Rahul Jagtap, Nitin Kaistha, Sigurd Skogestad*
Chemical Engineering
IIT Kanpur (India),*NTNU Norway
1
Plant-wide Control for Economic Operation of a Recycle Process
Objective
• To evaluate impact of plant wide control systems on the Economic Operation of a Recycle process.
2
REACTOR
A + B CB + C D
CoolingWater
Fresh ARecycle A + B
COLUMN
COLUMN
Byproduct D
Product C
Fresh B
Recycle Process
3
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)
4
Base case designVRxr 6 m3 Trxr 78 OCA:B in rxr feed 1.5 (xC
D)col1 0.01
Process Design
Optimize Operating conditions for max operating profit (m$/yr) Objective Function = Product cost – (Reactant cost + Utility cost)
8 Steady State Operating Degrees of Freedom
Process Operation ModesMode I: Fixed Feed Processing Rate (FA fixed)
Mode II: Maximum Throughput
5
Steady State Economic Optimization
Reactor VolumeReactor Temperature
Excess RatioFresh A
(xCD)1
Operating Profit
6
Mode I
6.0 m3 70.47 oC2.327100 kmol/hr0.123.304 m$/yr
Mode II
6.0 m3 100 oC1.67184.6 kmol/hr0.245.155 m$/yr
Active Constraints Column 1 Boilup Column 1 Boilup Reactor Volume Reactor Volume
FA fixed Reactor Temperature
Constrained Optimization Results
REACTOR
A + B CB + C D
CoolingWater
Fresh ARecycle A + B
COLUMN
COLUMN
Byproduct D
Product C
Fresh B
Degrees of Freedom
7
Operation DOF = 8
Need 8 associated CVs
2 Unconstrained DOFs
8
Managing Unconstrained DOFs
Mode I Mode II
OptimumBase Case 3.304 5.155
StripperBase Case 3.304 5.154
Optimumw/ disturbance 3.279 5.003
Stripperw/ disturbance 3.279 5.007
Reflux Rate L in Column I
Operating Column 1 as a Stripper is Self Optimizing
Trxr (Mode I)
Mode I
OptimumBaseCase 3.304
Optimumw/ disturbance 3.279
Const Rxr Tw/ disturbance 3.279
Trxr is self optimizing
(xA)rxr in (Mode II)
Mode I
OptimumBaseCase 5.155
Optimumw/ disturbance 5.007
Const (xA)w/ disturbance 5.000
(xA)rxr in is self optimizing
A + B → CB + C → D
A
B
FC
set
setCC
TC
FC
X
LCC
D
TPM
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Control Structure 1 Optimal
LC
LC
CC
PC
FC
set
PC
LC
FC
LC
TC
XC
set
OCOC
Mode I
FC
Max Boilup
TPM
A + B → CB + C → D
A
B
FC
set
setCC
TC
FC
X
LCC
D
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Control Structure 1 Optimal
LC
LC
CC
PC
FC
set
PC
LC
FC
LC
TC
XC
Mode II
FC
Max Boilup
Max
A + B → CB + C → D
A
B
C
D
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Control Structure 2Conventional Temperature Control on Column 1
FC
set
setCC
TC
FC
X
LC
setTC
PC
LC
FC
LC
XC
LC
LC
CC
PC
FC
FC
Mode I
OCOC
set
OCOC TPM
Max boil upTPM
A + B → CB + C → D
A
B
C
D
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Control Structure 2Conventional Temperature Control on Column 1
FC
set
setCC
TC
FC
X
LC
setTC
PC
LC
FC
LC
XC
LC
LC
CC
PC
FC
FC
Mode II
OCOC
Max boil upTPM
Max
A + B → CB + C → D
A
B
C
D13
Control Structure 3Fix Total Flow to Reactor (Luyben)
LC
LC
CC
PC
FC
FC
set
setCC
TC
X
LC
FC
setTC
PC
LC
FC
LC
XC
set
OCOC
set OCOC
Mode I
TPM
Max boil up
TPM
A + B → CB + C → D
A
B
C
D14
Control Structure 3Fix Total Flow to Reactor (Luyben)
LC
LC
CC
PC
FC
FC
set
setCC
TC
X
LC
FC
setTC
PC
LC
FC
LC
XC
set OCOC
Mode II
Max boil up
TPM
Max
A + B → CB + C → D
B
A
C
D
from Boilup(for Mode I)
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Control Structure 4 Traditional: Fixed Fresh Feed
FCTPM
FC
set
setCC
TC
X
LC
setTC
PC
LC
FC
LC
XC
LC
LC
CC
PC
FC
setOCOC
Mode I
Max boil up
set
OCOC
A + B → CB + C → D
B
A
C
D16
Control Structure 4 Traditional: Fixed Fresh Feed
FCTPM
FC
set
setCC
TC
X
LC
setTC
PC
LC
FC
LC
XC
LC
LC
CC
PC
FC
setOCOC
Mode II
Max boil up
Max
5% step increase of heavy impurity in the Fresh B feed stream
For Mode I: VrxrSP, TPMSP(OCSP) adjusted such that Vrxr and Boilup1
Col1 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
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Quantification of Back-off
Worst Case Disturbance :
Reducing Boilup Back-off
• Apply advanced MPC algorithm in boil up Optimizing Controller• DMC applied here
• Apply dynamic lead lag element
Regulatory control Supervisory PI control
Dynamic Matrix Control Lead-Lag Control
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Boilup Back-off Illustration: Mode II
FA
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 2.318 2.318 2.318 321.1 321.1 321.1 321.1 3.303 3.303 3.303 3.303
CS2 100 2.234 2.259 2.245 2.279 311.2 314.6 312.9 316.9 3.299 3.300 3.299 3.301
CS3 100 2.16 2.213 2.185 2.243 302.2 308.6 305.3 312.2 3.294 3.298 3.296 3.300
CS4 100 2.13 2.177 2.191 2.202 299 304.5 306.2 307.5 3.290 3.295 3.296 3.297
a:Regulatory control b:with PI optimizing control c:with DMC control d:with Lead-Lag control
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Quantitative Back-off Results: Mode I
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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
FA
kmol/hr
a b c d
Col 1 Boilup
kmol/hr
a b c d
Profit
x106 $/year
a b c d
Base 184.6 321.1 5.155
CS1 179.11 179.11 179.11 179.11 321.1 321.1 321.1 321.1 5.003 5.003 5.003 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
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Quantitative Back-off Results: Mode II
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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
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Interpretation of Trend
As active constraint control MV location moves away from constraint location, back off due to transients increases
KEY HEURISTICTight active constraint control essential for optimal operation
Locate active constraint control MV as close as possible (or at) the primary bottleneck constraint
Loss in ProfitCS1 < CS2 < CS3 < CS4
Where regulatory CS is already implemented, supervisory optimizing control mitigates back-off
• 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
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Conclusions
Thank You ?
Thank you
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Main reactionA + 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)
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Reaction kinetics and data
Relative volatilities αA > αB > αC > αD
Hypotheticals MW NBP (C) A 50 80 B 80 100 C 130 130 D 210 180
VLE Model Soave-Redlich-Kwong
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•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)
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•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)