1/31 E. S. Hori, Self-optimizing control… Self-optimizing control configurations for two-product distillation columns Eduardo Shigueo Hori, Sigurd Skogestad Norwegian University of Science and Technology – NTNU N-7491 Trondheim, Norway Muhammad Al-Arfaj King Fahd University of Petroleum and Minerals - KFUPM

2/31 E. S. Hori, Self-optimizing control… Outline 1.Introduction. Indirect composition control 2.Alternative approaches for selecting controlled variables 3.Temperature profile heuristic 4. Self-optimizing control: Exact local method 4.1 Results for binary distillation columns 4.2 Results for multicomponent distillation columns 5. Conclusions

3/31 E. S. Hori, Self-optimizing control… 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 (z F ) - feed enthalpy (q F ) Notation Stages: - top and bottom (both 0%) - feed (100%)

4/31 E. S. Hori, Self-optimizing control… 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

5/31 E. S. Hori, Self-optimizing control… 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 3 b. “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?

6/31 E. S. Hori, Self-optimizing control… 3. Temperature profile (Heuristic method 1) Control a temperature where the temperature slope is large Slope rule makes sense from a dynamic point of view Initial gain → proportional to temperature difference BUT for Indirect composition control: steady state gain (sensitivity) is more important (maximum gain rule)

7/31 E. S. Hori, Self-optimizing control… Binary column slope closely correlated with steady state gain STAGE TEMPERATURE PROFILE

8/31 E. S. Hori, Self-optimizing control… Multicomponent column Slope NOT correlated with steady-state gain TEMPERATURE PROFILE Conclusion: Temperature slope OK only for binary columns

9/31 E. S. Hori, Self-optimizing control… 4. Self-optimizing control: Exact local method Evaluate ”local” steady-state composition deviation: e c includes: - disturbances (F, z F, q F ) - implementation measurement error (0.5 for T)

10/31 E. S. Hori, Self-optimizing control… Outline 1.Introduction. Indirect composition control 2.Alternative approaches for selecting controlled variables 3.Temperature profile heuristic 4. Self-optimizing control: Exact local method 4.1 Results for binary distillation columns 4.2 Results for multicomponent distillation columns 5. Conclusion

11/31 E. S. Hori, Self-optimizing control… 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

12/31 E. S. Hori, Self-optimizing control… Table: Binary mixture - Steady-state relative composition deviations ( )for binary column A Fixed variables T b,55% – T t,55% *0.530 T b,70% – L/F*0.916 T b,50% – L/F0.975 T b,75% - V/F*1.148 T b,90% – L*1.223 T b,70% – L/D*1.321 T b,50% – L1.386 T t,95% – V*1.470 L/D – V/B15.84 L/F – V/B18.59 L – B21.06 D – V21.22 L – V63.42 D – Binfeasible * Temperature optimally located ** Optimal temperature in opposite section.

13/31 E. S. Hori, Self-optimizing control… Table: Binary mixture - Steady-state relative composition deviations ( )for binary column A Fixed variables T b,55% – T t,55% *0.530 T b,70% – L/F*0.916 T b,50% – L/F0.975 T b,75% - V/F*1.148 T b,90% – L*1.223 T b,70% – L/D*1.321 T b,50% – L1.386 T t,95% – V*1.470 L/D – V/B15.84 L/F – V/B18.59 L – B21.06 D – V21.22 L – V63.42 D – Binfeasible * Temperature optimally located ** Optimal temperature in opposite section.

14/31 E. S. Hori, Self-optimizing control… Table: Binary mixture - Steady-state relative composition deviations ( )for binary column A Fixed variables T b,55% – T t,55% *0.530 T b,70% – L/F*0.916 T b,50% – L/F0.975 T b,75% - V/F*1.148 T b,90% – L*1.223 T b,70% – L/D*1.321 T b,50% – L1.386 T t,95% – V*1.470 L/D – V/B15.84 L/F – V/B18.59 L – B21.06 D – V21.22 L – V63.42 D – Binfeasible * Temperature optimally located ** Optimal temperature in opposite section.

15/31 E. S. Hori, Self-optimizing control… Table: Binary mixture - Steady-state relative composition deviations ( )for binary column A Fixed variables T b,55% – T t,55% *0.530 T b,70% – L/F*0.916 T b,50% – L/F0.975 T b,75% - V/F*1.148 T b,90% – L*1.223 T b,70% – L/D*1.321 T b,50% – L1.386 T t,95% – V*1.470 L/D – V/B15.84 L/F – V/B18.59 L – B21.06 D – V21.22 L – V63.42 D – Binfeasible * Temperature optimally located ** Optimal temperature in opposite section.

16/31 E. S. Hori, Self-optimizing control… Table: Binary mixture - Steady-state relative composition deviations ( )for binary column A Fixed variables T b,55% – T t,55% *0.530 T b,70% – L/F*0.916 T b,50% – L/F0.975 T b,75% - V/F*1.148 T b,90% – L*1.223 T b,70% – L/D*1.321 T b,50% – L1.386 T t,95% – V*1.470 L/D – V/B15.84 L/F – V/B18.59 L – B21.06 D – V21.22 L – V63.42 D – Binfeasible * Temperature optimally located ** Optimal temperature in opposite section.

17/31 E. S. Hori, Self-optimizing control… Table: Binary mixture - Steady-state relative composition deviations ( )for binary column A Fixed variables T b,55% – T t,55% *0.530 T b,70% – L/F*0.916 T b,50% – L/F0.975 T b,75% - V/F*1.148 T b,90% – L*1.223 T b,70% – L/D*1.321 T b,50% – L1.386 T t,95% – V*1.470 L/D – V/B15.84 L/F – V/B18.59 L – B21.06 D – V21.22 L – V63.42 D – Binfeasible * Temperature optimally located ** Optimal temperature in opposite section.

18/31 E. S. Hori, Self-optimizing control… Composition deviation: 1- L/F and one temperature 2- V/F and one temperature 3- Two temperatures symmetrically located Effect of T-location on column A Conclusion: Avoid temperature at the ends

19/31 E. S. Hori, Self-optimizing control… Dynamic simulation – Column A F qFqF zFzF F qFqF zFzF Conclusion: z F is the main disturbance

20/31 E. S. Hori, Self-optimizing control… Add composition layer on top Fixed variables T b,55% – T t,55% * T b,70% – L/F* T b,75% - V/F* T b,90% – L* T t,50% – L/F T b,70% – L/D* T t,95% – V* L/D – V/B L – V column A Dynamic-ISE Conclusion: For large measurement delays self- optimizing variables are best

21/31 E. S. Hori, Self-optimizing control… Table: Steady state data for binary distillation column examples (Skogestad et al., 1990) Column  NNFNF D/FL/F A B C D E F G H I M1* M2* M3* M4* M5* M6* * Luyben’s columns (Luyben, 2005b). These columns are simulated using ASPEN PLUS© MORE BINARY COLUMNS...

22/31 E. S. Hori, Self-optimizing control… Table: Binary mixtures - steady-state composition deviations. Column B Column C Column D Column E T b,55% -T t,65% 0.78T t,25% – L/F0.70T b,58% – L/D1.10T b,0% -T t,45% 0.75 T t,65% – L/F0.90T t,45% – V/F0.70T b,50% – L/F1.29T t,45% – L/F1.03 T t,65% – V/F1.04T b,75% – T t,35% 0.82T b,50% – V/F1.32T t,36% - L1.36 T t,75% - L1.12T t,50% - L0.88T b,53% - L1.45T t,36% – V/F1.58 T t,75% - V1.24T b,85% – L/D0.91T b,53% - V1.50T t,36% – V/B1.67 T t,70% – V/B1.38T t,55% - V0.93T t,78% – V/B2.04T t,36% - V1.83 T b,50% – L/F2.88T t,5% – V/B1.20T b,29% -T t,72% 2.44T b,75% – L/D4.86 T b,50% – L3.00T b,80% – L/F1.53L/D – V/B3.85T b,50% – L/F7.15 T b,25% – L/D5.48L/D – V/B2.19L/F – V/B4.48T b,50% – L8.77 L/D – V/B19.1T b,50% – L3.13L – B4.85L/D – V/B10.7 D – V19.1D – V3.41D – V5.23D – V12.4 L – B44.7L – B8.94L/D – V5.85L – V19.4 L – V71.1L – V8.94L – V56.0L – B31.9 Conclusion: L/F, L and two-point control are the best choices

23/31 E. S. Hori, Self-optimizing control… Table: Binary mixtures - steady-state composition deviations. Column F Column G Column H Column I T b,0% –T t,67% 0.76T b,64% -T,68% 1.24T t,35% – L/F0.87T b,30% – L/F0.93 T t,83% - L0.89T b,79% – L/F1.90T t,35% – V/F0.99T b,35% – V/F0.96 T b,75% – L/F1.03T t,93% – V/F2.07T t,40% - L1.12T b,50% – L/F0.99 T b,50% – L/F1.50T b,97% - L2.52T t,40% - V1.22T b,35% - L1.13 T b,50% – L1.64T b,77% – L/D2.60T t,30% – V/B1.43T b,50% – L1.16 T t,83% – V/F4.44T t,98% - V2.95T t,50% – L/D3.91T b,40% – V1.26 T t,83% – V5.01T b,51% – L/F3.01T b,80% -T t,5% 3.91T b,25% – L/D1.34 T t,83% – V/B7.22T b,51% – L3.39L/D – V/B10.4T b,0% –T t,75% 3.62 L/D – V/B1600T t,88% – V/B3.69D – V10.5T b,40% – V/B4.72 L/F – V/B1667L/D – V/B1593L/F – V/B17.1L/D – V/B10.3 L – B2127L – B2140L – B21.0L – B10.5 D – V2127D – V2141T b,50% – L34.9D – V21.0 L – V2683L – V6344L – V46.2L – V53.8 Conclusion: L/F, L and two-point control are the best choices

24/31 E. S. Hori, Self-optimizing control… Table: Binary mixtures (Luyben 2005): steady-state composition deviations. 87.5T b,48% – L434T b,59% – L/D $ 105T t,53 – L/D76.2T b,48% – L/F186T b,48% – L 15.3T b,81% – V/B*75.1T b,65% – L/F**150T b,48% – L/F 14.1T b,69% - V*24.2T t,15% – V/B*33.2T t,50% – L/D* $ 9.72T b,50 – L/D*23.3T t,85% – L/D*11.4T t,8% – V/B* 8.99T b,69% – V/F*20.4T t,54% - V*9.74T t,8% - V* 7.16T b,50% - L*18.0T t,23% – V/F*8.41T t,8% – V/F* 4.85T b,50% – L/F $ 9.25T t,23% - L*4.84T t,17% - L* 4.67T b,19% – L/F*8.67T t,46% – L/F $ 4.55T t,50% – L/F $ 2.94T b,50% -T t,53% $ 8.61T t,23% – L/F*4.07T t,17% – L/F* 1.45T b,19% -T t,27% *1.36T b,39% –T t,23% *2.29T b,10% -T t,17% * Column M3Column M2Column M1 Conclusion: L/F, L and two-point control are the best choices

25/31 E. S. Hori, Self-optimizing control… Table: Binary mixtures (Luyben 2005): steady-state composition deviations. 182T t,50% – L/F32.8T b,38% – V/B 216T t,50% - L88.0T 100% – V/B19.4T b,77% - V 117T b,0% – V/B21.8T b,25% – V13.5T b,38% – V/F 8.54T b,18% - V15.4T b,25% – V/F7.72T b,8% – L/D 8.03T b,0% - V/F5.62T b,50% – L6.76T b,46% – L 3.35T b,45% – L5.62T b,33% - L6.76T b,23% - L 3.27T b,9% – L/D5.13T b,8% – L/D4.71T b,46% – L/F $ 3.21T b,9% - L3.85T b,50% – L/F $ 4.67T b,15% – L/F 2.12T b,45% – L/F $ 3.85T b,25% – L/F1.54T b,46% –T t,56% $ 1.62T b,18% -T t,30% 0.96T b,25% -T t,29% 1.19T b,23% –T t,22% Column M6Column M5Column M4 Conclusion: L/F, L and two-point control are the best choices

26/31 E. S. Hori, Self-optimizing control… Outline 1.Introduction. Indirect composition control 2.Alternative approaches for selecting controlled variables 3.Temperature profile heuristic 4. Self-optimizing control: Exact local method 4.1 Results for binary distillation columns 4.2 Results for multicomponent distillation columns 5. Conclusion

27/31 E. S. Hori, Self-optimizing control… 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

28/31 E. S. Hori, Self-optimizing control… Multicomponent columns Table: Multicomponent column data. Key components (L/H)NNFNF D/FL/F A/B B/C C/D “Real” B/C split: C5/nC6* *Feed composition: nC4/nC5/nC6/nC7 (25% each)

29/31 E. S. Hori, Self-optimizing control… Table: Multicomponent Column: steady-state composition deviations. Conclusion: L/F and L are the best choices

30/31 E. S. Hori, Self-optimizing control… 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