12. Diffusion and Reaction in Porous Catalysts^*

Topics

1. Diffusion and Reaction in Catalyst Pellets
2. Fluidization Engineering

We now focus on steps 2 and 6 of our catalytic reaction . We shall carry a mole balance on species A as it diffuses and reacts in a catalyst pellet.

1. Mole Balance (on material between r and r + delta r)
2. Rate Law / Constitutive Equation
	2A. Constitutive Equation
	2B. Rate Law
	(mol/g cat/s)
	(mol/cm2/s)
3. Boundary Conditions
	r = R, CA = CAs and r = 0, CA is finite
4. Combine and Put the Equation in Dimensionless Form
	Let
Boundary Conditions: y = 1 at l = 1, y finite at l = 0	Then
	where
5. Concentration Profile (see text for derivation)
for large values of phi1 the molecules don't diffuse very far into the pellet before they react

6. Effectiveness Factor
For a first order reaction trade off But R is small and there are Large Pressure Drops through the bed. But only part of the catalyst pellet is used so and for Large F

For the nth order reaction

(12-38)

(12-39)

The true reaction order is

The true activation energy(12-43)

Summary on the Swimming of Small Creatures

First read over Problem 12-7 on pages 798 and 799concerning the swimming of small animals. We shall divide the animal into a head section, a mid-piece, and a tail. ATP is produced in the mid-piece and is used as an energy source in the tail to swim. Therefore, ATP must get into the tail in order for the animal to swim.

The rate of swimming is a function of the rate of diffusion into the tail. Therefore, consider only diffusion in the tail.

1. Mole Balance

2. Constitutive Equation and Rate Law

3. Boundary Conditions

at z = 0, C_A = C_A0

at z = L, dC_A / dz = 0

4. Combine and Put the Equation in Dimensionless Form

When= 0, then= 1.

When= 1, then= 0.

5. Solve for Concentration Profile

We shall assume the reaction is zero order:

where:

Solving:

NOTE: effectiveness factor = 1.0 (for zero order reactions)

Finding the length of the tail of the creatures is easily found by equating the overall rate (R_A = 23 * 10^-18 mol/s) to the rate of diffusion of ATP into the tail using the above dimensionless concentration profile.

Dependence of Reaction Rate on Catalyst Particle Size:

12.1 Applications of Diffusion and Reaction to Tissue Engineering

A.  Fluid Mechanics

Ergun Equation for pressure drop across the bed,

Nomenclature Note: In the text and lecture = porosity, while in the CD-ROM section on Fluidization = porosity. (Our apologies for the inconsistency.)  

At fluidization, the weight of the catalyst suspended equals the pressure drop (force) necessary to suspend it.  

1.  Minimum Fluidization Velocity, U_mf

        Solving equations [1] and [2]

 

valid for Re_d < 10

Need !!!

2.  Minor Break Through to Find

3.  Terminal Velocity, (Make sure we don't blow the particles out of the bed.)

4.  Slugging Velocity,

U_mf < U_o< U_ms< U_t

First calculate

then

then

Assumptions of the Bubbling Bed Model

1. The emulsion exits at minimum fluidization conditions, and .
2. All bubbles are the same size.
3. The concentration of solids in the wake is the same as the emulsion.
4. The solids in the emulsion phase flow downward in plug flow with velocity, .
5. Velocity of a Single Bubble Rise

For two or more bubbles, bubble rise is:

6.  Factors That Determine Bubble Diameter (d_b)

1. bed diameter,
2. type of distributor plate
3. height of bubble above plate
4. gas velocity
5. internals (i.e., baffles)

One usually evaluates d_b at h/2, but this is an area for future research.

= Fraction of the total bed occupied by bubbles (not including wakes)

7.  Balance on Solid

Solids flowing down = Solids flowing up in wakes

B.  Mass Transport Between Bubble, Cloud, and Emulsion

1.  Transport Between Bubble and Cloud

2.  Transport Between Cloud and Emulsion

  Mole Balances

1.  Balance on Bubble for Species A

 Divide by V_b, then:

 

2.  Balance on Cloud for Species A

or

 

3.  Balance on Emulsion for Species A

 

 
 

 

For first order reaction:

where:

 

Object Assessment of Chapter 12

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

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^** This material was developed from notes by Dr. Lee F. Brown and H. Scott Fogler.