1/31 e. s. hori, self-optimizing control… self-optimizing control configurations for two-product...

1/31

E. S. Hori, Self-optimizing control…

Self-optimizing control configurations for two-product distillation columns

Eduardo Shigueo Hori, Sigurd SkogestadNorwegian University of Science and Technology – NTNUN-7491 Trondheim, Norway

Muhammad Al-Arfaj King Fahd University of Petroleum and Minerals - KFUPM

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Outline

1. Introduction. Indirect composition control

2. Alternative approaches for selecting controlled variables

3. Temperature profile heuristic

4. Self-optimizing control: Exact local method4.1 Results for binary distillation columns

4.2 Results for multicomponent distillation columns

5. Conclusions

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1. Introduction

• Distillation column with given feed and pressure: Two steady-state degrees of freedom

• Issue: What should we control (”fix”) to achieve indirect composition control?

• Disturbances:- feed flow (F), - feed composition (zF) - feed enthalpy (qF)

• Notation Stages:- top and bottom (both 0%)- feed (100%)

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• Variables available for control:

- temperatures

- flows (including flow ratios L/D, L/F, etc)

- 15 different binary columns

- 4 multicomponent columns

• No single ”best” structure for all columns

• Find reasonable structure for most columns

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2. Alternative approaches

1. Heuristic 1: Steep temperature profile

2. Heuristic 2: Small optimal variation for disturbances (Luyben, 1975)

3. Heuristic 3: Large sensitivity, or more generally, large gain in terms of the minimum singular value (Moore, 1992)

4. Self-optimizing control (Skogestad et al.)a. “Maximum scaled gain rule”: Combines heuristic 2 and 3b. “Exact” local method (main method used in this work)c. Brute-force evaluation of loss

•What should we control (”fix”) to achieve indirect composition control?

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3. Temperature profile (Heuristic method 1)

• Control a temperature where the temperature slope is large

• Slope rule makes sense from a dynamic point of viewInitial gain → proportional to temperature difference

• BUT for Indirect composition control: steady state gain (sensitivity) is more important (maximum gain rule)

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Binary columnslope closely correlated with steady state gain

STAGE

TEMPERATURE PROFILE

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Multicomponent columnSlope NOT correlated with steady-state gain

TEMPERATURE PROFILE

Conclusion: Temperature slope OK only for binary columns

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4. Self-optimizing control: Exact local method

• Evaluate ”local” steady-state composition deviation:

• ec includes:

- disturbances (F, zF, qF)

- implementation measurement error (0.5 for T)

2

2 2H H L Ldeftop top,s btm btm,s

max H L1top,s btm,s

maxce

x x x xX L

x x¢ £

æ ö æ ö- -÷ ÷ç ç÷ ÷ç çD = = +÷ ÷ç ç÷ ÷ç ç ÷÷ç è øè ø

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Outline






5. Conclusion

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• Have looked at 15 binary columns

• Main focus on “column A”– 40 theoretical stages

– Feed in middle

– 1% impurity in each product

– Relative volatility: 1.5

– Boiling point difference: 10K

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Table: Binary mixture - Steady-state relative composition deviations ( )for binary column AXD

Fixed variables

Tb,55% – Tt,55%* 0.530

Tb,70% – L/F* 0.916

Tb,50% – L/F 0.975

Tb,75% - V/F* 1.148

Tb,90% – L* 1.223

Tb,70% – L/D* 1.321

Tb,50% – L 1.386

Tt,95% – V* 1.470

L/D – V/B 15.84

L/F – V/B 18.59

L – B 21.06

D – V 21.22

L – V 63.42

D – B infeasible

* Temperature optimally located** Optimal temperature in opposite section.

X

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Table: Binary mixture - Steady-state relative composition deviations ( )for binary column A

X

XD

Fixed variables

Tb,55% – Tt,55%* 0.530

Tb,70% – L/F* 0.916

Tb,50% – L/F 0.975

Tb,75% - V/F* 1.148

Tb,90% – L* 1.223

Tb,70% – L/D* 1.321

Tb,50% – L 1.386

Tt,95% – V* 1.470

L/D – V/B 15.84

L/F – V/B 18.59

L – B 21.06

D – V 21.22

L – V 63.42

D – B infeasible


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X

XD

Fixed variables

Tb,55% – Tt,55%* 0.530

Tb,70% – L/F* 0.916

Tb,50% – L/F 0.975

Tb,75% - V/F* 1.148

Tb,90% – L* 1.223

Tb,70% – L/D* 1.321

Tb,50% – L 1.386

Tt,95% – V* 1.470

L/D – V/B 15.84

L/F – V/B 18.59

L – B 21.06

D – V 21.22

L – V 63.42

D – B infeasible


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X

XD

Fixed variables

Tb,55% – Tt,55%* 0.530

Tb,70% – L/F* 0.916

Tb,50% – L/F 0.975

Tb,75% - V/F* 1.148

Tb,90% – L* 1.223

Tb,70% – L/D* 1.321

Tb,50% – L 1.386

Tt,95% – V* 1.470

L/D – V/B 15.84

L/F – V/B 18.59

L – B 21.06

D – V 21.22

L – V 63.42

D – B infeasible


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X

XD

Fixed variables

Tb,55% – Tt,55%* 0.530

Tb,70% – L/F* 0.916

Tb,50% – L/F 0.975

Tb,75% - V/F* 1.148

Tb,90% – L* 1.223

Tb,70% – L/D* 1.321

Tb,50% – L 1.386

Tt,95% – V* 1.470

L/D – V/B 15.84

L/F – V/B 18.59

L – B 21.06

D – V 21.22

L – V 63.42

D – B infeasible


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X

XD

Fixed variables

Tb,55% – Tt,55%* 0.530

Tb,70% – L/F* 0.916

Tb,50% – L/F 0.975

Tb,75% - V/F* 1.148

Tb,90% – L* 1.223

Tb,70% – L/D* 1.321

Tb,50% – L 1.386

Tt,95% – V* 1.470

L/D – V/B 15.84

L/F – V/B 18.59

L – B 21.06

D – V 21.22

L – V 63.42

D – B infeasible


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Composition deviation:1- L/F and one temperature2- V/F and one temperature3- Two temperatures symmetrically located

Effect of T-location on X

column A

Conclusion: Avoid temperature at the ends

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Dynamic simulation – Column A

F qFzF F qF

zF

Conclusion: zF is the main disturbance

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Add composition layer on top

Fixed variables

Tb,55% – Tt,55%* 0.530 10.6 1.18

Tb,70% – L/F* 0.916 15.2 2.18

Tb,75% - V/F* 1.148 20.1 6.92

Tb,90% – L* 1.223 40.1 2.33

Tt,50% – L/F 1.256 101 3.82

Tb,70% – L/D* 1.321 23.1 1.35

Tt,95% – V* 1.470 67.3 4.78

L/D – V/B 15.84 94.2 0.73

L – V 63.42 309 3.35

XD m 1 min m 60 min

column A

Dynamic-ISE

Conclusion: For large measurement delays self-optimizing variables are best

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Table: Steady state data for binary distillation column examples (Skogestad et al., 1990)

Column N NF D/F L/F

A 0.5 1.5 41 21 0.01 0.01 0.500 2.706 10

B 0.1 1.5 41 21 0.01 0.01 0.092 2.329 10

C 0.5 1.5 41 21 0.01 0.002 0.555 2.737 10

D 0.65 1.12 111 39 0.005 0.10 0.614 11.862 2.9

E 0.2 5 16 5 0.0001 0.05 0.158 0.226 40.9

F 0.5 15 11 5 0.0001 0.0001 0.500 0.227 68.7

G 0.5 1.5 81 40 0.0001 0.0001 0.500 2.635 10

H 0.1 1.5 41 21 0.01 0.0011 0.109 3.314 10

I 0.9 1.5 41 21 0.0011 0.01 0.891 3.305 10

M1* 0.1 - 42 30 0.001 0.001 0.099 0.408 -

M2* 0.2 - 37 24 0.001 0.001 0.199 0.404 -

M3* 0.4 - 32 17 0.001 0.001 0.400 0.404 -

M4* 0.6 - 32 14 0.001 0.001 0.600 0.386 -

M5* 0.8 - 37 13 0.001 0.001 0.801 0.366 -

M6* 0.9 - 32 12 0.001 0.001 0.901 0.357 -

* Luyben’s columns (Luyben, 2005b). These columns are simulated using ASPEN PLUS©

Htopx L

btmx b,H b,LT T-LFz

MORE BINARY COLUMNS...

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Table: Binary mixtures - steady-state composition deviations.

Column B Column C Column D Column E

Tb,55%-Tt,65% 0.78 Tt,25% – L/F 0.70 Tb,58% – L/D 1.10 Tb,0%-Tt,45% 0.75

Tt,65% – L/F 0.90 Tt,45% – V/F 0.70 Tb,50% – L/F 1.29 Tt,45% – L/F 1.03

Tt,65% – V/F 1.04 Tb,75% – Tt,35% 0.82 Tb,50% – V/F 1.32 Tt,36% - L 1.36

Tt,75% - L 1.12 Tt,50% - L 0.88 Tb,53% - L 1.45 Tt,36% – V/F 1.58

Tt,75% - V 1.24 Tb,85% – L/D 0.91 Tb,53% - V 1.50 Tt,36% – V/B 1.67

Tt,70% – V/B 1.38 Tt,55% - V 0.93 Tt,78% – V/B 2.04 Tt,36% - V 1.83

Tb,50% – L/F 2.88 Tt,5% – V/B 1.20 Tb,29%-Tt,72% 2.44 Tb,75% – L/D 4.86

Tb,50% – L 3.00 Tb,80% – L/F 1.53 L/D – V/B 3.85 Tb,50% – L/F 7.15

Tb,25% – L/D 5.48 L/D – V/B 2.19 L/F – V/B 4.48 Tb,50% – L 8.77

L/D – V/B 19.1 Tb,50% – L 3.13 L – B 4.85 L/D – V/B 10.7

D – V 19.1 D – V 3.41 D – V 5.23 D – V 12.4

L – B 44.7 L – B 8.94 L/D – V 5.85 L – V 19.4

L – V 71.1 L – V 8.94 L – V 56.0 L – B 31.9

X X XX( )1.5a = ( )1.5a = ( )1.12a = ( )5a =

Conclusion: L/F, L and two-point control are the best choices

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Table: Binary mixtures - steady-state composition deviations.

Column F Column G Column H Column I

Tb,0%–Tt,67% 0.76 Tb,64%-T,68% 1.24 Tt,35% – L/F 0.87 Tb,30% – L/F 0.93

Tt,83% - L 0.89 Tb,79% – L/F 1.90 Tt,35% – V/F 0.99 Tb,35% – V/F 0.96

Tb,75% – L/F 1.03 Tt,93% – V/F 2.07 Tt,40% - L 1.12 Tb,50% – L/F 0.99

Tb,50% – L/F 1.50 Tb,97% - L 2.52 Tt,40% - V 1.22 Tb,35% - L 1.13

Tb,50% – L 1.64 Tb,77% – L/D 2.60 Tt,30% – V/B 1.43 Tb,50% – L 1.16

Tt,83% – V/F 4.44 Tt,98% - V 2.95 Tt,50% – L/D 3.91 Tb,40% – V 1.26

Tt,83% – V 5.01 Tb,51% – L/F 3.01 Tb,80%-Tt,5% 3.91 Tb,25% – L/D 1.34

Tt,83% – V/B 7.22 Tb,51% – L 3.39 L/D – V/B 10.4 Tb,0%–Tt,75% 3.62

L/D – V/B 1600 Tt,88% – V/B 3.69 D – V 10.5 Tb,40% – V/B 4.72

L/F – V/B 1667 L/D – V/B 1593 L/F – V/B 17.1 L/D – V/B 10.3

L – B 2127 L – B 2140 L – B 21.0 L – B 10.5

D – V 2127 D – V 2141 Tb,50% – L 34.9 D – V 21.0

L – V 2683 L – V 6344 L – V 46.2 L – V 53.8

X X X X( )15a = ( )1.5a = ( )1.5a = ( )1.5a =


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Table: Binary mixtures (Luyben 2005): steady-state composition deviations.

87.5Tb,48% – L434Tb,59% – L/D$

105Tt,53 – L/D76.2Tb,48% – L/F186Tb,48% – L

15.3Tb,81%– V/B*75.1Tb,65% – L/F**150Tb,48% – L/F

14.1Tb,69% - V*24.2Tt,15% – V/B*33.2Tt,50% – L/D*$

9.72Tb,50 – L/D*23.3Tt,85% – L/D*11.4Tt,8% – V/B*

8.99Tb,69% – V/F*20.4Tt,54% - V*9.74Tt,8% - V*

7.16Tb,50% - L*18.0Tt,23% – V/F*8.41Tt,8% – V/F*

4.85Tb,50% – L/F$9.25Tt,23% - L*4.84Tt,17% - L*

4.67Tb,19% – L/F*8.67Tt,46% – L/F$4.55Tt,50% – L/F$

2.94Tb,50%-Tt,53%$8.61Tt,23% – L/F*4.07Tt,17% – L/F*

1.45Tb,19%-Tt,27%*1.36Tb,39%–Tt,23%*2.29Tb,10%-Tt,17%*

Column M3Column M2Column M1 X X X


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Table: Binary mixtures (Luyben 2005): steady-state composition deviations.

182Tt,50% – L/F32.8Tb,38% – V/B

216Tt,50% - L88.0T100% – V/B19.4Tb,77% - V

117Tb,0% – V/B21.8Tb,25% – V13.5Tb,38% – V/F

8.54Tb,18% - V15.4Tb,25% – V/F7.72Tb,8% – L/D

8.03Tb,0% - V/F5.62Tb,50% – L6.76Tb,46% – L

3.35Tb,45% – L5.62Tb,33%- L6.76Tb,23%- L

3.27Tb,9%– L/D5.13Tb,8% – L/D4.71Tb,46% – L/F$

3.21Tb,9% - L3.85Tb,50% – L/F$4.67Tb,15% – L/F

2.12Tb,45% – L/F$3.85Tb,25% – L/F1.54Tb,46%–Tt,56%$

1.62Tb,18%-Tt,30%0.96Tb,25%-Tt,29%1.19Tb,23%–Tt,22%

Column M6Column M5Column M4 X XX


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Outline






5. Conclusion

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Multicomponent columns

• Four components: A (lightest), B, C, and D (heaviest)

• Equal relative volatilities (AB=BC=CD=1.5)

• The temperatures are adjusted to be compatible with relative volatility

• Feed composition: 25% of each component

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Multicomponent columns

Htopx

Table: Multicomponent column data.

Key components (L/H) N NF D/F L/F

A/B 41 21 0.01 0.0033 0.250 2.767

B/C 41 21 0.005 0.005 0.500 1.659

C/D 41 21 0.0033 0.01 0.750 2.543

“Real” B/C split: C5/nC6* 45 15 0.005 0.005 0.344 1.185

*Feed composition: nC4/nC5/nC6/nC7 (25% each)

Lbtmx

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Table: Multicomponent Column: steady-state composition deviations.

32.0L/D – V/B44.7L/F – V/B

3.08Tb,50% – L/F31.8L/D – V/B2.60Tt,90% – V/B2.00Tb,50% – L

2.95Tt,33% – L/D4.45Tt,80% – V/B2.29Tb,50% – L2.00Tb,65% – L/D

2.94Tb,50% - L2.28Tt,90% – V2.22T100% – V1.98Tb,50% – L/F

2.19Tt,33% - V/F2.26Tb,95% – Tt,75%2.11Tb,50% – L/F1.86Tb,80% – Tt,100%

2.17Tt,33% - V/B2.07Tb,40% - V/F2.03Tb,95% - V/F1.08Tb,75% – L

1.85Tt,33% – L/F1.88Tb,45% – L1.91Tb,75% – L/D1.07Tb,80% – V

1.78Tt,33% – L1.64Tb,50% – L/F1.88Tb,95% – L1.05Tb,80% – L/F

1.74Tt,33% – V1.63Tb,40% – L/F1.77Tb,90% – L/F1.03Tb,80% - V/F

1.07Tb,30% – Tt,33%1.38Tb,85% – L/D1.71Tb,70%– Tt,75%0.96Tt,95% - V/B

“Real” B/CnC5/nC6

C/DB/CA/B X X X X

Conclusion: L/F and L are the best choices

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5. Conclusions• Optimal temperature location: most sensitive stage (maximize

scaled steady-state gain)

• Avoid temperature close to column end (especially for high purity) due to implementation errors and low sensitivity

• Avoid stage with small temperature slope: For dynamic reasons

• Binary and multicomponent separations: good control structure is L and a single temperature (usually in bottom section)

• Two-point temperature control: good for cases with ”binary” separations and no pinch

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