A Batch Reactor Heat Recovery Problem description Challenge - - PowerPoint PPT Presentation

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A Batch Reactor Heat Recovery Problem description Challenge - - PowerPoint PPT Presentation

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Heat Recovery Challenge Problem J. Jschke Introduction A Batch Reactor Heat Recovery Problem description Challenge Problem Simulations Discussion Conclusions Johannes Jschke, Sigurd Skogestad Department of Chemical Engineering NTNU

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SLIDE 1

Heat Recovery Challenge Problem

  • J. Jäschke

Introduction Problem description Simulations Discussion Conclusions

A Batch Reactor Heat Recovery Challenge Problem

Johannes Jäschke, Sigurd Skogestad

Department of Chemical Engineering NTNU Trondheim, Norway

Trondheim, 9. June 2012

  • J. Jäschke

Trondheim, 9. June 2012 1

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SLIDE 2

Heat Recovery Challenge Problem

  • J. Jäschke

Introduction Problem description Simulations Discussion Conclusions

Outline

1

Introduction

2

Problem description

3

Simulations

4

Discussion

5

Conclusions

  • J. Jäschke

Trondheim, 9. June 2012 2

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SLIDE 3

Heat Recovery Challenge Problem

  • J. Jäschke

Introduction Problem description Simulations Discussion Conclusions

Introduction

Optimizing real processes consists of 2 parts:

1

Optimization problem

Formulating the problem Solving it systematically, often using a model

Minimum

2

Implement the solution in the real process

This presentation:

Challenge problem to test

Optimization Implementation

Discussion

  • J. Jäschke

Trondheim, 9. June 2012 3

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SLIDE 4

Heat Recovery Challenge Problem

  • J. Jäschke

Introduction Problem description Simulations Discussion Conclusions

Introduction

Some challenges when optimizing real systems Optimization part

Non-linearity Non-convexity Integer variables Non-smoothness Time-varying systems (Dynamic systems)

Implementation part

Missing information Uncertainty

Disturbances (parametric uncertainty) Noise Structural model mismatch Temporal uncertainty

  • J. Jäschke

Trondheim, 9. June 2012 4

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SLIDE 5

Heat Recovery Challenge Problem

  • J. Jäschke

Introduction Problem description Simulations Discussion Conclusions

Heat recovery challenge problem

Qheater qh1 qh4 qh3 qh6 qh7 qh8 qh9 qh2 qh5 qh10 Ttarget

Tmix

q0 2 1 9 4 7 8 10 6 5 3 q3 q4 q5 q6 q7 q8 q9 q10 q1 q2 T0 Th4 Th6 Th8 Th10 T2 Th9in Th8in Th10in Th7in Th6in Th5in Th4in Th3in Th2in Th1in Th1 Th3 Th5 T1 T1 T1 T1 T1 T1 T7 T8 T8 T10 Th9 Th7

Objective: Adjust split to maximize Tmix

  • J. Jäschke

Trondheim, 9. June 2012 5

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SLIDE 6

Heat Recovery Challenge Problem

  • J. Jäschke

Introduction Problem description Simulations Discussion Conclusions

Heat recovery challenge problem

Qheater qh1 qh4 qh3 qh6 qh7 qh8 qh9 qh2 qh5 qh10 Ttarget Tmix q0 2 1 9 4 7 8 10 6 5 3 q3 q4 q5 q6 q7 q8 q9 q10 q1 q2 T0 Th4 Th6 Th8 Th10 T2 Th9in Th8in Th10in Th7in Th6in Th5in Th4in Th3in Th2in Th1in Th1 Th3 Th5 T1 T1 T1 T1 T1 T1 T7 T8 T8 T10 Th9 Th7

Cold flow rate and temperature

200 400 600 800 1000 1200 1400 0.05 0.1 Total cold flow rate [m3/min] time [min] 200 400 600 800 1000 1200 1400 60 80 Cold stream temperature Temperature [

° C]

time

Hot flow rates

200 400 600 800 1000 1200 1400 0.05 [m3/min] time [min] 200 400 600 800 1000 1200 1400 0.05 [m3/min] time [min] 200 400 600 800 1000 1200 1400 0.05 [m3/min] time [min] 200 400 600 800 1000 1200 1400 0.05 [m3/min] time [min] 200 400 600 800 1000 1200 1400 0.05 [m3/min] time [min] 200 400 600 800 1000 1200 1400 0.05 [m3/min] time [min] 200 400 600 800 1000 1200 1400 0.05 [m3/min] time [min] 200 400 600 800 1000 1200 1400 0.05 [m3/min] time [min] 200 400 600 800 1000 1200 1400 0.05 [m3/min] time [min] 200 400 600 800 1000 1200 1400 0.05 [m3/min] time [min]

Hot stream temperatures

1 2 3 4 5 6 7 8 9 10 100 200

° C

Hot stream

  • J. Jäschke

Trondheim, 9. June 2012 6

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SLIDE 7

Heat Recovery Challenge Problem

  • J. Jäschke

Introduction Problem description Simulations Discussion Conclusions

Heat recovery challenge problem

Batch discharge

hi hhead

Flow rate:

qj

hi(t) =

     for t < ts ki

  • ∆pj

i

for tj

sj ≤ t ≤ tj si + tj ei

for t > tj

si + tj ei

tj

si Start time of discharge j

tj

ei End time of discharge j (hj i = 0)

Pressure drop at valve ∆pj

i = ρg(hj i + hhead)

Level during discharge j Adhj

i

dt = −qj

i

  • J. Jäschke

Trondheim, 9. June 2012 7

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SLIDE 8

Heat Recovery Challenge Problem

  • J. Jäschke

Introduction Problem description Simulations Discussion Conclusions

Heat exchangers

T T T

i

Thi

in hi

  • ut

q hi q0i

SS-assumption: Energy balances Qi = q0i(Ti − T0) Qi = qhi(T in

hi − T out hi )

Heat transfer Qi = UA(qhi)∆Tlog,i Heat transfer ∆Tlog,i = (Th,i − T0) − (T in

hi − Ti)

log (Th,i−T0)

(T in

hi −Ti)

UAi(qhi) = UA0i qhi(t) qh0i 0.8

  • J. Jäschke

Trondheim, 9. June 2012 8

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SLIDE 9

Heat Recovery Challenge Problem

  • J. Jäschke

Introduction Problem description Simulations Discussion Conclusions

Splitter and mixer

q f q

N

f q f q f q

i 1 2

T T T

1

T

N i 2

Splitter Ti = T0 qi = fiq0

N

  • i=1

fi = 1

T q T q T q

1 1 2 i 2 i

T q

N N

q 0 T

mix

Mixer Tmix = 1 q0

N

  • i=1

qhiTi q0 =

N

  • i=1

qi

  • J. Jäschke

Trondheim, 9. June 2012 9

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SLIDE 10

Heat Recovery Challenge Problem

  • J. Jäschke

Introduction Problem description Simulations Discussion Conclusions

Objective function and heater

Heater duty Qheat(t) = q0cp

  • Ttarget − Tmix(t)
  • q 0 Tmix

T

target

Objective:

min

fi

24h Qheater(t)dt

  • J. Jäschke

Trondheim, 9. June 2012 10

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SLIDE 11

Heat Recovery Challenge Problem

  • J. Jäschke

Introduction Problem description Simulations Discussion Conclusions

Open-loop Simulation – equal fi

Equal fractions in all parallel branches

200 400 600 800 1000 1200 1400 50 100 150 200 Mixing temperature Temperature [

° C]

time [min] 200 400 600 800 1000 1200 1400 200 400 600 Heater Duty kW time [min]

  • J. Jäschke

Trondheim, 9. June 2012 11

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SLIDE 12

Heat Recovery Challenge Problem

  • J. Jäschke

Introduction Problem description Simulations Discussion Conclusions

Open-loop Simulation – equal fi

Equal fractions in all parallel branches

200 400 600 800 1000 1200 1400 −0.2 0.2 0.4 0.6 0.8 1 1.2 Cold stream split time [min]

J = 24h Qheatdt = 35005.17MJ

  • J. Jäschke

Trondheim, 9. June 2012 12

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SLIDE 13

Heat Recovery Challenge Problem

  • J. Jäschke

Introduction Problem description Simulations Discussion Conclusions

“Optimization”

Definition

An active branch is a branch connected to a no-zero hot stream

Idea

qi = fiq0 assign flow only to active branches fi,active = 1/nactive fi,inactive = 0 if no branch is active, then fi = 1/ntotal

  • J. Jäschke

Trondheim, 9. June 2012 13

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SLIDE 14

Heat Recovery Challenge Problem

  • J. Jäschke

Introduction Problem description Simulations Discussion Conclusions

“Optimized”

200 400 600 800 1000 1200 1400 50 100 150 200 Mixing temperature Temperature [

° C]

time [min] 200 400 600 800 1000 1200 1400 200 400 600 Heater Duty kW time [min]

  • J. Jäschke

Trondheim, 9. June 2012 14

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SLIDE 15

Heat Recovery Challenge Problem

  • J. Jäschke

Introduction Problem description Simulations Discussion Conclusions

“Optimized”

200 400 600 800 1000 1200 1400 0.5 1 Cold stream split time [min]

J = 24h Qheatdt = 25364.11MJ

  • J. Jäschke

Trondheim, 9. June 2012 15

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SLIDE 16

Heat Recovery Challenge Problem

  • J. Jäschke

Introduction Problem description Simulations Discussion Conclusions

Discussion

Implementation of “optimal solution”

Very simple Assumption: Only hot flows measured Clearly sub-optimal

Optimization

Nonlinear problem Time-varying Static optimization at each time instant Suboptimal policy

Temperatures not used. Piecewise constant fi

Large improvement 35, 005.17MJ = ⇒ 25, 364.11MJ

  • J. Jäschke

Trondheim, 9. June 2012 16

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SLIDE 17

Heat Recovery Challenge Problem

  • J. Jäschke

Introduction Problem description Simulations Discussion Conclusions

Conclusions

Nonlinear optimization problem:

Sub-optimal solution Simple implementation

For true optimal solution:

More information required

Temperatures Flow rates Estimate unmeasured parameters (UA0)

Future work

Improve “optimization” algorithm

Include temperature measurements Time varying fi

Assume flows are not measured Modify problem

Add buffer tank before split

  • J. Jäschke

Trondheim, 9. June 2012 17

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SLIDE 18

Heat Recovery Challenge Problem

  • J. Jäschke

Introduction Problem description Simulations Discussion Conclusions

Thank you! A simulink model will be made available on http://www.nt.ntnu.no/users/skoge/ publications/2012/BatchChallenge

  • J. Jäschke

Trondheim, 9. June 2012 18