1

Design of Chemical Reactors in Recycle Systems

fromPlantwide Control Perspective

C.S. Bildea and A.C. DimianUniversity of Amsterdam

2

Outline

• Plantwide control• Isothermal reactor

– One-reactant– Two-reactants

• Adiabatic reactor• Non-adiabatic reactor

3

Plantwide control

• “control loops needed to operate an entire process and achieve its design objectives” (Luyben)

• “not concerned with tuning and behaviour of all control loops … , but rather with the control philosophy of the overall plant” (Skogestad)

4

Systemic approach to Plantwide control

Chemical plant

Heat-integrated reactors

AB

BC

C

A

BABC

HX1

HX1

PF

C

Heat-integrated distillation

Azeotropic distillation with solvent recycle

Unit operation

Connections

Raw materials

Unit operation

Products

By-products

Purge

5

Systemic approach to Plantwide control (2)

• Local control – unit operations, complex structures

• Plantwide control – Mass balance

• Reactants• Products• Impurities

– Energy balance

•Reactor•Separation•Recycle

6

Reactor – Separator –Recycle

Gasseparation

Liquid separation

G-L

F

R

S

Y

P

Reactor

RecycleFeed

Products

7

First-order reaction in isothermal CSTR

( ) ( ) ( )( ) 0111

,,,

, =−⋅−⋅−

−=ASYA

ASYA xx

xDaDaxgα

α

Dimensionless mass balance

Aµ,AVFVkDa ⋅= (first-order reaction)

Reactor: Plant Damkohler number:

Separation:recovery / purity of reactants / products

8

Solution of mass balance equation

-1

-0.5

0

0.5

1

0.1 1 10Da

xA

α Y,S=1α Y,S=0.9

α Y,S=0.9

α Y,S=1T

α Y,S =0

Dacr = 1

9

Other one-reactant systems

PFR

nth-order (CSTR, PFR)

Purity < 1

1=> crDaDa

YA,

PB,cr

zz

DaDa =>

1

Aµ,Aµ,A

1−

⋅⋅=

n

VVFVkDa

10

Design and control (1)

LC

CC

CC

FC

FA

V

zB,P=1Sepa

ratio

n

(a)

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Production change (1)

0

2

4

6

0.7 1 1.3F A/F *A

S/ F

* A

Da *=10

Da *=1.5

Da *=2

Da *=3

Da *=5

z A,Y=0.95

12

Design and control (2)

FC

CC

CCLC

V

S

zB,P=1Sepa

ratio

n

(b)

13

Production change (2)

0

5

10

0.7 1 1.3F A/F *A

kV/(V

µµ µµF* A

)

Da *=5

Da *=1.2

Da *=1.5

Da *=2

Da *=3

z A,Y=0.95

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Bifurcations

T

Transcritical

“Perturbed” Transcritical (1) “Perturbed” Transcritical (2) ????

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Two-reactants system

A

B

P

LC3LC3

LC2LC2

LC4LC4

LC1LC1

FCFC

FCFCB feed(fB,0)

A recycle (f3, zA,3)

B recycle

SP=fRec, B

(fRec, B)

f2, zA,2, zB,2

(f5, zB,5)

A feed

Products→+ BA

Products

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Multiple steady states

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20 25Da

X A

f Rec,B=10

53

2

1.21.5

(Dacr)min=4

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Complex kinetics - polymerization

0.00001

0.0001

0.001

0.01

0.1

1

0 100 200 300 400 500Da

X

18

Conclusions (1)

• Plant Damkohler number

• Feasibility Da > Dacr

• Design Control– Small reactor – manipulate reaction conditions– Large reactor – reaction conditions may be constant

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Bifurcations

T

Transcritical Pitchfork

P

????

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First-order reaction in adiabatic CSTR

LC

CC

CC

FC

FA

V

zB,P=1Sepa

ratio

n

LC

CC

CC

FC

FA

V

zB,P=1Sepa

ratio

n

Model parameters:• Reactor : Da• Separation : zA,3• Reaction

•Adiabatic temperature rise : B•Activation energy : γ

zA,3

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Results

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5Da

X

γ=25z A3=1

Β =0.04=1/γ

B =0.08

B =0.12B =0.16

B =0.2

B < 1/γ

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Which reactor ?

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4B

Da LP

z A3=12 steady states

no steady state

γ=40 2030

B=1/γ

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What conversion ?

0

0.2

0.4

0.6

0.8

1

0 0.05 0.1 0.15 0.2 0.25B

X

z A3=1

γ=4030

2015

10

Unstable

Stable

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Non-adiabatic CSTR

LC

CC

CC

FC

FA

V

zB,P=1Sepa

ratio

n

LC

CC

CC

FC

FA

V

zB,P=1Sepa

ratio

n zA,3

Model parameters:• Reactor

•Volume : Da•Heat transfer capacity : β•Coolant temperature : θc

• Separation : zA,3• Reaction

• Adiabatic temperature rise : B• Activation energy : γ

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Steady-state classification (1)

0

20

40

60

80

100

0 0.2 0.4 0.6 0.8 1B

γγγγ

(A)

(B)

-1

-0.8

-0.6

-0.4

-0.2

0

0 0.2 0.4 0.6 0.8 1ββββ

θθθθ c (I)

(II)

γ=20B =0.1

-0.4

-0.2

0

0.2

0 20 40 60 80 100ββββ

θθθθ c

(I)

(III)

γ=40B =0.3

(IV) (II)

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Steady-state classification (2)

0

0.01

0.02

0.001 0.1 10Da

X

γ=40B =0.3β =20θ c=-0.22

0

0.2

0.4

0.6

0.8

1

0.001 0.1 10Da

Xγ=40B =0.3β =20θ c=0.05

0

0.2

0.4

0.6

0.8

1

0.001 0.1 10Da

Xγ=40B =0.3β =20θ c=-0.05 0

0.2

0.4

0.6

0.8

1

0.001 0.1 10Da

Xγ=40B =0.3β =35θ c=0.02

(I)(II)

(III)(IV)

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Dynamic classification (1)Additional parameters:• Reactor : Le• Separation : τS

Stability• Steady state analysis (“slope condition”):

- Instability can be detected - Stability cannot be guaranteed

• “Dynamic condition” : Hopf bifurcation

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Dynamic classification (2)

0

0.05

0.1

0.15

0.2

0.25

10 100 1000B

θθθθ c

I1, ZH1I2, ZH2

DH2

DH1

ZH2

(I)(II)

(IV)

(V)

(I) (VI)

(VII)

0.075

0.08

0.085

0.09

65 70 75B

θθθθ c

DH1, ZH2

DH1, ZH2

DH2

I1,ZH1

ZH1

(I)

(VII)

(VIII)

(IX)(V)

(IV)

β

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Dynamic classification (3)

(I) (II) (III)

(IV) (V) (VI)

(VII) (VIII) (IX)

X

Da

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Conclusions

• Unfeasible steady state (reactant accumulation)

• Feasible steady states through bifurcations– Da > Dacr

• Unstable steady states– Lower limit on achievable conversion

• Avoid design close to critical points

Recycle systems with reaction-separation