Mo hinh Hoa

8/9/2019 Mo hinh Hoa

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M hnh ha, m phng v tiu hacc qu trnh ha hc

Modeling, simulation and optimization for chemical process

Instructor: Hoang Ngoc Ha

Email: [email protected]

B mn QT&TBCurriculum/syllabi

Seminar group


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Outline General introduction

Structure and operation of chemical

engineering systems

What is a chemical process?

Motivation examples

Part I: Process modeling

Part II: Computer simulation

Part III: Optimization of chemical

processes


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General introduction Structure of chemical engineering system

(Copyright by Prof. Paul Sides at CMU, USA)


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General introduction Conservation laws:

Give some balance equations such as mass balance (or the molar

number by species), energy balance and momentum equation of thesystem under consideration

Equilibrium thermodynamics The extensive variables/intensive variables

The laws of thermodynamics

Reaction engineering Reaction mechanism

The rate of a chemical reaction

Transport processes How materials and energy move from one position to another (heat

conductivity, diffusion and convection) Biological processes

Transform material from one form to another (enzyme process) orremove pollutants (environmental engineering)


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General introduction References (complements) :

1. Sandler S. I. (1999). Chemical and EngineeringThermodynamics. Wiley and Sons, 3rd edition.

2. H.B. Callen. Thermodynamics and an introduction to

thermostatics. JohnWiley & Sons Inc, 2nd ed. New York,1985.

3. De Groot S. R. and P. Mazur (1962) Non-equilibriumthermodynamics. Dover Pub. Inc., Amsterdam.

4. V B Minh. (tp 4) K thut phn ng. NXBHQG Tp. HCh Minh, 2004

5. Nguyn Bin, (tp 5) Cc qu trnh ha hc. NXB Khoa hcv K thut, 2008


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General introduction Conservation laws:

Give some balance equations such as mass balance (or the molar

number by species), energy balance and momentum equation of thesystem under consideration

Equilibrium thermodynamics The extensive variables/intensive variables

The laws of thermodynamics

Reaction engineering Reaction mechanism

The rate of a chemical reaction

Transport processes How materials and energy move from one position to another (heat

conductivity, diffusion and convection) Biological processes

Transform material from one form to another (enzyme process) orremove pollutants (environmental engineering)


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General introduction

Operation of a chemical engineering plant

Copyright by T. Marlin

()

Dynamical behavior


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Oil and gas production plant


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The system may be

Isolated: There is no transfer of

mass or energy with the

environment

Closed: There may be transfer ofmechanical energy and heat

Open: There is mass transfer withthe environment


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Gas

BA,JQ

.

BA BA

Question: determinate physical volume of

the following systems?


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Process: A set of actions performed intentionally in order to reach

some result (Longmans Dictionary of Contemporary English)

Processes that involve energy conversion, reaction, separationand transport are called chemical processes (Prof. Erik Ydstie atCMU, USA)

Definition: Chemical processes are a special subclass ofprocesses since their behavior is constrained by a range oflaws and principles which may not apply in othercircumstances (mechanical/electrical systems)

Properties:

Highly nonlinear Complex network May be distributed


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Chemical processes

Thermal conductivity process

Transport (reaction) process


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Why we need informations about dynamical

behavior?

Research and development

Process design

Process control

Plant operation

Process modeling,

computer

simulation and optimization

()Ordinary Differential Equations

(ODEs) or Partial Differential

Equations (PDEs) or

Differential and Algebraic

Equations (DAEs)


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Motivation examples

Example 1: Gravity-flow tank

The higher the flow rate F, the higherh will beh

F0

F F

F0 =F0(t), h=h(t) and F =F(t)

F0, h and F: steadystate values

Overshoot

How to understand dynamical behavior to design thesystem avoiding Overshoot ?


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Motivation examples

Example 2: Heat exchanger

Thermocouple

Temperature transmitter

Temperature controller

Final control element


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Motivation examples

Example 3: Typical chemical plant and control system

Two liquids feeds are pumped intoa reactor

They react to form products

Reactor effluent is pumped through

a preheater into a distillation

To specify the various piecesof equipment:

Fluid mechanics

Heat transfer

Chemical kinetics

Thermodynamics and mass

transfer


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Motivation examples

Example 4: Optimization of a silicon process

The silicon reactor


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Motivation examples

Example 4: Optimization of a silicon process


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Outline


Structure and operation of chemical engineeringsystems


Motivation examples

Part I: Process modeling

Part II: Computer simulation Part III: Optimization of chemical processes


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Process modeling

Introduction

Fundamental laws

Continuity equations

Energy equation

Equations of motion


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Introduction

Uses of mathematical models Can be useful in all phases of chemical engineering, from

research and development to plant operations, and even inbusiness and economic studies Research and development:

Determinating chemical kinetic mechanisms and parameters fromlab. or pilot-plant reaction data

Exploring the effects of different operating conditions

Adding in scale-up calculations

Design Exploring the sizing and arrangement of processing equipment

Studying the interactions of various parts Plant operation

Cheaper, safer and faster

Troubleshooting and processing problems


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Introduction

Scope of course

A deterministic system is a system in which norandomness is involved in the evolution of states

of the system

Random effects such as noise

A stochastic system is non-deterministic system


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Introduction

Principles of formulation

Basis Fundamental physical and chemical laws such as laws

of conservation of mass, energy and momentum

Assumptions Impose limitations reasonable on the model

Mathematical consistency of model

Number of variables equals the number of equations(degrees of freedom)

Units of all terms in all equations are consistent


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Introduction

Solution of the model equations

Initial and/or boundary conditions Available numerical solution techniques and tools

Solutions are physically acceptable?

Verification

The mathematical model is proving that the model

describes the real-world situation

Real challenge


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Fundamental laws

Continuity equations

Total continuity equations (total mass balance)

EXERCISE ?

Component continuity equations (component balance)


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Fundamental laws

Energy balance

EXERCISE ?


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Fundamental laws

Equations of motion

Pushing in the i direction (i=x,y,z)

F =

dMv

dt

Where v = velocity,

F= total force and M= mass

Fi =d

Mvi

dt

EXERCISE ?


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Fundamental laws

Consider a system with n components

Number of equations obtained from thefundamental laws

n balance equations by species

1 total mass balance equation 1 energy balance equation

3 equations of motion (if the system is under

movement)

Not independent

n + 1 +(3)equations


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Constitutive equations

Reaction kinetics of

(bio)chemical reaction

Transport equations

k=k(T, C)


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Other equations

As we saw, we need equations that tell us how the

physical properties, primarily density and enthalpy,change with temperature, pressure, and

composition to rewrite alternative mathematicalmodels

Equations of state


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Other equations (cont.)

In some cases, simplification can be made without

sacrificing much overall accuracy

Or more complex, Cp is considered as a function of

temperature

H=CpT (liquid)

H=CpT+v (vapor)

H=RTTref

Cp(T)dT


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A polynomial in T is used for Cp

We obtain

Cp(T) =A1+ A2T

H =h

A1T+ A2T2

2

iTTref

=A1(T T0) +A22 (T

2 T20 )


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If the mixture is composed of components

(which we know the pure-componententhalpies) then the total enthalpy can be

averaged

H=P

N

j=1 xjhjMjPNj=1

xjMj

xj

Mj

hj

- mole fraction of jth component

- molecular weight of jth component

- pure-component enthalpy of jth component (energy per unit mass)


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Liquid densities can be assumed constant in

many systems Vapor densities usually cannot be considered

invariant in many systems and the PVT

relationship is almost always required. The simplest and most often used case is the

perfect gas law

P V =nRT v = nMV

= PMRT


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Examples of mathematical modeling of

chemical process

(Distributed) Transport reaction systems

De Groot S. R. and P. Mazur (1962) Non-equilibrium thermodynamics. Dover Pub. Inc.,Amsterdam.


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chemical process

Distributed reaction systems (reactor tubular

for example)

n chemical species

Inlet material and/orenergetic flux

Outlet materialand/or energetic flux

V,

PkkSk = 0() dV


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chemical process

Mass conservation by species

dmkdt

= ddt

RV kdV =

RV

kt

dV

RV kMkrvdV

kt

= div(Jk) +kMkrv

= RVdiv(Jk)dV Gauss theoremJk = vkk

R Jk d

Totalma

terialflux


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chemical process

=P

kk v=P

kJk

Jdk =k(vk v)

Jck =kv

Jk = Jdk+ J

ck

(P

kk)

t = div(Pk Jk)

t = div(v) v=

1

vt

+ v v=vdiv(v)

DvDt


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chemical process

J0

q

= (u +pv)

| {z }=hv + JqJu =uv+pv + Jq

ut

= divJu= R Ju d

PkhkJ

ck

PkhkJ

dk

dU

dt = RVu

t dV


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chemical process

Seminar:

Nonisothermal CSTR

Batch reactor

pH systems

Distillation column


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chemical process

Seminar:

Nonisothermal CSTR

Batch reactor

pH systems

Distillation column


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Phng trnh dng

S vn chuyn trong thit b phn ng cahn hp phn ng, bao gm:

Dng vt liu (khi lng/nng ) Dng nhit nng (nng lng)

Dng ng lng (xung)

C dngi lu, dng dn, dng cp vdng pht sinh Dng i lu hoc dng dn c th tn ti c lp hocng thi nhng ch trong mt pha

S vn chuyn xy ra qua lp bin ca hai pha l dng

cp

(lng/th tch) c c trng bi mt dng


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Phng trnh dng

Cc qu trnh vn chuyn trong thit b

Dng i lu S thay i v tr trong khng gian ca mt dngc gi l i lu (dng vn chuyn vm)

Mt dng i lu c biu th

Dng dn (khuch tn) Chuyn ng phn t trong lng pha kh hoc pha lng

l chuyn ng vi m to thnh dng dn

j c = v (lng/thi gian/din tch)

(lng/thi gian/din tch)j d = D

gradC


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Phng trnh dng

Cc qu trnh vn chuyn trong thit b (tt)

Dng cp S vn chuyn ca i lng c trng t pha ny

sang pha khc gi l s cp

Cc qu trnh xy ra gia cc pha thng c m tbng cc i lng qung tnh

(lng/thi gian/din tch)

- h s cp, - b mt ring (xt trn mt n v th tch)f

j =f

- ng lc

h h d


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Phng trnh dng

Dng pht sinh

Dng pht sinh vt cht do phnng ha hc

G=gradP

Gj =Pm

i=1jiri

Gi = (Hi)ri

Dng pht sinh cu nhit nng do phnng ha hc

Dng pht sinh ca ng lng do chnh lch p sut

c hnh thnh do s thay i ca p sut trong h, tcl c tc dng ca xung lc

Cc qu trnh vn chuyn trong thit b (tt)

Ph h d


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Phng trnh dng

Xt trng hp h tng qut (ng th hay

d th) c phn ng ha hc

n chemical species

Inlet material and/orenergetic flux

Outlet materialand/or energetic flux

dV

PjijSj = 0

Ph h d


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Phng trnh dng

Phng trnh cn bng tng qut c dng caphng trnh vi phn ring phn cDamkhlerthit lp (1936)

j c

j d

Dng cpDng

pht sinh

t

= div(v ) + div(grad) f+ G

= Cj CpT v

Ph h d


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Phng trnh dng

Vit li cc phng trnh cn bng

t = div(v ) + div(

grad) f+ G

t = div(v) + div(D?

grad) ?f+ G

vt

= div(v v) + div(gradv)

f(

v) + G

CpT

t = div(vCpT) + div(T

gradCpT)

?fCpT+ G

Cjt

= div(v Cj) + div(DgradCj)

jfCj+ Gj

Ph h d


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Phng trnh dng

Example: xem chng 5, tp 5 (sch Cc

qu trnh, thit b TRONG CNG NGHHA CHT V T HC PHM, Nguyn Bin)

M hnh ton cho h khuy l tng Chui thit b khuy l tng

Thit b khuy gin on

Thit by l tng Cc bi ton thc t

t = div(v ) + div(

grad) f+ G

O tli


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Outline


Structure and operation of chemical engineeringsystems


Motivation examples Part I: Process modeling

Part II: Computer simulation

Part III: Optimization of chemical processes

Ref.: Burden R. L. and Faires J. D. Numerical analysis.

Mo hinh Hoa

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