Chemical Reaction Engineering

(S1.2012)Fogler Chapter 11

External Diffusion Effects on Heterogeneous Reactions

Gia Hung Pham

Catalysis reactor types

1. Two phase reactor

- Fixed bed reactor

- Fluidized bed reactor

2. Three phase reactor

- Slurry reactor

Fixed bed reactor

Lit.: Jens Hagen; Industrial Catalysis A Practical Approach; Wiley-VCH; 1999

Fluidised bed reactor

Gas

Gas

Solid catalyst

Reactor

Cyclone

Compare: Fixed bed and Fluidised bed reactor

1. Catalyst pellet size

Fixed bed reactor : large (Heat and mass transfer will influence the rate and product selectivity)

Fluidised bed reactor: small

2. Catalyst weight

Fixed bed reactor requires much more catalyst than fluidised bed reactor.

3. Temperature control

Fixed bed reactor: bad, non-isothermal operation and hot spots ruin the catalyst.

Fluidised bed reactor: very good (rapid mixing of solid)

4. Pressure drop

Fixed bed reactor: high

Fluidised bed reactor: low

5. Catalyst deactivation - regeneration

Fixed bed reactor: less advantages (not suitable)

Fluidised bed reactor: more advantages

6. Scale-up

Fixed bed reactor: easy

Fluidised bed reactor: difficult

Three phase reactor

Lit.: Jens Hagen; Industrial Catalysis A Practical Approach; Wiley-VCH; 1999

Notes: reaction rate units

smmolCkdt

dN

Vr A

AA

3/1

sgmolCkdt

dN

wr catA

AA /

1 ''

smmolCkdt

dN

Sr A

AA

2'''' /1

Chapter 11: External diffusion effects on heterogeneous reaction

Effective reaction rate constant

Two steps involve in the reaction (External mass transfer and surface reaction )

Catalyst pellet

1

4Gas

Boundary layer

δ

CAb

CAs

A

P

4

1

P

Reaction first-order

A P

External mass transfer

Fick’s law

with

- kc : Mass transfer coefficient (m/s)

- DAB : Diffusion coefficient (m2/s) (is a function of T and P)

- δ : Boundary layer thickness (m) (is unknown, depends on fluid velocity, particle diameter, viscosity, density, temperature….)

- JAZ: average molar flux from the bulk fluid to the surface (mol/m2.s)

AsAbcA

ABAz CCkdz

dCDJ

AB

c

Dk

Concentration

Positional coordinate

Gasδ Cat

CAb

CAs

Mass transfer rate

Surface reaction rate (first order reaction)

Determination of CAs

At steady state rMT = rs

)( AsAbcMTAZ CCkrJ

AsrS Ckr

AsrAsAbc CkCCk )(

rc

AbcAs

kk

CkC

Derive the effective reaction rate

keff

Rate limiting1. Mass transfer is faster than surface reaction rate

kc » kr we have kc + kr ≈ kc

keff = kr

2. Surface reaction is faster than mass transfer kr » kc we have kc + kr ≈ kr

keff = kc

Ab

rc

rceffA C

kk

kkr

,

,

Determination of kc by using correlation equation

Sherwood number

Flow over a sphere

Reynolds and Schmidt number

u : fluid flow velocity (m/s)

l : characteristic length (particle diameter) (m)

ν : kinematic viscosity (m2/s)

kc increases with increasing fluid velocity. (Why ?)

AB

c

D

lkSh

3/12/1Re6.02 ScSh

ABDSc

luRe

Frossling correlation

From Sherwood number and Frossling correlation equation

3/12/1Re6.02 ScD

lk

AB

c

l

D

D

luk AB

AB

c

3/12/1

6.02

Fluid velocity affects kc

Effect of fluid velocity on the effective reaction rate

reff

u

With mass transfer effect

Without mass transfer effect

Example: Rapid reaction on a catalyst surface

Determine the effective rate of reaction per unit surface area of catalyst.

l = dp = 1 cm

CAs = 0 mol/L

CAb = 1 mol/L

u = 0.1 m/s

ν = 0.5x10-6 m2/s

Catalyst pellet

1

4

Fluid

Boundary layer

δ

CAb

CAs

A

PP

Reaction first-order

A P

DAB = 10-10 m2/s

Solution

AsAbcMT CCkr

7.460Re6.02 3/12/1 ScD

dkSh

AB

pc

2000105.0

1.0()01.0(Re

126

1

sm

msmud p

500010

1051210

127

sm

sm

DSc

AB

161210

1061.401.0

7.46010

msm

sm

d

ShDk

p

ABc

CAb = 103 mol/m3

rMT = 4.61x10-6 m/s x (103 – 0) mol/m3 = 4.61x10-3 mol/m2s

This is the effective reaction rate.

smmolr effA

23''

, /106.4

Mass transfer-limited reaction in packed bed

Reaction A + B P

At steady state

z z+∆z

Mass balance for this slice

of the catalyst bed

0''

\\ zAarFF ccAzzAzzAz

Molar rate in

Molar rate out

Molar rate of accumulation

0''

\\ zAarFF ccAzzAzzAz

Rate of generation of A per unit

Catalytic surface area (mol/s.m2)

External surface area of catalyst per volume of

catalyst bed (m2/m3)

Pd

16

Particle diameter (m)

Porosity of the bed (-)

Cross-sectional area of tube (m2)

Dividing the above equation by Ac∆z and ∆z →0

δ

flow in tube: JAz<<BAz

01 ''

cA

Az

c

ardz

dF

A

cAzAzAzcAz ABJWAF

Molar flux of A (mol/m2s)

Molecular diffusive flux (mol/m2s)

Flux of A resulting from

Bulk flow (mol/m2s)

cAAzcAzcAz AUCBAWAF

superficial velocity (m/s) = constant

Cat

SurfaceCA

CAs

)(''

AsAcArA CCkWr

= 0

AccA Cak

dz

dCU

z

U

ak

C

C cc

A

A exp0

Axial concentration profile in the reactor

CA/CA0

1

z

Integrating with the limit, at z =0, CA = CA0

0

Determine the reactor length L necessary to achieve a conversion X

At z = L

z

U

akCkr cc

AcA exp0

''

Reaction rate along the length of the reactor

0

0

A

ALA

C

CCX

LU

ak

X

cc1

1ln

In class exercise

Tubular fixed bed reactor with spherical catalyst

External mass transfer control

Calculate final conversion X of the reaction A P

Additional information:

- Catalyst bed length L = 2 m

- Catalyst bed diameter dR = 6 cm

- Bed porosity φ = 0.5

- Catalyst sphere diameter dp = 3 mm

- Superficial gas velocity U = 3 m/s

- Sherwood number Sh = 60

- Diffusion coefficient DAB = 10-7 m2/s

Solution

- Reorganise the equation

- Calculate kc

- Calculate ac (specific surface area)

- Calculate kc ac L / U

- Calculate X