Post on 03-Apr-2018
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PRINCIPLES OFCATALYSIS
Part 1c: Diffusion
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Steps in the Catalytic Reaction
A schematic diagram of a tubular packed bed withcatalyst pellets is shown below:
The overall rate of reaction is equal to the sloweststep in the mechanism (Step 1-7): Physical kinetics
Chemical kinetics (rate of adsorption, rate of desorption,rate of chemical reaction)
Pores
Packed catalyst bed Catalyst pellet Catalyst pellet surface
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Steps in the Catalytic Reaction
STEPS IN A CATALYTIC REACTION (Table Form)
1. Mass transferof the reactant(s) or External Diffusion In from the
bulk fluid to the external surface of the catalyst pellet.
2. Diffusion of the reactant or Internal Diffusion In from the pore
mouth through the catalyst pores to the immediate vicinity of the
internal catalytic surface.
3. Adsorption of reactant A onto the catalyst surface.
4. Reaction on the surface of the catalyst (e.g.,A B)
5. Desorption of product B from the catalyst surface
6. Diffusion of the products or Internal Diffusion Out from the interiorof the pellet to the pore mouth at the external surface.
7. Mass transfer of the products or External Diffusion Out from the
external pellet surface to the bulk fluid.
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Steps in Catalytic Reaction
1. Diffusion of the reactant(s) (e.g., species A) from the bulk fluid to the
external surface of the catalyst pellet
2. Diffusion of the reactant from the pore mouth through the cat. pores to the
immediate vicinity of the internal catalytic surface
3. Adsorption of reactant onto the catalyst surface
4. Reaction on the surface of the catalyst (e.g., A B)
5. Desorption of the product
6. Diffusion of the products from the interior of the pellet to the pore mouth atthe external surface
7. Diffusion of the products from the external pellet surface to the bulk fluid
62
A
B
2
B
7
53
A
1
6
External
diffusion
Internal
diffusion
Catalytic
surface
4
A B
A
B
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Steps in the Catalytic Reaction
Steps in the catalytic reaction can be dividedinto two categories:
Diffusion steps (1, 2, 6, and 7 in table in the next
slide)
Reaction steps (3, 4, and 5)
The overall process can be broken down into
sequence of individual steps.
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Types of Adsorption
Types of
Adsorption
Characteristic
Physical adsorption(physisorption)
Unselective, low energy of adsorption.
Extent of adsorption related to boiling point ofgas, not nature of solid surface.
No breaking of bonds in molecules andnegligible changes in bond energies.
Associative
chemicaladsorption
(chemisorption)
Selective, strongly dependent on both gas and
solid surface.Higher energies of adsorption than those ofphysisorption.
Bonds in the adsorbed molecules are changedin strength but not broken, i.e. moleculesadsorbed whole molecular fragments
Dissociativechemical
adsorption
(chemisorption)
Selective, strongly dependent on both gas andsolid surface.
Higher energies of adsorption than those ofphysisorption.
Bonds are in the adsorbed molecules arebroken, i.e. molecules adsorbed as two or more
molecular fragments
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C - O
C - O
C O
C
O
C O
Increasing interaction with metal surface
Molecule
approaches
surface
Physical
adsorption
Associative
chemisorption
Dissociative
chemisorption
Reaction and
adsorption
Types of Adsorption (contd)
Representation of adsorption, and possible subsequent reaction of CO onvarious solid surfaces
Example: CO adsorption on Al2O3 ,Bu ,Ni
Associative Chemisorption: CO + 3H2 CH4 +H2OCO + H2 CH3OHCu
Dissociative Chemisorption: CO C + ONi
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Reaction Steps
Example:The decomposition of cumene to form benzene and
propylene.
C6H5CH(CH3)2 C6H6 + C3H6
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Reaction Steps (Adsorption)STEP 3
The catalytic mechanism extends beyond the surface to involvephysical diffusion to & inside the particle leading to the following:
Adsorption on the surface:
kads Chemisorption
Results from chemical bonds between the molecule (adsorbate-reactant/product) and the solid surface (adsorbent-catalyst)
Very specific because receptive sites for chemisorption must exist
Physical adsorption Comes from Van der Waals forces & physical in origin
Weaker than chemisorption & not specific Adsorption on the catalyst surface:
rate of adsorption = rateattachment ratedetachment= kadsf(reactant,products)
kads = adsorption equilibrium constant
R ti St (S f R ti )
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Reaction Steps (Surface Reaction)VARIOUS TYPES OF KINETIC MODELS
Single siteA S B S
Dual site (Langmuir-Hinshelwood kinetics):
1. A S + B S C S + D S
1. A S + B S C S + D S
Eley Rideal
A S + B(g) C S + D(g)
A B C D
B A C D
A C DB
A B
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R(g) + OL P + and + O2
OL
OL = Lattice oxygen
Mechanistic Transformation at The Surface of Catalyst
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Steps in the Catalytic Reaction (4)
The catalytic mechanism extends beyond the surface toinvolve physical diffusion to & inside the particle leading to
the following: (cont.)
SURFACE REACTION: ks
Single site (A S B S)A B
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Reaction Step 5 (Desorption)
The catalytic mechanism extends beyond thesurface to involve physical diffusion to & inside
the particle leading to the following: (cont.)
Desorption of product/sB S B + S
Rate of desorption = -rate of adsorption
B B
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Diffusion Steps (1 & 7) (External)
The catalytic mechanism extends beyond the surface to
involve physical diffusion to & inside the particle leadingto the following:
External Diffusion of Molecule A:
k ext.diff. = kg Sext.
Motion of A through the fluid outside the particle is governed byexternal or bulk diffusion or mass transfer diffusion
Decreasing particle diameter/size, density & viscosity result inan increase in the external diffusion rate
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Diffusion Step (External)
Ficks first law of diffusion:
In term of molar flux of species A:
AoffractionmoleyBinAofydiffusivitD
ionconcentrattotalc
AspeciesoffluxdiffusivemolarJ
cD-J
A
AB
A
yABA A
BoffluxmolarW
AoffluxmolarW
)W(WyJW
B
A
BAAAA
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Diffusion Steps 6 & 7 (External)
Types of molar flux
1. Equimolar Counterdiffusion
2. Dilute concentration
When the mole fraction of the diffusing solute and the bulkmotion in the direction of the diffusion are small. Then,
A B
A B
C-DW-W AABBA
C-DJWAABAA
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Diffusion Steps 6 & 7 (External)
Types of molar flux
3. Diffusion Through a Stagnant Gas
The diffusion of a solute A through a stagnant gas B oftenoccurs in systems in which two phases are present. If gas B isstagnant, there is no net flux of B with respect to a fixedcoordinate: that is,
WB = 0then,
4. Forced Convection
Wyy-cDW AAAABA
JAZ
JAx
AofionConcentratC
areanalCrossectioA
velocityTerminalV
flowbulkB
CAVCBW
A
c
z
AZ
A
C
zAAZA
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Diffusion Steps 2 & 6 (Internal)
Overview of the internal diffusion
Porous
catalyst pellet External
surface
Internal
diffusion
External
diffusion
A
A B
A
External
diffusion
B B
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Diffusion Step (Internal)
The catalytic mechanism extends beyond the surface to
involve physical diffusion to & inside the particle leadingto the following: (cont)
Internal Pore Diffusion:
k int.diff. = ks Sint.h
Second step in the mechanism is diffusion into the poresleading to the reacting surface sites
Resistance to this diffusion is through collisions either withother molecules (bulk diffusion) or with the walls of the pore(Knudsen Diffusion)
Rates of pore diffusion-controlled reactions can be increasedby decreasing the particle radius or increasing the diffusivity
(by increasing the pore radius)
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External Diffusion
Diffusion of the reactants and products between the bulk fluid and the external
surface of the catalyst. An essential condition for successful kinetic
measurements is to ensure that the reaction is free of mass transfer limitations
(external and internal diffusion)
Detecting a limitation in ExternalDiffusion
conversion
Limitation by
external diffusion
No limitation from
externaldiffusion
v 2v 3v 4v
F1
G1
F2
G2
F3G3
F4
G4 conversion
5v
F
G
5F
5G
v
Limitation by
external diffusion
No limitation by
external diffusion
Two diagnostic tests to indicate if a reaction is limited by external diffusion (a) if the flow rate is
increased proportionately to the catalyst volume, so that the space velocity is constant as the mass flow
increases; a constant conversion indicates no limitation by external diffusion. (b) if plots conversion
versus contact time for two markedly different catalyst volumes are compared, superimposable curves
indicate no limitation by external diffusion
(a) (b)
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Internal Diffusion
Diffusion of the reactants or products from the external pellet surface (pore mouth)
to the interior of the pellet
Detecting a limitation in InternalDiffusion
dp/4dp/3dp/2
conversion
Limited by internal
diffusion
Chemical
kinetic control
dp
F
G
F
G
FG
F
G
dp
Experiment to find out whether reaction kinetics or internal diffusion limits a conversion.
Maintain constant all operating variables (volumetric gas flow, space velocity, contact time,
reaction temperature, inlet gas composition, and catalyst volume) as the particle sizes of the
catalyst are progressively varied, as dp, dp/2, dp/3, and dp/4. Then plot conversion against particle
size; and if the conversion varies, internal diffusion is limiting, whereas a constant conversion
indicates limitations of reaction kinetics only
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- Reaction takes place only on the catalyst and not in the fluid surrounding it
- The fluid velocity in the vicinity of the spherical pellet will very with position around the
sphere
As illustrated, the change in concentration of A from CAb to CAs takes place in a very narrow fluid
layer next to the surface of the sphere
- At low velocities the mass transfer boundary layer thickness is large and diffusion
limits the reaction
-As the velocity past the sphere is increased, the boundary layer thickness decreases and
the mass transfer across the boundary layer no longer limits the rate of reaction
- Reaction-limiting conditions can be achieved by using very small particles, but the
smaller particle size, the greater the pressure drops in a packed bed.
Phenomena of Diffusion
The flow of gas
Boundary
layer
Catalyst
pellet
CAb
CAs
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Rate-controlling
When heterogeneous reactions are carried out at steady state, the
rates of each of the three reaction steps in series (adsorption, surface
reaction, and desorption) are equal to one another. However, oneparticular step in the series is usually found to be rate-limitingor
rate-controlling.
0
1
2
3
4
5
6
0 1 2 3 4 5 6
initial concentration of reactant
initialrate
Adsorption-limited reaction
0
0 . 0 5
0. 1
0 . 1 5
0. 2
0 . 2 5
0. 3
0 . 3 5
0. 4
0 . 0 9 2 . 0 9 4 . 0 9 6 . 0 9 8 . 0 9 10 . 0 9 12 . 0 9
initial concentration of reactant
initialrate
Surface-reaction-limited
0
0. 5
1
1.5
2
2. 5
3
3. 5
0 1 2 3 4 5 6
initial concentration of reactant
initialrate
Desorption-limited reaction
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External DiffusionExample
For NRE = 1000 for NRE = 10
Mass transfer factor Mass transfer factor
= 0.57 X (1000) = 0.84 (10)
= 0.03 = 0.25
When does NRE become small, < 50
NRE = 2R . G liner mass velocity
Increase particle size, NRE
Increase linear mass velocity NRE
To circumvent this in the LAB
1. Make catalyst chips2. Feed + diluent (ballast)
How to check for external diffusion
- Vary catalyst bed volume
-0.41 -0.51
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DETECTING A LIMITATION IN EXTERNAL DIFFUSION
Test 1
V 2V3V 4V
G = mass flow of reacting gas, vary
= constant catalyst pellet-diameter ( const. int. diffusion)
Limitaton by externaldiffusion
No limitation from
external diffusion
IF FLOW RATE IS INCREASED PROPORTIONATELY TO THE CATALYST OLUME, SO THAT
SPACE VELOCITY IS CONSTANT (LHSV = FO ) AS THE MASS FLOW INCREASES, THEN
CONSTANT CONVERSION = NO LIMITATION
Flow rateFo
Conv
ersion
C F1
G1
2F1
2G1
3F1
3G1
4F1
4G1
G
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1.8.2 Internal Pore Diffusion
The second step in reaction mechanism is diffusion ino the catalyst pores
leading to the reacting surface sites. Resistance to this diffusion isthrough collisions either with
1. Other molecules (bulk diffusion), DB or
2. The walls of the pore (Knudsen diffusion) DK
DB=T /PT Bulk Diffusion, DB Eqn 6
DK = T TP Knudsen Diffusion, DK Eqn 7
Where
T = temperature
PT = total pressure
TP = radius of the pore
Usually DB and DK are combined
Dave = DB DK
DB + DK Eqn 8
3/2
1/2
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And corrected for particle porosity, and tortuosiity of the pores
Eeff= Dave Eqn 9
Porosity is measurable but is difficult to characterize. As an approximation
= 1/0 Eqn 1
Is useful. If not known, sufficient accuracy is achieved by the approximation that =
0.5. thus it is good enough to assume
Deff = (0.25) D ave Eqn 11
For simple nth order irreversible reactions models for diffusion-reaction lead to
the relationship
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