1
Design of Chemical Reactors in Recycle Systems
fromPlantwide Control Perspective
C.S. Bildea and A.C. DimianUniversity of Amsterdam
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Outline
• Plantwide control• Isothermal reactor
– One-reactant– Two-reactants
• Adiabatic reactor• Non-adiabatic reactor
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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)
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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
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Systemic approach to Plantwide control (2)
• Local control – unit operations, complex structures
• Plantwide control – Mass balance
• Reactants• Products• Impurities
– Energy balance
•Reactor•Separation•Recycle
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Reactor – Separator –Recycle
Gasseparation
Liquid separation
G-L
F
R
S
Y
P
Reactor
RecycleFeed
Products
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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
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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
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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
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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
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Design and control (2)
FC
CC
CCLC
V
S
zB,P=1Sepa
ratio
n
(b)
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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
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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
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