Chemical Reaction Engineering

Chapter 2:

Conversion and Reactors in Series

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

VFA01

rA

dX

0

X

00.01

Example

0

VFA01

rA

dX

0

X

00.01

Example

0

VFA01

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

VFA0 X 0 rA EXIT Equivalent to area of rectangle

on 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

VFA0 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