General

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ADSORPTION
Outline
1) Adsorption Phenomena Adsorption Forces,
Definitions and Types 2) Adsorbents 3)
Adsorption Equilibrium 4) Characterization of
adsorbents 5) Rate proccesses in adsorption and
simple design methods for fixed bed adsorption 6)
Adsorption Process Cycles 7) Applications
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RATE PROCESSES IN POROUS MEDIA
For a single adsorbent particle effective rate
of adsorption or desorption is determined by one
or more of several diffusional steps
Performance of a large number of particles
depends on size and overall arrangement of the
apparatus whether

• countercurrent
• fixed bed
• batch

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Individual steps in the transport mechanism

• 1-3-4, 1-4-2 occur in series
• two mechanism may occur in parallel, fastest
  controls the rate

• Mass transfer from the flowing phase to the
  external surfaces of the sorbent particles
• 2. Diffusion in the sorbed state in a pore
  surface layer
• 3. Pore diffusion in the fluid phase (bulk
  fluid) within the particles
• 4. Adsorption-desorption at the phase
  boundaries (assumed to be very fast)
• 5. Mixing or lack of mixing between different
  parts of the contacting
• equipment

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main mechanisms of axial dispersion
1. molecular diffusion 2. turbulent mixing
(splitting and recombination of flows around the
adsorbent particles
In column operation, with slow rates , the
brakthrough curves may be broadened by eddy
diffusion or molecular diffusion , collectively
termed as axial dispersion
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Diffusion in porous media
complications to analyze mass transfer in
pores a) pore geometry is extremely complex
and hard to re model in terms of small number of
parameters b) different molecular mechanisms may
occur in pores
Pore diffusivity Jp - ?p Dp (?C/? x) ?p
porosity of particle
Dp is based on pore cross sectional area, and is
smaller than D in a straight cylindrical pore due
to random orientation of pores Dp D/? ?
tortuosity factor
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? tortuosity factor

• random orientation of pores gives
• longer diffusion path and reduced
• concentration gradient in the direction of
  flow
• b) variation in pore diameter

• ? independent of the nature of diffusing
  species
• ? 3 for randomly oriented cylindrical pores
• Generally ? 2-6
• ? ? 1/?P ?P particle
  porosity
• higher ? with low porosity pellets

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Transport mechanisms in porous media

• molecular diffusion
• Knudsen diffusion
• Poiseuille flow
• Surface diffusion

The most significant ones 1. molecular
diffusion 2. Knudsen diffusion
The relative importance of these processes
depend on the relative values of the mean free
path and the pore dimensions
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molecular diffusion is important
when mean free path ? is small compared with the
diameter of the pore, d/ ? gt10 ? ? 10-5 cm
(103 Å ) for gaseous species at 1atm In pores d
gt 10-4 cm (104 Å) dominant mechanism is
molecular diffusion, since collisions between
molecules will occur more frequently than
collision with the pore walls
in this case pore diffusivity is independent is
of d ordinary molecular diffusion coefficient
may be used in Ficks first law Dp Dm /
? Dm molecular diffusivity
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Dm may be estimated from equations such as
Chapman-Enskog equation

• Dm molecular diffusivity, cm2/s
• T absolute temperature,K
• MA, MB molecular weights of gaseous A and B,
  respectively, g/mol
• P total pressure, atm
• ? collision integral (? f (kT / ? AB)
• k Boltzman constant
• AB collision diameter, Å
• ?AB Lennard-Jones force constant

? AB 1/2 (? A ? B ) ?AB (?A
?B)1/2
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Dm ?1/P Dm
? T1.65 -2.00 Dm ? T1.75 (as
average) at room T and P
Dm 0.10- 10 cm2/s
Molecular diffusion may be present predominantly
in
1) liquid systems 2) high pressure gas
adsorption 3) low pressure gas adsorption in
large pores
Another correlation Fuller-Schettler and
Giddings equation
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Knudsen diffusion will be the dominant mechanism
whenever the mean free path is large compared
with the pore diameter. Collisions with the pore
walls will be more frequent than those between
the molecules
Knudsen diffusion prevails 1) when gas density
is low 2)when pore dimensions are very
small It is not observed with liquids
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Gas flow in a straight circular pore for Knudsen
flow
Dk 9700 (r) (T/M)1/2 cm2/s r mean pore radius
in Å T temperature, K M molecular weight of the
diffusing species

• composition independent
• total gas concentration (pressure)
  independent
• temperature dependence is slight, Dk ? T0.5
• inverse dependence with M1/2

for air M 29 T 298 K r 10 Å
Dk 0.01 cm2/s r 10000 Å Dk 10 cm2/s
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TRANSITION REGION
Both wall collisions and intermolecular
collisions Contribute to the diffusional
resistance

• In the intermediate regime
• Effective diffusivity depends on both
• Knudsen diffusivity
• molecular diffusivity

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Diffusion in transition region (binary gas)
1/D 1/Dk 1/Dm 1- (1JA/JB)YA
JA, JB fluxes of components A and B YA mole
fraction of component A for equimolar counter
diffusion JA - JB
1/D 1/Dk 1/Dm eqn. 1
eqn. 1 can be used as an approximation for other
condition also Dk ?? Dm molecular diffusion is
dominant Dm ?? Dk Knudsen diffusion is dominant
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SURFACE DIFFUSION
A direct contribution to the flux from transport
through the physically adsorbed layer on the
surface of the macropore Under conditions such
that the thickness of the adsorbed layer is
appreciable, a significant contribution to the
flux is possible
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Significant physical adsorption is a prerequisite
for surface diffusion

• temperature is not too far above the boiling
  point of species

Surface diffusion is an activated process
Temperature dependence (Eyring eqn.) Ds D exp
(-Es/RT) Es activation energy
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• Surface diffusion is significant only in
• small diameter pores in which the flux through
  the gas phase can generally be attributed to
  Knudsen diffusion

Overall diffusivity D Dk (1-?p ) / ? p
KDs K Henrys law constant Ds surface
diffusivity, strongly concentration dependent
except within the Henrys law region
Ds 10-3 - 10-5 cm2/s for physically adsorbed
molecules such as H2, N2, Kr, CO2, CH4, C3H8,
C4H10 on carbon, silica gel
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Poiseuille Flow
If there is a difference in total pressure across
a particle Then a direct contribution to the
adsorption flux from forced laminar flow through
macropores

• This effect
• negligible in packed bed (pressure drop is low)
• significant in the direct measurement of uptake
  rates in a vacuum system

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Equivalent diffusivity (Poiseuille eqn.)
D Pavg r2/8?? P absolute pressure,
dynes/cm2 ?? viscosity, poise r mean pore
radius, cm
JA Pavg r2 (Ci1- Ci2)/8?? Pavg (Pi1 Pi2)/2