1. Self-Optimizing Control of the HDA Process Outline of the presentation –Process description. –Self-optimizing control procedure. –Self-optimizing control of the HDA process. –Concluding remarks.

2. Process Description Benzene production from thermal-dealkalination of toluene (high- temperature, non-catalytic process). Main reaction: Toluene + H 2 → Benzene + CH 4 Side reaction: 2·Benzene ↔ Diphenyl + H 2 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 reference about the optimization of the process for control purposes.

3. Process Description 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 )

4. Self-Optimizing Control Procedure Objective: Optimize operation –Find the optimum. –Implement the optimum (in practice). Self-optimizing control: –Set point control which optimize the operation with acceptable loss. Loss = J – J opt Pure steady state considerations. Stepwise procedure for evaluating the loss: –Degree of freedom analysis; –Cost function and constraints; –Identification of the most important disturbances (uncertainty); –Optimization; –Identification of candidate controlled variables; –Evaluation of loss; –Further analysis and selection.

5. Self-Optimizing Control of the HDA Process Steady-state degrees of freedom 1 2 4 10 9 7 8 6 3 5 17 12 11 14 13 16 15

6. Self-Optimizing Control of the HDA Process 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 ), i = 1,…,n c. Where: –Q cw = Q cw,cooler + Q cw,stab + Q cw,ben + Q cw,tol ; –Q steam = Q steam,stab + Q steam,ben + Q steam,tol ; –F v,i = F purge + D stab,i + B tol,i, i = 1,…,n c. Constraints during operation: –Production rate: D ben ≥ 265 lbmol/h. –Hydrogen excess in reactor inlet: F H2 / (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. –Quench outlet temperature: T quencher ≤ 1150 °F. –Product purity: x Dben ≥ 0.9997. –Separator inlet temperature: 95 °F ≤ T flash ≤ 105 °F. –+ some distillation recovery constraints Manipulated variables are bounded.

7. Self-Optimizing Control of the HDA Process Identification of the Most Important Disturbances DisturbanceNominalLowerUpper 1 - Gas feed temperature10080112 2 - Toluene feed temperature10080120 3 - Gas feed composition0.950.901.00 4 - Benzene price9.048.349.74 5 - Toluene recycle temperature212202230 6 - Relative volatility boil-up stabilizer3632.439.6 7 - Relative volatility boil-up benzene column2.672.412.94 8 - Relative volatility boil-up toluene column10911 9 - Upper bound on toluene feed flow rate300285315

8. Self-Optimizing Control of the HDA Process Optimization

9. Active constraint control: –(1) Benzene product purity (lower bound); –(2) Recovery (benzene in feed/benzene in top) in stabilizer (lower bound); –(3) Loss (toluene in feed/toluene in bottom) in benzene column (upper bound); –(4) Loss (toluene in feed/toluene in top) in toluene column (upper bound); –(5) Toluene feed flow rate (upper bound); –(6) Separator inlet temperature (lower bound); –(7) Inlet hydrogen to aromatic ratio (lower bound); –(8) By-pass feed effluent heat exchanger (lower bound). 9 remaining unconstrained degrees of freedom. 1 2 3 4 5 6 7 8

10. Self-Optimizing Control of the HDA Process Identification of Candidate Controlled Variables Candidate controlled variables: –Pressure differences; –Temperatures; –Compositions; –Heat duties; –Flow rates; –Combinations thereof. 137 candidate controlled variables can be selected. 17 degrees of freedom. Number of different sets of controlled variables: 8 active constraints (active constraint control). What to do with the remaining 9 degrees of freedom? –Self-optimizing control implementation!!!

11. Analysis of linear steady-state model from 9 u’s to 137 candidate outputs Scale variables properly! G: matrix with 9 inputs and 137 outputs –  (G large )=5 Select one output at the time: –Select output corresponding to largest singular value (essentially largest row sum) –“Control” this output by pairing it with an input (which does not matter for this analysis), and obtain new matrix with one input (and output) less –Final result: –  (G 9x9 )=2.5 which is OK (“close” to 5) –Method is not optimal but works well

12. Self-Optimizing Control of the HDA Process Further Analysis and Selection Minimum singular value analysis of G gives that we should control (i.e. keep constant) –(9) Hydrogen in reactor outlet flow; –(10) Methane in reactor outlet flow; –(11) Reboiler duty in benzene column; –(12) Condenser duty in toluene column; –(13) Compressor power; –(14) Separator feed valve opening; –(15) Separator vapor outlet valve opening; –(16) Separator liquid outlet valve opening; –(17) Purge valve opening. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

13. Self-Optimizing Control of the HDA Process Concluding Remarks Demonstration of a self-optimizing procedure. The economy in the HDA process is rather insensitive to disturbance in the process variables. A set of controlled variables is found from an SVD screening of the scaled linearized model.