Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of

chemical reactions and the design of the reactors in which they take place.

Lecture 2

1

Lecture 2

Review of Lecture 1

Definition of Conversion, X

Develop the Design Equations in terms of X

Size CSTRs and PFRs given –rA= f(X)

Conversion for Reactors in Series

Review the Fall of the Tower of CRE

2

Chapter 2

Reactor Differential Algebraic Integral

The GMBE applied to the four major reactor types

(and the general reaction AB)

V FA 0 FA

rA

CSTR

Vrdt

dNA

A

0

A

A

N

N A

A

Vr

dNtBatch

NA

t

dFA

dV rA

A

A

F

F A

A

dr

dFV

0

PFR

FA

V

dFA

dW r A

A

A

F

F A

A

r

dFW

0

PBRFA

W3

Reactor Mole Balances Summary

Review Lecture 1

4

CSTR – Example Problem

000

0

3

0 mindm 10

AA

A

CF

C

AA

AA

CF

CC

0

3

0

1.0

mindm 10

0

FA 0CA

Liquid phase

V ?

Given the following information, Find V

Review Lecture 1

5

CSTR – Example Problem

(1) Mole Balance:

A

AA

A

AA

A

AA

r

CC

r

CC

r

FFV

000000

AA kCr

(2) Rate Law:

(3) Stoichiometry:

0AA

A

FFC

Review Lecture 1

6

CSTR – Example Problem

(4) Combine:

V 0 CA 0 CA

kCA

(5) Evaluate:

3

0

1

00

3

0

1.023.0

1.0110

1.0min23.0

1.0min

10

1.0

dmC

CCdm

V

CC

A

AA

AA

3 3913.2

900dmV

Review Lecture 1

Define conversion, X

7

D d C c B b A a

Consider the generic reaction:

D a

d C

a

c B

a

b A

Chose limiting reactant A as basis of calculation:

fedA moles

reactedA moles X

Define conversion, X

Chapter 2

Batch

8

Vrdt

dXN

dt

dN

dXNdN

XNNN

reacted

AMoles

initially

AMoles

remaining

AMoles

AAA

AA

AAA

0

0

00

0

Chapter 2

Batch

9

X

A

AVr

dXNt

0

0

Integrating,

The necessary t to achieve conversion X.

XXtt

Xt

0 0

0

A A

A

dN r V

dt N

Chapter 2

CSTR

10

D d C c B b A a

Consider the generic reaction:

D a

d C

a

c B

a

b A

Chose limiting reactant A as basis of calculation:

fedA moles

reactedA moles X

Define conversion, X

Chapter 2

CSTR

11

dNA

dt 0Steady State

VrdVr AA

Well Mixed

V FA 0 FA

rA

Chapter 2

CSTR

12 CSTR volume necessary to achieve conversion X.

V FA 0 FA 0 FA 0X

rA

A

A

r

XFV

0

XFFF

reacted

AMoles

entering

AMoles

leaving

AMoles

AAA 00

00 dVrFF AAA

Chapter 2

PFR

13

AA r

dV

dF

XFFF AAA 00

0A

A

F

r

dV

dX

XFdF AA 00Steady State

Chapter 2

PFR

14

XXVV

XV

0 0

PFR volume necessary to achieve conversion X.

dXr

FV

X

A

A

0

0

Integrating,

Chapter 2

Reactor Differential Algebraic Integral

V FA 0X

rA

CSTR

FA 0

dX

dV rA

X

A

A

r

dXFV

0

0PFR

Vrdt

dXN AA 0

0

0

X

A

AVr

dXNtBatch

X

t

FA 0

dX

dW r A

X

A

A

r

dXFW

0

0PBR

X

W15

Reactor Mole Balances Summaryin terms of conversion, X

Chapter 2

Levenspiel Plots

16

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

(FA0/-rA) or (1/-rA) as a function of X. For (FA0/-rA) vs.

X, the volume of a CSTR and the volume of a PFR

can be represented as the shaded areas in the

Levenspiel Plots shown as:

)(0 Xgr

F

A

A

Chapter 2

Levenspiel Plots

17

FA 0

rA

X

Chapter 2

FA 0

rA

X 1

Area = Volume of CSTR

10

1

Xr

FV

XA

A

18

CSTR

Chapter 2

19

PFR

Chapter 2

20

Levenspiel Plots

Chapter 2

Numerical Evaluations of Integrals

The integral to calculate the PFR volume can be

evaluated using method as Simpson’s One-Third

Rule: (See Appendix A.4)

)(

1

)2/(

4

)0(

1

30

0

0

XrXrrF

xdX

r

FV

AAA

A

X

A

A

21

Other numerical methods are:

Trapezoidal Rule (uses two

data points)

Simpson’s Three-Eight’s

Rule (uses four data points)

Five-Point Quadrature

Formula

)(

1

2XrA

)(

1

1XrA

)0(

1

Ar

Ar

1

0 1X 2X

Chapter 2

Given: rA as a function of conversion, one can also

design any sequence of reactors in series by defining

X:

reactorfirst tofedA of moles

ipoint toup reactedA of moles total Xi

Only valid if there are no side streams.

22

Reactors in Series

Molar Flow rate of species A at point i:

0 0Ai A A iF F F X

Chapter 2

23

Reactors in Series

Chapter 2

Reactor 1:

1001 XFFF AAA

1

10

1

1000

1

101

A

A

A

AAA

A

AA

r

XF

r

XFFF

r

FFV

24

V1

A

0A

r

F

X1X

Reactors in Series

Chapter 2

Reactor 2:

dXr

FV

X

X A

A

2

1

02

25

V2

A

A

r

F

0

X1X 2X

Reactors in Series

Chapter 2

0

0

33300200

3332

VrXFFXFF

VrFF

AAAAA

AAA

V3 FA 0 X3 X2

rA 3

26

V3

A

0A

r

F

X 3X1X 2X

Reactors in Series

Reactor 3:

27

Reactors in Series

Space time τ is the time necessary to process 1

reactor volume of fluid at entrance conditions.

V

0

28

Reactors in Series

Chapter 2

KEEPING UP

The tower of CRE, is it stable?

29

Chapter 2

Reaction Engineering

Mole Balance Rate Laws Stoichiometry

These topics build upon one another.

30

Algorithm

Mole Balance

Rate Laws

Stoichiometry

Isothermal Design

Heat Effects

31

CRE Algorithm

Algorithm

Mole Balance

32

Be careful not to cut corners on any of the

CRE building blocks while learning this material!

Rate Laws

Algorithm

Mole Balance

Rate Laws

Stoichiometry

Isothermal Design

Heat Effects

33

Otherwise, your Algorithm becomes unstable.

Algorithm

End of Lecture 2

34