an integrated framework for optimal solvent selection and...

An Integrated Framework for Optimal Solvent Selection and Separation Process Design Based on

Economic and Controllability Criteria

Panos Seferlis and Athanasios PapadopoulosPanos Seferlis and Athanasios Papadopoulos

Department of Mechanical EngineeringAristotle University of Thessaloniki (AUTh)

Thessaloniki, Greeceand

Chemical Process Engineering Research Institute (CPERI)Centre for Research and Technology – Hellas (CERTH)

Outline

• Introduction - Motivation

• Proposed integrated solvent, process and control design framework

• Solvent selection method

• Optimal process design• Optimal process design

• Controllability analysis using nonlinear sensitivity analysis

• Illustrative example

• Concluding Remarks

Aristotle University of Thessaloniki CPERI

Introduction

• Existing solvent design methods generally enable optimal solvent design in terms of economic performance in the process it is utilized.

Solvent Design

• Solvents are designed using CAMD methods

• Solvents that satisfy certain

Process Design

Optimal Solvent/Process

• Solvents that satisfy certain performance constraints (thermodynamic or process) are introduced in process design

• Iterations between solvent and process design are allowed to refine results


Introduction - Motivation

• Processes are inherently dynamic environments susceptible to external disturbances

• Processes and the associated control system should be able to compensate for disturbances and maintain the satisfaction of predefined specifications

• Solvent selection and process design considers the static • Solvent selection and process design considers the static controllability properties of the system that has notbeen addressed systematically in available published work

• Ulas and Diwekar (2006) proposed an integrated solvent, process and control design scheme, with the focus maintained on the optimal control profiles of a batch distillation column.


• “Ability of the control system to perform satisfactorilyin spite of process disturbances that persistently influence the operation of the system ” Postlethwaite, Skogestad

• Controllability is considered a property that is inherent

Controllability Analysis of Processes

• Controllability is considered a property that is inherent of the solvent and process design

• Solvent and process design imposes limits on the dynamic performance of the control system

• Controllability is considered independent of the selection of a control algorithm and its tuning


Integrated solvent, process and control system design

An integrated framework for the design of solvents based on their economic and controllability process performance

Solvent screening for optimum economic process performance

Multi-objective solvent synthesis

Solvent screening based on static controllability

Chart of economic solvent performance

Representative discrete solvent options

Clustering of optimal solvent set

Conceptual process design

Rigorous process design

Non-linear sensitivity analysis

Chart of economic and controllability

solvent performance


Advantages of the proposed method

• At the economic solvent screening stage:

– No potentially useful solvent options are excluded from the solution space

– Solvent-process design decisions are based on economic – Solvent-process design decisions are based on economic process performance criteria

– Major solvent-process design drives are rapidly captured using conceptual process models


Advantages of the proposed method

• At the solvent screening stage based on static process controllability:

– The entire economic solvent performance chart can be screened using rigorous process models

– The rigorous models rapidly provide realistic process behavior informationbehavior information

– Nonlinear sensitivity analysis provides accurate information about the solvent-process behavior under multiple parameter variations for specified control objectives


1st stage - Solvent and process design

The first stage is based on the approach by Papadopoulos and Linke (2005,2006)

CAMD Solvent Design

Optimal Process and Solvent

System

Set of Optimal Solvents

Process Design

Multi-objective optimization

Solvent Clusters

Solvent and ProcessDesign Interface


Multi-objective solvent design

)(),.....(),( 21 xfxfxf p

SatP∞γ

Set of Optimal Solvents

Optimize

∞γ

Process related objective functions

f1•••

••f2

fp

Multi-objective optimization

SatA

SatB

SA

SB

P

Pf ⋅= ∞

∞

,

,1 γ

γ

B

A

SA

SB

MW

MWf ⋅= ∞

∞

,

,2 γ

γ

•

•••

•••f1

f2

Pareto optimalset

sMWf =2

Solvent related objective functions

∞= SBf ,1 γ

fp

Pareto optimal front


Clustering of optimal solvent set

Solvent Clusters

•••• ••

•

Pro

pert

y 1• • •

••• •

• •

Step 1: Partition optimal solvent set into groups of molecules with similar properties

Process Synthesis:•Models•VLE/LLE•Objective Function

Pro

pert

y 1• •• •

••

••• •

Property 2Step 2: Introduce a representative

molecule from each cluster into

process synthesis


Economic solvent performance decision chart

New cluster1Iteration 1 Iteration 2 Iteration N. . .

• Subsequent clustering iterations result in a decision chart that combines: – Statistical solvent property information– Economic process performance of representative molecule from

each cluster– Decisions on the emerging clustering paths are based on a

probability function that combines economic and statistical information

New cluster1

New cluster1

Original set

Cluster 1

Cluster 2

Cluster 3

Cluster N

New cluster1Optimum cluster

.

.

.New cluster2

New cluster N

New cluster2

New cluster N

New cluster2

New cluster N


Clustering probability function

)T/E∆exp(P new−=

oldnew TaT ⋅=

SSWSSB

SSB1a

+−=

• Unifies statistical and economical clustering information under one index

• Uses the Simulated Annealing probability function to quantify the SSWSSB

1a+

−= function to quantify the uncertainties involved in clustering decisions

• Temperature parameter is reduced based on the information included in the clusters

• ∆E: Difference between tested cluster center OF and best cluster center OF

• SSB: Distance between cluster centres

• SSW: Distance within cluster points


2nd stage – Rigorous process design

• Stage 1 models are short cut distillation models

• Stage 2 models are accurate but compact in size

• Orthogonal collocation on finite element models are

Top product

Side productSide feed

Heat stream

Side heat

Collocation points

finite element models are employed

• Columns section sizes are continuous variables

• Polynomial approximation of molar and enthalpy flows within column sections is implemented

Bottoms product

Side productSide feed

Heat duty

Elementbreakpoints


2nd stage - Process and controllability properties for representative solvents

• The second stage is based on the integrated process and control system design method by Seferlis and Grievink (2001, 2004)

MV, u CV, y

disturbances, εεεε

y2u2

For each candidateset of MV

For each candidateset of CV

y1

Process

u1

For a given disturbance scenario calculate:

• the steady-state variation for the MVs to maintain the CVs within predefined levels


• Large variation in the steady-state position of the MVs required for the compensation of relatively small in magnitude disturbances implies lack of “power” for the system

Controllability evaluation

Solvents, process design and control structure performance is evaluated and rank ordered


Optimization framework with objective function that:• penalizes deviations from setpoint for CV

• penalizes usage of available MV

( ) ( ) ( ) ( )( )( )

ssuT

ssspyT

spuy

0εd,u,y,x,h

uuWuuyyWyy

=

−−+−−=

s.t.

fMin,

Disturbance sensitivity control problem

( )( )

ulululopt xxx,uuu,yyydd

0εd,u,y,x,g0εd,u,y,x,h

≤≤≤≤≤≤=≤=

,

s.t.

Weights in the objective function determine:• relative importance of control objectives

• cost related preference of system resources for corrective actions


Solution method

• Solve the parameterized Karush-Kuhn-Tucker (KKT) optimality conditions

• gA: active inequalities

• ∆ε∆ε∆ε∆ε: disturbance relative variation0

gh

f

=

∇+∇+∇

=

gµhλ

FA

TT

• θθθθ: direction of perturbation

• ζ : free continuation parameter

0ghA

=

−

=

ζθ∆ε

F

( ) ( ) ( ) ( )( ) ( ) ( ) ( )

( ) ( ) ( ) ( )( )

p

i*i,p

*i,p

*i,p

ii

p

*i

*i

*i

ii

p

*i

*i

*i

iSC 0f

0fζfζw

0y

0yζyζw

0u

0uζuζwζΩ ∑∑∑

−+

−+−=

Controllability index


Derive sensitivity information of process variables w.r.t. disturbances

Disturbance sensitivity control problem

( )[ ]Trefopt

εε εXP ∇=

• Disturbance sensitivity decomposition (SVD) for the determination of key directions, θ, of variability

• Equivalent to the worst case scenario for disturbance influence


• Integrated solvent/process/control design for the separation of a Cyclohexene-Benzene mixture

Illustrative example

• Design a solvent/ extractive distillation system for the separation of a Cyclohexene-Benzene mixture

• Multiple objectivesMaximizing: Minimizing:

• Molecules that create azeotropic mixtures are not allowed

Maximizing: Minimizing:Relative volatility (aB,A)

Solvent power (Sp)

Heat of vaporization (Hv)

Molecular weight (MWs)

Process Cost


• Identified in total 109 solvent molecules

1st Stage - Economic solvent screening

Cl Nm COF(k$/yr) P1 1 1810 0.002 14 1337.1 0.993 23 1404.2 0.974 34 1689.1 0.92

Cl Nm COF(k$/yr) P1 8 1359.8 0.942 6 1316 0.993 6 1315.8 1.004 1 1580 0.00

(2,3,5)

Iteration 1 Iteration 2

4 34 1689.1 0.925 6 1315.8 1.006 31 1742.4 0.88

4 1 1580 0.005 1 1537 0.006 21 1377 0.96

• Optimum solvents are included in clusters 2 and 3 of iteration 2 based on the high probability values

• We only screened 12 molecules in terms of process performance out of the 109 molecules


2nd Stage - Rigorous process design

StgSfl

(kmole/hr) RQD

(MJ/hr)QB

(MJ/hr) H(m) D(m) Xd Rv(%)74 78 8.4 1430 1946 47 1.8 0.77 75.68 50.4 0.2 24.2 1752 7.1 0.45 0.96 97.9

24 54.2 0.3 43.6 2078 16.7 0.77 0.8 99.927 70.9 0.3 48.2 2439 19 0.77 0.72 1008 49.11 0.28 34.9 1422 7.1 0.48 0.96 99.4

17 67 0.5 65.4 3147 13.2 0.53 0.91 99.9

• Detailed design information is obtained through rigorous OCFE process models

• Such information can not be obtained by use of conceptual models


Recalculation of probability

Economic solvent screening

Rigorous economic solvent screening

Cl Nm P (COF)

1 1 0.002 14 0.993 23 0.974 34 0.925 6 1.006 31 0.88

P(ROF) StgSfl

(kmole/hr)R

QD (MJ/hr)

QB (MJ/hr)

H(m) D(m) Xd Rv(%)

0.00 74 78 8.4 1430 1946 47 1.8 0.77 75.60.95 8 50.4 0.2 24.2 1752 7.1 0.45 0.96 97.90.94 24 54.2 0.3 43.6 2078 16.7 0.77 0.8 99.90.89 27 70.9 0.3 48.2 2439 19 0.77 0.72 1001.00 8 49.11 0.28 34.9 1422 7.1 0.48 0.96 99.40.85 17 67 0.5 65.4 3147 13.2 0.53 0.91 99.9

• The probability function calculation utilizing rigorous models provides similar solvent ranking as in 1st stage

• However, the ranking at this stage involves higher certainty regarding the solvent-process design decisions


Recalculation of probability

Economic solvent screening

Rigorous economic solvent screening

Cl Nm P (COF)

1 1 0.002 14 0.993 23 0.974 34 0.925 6 1.006 31 0.88

P(ROF) StgSfl

(kmole/hr)R

QD (MJ/hr)

QB (MJ/hr)

H(m) D(m) Xd Rv(%)

0.00 74 78 8.4 1430 1946 47 1.8 0.77 75.60.95 8 50.4 0.2 24.2 1752 7.1 0.45 0.96 97.90.94 24 54.2 0.3 43.6 2078 16.7 0.77 0.8 99.90.89 27 70.9 0.3 48.2 2439 19 0.77 0.72 1001.00 8 49.11 0.28 34.9 1422 7.1 0.48 0.96 99.40.85 17 67 0.5 65.4 3147 13.2 0.53 0.91 99.9

(2,3,5)

6 31 0.88

Cl Nm P(COF)

1 8 0.942 6 0.993 6 1.004 1 0.005 1 0.006 21 0.96

P(ROF) StgSfl

(kmole/hr)R

QD (MJ/hr)

QB (MJ/hr)

H(m) D(m) Xd Rv(%)

0.51 20 67.6 0.2 22.1 2457.9 14.9 0.59 0.96 95.20.90 8 41.7 0.2 23.7 1892.9 7.1 0.47 0.96 95.61.00 8 39.13 0.283 34.9 1422.7 7.1 0.48 0.96 99.40.00 220 34.7 12.2 2081 2685 139.9 5.5 0.77 99.70.00 31 97.4 0.54 69.9 2099 21.3 0.85 0.92 99.90.70 21 74.4 0.2 20.2 2954 15.1 0.6 0.96 94.1


Controllability analysis

Controlled variables:

top product cyclohexane purity level 0.96 (0.94)

cyclohexane % recovery

Manipulated variables:

reboiler duty (bound at +40% of base design point)

reflux flow (bound at +40%)


reflux flow (bound at +40%)

solvent feed flow (bound at +40%)

w=[1000, 10, 10, 10, 100]

disturbances: feed composition, temperature

Nonlinear sensitivity analysis - I

5

10

15Feed temperature

% c

hang

e

-30

-20

-10

0Cyclohexane at feed

40

60

80

100Benzene at feed

0 5 100

5

zeta0 5 10

-50

-40

zeta0 5 10

0

20

zeta


Disturbance characterization along the major direction of variability of the process system

0 2 4 6 8 10 12-50

-40

-30

-20

-10

0Condenser duty

% c

hang

e

0 2 4 6 8 10 12-10

0

10

20

30Reboiler duty

% c

hang

e

Reflux ratio Solvent flowrate

purity bound active

solvent flow bound active

Nonlinear sensitivity analysis - II

0 2 4 6 8 10 120

10

20

30

40Reflux ratio

zeta

% c

hang

e

0 2 4 6 8 10 120

10

20

30

40Solvent flowrate

zeta%

cha

nge


• Variation of key process (manipulated) variables for disturbances along major directions of variability

0.95

0.955

0.96

0.965Distillate xd

93

94

95

96

97CY Recovery

Nonlinear sensitivity analysis - III

0 5 100.935

0.94

0.945

zeta0 5 10

90

91

92

93

zeta


• Variation of key controlled variables for disturbances along major directions of variability

Controllability index

15

20

25

Co

ntr

olla

bilit

y in

dex

, om

ega

S1S2S3S4S5

0 2 4 6 8 100

5

10

disturbance magnitude parameter, zeta

Co

ntr

olla

bilit

y in

dex

, om

ega


8

10

12

14

Con

trol

labi

lity

inde

xS2

S1

Economic - controllability performance chart

34 36 38 40 42 44 460

2

4

6

Economic objective function value, k$/yr

Con

trol

labi

lity

inde

x

S4

S3S5

Concluding remarks

• The effects of solvent selection on the optimal process design and static controllability properties have been investigated

• Solvents are evaluated and rank ordered based on economic and static controllability performance criteria

• Static controllability is performed using nonlinear sensitivity analysis and rigorous process models

• Static controllability is performed using nonlinear sensitivity analysis and rigorous process models


an integrated framework for optimal solvent selection and...

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