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 – Tuesday 1/10/2011Review of Lecture 1Definition of Conversion, XDevelop the Design Equations in Terms of XSize CSTRs and PFRs given –rA= f(X)Conversion for Reactors in SeriesReview the Fall of the Tower of CRE

2

Reactor

Differential Algebraic Integral

V FA 0 FA

rA

CSTR

Vrdt

dNA

A 0

A

A

N

N A

A

Vr

dNtBatch

NA

t

dFA

dVrA

A

A

F

F A

A

dr

dFV

0

PFR

FA

V3

Reactor Mole Balance Summary

CSTR Homework Problem Solution

4

min

dm10

3

0

CA 0

FA 0 0CA 0

0 10dm3

min

CA 0.1CA 0

AA CF

0

FA 0CA

Liquid phase

V ?

Given the following information, Find V

(1) Mole Balance:

V FA 0 FA

rA

0CA 0 0CA

rA

0 CA 0 CA

rA

rA kCA

(2) Rate Law:

(3) Stoichiometry:

CA FA

FA

0

5

CSTR

(4) Combine:

V 0 CA 0 CA

kCA

(5) Evaluate:

CA 0.1CA 0

V

10dm3

minCA 0 0.1CA 0

0.23min 1 0.1CA 0

10 1 0.1 0.23 0.1 dm3

V 900

2.3391 dm3

6

CSTR

fedA moles

reactedA moles

X ,conversion Define

D a

d C

a

c B

a

b A

ncalculatio of basis asA reactant limiting Choose

D d C c B b A a

X

Consider the generic reaction

7

CSTR

XNNN

reacted

AMoles

initially

AMoles

remaining

AMoles

AAA 00

dXNdN AA 00

Vrdt

dXN

dt

dNAA

A 0

8

Batch

XXtt

Xt

0 0

X

AA Vr

dXNt

0

0

Integrating

The necessary t to achieve conversion X.

9

0A

AA

N

Vr

d

dN

Batch

CSTR

dNA

dt0Steady State

10

VrdVr AA

Well Mixed

V FA 0 FA

rA

V FA 0 FA 0 FA 0X

rA

A

A

r

XFV

0

CSTR volume necessary to achieve conversion X.

11

XFFF

reacted

AMoles

entering

AMoles

leaving

AMoles

AAA 00

00 dVrFF AAA

CSTR

0A

A

F

r

dV

dX

XFdF AA 00 Steady State

PFRA

A rdV

dF

XFFF AAA 00

12

PFR volume necessary to achieve conversion X.

XXVV

XV

0 0

dXr

FV

X

A

A

0

0

Integrating

13

PFR

Reactor Differential Algebraic Integral

V FA 0X

rACSTR

FA 0

dX

dV rA

X

AA r

dXFV

0

0PFR

Vrdt

dXN AA 0

0

0

X

AA Vr

dXNtBatch

X

t

FA 0

dX

dW r A

X

AA r

dXFW

0

0PBR

X

W14

Reactor Mole Balance SummaryIn terms of conversion

Levenspiel PlotsReactor SizingGiven –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 Xg

r

F

A

A

15

FA 0

rA

X

16

Levenspiel Plots

FA 0

-rA

Area = Volume of CSTR

X1

10

1

Xr

FV

XA

A

17

CSTR

FA 0

rA

Area = Volume of PFR

V 0

X1FA 0

rA

dX

X1

18

PFR

19

Levenspiel Plots

Numerical Evaluations of IntegralsThe 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

3 0

0

0

XrXrrF

xdX

r

FV

AAAA

X

A

A

20

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

Ar1

0 1X 2X

Reactors in Series

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 X i

Only valid if there are no side streams.

Molar Flow rate of species A at point i:

iAAi XFF 021

22

Reactors in Series

Reactor 1:

1001 XFFF AAA

1

10

1

1000

1

101

A

A

A

AAA

A

AA

r

XF

r

XFFF

r

FFV

V1

A

0A

r

F

X23

1X

Reactors in Series

Reactor 2:

dXr

FV

X

X A

A

2

1

02

V2

A

A

r

F

0

X24

1X 2X

Reactors in Series

Reactor 3:

0

0

33300200

3332

VrXFFXFF

VrFF

AAAAA

AAA

V3 FA 0 X3 X2

rA 3

V3

A

0A

r

F

X253X1X 2X

Reactors in Series

26

Reactors in Series

Space time τ is the time necessary to process 1 reactor volume of fluid at entrance conditions.

V

0

27

Reactors in Series

KEEPING UPThe tower of CRE, is it stable?

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Reaction Engineering

Mole Balance Rate Laws Stoichiometry

These topics build upon one another.

29

Mole Balance

Rate Laws

Stoichiometry

Isothermal Design

Heat Effects

30

CRE Algorithm

Mole Balance

31

Be careful not to cut corners on any of the CRE building blocks while learning this material!

Rate Laws

Mole Balance

Rate Laws

Stoichiometry

Isothermal Design

Heat Effects

32Otherwise, your Algorithm becomes unstable.

End of Lecture 2

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