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 21

Today’s lectureCSTR With Heat Effects

Multiple Steady StatesIgnition and Extinction Temperatures

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CSTR with Heat Effects

Courtesy of Pfaudler, Inc.

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dtEd

HFHFWQ sysn

1iii

n

1i0i0iS

Unsteady State Energy balance

Using

PVHNPVHNENE iiiiiiisys

Neglect

dt

dNHdt

dHNdt

HNddt

dEi

ii

iiisys

dtdTC

dtdH

Pii

i0iAii FFVr

dtdN

4

We obtain after some manipulation:

Pii

ARx0iPi0iS

CNVrTHTTCFWQ

dtdT

Collecting terms with and high coolant flow rates,and

TTUAQ a

i0A0i FF 0WS

Unsteady State Energy balance

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TRTG

aP0A

0P0A

AR

Pi

0A

Pi

a0Pi0AARx

TTCF

UATTCF

VrHCN

F

CN

TTUATT0PC

CFVrH

dtdT

S

0

i

i

i

Unsteady State Energy balance

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a0P

RxA

Pi

0A

TTT1CTR

HVrTG

CNF

dtdT

0

i

TRTG

Unsteady State Energy balance

CPa0

P TT1C1

TTT1C)T(R00

7 0P0A CFUA

1

TTT a0C

8

€

dTdt

=G T( ) −R T( )

If G(T) > R(T) Temperature IncreasesIf R(T) > G(T) Temperature Decreases

Unsteady State Energy balance

0TTUATTCFXFH

XFVr

0dt

dNdtdT

a0Pi0A0ARx

0AA

A

i

0TRTG

At Steady State

Steady State Energy balance for CSTRs

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Solving for X.

Solving for X

EB

Rx

a0A

0Pi

XH

TTFUATTC

Xi

Solving for T

i

i

Pi0A

0Pi0AaRx0A

CFUATCFUATHXF

T

Steady State Energy balance for CSTRs

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1

TTT a0C

a

P0A0PRx TT

CFUATTCHX

0

0

0P0A CFUALet

CP

a0Pa0PRx

TT1C1

TTT1CTTTTCHX

0

00

Energy balance for CSTRs

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)T(RTT1C

)T(G

HX C0PRx

T TC H

Rx X CP 0 1

Rx

C0P

HTT1CX

Energy balance for CSTRs

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R(T)

TVariation of heat removal line with inlet temperature.

Increasing T0

Energy balance for CSTRs

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R(T)

T0Ta T

κ=∞

κ=0

Increase κ

Variation of heat removal line with κ (κ=UA/CP0FA0)

Energy balance for CSTRs

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T,XrXFV

A

0A

BA

1) Mole Balance: A

0A

rXFV

2) Rate Law:

AA kCr

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4) Combine:

X1Xk

X1kCXC

X1kCXFV

0A

00A

0A

0A

3) Stoichiometry: X1CC 0AA

RxRTE

RTE

Rx

RTE

RTE

HAe1

AeHXTG

Ae1Ae

k1kX

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Variation of heat generation curve with space-time.

Multiple Steady States (MSS)

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Finding Multiple Steady States with T0 varied

Multiple Steady States

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Finding Multiple Steady States with T0 varied

Multiple Steady States

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Temperature ignition-extinction curve

Multiple Steady States

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Stability of multiple state temperatures

Multiple Steady States

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CP

Rx

TTkappa1CR

HXTG

1dtdT

0

Need to solve for X after combining mole balance rate law and stoichiometry.

MSS - Generating G(T) and R(T)

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For a first order irreversible reaction

T1

T1

REexpkk

ktau1ktauX

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MSS - Generating G(T) and R(T)

Parameters

0PC11Rx C kappa, ,T ,T ,R ,E ,k ,H ,Tau

Then plot G and R as a function of T.23

End of Lecture 21

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