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Reactor Design H83RED
Course Syllabus
Lectures: 2-hour Lecture and 1-hour Example class per week
•Tuesday, 11-1 pm @ F1A15
•Thursday, 4-5 pm @ F3A12
Assessment: 10% quizzes; 20% coursework; 70% final exam (two hours)
Aims:
To learn how to apply the fundamental principles of chemical kinetics, along with heat and
mass transfer transport, to the design of chemical reactors for both homogenous and
heterogeneous cases. Emphasis will be placed on developing basic concepts which will then
be used to analyze problems of increasing sophistication including non-isothermal and
catalytic reactors.
Convener: Dr Chan Yi Jing [email protected]
Reactor Design H83RED
Course Structure
The course is made of 8 topics, which are detailed as below. The course consists of lectures,
which will include problem solving, tutorials, and a week long game based on designing a
reactor. Problems are to be worked primarily at home by the students. We will closely follow
the textbook Fogler, H. Scott. “Elements of chemical reaction engineering” 3rd ed., Prentice
Hall, 2000.
Course Schedule (This might change as we move through the course)
Week 1 – Introduction to module, rate of reaction, mole balance
Week 2 – Design equations
Week 3 – Stoichiometry
Week 4 – Stoichiometry
Week 5 – Isothermal reactors
Week 6 – Isothermal reactors
Week 7 – Non-isothermal reactors
Week 8 – Non-isothermal reactors
Week 9 – Multiple reactions
Week 10 – Catalysts and Catalytic reactors
Week 11 – Catalysts and Catalytic reactors
Week 12 – Student study
Reactor Design H83RED
Learning Outcomes:
A student who has successfully completed this module will be able to:
•Perform material balances to derive general reactor design equations
•Use the appropriate reaction kinetics in the reactor design equations
•Express concentrations and molar flow rate in terms of conversion
•Perform energy balances for the basic reactor types
•Use the energy balances for reactor design
•Calculate the parameters corresponding to optimal reactor design
•Extend these operations to the case of multiple reactions and reactor sequences
Summary:
Combine material balance, rate law, stoichiometry, energy balance for optimal reactor design
and operation
Reactor Design Outline
1. Introduction
2. The Place of “Reactor Design” in Chemical Engineering
3. Type of Reactors: Batch, Continuous
4. Definition of Rate of Reaction, - rA
5. The General Mole Balance Equation
6. Mole Balances for PFR, CSTR, PBR, and Batch Reactors
Outline
Reactor Design Introduction
The Place of “Reactor Design” in Chemical Engineering
ProductsRaw
materials
Chemical
Reactions
Physical
treatment
steps
Physical
treatment
steps
Recycle
Typical chemical process
Chemical treatment steps are carried out in chemical reactors.
Reactor design based on information, knowledge and experience from a variety of
areas:
Thermodynamics
Chemical kinetics
Fluid Mechanics
Heat Transfer
Mass Transfer
Economics
Knowledge of chemical kinetics and reactors design distinguishes the chemical
engineer from both chemists and other engineers
Reactor Design Introduction
Types of Reactors
Relatively Small Scale (a few thousands of tons per year)
High Flexibility
Low Cross-contamination
Short Period for Reactor Start-up
Batch Reactors
Description
Reactants are charged into the vessel, react for a
specific period of time. Products are discharged after
the reaction.
Applicability
Advantages Disadvantages
High demands in manpower
Lower efficiency of services (heating & cooling)
Complicated automatic control
Reactor Design Introduction
Types of Reactors
Large Tonnage Production (tens or hundreds of
thousands tons per year)
Steady-State Operation
Lower demands in manpower
Easy automatic control
Efficient services
Continuous Reactors
Description
Reactants flow continuously into the vessel, and
products flow continuously out of the reactor
Applicability
Advantages Disadvantages
Long Start-up
High cost of halting operation
Low flexibility
Continuous
Stirred Tank
Reactor
(CSTR)
Tubular or
Packed Bed
Reactor
Reactants
Products
Reactor Design Definition of rate of reaction
Definition of rate of reaction
(Homogeneous reaction systems)
Rate of reaction, - rA, is the rate of disappearance of species A per unit volume or
it is the number of moles of species A reacted per unit time per unit volume
Units:
Consider the reaction: A B
Rate of reaction, rB, is the rate of formation of species B per unit volume or it is the
number of moles of species B formed per unit time per unit volume
- rA = rB timevolume
moles
Rate of reaction, - r’A, is the number of moles of species A reacted per unit time per
unit mass of catalyst (or per unit surface area of catalyst), (or per unit volume of
catalyst)
Consider the reaction: A B
over a catalyst
timecatalyst mass
moles
Definition of rate of reaction
(Heterogeneous reaction systems)
timecatalyst area surface
moles
timecatalyst volume
moles
Units:
- r’A = r’B
Reactor Design Definition of rate of reaction
Source of confusion
dt
dCr A
A
NaOH CH3COOC2H5
C2H5OH
CH3COONa
unreacted:
CH3COOC2H5
NaOH
CH3COOC2H5 + NaOH CH3COONa + C2H5OH
Perfect mixing and steady-state operation
result in identical concentration of each
species in any point:
0dt
dCA Wrong for continuous
systems
In flow system the differential form :
dt
dCr A
A
does not represent the rate of reaction
Consider the reaction: A B
Constant volume batch reactorA
C
Time
A
B
Reactor Design The rate law
The chemical reaction rate:
• An intensive quantity
•Depends on the properties of the reacting materials (concentration, temperature,
pressure, type of catalysts) at a point in the system
• Independent of the type of system (i.e. batch or continuous flow) in which the
reaction is carried out.
Different forms of the dependencies of the reaction rate on concentration:
AA kCr 2
AA kCr
A
AA
Ck
Ckr
2
1
1
The reaction rate is essentially an algebraic equation involving
concentration, not a differential equation.
The rate law
Consider the reaction: A products
Reactor Design Mole balance
General Mole Balance Equation
Main Task of Reactor Design: to determine the degree of conversion of a particular
reactant, or to determine the reactor volume to achieve a particular conversion.
The system volume is defined as the volume enclosed by physical boundaries
of the reactor. System
Volume
GjFj0 Fj
Focus on species which are able to participate in a chemical reaction or are
generated as a result of it. Molar fluxes of such components must be balanced
A mole balance on species j at any instant of time, t:
)/(
j
onaccumulati
)/(
outj
)/(
j
generation
)/(
intoj
timemoles
systemthe
withinof
ofrate
timemoles
systemthe
of
flowofrate
timemoles
systemthe
withinreaction
chemicalbyof
ofrate
timemoles
systemthe
of
flowofrate
in + generation out = accumulation
Reactor Design Mole balance
General Mole Balance
If all the system variables are spatially uniform throughout the system volume, the
rate of generation of species j, Gj:
in + generation out = accumulation
dt
dNFGF
j
jjj 0(1)
VrG jj (2)
)/(
j
onaccumulati
)/(
outj
)/(
j
generation
)/(
intoj
timemoles
systemthe
withinof
ofrate
timemoles
systemthe
of
flowofrate
timemoles
systemthe
withinreaction
chemicalbyof
ofrate
timemoles
systemthe
of
flowofrate
volumetimevolume
moles
time
moles
Reactor Design Mole balance
General Mole Balance
The rate of reaction could vary through the system volume due to variation of
concentration, temperature, etc.. This means that rate of generation of species j is
dependant on the location within the system volume.
Consider indefinitely small volumes, Vi,
so that the rate of reaction
Using equation (2):
V1
V2
rj1
rj2
V
rj1 in V1; rj2 in V2 … rji in Vi
ijiji VrG (3)
Total rate of generation within the system
divided into M sub-volumes :
M
i
iji
M
i
jij VrGG11
Let M and V0:
V
jj dVrG0
Returning to the equation of mole
balance (1):
(4)
(5)
Vj
jjjdt
dNdVrFF
0
0(6)
General Mole Balance Equation
Reactor Design Mole balance (Batch reactor)
Mole Balance for Batch Reactors
A batch reactor has neither inflow nor outflow of reactant or products in the
course of reaction
If the reaction mixture is perfectly mixed (rj = const)
General mole balance on species j:
(8)
Vj
jjjdt
dNdVrFF
0
0
V
j
jdVr
dt
dN
0
(7)
Vrdt
dNj
j
Reactor Design Mole balance (Batch reactor)
Mole Balance for Batch Reactors
Vrdt
dNA
A Consider the reaction: A B
NA
t
NA0
t1
NA1
Question:
Time, t1 necessary to reduce the initial number of moles
from NA0 to a final desired number NA1?
Vrdt
dNA
A
Rearranging,
Vr
dNdt
A
A
Integrating with limits at t=0, then NA=NA0, and t=t1, then NA=NA1,
Time, t1 necessary to reduce the number of moles from NA0 to NA1 is:
0
1
A
A
N
N A
A
Vr
dNt
(8)
Mole balance (Batch reactor)Reactor Design
Batch Reactor
Constant Volume or Constant Pressure:
Does it make a difference?Vr
dt
dNA
A
Constant volume Constant pressure
Consider the reaction:
(CH3)2O CH4 + H2 + CO
A M + H + C
Vrdt
dNA
A AA r
dt
dN
V
1
Perfectly mixed No spatial variation of rate
Constant-volume batch reactorA
AAA rdt
dC
dt
VNd
dt
dN
V
)/(1
Constant-pressure batch reactor
AAAAA r
dt
dV
V
C
dt
dC
dt
VCd
Vdt
dN
V
)(11
VCN AA
AAA r
dt
VdC
dt
dC
)(ln
Mole Balance (CSTR)Reactor Design
Mole Balance for CSTR
CSTR are operated at steady state:
The CSTR is a well mixed reactor operated continuously
There are no spatial variations in concentration,
temperature, or reaction rate throughout the tank
(9)
(10)
Vj
jjjdt
dNdVrFF
0
0
(11)0dt
dN j
and rj = const
V
jj VrdVr0
Using equations (9) and (10):
00 jjj VrFF
Design equation for a CSTR
(12)
Reactants
Products
The molar flow rate Fj is just the product of concentration
of species j and the volumetric flow rate v
vCF jj
j
jj
r
FFV
0
time
volume
volume
moles
time
moles
Reactor Design Mole Balance (PFR)
Mole Balance for Tubular Reactors
Tubular reactors consist of a cylindrical pipe and are
normally operated at steady state
Fj(V) - the molar flow
rate of species j into
subvolume V
Vj
jjjdt
dNdVrFF
0
0
Fj0 Fj,exitV
VFj(V) Fj(V+V)
(13)
In spatially uniform subvolume V:
V
jjj VrdVrG0
- steady state operation: 0dt
dN j
Fj(V+V) the molar flow
rate of species j out of
the subvolume
Model of a plug-flow reactor (PFR)
Highly turbulent flow
No radial variations in concentrations
(16)
(15)
(18)
General mole balance for the
subvolume:
(14)
0VrFF jVVjVj
After rearranging:
jVjVVj
rV
FF
taking the limit as V0
dV
dF
V
FFlim
jVjVVj
0V
General Mole Balance Equation
(17)or
Differential Integral
j
jr
dV
dF
j
j
F
F j
j
r
dFV
0
Reactor Design Mole Balance (PFR)
Mole Balance for Packed-Bed Reactors
Packed-Bed Reactors are designed to carry out
heterogeneous reaction.
(19)
Wj
jjjdt
dNdVrFF
0
'
0
(21)
Differential form of the general mole
balance for PBR:
(20)
PBR Features
Replacing volume coordinate with the
catalyst weight coordinate and assuming
that there are no radial gradients in
concentration, temperature, or reaction
rate:
W
Fj0 Fj,exitW
W
Fj(W) Fj(W+W)
Reactor volume is filled with catalysts
Reaction kinetics is dependant on a quantity of catalyst
timecatalystofmass
A moles'
jr
After rearranging:
If the limit is W0
Integral form of the general mole
balance for PBR:
j
jr
dW
dF
j
j
F
F j
j
r
dFW
0
0WrFF jWWjWj
jWjWWj
rW
FF
Reactor Design Mole Balance
Mole Balance for Different Types of Reactors
Vrdt
dNA
A
Reactor Type Differential Algebraic Integral
Batch
CSTR
PFR
PBR
AA r
dV
dF
AA r
dW
dF
j
jj
r
FFV
0
A
A
N
N A
A
Vr
dNt
0
0A
A
F
F A
A
r
dFV
0A
A
F
F A
A
r
dFW
Reactor Design Mole Balance (Example 1-3)
Example 1: The first-order reaction A B is carried out in a tubular reactor in which the
volumetric flow rate, v, is constant.
Derive an equation relating the reactor volume to the entering and exiting concentrations of A, the rate constant k, and the volumetric flow rate v.
Determine the reactor volume necessary to reduce the exiting concentration to 10% of the entering concentration when the volumetric flow rate is 10 dm3/min and the specific reaction rate, k, is 0.23 min-1.
Solution
The mole balance on species A in tubular
reactor is:
AA r
dV
dF
Molar flow of the species A into reactor is:
AA CvF For a first-order reaction, the rate law is:
-rA = kCATherefore
dV
dCv
dV
Cvd
dV
dF AAA
)(
Reactants Products
Reactor Design Mole Balance (Example 1-3)
Solution (continuation)
Example 1: The first-order reaction A B is carried out in a tubular reactor in which the
volumetric flow rate, v, is constant.
Derive an equation relating the reactor volume to the entering and exiting concentrations of A, the rate constant k, and the volumetric flow rate v.
Substitutions into molar balance equation results in:
AA kC
dV
dCv
Rearranging gives:
dVC
dC
k
v
A
A
Using the conditions at the entrance of the reactor that when V=0, CA=CA0
VC
C A
A dVC
dC
k
v A
A 00
After integration:
A
A
C
C
k
vV 0ln
Reactor Design Mole Balance (Example 1-3)
Solution (continuation)
Example 1: The first-order reaction A B is carried out in a tubular reactor in which the
volumetric flow rate, v, is constant.
Determine the reactor volume necessary to reduce the exiting concentration to 10% of the entering concentration when the volumetric flow rate is 10 dm3/min and the specific reaction rate, k, is 0.23 min-1.
Substituting v=10 dm3/min; k=0.23 min-1; CA=0.1CA0:
A
A
C
C
k
vV 0ln
Reactor Design Mole Balance (Example P1-3)
Solution
Example 2: The first-order reaction A B is carried out in a CSTR in which the
volumetric flow rate, v, is constant.
Determine the reactor volume necessary to reduce the exiting concentration to 10% of the entering concentration when the volumetric flow rate is 10 dm3/min and the specific reaction rate, k, is 0.23 min-1.
The mole balance on species A in CSTR
is:
Molar flow of the species A into reactor is:
AA CvF
For a first-order reaction, the rate law is:
-rA = kCA
A
AA
r
FFV
0
Reactants
Products
Reactor Design Mole Balance (Example P1-4)
Solution
Example 3: The first-order reaction A B is carried out in a Constant Volume Batch
Reactor.
Determine the time necessary to reduce the number of moles of A to 10% of its initial value when the specific reaction rate, k, is 0.23 min-1.
The mole balance on species A in Batch
reactor is:
The moles of A into reactor is given by:
VCN AA
For a first-order reaction, the rate law is:
-rA = kCA
Vrdt
dNA
A
VkCdt
VCdA
A )(