Chapter 1 Lecture Note Part 2

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

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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:

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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 

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Diffusion in Porous Spheres • Shell balance:

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



where,

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=

= k" C A

3  coth   1



 S g ρck " DA

1

Total radius of catalyst pellet

2

R0

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• 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

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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

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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