Department of Chemical Engineering Budapest University of Technology and Economics

andResearch Group of Technical Chemistry

Hungarian Academy of Sciences

 

OOPTIMAL DESIGN OF PTIMAL DESIGN OF INTEGRATED SEPARATION SYSTEMSINTEGRATED SEPARATION SYSTEMS

  

Zsolt Fonyo  

23 March 2004, Trondheim, Norway

Research activities

• DISTILLATION AND ABSORPTION• Determination of Vapour-Liquid Equilibria and design of Packed Col• umns.• Development on distillation and absorption technologies• Modelling and calculation of thermodynamic properties• Modelling of batch and continuous countercurrent separation processes

• EXTRACTION AND LEACHING• Kinetics of Soxhlet-type and Supercritical Solid-Liquid Extraction of Natural Products.

Mathematical modelling and optimization of the process.• Supercritical fluid extraction equipment and R&D capabilities

• REACTIONS• Mathematical modelling of residence time distribution and chemical reactions

• MIXING OF LIQUIDS

• PROCESS DESIGN AND INTEGRATION

• Feasibility of distillation for non/ideal systems• Hybrid separation systems• Reactive distillation• Design of Energy Efficient Distillation Processes• Energy integrated distillation system design enhanced by heat

pumping and dividing wall columns• Energy recovery systems• A global approach to the synthesis and preliminary design of• integrated total flow-sheets• Process Integration in Refineries for Energy and Environmental

Management

• CONTROL AND OPERABILITY• Assessing plant operability during process design• Transformation of Distillation Control Structures

• ENVIRONMENTALS• Waste reduction in the Chemical Industry

• CLEAN TECHNOLOGIES• Membrane separations• Cleaning of waste water with physico-chemical tools.• Solvent recovery• Synthesis of mass exchange networks with mixed integer

nonlinear programming • Economic and controllability study of energy integrated separation

schemes• Process synthesis of chemical plants

Analysis of energy integrated separations(distillation based)

Synthesis of Mass Exchange NetworksUsing Mathematical Programming

Solvent Recovery from Non-Ideal Quaternary Mixtures with Extractive Heterogeneous-

Azeotropic Distillation

23 March 2004, Trondheim, Norway

Integrated process design

• Challenge in chemical engineering

• Economical and environmental aspects

• Heat integration (HEN) & mass integration (MEN)

• Several synthesis strategies

• The design needs CAPE

Analysis of energy integrated separations(distillation based)

Budapest University of Technology and EconomicsDepartment of Chemical Engineering

(Economic and Controllability Analysis of Energy-Integrated Distillation Schemes)

Aims of the work

• Separation of ternary mixture by energy-integrated distillation schemes

• Optimization of the schemes

• Economic evaluation and comparison of the schemes

• Optimal schemes are investigated for controllability features

• Estimation of the environmental effects

•Mixture: (Ethanol – n-Propanol– n-Butanol)

Case study

•Product purity specifications: 99 mole %

•Feed compositions:

Case 1: (0.45/ 0.10/0.45)Case 2: (0.33/ 0.33/0.33)Case 3: (0.10/ 0.80/0.10)

A B

C

*Case 1

*Case 3

*Case 2

Composition Triangle

Techniques and assumptions

•NRTL and UNIQUAC activity models are used

•The impurities in B product stream are symmetrically distributed.

•Total condensers and reboilers are used.

•Exchange min. approach temperature (EMAT)=8.5 oC.

•Valve trays (Glitsch type) are used as column internals.

HYSYS Process Simulator

Modeling of the schemes

Steady-state simulation

Dynamic simulation

Conventional distillation schemes

Direct sequence

Indirect sequence

Base case for comparison

Col.1

ABC

Col.2

A

BC

AB

Col.1ABC

Col.2

A B

C

BC

L1 D1 L2 D2

Q2

B2

Conventional-heat integration

Forward heat integrationdirect sequence (DQF)

Backward heat integrationdirect sequence (DQB)

Col.1

ABC

Col.2

A B

CBC

L1 D1L2 D2

Q2

B2

R1=L1/D1

BR2=V2/B2

V2

Col.1`ABC

Col.2

A B

C

BC

L1 D1 L2 D2

Q2

B2

Thermo-coupling

Col.1 Col.2

ABC

A

B

C

V21

L21

L 12

S

Q

B

L D

V

R=L/D

SR

BR=V/B

V12

Petlyuk column (SP)

Sloppy separation sequences

Forward heat integration (SQF)

Col.1

ABC

Col.2

A

B

C

AB

BC

B

L D

S

Q

Sloppy separation sequence, backward heat integration (SQB)

Col.1

ABC

Col.2

A

B

C

AB

BC

L D

S

Q

B

The objective function is total annual cost (TAC), which includes annual operating and capital costs.

Utilities cost dataHigh utility prices

(a)Low utility prices

(b)

Utility Temperature(C)

Price($/ton)

Temperature(C)

Price($/ton)

LP-steam 160 17.7 160 6.62MP-steam 184 21.8 184 7.31Coolingwater

30-45 0.0272 30-45 0.0067

Electricity -------- 0.1 $/kwh --------- 0.06$/kwh

(a) Based on European prices(b) Based on U.S. prices

Estimation of capital cost

Douglas, J. M., Conceptual design of chemical processes, McGraw-Hill Book Company

Marshall & Swift index: (1056.8/280)Project life: 10 years

Sizing of columns and heat exchangers are estimated byHYSYS flowsheet simulator

Optimal fractional recovery of the middle component

Comparison of theoretical and optimal fractional recovery of the middlecomponent

Case 1,(0.45/0.10/0.45)

Case 2,(0.33/0.33/0.33)

Case 3,(0.10/0.80/0.10)

Schemes

* o

* o

* o

Petlyukcolumn (SP)

0.36 0.36 0.35 0.37 0.33 0.33

TAC ($/yr) 8.42E+05 8.42E+05 1.05E+06 1.04E+06 1.31E+06 1.31E+06

SQF scheme 0.39 0.32 0.37 0.33 0.35 0.35

TAC ($/yr) 1.03E+06 1.01E+06 1.01E+06 9.62E+05 9.80E+05 9.80E+05

SQB scheme 0.36 0.35 0.35 0.35 0.33 0.33

TAC ($/yr) 1.03E+06 1.02E+06 9.59E+05 9.59E+05 1.19E+06 1.19E+06

Mixture: ethanoln-propanoln-butanol

Equimolar feed composition (0.333, 0.333, 0,333)

Product purity specification: 99 m%

Case study

Table 3. Results of the economic optimizationD I DQF DQB SP SQF SQBDescription

Col.1 Col.2 Col.1 Col.2 Col.1 Col.2 Col.1 Col.2 Col. 1 Col.2 Col. 1 Col.2 Col. 1 Col.2Bottom temperature (oC) 102.32 117.22 117.19 96.93 153.60 117.21 102.32 134.11 102.37 117.19 150.45 117.24 103.82 158.77Column pressure (kPa) 101.33 101.33 101.33 101.33 511.00 101.33 101.33 178.50 101.33 101.33 451.00 101.33 101.33 367.00Column diameter (m) 0.84 0.82 0.96 0.78 0.76 0.87 0.84 0.85 0.72 0.98 0.65 0.74 0.71 0.71

Reflux ratio 2.25 1.67 0.90 1.87 2.56 2.38 2.25 2.20 0.67 2.99 0.82 1.92 0.67 1.61Overall column efficiency 0.52 0.49 0.46 0.49 0.63 0.49 0.52 0.53 0.51 0.49 0.59 0.48 0.49 0.56

Actual number of trays 91 98 93 88 93 55 92 61 87 145 57 147 79 143Total actual trays 189 181 148 153 232 204 223

Heating rate (kJ/hr) 8.01E+06 8.99E+06 5.19E+06 4.56E+06 5.28E+06 3.91E+06 3.94E+06Cooling rate (kJ/hr) 7.88E+06 8.85E+06 4.78E+06 4.19E+06 5.15E+06 3.78E+06 3.00E+06

Main HX duty (kJ/hr) ………….. ………….. 3.94E+06 4.26E+06 ………….. 2.89E+06 3.07E+06Auxiliary heat exchanger ………….. ………….. TC,MP TR,LP LP TC,MP TC,MP

Steam cost ($/yr) 5.45E+05 6.11E+05 4.52E+05 3.10E+05 3.59E+05 3.41E+05 3.43E+05C.W cost ($/yr) 2.73E+04 3.07E+04 1.66E+04 1.45E+04 1.79E+04 1.31E+04 1.04E+04

Operating cost ($/yr) 5.72E+05 6.41E+05 4.69E+05 3.25E+05 3.77E+05 3.54E+05 3.54E+05Capital cost ($/yr) 7.54E+04 7.85E+04 7.80E+04 8.14E+04 8.18E+04 7.62E+04 7.98E+04

TAC ($/yr) 6.48E+05 7.20E+05 5.47E+05 4.06E+05 4.59E+05 4.30E+05 4.33E+05Capital cost saving (%) 0 -4 -3 -8 -8 -1 -6

Operating cost saving (%) 0 -12 18 43 34 38 38TAC saving (%) 0 -11 16 37 29 34 33

Detailed results of economic studies

-20

-10

0

10

20

30

40%

D base case

I

DQF DQB SP SQF SQB

Comparison of TAC savings (%)

Heat loads of the studied schemes

0.0E+00

5.0E+06

1.0E+07

1.5E+07

2.0E+07

2.5E+07

3.0E+07

3.5E+07

Hea

t loa

d (k

J/h)

D DQB SP SQF SQB

Studied distillation schemes

Case 1 (0.45/0.1/0.45)

Case 2 (0.33/0.33/0.33)

Case 3 (0.1/0.8/0.1)

0.E+00

1.E+05

2.E+05

3.E+05

4.E+05

5.E+05

6.E+05

7.E+05

8.E+05

Capital cost

Utility cost

Total annual cost

Comparison of costs ($/yr)

D I DQF DQB

SP SQF SQB

Case (2), (0.33/0.33/0.33)

TAC savings of studied schemes

0

10

20

30

40

50

60

TA

C s

avin

gs (

%)

D DQB SP SQF SQB

Studied distillation schemes

Case 1 (0.45/0.1/0.45)Case 2 (0.33/0.33/0.33)Case 3 (0.1/0.8/0.1)

Results of the economic study

Energy-integrated schemes are more economical than the best conventional schemes.

Operating cost proved to be dominant on TAC.

Petlyuk column is the best in TAC saving at low concentration of the

middle component (case 1) with 33 % . The heat requirements for the separation increases with increasing

concentration of the middle component, and heat-integrated schemes prove to be the best.

The maximum TAC saving is achieved in case 3 with 53 % by

sloppy sequence with backward heat integration.

Controllability study

•Selection of controlled variables & manipulated variables,

•Degrees of freedom analysis

Steady-state control indices

•Niederlinski index (NI)•Morari index (MRI)•Condition number (CN)•Relative gain array (RGA)

Dynamic simulations

Open-loop Closed-loop

Steady state controllability indicesSteady state controllability indices for the optimized schemes

Studied Schemes NI MRI CN 11 22 33

D, (D1-L2-B2) 1.137 0.099 8.890 1.000 0.880 0.880

D, (L1-D2-Q2) 1.995 0.065 32.113 1.000 0.500 0.500

D, (L1-D2-B2) 1.865 0.234 4.934 0.580 0.540 0.920

DQF, (D1-L2-B2) 1.136 0.024 36.320 1.000 0.880 0.880

DQF, (L1-D2-Q2) 1.890 0.033 21.290 1.000 0.530 0.530

DQF, (L1-D2-B2) 1.678 0.226 5.240 0.586 0.595 1.020

DQB, (D1-L2-B2) 1.093 0.023 39.660 1.000 0.910 0.910

DQB, (L1-D2-Q2) 2.283 0.040 18.110 1.000 0.440 0.440

DQB, (L1-D2-B2) 1.540 0.246 5.040 0.647 0.645 1.000

SP, (D-S-Q) 3.515 0.182 6.890 1.000 0.320 0.280

SP, (L-S-B) 7.438 0.089 14.380 0.130 0.570 0.990

SQF, (D-S-Q) 6.470 0.010 137.400 1.000 0.250 0.150

SQF, (L-S-B) 4.030 0.008 158.100 0.250 0.250 0.998

SQB, (D-S-Q) 5.080 0.038 33.310 0.997 0.470 0.196

SQB, (L-S-B) 1.287 0.022 64.388 0.770 0.827 1.000

• Base case D and heat-integrated schemes (DQF and DQB) show less interactions.

• (D1-L2-B2) manipulated set proves to be better than (L1-D2-Q2) and (L1-D2-B2) for D, DQF and DQB.

Evaluation of steady state indices

• Serious interactions can be expected for the sloppy schemes (SQF, SQB and SP).

• (L-S-B) manipulated set proves to better than (D-S-Q) for SP, SQF and SQB schemes.

Dynamic simulations

1. Open composition control loops:

•Feed rate disturbance: 100 100.5 kmol/h

•Feed composition disturbance:

(0.33/0.33/0.33) (0.30/0.40/0.30)

Composition control loops are not installed

Results of open loop dynamic simulation

0.977

0.981

0.985

0.989

0.993

0 10 20 30 40 50 60 70 80 90Time (unit)

Prod

uct m

ole

frac

tion

99.5

100.5

101.5

102.5

103.5

104.5

105.5

Feed

rat

e (k

mol

/h)

Ethanol Propanol Butanol

Feed rate disturbance

Heat integrated (DQB) column, open loop, feed rate disturbance

0.97

0.975

0.98

0.985

0.99

0.995

0 10 20 30 40 50 60 70Time (unit)

Prod

uct m

ole

frac

tion

0.31

0.34

0.37

0.4

0.43

Feed

mol

e fr

acti

on

Ethanol Propanol Butanol

Feed composition disturbance

Heat integrated (DQB) column, open loop, feed composition disturbance

0.975

0.980

0.985

0.990

0.995

0 10 20 30 40 50 60 70

Time (unit)

Prod

uct m

ole

frac

tion

99.5

100.5

101.5

102.5

103.5

104.5

Feed

rate

(km

ol/h

r)

Ethanol Propanol Butanol

Feed rate disturbance

Petlyuk column, open loop, feed rate disturbance

0.97

0.974

0.978

0.982

0.986

0.99

0.994

0 10 20 30 40 50 60 70 80

Time (unit)

Prod

uct m

ole

frac

tion

0.31

0.34

0.37

0.4

0.43

Feed

mol

e fr

actio

n

Ethanol Propanol Butanol

Feed composition disturbance

Petlyuk column, open loop, feed composition disturbance

Open loop performance for feed rate disturbance

Ethanol (XA) n-Propanol (XB) n-Butanol (XC)

Studied

schemes

Time constant

(time unit)

Time constant

(time unit)

Time constant

(time unit)

Average time

constant

(time unit)

D 16 8 3 9

DQF 20 11 2 11

DQB 14 9 6 10

SP 16 5 6 9

SQF 16 3 5 8

SQB 23 13 11 16

•quite similar dynamic behaviour but

• sloppy backward heat integrated (SQB) is the slowest scheme

Summary of open-loop simulation results

2. Closed composition control loops:

Composition and level controller are installed

Controllers tuning by Tyerus-Luyben cycling method

Overshoot, settling time, and their product are evaluated.

P-controller

PI-controller

For level control

For composition control

Heat integrated (DQB) column, closed loop (D1-L2-B2), feed rate disturbance

0.9895

0.9898

0.9900

0.9903

0 5 10 15 20 25 30 35 40 45 50 55

Time (unit)

Prod

uct m

ole

frac

tion

99.5

101.5

103.5

105.5

Feed

rat

e (k

mol

/h)

Ethanol (A)Propanol (B)Butanol (C)

Feed rate disturbance

Results of closed-loop dynamic simulation

0.9894

0.9896

0.9898

0.9900

0.9902

0 5 10 15 20 25 30 35

Time (unit)

Prod

uct m

ole

frac

tion

0.31

0.34

0.37

0.4

0.43

Feed

mol

e fr

actio

n

Ethanol (A)Propanol (B)Butanol (C)

Feed composition disturbance

Heat integrated (DQB) column, closed loop (D1-L2-B2), feed composition disturbance

Petlyuk column, closed loop (L-S-B), feed rate disturbance

0.9897

0.9898

0.9899

0.9900

0.9901

0.9902

0 5 10 15 20 25 30 35 40

Time (unit)

Pro

du

ct m

ole

fra

ctio

n

99

102

105

108

Fee

d r

ate

(km

ol/

hr)

Ethanol(A)Propanol(B)Butanol(C)

Feed rate disturbance

Petlyuk column, closed loop (L-S-B), feed composition disturbance

0.9895

0.9897

0.9899

0.9901

0.9903

0 5 10 15 20 25 30 35 40

Time (unit)

Prod

uct m

ole

frac

tion

0.31

0.34

0.37

0.4

0.43

Feed

mol

e fr

acti

on

Ethanol(A)

Propanol(B)Butanol(C)

Feed composition disturbance

Summary of closed-loop simulation results

Closed-loop performance for feed rate disturbance

Studied schemes ST OS PSO FBL

D (D1-L2-B2) 10.580 0.010 0.075 1.3

D (L1-D2-B2) 32.740 0.011 0.227 1.0

DQF (D1-L2-B2) 11.620 0.006 0.051 1.3

DQF (L1-D2-Q2) 20.100 0.012 0.178 1.0

DQF (L1-D2-B2) 36.550 0.012 0.346 1.0

DQB (D1-L2-B2) 23.330 0.024 0.310 3.0

DQB (L1-D2-Q2) 26.750 0.033 0.751 1.0

DQB (L1-D2-B2) 34.250 0.034 0.677 1.0

SP (L-S-B) 30.610 0.023 0.238 2.0

SP (D-S-Q) 39.440 0.020 0.262 5.0

SQF (L-S-B) 40.500 0.057 0.813 2.0

SQF (D-S-Q) 59.960 0.042 0.903 3.0

SQB (L-S-B) 70.150 0.030 0.799 6.0

SQB (D-S-Q) 150.000 0.031 1.564 20

Closed-loop performance for feed composition disturbanceStudied schemes ST OS PSO FBLT

D (D1-L2-B2) 14.200 0.006 0.044 1.3

D (L1-D2-B2) 21.200 0.021 0.264 1.0

DQF (D1-L2-B2) 13.160 0.003 0.025 1.3

DQF (L1-D2-Q2) 23.340 0.041 0.631 1.0

DQF (L1-D2-B2) 31.950 0.081 1.951 1.0

DQB (D1-L2-B2) 16.530 0.019 0.133 3.0

DQB (L1-D2-Q2) 37.850 0.130 3.790 1.0

DQB (L1-D2-B2) 44.840 0.130 3.512 1.0

SP (L-S-B) 28.390 0.043 0.441 2.0

SP (D-S-Q) 42.680 0.064 0.907 5.0

SQF (L-S-B) 41.600 0.017 0.261 2.0

SQF (D-S-Q) 68.290 0.030 0.789 3.0

SQB (L-S-B) 104.850 0.076 3.398 6.0

SQB (D-S-Q) 107.310 0.083 4.654 20

Conclusions of closed-loop dynamic simulations

•Simple energy integration (heat integration) doesn’t influence dynamic behaviour compared to the non-integrated base case

•The cases, where material and energy flows (energy integration) go into the same direction (DQF, SQF), are better than the opposite

•Since the sloppy schemes show similar economic parameters, their controllability features make the decision to the favour of SQF !

•Petlyuk columns controllability parameters are between the ones of the heat-integrated and the sloppy schemes

•Higher detuning factor is needed due to stronger interactions in complex distillation systems (they became slower in closed loop)

Estimation of the flue gas emissions

The main gaseous pollutants that are considered in this work are: CO2, SO2, and NOx

The flue gas emissions of Case 1

Schemes D DQB SP SQF SQBHeating rate

(MW) 5.5 3.7 3.5 3.4 3.5Fuel type Natural

gasOil Natural

gasOil Natural

gasOil Natural

gasOil Natural

gasOil

CO2 emissions(kg/hr) 1030 1447 691 971 659 926 689 968 716 1006

SOx emissions(kg/hr) 0.75 3.57 0.50 2.39 0.48 2.28 0.50 2.39 0.52 2.48

NOx emissions(kg/hr) 0.16 0.66 0.11 0.44 0.11 0.42 0.17 0.47 0.18 0.49

Total emissions(kg/hr) 1031 1451 692 974 660 928 689 971 717 1009

Emissionssaving % 0 33 36 33 31

Final conclusions

with energy-integration about 53 % TAC saving can be realised in case of SQF scheme

Petlyuk column has a limited TAC saving of 30-33 % in all the three feed composition cases

conventional heat-integration shows the best economic and controllability features considering all the three feed compositions

sloppy schemes show good economic features but the selection is made according to their different controllability features (SQF has better features than SQB)

economic and controllability features are to be handled simultaneously during process design.

Closed loop dynamic simulations

•Simple energy integration (heat integration) doesn’t influence dynamic behaviour compared to the non-integrated base case

•The cases, where material and energy flows (energy integration) go into the same direction (DQF, SQF), are better than the opposite

•Since the sloppy schemes show similar economic parameters, their controllability features make the decision to the favour of SQF (!)

•Petlyuk (dividing wall) column‘s controllability parameters are between the ones of the heat integrated and the sloppy structures.

•more complicated systems: higher detuning factor is needed due to stronger interactions (they became slower in closed loop)

Synthesis of Mass Exchange NetworksUsing Mathematical Programming

Budapest University of Technology and EconomicsDepartment of Chemical Engineering

Outline

I. Mass Exchange Network Synthesis (MENS)

A Extension of the MINLP model of Papalexandri et al. (1994)

B Comparison of the advanced pinch method of Hallale and Fraser (2000) and the extended model of Papalexandri et al.

C New, fairly linear MINLP model for MENS

Approach:Mixed Integer Nonlinear Programming (MINLP)optimisation software: GAMS / DICOPT

II. Rigorous MINLP model for the design ofdistillation-pervaporation systems

III. Rigorous MINLP model for thedesign of wastewater strippers

I. Mass Exchange Network SynthesisEl-Halwagi and Manousiouthakis, AIChE Journal, Vol 35, No.8, pp. 1233-1244

21

NR

ysi

2

NS=NSE+NSP

yti

xsj

xtj

1

RICH

STR

EAM

S

LEAN STREAMS

MASS EXCHANGENETWORK

. . .

.

.

.

Gi

yi=f(xj)

Mass integration for the analogy of the concept of heat integration. Absorber, extractor etc. network synthesis

(MSAs)

The synthesis task:Stream data + equipment data +equilibrium data + costing

Network structurelean stream flow ratesmin (Total Annual Cost, TAC)

Previous work:early pinch methods (no supertargeting)Water pinch: Wang & Smith (1994, 1995), Kuo & Smith (1998)El-Halwagi & Manousiouthakis (1989a)El-Halwagi (1997)

advanced pinch method (includes supertargeting)

Hallale & Fraser (1998, 2000)

sequential mathematical programming methodsEl-Halwagi (1997), Garrison et al. (1995)Alva-Argaez et al. (1999)

simultaneous mathematical programming modelsPapalexandri et al. (1994)Papalexandri & Pistikopoulos (1995, 1996)Comeaux (2000); Wastewater: Benkő, Rév & Fonyó (2000)

I/A Extensions of the MINLP model of Papalexandri et al. (1994)

• Integer stage numbers• Generation of feasible initial values

• Kremser equation:

A

Abxmy

bxmy

AN

ijinjij

outi

ijinjij

ini

A ln

111ln

1

iij

j

Rm

LA

ijinjij

outi

outi

ini

A bxmy

yyN

1

yi*=mijxj*+bij Removable discontinuity at A=1

cx

cxxfxf

if definednot

if 1

UPLO xxx

f(x)

xc

f1(x)

xLO xUP

• Previous mathematical programming models for MENS assumed that A is always greater than 1

• Numerical difficulty when using GAMS

Handling of removable discontinuities in MINLP models:

ij

j

Gm

LA

Example: The Kremser-equation

if

if

• The usual form of the Kremser equation has a removable discontinuity at A=1

• Using only the first form of the Kremser equation in MINLP models leads to a division by zero error or gives solutions that have no physical meaning

• Restricting all the values of A under or over 1 very likely excludes the real optimal solution from the search space

11 1 AA NTPYNTPYNTP

Different possibilities for handling the discontinuity of theKremser equation:

• For all mass exchangers in the superstructure both formulas are used to calculate the theoretical number of stages

• A binary variable Y has to be generated to be able to choose between the two calculated stage numbers

Y=1 A=1

Y=0 A1

then

The binary variable Y can be generated in the following ways:

Methods for calculating Y taken from the literature:

y1 y2 y3

0.01 1000.99 1.01

y1=1 when 0.99A0.01 etc.

y1+y2+ y3=1

Three (or two, y3=1-y1-y2) binary variables are used to denote theinterval in which the actual value of A lies

Big-M method:

)1(99.0 11 yMA ; )1(01.1 22 yMA ;

)1(100 33 yMA

)1(01.0 11 yMA ; )1(99.0 22 yMA ;

)1(01.0 33 yMA

1 ; 99.98 ; 01.99 321 MMM

10001.0 A ; 1321 yyy ; 1 0oryi ; 2yY

Multi-M method:

)1(99.0 12,1 yMA ; )1(01.1 21,2 yMA ;

)1(100 31,3 yMA

)1(01.0 13,1 yMA ; )1(99.0 23,2 yMA ;

)1(01.0 32,3 yMA

1 ;0 ;98.0 ;99.98 ; 0 ; 01.99 2,31,33,21,23,12,1 MMMMMM

10001.0 A ; 1321 yyy ; 1 0oryi ; 2yY

Convex hull:

A formulation of Raman & Grossmann:

321321 10001.199.001.199.001.0 yyyAyyy

1321 yyy ; 1 0oryi; 2yY

A simple logical formulation (L-formulation):

101.0991 Az 1321 yzz

11991 zA 031 yz

111 2 Az 032 yz

01.0991 2 zA 3yY

The main drawback of the methods taken from the literature is, that they usethree binary variables for each removable discontinuity or mass exchanger.

Solving MEN synthesis problems this may mean that in case of largesuperstructures the problem size exceeds the practical solvability limit

(approx. 80-100 binary variables in an MINLP model).

New formulation for handling removable discontinuities:

yVcA n )(

( A - c ) 2

AA = c

LOV2

y = 0 y = 1y = 1

10001.0 A

981010 4 V

V is continuous y is a binary variable n=2

This method uses only onebinary variable for calculatingthe binary variable Y.

Y=1-y

For the Kremser equation: (A-1)2=Vy

Several mass exchange network synthesis problems were solved using our method.It proved to be fast and well applicable.

Adopted literature methods

New method

(the models are nonconvex anyway)

11 1 AA NYNYN

y1 y2 y3

0.01 1000.99 1.010

yVcA 2)(

UPLO AAA

UPLO VVV

A U PA = 1

y = 0 y = 1y = 1

A L O

LOLO VAA 1 UPLO AAV 1

are linear but use 3 binary variables

nonlinear but uses 1 binary variable only

• Big-M formulation• Multi-M formulation• a Convex-hull like formulation• Raman & Grossmann (1991)• Simple logic formulation

Advantages:1. faster2. larger problems can be solved

Large nonconvex MINLP problems solved by DICOPT++:There exists a critical upper limit of the number of binary variables

Example Objective

function

Pinch solution of

Nick Hallale

Target / Design

MINLP

Solution

(CMINLP-CPinch) /

CMINLP *100

3.1 CAP 830 000 / 860 000 1 044 285 +17.6 %

3.2 CAP 448 000 / 455 000 453 302 -0.4 %

3.3 CAP 819 000 / 751 000 637 280 -17.8 %

3.4 CAP 591 760 / 637 000 637 000 0.0 %

4.1 CAP 296 000 / 298 000 255 068 -16.8 %

5.1 TAC 226 000 / 228 000 226 000 -0.9 %

5.2 TAC 226 000 / 228 000 226 000 -0.9 %

5.3 TAC 226 000 / 228 000 226 000 -0.9 %

5.4 TAC 49 000 / 49 000 50 279 +2.5 %

5.5 TAC 524 000 / 526 000 527 000 +0.2 %

6.1 TAC 692 000 / 706 000 720 000 +1.9 %

6.2 TAC 28 000 / 28 000 32 000 +12.5 %

6.3 CAP 591 000 / 539 000 536 000 -0.6 %

TAC-total annual cost in USD/yr, CAP–annualised capital cost in USD, C - cost

I/B Comparison of the advanced pinch method ofHallale and Fraser (2000)and the extended model of Papalexandri et al. (1994)

13 exampleproblems

have been solved

The two methods perform more or less the same.Why are the MINLP solutions not always better? The MINLP model is nonconvex.

I/C New, fairly linear MINLP model for MENS

The stagewise superstructure enables almost linear mass balance formulation

L1

R1

k=1 k=2concentrationlocation 1

concentrationlocation 2

concentrationlocation 3

R1-L1

R1-L2

R1-L1

R1-L2

L2

R2

R2-L1

R2-L2

R2-L1

R2-L2

y 1,T

x 1,S

y 2,S

y 1,S

y 2,T

x 2,T x 2,S

x 1,T x 1,1

x 2,1

y 1,1

y 2,1

x 1,2

x 2,2

y 1,2

y 2,2

x 1,3

x 2,3

y 1,3

y 2,3

Similar to the HEN superstructure of Yee & Grossmann (1990)

j

kjime

kiy

kiy

iR

,,1,,

stjstji

melasti

ysi

yi

R,

,,,

i

kjime

kjx

kjx

jL

,,1,,

stistji

mesj

xfirstj

xj

L,

,,,

1,, ki

yki

y

1,, kj

xkj

x

Ti

Ylasti

y ,

Tj

Xfirstj

x ,

si

Yfirsti

y ,

sj

Xlastj

x ,

0,,,,,

kjiz

jikjime

kjiz

kjijib

kjx

jim

kiy

kjidy

,,1

,,,,,,,,

kji

zkjiji

bkj

xji

mki

ykji

dy,,

1,,,1,,1,1,,

kji

kjiz

,,

maxU,,

kji

kjizU

,,,,

min

3/1

2/1,,,,1,,,,,,

kji

dykji

dykji

dykji

dykji

lmcd

kjime

kjilmcdK

kjimass W ,,,,,,

jj

Lj

ckji

kjimassfTAC

,,,,

Model equationsminimise s.t.

mass balances

concentration constraints

big-M constraints for the existenxe of the units

driving force constraints

constraints on the number of existing units

Chen’s approximation for the log mean conc differences

calculation of the mass of the exchangers

Only the lean stream mass balances are bilinear

Example problems

Extensions: stagewise exchangers, multiple components

Example 4.1 (Hallale, 1998)

S3

R1

S1

R2

Capital cost, based on exchanger mass: 284,440 USD

S2

4.08e-3

1e-3

7.1e-3

2.5e-3

5e-3

1 kg/s

2.48 kg/s

8e-3

4.05e-3

9.16e-3

5e-3

3.66e-32.5e-3 1.059e-2

3.26e-3

R3

R4

R5

0

2.5e-3 5e-3

1e-2

0.01

1.8 kg/s

2 kg/s

2.5e-3

1.7e-3 3.63e-3

8.48e-35.82e-33.86e-3

1.64e-3 3.77e-3 7.79e-3 1.7e-2

4 kg/s

0.5kg/s

1.5kg/s

3.5kg/s

S1

R1

S2

N=4.23

R2

2.169 kg/s

0.9 kg/s

0.1 kg/s

0.566 kg/s

0.487 kg/s

N=2.73

N=4.93

N=3.25

N=2.88

TAC=436,289 USD/yr

1.752 kg/s

0.022 kg/s 0.062 kg/s

Two component exampleThe new model is most suitable for solving single component

MENS problems, where packed columns are used exclusively.In this case, no special initialisation is needed.

II. Rigorous MINLP model for the design of distillation-pervaporation systems

Vacuum vessel

retentate(dehydratedethanol)

permeate(mainly water)

Inlet ethanol~80 m/m% EtOH

Pervaporationunit

Distillationcolumn The synthesis task

is to determine:

• Nth of the column• feed tray position• reflux ratio• membrane structure• reflux scheme

Rigorous modelling: Dist. Column: 1 bar, MESH equations, tray by tray, Margules activity coeff. for the liquid phase, ideal vapour phase, latent heat enthalpy

Membrane unit: transport calculation is based on experimental data 1/3 m2 flat membranes, costing - industrial practice

Adequate costing equations, utility prices

Superstructure

Distillation column superstructure:Viswanathan & Grossmann (1993)

Membrane superstructure: new

N-1

N

bui

P2

refi

P1

ifeed

ibmax

imin

12

feed

column bottomproduct

columnfeed

mixer

RFF

P4recycledpermeate

P3

1

2

n

pump

to the vacuum pump

con-denser

heatexchanger

feed pump

i=1…m

ethanolproduct

to the nextsection of

membranes

recycledpermeate

distillatefrom thecolumn

max n pieces ofmembranemodules

permeate

retentate

max m sectionslike this

permeatesplitter

permeatecondensate

1/3 m2 flatPVA membranes

in blocks

The blocks (or modules)can be connected in both

series or parallel

Multiple level optimisation (successive refinement)enables reducing the number of binary model variables

Modelling of the membranes is based on experimental data

Industrial example

80theor.stages

reflux ratio:3.262

retentate (product): 920.7 kg/hr99.7 mass % EtOH

1175kg/hr

4

1

TAC=373,820 USD/yr

feed80 mass%

EtOH

992.7 kg/hr 94.56 mass%

D=0.875 m

72 kg/hr28.96 mass% EtOH

recycled permeate bottom product254.3 kg/hr

0.087 mass% EtOH

12 x 81 piecesof 1/3 m2 flat membranes

=324 m2 total(fixed industrial configuration)

total permeate recycling

membrane capital investment : 52,362 USDmembrane replacement : 83,936 USDcolumn capital investment : 18,05 USDcolumn operating cost : 219,472 USD

min=97.5%

Base case

84theor.stages

reflux ratio:1.38

retentate (product): 920.7 kg/hr99.7 mass % EtOH

1175kg/hr

7

1

TAC=328,124 USD/yr

feed80 mass%

EtOH

1046.3 kg/hr 91.44 mass%

D=0.679 m

125.6 kg/hr30.86 mass% EtOH

recycled permeate bottom product 254.3 kg/hr

0.087 mass% EtOH

12 x 107 piecesof 1/3 m2 flat membranes

= 428 m2 total

total permeate recycling

membrane capital investment : 69,058 USDmembrane replacement : 110,758 USDcolumn capital investment : 13,931 USDcolumn operating cost : 134,377 USD

min=97.5%

Optimised12% savings in the TAC

0

50

100

150

200

250

300

350

400

300 350 400 450 500

overall membrane surface in square meters

TAC

(tho

usan

d U

SD

/yr)

0,5

1

1,5

2

2,5

3

3,5

reflu

x ra

tio

membrane capital investment

membrane replacement

column capital investment

column operational cost

TAC

reflux ratio

base case optimally designedsystem

Membrane surface - TAC

100

150

200

250

300

350

400

94,5 95 95,5 96 96,5 97 97,5 98 98,5 99 99,5

specified ethanol yield (%)

TAC

(th

ou

sa

nd

US

D/y

r)

plant membrane cost

plant TAC

optimised membrane cost

optimised TAC

optimised column cost

plant column cost

Ethanol yield - TAC

Other calculationsusing the MINLPmodel

OPTIMISATION OF HYBRIDOPTIMISATION OF HYBRIDETHANOL DEHYDRATION SYSTEMETHANOL DEHYDRATION SYSTEM

Department of Chemical Engineering, H-1521 Budapest, Hungary

Z. Fonyo, Z. Lelkes, Z. Szitkai, E. Rev

• Introduction & problem statement• MINLP model and superstructure• Membrane model• Industrial case study• Conclusions

plant membrane configuration12 sections in series

each consisted of 81 piecesof 1/3 m2 flat membranes

in parallel

inlet stream1000 kg/hr

94 mass% EtOH

permeate

measured: 60 kg/hr 15 mass% EtOHcalculated: 78.5 kg/hr 28 mass% EtOH

retentate(abs. EtOH product)

measured:940 kg/hr99.6-99.7 mass% EtOH

calculated:921.5 kg/hr99.6 mass% EtOH

Calculated and measured output stream propertiesfor the fixed industrial inlet stream and membrane configuration

Base case: optimised hybrid ethanol dehydration plantwith fixed industrial membrane structure

80theor.stages

reflux ratio:3.262

retentate (product): 920.7 kg/hr99.7 mass % EtOH

1175kg/hr

4

1

TAC=373,82 USD/yr

feed80 mass%

EtOH

992.7 kg/hr 94.56 mass%

D=0.875 m

72 kg/hr28.96 mass% EtOH

recycled permeate bottom product254.3 kg/hr

0.087 mass% EtOH

12 x 81 piecesof 1/3 m2 flat membranes

=324 m2 total(fixed industrial configuration)

total permeate recycling

membrane capital investment : 52,362 USDmembrane replacement : 83,936 USDcolumn capital investment : 18,05 USDcolumn operational cost : 219,472 USD

min=97.5%

84theor.stages

reflux ratio:1.38

retentate (product): 920.7 kg/hr99.7 mass % EtOH

1175kg/hr

7

1

TAC=328,124 USD/yr

feed80 mass%

EtOH

1046.3 kg/hr 91.44 mass%

D=0.679 m

125.6 kg/hr30.86 mass% EtOH

recycled permeate bottom product 254.3 kg/hr

0.087 mass% EtOH

12 x 107 piecesof 1/3 m2 flat membranes

= 428 m2 total

total permeate recycling

membrane capital investment : 69,058 USDmembrane replacement : 110,758 USDcolumn capital investment : 13,931 USDcolumn operational cost : 134,377 USD

min=97.5%

Optimised hybrid ethanol dehydration plantwith optimised membrane structure

100

150

200

250

300

350

400

94,5 95 95,5 96 96,5 97 97,5 98 98,5 99 99,5

specified ethanol yield (%)

TAC

(th

ou

sa

nd

US

D/y

r)

plant membrane cost

plant TAC

optimised membrane cost

optimised TAC

optimised column cost

plant column cost

Influence of the specified ethanol yield on the TACoptimised system vs. plant existing in the industry

TAC, industrial

TAC, optimised

Influence of the specified ethanol yield on the TAC,optimised systems only

TAC

0

50

100

150

200

250

300

350

400

300 350 400 450 500

overall membrane surface in square meters

TAC

(th

ou

san

d U

SD

/yr)

0,5

1

1,5

2

2,5

3

3,5

reflu

x ra

tio

membrane capital investment

membrane replacement

column capital investment

column operational cost

TAC

reflux ratio

Dependence of the TAC and the reflux ratioon the overall membrane surface

industrial case optimised

Power function:

Shepard’s metric interpolation:

parameter fitting: method of least squares

Sheppard's metric interpolationalpha=2

0

0,5

1

1,5

2

2,5

3

3,5

4

0 5 10 15 20 25 30 35 40 45 50

j0, kg/hr (c0=4.06 mass%)

c T ,

ma

ss

%

cT calculated by differential equations

cT, metric interpolated

i jij

i jijiT

TPr

Prc

Pc)(

)()(

)(

depending on the value of alpha:• local minima• step function• peaks

145,00055,0 JCCT

00 031,0999,0 CJJT

314

316

318

320

322

324

326

328

330

332

334

94 95 96 97 98 99 100

Specified ethanol yield in %

TAC

(th

ou

san

d U

SD

/yr)

TAC, optimised

Influence of the specified ethanol yield on the TAC

Results:Results:

• Design tool to optimise the hybrid ethanol dehydration process

• Large, but solvable MINLP model

• In case of an industrial dehydration plant: 12% saving in TAC is possible by addition of 32% more membrane surface

• Sensitivity analysis on membrane replacement cost, membrane surface and ethanol yield

III. Rigorous MINLP model for the design ofwastewater strippers

1

20

18

2

3

17

.

.

.

feedtop product

bottom product

boil-up vapour

5 mol/sxacetone = 0.05xmethanol= 0.04xwater = 0.90xethanol = 0.01

Xwater0.999

water85%

Nth=?19

total condenser

Wilson binary interactionsIdeal vapour phaseTheoretical stages1 barLatent heat enthalpyAntoine vapour pressure

Wastewater cleaning by stripping

VLE calculation

Superstructure

Similar to the distillation columnsuperstructure of Viswanathan &Grossmann (1993)

Minor quantities of acetone,methanol, and ethanol in water

Conclusions:Complex evaluation of distillation based heat integrated separation schemes is presented. New sloppy structures proved to be competitive.

New, fairly linear, MINLP modell for MENS is developed and succesfully tested for literature examples and industrial case studies.

.

Utility Temperature

level (ºC)

Price

($/ton, kWh)

Low pressure steam 160 17.7

Middle pressure steam 184 21.8

Cooling water 30-45 0.0272

Electricity -------- 0.1 $

Utility prices

Controllability investigations, design

– interactive and challenging part of process design or development.

Control structure synthesis* control targets are defined, * the sets of controlled variables and possible manipulated

variables are determined (degrees of freedom)* pairing of the controlled and manipulated variables: steady

state control indices, dynamic behaviours in the cases of open and closed control loops of the promising control structures.

Demonstration of interaction between design and control

• comprehensive design of five energy integrated separation schemes

• three-component-alcohol-mixture is separated in five distillation based energy integrated two-column separation systems:– two heat integrated distillation schemes

– fully thermally coupled distillation column (Petlyuk, Kaibel)

– sloppy separation sequences

Solvent Recovery from Non-Ideal Quaternary Mixtures

with Extractive Heterogeneous-Azeotropic Distillation

Budapest University of Technology and EconomicsChemical Engineering Department

Motivation• Industrial companies ( printing, pharmaceutical) have

waste streams of solvents (quaternary mixtures)

• 4 groups of solvents with different VLLE, azeotropes

• Separation of non-ideal quaternary mixtures is less studied

Goal

Guideline for the design of separation schemes for non-ideal quaternary mixtures

Heterogeneous-azeotropic distillation Extractive distillation

Extractive heterogeneous – azeotropic distillation

W1

Feed

D1F2

Extr. agent

Group 1

Acetone, ETOH, MEK, Water Acetone, ETAC, ETOH, Water

Acetone

One volatile component forming no azeotropes

Water-ETOH

Water-MEK

ETOH-MEK

Water-ETOH-MEK

Binary azeotropes

Ternary azeotrope

Binary azeotropesWater-ETOH

Water-ETAC

ETOH-ETAC

Ternary azeotropeWater-ETOH-ETAC

Investigated separation schemesA

ETOH95 w%

H2O

B2

C2

D2Aceton

MEK(ETAC)

W1

Feed Fmix

C1

D1F2

Group 1

Water

Representation of separation in Column 1

F

D 1W 1

W ater ad d itio n

S ep ara tio n in C 1H y p o th e th ica l fee d

Water – Acetone - MEK Ternary mixture

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1WaterMEK

Acetone

F2

BB2

D2

B2MEK RPhase sep.

Investigated separation schemesB

ETOH95 w%

H2O

Feed

D1

B1

ACETONE

WaterETOHMEK(ETAC)

C1

Water

B2

C2

MEK(ETAC)

D2

Group 1

Water – ETOH – MEKTernary mixture

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1WaterMEK

ETOH

F2

B2D2 Phase sep.MEK C3

Water addition

Economic comparison of structures A and B

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5 0.6

mole fraction Acetone in Feed

To

tal A

nn

ua

l Co

st

[1e

5 €

]

B

A

Group 2

ETAC, ETOH, IPAC, Water ETOH, MEK, IPAC, Water

Water-ETOH

Water- ETAC

Water-IPAC

ETOH-ETAC

ETOH-IPAC

Water-ETOH-IPAC

Water-ETOH-IPAC

Binary azeotropes

Ternary azeotropes

Binary azeotropes

Water-ETOH

Water-MEK

Water-IPAC

ETOH-MEK

ETOH-IPAC

Ternary azeotropes

Water-ETOH-MEK

Water-ETOH-IPAC

Investigated separation schemes for the mixtures of Group 2

Water C2

IPAC

D2

B2

C3

ETAC(MEK)

B3

D3

ETOH95 w%

H2O

Feedmix

C1F1

W1

D1F2

Group 2

The VLLE Data and representation of separation

ETOH ETAC

Water

IPAC

Water feed addition

F R1

B1

D1

Separation in C1

R

F2

F1

Operating line of phase separator

Hypothetical feed

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Water

ETAC

D2(F3)

D3(R1)

B3

F2

B2

Immiscibility region

IPAC

Water – ETAC – IPACTernary mixture

Group 3

ETAC, ETOH, MEK, Water ETAC, IPOH, MEK, Water

Water-ETAC

ETOH-ETAC

Water-MEK

ETOH-MEK

ETAC-MEK

Water - ETOH

Water-ETOH-ETAC

Water-ETOH-MEK

Water-ETAC-MEK

Binary azeotropes

Ternary azeotropes

Binary azeotropes

Water-ETAC

Water-MEK

Water-IPOH

IPOH-ETAC

IPOH-MEK

ETAC-MEK

Ternary azeotropesWater-IPOH-MEK

Water-ETAC-MEK

MEK-IPOH-ETAC

Water

ETOH 95 w%(IPOH 85 w%)

Water

C2

ETAC95 w%

D2

B2

R2

Feed F

B1

V1

R1

F2

C1

ETACMEKWater

D3

Water

C3

MEK93 w%

Separation schemes for the mixtures of Group 3

Water

Group 3

WaterETAC

MEK

ETOH

Separation in C1

B1

F

D1F2

R

Water addition

Operating line ofphase separator Hypothetical

feed

Representation of extractive heterogeneous-azeotropic distillation for the separation of mixtures of Group 3

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Water

MEK

ETAC

F2

B2

D2ETAC

D3

B3

MEK

Phase sep.

Phase sep.

C3

C2

R2

R3

Water – ETAC – MEKTernary mixture

Group 4

ETOH, MEK, N-Heptane, Water

Binary azeotropes Water-ETOH

Water-MEK

Water- N-Heptane

ETOH-MEK

ETOH- N-Heptane

MEK – N-Heptane

Ternary azeotropes Water-ETOH-MEK

Water-ETOH- N-Heptane

Water – MEK – N-Heptane

ETOH – MEK – N-Heptane

Total possible combination

Water

ETOH95 w%

Water

Feed F

B1

V1

R1

F2

C1

N-HeptaneMEKWater

MEK93 w%

Water

C4

Water

C3

B3MEKWater

N-Heptane

C2

Separation schemes for mixture of Group 4

M E K W ater

N -H ep tane

E TO H

The VLLE Data

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 WaterN-Heptane

MEK

F2

R3

D1

D2

B2

Water addition

C3

B3

D3

C2C4

MEK

Phase sep.

Water – N-Heptane – MEKTernary mixture

F

B2

C2C1

P1 Water P2

F1

P2

RWater

B1

C1

C2 C3

P3

F

D2

R1

P3

B2

RWater

B1

F C1

C2

Water

C3

B3

P2

P2

RWater

B1

F C1

C2

C3

Water

P4

C4

P3

Group 1 Group 2

Group 3 Group 4

Classification of processes

Thank you for your attention!