Optimal synthesis of batch separation processes

Taj Barakat and Eva Sørensen

University College London

iCPSE Consortium Meeting, Atlanta, 30-31 March 2006

2

Motivations

Many valuable mixtures are difficult to separate

Need to optimise efficiency of current processes

Select most economical separation process Explore novel techniques and alternatives

3

Objectives

Development of models/superstructure to determine the best design configuration, operating policy and control strategy for hybrid separation (distillation/membrane) processes.

Develop general guidelines for design, operation and control of such processes

4

Project Features

Economics objective function Rigorous dynamic models Encompassing (most of) the available

decision variables Considering novel configurations

5

Outline

1. Optimal synthesis of batch separation processes

2. Multi-objective optimisation of batch distillation processes

3. Concluding remarks

6

Optimal synthesis of

batch separation processes

7

Configuration Decisions

Separation problem

Process Superstructure

?

Batch Distillation Batch Pervaporation Batch Hybrid

8

Design and Operation DecisionsDesign Alternatives Operational Alternatives

Mincapital

cost

Minrunning

cost

• Trays• Membrane stages• Membrane modules

• Vapour loading rate• Reflux/reboil ratios• Recovery/No. batches• Withdrawal rate• Task durations

9

Process Superstructure

Feed

Retentate

Permeate

Offcut

Nt

Rc

Qr

Rp

Ns , Nm,s

P

Rr

Lr

Fs

Qs

10

Batch Distillation

Product 1

Product 2

Offcut

Reboiler

Nt

Rc

Qr

Rp

11

Batch Pervaporation

Offcut

Feed

Separation Stage

Retentate

Permeate

Ns

Nm,s Rr

Rp

P

Qf

12

Hybrid Distillation I

Feed

Product

PermeateReboiler

Offcut

Nt

Rc

Qr

RpP

Ns Nm,s

13

Hybrid Distillation II

Feed

Retentate

Permeate

Offcut

Nt

Rc

Qr

Rp

P

Ns Nm,s

14

Hybrid Distillation III

Retentate

Permeate

Offcut

Feed

Nt

Rc

Qr

Rp

Ns

, Nm,s

P

Rpr

Lr

Fs

Rr

15

Problem Formulation – Objective Function

Maximise

Annual Profit = Revenues – Operating Costs

Batch Processing TimeAv. Time – Capital Costs

Subject to :

Model equations DAE/PDAE, nonlinear

Design variable bounds discrete and continuous

Operational variable bounds continuous

To determine :

Design variables

Operation variables (time dependent)

Nonlinear, (OC/CC, Guthrie’s correlations)

16

Problem Formulation - Solution

DAE gPROMS (Process Systems Enterprise Ltd., 2005)

MIDO Genetic Algorithm (GA)

• Mixed integer dynamic optimisation (MIDO) problem • Complex search space topography (local optima, nonconvex)• Need robust, stable and global solution method

17

Optimisation Implementation

GeneticAlgorithmModule

Batch Distillation/Pervap

Model

ThermodynamicsModel

Genome Set

Model State

Simulation Output

Physical Properties

GAlib

gPROMS

Multiflash

18

Case Study

19

Case Study ( Acetone – Water )

Separation of a binary tangent-pinch mixture Acetone dehydration system ( 70 mol % acetone feed ) 20,000 mole feed

Subject to: Purity ≥ 97% Recovery ≥ 70%

Maximise: Annual profit

Assuming: Single membrane stage Single retentate recycle location

20

Case Study Superstructure

Retentate

Permeate

Offcut

Feed

Nt

Rc

Qr

Rp

NsNm,s

P

Rr

Lr Fs

21

Optimal Process - Hybrid

Feed

Retentate

Permeate

Offcut

Rp

0.79 – 1.8%

1.00 – 96.3%

0.88 – 1.9%

Rr

1.00 – 1.8%

0.83 – 96.3%

0.24 – 1.9%Lr =3

Nt = 30

Fs = 9

VReb = 5 mole/s

Fside = 2.5 mole/s

P = 300 Pa

Nm = 2

Profit 18.07 M£/yr

tf = 5119 s

To = 330 K

22

Fixed Configuration – Distillation only

Product 1

Product 2

Offcut

Reboiler

Rp

1.00 – 0.10%

1.00 – 99.7%

0.00 – 0.20%

Rr

1.00 – 0.10%

0.68 – 99.7%

0.70 – 0.20%

Nt = 30

VReb = 5 mole/s

tf = 8964 s

Profit 14.30 M£/yr

-26%

23

Case Study Summary

Approach for process selection based on overall economics

Allows determination of best process alternative for maximum overall profitability

Company specific costing can easily be included

24

Multi-objective optimisation of

batch distillation processes

25

Batch Distillation

Product 1

Product 2

Offcut

Reboiler

Nt

Rc

Qr

Rp

26

Problem Formulation – Objective Function

Minimise

Investment Costs

Subject to :

Model equations DAE/PDAE, nonlinear

Design variable bounds discrete and continuous

Operational variable bounds continuous

To determine :

Design variables

Operation variables (time dependent)

Minimise

Operating Costs&

27

Optimisation

Single-objective optimisation:

To find a single optimal solution x* of a single objective function f(x)

Multi-objective optimisation:

To find array of “Pareto optimal” solutions with respect to multiple objective functions

xx*

f(x)

0

28

Multiobjective Optimization Problem

))(...,),(),(()( 21 xxxxf kfffMaximize

Xxsubject to

Several Pareto-optimal sets Pareto Optimal Solutions

Min

imis

e

Minimise)(1 xf

)(2 xf

29

Ranking

3

2)(1 i

ni k

gf

c if solution is infeasible

if solution is feasible but dominated

if solution is feasible and non-dominated

30

Ranking

3

F2

F1

3

better

bett

er

3

2

22

2

Max = 1

3

3

3

31

Problem Formulation - Solution

DAE gPROMS (Process Systems Enterprise Ltd., 2005)

MO-MIDO Multi-Criteria Genetic Algorithm (MOGA)

• Multi-objective Mixed integer dynamic optimisation (MO-MIDO) problem• Need robust, stable and global solution method

32

Case Study

33

Case Study ( Acetone – Water )

Separation of a binary tangent-pinch mixture Acetone dehydration system ( 70 mol % acetone feed ) 20,000 mole feed

Subject to: Purity ≥ 97% Recovery ≥ 70%

Minimise: Investment costs Annual operating costs

34

Case Study Summary

35

Case Study Summary

Approach for multi-criteria process optimisation using Genetic Algorithm

Allows determination of process alternatives through Pareto optimality

Company specific costing can easily be included

36

Concluding RemarksFor hybrid batch separation processes: Optimum synthesis and design procedure Multi-criteria optimisation

Simple extension to continuous hybrid processes