1. 1 A Plantwide Control Procedure Applied to the HDA Process Antonio Araújo and Sigurd Skogestad Department of Chemical Engineering Norwegian University of Science and Technology (NTNU) Trondheim, Norway November, 2006

2. 2 Outline General procedure plantwide control HDA process Active constraints Self-optimizing variables Maximum throughput mode Regulatory control Dynamic simulations –comparison with Luyben

3. 3 General procedure plantwide control y 1s y 2s Control of primary variables (MPC) “Stabilizing” control: p, levels, T (PID) Part I. “Top-down” steady-state approach - identify active constraints and primary controlled variables (y 1 ) – Self-optimizing control Part II. Bottom-up identification of control structure – starting with regulatory (“stabilizing”) control layer. –Identify secondary controlled variables (y 2 ) RTO. min J (economics). MV = y1s u (valves) Skogestad, S. (2004), “Control structure design for complete chemical plants”, Computers and Chemical Engineering, 28, 219-234.

4. 4 Part I. Top-down steady-state approach Step 1. IDENTIFY DEGREES OF FREEDOM Need later to choose a CV (y 1 ) for each Step 2. OPERATIONAL OBJECTIVES Optimal operation: Minimize cost J J = cost feeds – value products – cost energy subject to satisfying constraints Step 3. WHAT TO CONTROL? (primary CV’s c=y 1 ) What should we control (y 1 )? 1.Active constraints 2.“Self-optimizing” variables These are “magic” variables which when kept at constant setpoints give indirect optimal operation by controlling some “magic” variables at –Maximum gain rule: Look for “sensitive” variables with a large scaled steady-state gain Step 4. PRODUCTION RATE y 1s

5. 5 Part II. Bottom-up control structure design Step 5. REGULATORY CONTROL LAYER (PID) Main objectives –“Stabilize” = Avoid “drift” –Control on fast time scale Identify secondary controlled variables (y 2 ) –flow, pressures, levels, selected temperatures –and pair with inputs (u 2 ) Step 6. SUPERVISORY CONTROL LAYER – Decentralization or MPC? Step 7. OPTIMIZATION LAYER (RTO) –Can we do without it? y 2 = ? u (valves)

6. 6 Two main modes of optimal operation for chemical plants Depending on marked conditions: Mode I: Given throughput When: Given feed or product rate Optimal operation: Max. efficiency Mode II: Maximum throughput (feed available). When: High product prices and available feed Optimal operation: max. flow in bottleneck 1. Desired: Same or similar control structure in both cases 2. Operation/control: Traditionally: Focus on mode I But: Mode II is where the company may make extra money!

7. 7 MixerFEHE FurnacePFR Quench Separator Compressor Cooler Stabilizer Benzene Column Toluene Column H 2 + CH 4 Toluene Benzene CH 4 Diphenyl Purge (CH 4 + H 2 ) HDA process Toluene + H2 = Benzenje + CH4 2 Benzene = Diphenyl + H2 References for HDA: McKetta (1977) ; Douglas (1988) Wolff (1994) Luyben (2005) ++....

8. 8 Step 1 - Steady-state degrees of freedom NEED TO FIND 13 CONTROLLED VARIABLES (y 1 )

9. 9 Step 2 - Definition of optimal operation The following profit is to be maximized: -J = p ben D ben + Σ(p v,i F v,i ) – p tol F tol – p gas F gas – p fuel Q fuel – p cw Q cw – p power W power - p steam Q steam Constraints during operation: –Production rate: D ben ≥ 265 lbmol/h. –Hydrogen excess in reactor inlet: F hyd / (F ben + F tol + F diph ) ≥ 5. –Reactor inlet pressure: P reactor,in ≤ 500 psia. –Reactor inlet temperature:T reactor,in ≥ 1150 °F. –Reactor outlet temperature: T reactor,out ≤ 1300 °F. –Quencher outlet temperature: T quencher,out ≤ 1150 °F. –Product purity: x Dben ≥ 0.9997. –Separator inlet temperature: 95 °F ≤ T separator ≤ 105 °F. –Compressor power:W S ≤ 545 hp –Furnace heat duty:Q fur ≤ 24 MBtu –Cooler heat duty:Q cool ≤ 33 MBtu –+ Distillation heat duties (condensers and reboilers).

10. 10 Disturbances D1Fresh toluene feed rate [lbmol/h]300285 D2Fresh toluene feed rate [lbmol/h]300315 D3Fresh gas feed rate methane mole fraction0.030.08 D4Hydrogen to aromatic ratio in reactor inlet5.05.5 D5Reactor inlet pressure [psi]500520 D6Quencher outlet temperature [ o F]11501170 D7Product purity in the benzene column distillate0.99970.9960 Typical disturbances : Feeds Utilities Constraints Caused by: implementation error or change

11. 11 Step 3: What to control? 13 steady-state degrees of freedom 70 Candidate controlled variables –pressures, temperatures, compositions, flow rates, heat duties, etc.. Number of different sets of controlled variables: Cannot evaluate all ! OPTIMAL OPERATION: 1. Control active constraints! Find from steady-state optimization (step 3.1) 2. Remaining unconstrained DOFs: Look for “self-optimizing” variables (step 3.2)

12. 12 Operation with given feed Mode I

13. 13 Step 3.1 – Optimization distillation Distillation train: –Optimized separately using detailed models –Generally: Most valuable product at its constraint –Other compositions: Trade-off between recovery and energy –Results: Stabilizer x D,benzene 1 · 10 -4 x B,methane 1 · 10 -6 Benzene column x D,benzene 0.9997 x B,benzene 1.3 · 10 -3 Toluene column x D,diphenyl 0.5 · 10 -3 x B,toluene 0.4 · 10 -3

14. 14 Step 3.1 – Optimization entire process Reactor-recycle part With simplified distillation section (constant compositions) Distillation compositions

15. 15 Step 3.1 – Optimization: Active Constraints 79 11 1.Max. Toluene feed rate 2.Min. H2/aromatics ratio 3.Min. Separator temperature 4.Min. quencher temperature 5.Max. Reactor pressure 6.Max. impurity product + 5 distillation purities

16. 16 Step 3.2: What more to control? So far: Control 6 active constraints + 5 compositions (“self-optimizing”) What should we do with the 2 remaining degrees of freedom? –Self-optimizing control: Control variables that give small economic loss when kept constant But still many alternative sets Prescreening: Use “maximum gain rule” (local analysis) for prescreening –Maximize σ(S 1 ·G 2x2 ·J uu -1/2 ). –Optimal variation and implementation error enters in S 1

17. 17 σ(S 1 ·G 2x2 ·J uu -1/2 ) = 2.33·10 -3 Average Loss (k$/year) Mixer outlet inert (methane) mole fraction Quencher outlet toluene mole fraction 15.39 σ(S 1 ·G 2x2 ·J uu -1/2 ) = 2.27·10 -3 Average Loss (k$/year) Mixer outlet inert (methane) mole fraction Toluene conversion at reactor outlet 26.55 σ(S 1 ·G 2x2 ·J uu -1/2 ) = 2.25·10 -3 Average Loss (k$/year) Mixer outlet inert (methane) mole fraction Separator liquid benzene mole fraction 31.39 Linear model All measurements: σ(S 1 G full ·J uu -1/2 ) = 6.34·10 -3 Best set of two measurements involves two compositions: c1 c2 Step 3.2 – “Maximum gain rule”

18. 18 Step 3 - Final selection in mode I c1 c2 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 1 4 2 7 6 9 10 11 4 3 5

19. 19 Step 3: What to control in Mode II ? Available feed and good product prices Maximum throughput

20. 20 Optimization in mode II: Maximum throughput 14 steady-state degrees of freedom (one extra) Reoptimize operation with feedrate F tol as parameter: –Find same active constraints as in Mode I. –At F tol = 380 lbmol/h: Compressor power constraint active. –At F tol = 390 lbmol/h: Furnace heat duty constraint active. –Further increase in F tol infeasible: Furnace is BOTTLENECK!

21. 21 Step 3 - Controlled variable mode II 8 active constraints (including W S and Q fur ) + 5 distillation compositions One unconstrained degree of freedom: –To reduce the need for reconfiguration we control x-methane –Average loss 68.74 k$/year c1

22. 22 Step 4 – Throughput manipulator Mode I: Toluene feedrate (given) Mode II: Optimal throughput manipulator is furnace duty (bottleneck) –Minimizes back-off –But furnace duty is used to stabilize reactor –So use toluene feedrate also in mode II c1

23. 23 Part II: Bottom-up design starting with regulatory layer

24. 24 Step 5: Regulatory layer - Stabilization Control reactor temperature and liquid levels in separator and distillation columns (LV configuration). LC01 LC11LC21LC31 LC32 LC22LC12 TC01

25. 25 Regulatory layer - Avoiding drift I: Pressure control LC01 LC11LC21LC31 LC32 LC22LC12 PC01 PC11PC22PC33 TC01

26. 26 Regulatory layer - Avoiding drift II: Temperature control LC01 LC11LC21LC31 LC32 LC22LC12 PC01 PC11PC22PC33 TC02 TC03 TC22 TC11 #20 #3 #5 TC33 TC01

27. 27 Regulatory layer - Avoiding drift III: Flow control LC01 LC11LC21LC31 LC32 LC22LC12 PC01 PC11PC22PC33 TC02 TC03 TC22 TC11 #20 #3 #5 TC33 FC01 FC02 TC01

28. 28 Step 6: Supervisory layer – Mode I LC01 LC11LC21LC31 LC32 LC22LC12 TC01 PC01 PC11PC22PC33 TC02 TC03 TC22 TC11 #20 #3 #5 TC33 FC01 FC02 RC01 CC01 CC02 CC21 CC22 CC32 CC31 CC12 CC11 Decentralized control (PID-loops) seems sufficient

29. 29 Step 6: Supervisory layer – Mode II LC01 LC11LC21LC31 LC32 LC22LC12 TC01 PC01 PC11PC22PC33 TC02 TC03 TC22 TC11 #20 #3 #5 TC33 SETPOINT= Max.fuel-backoff FC02 RC01 CC01 CC21 CC22 CC32 CC31 CC12 CC11 Fixed Decentralized control (PID-loops) seems sufficient

30. 30 Dynamic simulations – Mode I Disturbance D1: +15 lbmol/h (+5%) increase in F tol. OursLuyben’s

31. 31 Dynamic simulations – Mode I Disturbance D2: -15 lbmol/h (-5%) increase in F tol. OursLuyben’s

32. 32 Dynamic simulations – Mode I Disturbance D3: +0.05 increase in x met. OursLuyben’s

33. 33 Dynamic simulations – Mode I Disturbance D4: +20 psi increase in P rin. OursLuyben’s

34. 34 Conclusion Procedure plantwide control: I. Top-down analysis to identify degrees of freedom and primary controlled variables (look for self-optimizing variables) II. Bottom-up analysis to determine secondary controlled variables and structure of control system (pairing).