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.
Process Description
• Benzene production from thermal-dealkalination of toluene (high-temperature, 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
Mixer FEHE Furnace PFR Quench
Separator
Compressor
Cooler
StabilizerBenzeneColumn
TolueneColumn
H2 + CH4
Toluene
Toluene Benzene CH4
Diphenyl
Purge (H2 + CH4)
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:
– 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 ProcessSteady-state degrees of freedom
1
2
4
10 9
7
8
6
3
5
17
12
11
14
13
16
15
Self-Optimizing Control of the HDA ProcessCost Function and Constraints
• 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:– Production rate: Dben ≥ 265 lbmol/h.– Hydrogen excess in reactor inlet: FH2 / (Fben + Ftol + Fdiph) ≥ 5.– Bound on toluene feed rate: Ftol ≤ 300 lbmol/h.– Reactor pressure: Preactor ≤ 500 psia.– Reactor outlet temperature: Treactor ≤ 1300 °F.– Quench outlet temperature: Tquencher ≤ 1150 °F.– Product purity: xDben ≥ 0.9997.– Separator inlet temperature: 95 °F ≤ Tflash ≤ 105 °F.– + some distillation recovery constraints
• Manipulated variables are bounded.
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
Self-Optimizing Control of the HDA Process Optimization
2
2,5
3
3,5
4
4,5
5
5,5
6
6,5
Pro
fit
(M$/y
ear)
Self-Optimizing Control of the HDA ProcessOptimization
• 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
234
5
6
7
8
Self-Optimizing Control of the HDA ProcessIdentification 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!!!– Still have many possibilities of single measurements:
21137 137!= =2.1×10
17 17!120!
21137 137!= =2.1×10
17 17!120!
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)=37
• 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)=10 which is OK (“close” to 37)
– Method is not optimal but works well
Self-Optimizing Control of the HDA Process• Linearized model before scaling:
Gsc 1 2 3 4 5 6 7 81 -0,1648 -0,034165 -1,14E-13 0,055526 1,0572 0,000702 6,54E-08 0,0011052 0,50825 0,0482 649,67 0,1234 0,94882 0,001241 8,55E-06 0,0069863 0,50246 0,049243 -276,46 0,12254 0,94866 0,001229 8,43E-06 0,0069314 0,39892 -0,12961 264,76 -0,20715 -0,97408 -0,001962 3,60E-06 -0,0166765 1 0 0 0 0 0 0 06 1,0575 0,000829 0 -0,014825 0,005418 -0,000167 2,30E-08 -0,0014137 1,118 0,001314 0 -0,031167 0,010355 -0,00035 4,87E-08 -0,0029618 1,1812 0,001336 0 -0,049099 0,014534 -0,00055 7,70E-08 -0,0046499 1,2462 0,000751 0 -0,06865 0,01754 -0,000766 1,08E-07 -0,00647610 1,312 -0,000611 0 -0,089775 0,018878 -0,000998 1,43E-07 -0,00843511 1,3769 -0,002944 0 -0,11232 0,017889 -0,001242 1,80E-07 -0,01050612 1,4387 -0,006468 0 -0,13598 0,013822 -0,001496 2,19E-07 -0,01265813 1,4948 -0,0114 0 -0,16028 0,005801 -0,001754 2,60E-07 -0,01483914 1,5415 -0,017947 0 -0,18451 -0,007039 -0,002006 3,02E-07 -0,01697915 1,5753 -0,026248 0 -0,20775 -0,025609 -0,002243 3,43E-07 -0,01898716 1,5922 -0,03635 0 -0,22889 -0,050548 -0,002451 3,82E-07 -0,0207617 1,5891 -0,048158 0 -0,24675 -0,082195 -0,002619 4,17E-07 -0,02218818 1,5638 -0,061408 0 -0,26022 -0,12031 -0,002734 4,46E-07 -0,02317219 1,5161 -0,075676 0 -0,26846 -0,16405 -0,002788 4,66E-07 -0,02364220 1,4477 -0,090403 0 -0,27104 -0,21201 -0,002777 4,78E-07 -0,02356921 1,3623 -0,10498 0 -0,26807 -0,26233 -0,002706 4,82E-07 -0,02297722 1,2649 -0,11884 0 -0,26015 -0,31299 -0,002581 4,77E-07 -0,02193523 1,1613 -0,13152 0 -0,24829 -0,36202 -0,002415 4,65E-07 -0,02054724 1,0569 -0,1427 0 -0,23366 -0,40789 -0,002223 4,48E-07 -0,01893125 0,001142 -0,000341 0 -0,004326 -0,00476 0,00084 4,64E-08 -0,00034326 -0,016537 -0,051007 0 0,014047 0,080501 0,000282 8,35E-08 -0,00503827 -1,6775 -0,48339 0 -0,12069 7,1808 -6,30E-05 -1,61E-06 -0,00100228 -3,0064 6,404 0 9,388 12,613 0,087528 -6,06E-06 0,7462729 -1,3724 6,4157 0 9,3748 9,2513 0,08735 8,29E-06 0,7447730 -1,3634 6,3736 4846,4 9,3133 9,1906 0,086776 2,02E-05 0,73988… … … … … … … … …
Self-Optimizing Control of the HDA Process
• Output scaling factors:
• Input scaling factors:
• Scaled matrix:
, ,
, , 0 ,max{ ( ) ( )}
i i opt i imp
i opt i opt i opt
c c c
c c d c d
1 1
,( ) ( )sc i opt iG diag c G diag u
( )
( )ii
dJ du
du d
Self-Optimizing Control of the HDA Process
• Output scaling factors:Variable Scaling factor
1 10,5802 16,9263 19,0804 55,3305 59,5306 59,7557 60,2018 60,9679 61,78610 62,65611 63,57112 64,51813 65,48114 66,43515 67,34716 68,18217 68,90218 69,47619 69,88220 70,11321 70,17822 70,10223 69,91524 69,65425 4,77326 6,71527 96,81628 505,27529 534,70330 526,466
0,0
100,0
200,0
300,0
400,0
500,0
600,0
1 21 41 61 81 101 121
Controlled variable
Sca
lin
g f
acto
r
Self-Optimizing Control of the HDA Process
• Input scaling factors:Variable Scaling factor
1 0,0052 0,0033 0,0044 0,0015 0,0466 0,0007 0,0008 0,000
-0,010
0,000
0,010
0,020
0,030
0,040
0,050
0 1 2 3 4 5 6 7 8 9
Manipulated variables
Sca
lin
g f
acto
r
Self-Optimizing Control of the HDA Process• Linearized model after scaling:
Gsc 1 2 3 4 5 6 7 81 -3,0218 -1,2371 -2,92E-12 3,6872 -2,156 5,2147 0,067145 0,947322 5,8253 1,0909 10363 5,122 -1,2094 5,7612 5,4917 3,74543 5,1087 0,98872 -3911,9 4,512 -1,0727 5,0602 4,7994 3,29614 1,3987 -0,89742 1291,9 -2,6303 0,37983 -2,7864 0,70747 -2,7355 3,2589 0 0 0 0 0 0 06 3,4332 0,005316 0 -0,1743 -0,001956 -0,21985 0,004187 -0,214567 3,6028 0,008358 0 -0,36372 -0,003711 -0,45727 0,008783 -0,446348 3,7585 0,008392 0 -0,5658 -0,005144 -0,70881 0,013731 -0,691979 3,9128 0,004659 0 -0,78061 -0,006125 -0,97416 0,019051 -0,9511710 4,0621 -0,003735 0 -1,0066 -0,006501 -1,2509 0,024719 -1,221611 4,2018 -0,017739 0 -1,2413 -0,006071 -1,5354 0,030684 -1,499712 4,3261 -0,038408 0 -1,4807 -0,004622 -1,8222 0,036868 -1,780313 4,4285 -0,066699 0 -1,7196 -0,001912 -2,1042 0,043157 -2,056314 4,5014 -0,1035 0 -1,9512 0,002286 -2,3725 0,049396 -2,319115 4,5377 -0,14931 0 -2,1672 0,008204 -2,6164 0,055394 -2,558416 4,5303 -0,20424 0 -2,3585 0,015996 -2,8247 0,060926 -2,76317 4,4741 -0,26776 0 -2,516 0,025738 -2,9862 0,065763 -2,922218 4,3667 -0,33862 0 -2,6314 0,037361 -3,0914 0,069684 -3,026619 4,2089 -0,41487 0 -2,6989 0,05065 -3,134 0,072515 -3,0720 4,0058 -0,49397 0 -2,7159 0,065241 -3,1122 0,074153 -3,050421 3,7659 -0,57311 0 -2,6836 0,08065 -3,029 0,074587 -2,971122 3,5006 -0,64947 0 -2,6072 0,096329 -2,8924 0,0739 -2,839523 3,2224 -0,72066 0 -2,4949 0,11172 -2,714 0,072256 -2,666924 2,9437 -0,78486 0 -2,3568 0,12635 -2,5072 0,069872 -2,466425 0,046406 -0,027331 0 -0,63675 0,021517 13,829 0,10564 -0,6515326 -0,4778 -2,9103 0 1,4697 -0,25867 3,2972 0,13507 -6,808627 -3,3613 -1,9128 0 -0,87576 -1,6002 -0,051127 -0,18094 -0,09393628 -1,1543 4,8555 0 13,053 -0,53858 13,61 -0,13025 13,40229 -0,49792 4,5967 0 12,318 -0,3733 12,835 0,16851 12,6430 -0,50239 4,638 2485,4 12,428 -0,37665 12,95 0,41627 12,753… … … … … … … … …
Self-Optimizing Control of the HDA Process
• Linearized model before scaling: • Linearized model after scaling:
02
46
8
0
50
100
150-50
0
50
100
ColumnsRows
Va
lue
02
46
8
0
50
100
150
0
200
400
600
800
1000
ColumnsRows
Va
lue
• more details in here about results
• and also present RGA-method...
Self-Optimizing Control of the HDA ProcessFurther 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
234
5
6
7
8
9 10
11
12
13
14
15
16
17
Self-Optimizing Control of the HDA ProcessConcluding 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.
