Lecture 2 Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of...

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

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Lecture 2 – Tuesday 1/15/2013Review 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

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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

VrdNtBatch

NA

t

dFA

dVrA

A

A

F

F A

A

drdFV

0

PFRFA

V

dFA

dW r A

A

A

F

F A

A

rdFW

0

PBRFA

W3

Reactor Mole Balances Summary

Review Lecture 1

4

CSTR – Example Problem

000

0

3

0 mindm 10

AA

A

CFC

AA

AA

CFCC

0

3

0

1.0min

dm 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

rCC

rCC

rFFV

000000

AA kCr (2) Rate Law:

(3) Stoichiometry:

0AA

AFFC

Review Lecture 1

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CSTR – Example Problem (4) Combine:

V 0 CA 0 CA

kCA

(5) Evaluate:

3

01

00

3

0

1.023.01.0110

1.0min23.0

1.0min

10

1.0

dmC

CCdm

V

CC

A

AA

AA

3 3913.2

900 dmV

Review Lecture 1

Define conversion, X

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D d C c B b A a Consider the generic reaction:

D ad C

ac B

ab A

Chose limiting reactant A as basis of calculation:

fedA moles reactedA moles X

Define conversion, X

Batch

8

VrdtdXN

dtdN

dXNdNXNNN

reactedAMoles

initiallyAMoles

remainingAMoles

AAA

AA

AAA

0

0

00

0

Batch

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X

AA Vr

dXNt0

0

Integrating,

The necessary t to achieve conversion X.

XXttXt

0 0

0

A A

A

dN r Vdt N

CSTR

10

D d C c B b A a Consider the generic reaction:

D ad C

ac B

ab A

Chose limiting reactant A as basis of calculation:

fedA moles reactedA moles X

Define conversion, X

CSTR

11

dNA

dt0Steady State

VrdVr AA

Well Mixed

V FA 0 FA

rA

CSTR

12 CSTR volume necessary to achieve conversion X.

V FA 0 FA 0 FA 0X

rA

A

A

rXFV

0

XFFFreacted

AMolesentering

AMolesleaving

AMoles

AAA 00

00 dVrFF AAA

PFR

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AA r

dVdF

XFFF AAA 00

0A

A

Fr

dVdX

XFdF AA 00 Steady State

PFR

14

XXVVXV

0 0

PFR volume necessary to achieve conversion X.

dXr

FVX

A

A

0

0

Integrating,

Reactor Differential Algebraic Integral

V FA 0X rA

CSTR

FA 0dXdV

rA

X

A

A

rdXFV

0

0PFR

VrdtdXN AA 0

0

0

X

AA Vr

dXNtBatch

X

t

FA 0dXdW

r A

X

A

A

rdXFW

0

0PBR

X

W15

Reactor Mole Balances Summaryin terms of conversion, X

Levenspiel Plots

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Reactor 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 Xgr

F

A

A

Levenspiel Plots

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FA 0

rA

X

FA 0

rA

Area = Volume of CSTR

X1

10

1

Xr

FVXA

A

18

CSTR

19

PFR

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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(

13 0

0

0

XrXrrFxdX

rFV

AAAA

X

A

A

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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

Given: rA as a function of conversion, one can also design any sequence of reactors in series by defining X:

reactorfirst tofedA of molesipoint toup reactedA of moles total Xi

Only valid if there are no side streams.

Molar Flow rate of species A at point i:

0 0Ai A A iF F F X 22

Reactors in Series

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Reactors in Series

Reactor 1:

1001 XFFF AAA

1

10

1

1000

1

101

A

A

A

AAA

A

AA

rXF

rXFFF

rFFV

V1A

0A

rF

X241X

Reactors in Series

Reactor 2:

dXr

FVX

X A

A

2

1

02

V2

A

A

rF

0

X251X 2X

Reactors in Series

00

33300200

3332

VrXFFXFFVrFF

AAAAA

AAA

V3 FA 0 X3 X2

rA 3

V3

A

0A

rF

X263X1X 2X

Reactors in SeriesReactor 3:

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Reactors in Series

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

V0

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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.

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Mole BalanceRate Laws

StoichiometryIsothermal Design

Heat Effects

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CRE Algorithm

Mole Balance

32

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

Rate Laws

Mole Balance

Rate LawsStoichiometry

Isothermal DesignHeat Effects

33Otherwise, your Algorithm becomes unstable.

End of Lecture 2

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