reactors design, adiabatic and non- adiabatic processes
DESCRIPTION
Ideal Reactores, Reactor Design, Batch Reactor, CST Reactors, Transient behvior in CSRT, Phenol Production in CSTR, Energy Balance, Temperature Conntrol, Adiabatic, Heat Exchangers, Non Adiabatic processesTRANSCRIPT
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
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
CST Reactor
Material Balance
mean residence time
steady state conversion
Ideal Reactors
Transient behavior in CSTRIdeal Reactors
Transient behavior in CSTRIdeal Reactors
Phenol Production in CSTRIdeal Reactors
Energy BalanceCSTR Reactors
Where:
of feed stream
Energy BalanceCSTR Reactors
0
-feed
Energy BalanceCSTR Reactors
Energy BalanceCSTR Reactors
from material balance
General Energy Balance Equation for CSTR
Summary of Energy Balance-1CSTR
Summary of Energy Balance-1CSTR
(1) Please derive the constant volume-ideal gas for a CSTR reactor
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
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.
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
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
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:
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
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
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
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
−−−=
∂∂
=−=∂
∂
⎥⎦
⎤⎢⎣
⎡
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⇒ ⇒
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)
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
Nonadiabatic CSTR – 2
(1) Solving the New Problem
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Nonadiabatic CSTR – 3
(2) Temperature and Conversion Oscillation – 1
Phase Plot
limit cycle
Oscillatory Behavior
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
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.
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
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.
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
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
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.
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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