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

9

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

10

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

11

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

12

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)

15

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

17

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

19

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

20

Quantitative Back-off Results: Mode I

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

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

22

Quantitative Back-off Results: Mode II

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

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

25

Conclusions

Thank You ?

Thank you

26

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)

27

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

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)