(b)

1

09 08 8 CM H 07 2x2 06 - 0 1x1 05 04 03 02 01


0 1 2 3 4 5 6 7 8 9

Stage number

(c)


63

1

09 -08-07 06 05 04 -03-02 -01

0 0

1

09 08 07 -06 -05 04 03 02 01 -

0 0

1

09 08 07 06 05 04 03 02 01

0 0


1I I I I I

1 2 3 4 5 6

Stage number

(a)

1 2 3 4 5 6

Stage number

(b)

t 1 I 1

1 2 3 4 5 6

Stage number

(c)

$ TDMH CMH

1 1

7 8 9

--e TDM H o 2x2

0 1x1

7 8 9

9-- CM H 2x2

0 1x1

7 8 9


64


09 08 07 06 05 04 03 02 01

0 0

I

1

i

2 3

I

4 I

5 6

p TDMH

CMH

7 8 9

Stage number

(a)

1

09 08 07 06 05 04 03 02 01

0 0

I

1

I

2 3 4 5 6

e TDMH 2x2

O 1x1

7 8 9

Stage number

(b)

1

09 08 07 06 05 04-03 02 01

0 0

I

1 2 3 4 5 6

--eCMH 2x2

O 1x1

7 8 9

Stage number

(c)


65


700

600

500

400

300

$ TDMH CMH

200

100

0 0 1 2 3 4 5


(a)

800

700

600 Vapor

500

400

300

200

Liquid

9 TDM H 2x2

O 1x1

100

0


6 7 8 9

(b)

800

700

600 Vapor

500

400

300

200

Liquid 8CMH

2x2

O 1x1

100

0 0

F

1

f

2 I

3 I I

4 5 Stage number

i

6 I

7 i

8 9

(c)


66





TDMH CMH

(2x2) (1x1) Full (3x3) (2x2) (1x1)

T (degF)2 75654E-05 32486E-02 64722E-02 59785E-05 18506E-02

XA 18871E-07 28772E-05 97558E-05 20379E-07 29484E-05

XR 37528E-07 18061E-04 90993E-05 45029E-07 90603E-05

xs 90549E-08 11304E-04 22755E-06 99641E-08 44224E-05

L (lbmolmin)2 16683 3641945 317355 23006 2405854

V (lbmolmin)2 16822 3058993 317355 34804 2278430









67























68






model










69


003

0025

002 0015

001

0005

TDMH

CMH

0 0 10 20 30

time (min)

40 50

(a)

0035

003

0025

002

0015

001

0005

TDMH

2x2 1x1

0 0 10 20 30

time (min)

40 50

(b)

0035

003

0025

002-0015

001

0005

0 0 10 20 30 40

CMH 2x2 1x1

50

time (min)

(C)


70


-001

-002

TDMH

CMH

-003

-004 _ _ _

-005

-006 0 10 20 30

time (min)

40 50

(a)

I I I I

-001

-002

-003

TDMH

2x2 1x1

-004

-005

-006 0 10 20 30

time (min)

40 50

(b)

-001

-002

CMH

2x2 1x1

-003

-004

-005

-006 0 10 20 30

time (min)

40 50

(c)


71


002 _-____

0015

001

0005 TDMH

CMH

0 10 20 30

time (min)

40 50

(a)

0025

002

0015

001

0005

TDMH

2x2 lx1

0 10 20 30

time (min)

40 50

(b)

0025

002

0015

001

0005

CMH

2x2 1x1

0 10 20 30

time (min)

40 50

(c)


72




xA initial 00858 00859 00829 01041 01042 01009

final 01160 01160 01138 01248 01248 01212

XR initial 08237 08237 08257 08040 08040 08077

final 07706 07706 07705 07614 07614 07647

xs initial 00905 00905 00914 00919 00918 00915

final 01135 01134 01158 01138 01138 01141


Model Relative time

TDMH Full (3x3) 1

2x2 08972

lx1 06576


2x2 06150

lx1 04706






73



















behavior

74


0 1 2 3 4 5 6 7 8 9

stage number













75


001

0008

0006

0004

0002

0 0 10 20 30 40 50 60

time (m in)

(a)

0012

001- MAC 2x2

0008 1x1

0006

0004

0002

0 0 10 20 30 40 50 60

time (min)

(b)

0012

001

0008

0006

0004

0002

0 0 10 20 30 40 50 60

time (m in)

(C)


76


-0002 -0004 -0006 -0008 -001

-0012 -0014 -0016 -0018 -002

0 10 20 30 40 50 60

time (m in)

(a)

0 -0002 -0004 -0006 -0008

-001 -0012 -0014 -0016 -0018

-002 0 10 20 30 40 50 60

time (min)

(b)

0 -0002 -0004 -0006 -0008

-001 -0012 -0014 -0016 -0018

-002 0 10 20 30 40 50 60

time (m in)

(C)


77


0007 0006 TUC 0005 CM-I 0004

0003

0002

0001

0 0 10 20 30 40 50 60

time (min)

(a)

0008

0007 0006

0005 0004

0003 0002

0001

0 0 10 20 30 40 50 60

time (min)

(b)

0008

0007 0006

0005 0004

0003 0002

0001

0 0 10 20 30 40 50 60

time (m in)

(c)


78



fractions




















001 10

0

v 0001 0 E

TDMH

CMH

00001 000001 00001 0001 001


01

000001 00001 0001 001


20

10

-90 TDMH

CMH

-180 000001 00001 0001 001 01 1

Frequency ( radmin)

0

-10

CMH

000001 00001

(a)


0001 001

Frequency (radmin)

01

(b)


10

2x2 1x1

1

01

00001 0001 001 01 000001 00001 0001 001 01


90 10

2x2 1x1

0

-90 TDMH

2x2 1x1

-180 -10 000001 00001 0001 001 01 000001 00001 0001 001 01 1


(a) (b)


001 10

CMH

2x2

1x1

00001 01

000001 00001 0001 001 01 1 000001 00001 0001 001 01


10

0

-90 CMH

2x2 1x1

-180 -10 000001 00001 0001 001 01 1 000001 00001 0001 001 01 1


(a) (b)


82



















83

6 EXAMPLE PROBLEM 2







Design Variables







AcOH zA 04962

EtOH zs 04808

water zc 00229

AcOEt zD 0








84












8x16 7x14 6x12 4x9 3x6


10003 10036 10209 12230 15649

0 = condenser 20129 20873 22952 35293 50000

10 = vapor feed stage 31068 34290 40295 64707 84351

43453 50000 59705 87770 100000

56547 65710 77048 100000

68932 79127 89791

79871 89964 100000

89997 100000

100000

85


8x16 7x14 6x12 4x9 3x6


120000 120000 120005 120210 122214


30 = reboiler 140008 140282 142129 152490 183980

150112 151682 157096 177252 226020

160676 165036 174991 205000 263291

172205 180226 194781 232748 287786

184815 196607 215219 257510 300000

198183 213393 235009 276750

211817 229774 252904 289790

225185 244964 267871 300000

237795 258318 279742

249324 269718 289995

259888 279984 300000

269992 290000

280000 300000

290000

300000







86




8x16 7x14 6x12 4x9 3x6

T (K)2 34681E-06 61907E-06 99419E-06 78225E-05 77447E-03

XAcOH 40090E-11 25666E-10 10937E-09 52778E-08 79956E-06

xEioll 34920E-09 56707E-09 89310E-09 47621E-08 40108E-06

Xwater 18735E-09 37718E-09 63574E-09 26774E-08 86463E-07

XAcOEt 86031E-09 13058E-08 16382E-08 53505E-08 85873E-07

YAcoH 29980E-11 14345E-10 58830E-10 11738E-07 18645E-05

YEt0H 67593E-09 96737E-09 12643E-08 76121E-08 80113E-06

Ywater 24000E-09 47672E-09 80790E-09 45331E-08 19307E-06

YAcOEt 15738E-08 22710E-08 27523E-08 82866E-08 16307E-06

L (gmolmin)2 14936E-10 24385E-10 60968E-10 25848E-09 13842E-07

V (gmolmin)2 43025E-09 40383E-09 60686E-09 70445E-09 14962E-07

M (gmol)2 42749E-07 31854E-06 25227E-05 61481E-04 21716E-03




(gmolmin)

Full (9x18) 0014071

8x16 0014071

7x14 0014069

6x12 0014067

4x9 0014063

3x6 0014038



0 3 6 9 12 15 18 21 24 27 30

Stage number



0 3 6 9 12 15 18 21 24 27 30

Stage number

1

09 c 08 ot 07 E 06 e 05 oE 04 a 03 3 02

01 0

0

1

09 08 07 06 05 04 03 02 01

0 0


- full A 6x12

o 4x9 x 3x6

iiiii isii 1 3 6 9 12 15 18 21 24 27 30

Stage number


3 6 9 12 15 18 21 24 27 30

Stage number




o) 365

E 25

20

a)

L

360

355 -

E o E

15

10

sect 350I-

0 E

5

0

345 5 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(a) (b)



03

025

02

vapor 19 17 -15 -13 -

0 4x9

p

x

6x12

3x6

015

01

005

0

liquid

4-1 I I I

full

o 4x9

I it N 1 4 I

p

x 6x12

3x6


s1 1 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(c) (d)


89









25

AcOH

EtOH

-

- - water_

1 05 _ - -- AcOEt

0 1

345 350 355 360 365 370

Temperature (K)






90








reduced models







in Figure 64



column

91



Full (9x18) 1

8x16 09715

7x14 08797

6x12 07190

4x9 05733

3x6 04794








stream






048

2 046

to - 044

E 042V 04

TEM 7x14 4x9

8x16 6x12 3x6

018

0175

017

0165

016

0155

IDVH 7x14 4x9

8x16 6x12 3x6

038 0 10 20 30 40 50 60 70 80

015 0 10 20 30 40 50 60 70 80

time (hr) time (hr)



04

038

036

0 034 3 7 032

TDM-I 7x14 4x9

8x16 6x12 3x6

g 0033 ra co 1- 0031

Edeg 0029

yor 0027

TDMI-1

7x14 4x9

8x16 6x12 3x6

03 0 10 20 30 40 50 60 70 80

0025 0 10 20 30 40 50 60 70 80

time (hr) time (hr)



09 - full p 6x12 08 07 o 4x9 x 3x6 06 05 04 03 02 01


Stage number


09 08 07 06 05

6x1204 - full p03 02 o 4x9 x 3x6 01

0 i I I I I I I I

0 3 6 9 12 15 18 21 24 27 30

Stage number


09 -08

full p 6x12

07 o 4x9 x 3x6 06 05 04 03 02 -01

0 T 0 3 6 9 12 15 18 21 24 27 30

Stage number


09 08 full A 6x12 07 06 0 4x9 x 3x6

05 04 03 02 01

0 I I I

0 3 6 9 12 15 18 21 24 27 30

Stage number


46

370

365

360

355

- full

Temperature profile

p 6x12

o 4x9 x 3x6

E

E 5 E


25 -20 -15-10 -

- full A 6x12

o 4x9 x 3x6

sect 350

345

-6 E cr)


5 0 3 6 9 12 15 18

Stage number 21 24 27 30 0 3 6 9 12 15 18


(a) (b)



03 19

025

02

vapor 17 15 13

015

01

005

0 1-

liquid

I 4 4 I

full o 4x9

I i l I III I

A

x 6x12

3x6

I I

11

9-7-5-3

0 3 6 9 12 15 18 Stage number

21 24 27 30 0 3 6 9 12 15 18 Stage number

21 24 27 30

(c) (d)


95
















68




00004

00002 0

-00002 -00004 -00006 -00008 -0001

-00012 -00014

00012

0001

00008

00006

00004

00002

0

-00002

-00004


time (hr)


time (hr)

000015

00001

000005

0

-000005

-00001

-000015

-00002

000006

000005

000004

000003

000002

0

000001 -0

-000001 0


10 20 30 40 50

time (hr)


10 20 30 40 50

time (hr)


10 10

1

01

13 001 1

c E 0001 TDIVI-1 8x16 8x16 7x14

00001 7x14 4x9

6x12 3x6

6x12 3x6

4x9

000001 01



01

90 60 IDN1-1 8x16 50

407x 14 6x12 30

4x9 3x6 T 20 20 5 10

0 2 -10 0

-20 8x16 7x14o -30 6x12 4x9-40 3x6cc -50

-180 -60 000001 00001 0001 001 01 000001 00001 0001 001 01 1


(a) (b)


98












for simpler columns

99

7 EXAMPLE PROBLEM 3










problem




column was studied








100


Design Variables







AcOH za 04962

EtOH zB 04808

water zc 00229

AcOEt zD 0




Weir length [m] 009

Weir height [m] 003








101


each model






98597 109356 120000 109913 120000 120000










102






column





(2x5) (2x4) (1x3)

T (K)2 60609E-05 13436E-03 29741E-02

XAeOH 35046E-08 10320E-06 17373E-05

XEtOH 73801E-07 12009E-06 16073E-05

xwater 23561E-08 13345E-07 46047E-06

Xite0Et 78982E-07 78798E-07 17033E-05

Y AcOH 53545E-08 23869E-06 40598E-05

Y Et0H 60827E-07 15434E-06 26427E-05

Ywater 25369E-08 30654E-07 59017E-06

YAcOEt 64649E-07 64980E-07 16455E-05

L (gmolmin)2 16799E-09 26341E-08 35570E-07

V (gmolmin)2 18206E-09 33777E-08 48041E-07

M (gmol)2 11613E-03 11617E-03 10803E-02




10 EMI Cl 0111111 1111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12



09 09 -a- MAC08 08 07 07 x 2x5 06 06 4 2x4 05 -s- TEAM 05

0 1x304 04x 2x503 03

o 2x402 02 01 O 1x3 01

0 011111111 1411 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12




TDM-I aTow 30 Y 365 x 2x5 25 x 2x5

360 2x4 20 2x4 E 070o 1x3 15 0 1x3

11 355 E10 IP EX

a 0 5g 350

1- rn 0 i

345 i i -51111 E

1



035 21

03 19 6 TDMH 17VaporE 025 x 2x5

8 15-2x402 13E


01 2x4 7-=005- 5o 1x3

0 3 il 111111 1 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)


105




2x5 0011345

2x4 0011343

lx3 0011364














106



Full (3x6) 1

2x5 09313

2x4 08556

1x3 06608


















0485 - 0145C TDVH0048 0475 1 014 2x5

IMF 2x4 047 0 0135

2x5 o lx3E0465 0132x4 733 lx3 5r 0125

046

0455 I I I045 012

0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)


0375 00295 037 -

00290365 -036 00285 TDVHTDVH

0355 2x52x5 0028 035 2x42x4

002750345 1x3lx3 034 0027 4 I I I

0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)


0

108






respectively














0 -00001 -00002 -00003 -- 00004 -00005 2x5 -00006 -00007

2x4

-00008 lx3 -00009

0 10 20 30 40 50

time (hr)


0 -00001

0 10 20 30 40 50

time (hr)


000008 000006 TDMr1 2x5

000004 2x4 1x3 000002

0 -000002 -000004 -000006 -000008

-00001 0 10 20 30 40 50

time (hr)


000003

0000025

000002

0000015 000001

0000005

0

-0000005 0 10 20 30 40 50

time (hr)


10 10

1

01

1

001 full

2x5

0001 2x4

lx3 00001 01

000001 00001 0001 001 01 000001 00001 0001 001 01 1


90

0

full -90 2x5

2x4 1x3

-180 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


10 10

2x5 1 2x4

0 1x3 0 s 01 0is c= 001 full Tx E4 2x5

0001 2x4

lx3 00001 01


90 10

clii0 ii 13

w 0 0to



c- 1 0 2x5


-360 -20 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


112






operations





column in each case

pressure atm) 2

18

16

14

12

1

08

06

0--AP=005 X--AP=OA

AP= 015

04

02

0 I I I l iti 0 1 2 3 4 5 6 7 8 9 10 11 12

stage number




113







Table 712



T (K)2 250357 1175582 4137036

xAcoH 61711E-05 21799E-04 45062E-04

xEroll 86611E-04 23323E-03 33668E-03

Xwater 10578E-04 35052E-04 71882E-04

XAcOEt 10156E-03 25721E-03 34075E-03

YAcOH 36414E-05 12001E-04 22977E-04

YEt0H 14054E-03 41997E-03 76426E-03

Ywater 10252E-04 32920E-04 67493E-04

YAcoEt 15273E-03 43664E-03 77664E-03

L (gmolmin) 2 33027E-06 19272E-05 80700E-05

V (gmolmin)2 32945E-06 19270E-05 80678E-05

M (gmol) 2 77791E-03 17231E-02 16933E-02

11AcOH (gmolmin)2 23729E-07 81195E-07 15842E-06



(2x5) (2x4) (1x3) (2x5) (2x4) (1x3) (2x5) (2x4) (1x3)

T 1035E-04 1426E-03 2166E-02 6500E-04 1982E-03 7342E-02 1339E-01 1352E-01 4376E+00

xAcoH 3449E-08 9791E-07 1516E-05 3483E-08 9113E-07 1324E-05 4424E-08 8416E-07 1161E-05

XEt0H 4048E-07 7949E-07 1783E-05 3143E-07 6492E-07 1769E-05 4013E-06 4320E-06 2098E-04

xwate 1055E-08 1436E-07 5492E-06 9188E-09 1514E-07 5428E-06 2914E-07 4453E-07 1212E-05

XAr0Et 3785E-07 3776E-07 2799E-05 2746E-07 2758E-07 2852E-05 5805E-06 5805E-06 2511E-04

YACOH 5878E-08 2296E-06 3546E-05 6219E-08 2153E-06 3092E-05 6902E-08 1982E-06 2702E-05

Y DOH 3397E-07 1107E-06 2434E-05 2647E-07 9055E-07 2223E-05 3398E-06 3928E-06 1891E-04



L 1259E-09 2441E-08 2874E-07 1710E-09 2253E-08 2670E-07 8557E-08 1044E-07 4197E-06

V 1283E-09 2963E-08 3925E-07 1497E-09 2656E-08 3329E-07 1008E-07 1231E-07 5191E-06

M 1064E-03 1064E-03 1077E-02 1052E-03 1053E-03 1086E-02 1306E-03 1308E-03 1878E-02

17awn 9882E-13 3055E-11 3667E-10 1565E-12 4471E-11 4994E-10 1379E-11 7137E-11 1149E-09


320 -4 310 300 -- 290 CI

CY

I t f

A

1 flAP=010

0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


1x3300 290 tIllli11111

2x4

0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(c)

390 380 370 360 350 340 330 320 310 300 290

0 f III-1111111 1 2 3 4 5 6 7 8 9 10 11

Stage number


9-- TDMH x 2x5 o 2x4 o 1x3

12

(b)

390 380 370 360 350 340 330 320 310 300 290

0 1111f-1-11111

2 3 4 5 6 7 8 9 10 11

Stage number


9 TDMH 2x5

o 2x4 o 1x3

1 12

(d)


- --

09 -08 07 -06 -05 -04 03 -02 -01

0 II 0

1

09 -08 07 06 05 -04 -03 02 01 -

0 0


--B--AP=0 - -AP= 005

A AP= 010 ---G---AP= 015

1111111 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


-B-TDMH 2x5

o 2x4 o 1x3

i BM El i I I I

1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(c)

1

09 -08 -07 -06 05 -04 -03 -02 01 -

0 0

1

09 08 07 06 05 04 03 02 01

0 0


-13-TDMH x 2x5

2x4

O 1x3

1111111 OE U 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)


1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(d)



AP = 00503 02 fi AP - 010 01 - - -G - -AP= 015

0 11111111111 O 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a)


09 08 07 06 05 -8- TDM H04 x 2x503

O 2x4 02 01 0 1x3

0 O 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(c)



09 -08 -07 -06 -05 - -9- TDM H04 - x 2x503 -

O 2x402 -01-

0 loi1x3i i I f iiii0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)


09 -08 07 06 05 -04 -9- TDMH 03 - x 2x5 02 - p 2x4 01 - 0 1x3

0 0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(d)



09 -09 - --B--AP=0 -e-TDMH0808 07 07 - x 2x5

A AP=01006 06 2x4 05 05 O 1x3 04 - 04 -03 - 03 02 - 02 -01 01 -

0 0 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)


0909 -08 - TDMH 08

07 x 2x5 07

06 o 2x4 06 0505 o 1x3

04 - 04

03 - 03 02 - 02 01 01111111110 0


(c) (d)



09 09--B--AP=0 -B- TDMH08 - 08 -07 - 07 2x5

A AP= 01006- 06 - 2x4 ---0---AP= 01505 05 O 1x3

04 04 -03 - 03 -02 02 01 01lilt0 0I


(a) (b)


09 - 09 08 - -9- TDMH 08 07 x 2x5 07 06 - 06o 2x4

0505 o 1x3 04 - 04 03 - 03 02 02 01 - 01

0 0Iflit 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



035

2r

03

025

02

015

01

005

-13-- AP = 0 AP = 005

A AP= 010 --0---4P= 015

03

025

02

015

01

005

0

03

025

02

015

01

005

Vapor


2x4 o 1x3111114-11111

03

025 B

02 g0

015 8 0

01

005

0 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(a) (b)



035

03

025

02

015

01 -

005

Vapor

c CI 113 Liquid

NION101 -B-TDMH

X 2x5 2x4

II 1x3 t I 0

03

025

02

015

01

005

03 -

025 -

02

015

01

005

O NID Liquid x 2x5

O 2x4 O 1x3

I I 114111+1-f

Vapor

- 8- TDMH

03

025

02

015

01

005

0 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(c) (d)



21


9 9 7 7 5

3 3111111111 111111111 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)


19 - 19 8 TDMH-8 TCM-I 17

g 15 x 2x5 -6 17 rA 15

2x5

a 13 o 2x4 cl 13 o 2x4

31- 11 - 0 1x3 12 11 1x3 c

9 c

9 co 03 75 E

7 5 111--0K 3 1 i 111111111

7 5 3 i i 111111111


(c) (d)




E0005o 0005 o 1x3E E 9 0003 0) 0003

0001 0001 III

-0001 -0001 i



0011 0011

e TDVH0009 0009 -x 2x5

0007 s 0007 o 2x4

t 0005 t 0005o 1x3 E E a) 0003 0)0003

0001

-0001 El OK 0 4 I I I

0001

-0001 0 1 2 3 4 5 6 7

Stage number 8 9 10 11 12 0 1 2 3 4 5 6 7


(c) (d)


123







(MSE=4376)
















124




3

25

2 MOH

15 EtOH

1 - - water

05 Ac0Et

0

290 310 330 350 370

Temperature (K)











125









results










case



048 047

02 - AP - 0 AP= 010

AP - 005 AP- 015

046 018 -045 044

016

043 014 042 AP = 0 AP= 005 012 -041 AP = 010 AP= 015 04 01

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)


036 006 035 005 --034 004 -033


03 001 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)



0005 0

-0005 -001

-0015 -002 APdeg AP=005

-0025 AP=010 AP=015

-003 0 10 20 30 40 50

time (hr)

(a)


0005 0

-0005 -001

-0015 -002 TDVH 2x5

-0025 2x4 1x3

-003 0 10 20 30 40 50

time (hr)

(c)


0005 0

-0005 -001

-0015 -002 TDAH 2x5

-0025 2x4 1x3

-003 0 10 20 30 40 50

time (hr)

(b)


0005 0

-0005 -001

-0015 TEM 2x5-002

-0025 2x4

-003 0 10 20 30 40

time (hr)

(d)


50



003 003

0025 0025

002 002

0015 0015

001 AP-0 AP- 005

001 IDA4-1 2x5

0005 itP =010 AP-015 0005 1 2x4 1x3

0 i I I i 0 i 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)



003 003

0025 0025

002 002

0015 0015

001 -MINH 2x5 001

0005 2x4 1x3 0005

0 1 1 1 0

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)




0 0

-0005 APdeg AP= 005 -0005 TDVH 2x5

-001 AP- 010 AP- 015 -001 2x4 1x3

-0015 -0015

-002 -002

-0025 -0025

-003 -003 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(a) (b)



0 0

-0005 TDM- 2x5 -0005 MAC 2x5

-001 2x4 1x3 -001 2x4

-0015 -0015

-002 -002

-0025 -0025

-003 -003 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)




00035 - 00035 -0003 - 0003

00025 00025 -0002

00015 0001 TCMI 2x5

00005 2x4 1x3

0 50 0 10 20 30 40 50

time (hr)

(a) (b)



00035 00035 0003 0003

00025 00025 0002 0002

00015 00015 0001 0001

00005 00005 0 0

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)


131






















0 -00001 -00002 -00003 A- AP = 0 -0 0004 AP= 005 -00005 AP= 010 -00006 -00007 AP=015 -00008

0 500 1000 1500 2000 2500 3000 time (min)

(a)


0 -00001 -00002 -00003 -00004 -00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)


0 -00001 --00002 T -00003 -00004 --00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)

(b)


0 -00001 1--00002 + -00003 4 -00004 -t--00005 -00006 -00007 -00008

0 500 1000 1500 2000 2500 3000 time (min)



0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)

(a)


0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)


2x400003 J-lx300002 4-

00001 0

-00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)

(b)


0 -00001 -00002

0 500 1000 1500 2000 2500 3000 time (min)



000005

0

-000005 AP = 0 AP = 005-00001 AP= 010

-000015 AP= 015

-00002 0 500 1000 1500 2000 2500 3000

time (min)

(a)


000005

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)


000005

0

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)

(b)


000005

0

-000005

-00001

-000015

-00002 0 500 1000 1500 2000 2500 3000

time (min)



500 1000 1500 2000 2500 3000 time (min)

(a)


0 -000001

0 500 1000 1500 2000 2500 3000 time (min)



0

-000001 0 500 1000 1500 2000 2500 3000

time (min)

(b)


000005 000004

000003 000002 -r 000001 VI

0

-000001 0 500 1000 1500 2000 2500 3000

time (min)


10

0001

00001 000001

90

-90

-180 000001

OP -0 4P =005 AP- 010 AP= 015

00001 0001 001


4P =0 AP= 005 AP- 010 AP= 015

00001 0001 001

Frequency (radmin)

(a)

01

10

0

0V

ac 1

0 O 0 0

CC

01

000001

20

10

O 0 0 S -10 0 c a -20 0

w -30 flo cc

-40 000001

AP- 005 AP= 010 AP= 015

00001 0001 001


AP= 005 AP= 010 AP= 015

00001 0001 001

Frequency (radm in)

(b)

01


10 10

01 =0I0

GI

1 01 1774) a= 3 iTDMI-10010 E 2x5 rozQ 0

0001 2x4 el a)

lx3 cc

00001 01

000001 00001 0001 001 01 000001 00001 0001 001 01 1


90 50

of 40 a)a

---tu 30 co cco 20 a)


-180 -20 000001 00001 0001 001 01 1 000001 00001 0001 001 01


(a) (b)


10 10

1

0

01 a)

a 001 E 2x5

2x4 0001

lx3

00001 01



01

90 50

S40 2x5

30 rn

2x4

1x3 20

210 0 -g 0

X10 cc

-180 -20 000001 00001 0001 001 01 000001 00001 0001 001 01


(a) (b)


10

1

0

01 0

ma a fi 001

0001

00001 000001

90

rn

a)

a) -90

a

-180 000001

TDM-I

2x5

2x4

lx3


TDIVH

2x5

2x4

1x3


(a)

10

1

01 01

000001 00001

01

90 80

O 70 60

40 50

40 30

c 0 20 713 10

2 00 cca) - 1 0

-20 000001 00001


01


(b)

01


140







the 1x3 model











Weir length [m] 009 009 009 002

Weir height [m] 003 003 003 006

Volume holdup [1] 0301 0181 0741 0301

141





















lower in case 32c



(2x5) (2x4) (1x3) (2x5) (2x4) (1x3) (2x5) (2x4) (1x3)

T 24206E-04 15413E-03 35626E-02 56883E-05 11573E-03 14283E-02 46403E-05 13594E-03 31742E-02


XEOH 61717E-07 11827E-06 72673E-05 25819E-08 38742E-07 16468E-05 92104E-07 14047E-06 17848E-05



YAcOH 47334E-08 22850E-06 46167E-05 64134E-08 22165E-06 29649E-05 54052E-08 24397E-06 42173E-05

YEt0H 48963E-07 16300E-06 78916E-05 26729E-08 70829E-07 20844E-05 75289E-07 17309E-06 29040E-05



L 86334E-10 27762E-08 48216E-07 12360E-09 21860E-08 26573E-07 17252E-09 27603E-08 36756E-07

V 18824E-09 43611E-08 60301E-07 11625E-09 21731E-08 27373E-07 19103E-09 36782E-08 49566E-07

M 28172E-03 28172E-03 19939E-02 19775E-04 20413E-04 48878E-03 38266E-06 42605E-06 18753E-04

1Acoll 26856E-13 83250E-12 14633E-10 20313E-12 52102E-11 57418E-10 53902E-13 19199E41 28894E40


370 Case 32b

365 9 case 32a - -o- - case 32b

365 a TDVH


360 360 o 2x4

355

350

345

14

A AAA g 355

) 350

345

O 1x3

Ii 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)

370 Case 32c

370 Case 32d

365 TDVH

365 a TDVH

x 2x5 x 2x5

360 o 2x4 360 o 2x4

17a 355 o 1x3

a co 355 O 1x3

350

345 I I

350

345 i III ill ill 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



09

08 13- case 32a - - - - case 32b

09 -

08 --a- TDVH

07 A case 32c case 32d 07 - x 2x5

06 06 - o 2x4

05 05 - 0 1x3 04 04 -

03 03 -

02 02 -

01 01

0 0 ml( a 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(a) (b)

Case 32c Case 32d 1

09 -a- TDMH 09 -e-1DtVH 08 08

07 x 2x5 07

$ 2x5

06 2x4 06 2x4 05 O 1x3 05 o 1x3 04 04

03 03

02 02

01 01

0 MK 0 al a 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)



09 09 08 08 07 - 07 06 e 06




(a) (b)

Case 32c Case 32d 1


2x4 02 02o 2x4 0 1x301 01 0 1x3

0 0 Iiili11111 03

441 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)




0 ilf111 0 S- 1111111


(a) (b)


09 09 08 -8- TCM-I -9-11)Virl08 07 x 2x5 07- x 2x5 06 062x4 2x4 05 05

O 1x3 0 1x304 04 03 03 02 02 01 01

0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12


(c) (d)




o 1x3 04 E 04 03 03 02 - 7 02 01 - A- 01

-0- -0 01111


(a) (b)


09 - 09-a- TDVH08 08

07- x 2x5 07 06 - 06p 2x4 05 S 05

0 1x304 - 04 03 - 03 02 - 02 01 - 01

0 0 11111111111 1


(c) (d)


035

03

025

02

015

01

005

0 0

035

03

025


Vapor


a case 32c + case 32d11111111111 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(a) Case 32c

Vapor


01 TDM-I x 2x5

005

0 0

2x4 o 1x311111111111 1 2 3 4 5 6 7 8 9 10 11

Stage number 12

(c)

Case 32b 035

03 Vapor 025 -

02 IF_

015

01

005 -

0 0

035

03

025

02

015

01

005

0 0

Liquid

11111111 1 2 3 4 5 6 7 8

Stage number

(b) Case 32d

1 2 3 4 5 6 7 8 Stage number

(d)

-9- TUC x 2x5

2x4

0 1x3

9 10 11 12

9 10 11 12



40 35 30


- -0- - - case 32b

+ case 32d

25

20 15


5

0 1 2 3 4 5 6 7 Stage number

8 12

(a)

45 40 35 30 25 20

a IDNI-1 x 2x5

o 2x4

o 1x3

Case 32c

15

10

5 0

0 1 2 3 4 5 6 7 Stage number

8 9 10 11 12

(c)

45 Case 32b

40 35 30 25 20 15 10

5

0 0 1 2 3 4 5 6 7 8 9 10 11 12

Stage number

(b)

45 Case 32d

40 35 30 25

20 15 10

5 0

0 1 2 3 4 5 6 7 8 9 10 11 12 Stage number

(d)




t 0005 - g 0005 2x4

O 1x3E SI 0003 - Cn 0003

0001 - 0001 TT El 19

-0001 -0001



0011 0011

0009 B-- MAC 0009

0007 - x 2x5 -2- 0007

E 0005 -0 o

o

2x4

1x3 0005

EDI 0003 - c7) 0003

0001 - 0001 III En CI

-0001 -0001


(c) (d)


151















used







152




products was larger





















051

049 c 02 -

047 045 015

043 E 01

041 039 037

- case 32a

case 32c

case 32b


case 32c

case 32b

case 32d 035 0

0 10 20 30 time (hr)

40 50 0 10 20 30 time (hr)

40 50

(a) (b)



037 006 c 035 -0 005

033 1 004 o deg 031 cd 003 _

12= 029 - case 32a case 32b 002



case 32b case 32d

025 0 L

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)



001 Case 32b

0005 0

c 0005 0

0 -0005 k b -0005 -001 o -001

-0015 E -0015 -002 case 32a case 32b o -002


-003 v -003 2x4 1x3

-0035 -0035 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(a) (b)


0005 0005 o 0 0

-0005 -0005

o -001 -001 E -0015 -0015 o o -002

- 0025 TDVH 2x5

-002 -0025

1DM-I 2x5

s -003 - 2x4 1x3 -003 2x4 1x3

-0035 -0035 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)



0035 Case 32b

003 g 003 TDA11 2x5 0025 I 0025 2x4 1x3

002

0015 ----___--- _____ -- ebe 0020 E 0015


0005 case 32c case 32d gt0 0005 13

0 f I I 0 1 1 1 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)

Case 32c Case 32d 0035 0035

g 003 TDM-1 2x5 003 TEM-I 2x5

a 0025 2x4 1x3 0025 2x4 1x3

m 0020 002

E 0015 0015 cG1 001 001 gt0 0005 0005 13

0 I I t 1 0 1 1 1

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)



0005 Case 32b



O -001 - 2x4 1x3

0-0015 ro

-002

-0025 -0025

0 10 20 30 time (hr)

40 50 0 10 20 30 time (hr)

40 50

(a) (b)

Case 32c Case 32d 0005 0005

0 0 0

-0005 TDIVI-1 2x5 -0005 111vH 2x5

O -001 2x4 1x3 -001 2x4 1x3

o -0015 -0015

-002 -002

-0025 -0025 0 10 20 30 40 50 0 10 20 30 40 50

time (hr) time (hr)

(c) (d)



0007 Case 32b


o 0003 E 0003 _

c 0002 o

laquo- 0002 W

0001 gt0 0001 11

0 r-411egel7 I I I

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(a) (b)

Case 32c Case 32d 0007 0007

5 0006 0006 TIM-I 2x5 V 0005 0005 2x4 1x3 w 00040 0004

E 0003 C

0003

0002 TI341-1 2x5 0002 es

0001 2x4 1x3 0001

0 i 1 i

0 10 20 30 40 50 0 10 20 30 40 50 time (hr) time (hr)

(c) (d)


158











large plates











00002 Case 32b

0 0

-00002 -00002 -- 00004 case 32a m -00004 -


-00012 -00012 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

00002 Case 32c

00002 Case 32d

0 0

-00002 -00002

-00004 -00004 TEM -00006 -00006 2x5 -00008 -00008 2x4

-0001 -0001 lx3 -00012 -00012

0 10 20 30 40 0 10 20 30 40 50 time (hr) time (hr)

(C) (d)



00012 Case 32b

0001 - case 32a 0001

00008 case 32b 00008

00006 case 32c 00006

00004 - case 32d 00004

00002 00002

0 -4 0

-00002 -00002 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

Case 32c Case 32d 00012 00012

0001 0001 TUC 00008 00008 2x5 00006 00006 2x4 00004 00004 lx3 00002 00002

0 0

-00002 -00002 0 10 20 30 40 0 10 20 30 40 50

time (hr) time (hr)

(C) (d)




000005

0

-000005

-00001

-000015 0 10 20 30 40

time (hr)

(a)

Case 32c 000015

00001

000005

0

-000005

-00001

-000015 0 10 20 30 40

time (hr)

(C)

000015

00001

000005

Case 32b

TDAH

2x4

2x5

1x3

0 i 1 impoomponn

-000005

-00001

-000015 0 10 20

time (hr) 30 40

(b)

000015 Case 32d

00001 -

000005

TDIVH

2x4

2x5

1x3

0

-000005 -

00001 -

-000015 0 10 20 30

time (hr) 40 50

(d)



case 32c 000003 000003

case 32d 000002 000002 000001 000001

0 0

-000001 -000001 0 10 20 30 40 0 10 20 30 40

time (hr) time (hr)

(a) (b)

000007 Case 32c

000007 Case 32d

000006 TDIVH 000006 000005 2x5 000005 000004 2x4 000004 000003 lx3 000003 000002 000002 000001

000001 0

0 -000001

0 10 20 30 40 -000001

time (hr) 0 10 20 30

time (hr) 40 50

(C) (d)


10

0001

00001 000001

90

-180 000001

case 32a

case 32b

case 32c

case 32d


case 32a

case 32b

case 32c

case 32d


(a)

01 1

01

10

0

V ac 1

a)

cc

01

000001 00001

80

60 cn 4140

SI 20

63 0

120 o--40 0-60

1E)-80

-100 000001 00001


case 32b

case 32c

case 32d

01


(b)

01 1


10 10

1 0

0

01 V

o 001

E

0001

TD 1-i

2x5

2x4

lx3

113

V

CC

00001 000001 00001 0001 001


01


01

90 250

200 2x5

V Ilk 150

ca) 100

2x4

lx3

a) -90 C)

a=-180

TDA1-1

2x5

2x4

lx3

S 50 c a 0 To

-50

m-100

-270 000001 00001 0001 001


-150 000001 00001 0001 001


(a) (b)


10 10

2x5 1 2x4

1x3

TDVH E4

0001

2x5

2x4

00001 lx3

01



01

90 20

Si0 013 0 m c0 0 -90 c a

-180 000001

TDMI 2x5

2x4

lx3


01 1

s 15 as0 10 0 1n 5 c0 0 o c so -5as

deg -10-10 co =

-13 -15 0 0 -20 CE

-25 000001 00001 0001 001


(a) (b)


10 10

0

0

01

-enV

V 001 TUC E

ao

E

0001

2x5

2x4

lx3

V 0 cc

00001 01 000001 00001 0001 001



90 80

rn 0

TDV1-1

2x5

2x4 1x3

rn 70

43 60 O 50 of g 40 S 30

o c 20 To 10 13 00

-10

2x5

2x4

1x3

-270 -20 000001 00001 0001 001



(a) (b)


167







holdups (CMH)














model

168







169

BIBLIOGRAPHY












170














171










172

APPENDICES

173

APPENDIX A



Species Tc V Z

[K] [cm3gmol]

AcOH 5944 171 02

EtOH 5162 167 0248

Water 6473 56 0229

AcOEt 5232 286 0252





Species Aj 13j

AcOH -242129 20142

EtOH -300324 475

Water 0 04077

AcOEt -498159 1031


Normal Heat of



571 3911 5660

63 3515 9260

2176 3732 9717

378 3503 7700


Cj Dj EJ

28033x10-2 -01136x10-4 00020x10-6

25030x10-2 -08263x10-5 11975x10-9

36657x10-3 00615x10-4 0

30495x102 -53900x106 0

174



3

1-


+ aap6

AcOH EtOH

Ao (1gmol)2atm 1004538 686619

Bo lgmol 006519 005087

Co (1gmo1)2K2atm 3121503 1605577

ao (1gmo1)3atm 15616 084012

bo (1gmo1)2 002703 001674

Co (1gmo1)3K2atm 8087892 3279836

ao (1gmo1)3 0001601 0000781

yo (1gmo1)2 004365 002704


Water

1175617

008668

2828098

242981

004778

9748118

0003763

007717

AcOEt

311069

001856

1141020

013766

000219

8428061

369E-05

000354


log = A + C


Species Adeg Bdeg

AcOH 75596 164405

EtOH 783124 144052

Water 796681 166821

AcOEt 709808 123871


Cdeg

233524

21271

228

217

175



A -05543 0581778 0688636 -006014

A2 -032436 0209245 0024303 0229575

A3 -010369 -025733 0375534 186575

A4 -070546 -056264 127548 0355191

A5 -201335 -031485 177863 0468416

A6 -225362 0451732 0696279 15111

A7 0837926 -011541 0936722 -005997

A8 052376 0069531 0449357 0067399

A9 0434061 0074053 071779 -315997

A10 -053406 018701 144979 0941858

A -325231 -036999 -211099 -192225

Al2 590329 -008234 0746905 -075573

A13 3354 -040947 112914 103791

A14 0197296 109247 0120436 0365254

A15 -045266 0192416 -164268 -136587

A16 0014715 -017257 0330018 -213818


176

APPENDIX B







177

Start
















Continue simulation


178







at each plate






No




C Stop


179

APPENDIX C






0 0000 0003 0017 0001 0003 1 0032 0046 0041 0006 0024 2 0159 0205 0258 0172 0174 3 0167 0203 0261 0146 0156 4 0169 0201 0267 0129 014 5 0173 0200 0267 0119 0128 6 0188 0206 0267 0103 0119 7 0216 0278 0314 0118 0145



0 0649 0693 0752 0543 0539 1 0741 0734 0755 0633 0617 2 0649 0638 0583 0579 0576 3 0653 0634 0579 0551 0545 4 0677 0631 0573 0529 0521 5 0723 0630 0572 0516 0504 6 0659 0626 0572 0512 0496 7 0386 0573 0518 0482 0471

180



0 0067 0090 0115 0043 0048 1 0067 0100 0100 0076 0077 2 0070 0084 0089 0100 0100 3 0070 0088 0089 0121 0121 4 0075 0092 0090 0138 0138 5 0079 0096 0090 0156 0155 6 0077 0102 0087 0191 0179 7 0364 0099 0097 0238 0240



0 0284 0214 0116 0413 0411 1 0160 0121 0104 0289 0282 2 0122 0073 0070 0149 0150 3 0110 0076 0070 0183 0179 4 0089 0077 0071 0204 0201 5 0086 0074 0071 0208 0213 6 0076 0066 0071 0194 0206 7 0034 0050 0070 0162 0144

Physical and numerical approximations of reactive distillation ...than models using the physical...

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Transcript of Physical and numerical approximations of reactive distillation ...than models using the physical...