1. Plant-wide Control for Economic Operation of a Recycle Process
Rahul Jagtap, Nitin Kaistha, Sigurd Skogestad*
Chemical Engineering
IIT Kanpur (India),*NTNU Norway

2. Objective
To evaluate impact of plant wide control systems on the Economic Operation of a Recycle process.

3. Recycle Process Recycle A + B Fresh A Fresh B C O L U M N Byproduct D
Product C
REACTOR
A + B C
B + C  D
Cooling
Water C O L U M N

4. Base Case Process Design
FA Processing Rate: 100 kmol/h
Desired C Product Purity: >99 mol%
# of trays in columns: 2.5*NminFenske (for 1% key recoveries)
Base case design
VRxr m3
Trxr OC
A:B in rxr feed
(xCD)col

5. 8 Steady State Operating Degrees of Freedom Process Operation Modes
Steady State Economic Optimization
Optimize Operating conditions for max operating profit (m$/yr) Objective Function = Product cost – (Reactant cost + Utility cost)
8 Steady State Operating Degrees of Freedom
Process Operation Modes
Mode I: Fixed Feed Processing Rate (FA fixed)
Mode II: Maximum Throughput

6. Constrained Optimization Results
Mode I
6.0 m3
70.47 oC
2.327
100 kmol/hr
0.12
3.304 m$/yr
Mode II
6.0 m3
100 oC
1.67
184.6 kmol/hr
0.24
5.155 m$/yr
Reactor Volume Reactor Temperature Excess Ratio Fresh A (xCD)1 Operating Profit
Active Constraints Column 1 Boilup Column 1 Boilup Reactor Volume Reactor Volume
FA fixed Reactor Temperature

7. Degrees of Freedom 2 Unconstrained DOFs Operation DOF = 8
Recycle A + B
Fresh A
Fresh B C O L U M N
Byproduct D
Product C
REACTOR
A + B C
B + C  D
Cooling
Water C O L U M N
Operation DOF = 8
Need 8 associated CVs
2 Unconstrained DOFs

8. Managing Unconstrained DOFs
Reflux Rate L in Column I
Mode I
Mode II
OptimumBase Case
3.304
5.155
StripperBase Case
5.154
Optimumw/ disturbance
3.279
5.003
Stripperw/ disturbance
5.007
Operating Column 1 as a Stripper is Self Optimizing
(xA)rxr in (Mode II)
Trxr (Mode I)
Mode I
OptimumBaseCase
3.304
Optimumw/ disturbance
3.279
Const Rxr Tw/ disturbance
Mode I
OptimumBaseCase
5.155
Optimumw/ disturbance
5.007
Const (xA)w/ disturbance
5.000
Trxr is self optimizing
(xA)rxr in is self optimizing

9. Control Structure 1 Optimal Mode I A + B → C B + C → D FC set CC TC XLC
set PC LC FC TC XC LC CC PC FC
set OC
TPM A C B
A + B → C
B + C → D
Max Boilup
TPM FC D

10. Control Structure 1 Optimal Mode II A + B → C B + C → D PC PC X CC setFC
set CC TC X LC PC LC FC TC XC LC CC PC FC A C B
Max
A + B → C
B + C → D
set
Max Boilup FC D

11. Conventional Temperature Control on Column 1
Control Structure 2
Conventional Temperature Control on Column 1
Mode I FC
set CC TC X LC
set TC PC LC FC XC LC CC PC FC
set OC
TPM A C B
Max boil up
TPM FC OC
A + B → C
B + C → D D

12. Conventional Temperature Control on Column 1
Control Structure 2
Conventional Temperature Control on Column 1
Mode II FC
set CC TC X LC
set TC PC LC FC XC LC CC PC FC A C B
Max boil up
TPM FC OC
Max
A + B → C
B + C → D D

13. Fix Total Flow to Reactor (Luyben)
Control Structure 3
Fix Total Flow to Reactor (Luyben)
Mode I
set OC
Max boil up
set TC PC LC FC XC FC
set CC TC X LC LC CC PC FC
set OC
TPM A
TPM FC C B
A + B → C
B + C → D D

14. Fix Total Flow to Reactor (Luyben)
Control Structure 3
Fix Total Flow to Reactor (Luyben)
Mode II
set OC
Max boil up
set TC PC LC FC XC FC
set CC TC X LC LC CC PC FC A
TPM FC C B
Max
A + B → C
B + C → D D

15. Traditional: Fixed Fresh Feed
Control Structure 4
Traditional: Fixed Fresh Feed
Mode I
set OC
Max boil up
from Boilup(for Mode I) FC
set CC TC X LC
set TC PC LC FC XC LC CC PC FC
set OC B FC
TPM C A
A + B → C
B + C → D D

16. Traditional: Fixed Fresh Feed
Control Structure 4
Traditional: Fixed Fresh Feed
Mode II
set OC
Max boil up FC
set CC TC X LC
set TC PC LC FC XC LC CC PC FC B FC
TPM C A
Max
A + B → C
B + C → D D

17. Quantification of Back-off
Worst Case Disturbance :
5% step increase of heavy impurity in the Fresh B feed stream For Mode I: VrxrSP, TPMSP(OCSP) adjusted such that Vrxr and Boilup1Col1 do not violate the constraints during transients For Mode II: VrxrSP, Trxr , TPMSP(OCSP) adjusted such that Vrxr ,Trxr and Boilup1Col1 do not violate the constraints during transients

18. Reducing Boilup Back-off
Apply advanced MPC algorithm in boil up Optimizing Controller
DMC applied here
Apply dynamic lead lag element

19. Boilup Back-off Illustration: Mode II
Regulatory control Supervisory PI control
Dynamic Matrix Control Lead-Lag Control

20. Quantitative Back-off Results: Mode IFA
kmol /hr
(xA/xB)rxr feed
a b c d
Col 1 Boilup kmol/hr
a b c d
Profit x106 $/year
a b c d
Base
2.327
321.1
3.304
CS1
100
2.318
3.303
CS2
2.234
2.259
2.245
2.279
311.2
314.6
312.9
316.9
3.299
3.300
3.301
CS3
2.16
2.213
2.185
2.243
302.2
308.6
305.3
312.2
3.294
3.298
3.296
CS4
2.13
2.177
2.191
2.202
299
304.5
306.2
307.5
3.290
3.295
3.297
a:Regulatory control b:with PI optimizing control c:with DMC control d:with Lead-Lag control

21. Role of Regulatory CS and OC: Mode I
Slight decrease in profit CS1 < CS2 < CS3 < CS4
Reason: Decreased yield due to lower recycle (lower [xA/xB]rxr in)
Lower boil up back-off with DMC OC and OC w/ dynamic lead-lag

22. Quantitative Back-off Results: Mode IIFA
kmol/hr
a b c d
Col 1 Boilup
Profit
x106 $/year
Base
184.6
321.1
5.155
CS1
179.11
5.003
CS2
173.96
176.22
176.5
177.06
309.4
314.8
315.4
316.7
4.853
4.921
4.930
4.949
CS3
170.27
173.74
175.2
176.08
299.2
307.2
310.4
312.3
4.726
4.827
4.871
4.896
CS4
167.8
173
173.46
175.5
294.2
306
307
311.6
4.660
4.814
4.826
4.882
a:Regulatory control b:with PI optimizing control c:with DMC control d:with Lead-Lag control

23. Role of Regulatory CS and OC: Mode II
Due to back off in VRxrSP and TRxrSP
Noticeable decrease in profit CS1 < CS2 < CS3 < CS4
Reason: Lower production due to higher boil-up back-off
Lower boil-up back-off with DMC OC and OC w/ dynamic lead-lag

24. Interpretation of Trend
Loss in Profit
CS1 < CS2 < CS3 < CS4
As active constraint control MV location moves away from constraint location, back off due to transients increases
KEY HEURISTIC
Tight active constraint control essential for optimal operation
Locate active constraint control MV as close as possible (or at) the primary bottleneck constraint
Where regulatory CS is already implemented, supervisory optimizing control mitigates back-off

25. Conclusions
Tight active constraint control key to economic process operation
Active constraint control MV should be located at (or close to)
the constraint variable location
Application of advanced control algorithms mitigates back-off and
hence the loss in profit
Thank You ?

26. Thank you

27. Reaction kinetics and data
Main reaction A + B C r1 = k1 XA XB kmol/m3.s ; k1 = 2x10e8*exp(-60000/RT) Side reaction B + C D r2 = k1 XB XC kmol/m3.s ; k1 = 2x10e9*exp(-80000/RT)
Relative volatilities αA > αB > αC > αD
Hypotheticals MW NBP (C) A B C D VLE Model Soave-Redlich-Kwong

28. Derating in boil up is increasing in order CS1< CS2 < CS3 < CS4
For a given control structure Lead Lag constraint controller requires minimum back-off from bottleneck constraint
Since the throughput is fixed , decrease in profit is very less (of the order of thousands)

29. Derating in boil up is increasing in order CS1< CS2 < CS3 < CS4
For a given control structure Lead Lag constraint controller requires minimum back-off from bottleneck constraint
Decrease in profit due to selection of control structure is of the order of hundreds of thousands(which is considerable)
Decrease in profit due to selection of contraint controller is of the order of hundreds of thousands(which is considerable)