José A. Caballero Institute of Chemical Process ... Caballero … · Distillation accounts for...

José A. Caballero

Institute of Chemical Process Engineering University of Alicante.

SPAIN

Seville, March 30 – April 1, 2015

Presentation Overview:

Motivation

Why thermally coupled distillation?

Three component systems

Extension to systems with more than three components

Structural considerations

Basic configurations

Design based on superstructures

Thermodynamically equivalent sequences

A step further: Intensification

Distillation accounts for about 13% of the energy consumption of

the industry as a whole, and up to 23% of the energy use in specific

sectors such as organic chemical production (Soave et al, 2006)

Equivalent to 2.87 1018 J/year = 2.8 millions TJ /year = 91 GW or

54 millions ton. of oil.

It is estimated that there are more than 40000 distillation columns in

operation in USA (Humphrey, 1995)

About 90% of product recovery and purification are distillation

processes.

Motivation:

Thermally Coupled Distillation

Energy savings up to 30-40%

(Fidkowski & Krolikowski,1987. Halvorsen & Skogestadt, 2003)

T

Q

QReb

QCond

Treb

Tcond

Liquid at their

bubble points Qreb

Qcond

QF

T

Tcond

Treb

Q

Qreb

Qcond

QF

TF

vapor

Why Thermally Coupled Distillation ? Carlberg y Westerberg (1989 a, b)

Side strippers and side enrichers

ABC

C

A

B

ABC

C

A

B

ABC

C

A

B

ABC

A

C

B

Equivalents

Equivalents

B C

A

11CV

11CL

21CV

22CV

21CL

22CL

ABC

C

A

B

11

111

CC LVD

11

112

2112

21

22

CCCCC LVqLDqLL

Liquid balance in the feed to the second column

Net flow going to column 2

Calling q2 to the liquid fraction in the net feed to

the second column

22

21

11

CCC LLL

111

11

11

2 RLV

Lq

CC

C

q < 0 Superheated vapor

Side Strippers: (Carlberg y Westerberg, 1989)

ABC

C

A

B ABC

C

A

B

T T

Q reb 1

Qreb 2

Q cond 2

Qreb 1

Qreb 2

Q cond 2

Q cond 1

Side strippers:

Q Q

With an analysis similar to side strippers:

11 1

1

12

2 SB

Vq

C

q > 1 Sub-cooled liquid

T Qreb

Qcond A

Qcond B

Q

ABC

A

C

B

Side enrichers:

ABC

A

B

C

Qreb_C

Qcond_A

Qreb_B

Qcond_B

T Qreb_C

Qcond_A

Qreb_B

Qcond_B

ABC

A

B

C

T Qreb_C

Qcond_A

Fully thermally coupled configuration (Petlyuk) :

Equivalent to

Superheated vapor

Equivalent to

Sub-cooled liquid

ABC

A

B

C

Equivalent to

Superheated vapor

Equivalent to

Sub-cooled liquid

ABC

A

B

C

1

2

3

4

5

6

A

ABC B

C

1

2

3

4

5

6

1949 First patent (Wright)

1965 Thermodynamic Analysis (Petlyuk y col.)

1985 First industrial application BASF

2007 BASF more than 50 active processes operating with DWC.

Besides the energy savings

there are important investment

savings

Typical total savings between

10 – 40 %

Divided Wall Columns :

Divided Wall Column: ADVANTAGES

Savings in Energy

Savings in investment a single column

only one condenser and one reboiler

reduced space for installation

reduced costs in piping, pumps,

electric systems, etc…

Divided Wall Column: DRAWBACKS

Heat is added and removed in the worst conditions (hottest and coldest

temperatures).

DWC will likely be taller and have larger diameter than either of the two

conventional columns, and may surpass construction restrictions for a single

tower

Important investment for revamping.

It is not adequate if flows at both sides of the wall are very different.

Ej. Shultz et al (2002) (UOP)

kerosene fractionation in a LAB complex:

30% Energy saving

28% Capital saving

ABC

BC

A

B

C

ABC

A

B

C

AB ABC

BC

A

B

C

ABC

A

B

C

AB

ABC

A

B

C

AB

BC

ABC

A

B

C

AB

BC

ABC

A

B

C

AB

BC

In three component mixtures we can evaluate all the «Basic» column configurations

State Task Representation:

STATES: Physical and Chemical Properties of a stream (or a set of streams)

Quantitative: composition, temperature…

Qualitative: phase (liquid or vapor)

TASKS: Physical or Chemical transformations between adjacent states.

Ex. Separate A from BC in a mixture ABC.

COLUMN SECTION: Portion of a distillation column which is not interrupted

by entering or exiting streams or heat flows.

What are and how to generate all the separation sequences?

ABCDE

C

AB

B

A

E

D

ABCD

CD

ABCDE ABCD/E

ABCD AB/CD

E

AB A/B

CD C/D

A

B

C

D

In conventional columns (one feed, two products, condenser and

reboiler) there is a one to one relationship between the column

sequence and the state-task representation

State Task

State – Task Representation :

(Sargent, 1988; Kondili, 1993)

ABCD

ABC

C

BC

B

A

D

R. Agrawal (1996) presented some structural characteristics that are the basis for

generating thermally coupled distillation sequences formed by N-1 columns:

1. Starting from a sequence of conventional columns it is possible remove the

heat exchangers associated to intermediate mixtures (no to final product

streams), without changing the structure of the system.

Extension to more than three component systems

ABCDE ABCD/E

ABC AB/C

D

A

BC B/C

C

D

2. It is possible continue removing the heat exchangers associated to products with

intermediate volatility (B and C in the example), but in this case we need to add two

new column sections for each heat exchanger removed. (R. Agrawal, 1996)

D

ABCD

A

C

B

C


ABCD ABC/D

ABC AB/C

D

A

BC B/C

C

D

ABCD

ABC AB/BC

AB A/B

A

B

CD C/D

C

D

BC B/C ABC/CD


3. It is possible reduce even more

the energy consumption by

adding extra column sections, in

such a way that key components

are always components with

extreme volatilities.

10 column

sections = 4N-6

A

B

C

D

ABCD

ABCD

ABC

C

A

BC

D

B

BCD

AB

CD

12 column

sections = N(N-1)

BCD BC/CD

ABC/BCD ABC/CD ABCD

ABC AB/BC

AB A/B

A

B

CD C/D

C

D

BC B/C

Thermodynamically equivalent configurations

A

B

C

AB*

BC*

ABC ABC

A

B

C

AB*

BC*

ABC

A

B

C

BC*

AB*

ABC

A

B

C

AB*

BC*

All thermodynamically equivalent

configurations have the same energy

consumption and differences in

investment cost are usually small.

The final decision about what

sequence to selected should be based

on other considerations like

controllability, operability, safety,

etc…

ABCD AB/CD

AB A/B

CD C/D

A

D

B

C

ABCD

AB

CD

A

D

B

C

ABCD

AB

CD

A

D

B

C

AB/CD

A/B

C/D

State Task network

Representation using only

States

Representation with column sections

included.

ABCD

AB

C

A

CD

B

D

ABCD

AB

C

A

CD

B

D

ABCD AB/CD

AB A/B

CD C/D

A

D

B

C

ABCD

AB

C

A

CD

B

D

ABCD

AB

C

A

CD

B

D

All the Thermodynamically Equivalent configurations share the same sequence of states and tasks

What are and how to generate all the separation sequences?

Non-basic (more than N-1 columns) configurations tend to have more capital

cost than basic distillation configurations because of additional columns and

their associated condensers and reboilers (Caballero, 2006; Agrawal 2009). Their

operating cost is also at least as much as that of some basic configurations as

shown by Giridhar & Agrawal (2009).

Basic configurations: configurations with exactly N-1 columns

Non-Basic configurations can thus be omitted from the search space.

Remark: Divided wall columns can be considered as two columns in the same shell,

therefore sequences using DWC can be considered sequences with N-1 columns

Sub-Column (less than N-1 columns) configurations has always larger

energy consumption than best Basic-configuration. However, the reduced

number of columns also reduce the investment costs.

How to generate basic separation sequences?

Mathematical Programming based approach

Using the concept of tasks and states is possible develop systematically different

superstructures (Yeomans & Grossmann 1999)

Define the states and tasks and then assign equipments.

Define the equipment and states and then decide with task is performed in each equipment

STATE TASK NETWORK

STATE EQUIPMENT NETWORK

We can consider the separation task a basic unit formed by two column

section : rectifying section and stripping section.

In other words, the separation task can be consider a pseudo-column, by

comparison with conventional columns.

(Although these column sections can be placed in different actual columns)

Rectifying section

Stripping section

State

Separation Task

Considered as a pseudo column

(Caballero et al 2001-2006)

Remark

AB/CD ABCD

A/B

C/D

AB

CD

A

D

C

B

ABC/D

B/CD

BC/CD

AB/BCD

ABC/BCD

ABC/CD

A/BCD

BC/D

A/BC

AB/BC

AB/C

B/C

ABC

BCD

BC

to D

to A

to A

to B

to C

to D

SUPERSTRUCTURE: State-Task Network

A/BC/D: A/BCD

AB/BCD

AB/CD

ABC/BCD

ABC/CD

ABC/D

A/B/C: A/BC

AB/BC

AB/C

B/C/D: B/CD

BC/CD

BC/D

A/B: A/B

B/C: B/C

C/D: C/D

SUPERSTRUCTURE: State-Task representation (some tasks have been grouped)

BCD

BC

ABC

AB

CD

A

B

C

D

A/BC/D

A/B/C

B/C/D

B/C

C/D

A/B

BASIC SEQUENCES: LOGICAL RELATIONSHIPS (Caballero & Grossmann 2001, 2006, 2015)

1. A given state can give rise to at most one task

Set of logical relationships between tasks and states that assures a basic sequence

of columns. These logical relationships can be written in terms of Boolean or

binary variables and being included in any mathematical model in order to

generate the best alternative (or if desired all the alternatives).

_

;s

tt OUT EST

Y K s COL

_

1 ;s

t

t OUT EST

y s COL

tY Boolean variable

True = task t is selected

False = task t is not selected

ty Binary variable

1 = task t is selected

0 = task t is not selected

2.- A given state can only be produced at most by two tasks

2.1. If produced by two tasks:

one must be a stripping section and

the other a rectifying section.

s

s

tt RECT

tt STRIP

Y K

s StatesY K

1

1

s

s

t

t RECT

t

t STRIP

y

s Statesy

BASIC SEQUENCES: LOGICAL RELATIONSHIPS

Note: The minimum number of column sections is obtained when all the

states are produced at most by one task. (Except the final products)

Increases the number of columns, the

number of heat exchangers and it is

sub-optimal from an energetic point

of view.

3. All products must be produced by at least one task

_ _;

s st

t P REC P STRY s PROD

_ _

1s s

t

t P REC P STR

y s PROD

If the product is generated by two contributions, one must come

from a stripping section and the other from a rectifying section.

There is not heat exchanger associated with this product.

_

_

s

s

t st P REC

t st P STR

Y W

s PROD

Y W

_

_

1

1

s

s

t s

t P REC

t s

t P STR

y w

s PRODy w

s

t k s s

t RECT

Y Y W k STRIP

s States

1 1 1 1

s

t k s s

t RECT

y y w k STRIP

s States

4. If a state is produced by two tasks there is no necessary a heat

exchanger in that state. ABC AB/BC

AB A/B

BC B/C

A

C

B

ABC AB/C

AB A/B

A

C

B

ABC A/BC

BC B/C

A

C

B

B

B

B

5. Connectivity. Directly from the superstructure

_

_

_

_

s

s

t k sk OUT EST

t k sk IN EST

Y Y t IN EST

s STATESY Y t OUT EST

_

_

1 1 _

1 1 _

s

s

t k s

k OUT ST

t k s

k IN ST

y y t IN ST

s STATESy y t OUT ST

6. If a heat exchanger associated to a given state is selected then at least one of

the tasks that produce that state must be selected

_ ss t

t IN STW Y s STATES

_

1 1s

s t

t IN ST

w y s STATES

7. Logical relationships used to determine if a heat exchanger is a reboiler or a

condenser

; ,

; ,

t s s s

t s s s

Y W WC t RECT s STATES

Y W WR t STRIP s STATES

;s s sW WC WR s STATES

1 1 1 ; ,

1 1 1 ; ,

t s s s

t s s s

y w wc t RECT s STATES

y w wr t STRIP s STATES

Other logical relationship (no necessary for generating basic configurations)

TACobj :min

( 1)

( 1) 1

PL

s s t t sPLs STATES t tasks s STATES

i iTAC CH Qheat CC Qcool Cost Vessel Cost Internals Cost Heat Excahnger

i

, , ,

, ,

, ,

,

,

,

,

,

,

1 1

2 2

; _

(1 ) ; _

1 2 0

1 0

2 0

t

t j j j t j

t t t

t t t

t j t j t s

t j t j t s

j t j

t t

j j t r

j t j

t

j j t r

j t j

t

i j t r

Y

FI DI BI

D V L mass balance

B L V

FI DI j LK t OUT ST Sharp

FI DI j HK t OUT ST Split

FIV V

DIV

BIV

,

,

L V

,

1 0

1 0

2 0

2 0

0.

0

ρ ,ρ , 1 , 2 ,

( , , )

( , )

t

t

t

t

t

t j

t j

t t t

trays

t t i

Y

V

L

Vj COMP

Lr RUAs

DIUnderwood eqs

BI

Ar f V V

Capital Cost f D P N

T f P FI

tY

,

,

1 0

1 0

2 0

2 0

0

0

t

t

t

t

t

t j

t j

Y

V

L

V

L

DI

BI

COLs

LLLL

VVVVVV

SCOLDss

sss

SCOLBss

sss

SCOLDss

sss

SCOLBss

sssss

01221

01221021

ss

WW

0

0

),,(

01 ,

s

s

lms

S

COMPi

iisssssss

condenserCost

Qcond

TArUfcondenserCost

COLDTssDVDQcond

ss WCWC

0

0

),,(

02 ,

s

s

lms

S

COMPi

iisssssss

reboilerCost

Qreb

TArUfreboilerCost

COLBTssBVBQreb

ss WRWR

Exists or no heat

exchanger

Heat exchanger is a

condenser

Heat exchanger is a

reboiler

Model (cont)

COLs

BB

DD

FF

COMPi

iss

COMPi

iss

COMPi

iss

,

,

, FEEDsCOLs

COMPiBIDIFI

SCOLBss

iss

SCOLDss

issis

/

,,,

( , )s sZ W True

State m

Sss COLB

Sss COLD

SS COL

State

State

Tasks

L2ss

L1ss

V1-L1s

V2-L2s

V1-L1s

L2s

V2ss

V1ss

Conceptual Model (cont): Detail of the balance in a state.

Model: Alternatives for

an intermediate state s

sZ

Total

condenser

Partial

condenser

Cond

sHE

Thermal

couple

sHE

1 2 0

1 2 0

1 2 0

s

s s

s s

ss ss

Z

V V

L L

L L

Reboiler

Reb

sHE

State m

Sss COLB

Sss COLD

SS COL

State

State

Tasks

L2ss

L1ss

V1-L1s

V2-L2s

V1-L1s

L2s

V2ss

V1ss

Conceptual Model (cont):

Alternatives in a product state

sZ

Cond

sHE sHEReb

sHE

What about Thermodynamically equivalent configurations

A

B

C

AB*

BC*

ABC ABC

A

B

C

AB*

BC*

ABC

A

B

C

BC*

AB*

ABC

A

B

C

AB*

BC*

A

C

B ABC

AB A/B

AB/BC

BC B/C

Given a feasible sequence of

tasks (and/or states) find all

thermodynamically equivalent

configurations using N-1

columns.

1

2

3

4

5

6

7

8

9

10

11

12

ABCD

ABC

BCD

AB

BC

CD

A

B

C

D

1,4,9

2, 5, 10 2, 5, 10

6, 11 6, 11 6, 11

3,8 3, 8

12 12 12

7 7

2, 5, 10

1, 4, 9 1, 4, 9

COLUMN 1 COLUMN 2 COLUMN 3

7

3, 8

Thermodynamically

equivalent

configurations

7

3

1

2

6

8

9

5

4

10

11

12

ABCD

ABC

BCD

AB

BC

CD

A

B

C

D

1

2

ABCD

A

D

7

3

4

5

6

12

8

9

10

11

ABC

BCD

AB

BC

CD

B

C

1

2

3

4

5

6

7

8

9

10

11

12

1

2

3

4

5

6

7

8

9

10

11

12

Column 1 Column 3 Column 2

THERMODYNAMICALLY

EQUIVALENT SEQUENCES

The problem of finding all the possible rearrangements in N-1 columns can

be reduced to solve a set of logical relationships among tasks states and columns

EXTENDED ASSIGNMENT PROBLEM

THERMODYNAMICALLY EQUIVALENT SEQUENCES

LOGICAL RELATIONSHIPS I

sectionstrippingafromcoming

estatetorisegivethatsectionsSTR

sectionrectifyingafromcoming

estateatorisegivethatsectionsREC

productpureaiskkPURE

stateaiseeSTATE

columnaisccCOLUMN

sectioncolumnaisssSECTION

e

e

|

|

|

|

SETS

Ps,c

1. Each column has at least one section

COLUMNcP csSECTIONs

,

2. A given section can only be assigned

to one column

SECTIONsP cs

COLUMNc

,

Boolean variable: True if if

section s is assigned to column c


LOGICAL RELATIONSHIPS I I

3. Connectivity equations

3.1. No heat exchanger associated to a given state: Among all the sections

that reach of exit from a given state only two, a rectifying section and

a stripping section, must be assigned to a given column c.

COLUMNceRECseSTRTleRECTrcsPclPcrP ;;_;_,,,

COLUMNcSTRsSTRTlRECTrPPP eeecscrcl ;;_;_,,,

COLUMNcSTRsRECTlRECrPPP eeecsclcr ;;_;,,,

COLUMNcRECsSTRlSTRTrPPP eeecscrcl ;;;_,,,

COLUMNcSTRTsRECTlRECrPPP eeecsclcr _;_;,,,

COLUMNcSTRTsRECTlSTRrPPP eeecsclcr _;_;,,,

BC

4

5

9

10

4

5 10

4 9

5

9

10

ABC

1

3

4

4

3

1

1

3

4


LOGICAL RELATIONSHIPS I I I

3.2 . Heat exchanger associated to a given state. Stripping and rectifying

sections produced by the state must be in the same column

COLUMNcSTRsRECTrPP eecscr ,_,,

4. The two sections produced by the feed state must be assigned to the same

column.

cscs PP ,2,1

5. For products of intermediate volatility that leave the system , the rectifying

and stripping section must be assigned to the same column. No heat exchanger

associated to that pure product.

COLUMNcPUREeSTRlRECsPP eeclcs ;;;,,

ABC

3

4

1

2

Feed

8

5

AB

BCD

B

1

2

3

4

5

6

7

8

11

12

ABCD

ABC

BCD

AB

CD

A

B

C

D

4

11

ABC

CD

C

Example a.

mixture of 5 components. 5 heat exchangers.

there are 8 thermodynamically equivalent configurations using 4 columns.

ABCDE

BCDE

CDE

DE

A

B

C

D

E

1

2 5

6 11

12 19

20

ABCDE A

B

C

D

E

BCDE*

CDE*

DE*

1

2 5

6 11

12 19

20

ABCDE

A

B

C

D

E

BCDE*

CDE*

DE*

1

2

6

5

11

12 19

20

ABCDE

BCDE*

CDE*

DE*

A

B

C

D

E

1

2

5

6 11

12 19

20

ABCDE

BCDE*

CDE*

DE*

A

B

C

D

1

2

5

6 11

12 19

20

E

19

ABCDE

BCDE*

CDE*

DE*

A

B

C D

E

1

2

5

6 11

12

20

ABCDE

BCDE*

CDE* DE*

A

B

C

D

E

1

2 5

6 11

12

20

19

19

ABCDE

BCDE*

CDE*

DE*

A

B

C

D

E

1

2

5

6

11

12

20

ABCDE

BCDE*

CDE*

DE*

A

B

C

D

E

1

2

5

6 11

12 19

20

A

B

C

D

ABCDE

ABCD

BCDE

ABC

BCD

CDE

AB

BC

CD

DE

ABCDE

ABCD

BCDE

ABC

BCD

CDE

AB

BC

CD

DE

A

B

C

D

E

Satellite column arrangement Sequential column arrangement

These column arrangements

are two out of the 512 possible

rearrangements for this state task sequence.

( R. Agrawal; 2000 )

Example b.

Number of Thermodynamically equivalent configurations:

º

1. . 2 2 I

n thermalNT NHElinksN C

NT number of separation tasks

NHEI number of heat exchangers associated

to intermediate states

1

2

1

2..

NN

CN

1

2

64

2..NHE

N

CN

Special cases:

Only two heat exchangers and N(N-1) sections:

Minimum number of column sections. (m.n.c.s)

Note: m.n.c.s = f(NHEII)

NHEII number of heat exchangers associated

to pure products

More Operable Arrangements:

Given a sequence of tasks find a thermodynamically equivalent sequence

in which the vapor flows from columns at higher to lower pressures.

A

B

C

AB*

BC*

ABC ABC

A

B

C

AB*

BC*

ABC

A

B

C

BC*

AB*

ABC

A

B

C

AB*

BC*

Difficult to operate More operable

(Agrawal, 1999)

s

e

r

l

Pcc > Pc

e

r

s l

Pcc < Pc

e

r

l

k

Pcc < Pc

r

e

k

l

Pcc > Pc

Vapor flow

Logical Relationships

1.- There is a reboiler in the column at higher pressure and a condenser in

the column at lower pressure.

2.- Vapor flow goes from higher to lower pressures.

Example.

ABCDE

ABCD

BCDE

ABC

CDE

AB

DE

A

B

C

D

E

1

2

3

4

5

6

7

8

11

12

13

14

19

20 Pc4 > Pc3 > Pc2 > Pc1

5 components. 14 column sections. 2 Heat exchangers.

64 thermodynamically equivalent configurations

19 more operable configurations

The integration of the knowledge of the system with optimization tools

(NLP, MINLP, Disjunctive programming) allows finding a good solution to

a difficult combinatorial problem.

Nº.

Comp.

4

5

6

7

Nº Config.

(1)

5

14

42

132

Nº Config

(2)

18

203

4373

185421

Nº config.

(3)

152

6128

506919

85216192

Nº Config.

(4)

~103

~2·105

~108

(1) Sharp splits, consecutive keys.

(2) Basic configurations.

(3) Basic + Thermal links

(4) Considering thermodynamically equivalent configurations as different.

A sequential approach

Step 1: Basic configurations extended with the internal structure of heat exchangers + DWC

Solution: Energy consumption + sequence of separation tasks Step 2: Among thermodynamically equivalent configurations select the

best taking into account : • operability • single diameter columns

(including other considerations is straightforward)

Solution: Best sequence of actual columns Step 3: Column Intensification. From a set of best basic sequences

search for sub-column sequences: • Kaibel Columns • Transfer blocks removal • Vertical partitions

Example.

Components Feed flow (kmol/h)

A = n-hexane 120 Pressure 1.2 atm

B = n-heptane 90 Feed liquid fraction 1

C = n-octane 60 Vapour Steam cost 14.05 $/GJ

D = n-nonane 30 Cooling water cost 0.354 $/GJ

Cost data source Turton et al (2013)

(Rest of physical data from Aspen-Hysys TM database)

Example.

The following constraints have been added to the model in order to generate non-difficult to operate sequences:

1. Divided wall columns must have a condenser and a reboiler. In other words, they cannot be thermally coupled with the rest of the system

2. The flow transfer between two columns using side streams is forced to be saturated liquid.

3. We search for actual columns with a single diameter.

4. We search for configurations for which it is possible to establish a gradient of pressures in such a way that the vapour flows from higher to lower pressures.

5. We consider only columns with a single internal wall

Solution after the first step:

Solution in terms of states and tasks

Costs Summary

Total Shell Cost (k$) 1123.72

Total trays costs (k$) 277.52

Total Heat Exchanger Costs(k$) 339.31

Investment cost /year (CT·0.18·1.68) 526.34

Energy cost (k$/year) 1683.62

TAC (k$/year) 2210

D

C

B

A

BCD

ABC

CD

BC

AB

ABC/BCD

BC/CD

AB/BC

A/B

B/C

C/D

Model Statistics: Nº Equations = 1443 Nº Variables = 663 Nº Binaries = 30

Solution after the first step: Solution in terms of states and tasks

Heat exchanger Cond/Reb Heat load

(kW)

area (m2)

(based on ΔTml = 20ºC)

A Condenser 3189.8 187.64

D Reboiler 4080.4 178.97

Area (m2) Nº trays Column Sections

Task REC STR NR NS

ABC/BCD 1.7884 1.7884 6 6 S1 S2

AB/BC 2.2125 0.4723 8 8 S3 S4

BC/CD 0.7084 2.6127 8 9 S5 S6

A/B 3.2590 1.1406 18 18 S7 S8

B/C 1.2697 1.0831 15 15 S9 S10

C/D 1.1892 3.9832 20 20 S11 S12

Best Solution after steps 1 and 2

8

9

10

11

1

2

6

12

D = 2.28 m 2.06 m 1.28 m

7

3

4

5

ABCD

ABC

BCD

CD

BC

AB

C

B

A

D

Q = 3275 kW

Q = 4190 kW

TAC = 2336.7 k$/year (it increases around a 3.3%)

PROCESS INTENSIFICATION: Sequences with less than N-1 columns.

1. Kaibel columns (Kaibel, 1984): separate four key components using a single DWC

2. Elimination of transfer blocks (Rong and Massimiliano, 2012). These blocks appear in sequences which have columns formed by a single section connecting other two columns

3. Columns that can be merged in a single shell to form «columns with vertical partitions» (Agrawal, 2001)

It is possible develop sequences with less than N-1 columns. Even though there is always a penalty in terms of energy, the reduction in the investment could compensate the extra energy consumption. We will consider three cases:


Even though it is possible to develop a model that takes into account those alternatives from scratch, this considerably complicates the model. A better approach consists of generating a set of «tasks based» solutions (say all the solutions inside a 10-15% of the best one) and check if some of this solutions can be “intensified”

A Kaibel sequence can be generated from a fully TCD sequence by removing intermediate mixtures that do not include extreme volatility components (BC in this case). If the energy penalty is not too large the reduction in the number of shells could become the Kaibel column the optimal one. In this example, a simple calculation at minimum reflux conditions shows that there is an energy penalty around 18.5%. Taking into account energy consumption is around the 70% of the TAC we can discard the Kaibel column


KAIBEL COLUMNS

A

B

C

ABCD

D


Elimination of transfer blocks

Continuing with previous example, consider the fifth solution:

7

8

9

10

11

12

1

2 5

6

This solution has a TAC = 2455 k$/year.

~8% higher than the best one.

A possible, but no-optimized column arrangement

7

8

9

10

11

12

1

2



Transfer Block

5

6

1

2

6

5

7

8

9

10

11

12

1

2



1

2

6

5

7

8

9

10

11

12

1

2

1

2

6


7

1 8

2 9

10 6

11

12

Vertical Partitions


7

1 8

2 9

10 6

11

12

The TAC of this configuration is reduced to 2276 k$/year. Similar to the optimal solution based on tasks and better than the best solution when the tasks are rearranged in N-1 columns!

Thank you

for your Attention

José A. Caballero Institute of Chemical Process ... Caballero … · Distillation accounts for...

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