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 10

Lecture 10 – Tuesday 2/12/2013

2

Block 1: Mole Balances

Block 2: Rate Laws

Block 3: Stoichiometry

Block 4: Combine

Definition of Selectivity

Semibatch Reactors

Selectivity in Multiple Reactions

3

)(Undesired

(Desired)

2

2

BAUU

k

BADD

k

CCkrUBA

CCkrDBA

U

D

Selectivity Yield

Instantaneous SD/U = rD/rU

Overall ŜD/U = FD/FU

BU

AD

BAu

BAD

U

DUD

Ck

Ck

CCk

CCk

r

rS

2

2

/

)/(ˆ0 AADD FFFY

ADD rrY /

Keep CA high and CB low.

Semibatch Reactors

Semibatch reactors can be very effective in

maximizing selectivity in liquid phase reactions.

The reactant that starts in the reactor is always

the limiting reactant.

4

Semibatch reactors

A + B → C + D

5

A

B, v0

Initial V

m

Liquid level and volume increase

Semibatch Reactors

6

1) Mass Balance: mdt

dm

andm 000Vm

000 dt

dV

dt

dm

0dt

dV

0 0 VVt

tVV 00

Semibatch Reactors

7

1) Mole Balance on Species A:

dt

dNVr AA 00

V

Cr

dt

dC AA

A 0

0dt

dV

Semibatch Reactors

[in] – [out] + [gen] = [acc]

dt

dVC

dt

dCV

dt

VCd

dt

dNA

AAA ][

8

1) Mole Balance on Species B:

Semibatch Reactors

V

CCr

dt

dC BBB

B 00

000 BB CF

dt

dNVrF BBB 00

[ ]B B BB

dN d C V dC dVV C

dt dt dt dt

0dt

dV

tVV

V

Cr

dt

dC

V

Cr

dt

dC

V

CCr

dt

dC

V

Cr

dt

dC

DD

D

CC

C

BBB

B

AA

A

00

0

0

00

0

5

4

3

)( 2

1

9

Semibatch Reactors

1) Mass and Mole Balance Summary

2) Rate Laws BAA CkCr 6

3) Stoichiometry 1111

DCBA rrrr

AB rr 7

AC rr 8

AD rr 9

0

0 10A

AA

N

NNX

000 11 VCN AA

VCN AA 12

4) Parameters 0000 , , , , BA CkVC

10

Semibatch Reactors

11

Semibatch Reactors

12

Semibatch Reactors

C

DCBAAA

K

CCCCkr

Everything is the same as for the irreversible case,

except for the rate law:

Consider the following reaction:

13

AB CD

Equilibrium Conversion in Semibatch

Reactors with Reversible Reactions

14

Equilibrium Conversion in Semibatch

Reactors with Reversible Reactions

Where:

V

XNtFC ABB

00

V

XNCC ADC

0

V

XNC AA

10

At equilibrium, then 0rA

eABe

eA

BeAe

DeCe

BeAe

DeCeC

XNtFX

XN

NN

NN

CC

CCK

00

2

0

1

Xe changes with time.

15

P6-6B - Semibatch Reactors

Sodium Bicarbonate + Ethylene Chlorohydrin Ethylene Glycol + NaCl + CO2

NaCHO3 + CH2OHCH2Cl (CH2OH)2 + NaCl + CO2

A + B C + D + CO2

16

P6-6B - Semibatch Reactors

Semibatch Reactors in terms of Moles

A + B C + D + CO2

2

22

22

)5(

0

)4(

)3(

)2(

)1(

2

0

CODCBA

COCO

COCO

CD

Cc

BBb

Aa

rrrrr

VrF

VrFCO

NND

Vrdt

dNC

VrFdt

dNB

Vrdt

dNA

Stoichiometry

Mole Balances

17

000

0

0

2

0

)14(

)13(

)12(

)11(

)10(

1000)9(

44)8(

)7(

)6(

2

2

2

aa

a

aa

BAA

BB

Aa

CO

CO

CO

CVN

N

NNX

CkCr

VNC

VNC

RHO

MWRHO

MWCOFdt

dV

Rest of the Polymath Statements

Similar to Concentration Program

Rate Laws

P6-6 Semibatch: Moles, Na, Nb, etc.

19

20

21

P6-6 Semibatch: Concentrations CA, CB, CC

23

24

Three Forms of the Mole Balances applied to Semibatch Reactors:

Vrdt

dNA

A

VrFdt

dNBB

B 0

1. Molar Basis

VCr

dt

dCAA

A 0

V

CCrdt

dCBBB

B 00

Vrdt

dNA

A

VrFdt

dNBB

B 0

2. Concentration

Basis

0A

A

N

Vr

dt

dX 3. Conversion

25

Semibatch Reactors

Consider the following elementary reaction:

A+B C+D

-rA=kCACB

The combined Mole Balance, Rate Law, and

Stoichiometry may be written in terms of number

of moles, conversion, and/or concentration:

Conversion Concentration No. of Moles

tV

XNtFNXk

dt

dX ABBi

00

001

VCr

dt

dCAA

A 0

V

CCrdt

dCBBA

B 00

Vrdt

dNA

A

VrFdt

dNBA

B 0

26

Semibatch Reactors

27

Polymath Equations

End of Lecture 10

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