Chemical Reaction Engineering Asynchronous Video Series Chapter 2 Conversion and Reactors in Series H Scott Fogler Ph D Reactor Mole Balance Summary

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```							Chemical Reaction Engineering

Asynchronous Video Series

Chapter 2:
Conversion and Reactors in Series

H. Scott Fogler, Ph.D.
Reactor Mole Balance Summary
Conversion
Conversion

moles reacted
X
moles fed
Conversion

moles reacted
X
moles fed
Batch Reactor Conversion
•   For example, let’s examine a batch reactor with the following design equation:

dN A
 rA V
dt
Batch Reactor Conversion
•   For example, let’s examine a batch reactor with the following design equation:

dN A
 rA V
dt

•   Consider the reaction:

moles reacted
moles remaining = moles fed - moles fed •
moles fed
Batch Reactor Conversion
•   For example, let’s examine a batch reactor with the following design equation:

dN A
 rA V
dt

•   Consider the reaction:

moles reacted
moles remaining = moles fed - moles fed •
moles fed
Batch Reactor Conversion
•   For example, let’s examine a batch reactor with the following design equation:

dN A
 rA V
dt

•   Consider the reaction:

moles reacted
moles remaining = moles fed - moles fed •
moles fed

Differential Form:

Integral Form:
CSTR Conversion

Algebraic Form:

There is no differential or integral form for a CSTR.
PFR Conversion

PFR
dF A
 rA
dV
FA  F A0  X
1
PFR Conversion

PFR
dF A
 rA
dV
FA  F A0  X
1
PFR Conversion

PFR
dF A
 rA
dV
FA  F A0  X
1

Differential Form:

Integral Form:
Design Equations
Design Equations
Design Equations
Design Equations

V
Design Equations

V
Example
Example

X    1 
V  F A0 0        dX
 rA         0.01
0
Example

X    1 
V  F A0 0        dX
 rA         0.01
0
Example

X    1 
V  F A0 0        dX
 rA                  0.01
0

50
1     40
30
 rA   20
10
0.2 0.4 0.6 0.8
X
Reactor Sizing
•   Given -rA as a function of conversion, -rA=f(X), one can size any type of reactor.
Reactor Sizing
•   Given -rA as a function of conversion, -rA=f(X), one can size any type of reactor.

•   We do this by constructing a Levenspiel plot.
Reactor Sizing
•   Given -rA as a function of conversion, -rA=f(X), one can size any type of reactor.

•   We do this by constructing a Levenspiel plot.                  50
1     40
30
 rA   20
F     1
•   Here we plot either r or r as a function of X.
A0                                        10
A     A                                       0.2 0.4 0.6 0.8
Reactor Sizing
•   Given -rA as a function of conversion, -rA=f(X), one can size any type of reactor.

•   We do this by constructing a Levenspiel plot.                   50
1      40
30
 rA    20
F     1
•   Here we plot either r or r as a function of X.
A0                                         10
A     A                                           0.2 0.4 0.6 0.8

F
A0
•   For r     vs. X, the volume of a CSTR is:
A
F A0 X  0
V                                                XEXIT
 rA
EXIT                          Equivalent to area of rectangle
on a Levenspiel Plot
Reactor Sizing
•   Given -rA as a function of conversion, -rA=f(X), one can size any type of reactor.

•   We do this by constructing a Levenspiel plot.                           50
1      40
30
 rA    20
F     1
•   Here we plot either r or r as a function of X.
A0                                                 10
A     A                                                   0.2 0.4 0.6 0.8

F
A0
•   For r     vs. X, the volume of a CSTR is:
A
F A0 X  0
V                                                       XEXIT
 rA
EXIT                            Equivalent to area of rectangle
on a Levenspiel Plot
F
•   For r
A0
vs. X, the volume of a PFR is:
A

XF                                                                      =area
VPFR  0    A0
 rA
dX     = area under the curve
Numerical Evaluation of Integrals

•   The integral to calculate the PFR volume can be evaluated using Simpson’s
One-Third Rule:
Numerical Evaluation of Integrals

•   The integral to calculate the PFR volume can be evaluated using Simpson’s
One-Third Rule (see Appendix A.4 on p. 924):
Reactors In Series
Reactors In Series
Reactors In Series
Reactors in Series
•   Also consider a number of CSTRs in series:
Reactors in Series
•   Finally consider a number of CSTRs in series:

•   We see that we approach the PFR reactor volume for a large number of CSTRs
in series:

FA 0
 rA

X
Summary
Summary
Summary
Summary
Summary

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