chemical reaction engineering asynchronous video series chapter 2: conversion and reactors in series...
TRANSCRIPT
Chemical Reaction Engineering
Asynchronous Video Series
Chapter 2:
Conversion and Reactors in Series
H. Scott Fogler, Ph.D.
Reactor Mole Balance Summary
Conversion
Conversion
€
X = moles reactedmoles fed
Conversion
€
X = moles reactedmoles fed
Batch Reactor Conversion
• For example, let’s examine a batch reactor with the following design equation:
€
dN Adt
= rAV
Batch Reactor Conversion
• For example, let’s examine a batch reactor with the following design equation:
• Consider the reaction:
€
dN Adt
= rAV
€
moles remaining = moles fed - moles fed • moles reacted
moles fed
Batch Reactor Conversion
• For example, let’s examine a batch reactor with the following design equation:
• Consider the reaction:
€
dN Adt
= rAV
€
moles remaining = moles fed - moles fed • moles reacted
moles fed
Batch Reactor Conversion
• For example, let’s examine a batch reactor with the following design equation:
• Consider the reaction:
€
dN Adt
= rAV
Differential Form:
Integral Form:
€
moles remaining = moles fed - moles fed • moles reacted
moles fed
CSTR Conversion
Algebraic Form:
There is no differential or integral form for a CSTR.
PFR Conversion
PFR
€
dFAdV
=rA
FA = FA0 1− X( )
PFR Conversion
PFR
€
dFAdV
=rA
FA = FA0 1− X( )
PFR Conversion
PFR
€
dFAdV
=rA
FA = FA0 1− X( )
Differential Form:
Integral Form:
Design Equations
Design Equations
Design Equations
Design Equations
V
Design Equations
V
Example
Example
€
V = FA01
−rA
⎛
⎝ ⎜
⎞
⎠ ⎟dX
0
X
∫00.01
Example
0
€
V = FA01
−rA
⎛
⎝ ⎜
⎞
⎠ ⎟dX
0
X
∫00.01
Example
0
€
V = FA01
−rA
⎛
⎝ ⎜
⎞
⎠ ⎟dX
0
X
∫
X0.2 0.4 0.6 0.8
1020304050
€
1−r
A
00.01
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.
• Here we plot either as a function of X.
€
FA0−rA
or 1−rA 0.2 0.4 0.6 0.8
1020304050
€
1−r
A
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.
• Here we plot either as a function of X.
• For vs. X, the volume of a CSTR is:
€
FA0−rA
€
FA0−rA
or 1−rA
€
V =FA0 X − 0( )
−rA EXIT Equivalent to area of rectangleon a Levenspiel Plot
XEXIT
0.2 0.4 0.6 0.8
1020304050
€
1−r
A
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.
• 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−rA
€
FA0−rA
or 1−rA
€
FA0−rA
Equivalent to area of rectangleon a Levenspiel Plot
XEXIT
€
VPFR = FA 0
−rA0
X
∫ dX
€
V =FA0 X − 0( )
−rA EXIT
= area under the curve=area
0.2 0.4 0.6 0.8
1020304050
€
1−r
A
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