Lec 2 Heterogeneous catalysis - eacademic.ju.edu.jo

Chemical Engineering Department | University of Jordan | Amman 11942, Jordan

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Dr.-Eng. Zayed Al-Hamamre

Advance Chemical Reaction Engineering

Heterogeneous Catalysis: Kinetic in Porous

Catalyst Particles


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Content

Introduction

Diffusion Mass Transfer

External Resistance to Mass Transfer

Mass Transfer-Limited Reactions in Packed Beds

Diffusion through a Spherical Catalyst Pellets

Thiele Modulus

Effectiveness Factor

Combining External Mass Transfer with Diffusion

Giving up is the ultimate tragedy


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Heterogeneous reactions are distinguished from homogeneous ones by the different phases

present during reaction.

Introduction

For the design of heterogeneous chemical reactors a special consideration should be taken for

The transfer of matter between phases,

Transport processes play a critical role, capable to have strong influence on the degree of

conversion and the selectivity. The heat and mass transfer coefficient as well as the

exchange area are the parameters that describe the transport rate,

The fluid dynamics and chemistry of the system.

Additional complexity enters into the problem

Complication of the rate expression, and

Complication of the contacting patterns for two-phase systems


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Introduction

The Complications of the Rate Equation.

Since more than one phase is present, the movement of material from phase to phase must be

considered in the rate equation.

The rate expression in general will incorporate mass transfer terms in addition to the usual

chemical kinetics term.

These mass transfer terms are different in type and numbers in the different kinds of

heterogeneous systems; hence, no single rate expression has general application

Thus, in addition to an equation describing the rate at which the chemical reaction proceeds,

one must also provide a relationship or algorithm to account for the various physical processes

which occur.


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Burning of carbon particle in air

Examples


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Aerobic fermentation : Air bubble pass thorough liquid tank to the microbial cell to form

product material.

There are up to seven possible resistance steps, only one involving the reaction

If the steps are in series

If the steps are in parallel

Examples


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Diffusion Mass Transfer Diffusion is the spontaneous intermingling or mixing of atoms or molecules by random

thermal motion.

It gives rise to motion of the species relative to motion of the mixture.

In the absence of other gradients (such as temperature, electric potential, or gravitational

potential), molecules of a given species within a single phase will always diffuse from regions

of higher concentrations to regions of lower concentrations.

The mass transfer flux law is given according to Ficks law by

The molar flux of A. WA is the result of two contributions:

i. JA the molecular diffusion flux relative to the bulk motion of the fluid produced by a

concentration gradient, and

ii. BA the flux resulting from the bulk motion of the fluid,


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Or

where the molar average velocity is

hence

and



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Since the flux of A must be constant through

the stagnant film (conservation of mass), the

derivative of the flux with respect to

distance in the film must vanish

With boundary conditions:


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Equimolar Counter Diffusion

Dilute Concentrations


When the mole fraction of the diffusing solute and the bulk motion In the direction of the

diffusion are small<<

For constant total concentration


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Diffusion Through a Stagnant Gas


Forced Convection,


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In a tubular flow reactor


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where

Mass Transfer to a Single Particle


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If the external mass-transfer rate is low, the concentrations in the bulk fluid and external

catalyst surface are Significantly different.

At steady state, the molar flux to the boundary equal to convective transport across the

boundary layer


Internal diffusion External mass transfer

Multiply by

in which is the Biot number or dimensionless mass-

transfer coefficient


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Example

For dilute concentrations of the solute the radial flux is

Because reaction is assumed to occur instantaneously on the external surface of the pellet,

also


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For the isomerization reaction

Example

If the temperature is sufficiently high, then we have very weak adsorption (i.e., low surface

coverage) of A and B: thus

At steady state


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Example Cont.

Or where


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Rapid Reaction:

The rate of mass transfer to the surface limits the overall rate of reaction.

Example Cont.

kc can be found using several correlations such as

And the surface centration of reactant approaches zero,


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Slow Reaction

Example Cont.

The external resistance decreases as

The velocity across the pellet is

Increased,

The particle size is decreased.

The boundary layer becomes smaller and

the mass transfer coefficient (mass transfer

rate) increases,

And the surface concentration approaches the bulk fluid concentration.


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Diffusion from the Bulk to the External Transport

: The diffusion coefficient


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Reactant Concentration Profiles

kr

kr

kr

Reactant concentration profiles around a catalyst

pellet for reaction control and for external mass

transfer control


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An interphase effectiveness factor, is defined as the reaction rate based on surface conditions

divided by the rate that would be observed in the absence of diffusional limitations:

Interphase effectiveness factor


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ExampleDilute A diffuses through a stagnant liquid film onto a plane surface consisting of B, reacts there

to produce R which diffuses back into the mainstream. Develop the overall rate expression for the

L/S reaction


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The flux of A to the surface is

Example Cont.

Reaction is first order with respect to A

At steady state the flow rate to the surface is equal to the reaction rate at the surface (steps in

series).


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The individual rate steps on the same basis (unit surface of burning particle, unit volume of

fermenter, unit volume of cells, etc.).

Definitions


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Definitions

And


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For the mass transfer-limited reaction

Curried out in PBR


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The molar flow rate of A in the axial direction is


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If the flow rate through the bed is very large, the axial diffusion can be neglected,

Or



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At steady state

Hence


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In most mass transfer-limited reactions, the surface concentration is negligible with respect to

the bulk concentration


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To determine L the reactor length necessary to achieve a conversion X


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Diffusion through a Spherical Catalyst Pellets The pores in the pellet are not straight and

cylindrical;

They are a series of tortuous, interconnecting

paths of pore bodies and pore throats with

varying cross-sectional areas.

Effective diffusion coefficient is used to describe the average diffusion taking place at any

position r in the pellet

where

accounts for the variation in the cross-sectional area that is

normal to diffusion


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Diffusion through a Spherical Catalyst Pellets


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Diffusion Effect of pore size on the diffusivity of gas molecules


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Diffusion through a Spherical Catalyst Pellets For the reaction

The material balance is


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Diffusion Through a Spherical Catalyst Pellets

But


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The boundary conditions are

whereThiele modulus

φ21 is a measure of the ratio of "a" surface reaction rate to "a" rate of diffusion through the

catalyst pellet.

When the Thiele modulus is large, internal diffusion usually limits the overall rate of reaction;

when φn is small, the surface reaction is usually rate-limiting.


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Reactant concentration

gradients in a sphere for a

first-order reaction.


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Reaction rate limitations.

Moderate effect of diffusion on the average rate

the concentration at the center is almost zero, and the reaction rate will be very

low in the central part of the catalyst (regime of diffusion controlled reaction)

Pore diffusion limitation


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Reactant concentration profiles around and

within a porous catalyst pellet for the cases

of reaction control, external mass transfer

control, and pore diffusion control. Each of

these situations leads to different reaction

rate expressions.


Quiz: If the initial concentration of species A is doubled, how will the Thiele modulus

change?


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For large pellets, it takes a long time for the reactant A

to diffuse into interior compared to the time it takes for

the reaction to occur on the interior surface

The reactant is only consumed n the exterior surface of

the pellet and the catalyst near the center of the pellet

wasted catalyst

For very small pellets it takes very little time lo

diffuse into and out of the pellet interior and, as a

result, internal (fusion no Longer limits the rate of

reaction.

The rare of reaction



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Remarks For a first order reaction take place within a spherical catalyst pellet

In the Thiele modulus,


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The Rate of Reaction At steady state, the amount of reactant entering the particle must equal that consumed by the

reaction

The overall rate is the diffusion flux into the pellet:


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Effectiveness Factor To measure how much the reaction rate is lowered because of the resistance to pore diffusion,

define the quantity the effectiveness factor as


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Effectiveness Factor The internal effectiveness factor for a first-order reaction in a spherical catalyst pellet


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apparent


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Generally

The characteristic length aFor 1st order reaction


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We observe that as the particle diameter becomes very small, φn decreases, so that the

effectiveness factor approaches 1 and the reaction is surface-reaction- limited.

For small value of φn

o The concentration of reactant does not drop appreciably within the pore;

o Pore diffusion offers negligible resistance.

o It means either a short pore, slow reaction, or rapid diffusion, all three factors tending to

lower the resistance to diffusion

For large value of φn

o when φn is large (about 30), the internal effectiveness factor η is small ( η << 1) and the

reaction is diffusion- limited within the pellet

o The reactant concentration drops rapidly to zero on moving into the pore,

o Diffusion strongly influences the rate of reaction (regime of strong pore resistance).

Thiele Modulus


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Effectiveness Factor For large values of the Thiele modulus,

the effectiveness factor for a first order reaction can be written as


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Other Catalyst Shapes

In which B.Cs

The characteristic length a


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Other Catalyst Shapes


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η


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Spherical pellet

Spherical pellet


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The overall rate of reaction in terms of φn and η


i. Decrease the radius of reaction be R (make pellets smaller);

ii. Increase the temperature;

iii. Increase the concentration; and

iv. Increase the internal surface area


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For a reaction to take place within a spherical catalyst pellet, with

then

Nth Order Reaction

shell balance equation on A


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For large values of the Thiele modulus, the effectiveness factor is

Nth Order Reaction

An approximate value for the Thiele modulus can be given as


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Nth-Order Reaction with Other Catalyst Shape

The reaction-diffusion equation

For the reaction

In which The characteristic

length a


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Nth-Order Reaction with Other Catalyst Shape

The equation for the effectiveness factor in

a slab is the simplest and will be used for

all pellet shapes with the appropriate

Thiele modulus.

η


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Combining External Mass Transfer with Diffusion For finite external mass transfer, the dimensionless model and boundary conditions for a

spherical catalyst pellet are


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With decreasing B, corresponding to slower external mass transfer the concentration profile in the pellet

becomes more uniform and the dimensionless surface concentration decreases. The lower concentration

leads to lower reaction rates.

1st order reaction in a spherical pellet with φ=1

Biot number



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First-order reaction in a spherical pellet.

As B goes to infinity, then the reaction proceeds without external mass-transfer limitations



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The controlling mechanisms for pellet reaction rate given finite rates of internal

diffusion and external mass transfer.



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Example


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Example Cont.

Assuming the porosity and tortuosity to be 0.5 and 4, respectively

0.745 cm


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Example

Use the production rate and pellet parameters for the 0.3 cm pellet to find the unknown values


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Example Cont.


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The smaller pellet is half the radius of the larger pellet,

Example Cont.

Decreasing the pellet size increases the production rate by almost 60%.

This is possible only when the pellet is in the diffusion-limited regime.


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Reactor Containing Porous Catalyst

Expanded views of a fixed-bed reactor

The pellet volume consists of both

void and solid. The pellet void

fraction (or porosity) is


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Plug Flow


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Mixed Flow


For a Reactor Containing a Batch of Catalyst


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Use the data presented in the previous example to

Example

the Thiele modulus


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Example Cont.

For an ideal gas mixture


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Example Cont.


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At steady state, the transport of the reactant.(s) from the bulk fluid to the external surface of

the catalyst is equal to the net rate of reaction of the reactant within and an the pellet.

For the case when the external and internal resistance to mass transfer to and within the pellet

are of the same order of magnitude

Overall Effectiveness Factor

And


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Overall Effectiveness Factor

Also


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Example


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Example Cont.

But

If the flow rate through the bed is very large, the

axial diffusion (dispersion) can be neglected, i.e., if

Then


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Example Cont.

For


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Example Cont.

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Lec 2 Heterogeneous catalysis - eacademic.ju.edu.jo