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					       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
                                                                                Purge (H2 + CH4)


                                     Compressor



H2 + CH4

Toluene                                                                     Quench
           Mixer              FEHE       Furnace              PFR


                                                                                 Separator
                                               Cooler
             Toluene                 Benzene            CH4



                               Toluene          Benzene        Stabilizer
                               Column           Column




                   Diphenyl
                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 Process
     Steady-state degrees of freedom
                     10                     9




            4
1

2                                               7
                          3
                                       17

                     5             6


                                                8
       16       14            12




       15       13            11
           Self-Optimizing Control of the HDA Process
                 Cost 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
               G
                   as                                                  Profit (M$/year)
                G       fe
            To as d        e
               lu fe tem
           To en ed                  p
              lu e fe tem era N
                                          t o




                                                             2,5
                                                                        3,5
                                                                                  4,5
                                                                                            5,5
                                                                                                       6,5




                                                         2
                                                                   3
                                                                              4
                                                                                        5
                                                                                                  6
                 en e
                      e       d pe ure mi
                        f te ra                    na
                 G eed mp tu - lo l
                     as                     r
                                te er e - we
                G fee mp atu up r
                    as d              e r         p
                        fe co rat e - er
                           ed m ur lo
                                co po e - we
      To                           m si         u r
           lu                 B po tion pp
     To ene                     en s               e
          lu r              B      ze itio - lo r
             en ec en ne n we
                e yc ze pr - u r
                   r        l                    p
             R ec e t ne ice pe
              el yc em p                       -     r
R                . V le              pe rice low
  el Re o
     .                  l. te           ra - e
R Vo l. V bo mp tur up r
  el l.               o       i       e
    . V bo l. l-u ra e - per
          o       i       bo p tu lo
  R l. l-u il- st re we
    el bo p u ab -
        . V il b p                             u r
 R                  -u en st ilize pp
   el ol.              p               a           e
       . V bo b zen bil r - r
                                                                                                                      Optimization




 B ol il- enz e c ize low
   ou . b u                      e      o r         e
 B       nd oi p t ne lum - u r
   ou o l-u olu co n ppe
        nd n t p t en lum - l r
                   o o              e            o
             on lu lu                  co n we
                        e        e
                to ne ne lu - up r
                     lu                     m
                        en fee col n - per
                           e d f um lo
                              fe lo n w
                                 ed w         - er
                                    flo rat up
                                        w e - pe
                                          ra lo r
                                            te w
                                              - u er
                                                                                                      Self-Optimizing Control of the HDA Process




                                                 pp
                                                    er
        Self-Optimizing Control of the HDA Process
                       Optimization
•   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:
     – 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!
                                    =
                              17  17!120! =2.1×1021
                                 
•   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:

                              137   137!
                                    =
                              17  17!120! =2.1×1021
                                 
  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        8
              1     -0,1648    -0,034165 -1,14E-13 0,055526 1,0572 0,000702 6,54E-08 0,001105
              2     0,50825      0,0482    649,67    0,1234   0,94882 0,001241 8,55E-06 0,006986
              3     0,50246     0,049243 -276,46    0,12254 0,94866 0,001229 8,43E-06 0,006931
              4     0,39892     -0,12961   264,76   -0,20715 -0,97408 -0,001962 3,60E-06 -0,016676
              5         1           0        0          0         0        0         0        0
              6      1,0575     0,000829     0     -0,014825 0,005418 -0,000167 2,30E-08 -0,001413
              7      1,118      0,001314     0     -0,031167 0,010355 -0,00035 4,87E-08 -0,002961
              8      1,1812     0,001336     0     -0,049099 0,014534 -0,00055 7,70E-08 -0,004649
              9      1,2462     0,000751     0      -0,06865 0,01754 -0,000766 1,08E-07 -0,006476
             10      1,312     -0,000611     0     -0,089775 0,018878 -0,000998 1,43E-07 -0,008435
             11      1,3769    -0,002944     0      -0,11232 0,017889 -0,001242 1,80E-07 -0,010506
             12      1,4387    -0,006468     0      -0,13598 0,013822 -0,001496 2,19E-07 -0,012658
             13      1,4948      -0,0114     0      -0,16028 0,005801 -0,001754 2,60E-07 -0,014839
             14      1,5415    -0,017947     0      -0,18451 -0,007039 -0,002006 3,02E-07 -0,016979
             15      1,5753    -0,026248     0      -0,20775 -0,025609 -0,002243 3,43E-07 -0,018987
             16      1,5922     -0,03635     0      -0,22889 -0,050548 -0,002451 3,82E-07 -0,02076
             17      1,5891    -0,048158     0      -0,24675 -0,082195 -0,002619 4,17E-07 -0,022188
             18      1,5638    -0,061408     0      -0,26022 -0,12031 -0,002734 4,46E-07 -0,023172
             19      1,5161    -0,075676     0      -0,26846 -0,16405 -0,002788 4,66E-07 -0,023642
             20      1,4477    -0,090403     0      -0,27104 -0,21201 -0,002777 4,78E-07 -0,023569
             21      1,3623     -0,10498     0      -0,26807 -0,26233 -0,002706 4,82E-07 -0,022977
             22      1,2649     -0,11884     0      -0,26015 -0,31299 -0,002581 4,77E-07 -0,021935
             23      1,1613     -0,13152     0      -0,24829 -0,36202 -0,002415 4,65E-07 -0,020547
             24      1,0569      -0,1427     0      -0,23366 -0,40789 -0,002223 4,48E-07 -0,018931
             25    0,001142    -0,000341     0     -0,004326 -0,00476 0,00084 4,64E-08 -0,000343
             26    -0,016537   -0,051007     0     0,014047 0,080501 0,000282 8,35E-08 -0,005038
             27     -1,6775     -0,48339     0      -0,12069   7,1808 -6,30E-05 -1,61E-06 -0,001002
             28     -3,0064       6,404      0        9,388    12,613 0,087528 -6,06E-06 0,74627
             29     -1,3724      6,4157      0       9,3748    9,2513   0,08735 8,29E-06 0,74477
             30     -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:


                      ci  ci ,opt  ci ,imp
                      ci ,opt  max{ci ,opt (d0 )  ci ,opt (d )}


• Input scaling factors:


                             dJ (d )
                      u i 
                             dui (d )

• Scaled matrix:

                      Gsc  diag ( ci ,opt )  G   diag ( ui )
                                               1                       1
                                             
             Self-Optimizing Control of the HDA Process

• Output scaling factors:
Variable   Scaling factor
   1           10,580
   2           16,926
   3           19,080
   4           55,330                   600,0
   5           59,530
   6           59,755
   7           60,201
   8           60,967                   500,0
   9           61,786
  10           62,656
  11           63,571                   400,0
  12           64,518
                       Scaling factor




  13           65,481
  14           66,435
                                        300,0
  15           67,347
  16           68,182
  17           68,902
  18           69,476                   200,0
  19           69,882
  20           70,113
  21           70,178                   100,0
  22           70,102
  23           69,915
  24           69,654
  25            4,773                     0,0
  26            6,715                           1   21   41        61               81   101   121
  27           96,816                                         Controlled variable
  28          505,275
  29          534,703
  30          526,466
             Self-Optimizing Control of the HDA Process

• Input scaling factors:
Variable   Scaling factor
   1           0,005
   2           0,003
   3           0,004
   4           0,001      0,050
   5           0,046
   6           0,000
   7           0,000      0,040
   8           0,000

                                       0,030
                      Scaling factor




                                       0,020



                                       0,010



                                       0,000



                                       -0,010
                                                0   1   2   3       4         5         6   7   8   9
                                                                Manipulated variables
        Self-Optimizing Control of the HDA Process
• Linearized model after scaling:

             Gsc       1           2        3          4         5        6          7        8
              1     -3,0218     -1,2371 -2,92E-12 3,6872      -2,156  5,2147    0,067145 0,94732
              2     5,8253      1,0909    10363     5,122    -1,2094  5,7612      5,4917   3,7454
              3     5,1087      0,98872  -3911,9    4,512    -1,0727  5,0602      4,7994   3,2961
              4     1,3987     -0,89742   1291,9   -2,6303   0,37983  -2,7864    0,70747   -2,735
              5     3,2589         0        0          0         0        0          0        0
              6     3,4332     0,005316     0      -0,1743 -0,001956 -0,21985   0,004187 -0,21456
              7     3,6028     0,008358     0     -0,36372 -0,003711 -0,45727   0,008783 -0,44634
              8     3,7585     0,008392     0      -0,5658 -0,005144 -0,70881   0,013731 -0,69197
              9     3,9128     0,004659     0     -0,78061 -0,006125 -0,97416   0,019051 -0,95117
             10     4,0621    -0,003735     0      -1,0066 -0,006501 -1,2509    0,024719 -1,2216
             11     4,2018    -0,017739     0      -1,2413 -0,006071 -1,5354    0,030684 -1,4997
             12     4,3261    -0,038408     0      -1,4807 -0,004622 -1,8222    0,036868 -1,7803
             13     4,4285    -0,066699     0      -1,7196 -0,001912 -2,1042    0,043157 -2,0563
             14     4,5014      -0,1035     0      -1,9512 0,002286 -2,3725     0,049396 -2,3191
             15     4,5377     -0,14931     0      -2,1672 0,008204 -2,6164     0,055394 -2,5584
             16     4,5303     -0,20424     0      -2,3585 0,015996 -2,8247     0,060926   -2,763
             17     4,4741     -0,26776     0       -2,516 0,025738 -2,9862     0,065763 -2,9222
             18     4,3667     -0,33862     0      -2,6314 0,037361 -3,0914     0,069684 -3,0266
             19     4,2089     -0,41487     0      -2,6989   0,05065   -3,134   0,072515    -3,07
             20     4,0058     -0,49397     0      -2,7159 0,065241 -3,1122     0,074153 -3,0504
             21     3,7659     -0,57311     0      -2,6836   0,08065   -3,029   0,074587 -2,9711
             22     3,5006     -0,64947     0      -2,6072 0,096329 -2,8924       0,0739  -2,8395
             23     3,2224     -0,72066     0      -2,4949   0,11172   -2,714   0,072256 -2,6669
             24     2,9437     -0,78486     0      -2,3568   0,12635  -2,5072   0,069872 -2,4664
             25    0,046406   -0,027331     0     -0,63675 0,021517 13,829       0,10564 -0,65153
             26     -0,4778     -2,9103     0       1,4697  -0,25867  3,2972     0,13507  -6,8086
             27     -3,3613     -1,9128     0     -0,87576 -1,6002 -0,051127    -0,18094 -0,093936
             28     -1,1543     4,8555      0       13,053  -0,53858    13,61   -0,13025   13,402
             29    -0,49792     4,5967      0       12,318   -0,3733  12,835     0,16851   12,64
             30    -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:




        100                                                       1000

                                                                   800
         50
                                                                   600
Value




                                                          Value
                                                                   400
          0
                                                                   200

        -50                                                          0
        150                                                       150
                                                      8                                                          8
              100                                                        100
                                                  6                                                          6
                       50                 4                                       50                 4
                                    2                                                          2
                Rows        0   0                                                      0   0
                                        Columns                            Rows                    Columns
• more details in here about results
• and also present RGA-method...
        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    10
                                                                      15

                 5                                      7
                                       1
                                                                       16
                                                                 6
                     12                                     14
                              4            3        2



                                  11
      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.

				
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