7 Steps in a Catalytic Reaction  top 
1. Mass transfer (diffusion) of the reactant(s) from the bulk fluid to the external
surface of the catalyst pellet
2. Diffusion of the reactant from the pore mouth through the catalyst pores to the
immediate vicinity of the internal catalytic surface
3. Adsorption of reactant A onto the catalytic surface
4. Reaction on the surface of the catalyst
5. Desorption of the products from the surface
6. Diffusion of the products from the interior of the pellet to the pore mouth at the
external surface
7. Mass transfer of the products from the external pellet surface to the bulk fluid
We shall now focus on steps 1, 2, 6, and 7. Because the reaction below does not occur in
the bulk phase (only at the surface, at z = delta), we shall first consider steps 1 and 7.
Diffusion is the spontaneous intermingling or mixing of atoms or molecules
by random thermal motion. Mass transfer is any process in which diffusion
plays a role.
The molar flux is just the molar flow rate, F_{A}, divided by the
cross sectional area, A_{C}, normal to the flow. W_{A} =
F_{A}/A_{C}
Molar flux of A W_{A} (moles/time/area) with respect to fixed coordinate system
W_{A} = J_{A} + B_{A}
J_{A} = diffusional flux of A with respect to bulk motion, i.e. molar average velocity
B_{A} = flux of A resulting from bulk flow
One dimension for constant total concentration Ficks First Law
Gases: D_{Ab}~10^{5}m^{2}/s
Liquids: D_{Ab}~10^{9}m^{2}/s
External Diffusion Across a Stagnant Film  top 
Species A diffuses from the bulk (z=0) to a catalytic surface (z=d) where it reacts instantaneously to form B.
InOut+Generation=Accumulation
Types of Boundary Conditions1. Specify a concentration a boundary
2. Specify a flux at a boundary a) No mass transfer across a boundary [E.g., at pipe wall]
therefore
b) Reaction at a boundary
c) Diffusional flux to a boundary is equal to the convective flux away from the boundary.
e.g.,
3. Planes of Symmetry [E.g., cylinder] at 
1) Dilute concentrations (liquids)
Constant total concentration
2) Equal Molar Counter Diffusion (EMCD)
3) Diffusion through a Stagnant Film

Relaitve Rates of Diffusion and Reaction  top 
1.  Mole Balance on Species A at steady state 


Integrating: 

W_{A}=K' 

2.  Rate Law / Constitutive Equation 
Constitutive Equation 



Rate Law on Surface 

3.  Boundary Conditions 
Z=0 C_{A}=C_{A0} 

Z=d C_{A}=C_{A0} 

The rate of arrival of molecules on the surface equals the rate of reaction on the surface.




k_{C} is the mass transfer transfer coefficient. It can be found from a correlation for the Sherwood number: 

which in turn is a function of the Reynolds Number 

and the Schmidt Number 

For packed beds: 

We see if we increased the velocity by a factor of 4, then the mass transfer coefficient, and hence the rate would increase by a factor of 2. 

The flux to the surface is equal to the rate of reaction on the surface: 

Let's look at the effect of increasing the velocity. We know that k_{c} increases with increasing velocity, while k_{r} is independent of velocity. At low velocities, the reaction is diffusion limited with k_{c} >>k_{r} and r_{A}=k_{c} C_{AO} 

CASE 1 when k_{c} >>> k_{r}, then reaction is diffusion limited 

, rapid reaction on the surface, meaning that the overall reaction rate () is a function of velocity 

CASE 2 when k_{c} >>> k_{r}, then reaction is reaction rate limited 

, slow surface reaction, meaning that the overall reaction rate (W_{A}=k_{r }C_{AO}) is independent of velocity 

At high velocities, k_{c} >> k_{r} and r_{A} is independent of velocity 

Mass Transfer in a Packed Bed of Catalyst Particles  top 
Mole Balance 

Rate Law / Constitutive Equation 

for single pellets 

for packed beds 

If 

k_{r} >>> k_{c} 

Then 

We want to know how the mass transfer coefficient varies with the physical properties (e.g., D_{AB}) and the system operating variables. 

For isothermal operation, taking the rates for case 1 and case 2, the product of the mass transfer coefficient and the area a_{c}is 

This equation tells us how the product of our mass transfer coefficient and surface area would change, if we were to change our operating conditions. In other words, it will help us answer "What if..." questions about our system. 

For example: What effect does pressure drop have when all other variables remain the same? 

For: 

Substituting: 

If 

Then 

Shrinking Core Model  top 
Time to complete consumption, t_{c}
_{}
^{*} All chapter references are for the 4th Edition of the text Elements of Chemical Reaction Engineering .