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Chemical Reaction Engineering
Lecture-4
Module 1: Mole Balances, Conversion & Reactor Sizing
(Chapters 1 and 2, Fogler)
Topics to be covered in today’s lecture
• Conversion (X)
• GMBE in terms of conversion (X) for the following reactors
– Batch Reactor
– Continuous Stirred Tank Reactor
– Plug Flow Reactor
• Compare Volume of CSTR and PFR
• Introduction to Levenspiel Plots
Chapter 2. Conversion and Reactor Sizing
Conversion (X)
• Conversion: quantification of how a reaction has progressed
fedAspeciesofMoles
reactedAspeciesofMolesX A
""
"" (A: limiting reactant)
)1(0 XNN AA
Batch Reactors
AO
AAO
N
NNX
Continuous (or Flow) Reactors
0
0
A
AA
F
FFX
)1(0 XFF AA
can be omitted
• Maximum conversion for irreversible reactions: X = 1.0
• Maximum conversion for reversible reactions: X = Xe
? 0
A
AA
C
CCXWhen
aA + bB → cC + dD ; A + b/a B → cC + dD Limiting Reactant
Batch Reactor Design Equation
Vrdt
dNA
A 0
0
A
AA
N
NNX
)1(000 XNXNNN AAAA
Vrdt
dXN AA 0
For a constant-volume batch reactor Vrdt
dXN AA 0 A
A rdt
dC
Therefore, a batch reactor has been widely used to investigate the rate law equation.
Vrdt
dXN AA 0
X
A
A
X
A
AXCf
dXC
Vr
dXNt
0 0
0
0
0),(
X
Vr
N
A
A
0
0 t
constant-volume reactor
NA = NA0 X
Design Equation in Differential Form
Design Equation in Integral Form
Design Equation for Flow Reactors
X = f (t) for Batch Reactor
X = f (V) for Flow Reactor
FA = FA0 (1 – X) [moles/time]
FA = CA0 0
CA0 : morality for Liquid System
CA0 = PA0/RT0 = yA0P0/RT0 for Gas System
),()()( 0
000
XCf
XF
r
XF
r
XFV
A
A
exitA
A
A
A
CSTR Design Equation
)(
0
A
AA
r
FFV
0
0
A
AA
F
FFX
)1(000 XFXFFF AAAA
000 AA CF 0For incompressible fluid
)(
0
A
A
r
F
X
CA0
CA
FA0
υ0
CA
FA
υ
X0
X
Area = Reactor volume
Design Equation
for CSTR
X
A
A
X
A
AXCf
dXF
r
dXFV
0 0
0
0
0),(
AA rdV
dXF 0
PFR Design Equation
AA r
dV
dF
0
0
A
AA
F
FFX
)1(000 XFXFFF AAAA
000 AA CF 0For incompressible fluid
)(
0
A
A
r
F
X
Area = Reactor volume
PFR
CA0
FA0
υ0
X0
CA
FA
υ
X
No radial gradients
Design Equation for PFR
X
A
Ar
dXFW
0
0'
AA rdW
dXF '0
PBR Design Equation
000 AA CF 0For incompressible fluid
)'(
0
A
A
r
F
X
Area = Catalysts weight
No radial gradients
Design Equation for PBR
Design Equation in terms of Conversion
REACTOR DIFFERENETIAL ALGEBRAIC INTEGRAL
FORM FORM FORM
Vrdt
dXN AAO )(
X
A
AOVr
dXNt
0
)( AAO rdV
dXF
X
A
AOr
dXFV
0
CSTR
PFR
ExitA
AO
r
XFV
)(
)(
BATCH
Batch and Levenspiel Plots
][])(
[ 0 Xr
FV
A
ACSTR
Continuous Stirred Tank Reactor (CSTR)
)(
0
A
A
r
F
X
xx
x A
APFR dX
r
FV
0
0
X
)(
0
A
A
r
F
Plug Flow Reactor (PFR)
Isothermal
system
xx
x A
ABatchVr
dXNt
0
0)(
X
Vr
N
A
A
)(
0
Batch Reactor
Class Problem # 1
The following reaction is to be carried out isothermally in a
continuous flow reactor:
A B
Compare the volumes of CSTR and PFR that are necessary to
consume 90% of A (i.e. CA=0.1 CAO). The entering molar and
volumetric flow rates are 5 mol/h and 10 L/h, respectively. The
reaction rate for the reaction follows a first-order rate law:
(-rA) = kCA where, k=0.0001 s-1
[Assume the volumetric flow rate is constant.]
Solution to Class Problem #1
0
2
4
6
8
10
12
14
16
18
20
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Conversion (X)
FA
0/(-
r A)
Homework #1
• Calculating Reaction rate in a CSTR
Pure gases reactant A(CAo=100 millimol/liter) is fed at steady rate into a
mixed reactor (V=0.1 liter) where it dimerizes (2A→R). For different gas feed
rates the following data are obtained
Find the expansion factor, conversion of each run
rate of equation for this reaction
- rA = k CAn
Run number 1 2 3 4
liter/hr 30.0 9.0 3.6 1.5
CA, out, millimil/liter 85.7 66.7 50 33.3
0
