Part II, Measures Other Than Conversion I · 2. Applications/Examples of the CRE Algorithm II Apr/07 2011 Spring 4 Reactor Mole Balance Rate Law Stoichiometry Batch CSTR PFR ³ X

Part II, Measures Other Than Conversion I

Apr/07 2011 Spring 1

Part II, Measures Other Than Conversion II


2. Applications/Examples of the CRE Algorithm I


Gas Phase

Elementary

Reaction

Additional Information

Only A fed P0 = 8.2 atm

T0 = 500 K CA0 = 0.2 mol/dm3

k = 0.5 dm3/mol·s vo = 2.5 dm3/s

Solve for X = 0.9 for A is limiting

2A → B

2. Applications/Examples of the CRE Algorithm II


Reactor Mole Balance Rate Law Stoichiometry

Batch

CSTR

PFR

X

A

AVr

dXNt

00

A

A

r

XFV

0

X

A

Ar

dXFV

00

2

AkCrA

2

AkCrA

2

AkCrA

Gas:

V = V0

Gas:

T =T0, P =P0

Gas:

T =T0, P =P0

2. Applications/Examples of the CRE Algorithm III


Reactor Stoichiometry 2

Batch

CSTR

PFR

Per mole A ?

Per mole A

A → ½B

ε = 1.0(1- ½) = -0.5

Per mole A

A → ½B

ε = 1.0(1- ½) = -0.5

)1(

)1(

A0

0

A0AA

XC

V

XN

V

NC

)ε1(

)1(

)ε1(

)1(

A0

0

A0AA

X

XC

Xv

XF

v

FC

2. Applications/Examples of the CRE Algorithm IV


Reactor Stoichiometry 3

Batch

CSTR

PFR

2

)2

1(

A0

0

A0B

B

XC

V

XN

V

NC

)ε1(2

)ε1(

)2

1(

A0

0

A0B

B

X

XC

Xv

XF

v

FC

2. Applications/Examples of the CRE Algorithm V


Reactor Combine Integration

Batch

CSTR

PFR

X

dXXkC

t0 2

A0 )1(

11

22

A0

2

0

)1(

)5.01(

XkC

XXFV A

X

dXX

X

kC

FV

0 2

2

2

A0

A0

)1(

)5.01(

)1(

1

A0 X

X

kCt

X

XX

X

kC

FV

1

)ε1(ε

)1ln()ε1(ε2

222

A0

A0

2. Applications/Examples of the CRE Algorithm VI


Reactor Evaluate For X = 0.9

Batch

CSTR

PFR

kCA0 = (0.5)(0.2)

= 0.1 s-1

kC2A0 = (0.5)(0.2)2

= 0.02mol/dm3·s

FA0 = CA0·v0

= (0.2)(2.5) = 0.5 mol/s

t = 90 s

V = 680.6 dm3

τ = V/v0 = 272.3 s

V = 90.7 dm3

τ = V/v0 = 36.3 s

7. Mole Balances on 4 Basic Reactors I


o Liquid phase

Batch and

CSTR and

PFR and

PBR and

AA r

dt

dC A

B ra

b

dt

dC

A

AA00 )(

r

CCvV

A

BB00

)/(

)(

rab

CCvV

AA

0 rdV

dCv A

B0 r

a

b

dV

dCv

'

AA

0 rdW

dCv '

AB

0 ra

b

dW

dCv

D C B A a

d

a

c

a

b

7. Mole Balances on 4 Basic Reactors II


o Gas phase 1

T

T

P

P

F

Fvv 0

0T

T00

T

T

P

P

F

F

v

F

v

FC 0

0T

T0

0

AAA

0

0T0

0

0T

T0AT0A ,

RT

PC

T

T

P

P

F

F

v

FCC

7. Mole Balances on 4 Basic Reactors III


o Gas phase 2

1. Mole balances

BatchCSTR PFR

D C B A a

d

a

c

a

b

Vrdt

dNA

A

Vrdt

dNB

B

Vrdt

dNC

C

Vrdt

dND

D

A

AA0

r

FFV

B

BB0

r

FFV

C

CC0

r

FFV

D

DD0

r

FFV

AA r

dV

dF

BB r

dV

dF

CC r

dV

dF

DD r

dV

dF

7. Mole Balances on 4 Basic Reactors IV


o Gas phase 3

2. Rate law

3. Stoichiometry

- Relative rate

- Then

- Concentration

β

B

α

AAA CCkr

d

r

c

r

b

r

a

r DCBA

AB ra

br

AC ra

cr AD r

a

dr

yT

T

F

FCC

0

T

AT0A y

T

T

F

FCC

0

T

B0TB y

T

T

F

FCC

0

T

CT0C

yT

T

F

FCC

0

T

D0TD

000T

T ,2 P

Py

T

T

F

F

ydW

dy

7. Mole Balances on 4 Basic Reactors V


o Gas phase 4

- Total molar flow rate

4. Combine

- Specify parameter values

- Specify entering numbers

IDCBAT FFFFFF

β

T

B

α

T

Aβα

T0AA

F

F

F

FCk

dV

dFβ

T

B

α

T

Aβα

T0AB

F

F

F

FCk

a

b

dV

dF

β

T

B

α

T

Aβα

T0AC

F

F

F

FCk

a

c

dV

dFβ

T

B

α

T

Aβα

T0AD

F

F

F

FCk

a

d

dV

dF

dcbaTCk ,,,,βα,,, ,0T0A

0000 ,,, DCBA FFFF

8. Microreactors I


o Description

- High surface area-to-volume ratio in their micro

structure regions

• 100μm width, 20,000μm length (2 cm)

• high surface area-to-volume ratio

☞ ca. 10,000 m2/m3

reduce or eliminate heat & mass transfer resistances

• to study intrinsic kinetics of reactions isothermally

• production of toxic or explosive intermediates

• shorter residence time

• narrow residence time distribution

8. Microreactors II


o Example

- 32 microreaction system in parallel produce 2000 t/yr

- Lab-on-a-chip

p 204, Ex 4-7

OHCHO-RO21 OHCH-R 2Ag22

9. Membrane Reactors I


o Description

- Really just a plug-flow reactor

• contains an additional cylinder of some porous material

within it, kind of like the tube within the shell of a shell-

and-tube heat exchanger

• this porous inner cylinder is the membrane that gives the

membrane reactor its name

- The membrane is a barrier that only allows certain

components to pass through it

• selectivity of the membrane is controlled by its pore

diameter, which can be on the order of Angstroms, for

microporous layers, or on the order of microns for

macroporous layers

9. Membrane Reactors II


o What is it?

- Combine reaction

with separation to

increase

conversion and/or

selectivity

9. Membrane Reactors III


o Typical reactors 1

- IMRCF (Inert Membrane Reactor with Catalyst Pellets

on the Feed Side)

9. Membrane Reactors IV


o Typical reactors 2

- CMR (Catalytic Membrane Reactor)

9. Membrane Reactors V


o Modeling 1

- IMRCF

9. Membrane Reactors VI


o Modeling 2

- Change the algorithm a little, V → W (= ρbV)

• mole balance for A

• mole balance for C

• mole balance for B

AA r

dV

dF

CC r

dV

dF

BBB Rr

dV

dF

0

Accu.Gen.Diffusion

byOut

flowby

Out

flowby

In

BBBB

VRVRFF

VVV

9. Membrane Reactors VII


o Modeling 3

- Rate of molar flux B out through the membrane

- Rate of transport B out through the membrane

- Let kC = k’Ca and CBS ≈ 0,

p 211, Ex 4-8

)( BSB

'

CB CCkW

)( BSB

'

CBB CCakaWR

DL

D

DLa

4

4

π

π

Volume

Area2

BCB CkR

9. Membrane Reactors VIII


o Enhance selectivity

- Fed species to the reactor through the sides of

membrane

BBB Rr

dV

dF

10. Unsteady-State Operation of Stirred

Reactors I


o Startup of a CSTR 1

- Mole balance equation

- For batch reactor, conversion means little

- 1st order rxn

- With initial conditions CA = 0 at t = 0

dt

dNVrFF A

AAA0

dt

dCrCC A

AAA0 ττ

ττ

τ1 A0A

A CC

k

dt

dC

τ

t)τ1(exp1

τ1

A0A k

k

CC


Reactors II


o Startup of a CSTR 2

- Steady state analysis

• assume time to reach 99% of st-st conc., CAS

• CA0 = 0.99CAS

• for slow rxn with small k (1 » τk)

• for rapid rxn with large k (1 « τk)

☞ most 1st-order system, st-st achieved in 3 ~ 4 space time

k

CC

τ1

A0AS

kt

τ1

τ6.4S

τ6.4S t

kt /6.4S


Reactors III


o Semibatch reactor 1

- Motivation

• to obtain high selectivity

• maintain A at high conc.

• feed B as low as possible


Reactors IV



- Mole balance equation 1

dt

dNtVr A

A )(00

Accum

of Rate

Generation

of Rate

out

Rate

in

Rate

dt

dVC

dt

VdC

dt

VCdVr A

AAA

)(


Reactors V



- Mole balance equation 2

- Since the reactor is being filled, V varies

dt

Vdv

)ρ(00ρ

Accum

of Rate

Generation

of Rate

out

Rate

in

Rate

00

dt

dVC

dt

VdC

dt

VCdVr A

AAA

)(


Reactors VI



- Constant density

- With initial condition V = V0 at t = 0

- Balance on A can be rewritten as

- For B, we have generation term, rBV

• balance on B can be

0vtd

Vd

tvVV 00

A0

AA C

V

vr

dt

dC

V

CCvr

dt

dC )( BB00B

B


Reactors VII



- Design equations in terms of conversion 1

• for species A

• for species B

XNNN

tt

A0A0A

time toup

reactedA of

moles of #

initially

vatin theA of

moles of #

at time

vatin theA of

moles of #

XNdtFNN

tt

t

Bi A00

0BB

time toup

reacted B of

moles of #

vat the to

added B of

moles of #

initially

vatin the B of

moles of #

at time

vatin the B of

moles of #

A + B C + D


Reactors VIII



- Design equations in terms of conversion 2

• for a constant molar feed rate & no B initially

• mole balance on species A

• for a reversible 2nd order rxn

• recalling

XNtFN 0A0BB

dt

dXN

dt

dNVr A0

AA

C

DCBAA

K

CCCCkr

tvV

XN

V

NC

00

0AAA

)1(

tvV

XNtFN

V

NC i

00

0A0BBBB

tvV

XNC

00

0AC

tvV

XNC

00

0AD

tvV

KXNXNtFNXk

dt

dX i

00

C

2

0A0A0BB )/())(1(

tvVV 00

A + B C + D


Reactors IX



- Equilibrium conversion 1

• at time t, equilibrium conversion

• for

A + B C + D

ee

ee

ee

ee

ee

ee

NN

NN

V

N

V

N

V

N

V

N

CC

CCK

BA

DC

BA

DC

BA

DCC

XNtFN ABB 00

)1

( then,

))(1())(1(

))((

2

C

0BC

0A

0A0B

2

0A

0A0B0A

0A0AC

e

ee

ee

e

ee

ee

X

XXK

FK

Nt

XNtFX

XN

XNtFXN

XNXNK


Reactors X



- Equilibrium conversion 2

• at a semibatch reactor

A + B C + D

)1(2

)1(411

C

0A

0BCC

2

0A

0BC

0A

B0C

K

N

tFKK

N

tFK

N

tFK

X e


Reactors XI


o Reactive distillation

- Applicable to reversible, liquid phase reactions

• the equilibrium point lies far to

the left and little product is formed

• if one or more of the products are removed more of

the product will be formed because of Le Chatlier's

Principle

Documents

Part II, Measures Other Than Conversion I · 2. Applications/Examples of the CRE Algorithm II Apr/07 2011 Spring 4 Reactor Mole Balance Rate Law Stoichiometry Batch CSTR PFR ³ X