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