Www.dbta.tu-berlin.de [email protected] d|b|t|a Fachgebiet Dynamik und Betrieb technischer...

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11

PSE Summer School 2012

Process Simulation and Optimization of Chemical Plants

DAAD Summer School 2012, Mexico

Sponsorship: DAADGerman Academic Exchange service


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(Process Optimization with MOSAIC

an short introduction)

Prof. Dr.-Ing. habil. Prof. h.c. Dr. h.c. G. Wozny

Problem formulationExamplesMOSAIC

Process Simulation and Optimization of Chemical Plants

Part III


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Process Simulation and Optimization

Solution methods Overview

• heuristic Rules, short cut Methods, „trial and error“,

Sensitivity studies

• Direct Methods Discretisation of the manipulated variables,

Discretisation of the manipulated variables and the state variables,

- SQP (Sequentially Quadratic Programming) (very general, often used z.B. Aspen, Bayer, BP, ICI, Linde, ... )

• direct Search (z.B. genetic Algorithm, Simulated Annealing, ...)

• OptimizationGAMS®ROMEOgOPTMOSAIC


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Problem formulation

F: Objective Function measure of goodness

min F(x,u)s.t.

y = {0,1}

f(dx/dt, x, u, y) = 0g(x, u, y) 0

xmin x x max

umin u umax

x: state variables (after discretization)

u: manipulated variables (peace wise constant)

f: equality equation Model equation MESH)g: inequality constraints (physical constraints or from construction e.g. F-Factor for Distillation)y: Integer variable


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Problem formulation with uncertainties

x: state variable (after Discretisation)u: manipulated variable (peace wise constant)

min F(x,u)

f: Model equation (MESH)

: stochastic Variable (distribution given)

g: probability restrictions g(x,u, ) = P { (x,u, ) ) } > p

s.t. f(dx/dt,x,u,) = 0g(x,u, ) 0

xmin x x max

umin u umax

Werk, S.; Barz, T.; Arellano-Garcia, H.; Wozny, G.:Performance Analysis of Shooting Algorithm in ChancedConstrained Optimization, PSE 2012, Singapore 15.19. July


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A simple example:min F(x,y) with: F = x2 + y2

Equality constraints x + y = 1

F/ x = 0 -> x = 0

F/ y = 0 -> y = 0

With Constraints:

x

y

F=const x+y=1

: F = x2 + y2 = x2 + ( 1 - x )2

F/ x = 0 = 2x -2 ( 1 - x)

Without constraints:

Introduction constraints


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Lagrangsche MultiplicatorF = x2 + y2 = Min x + y - 1 = 0

Add the constraints ( = 0)

F = x2 + y2 + 0 = x2 + y2 + ( x + y - 1 ) = Minimum!

Now: 3 equations, 3 Unknown

F / x = 0 = 2 x +

Solution: Formulate the objective functionFormulation of equality constraints(Balance equations), …

F / y = 0 = 2 y +

F / = 0 = x + y - 1 (that is the equality constraint)


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Process Simulation and OptimizationStart up

Feed

Topproduct

Bottomproduct

Qcond

Qreb

t = 0 : column cold and emty

t = t1 : reboiler switch on

t = t2 : vapor at top of the column

t = t3 : reflux switch on

t = t4 : all streams > 0

t = t5 : column in steady state

reflux


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Example: start up

Min ( t start up )

Subject to: f ( dx/dt, x , u, t ) = 0 (MESH – Model equation)

g (dx/dt, x , u, t ) 0 (vapour load, liquid load...Process constraint)

xmin x x max (Variable constraint);

umin u umax ; (manipulated variables)

+ start up conditions, Initialization

Objective Function


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Example: start up- many products- complex procedure- low Frequency -> less Training- different Solutions

- Basis: PhD Thesis Ch. Kruse, 1995 Main columnPhD Thesis E. Reuter, 1995, Batch distillation with reactionPhD Thesis P. Li, 1997, Batch distillation with ReactionPhD Thesis M. Flender, 1998, Column with side streamsPhD Thesis R. Schneider, 199 , Three phase distillationPhD Thesis K. Löwe, 2000, Two pressure column systemPhD Thesis Wang 2001, Batch distillationPhD Thesis F. Reepmeyer 2004 Reactive distillation homogeneousPhD Thesis Tran Trung Kien, 2004 Three Phase distillation with decanterPhD Thesis F. Forner, 2007 Reactive Distillation heterogeneous

min t start up (aim)


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conventional Strategy

Feed

LC

TC

xBB

L=u1

D

WF

xD

F zF

V Q

FFC

FC

LC

Switch overattime t=?from R1= to R2 and Q2

Feed

F zF

V Q

FC

LC

TC

WF

xBB

LC

xDL=u1

DFFC

Start t = 0:R = L/D = Q = Q1

Switch over atTime t=0 to thesteady state valuesR2 and Q2 and then wait


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modified Strategy

Switch overat time t=?from R1 = 0 and Q1to R2 and Q2

Feed

LC

TC

xBB

L=u1

D

WF

xD

F zF

V Q

FFC

FC

LC


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Process Simulation and OptimizationDerivation of the modified Strategy

F, xF

D, xD

B, xB

V L

HU

FpBB xKx

dt

dxT xB = xB0 - Kp ( 1- e-t/T )

HU dxB

dt= F xF - D xD - B xB

D = V - L F = D + B

KP = F

F + (K-1) (V-L)

xD = K xB

LVKF

HUT

1HU=const., V=const., F=const. K=const.

with

Balance volume


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modified StrategyConcentration xB

0,55

0,6

0,65

0,7

0 15 30 45 60 75 90 105 120

Time in Minutes

Con

cen

trati

on

in

mol/

mol

Reflux L=Lsteady state

Steady stateL=0

statBBum xtxMin t

Optimised


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2FeedFeed

DistillateDistillate

BottomproductBottomproduct

1

32

j

n

Condenser

ReboilerReboiler

D, xD

B, xB

F, xF

Balance volume 1condenser

j-1

Balance volume j

Balance volume nreboiler

FeedLj

Lj-1

Lj+1

Vj

Vj+1j+1

D

B

j

tray


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Process Simulation and Optimisation

Objective functionmodified Strategy

N

j

statjjum xtxMint

1

N

j

statjj TtTMT

1

statjjum xtxMint

statjjum xtxMint

statjjum xtxMint

statjjum xtxMint

statjjum xtxMint

X (concentration, molar fraction) not measurable in real PlantTherefore Temperature choosen


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Pilot plant

Bottom product

Column data:

diameter 70 mmPacking high 2,5 mNTS 28 ( Fa. Sulzer)Reflux ratio 1,5pressure 150 mbarReboiler duty 525 Wreboiler Hold-up 0,002 m**3

Distillate

Feed

C6=27,9%C8=72,1%

F=4,0 kg/h

C6=99,98%

C8=99,7%

Side stream


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Pilot plant

time

MT


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2020



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time in Minutes

Start up: conventional Strategy


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Start conditions

Steady stateFeed stream: 4 kg/hFeed concentration: 27,9%Feed temperature: 85 oCDistillate concentration: 99.98%Bottom concentration: 0,3%

?

Time optimal problem:

min tf [R(t), Q(t)] With model equations0.9998 xD (tf) 10 xB (tf) 0,0030,1 R(t) 200 Q(t) 1

Optimal StrategyReflux ratioReboiler duty



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Experimental resultsWithout side stream, two products

Reduction of start up time:

93 %*

* In comparison with the conventional procedure

0

300

600

900

1200

1500

0 60 120 180 240 300 360 420 480 540 600 660

Time in minutes

MT in

°C

Conventional strategyOptimised strategy

N

j

statjj TtTMT

1


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Conclusion Derivation of a time optimal start up procedure Model validation Column with and without a side stream

% deviation between Simulation - Experiment ca. 2%

Time reduction 54% for the side stream column conventional 366 min modified 168 min ( remark: reflux ration infinity -> 360 min ) outlook: Transfer to complex column systems (DFG ), DAAD Transfer to reactive distillation (Project sponsored by AIF ) Transfer to plant wide start up investigations


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Conclusion:

- „empirical“ Optimization is sometimes suitable but not general

- Basic: Process model, deep Process knowledge

- Optimization methods (objective function, constraints, mathematical methods, ...

- Applications in Industry not often up to now

- New research trends in PSE (stochastic Optimization, online Optimization, MIDO)


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MOSAIC

Optimization with MOSAIC


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Concept Optimization

Das Internet

Simulation Results

Programme codeEquation System, Derivatives

gPROMS

Aspen Custom Model

GAMS

Matlab Program

Custom Export

Model descriptionDocumentation / Publications

Docu 1 Docu 2

Docu 3 Docu 4

Docu 5

MOSAICModeling Tool

Web Server

jjiLV

jiojiji PyPx ,,,,,

Database Server

Model DatabaseMySQL

Publicmodellibrary

Privatework

spaces

Optimization results


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Modeling systematicModeling systematicProcess Simulation and Optimization

Min ( J )

Subject to: f ( dx/dt, x , u, t ) = 0 ( e.g. MESH – Model equation)

g (dx/dt, x , u, t ) 0 (vapour load, liquid load...Process constraint)

xmin x x max (Variable constraint);

umin u umax ; (manipulated variables, constraints)

+ Initialization ( at time 0)

General Formulation:Objective Function (cost, time, profit, energy, waste, …)

equilibrium constraints


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Workflow: Requirements:

- Extend existing MOSAIC elements

- Define the optimization statement, based

on an evaluation

- Keep compatibility - New symbols (≤, <, ...) can not

be defined

- Code generator for different optimizer


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NLP – Problem formulation

Constrained Optimization:

min f(x)

s.t. h(x) = 0g(x) ≤ 0

More general:

min f(x)

s.t. c (x) = 0xL ≤ x ≤ xU

Non equality constraints moved to equality constrains

c(x) -> any equation system from the MOSAIC library

Non equality constraints

Equality constraints (Model eq.)


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NLP Example – Hughes 1981

xi=2

x i=1

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

-4

-2

0

2

4

6

8

Min:Model equations - Equality constraints:


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Implement model in MOSAIC

Notation

Equations

Define Variables Initial Evaluation


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Reuse model as constrains


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Formulate the statement


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Formulate the statement


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Code export

Matlab Gams


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Solution

xi=2

x i=1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

-4

-2

0

2

4

6

8

F(x) = -5.0893xi=1 = 0.7395xi=2 = 0.3144


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Inequality constrains - example

-10 -5 0 5 10 15 20 25 30

0

5

10

15

20

25

30

B

A

BA

1

2

3

Objective:Min (P = 2(A + B))

Inequality constrains:Stay in box

xo ≥ Ro xo ≤ B - Ro

yo ≥ Ro yo ≤ A - Ro

No overlaps(xo=1 – xo=2)2 + (yo=1 – yo=2)2 ≤ (Ro=1 + Ro=2)2

(xo=1 – xo=3)2 + (yo=1 – yo=3)2 ≤ (Ro=1 + Ro=3)2

(xo=2 – xo=3)2 + (yo=2 – yo=3)2 ≤ (Ro=2 + Ro=3)2

Variables:x,y - Coordinates P - Perimeter

R - Radius A - Heighto - Number of circle B - Width


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Equality constrains

-10 -5 0 5 10 15 20 25 30

0

5

10

15

20

25

30

B

A

BA

1

2

3

Objective:Min (P = 2(A + B))

Equality constrains:Stay in box

No overlaps

Variables:x,y - Coordinates P - PerimeterR - Radius A - Height i - slack indexc - Slack variables B - Width o - circle index


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Define optimization parameter

-10 -5 0 5 10 15 20 25 30

0

5

10

15

20

25

30

B

A A

1

2

3

B


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Solution

Local optimum

Matlab – fmincon

Global MinimumNEOS Server - LINDOGLOBAL

-15 -10 -5 0 5 10 15 20

0

5

10

15

20

25

30

B

A

-15 -10 -5 0 5 10 15 20

0

5

10

15

20

25

30

B

A

1

3

B

2

1

3

2

A

P = 31.798A = 9.899

B = 6

P = 34.726A = 11.363

B = 6

-15 -10 -5 0 5 10 15 20 25

0

5

10

15

20

25

30

B

A

1

3

2

GAMS – CONOPT

P = 34.726A = 9.899B = 7.464


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Additional Examples in MOSAIC


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Challenges

• reuse of models• multi scale applications• data base models + meta data (ontology) • large nonlinear dynamic systems• mixed integer dynamic highly nonlinear systems• transfer to applications• experiment design• model discrimination• transfer to real world applications

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