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Chemical Reaction Engineering
Asynchronous Video Series
Chapter 2:
Conversion and Reactors in Series
H. Scott Fogler, Ph.D.
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Reactor Mole Balance Summary
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Conversion
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Conversion
X moles reactedmoles fed
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Conversion
X moles reactedmoles fed
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Batch Reactor Conversion
• For example, let’s examine a batch reactor with the following design equation:
dNA
dt r AV
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Batch Reactor Conversion
• For example, let’s examine a batch reactor with the following design equation:
• Consider the reaction:
dNA
dt r AV
moles remaining = moles fed - moles fed • moles reactedmoles fed
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Batch Reactor Conversion
• For example, let’s examine a batch reactor with the following design equation:
• Consider the reaction:
dNA
dt r AV
moles remaining = moles fed - moles fed • moles reactedmoles fed
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Batch Reactor Conversion
• For example, let’s examine a batch reactor with the following design equation:
• Consider the reaction:
dNA
dt r AV
Differential Form:
Integral Form:
moles remaining = moles fed - moles fed • moles reactedmoles fed
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CSTR Conversion
Algebraic Form:
There is no differential or integral form for a CSTR.
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PFR Conversion
PFR dF
A
dV r
A
FA
FA0
1 X
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PFR Conversion
PFR dF
A
dV r
A
FA
FA0
1 X
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PFR Conversion
PFR dF
A
dV r
A
FA
FA0
1 X
Differential Form:
Integral Form:
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Design Equations
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Design Equations
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Design Equations
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Design Equations
V
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Design Equations
V
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Example
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Example
V FA0
1 r
A
dX
0
X
00.01
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Example
0V FA0
1 r
A
dX
0
X
00.01
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Example
0V FA0
1 r
A
dX
0
X
X 0.2 0.4 0.6 0.8
1020304050
1
r A
00.01
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Reactor Sizing
• Given -r A as a function of conversion, -r A=f(X), one can size any type of reactor.
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Reactor Sizing
• Given -r A as a function of conversion, -r A=f(X), one can size any type of reactor.
• We do this by constructing a Levenspiel plot.
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Reactor Sizing
• Given -r A as a function of conversion, -r A=f(X), one can size any type of reactor.
• We do this by constructing a Levenspiel plot.
• Here we plot either as a function of X.
• For vs. X, the volume of a CSTR is:FA0
r A
FA0
r A
or 1
r A
V F
A0X 0
r A EXIT Equivalent to area of rectangle
on a Levenspiel Plot
XEXIT
0.2 0.4 0.6 0.8
1020304050
1
r A
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Reactor Sizing
• Given -r A as a function of conversion, -r A=f(X), one can size any type of reactor.
• We do this by constructing a Levenspiel plot.
• Here we plot either as a function of X.
• For vs. X, the volume of a CSTR is:
• For vs. X, the volume of a PFR is:FA0
r A
FA0
r A
or 1
r A
FA0
r A
Equivalent to area of rectangle
on a Levenspiel Plot
XEXIT
VPFR FA 0
r A0
X
dX
V F
A0X 0
r A EXIT
= area under the curve=area
0.2 0.4 0.6 0.8
1020304050
1
r A
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Numerical Evaluation of Integrals
• The integral to calculate the PFR volume can be evaluated using Simpson’s
One-Third Rule:
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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):
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Reactors In Series
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Reactors In Series
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Reactors In Series
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Reactors in Series
• Also consider a number of CSTRs in series:
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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 CSTRsin series:
FA0
r A
X
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Summary
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Summary
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Summary
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Summary
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Summary