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CH – 5010
Chemical Reactor Theory
Modules 5 & 6: Diffusion in Fluid-Solid Reactions
Dr. Niket Kaisare
Chemical Engineering, IIT Madras
Additional Reading
• This module derives material from
• Davis and Davis, Ch. 6
• Froment and Bischoff, Ch. 3
• To relate to your UG Material:
• Fogler, Ch. 11
Some notations
•
A A B
Processes in a Catalytic Reactor
Porous
catalyst
A(bulk)
A(s)
A
A*
P*
P(s)
P(bulk)
External
diffusion
Internal
diffusion
Reaction
Adsorption Desorption
Surface
Reaction
Previous and upcoming modules:
4. Reaction
5. External diffusion
6. Internal diffusion
Reactor
Overview: Particle and Reactor-Level Aspects
Analysis at the Level of an Individual Particle
Porous
catalyst
A(bulk)
A(s)
A
A*
P*
P(s)
P(bulk)
External
diffusion
Internal
diffusion
Reaction
Diffusion
Fundamentals
A Thought Problem
Species Flux
• Individual Species Balance (From Module-1):
Species Flux
•
Stefan-Maxwell Diffusion
•
Special Case: Binary Diffusion
•
Multi-Component Mixture
•
Special Cases
•
External Diffusion in Catalyst
External Diffusion Examples
Catalyst Pellet
Catalyst Foil/Plate
Catalytic Channel
Diffusion in the Boundary Layer
•
CA,b
CA,s
Analysis of boundary layer
•
CA,b
CA,s
𝛿
Mass Transfer Coefficient
•
Units are different for the three coefficients
Concept remains the same:
Flux (mol/m2
.s) = k * driving_force
Equivalence with Heat Transfer
•
Overall Balance for Surface Reaction
•
Mass Transfer Correlations
•
Analogy between heat / mass transfer
•
Internal Diffusion in Catalyst
“Continuum Model” for Internal Diffusion
• CA,s
CA,s
CA,s
Effective Diffusivity
•
Internal Diffusion: First-Order Reaction
•
Consider the three cases
CA,s
CA,s
CA,s
Expand the expressions similarly
Internal Diffusion in Catalyst
Recap: 19 Sept. 2023
What we have done so far
• Catalysts are (usually) highly porous
• Catalysts come in various shapes and sizes
• Small pellets (< 100 microns)
• Small spheres (< 5 mm)
• Medium spheres (< 5 cm)
• Cylinders (L/d ~ 2–5)
• “Hockey pucks” (L/d < 0.5)
• Hollow cylinders, rings, structured packing
• Wash-coated
• Ceramic or metallic foams
Diffusion to the surface
and within the catalyst pores
often becomes important
Diffusion within Pores
•
Diffusion and Reaction within a Porous Catalyst
•
Diffusion and Reaction within a Porous Catalyst
• •
Example: Solving for Rectangular Slab
CA,s
Remember the boundary conditions
at y = 0 and y = L
Example: Solving for Rectangular Slab
CA,s
Remember the boundary conditions
at y = 0 and y = L
Solution for First Order Reaction
Thiele Modulus
”
”
”
”
Effectiveness Factor
Which implies
Effectiveness Factor
Which implies
Final Solutions for the Three Cases
CA,s
CA,s
CA,s
Generalized Thiele Modulus
• •
Generalized Thiele Modulus
Module 6:
Internal Mass Transfer with Reactions in Solids
Tutorial Problem
Example: Similar to the Previous Tutorial
•

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M6-Int_Diffusion.pptx.pdf