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

mechanisms of chemical reactions andthe design of the reactors in which they

take place.

Lecture 4

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Lecture 4 Tuesday 1/18/2011Block 1

Size CSTRs and PFRs given r A=f(X)Block 2

Reaction Orders Arrhenius Equation

Block 3

Stoichiometric TableDefinitions of ConcentrationCalculate the Equilibrium Conversion, X e

2

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Reactor Differential Algebraic Integral

A

A

r

X F V 0CSTR

A A r dV dX F 0

X

A A r dX F V 0

0PFR

V r

dt

dX N A A 0

0

0

X

A

A V r dX

N t Batch

X

t

A A r dW

dX F 0

X

A A

r

dX F W

00

PBR

X

W3

ReviewLecture 2

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F A 0

r A

X

ReviewLecture 2

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F A 0r A

Are a = Volume of PF

V 0

X 1 F A 0

r A

dX

X 1

ReviewLecture 2

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6

reactor firsttofedAof molesi pointtoupreactedAof moles

X i

Only valid if there are no side streams

ReviewLecture 2

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7

ReviewLecture 2

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Two steps to get

Step 1: Rate Law

Step 2: Stoichiometry

Step 3: Combine to get

r A f X

r A

g C i

C i h X

r A f X

ReviewLecture 2

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BAA CkCr

Order RectionOverall

Binorder

AinorderPower Law Model

9

C3BA2 A reactor follows an elementary rate law if the

reaction orders just happens to agree with thestoichiometric coefficients for the reaction as written.e.g. If the above reaction follows an elementary ratelaw B

2AAA CCk r

ReviewLecture 3

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E = Activation energy (cal/mol)R = Gas constant (cal/mol*K)T = Temperature (K)

A = Frequency factor (same units as rate constant k)(units of A, and k, depend on overall reaction order)

10

RT E Aek

T k AT 0 k 0

A 10 13

T

k

ReviewLecture 3

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These topics build upon one another

Mole Balance Rate Laws Stoichiometry

11

ReviewLecture 3

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r A f X

r A g C i Step 1: Rate Law

C i h X Step 2: Stoichiometry

r A f X Step 3: Combine to get

12

ReviewLecture 3

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We shall set up Stoichiometry Tables using species A as our basis of calculation in the followingreaction. We will use the stochiometric tables toexpress the concentration as a function ofconversion. We will combine C i = f(X) with theappropriate rate law to obtain -r A = f(X).D

a

dC

a

cB

a

bA

A is the limiting Reactant.

13

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N A N A 0 N A 0 X

N B N B 0 b

a N A 0 N A 0 N B 0 N A 0

b

a X

For every mole of A that react, b /a moles of B react.Therefore moles of B remaining:

Let B = N B0 /N A0

Then:

N B N A 0 B ba X

N C N C 0 c

a N A 0 X N A 0 C

c

a X

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Species

Symbol

Initial Change Remaining

B B N B0 =N A0 B -b/aN A0 X N B=N A0 ( B-b/aX)

A A N A0 -N A0 X N A=N A0 (1-X)

Inert I N I0 =N A0 I ---------- N I =N A0 I

F T0 N T =N T0 +N A0 X

Wher e: 0

0

0

0

00

00

0

0

A

i

A

i

A

i

A

ii y

yC C

C C

N N

1

ab

ac

ad and

C C N C0 =N A0 C +c/aN A0 X N C =N A0 ( C +c/aX )D D N D0 =N A0 D +d/aN A0

XN D=N A0 ( D+d/aX)

15 = change in total number of mol per mol Areacted

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Note: If the reaction occurs in the liquid phaseor

if a gas phase reaction occurs in a rigid (e.g. steel)

batch reactorV V 0Then

C A N A

V N A 0 1 X

V 0C A 0 1 X

C B N B

V N A 0

V 0 B

ba

X

C A 0 B ba

X

etc.16

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Suppose r A k AC A2

C B

Batch: 0VV

17

r A k AC A 0 2 1 X 2

B ba X

Equimolar feed: B 1

Stoichiometric feed: B ba

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r A f X and we have

if r A k A C A2 C

B then

r A C A 03

1 X 2 B ba

X

Constant Volume Batch

18

Ar

1

X

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Consider the following elementary reaction withKC=20 dm 3/mol and C A0 =0.2 mol/dm 3.Xe for both a batch reactor and a flow reactor.

Calculating the equilibrium conversionfor gas phase reaction,X e

C

B2AAA K

CCk r

BA2

19

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Step 1: dX dt

r AV N A 0

30 2.0 dmmol C A

mol dm K C 3 20

Step 2: rate law, BB2AAA Ck Ck r

Calculate X e

B

AC

k

k K

C

B2AAA K

CCk r

20

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Symbol

Initial Change Remaining

B 0 N A0 X N A0 X/2

A N A0 -N A0 X N A0 (1-X)

Totals: N T0=N A0 NT=N A0 -N A0 X/2

@ equilibrium: -r A=0C

Be2Ae K

CC0

K e C BeC Ae

2 C Ae N Ae

V C A 0 1 X e

C Be C A 0 X e

221

Calculate X e

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Species Initial Change Remaining A N A0 -N A0 X N A=N A0 (1-X)B 0 +N A0 X/2 N B=N A0 X/2

NT0=N A0 NT=N A0 -N A0 X/2

S o l u t i o n :

2Ae

BeC C

CK

C

Be2AeAA K

CCk 0r At equilibrium

0VV 2/BAStoichiometry

ConstantvolumeBatch

Calculating the equilibrium conversion

for gas phase reaction

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2e0Ae

2e0A

e0A

eX1C2

X

X1C2

XC

K

82.0202

X1

XCK 2 2

e

e0Ae

X eb 0.703

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A A F A0 -F A0 X F A=F A0 (1-X)

Species

Symbol

ReactorFeed

Change

ReactorEffluent

B B F B0=F A0 B -b/aF A0 X

FB=F A0 ( B-b/aX)

i F i0

F A 0

C i 0 0

C A 0 0

C i0

C A 0

yi 0

y A 0Where:

Flow System Stochiometric Table

24

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Species Symbol ReactorFeed Change ReactorEffluent

0A

0i

0A

0i

00A

00i

0A

0ii y

yCC

CC

FFWhere:

Inert I F I0= A0 I ---------- F I=F A0 I FT0 F T=F T0+F A0 X

C C F C0 =F A0 C +c/aF A0 X F C=F A0 ( C+c/aX)

D D F D0=F A0 D +d/aF A0 X F D=F A0 ( D+d/aX)

1a

bac

adand

A

A

F

CConcentration Flow System

25

Flow System Stochiometric Table

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Species Symbol Reactor Feed Change Reactor Effluent

A A F A0 -F A0 X F A=F A0 (1-X)

B B F B0=F A0 B -b/aF A0 X F B=F A0 ( B-b/aX)

C C F C0 =F A0 C +c/aF A0 X F C=F A0 ( C+c/aX)

D D F D0=F A0 D +d/aF A0 X F D=F A0 ( D+d/aX)

Inert I F I0=F A0 I ---------- F I=F A0 I

FT0 F T=F T0+F A0 X

0A

0i

0A

0i

00A

00i

0A

0ii y

yCC

CC

FF

1a

bac

adWhere: and

AA

FCConcentration Flow System

26

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AA

FCConcentration Flow System:

0Liquid Phase Flow System:

C A F A

F A 0 1 X

0 C A 0 1 X

C B N B

N A 0

0

B ba

X

C A 0 B ba

X

Flow Liquid Phase

etc.

27

We will consider C A and C B for gas phasereactions in the next lecture

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Mole Balance

Rate LawsStoichiometry

Isothermal Design

Heat Effects

28

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End of Lecture 4

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