1. 1 Self-Optimizing Control HDA case study S. Skogestad, May 2006 Thanks to Antonio Araújo

2. 2 Self-Optimizing Control Process Description Benzene production from thermal-dealkalination of toluene (high- temperature, non-catalytic process). Main reaction: Side reaction Excess of hydrogen is needed to repress the side reaction and coke formation. References for HDA process: McKetta (1977) – first reference on the process; Douglas (1988) – design of the process; Wolff (1994) – discuss the operability of the process. No references on the optimization of the process for control structure design purposes. CH 3 +H2H2 → ++CH 4 Heat H2H2 + → 2 ← Toluene Benzene Diphenyl

3. 3 Self-Optimizing Control MixerFEHE FurnacePFR Quench Separator Compressor Cooler Stabilizer Benzene Column Toluene Column H 2 + CH 4 Toluene Benzene CH 4 Diphenyl Purge (H 2 + CH 4 ) Process Description

4. 4 Self-Optimizing Control Steady-state operational degrees of freedom Process units DOF External feed streams (feed rate)2 Heat exchangers duties (including 1 furnace)3 Splitters2 Compressor duty1 Adiabatic flash (*) 0 Gas phase reactor (*) 0 Distillation columns6 Equality constraint Quencher outlet temperature Remaining degrees of freedom at steady state 13 (*) No adjustable valves (assumed fully open valve before flash) 14

5. 5 Self-Optimizing Control Steady-state operational degrees of freedom MixerFEHE Furnace Reactor Quencher Separator Compressor Cooler Stabilizer Benzene Column Toluene Column H 2 + CH 4 Toluene Benzene CH 4 Diphenyl Purge (H 2 + CH 4 ) 1 2 7 4 3 5 6 8 1214 13119 10

6. 6 Self-Optimizing Control Cost Function and Constraints The following profit is maximized (Douglas’s EP): -J = p ben D ben – p tol F tol – p gas F gas – p fuel Q fuel – p cw Q cw – p power W power - p steam Q steam + Σ(p v,i F v,i ) Constraints during operation: –Production rate: D ben ≥ 265 lbmol/h. –Hydrogen excess in reactor inlet: F Hyd / (F ben + F tol + F diph ) ≥ 5. –Bound on toluene feed rate: F tol ≤ 300 lbmol/h. –Reactor pressure: P reactor ≤ 500 psia. –Reactor outlet temperature: T reactor ≤ 1300 °F. –Quencher outlet temperature: T quencher = 1150 °F. –Product purity: x Dben ≥ 0.9997. –Separator inlet temperature: 95 °F ≤ T flash ≤ 105 °F. –+ Distillation constraints Manipulated variables are bounded.

7. 7 Self-Optimizing Control Disturbances DisturbanceUnitNominalLowerUpper Toluene feed flow ratelbmol/h300285315 Gas feed composition mol% of H 2 9590100 Benzene price$/lbmol9.048.349.74 Energetic value of fuel to the furnaceMBTU/lbmol0.12470.120.13

8. 8 Self-Optimizing Control Optimization Benzene price Disturbance

9. 9 Self-Optimizing Control 14 steady-state degrees of freedom 10 active constraints: 1.Pure toluene feed rate (UB) 2.By-pass valve around FEHE (LB) 3.Reactor inlet hydrogen-aromatics ratio (LB) 4.Flash inlet temperature (LB) 5.Methane mole fraction in stabilizer bottom (UB) 6.Benzene mole fraction in stabilizer distillate (UB) 7.Benzene mole fraction in benzene column bottom (UB) 8.Toluene mole fraction in benzene column distillate (UB) 9.Toulene mole fraction in toluene column bottom (UB) 10.Diphenyl mole fraction in toluene column distillate (UB ) 1 equality constraint: 11. Quencher outlet temperature 3 remaining unconstrained degrees of freedom. Optimization

10. 10 Self-Optimizing Control Optimization – Active Constraints MixerFEHE Furnace Reactor Quencher Separator Compressor Cooler Stabilizer Benzene Column Toluene Column H 2 + CH 4 Toluene Benzene CH 4 Diphenyl Purge (H 2 + CH 4 ) 8 2 1 4 3 5 6 7 10 9 11 Equality

11. 11 Self-Optimizing Control Candidate Controlled Variables Candidate controlled variables: –Pressure differences; –Temperatures; –Compositions; –Heat duties; –Flow rates; –Combinations thereof. 138 candidate controlled variables might be selected. 14 degrees of freedom. Number of different sets of controlled variables: 10 active constraints + 1 equality constraint leaving 3 DOF: What should we do with the remaining 3 DOF? –Self-optimizing control!!!

12. 12 Self-Optimizing Control Analysis of the linear model Select 3 of 127 candidate measurements. Scale variables properly and linearize. Find max σ(G 3x3 ) by a branch-and-bound algorithm. Alternatively, find max σ(G 3x3 ·J uu -1/2 ) by a branch-and-bound algorithm. Calculate the loss by the exact local method for the most important disturbance: Namely, feed toluene rate. “input scaling”

13. 13 Self-Optimizing Control Analysis of the linear model σ(G 3x3 ) = 0.02382, Loss = 8.6461σ(G 3x3 ·J uu -1/2 ) = 0.10257, Loss = 6.6803 Toluene column reflux flow rate Compressor power Liquid (cooling) flow to quencher Toluene mole fraction in stabilizer bottom Compressor power Furnace heat duty σ(G 3x3 ) = 0.02381, Loss = 8.6474σ(G 3x3 ·J uu -1/2 ) = 0.10283, Loss = 6.7837 Diphenyl mole fraction in benzene column bottom Compressor power Liquid (cooling) flow to quencher Toluene mole fraction in separator liquid outlet Compressor power Furnace heat duty σ(G 3x3 ) = 0.02380, Loss = 8.6475σ(G 3x3 ·J uu -1/2 ) = 0.10129, Loss = 8.4168 Benzene mole fraction in benzene column bottom Compressor power Liquid (cooling) flow to quencher Diphenyl mole fraction in quencher outlet Compressor power Furnace heat duty a.All measurements: σ(G full ) = 0.0445; σ(G full ·J uu -1/2 ) = 0.1695 I II III I II III

14. 14 Self-Optimizing Control Self-optimizing variables MixerFEHE Furnace Reactor Quencher Separator Compressor Cooler Stabilizer Benzene Column Toluene Column H 2 + CH 4 Toluene Benzene CH 4 Diphenyl Purge (H 2 + CH 4 ) 8 2 1 4 1 5 6 7 10 9 I III 11 II F W I III x tol Q L Optimal set

15. 15 Self-Optimizing Control Analysis of the linear model b. Distillation train excluded and separator pressure constant (controllability): σ(G full ) = 0.0440; σ(G full ·J uu -1/2 ) = 0.1663 σ(G 3x3 ) = 0.02240, Loss = 7.9683σ(G 3x3 ·J uu -1/2 ) = 0.08971, Loss = 7.9683 Toluene mole fraction in separator liquid outlet Compressor power Separator pressure Toluene mole fraction in separator liquid outlet Compressor power Separator pressure σ(G 3x3 ) = 0.02266, Loss = 8.9112σ(G 3x3 ·J uu -1/2 ) = 0.08612, Loss = 8.9112 Benzene mole fraction in mixer outlet Compressor power Separator pressure Benzene mole fraction in mixer outlet Compressor power Separator pressure σ(G 3x3 ) = 0.02265, Loss = 8.9290σ(G 3x3 ·J uu -1/2 ) = 0.08598, Loss = 8.9290 Quencher outlet diphenyl mole fraction Compressor power Separator pressure Quencher outlet diphenyl mole fraction Compressor power Separator pressure I II III I II III Note: The two methods give the same order in this case

16. 16 Self-Optimizing Control Alternative self-optimizing variables MixerFEHE Furnace Reactor Quencher Separator Compressor Cooler Stabilizer Benzene Column Toluene Column H 2 + CH 4 Toluene Benzene CH 4 Diphenyl Purge (H 2 + CH 4 ) 8 2 1 4 1 5 6 7 10 9 11 P W I x tol II III

17. 17 Self-Optimizing Control Conclusion steady-state analysis Many similar alternatives in terms of loss Need to consider dynamics (Input-output controllability analysis): –RHP-zeros –RHP-poles –Input saturation –Easy of implementation (decentralized control of final 3x3 supervisory control problem)! Now: Consider “bottom-up” design of control system

18. 18 Self-Optimizing Control Bottom-up design of control system Start with stabilizing control –Levels –Pressure –Temperatures Normally start with fastest loops (often pressure) –but let is start with levels

19. 19 Self-Optimizing Control “Bottom-up”: Proposed Control Structure Stabilizing Control: Control 7 liquid levels MixerFEHE Furnace Reactor Quencher Separator Compressor Cooler Stabilizer Benzene Column Toluene Column H 2 + CH 4 Toluene Benzene CH 4 Diphenyl Purge (H 2 + CH 4 ) LC LV-configuration assumed for columns

20. 20 Self-Optimizing Control Avoiding “Drift” I – 4 Pressure loops MixerFEHE Furnace Reactor Quencher Separator Compressor Cooler Stabilizer Benzene Column Toluene Column H 2 + CH 4 Toluene Benzene CH 4 Diphenyl Purge (H 2 + CH 4 ) LC PC Column pressures are given Pressure with purge

21. 21 Self-Optimizing Control Avoiding “Drift” II – 4 Temperature loops MixerFEHE Furnace Reactor Quencher Separator Compressor Cooler Stabilizer Benzene Column Toluene Column H 2 + CH 4 Toluene Benzene CH 4 Diphenyl Purge (H 2 + CH 4 ) LC TC PC psps TsTs

22. 22 Self-Optimizing Control Now suggest pairings for supervisory control

23. 23 Self-Optimizing Control Control of 11 active constraints. MixerFEHE Furnace Reactor Quencher Separator Compressor Cooler Stabilizer Benzene Column Toluene Column H 2 + CH 4 Toluene Benzene CH 4 Diphenyl Purge (H 2 + CH 4 ) LC TC CC TC CC TC FC TC PC TC 3 DOF left PC SP SP methane SP psps TsTs

24. 24 Self-Optimizing Control Control of 3 self-optimizing variables: Optimal set MixerFEHE Furnace Reactor Quencher Separator Compressor Cooler Stabilizer Benzene Column Toluene Column H 2 + CH 4 Toluene Benzene CH 4 Diphenyl Purge (H 2 + CH 4 ) LC TC CC TC CC TC FC TC PC TC Supervisory control problem seems difficult PC SP SP methane SP psps TsTs I x toluene III II Q

25. 25 Self-Optimizing Control Control of 3 self-optimizing variables: Alternative set: SIMPLE MixerFEHE Furnace Reactor Quencher Separator Compressor Cooler Stabilizer Benzene Column Toluene Column H 2 + CH 4 Toluene Benzene CH 4 Diphenyl Purge (H 2 + CH 4 ) LC TC CC TC CC TC FC TC PC TC PC SP psps TsTs I x tol III II Could control another composition, e.g. quencher outlet diphenyl

26. 26 Self-Optimizing Control Conclusion HDA Follow systematic procedure May want to keep several candidate sets of “almost” self-optimizing variables Final evaluation: Non-linear steady- state simulations + Dynamic simulations using Aspen (ongoing!)