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CHAPTER 1 (Lecture Note Part 2)

CATALYTIC REACTION AND MASS TRANSFER

Subtopic covered in Chapter 1… Catalytic Reactions and Reactors Surface and Enzyme Reaction Rates Introduction of Porous Catalyst Transport and Reaction External Mass Transfer Pore Diffusion Temperature Dependence of Catalytic Reaction Rates Langmuir-Hinshelwood Kinetic Mechanism Catalytic Wall Reaction Application of Reaction Engineering in Microelectronic Fabrication Catalyst Deactivation

Steps in Catalytic Reaction External diffusion Internal diffusion Adsorption Surface reaction

External diffusion

Internal diffusion Desorption

Pore Diffusion r" k"C As

FACULTY OF CHEMICAL ENGINEERING

Pores in Pellet

Or

Diffusion in Single Pore • A shell balance: [Net flux in at x] – [net flux out at x+dx]= [rate of reaction on wall between x and x+dx]

• Assuming the single pore is cylinder, the shell balance for a first-order reaction is:

Diffusion in Single Pore (cont.)

• Letting dx 0 and then dividing the equation by dx yields:

CPE624

FACULTY OF CHEMICAL ENGINEERING

Diffusion in Single Pore (cont.) • Average rate within the pore: l

actual rate d p

k"C

A( x ) dx

x 0

• Rate in the pore if the concentration remained at CAs:

ideal rate [area] r" d p lk"C As actual rate ideal rate

Thiele modulus

• Effectiveness factor () – fraction which the rate is reduced by pore diffusion limitations

1 e e

e e

tanh

1

4k " 2 l l d pDA

Diffusion in Single Pore (cont.) • Thus,

r" k"C As • Relation between and η can be seen by the following log-log plot:

• The limits of η: – Φ « 1, – Φ=1 – Φ»1

η=1 η = 0.762 η = 1/ϕ

no pore diffusion limitation some limitation strong pore diffusion limitation

Diffusion in Honeycomb Catalyst

• The honeycomb porous slab is just a collection of many cylindrical pores so the solution is exactly the same as we have just worked out for a single pore.

Diffusion in Porous Catalyst Slab

• Consider slab with average diameter dp and length, l with irregular pores:

tanh

???

1

2 S k " g c l DA

CPE624

FACULTY OF CHEMICAL ENGINEERING

Diffusion in Porous Spheres • Shell balance:

1 d dC A R 2D A dR R 2 dR

where,

CPE624

=

= k" C A

3 coth 1

S g ρck " DA

1

Total radius of catalyst pellet

2

R0

FACULTY OF CHEMICAL ENGINEERING

• While the expressions for () appear quite differently for different catalyst geometry, they are in fact very similar when scaled appropriately, and they have the same asymptotic behavior:

• In consideration of the internal diffusion effect, the pseudo homogeneous rate of a catalytic reaction in a reactor with porous catalyst pellets can be written as: r rideal

Temperature Dependence of Catalytic Reaction Rates • Limiting rate expression for catalytic reaction rates: – r ≈ (area/volume) k”Cab – r ≈ (area/volume) kmACAb – r ≈ (area/volume) k”Cabη

Rate limiting step

CPE624

reaction limited external mass transfer limited pore diffusion limited

Temperature dependence

Reaction

Activation energy E

Mass transfer

Nearly constant

Pore diffusion

Activation energy E/2

FACULTY OF CHEMICAL ENGINEERING

CPE624

FACULTY OF CHEMICAL ENGINEERING

Answer: 14.7 cm

Schmidt, L.D. (1998). The Engineering of Chemical Reactions, New York: Oxford University Press

Schmidt, L.D. (1998). The Engineering of Chemical Reactions, New York: Oxford University Press

Answer: 190 cm

Answer: 548 cm

Schmidt, L.D. (1998). The Engineering of Chemical Reactions, New York: Oxford University Press

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CATALYTIC REACTION AND MASS TRANSFER

Subtopic covered in Chapter 1… Catalytic Reactions and Reactors Surface and Enzyme Reaction Rates Introduction of Porous Catalyst Transport and Reaction External Mass Transfer Pore Diffusion Temperature Dependence of Catalytic Reaction Rates Langmuir-Hinshelwood Kinetic Mechanism Catalytic Wall Reaction Application of Reaction Engineering in Microelectronic Fabrication Catalyst Deactivation

Steps in Catalytic Reaction External diffusion Internal diffusion Adsorption Surface reaction

External diffusion

Internal diffusion Desorption

Pore Diffusion r" k"C As

FACULTY OF CHEMICAL ENGINEERING

Pores in Pellet

Or

Diffusion in Single Pore • A shell balance: [Net flux in at x] – [net flux out at x+dx]= [rate of reaction on wall between x and x+dx]

• Assuming the single pore is cylinder, the shell balance for a first-order reaction is:

Diffusion in Single Pore (cont.)

• Letting dx 0 and then dividing the equation by dx yields:

CPE624

FACULTY OF CHEMICAL ENGINEERING

Diffusion in Single Pore (cont.) • Average rate within the pore: l

actual rate d p

k"C

A( x ) dx

x 0

• Rate in the pore if the concentration remained at CAs:

ideal rate [area] r" d p lk"C As actual rate ideal rate

Thiele modulus

• Effectiveness factor () – fraction which the rate is reduced by pore diffusion limitations

1 e e

e e

tanh

1

4k " 2 l l d pDA

Diffusion in Single Pore (cont.) • Thus,

r" k"C As • Relation between and η can be seen by the following log-log plot:

• The limits of η: – Φ « 1, – Φ=1 – Φ»1

η=1 η = 0.762 η = 1/ϕ

no pore diffusion limitation some limitation strong pore diffusion limitation

Diffusion in Honeycomb Catalyst

• The honeycomb porous slab is just a collection of many cylindrical pores so the solution is exactly the same as we have just worked out for a single pore.

Diffusion in Porous Catalyst Slab

• Consider slab with average diameter dp and length, l with irregular pores:

tanh

???

1

2 S k " g c l DA

CPE624

FACULTY OF CHEMICAL ENGINEERING

Diffusion in Porous Spheres • Shell balance:

1 d dC A R 2D A dR R 2 dR

where,

CPE624

=

= k" C A

3 coth 1

S g ρck " DA

1

Total radius of catalyst pellet

2

R0

FACULTY OF CHEMICAL ENGINEERING

• While the expressions for () appear quite differently for different catalyst geometry, they are in fact very similar when scaled appropriately, and they have the same asymptotic behavior:

• In consideration of the internal diffusion effect, the pseudo homogeneous rate of a catalytic reaction in a reactor with porous catalyst pellets can be written as: r rideal

Temperature Dependence of Catalytic Reaction Rates • Limiting rate expression for catalytic reaction rates: – r ≈ (area/volume) k”Cab – r ≈ (area/volume) kmACAb – r ≈ (area/volume) k”Cabη

Rate limiting step

CPE624

reaction limited external mass transfer limited pore diffusion limited

Temperature dependence

Reaction

Activation energy E

Mass transfer

Nearly constant

Pore diffusion

Activation energy E/2

FACULTY OF CHEMICAL ENGINEERING

CPE624

FACULTY OF CHEMICAL ENGINEERING

Answer: 14.7 cm

Schmidt, L.D. (1998). The Engineering of Chemical Reactions, New York: Oxford University Press

Schmidt, L.D. (1998). The Engineering of Chemical Reactions, New York: Oxford University Press

Answer: 190 cm

Answer: 548 cm

Schmidt, L.D. (1998). The Engineering of Chemical Reactions, New York: Oxford University Press

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