Self-Optimizing Control of the HDA Process
• Outline of the presentation
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Process description.
Self-optimizing control procedure.
Self-optimizing control of the HDA process.
Concluding remarks.
Process Description
• Benzene production from thermal-dealkalination of toluene (hightemperature, non-catalytic process).
• Main reaction:
Toluene + H2 → Benzene + CH4
• Side reaction:
2·Benzene ↔ Diphenyl + H2
• 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.
Process Description
Purge (H2 + CH4)
Compressor
H2 + CH4
Toluene
Mixer
FEHE
Furnace
PFR
Quench
Separator
Toluene
Benzene
Toluene
Column
Diphenyl
Cooler
CH4
Benzene
Column
Stabilizer
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 – Jopt
• Pure steady state considerations.
• Stepwise procedure for evaluating the loss:
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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.
Self-Optimizing Control of the HDA Process
Steady-state degrees of freedom
10
9
4
1
2
7
3
17
6
5
16
14
12
15
13
11
8
Self-Optimizing Control of the HDA Process
Cost Function and Constraints
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•
The following profit is maximized (Douglas’s EP):
(-J) = pbenDben – ptolFtol – pgasFgas – pfuelQfuel – pcwQcw – ppowerWpower - psteamQsteam +
Σ(pv,iFv,i), i = 1,…,nc.
Where:
– Qcw = Qcw,cooler + Qcw,stab + Qcw,ben + Qcw,tol;
– Qsteam = Qsteam,stab + Qsteam,ben + Qsteam,tol;
– Fv,i = Fpurge + Dstab,i + Btol,i, i = 1,…,nc.
•
Constraints during operation:
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–
–
–
–
–
–
–
•
Production rate:
Hydrogen excess in reactor inlet:
Bound on toluene feed rate:
Reactor pressure:
Reactor outlet temperature:
Quench outlet temperature:
Product purity:
Separator inlet temperature:
+ some distillation recovery constraints
Manipulated variables are bounded.
Dben ≥ 265 lbmol/h.
FH2 / (Fben + Ftol + Fdiph) ≥ 5.
Ftol ≤ 300 lbmol/h.
Preactor ≤ 500 psia.
Treactor ≤ 1300 °F.
Tquencher ≤ 1150 °F.
xDben ≥ 0.9997.
95 °F ≤ Tflash ≤ 105 °F.
Self-Optimizing Control of the HDA Process
Identification of the Most Important Disturbances
Disturbance
Nominal Lower Upper
1 - Gas feed temperature
100
80
112
2 - Toluene feed temperature
100
80
120
3 - Gas feed composition
0.95
0.90
1.00
4 - Benzene price
9.04
8.34
9.74
5 - Toluene recycle temperature
212
202
230
6 - Relative volatility boil-up stabilizer
36
32.4
39.6
7 - Relative volatility boil-up benzene column
2.67
2.41
2.94
8 - Relative volatility boil-up toluene column
10
9
11
9 - Upper bound on toluene feed flow rate
300
285
315
as
fe
e
G
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G
Profit (M$/year)
Self-Optimizing Control of the HDA Process
Optimization
6,5
6
5,5
5
4,5
4
3,5
3
2,5
2
Self-Optimizing Control of the HDA Process
Optimization
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•
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.
8
5
7
1
6
4
3
2
Self-Optimizing Control of the HDA Process
Identification of Candidate Controlled Variables
• Candidate controlled variables:
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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:
 137
137!
21
=
=2.1×10
 17  17!120!
• 8 active constraints (active constraint control).
• What to do with the remaining 9 degrees of freedom?
– Self-optimizing control implementation!!!
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
– (Glarge)=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:
 (G9x9)=2.5 which is OK (“close” to 5)
– Method is not optimal but works well
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.
13
17
8
9
5
10
15
7
1
16
6
12
14
3
4
11
2
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.