11. External Diffusion Effects on Heterogeneous Reactions*


  1. Seven Steps in a Catalytic Reaction
  2. External Diffusion Across a Stagnant Film
  3. Relative Rates of Diffusion and Reaction
  4. Mass Transfer in a Packed Bed of Catalyst Particles
  5. Shrinking Core Model

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.

Binary Diffusion

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, FA, divided by the cross sectional area, AC, normal to the flow. WA = FA/AC

Molar flux of A WA (moles/time/area) with respect to fixed coordinate system

WA = JA + BA

JA = diffusional flux of A with respect to bulk motion, i.e. molar average velocity

BA = flux of A resulting from bulk flow

One dimension for constant total concentration- Ficks First Law

Adolph Fick (1829-1901)

Gases: DAb~10-5m2/s

Liquids: DAb~10-9m2/s

Prediction of Gas Phase Diffusivities

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.


Types of Boundary Conditions

1. Specify a concentration a boundary

2. Specify a flux at a boundary

a) No mass transfer across a boundary

[E.g., at pipe wall]


b) Reaction at a boundary

c) Diffusional flux to a boundary is equal to the convective flux away from the boundary.


3. Planes of Symmetry

[E.g., cylinder]


4 Common Cases of the Constitutive Equation

1) Dilute concentrations (liquids)

Constant total concentration

2) Equal Molar Counter Diffusion (EMCD)

3) Diffusion through a Stagnant Film

4) Negligable Diffusion (Plug Flow)

WA=? for 2A<=>B
Relative Rates of Diffusional Transport
Comparing JA and BA for diffusion through a stagnant film
Measurement of Gas Phase Diffusivities
Mole Balance with Diffusion and Reaction in 3-D
Measurement of Liquid Phase Diffusivities

Relaitve Rates of Diffusion and Reaction top

Mole Balance on Species A at steady state




Rate Law / Constitutive Equation

Constitutive Equation

Rate Law on Surface


Boundary Conditions

Z=0 CA=CA0

Z=d CA=CA0

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

kC 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 kc increases with increasing velocity, while kr is independent of velocity. At low velocities, the reaction is diffusion limited with kc >>kr and -rA=kc CAO


when kc >>> kr, then reaction is diffusion limited

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


when kc >>> kr, then reaction is reaction rate limited

, slow surface reaction, meaning that the overall reaction rate (WA=kr CAO) is independent of velocity

At high velocities, kc >> kr and -rA 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


kr >>> kc


We want to know how the mass transfer coefficient varies with the physical properties (e.g., DAB) 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 acis

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?





What 4 things are worng with this solution?

Shrinking Core Model top

Time to complete consumption, tc

Object Assessment of Chapter 11
Transdermal Drug Delivery

  * All chapter references are for the 4th Edition of the text Elements of Chemical Reaction Engineering .