reactor cstr
TRANSCRIPT
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Ideal ReactorsTypes of Ideal Reactors
(Semi-)Batch reactor
Plug-Flow Reactor (PFR)
Continuous stirred tank (CSTR)
Recycle reactor
Stirred tank cascade
Reactor Design
Volumetric flow rate
Rate of reaction
Outlet concentrationInlet concentration
Reaction volume
Model
Outlet = f(inlet, kinetics, contacting pattern)
Ideal Reactors
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Batch Reactor – 1
Material Balance
Energy Balance(1) constant pressure
(2) constant volume
Ideal Reactors
Batch Reactor – 2Conversion and Temperature Profiles in Batch Reactor
Ideal Reactors
ADIABATIC POLYTROPIC
Numerical solution necessary!
t t
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CST Reactor
Material Balance
mean residence time
steady state conversion
Ideal Reactors
Transient behavior in CSTRIdeal Reactors
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Transient behavior in CSTRIdeal Reactors
Phenol Production in CSTRIdeal Reactors
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Energy BalanceCSTR Reactors
Where:
of feed stream
Energy BalanceCSTR Reactors
0
-feed
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Energy BalanceCSTR Reactors
Energy BalanceCSTR Reactors
from material balance
General Energy Balance Equation for CSTR
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Summary of Energy Balance-1CSTR
Summary of Energy Balance-1CSTR
(1) Please derive the constant volume-ideal gas for a CSTR reactor
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Energy Balance
Special Case: Incompressible fluid
CSTR
Energy BalanceSimplifying Assumptions
CSTR Reactors
(1) Steady-State Condition
0
(2) Liquid Phase(3) Excess Solvent or Diluent
heat capacity is constant independent of pressure
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Temperature Control in CSTR – 1 CSTR
Aqueous solution of specie A undergoes a reversible isomerization reaction in a 2000 L CSTR.
1. Find the reactor temperature for 80 % conversion.2. What are the heat duties of the two heat exchangers ? Approximate the
heat capacity of the reaction mixture with that of water.
Temperature Control in CSTR – 2 CSTR
(1) Steady-State Condition
whereAns.
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Temperature Control in CSTR – 3 CSTR
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1. (a) Plot conversion versus T (K) for CAf = 0.25, 4, 16.(b) Plot conversion versus T(K) for CAf = 4, if VR is 0.5 or 2 x the given value. (c) Plot conversion versus T(K) for CAf = 4, if activation energy of k1 is 0.5 or 2 x the
given values.(d) Plot conversion versus T(K) for CAf = 4, if activation energy of K1 is 0.5 or 2 x the
given values.Please summarize your observations.
Temperature Control in CSTR – 4 CSTR
(2) Heat duties of the two heat exchangers
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CSTRMultiple Steady-State
(1) The coupling between material and energy balances in CSTR can lead to complex behavior,
(2) The presence of multiple steady-state is possible even for the simplest kinetic mechanism.
Adiabatic CSTR – 1 Multiple Steady-State
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Adiabatic CSTR – 2 Multiple Steady-State
(1) Material Balance
(2) Steady-State, Liquid Phase, Constant Density
Adiabatic CSTR – 3 Multiple Steady-State
(3) Heat Capacity is Constant
heat transfer
where:
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Adiabatic CSTR – 4 Multiple Steady-State
(4) Material and Energy Balance for Adiabatic CSTR
(5) Solve the Nonlinear Equations(a) For isothermal case:
Adiabatic CSTR – 5 Multiple Steady-State
(5) (b) For nonisothermal case:
1. Find and for
2. You can then plot for different values of ∆HR
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Adiabatic CSTR – 6 Multiple Steady-State
(6) Multiple Steady-State(a) Reactions more exothermic than –10 x 104 kJ/kmole, there are multiple steady states,(b) Points at which steady-state curve turns correspond to the ignition and extinction
points.
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Adiabatic CSTR – 7 Multiple Steady-State
(7) Hysteresis
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ignition
decreasing flowrate decreasing flowrate
ignition
extinctionextinction
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Adiabatic CSTR – 8 Multiple Steady-State
(8) Stability of Steady-Statevan Heerden Diagram
Dynamic Model
Solving
Procedure(1) Qr = Qg then steady state condition occurs,(2) Qg(θ) vs. T is nonlinear, but Qr(θ) vs. T is linear,(3) The resulting plots is known as van Herdeen diagram
heat generation heat removal
Adiabatic CSTR – 9 Multiple Steady-State
(8a) van Heerden Diagram
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Adiabatic CSTR – 10 Multiple Steady-State
(8b) van Heerden Diagram
Adiabatic CSTR – 11 Multiple Steady-State
(9) Mechanical Analogy
Single Steady-State A Ignition Point A
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Standardized Stirred Tank Reactor Sizes Heat Exchanger in CSTR
Volume VR (m3) Diameter db (m) heat exchanger area A (m2)
0,1 0,508 0,80,16 0,6 1,160,25 0,7 1,480,4 0,8 2,32
0,63 1 2,871 1,2 3,87
1,6 1,4 5,62,5 1,6 7,94 1,8 9,1
6,3 2 13,18 2,210 2,4 18,7
12,5 2,416 2,8 2520 2,625 3 34,632 3,440 3,6 46
Types of Heat Exchangers – 1
(1) Jacketed Heating and Cooling
Heat Exchangers in CSTR
)(T- TcQUA
cQUA
)(T- TcQ
)UA(T- TQ
WFpww
pww
WFpww
Ww
+=
=
=
)(T- TcQUA
cQUA
)(T- TcQ
)UA(T- TQ
WFpww
pww
WFpww
Ww
+=
=
=
(2) Integrated Heat Exchanger
T
)T(T)cQUA/(exp1cQQ
A
TcQ) TU(T
A
Q
WFpwwpwww
wpwwW
−−−=
∂∂
=−=∂
∂
⎥⎦
⎤⎢⎣
⎡)T(T)cQUA/(exp1cQQ
A
TcQ) TU(T
A
Q
WFpwwpwww
wpwwW
−−−=
∂∂
=−=∂
∂
⎥⎦
⎤⎢⎣
⎡
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Types of Heat Exchangers – 2
(3) External Heat Exchanger with Recycle
Heat Exchangers in CSTR
Heat exchanger
Ratio between residence time and reaction time
Stable and Unstable Limit Cycle
Damköhler Number
0j
i0ji c
r)(Da
θν−=
0j
i0ji c
r)(Da
θν−=
0kj0jk
0j2jjj0j0k2jk2
0j2j2
j20j2
2j2
1jj0j1
0j
0j0
a0
c/c
ck)(-)X-1)(-X1(cck)cck(r2
ck)(-)-X1(ck)ck(r2
k)(--X1ck1
c
k)(-1k0
D(X) rorderreaction
νν=λ
τ⋅⋅⋅νλ⋅⋅=
τ⋅⋅⋅ν⋅=
τ⋅⋅ν⋅
θ⋅νΦ
0kj0jk
0j2jjj0j0k2jk2
0j2j2
j20j2
2j2
1jj0j1
0j
0j0
a0
c/c
ck)(-)X-1)(-X1(cck)cck(r2
ck)(-)-X1(ck)ck(r2
k)(--X1ck1
c
k)(-1k0
D(X) rorderreaction
νν=λ
τ⋅⋅⋅νλ⋅⋅=
τ⋅⋅⋅ν⋅=
⋅⋅ν⋅
⋅⋅νΦ
θ
θ
θ
)X()T(rr);X()T(rr j0i0ii Φ⋅=Φ⋅=( for any reaction) )X()T(rr);X()T(rr j0i0ii Φ⋅=Φ⋅=( for any reaction)
)X1(c)T(kc)T(kr j0j1j1 −⋅=⋅=e.g. for 1st order kinetics)X1(c)T(kc)T(kr j0j1j1 −⋅=⋅=e.g. for 1st order kinetics
where
Da < 0,1 low conversion ; Da < 100 nearly quantitative conversion⇒ ⇒
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Analysis – 1
(1) CSTR Energy Balance
Heat Exchangers in CSTR
Relative Cooling Intensity
Stanton Number, St =
Adiabatic Temperature Increase
∆Tad =cA0
vi
cA0
-viDa(T)Φ(X)1
θ
St ∆Tad (X)
Analysis – 2
(2a) Jacketed Heating and Cooling
Heat Exchangers in CSTR
St (T – TW) = κ (T – TWF)
=QWcPW
+ QWcPW
(T – TWF)
(2b) Integral Heat Exchanger
T
St (T – TW) = κ (T – TWF)
=QWcPW [1 – exp (- / QWcPW](T – TWF)
TW
TWF
T0
St ∆Tad (X)
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Analysis – 3
(3) Calculation of Reactor Temperature
Heat Exchangers in CSTR
κ ∆Tad (X)(T – TWF)
(T – T*W) = ∆Tad (X)(1 + κ)
T*W = (Tf – κTWF)
(1 + κ)where outlet temperature in
absence of temperature
(T – T*W) = ∆Tad (1 + κ) Daœ exp (-E/RT)
1 + Daœ exp (-E/RT)
Heat Removal Heat Generation
Oscillatory BehaviorNonadiabatic CSTR – 1
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Nonadiabatic CSTR – 2
(1) Solving the New Problem
conv
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Nonadiabatic CSTR – 3
(2) Temperature and Conversion Oscillation – 1
Phase Plot
limit cycle
Oscillatory Behavior
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Nonadiabatic CSTR – 4 Multiple Steady-State
(3) Initial Conditions
CA0 = CAf, T0 = Tf
CA0 = 0, T0 = Tf
global attractor
Nonadiabatic CSTR – 5
(4) Temperature and Conversion Oscillation – 2
Oscillatory Behavior
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Nonadiabatic CSTR – 6
(5) Stable and Unstable Limit Cycle
Oscillatory Behavior
Nonadiabatic CSTR – 7
(6) Complex Phase Plots
Oscillatory Behavior
X
Separatrix
Tmperature
Con
vers
ion
In General:Cooling Capacity > Heat Generationlead to a stable steady-state.
Heat Generation > Cooling Capacityusually lead to unstable steady-state such as (1) ignition, (2) extinction and(3) oscillatory behavior.
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Nonadiabatic CSTR – 8
(7) General Analysis(a) Effects of feed temperature (Tf)
Heat Removal in CSTR
(T – T*W) = ∆Tad (X)(1 + κ) T*W = (T0 – κTWF)
(1 + κ)where
•
Q Heat removal
Heat generation
•
Q Heat removalHeat removal
Heat generationHeat generation
Thermal Hysteresis
Nonadiabatic CSTR – 9
(b) Effects of residence time (θ)
Heat Removal in CSTR
(T – T*W) = ∆Tad (1 + κ) Daœ exp (-E/RT)
1 + Daœ exp (-E/RT)
Q
TWF
Flow Hysteresis
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CSTR – 1 Mixing and Residence Time Distribution
(1) Fluid Flow Pattern in Reactor(a) Computational Fluid Dynamics (CFD)
- fluid mixing is calculated by solving the equations of motion for fluid,- type of fluid flow (e.g., laminar and turbulent), and various transport
mechanisms (e.g., molecular and eddy diffusions) must be accounted.
CSTR – 2 Mixing and Residence Time Distribution
(b) Residence Time Distribution (RTD)- classical approach based on experimental probe,- do not use any structure of equation of motion, approximate idea of
mixing.- at short length scale: condition that maximizes diffusion also enhances
mixing and uniformity,at reactor length scale: condition that maximizes convection enhances mixing and uniformity.
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CSTR – 3 Mixing and Residence Time Distribution
(2) Gedanken Experiment
a
b
c
tracer
(a) Probability function
CSTR – 4 Mixing and Residence Time Distribution
(b) RTD MeasurementExperimental Method
Cf
C0
C0
Cf
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CSTR – 5 Mixing and Residence Time Distribution
(3) CSTR Experiment
Step response experiment
t ≤ 0, No tracert > 0, Add small amount of tracer
CSTR – 6 Mixing and Residence Time Distribution
(3) CSTR Experiment
(a) Material Balance
= 1
τ
τ is the mean residence time
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CSTR – 7 Mixing and Residence Time Distribution
(4) RTD in CSTR: Step-Change in Concentration
CSTR – 8 Mixing and Residence Time Distribution
(5) Mean RTD
2. Describe a Semibatch Reactor(a) Write the governing material balance equation,(b) Write the governing energy balance equation for a incompressible liquid, constant
pressure reactor.
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CSTR ReactorGroup No. 1, 3, 5, 7, 9, 11
Mini-Project 2
A → B
CSTR ReactorGroup No. 1, 3, 5, 7, 9, 11
Mini-Project 2
(1) Plot Conversion and T versus q (see below) as function of:(a) Cf 2, 4, 8, 16, 32 kmol/m3
(b) ∆HR -30, -20, -10, -5, 0, 5 x 104 kJ/kmolGroup 1 U° = 50 kJ/(m3minK)-1 Group 7 U° = 400
3 U° = 100 9 U° = 800 5 U° = 200 11 U° = 1600
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CSTR ReactorGroup No. 2, 4, 6, 8, 10
Mini-Project 2
A ↔ B K1 = k1/k-1
Note ∆HR is for the forward reaction, reverse reaction should give - ∆HR
CSTR ReactorGroup No. 2, 4, 6, 8, 10
Mini-Project 2
Plot Conversion and T versus q (see below) as function of ∆HR is -30, -20, -10, -5, 0, 5 x 104 kJ/kmol.
Group 2 K1 = 1 Group 8 U° = 20 4 K1 = 5 10 U° = 100 6 K1 = 10
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