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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
