CPE624_WEEK3

7/23/2019 CPE624_WEEK3

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CPE624: ADVANCED CHEMICAL REACTION ENGINEERING

1.1

Catalyticreactions

1.2

Catalyticreactors

1.3Surface and

EnzymeReaction Rates

1.4PorousCatalyst

1.5Transport

andReaction

1.6 Mass

TransferCoefficient

1.7External

MassTransfer

1.8-1.10Langmuir-Hinshelwood

Kinetic Mechanism

1.8Pore

Diffusion

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TRANSPORT AND

REACTION

Length scales in thereactor

Gradients in the

reactor

TransportSteps

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When a catalytic reaction occurs on the surfaces within a

catalyst pellet in a packed bed, there are inevitablyconcentration gradients around and within the pellet.

Need to consider several length scales in attempting to

describe catalytic reactors.

The reactor is on the order of 1 meter diameter and length,the pellet is typically 1 cm diameter , the pores within thepellet are 0.1 mm (10-4 m) or smaller in diameter, andcatalyst particles might be 100 Å, or lo-6 m in diameter, andthe reactant molecule might be 3 Å or l0-10 m in diameter.

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Catalyst particle

Catalyst pore

Pellet

Reactor

Reactor: in the bed z or height of the bed L .

We are interested in the position.........

Pellet : in the position x in the pellet with radius R

Pore : distance x down the pore diameter d pore

Walls of the pore : reactions on the catalyst particlediameter d particle

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Small gradient dC j /dz down the reactor from inlet to exit.

Then, gradient in C j around thecatalyst pellet.

Finally, there is the gradient withinthe porous catalyst pellet and

around the catalytic reaction sitewithin the pellet.

C Ab = concentration of reactant A in bulk fluid

C As = concentration of reactant A at external catalyst surface

C Ax = concentration of reactant A within the pellet

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Consider first the unimolecular reactionwhich occurs on a catalyst surface.....

Surface reaction rate coefficient as k” ,using units of k” (length/time) to satisfythe dimensions of r” (moles/area time)and C AS (moles/volume).

The steps that must be involved in acatalytic reaction on a surface are shownin Figure 7-8

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Reactant Ab in the bulkof the flowing fluid mustmigrate through aboundary layer over thepellet at the external

surface of the pellet.

It must then migratedown pores within thepellet to find surfacesites where it adsorbs

and reacts to form B,

STEPS INVOLVED ARE:

which then reverses the process to wind up in the flowing fluid,where it is carried out of the reactor

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The structures and concentration profiles of reactant near andin a catalyst particle might look as illustrated in Figure 7-9.

For the reactant to migrate into the particle, there must be aconcentration difference between the flowing bulk fluid C Ab, theconcentration at the external surface C As, and the concentrationwithin the pellet C A(x).

We write theconcentration within thepellet as C A(x), indicatingthat it is a function ofposition x, which will be

different for different geometries, as we willconsider later

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1. External mass transfer (diffusion) of the reactants (e.g.,species A) from the bulk fluid to the external surface of thecatalyst pellet

Steps in Heterogeneous Catalytic Reaction........

Low/High velocities of fluid flow Mass transfer resistance

Rate of reaction, ‐r A = k(C Ab–kC As)

2. Pore diffusion of the reactant from the pore mouth throughthe catalyst pores to the immediate vicinity of the internalcatalytic surface.

Transport from the pore mouth catalyst to the internalcatalytic surface

Reactant A diffuses into the interior of the catalyst pellet Large or small pellet will determine the diffusion time hence

the reaction rate

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3. Adsorption of reactant A onto the active site of catalystsurface


4. Reaction on the surface of the catalyst (A B)

conversion of A into product

5. Desorption of the products (e.g., B) from the surface.

Note : Langmuir ‐Hinshelwood Kinetics Mechanism

6. Pore diffusion of the products from the interior of the pelletto the pore mouth at the external surface

7. External mass transfer of the products from the externalpellet surface to the bulk fluid

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Mass transfer correlations for gases....

If there is a concentration difference of A between twolocations 1 and 2, then

J A = km A (C A

1

– C A2

)

J A is the mass transfer flux, [mol/s.m2 ]

k m is the mass transfer coefficient, [mol/(s·m2)/(mol/m3), or m/s]

C A1-C A2 , concentration difference [mol/m3

].

)( 21 A A

A

mA

C C

J k

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Mass transfer coefficient can be defined through the

Sherwood number:

l is length and D A is the diffusion coefficient of A

[convective mass transfer rate]

[diffusive mass transfer rate] Sh

l =

A

mA

l D

l k Sh

l

DShk

Al

mA

Then k mA can be defined:

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Sherwood numbers for several geometries:

1. Flow over a flat plate

2. Flow over a sphere

3. Flow through a tube

4. Flow over a cylinder

5. Tube banks and packed spheres

6. Heat transfer

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For flow over a flat plate of length L .......

Flow is laminar if ReL < 105 ,

3121Re66.0 ScSh L L

Flow is turbulent if ReL > 105 ,

318.0Re036.0 ScSh

L L

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The Reynolds number is

Schmidt SC number

μ is the velocity

v is the kinematic viscosity

D A the diffusivity ofspecies A, both of whichhave units of length2 /time.

For gases, SC =1

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2. Flow over a sphere

Important geometry in catalyst spheres, liquid drops, gasbubbles, and small solid particles

The characteristic length is the sphere diameter D

In the limit of slow flow over a sphere ShD = 2.0, and

this corresponds to diffusion to or from a spheresurrounded by a stagnant fluid.

4.032

21

Re06.0Re4.00.2 ScSh D D D

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3. Flow through a tube

the characteristic length is the tube diameter D

Flow is laminar if ReD < 2100,

Flow is turbulent if ReD > 2100,

38

D

Sh

318.0Re023.0 ScSh D D

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4. Flow over a cylinder

The transition from laminar to turbulence depends onposition around the cylinder

Flow is laminar if ReD < 4,

CPE624_WEEK3

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