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Adsorption Adsorbents: CENG 371 Environmental Control CENG 371 Environmental Control

environmental control

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0% found this document useful (0 votes)
46 views13 pages

Adsorption Adsorbents: CENG 371 Environmental Control CENG 371 Environmental Control

environmental control

Uploaded by

kelvinfungky
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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CENG 371 Environmental Control CENG 371 Environmental Control

Adsorption Adsorbents

In adsorption processes one or more components of Good adsorbents should have


a gas or liquid stream (adsorbate or solute) are • high surface area or micropore volume (for large
adsorbed on the surface of a solid (adsorbent) and a adsorption capacity)
separation is accomplished. • large pore network for the transport of molecules to
the interior (for fast kinetics)
The adsorbents are in the form of small pellets,
beads, or granules ranging from 0.1 mm to 12 mm The porous solid must have small pore size
in size. A particle of adsorbent has a very porous (micropore) with a reasonable porosity to satisfy the
structure with many fine pores. The pore volumes first requirement and have a network of large pore
can be up to 50% of the total particle volume. The size (macropore) for the second requirement.
adsorption often occurs as a monolayer on the Micropore: d < 2 nm
Mesopore: 2 < d < 50 nm
surface of the fine pores but sometimes as
Macropore: d > 50 nm
multilayer. Many adsorption processes are
reversible so that the adsorbed species can be
recovered later by desorption.

The overall adsorption process consists of a series


of steps. In a fixed bed when the fluid is flowing
past the particle, the solute first diffuses from the
bulk fluid to the gross exterior surface of the
particle. Then the solute diffuses inside the pore to
the surface of the pore. Finally, the solute is
adsorbed on the surface.

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Properties to characterize adsorbents:


Adsorbent Manufacturing Surface Pore Usage
method area
(m2/g)
diamete
o • Specific pore volume (cm3/g).
r (A )
Activated by thermal 300- 10-60 organics • Specific surface area (m2/g).
carbon decomposition 2000 adsorption • Particle density(g/cm-3).
of coal, wood, • Average pore diameter ( A ).
o

vegetable shells,
etc. • Pore size distribution
Silica gel by acid 600- 20-50 dehydrate
treatment of 800 gases &
sodium silicate liquids,
solution & then fractionate
dried hydrocarbon
Activated hydrated 200- 20-140 drying
alumina aluminum oxide 500
is activated by
heating to drive
off the water
Molecular porous 300- 3-10 drying,
sieve crystalline 1200 separation
zeolites aluminosilicate
containing
precisely
uniform pores
Synthetic by polymerizing adsorption
polymers two major types in aqueous
or resins of monomers solution

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CENG 371 Environmental Control CENG 371 Environmental Control

Entropy changes Adsorption isotherm

Physical adsorption from the gas phase is This is the equilibrium relationship between the
exothermic, why? Let us look at the concentration of a solute in the fluid phase and its
thermodynamic argument. concentration on the solid phase at a given
temperature. Some typical isotherm shapes are
Since the adsorbed molecules is more regular shown below.
™ the disorder degree is lower
™ entropy is lower
™ ΔS = Sads − Sgas < 0

For the adsorption to happen, the free energy


change, ΔG, should be negative,
™ ΔG = ΔH − TΔS < 0
™ ΔH < 0
™ adsorption is exothermic

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CENG 371 Environmental Control CENG 371 Environmental Control

• Linear isotherm The Langmuir isotherm is the simplest and still


This is similar to Henry's law the most useful equilibrium equation for both
q = Kc or q = K' p (1) chemical and physical adsorption. It is based on
where q is the adsorbed concentration and c is the the following assumptions:
solute concentration. K is called the Henry
constant. This linear isotherm is not common, 1. Adsorption is at fixed number of definite,
but many systems follow this relationship in the localized sites.
dilute region. 2. Each site can hold only one adsorbate
molecule (monolayer).
From the ideal gas law, K=K’RT. 3. All sites are equivalent.
4. No interaction between adsorbed molecules,
The temperature dependence of the Henry even on adjacent sites.
constant follows the vant Hoff equation:
d ln K' ΔH 0 d ln K ΔU 0
= 2
; = 2
(2)
dT RT dT RT
where ΔH0 and ΔU0 are the changes in enthalpy
and internal energy during adsorption.

• Irreversible (rectangular) isotherm


The adsorbed amount is independent of the solute
concentration (q = constant). It happens when
the adsorption affinity is extremely high (large
molecules). The Langmuir equation can be derived by the
kinetics of condensation and evaporation of gas
• Langmuir isotherm molecules at a unit solid surface. If θ is the
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CENG 371 Environmental Control CENG 371 Environmental Control

fraction of the solid surface covered by a


monolayer of adsorbate, then the rate of Eq. (5) can be used to calculate the heat of
evaporation from the surface (desorption) is adsorption. From the assumptions of identical
proportional to θ (i.e., kdθ). Similarly, the rate of sites and no interaction between adsorbed
condensation of gas molecules onto the surface molecules, the heat of adsorption should be
(adsorption) is proportional to the fraction of free independent of coverage (θ).
sites remaining, (1-θ), and the absolute gas
pressure, p, (i.e., kap(1-θ)). Equilibrium is In general, equation (4) can be written as:
bp bc
established when these two rates are equal. q = qs , or q = q s (6)
1 + bp 1 + bc
kap(1-θ)=kdθ (3)
where ka and kd are the rate constants for where q is the adsorbed phase concentration, qs is
condensation (adsorption) and evaporation the maximum (saturation) adsorption capacity, so
(desorption). By rearranging Eq. (3), the fraction θ=q/qs. The parameters qs and b are obtained by
of surface covered, θ, is obtained as: fitting the Langmuir model to experimental data.
ka p bp
θ= = (4)
kd + ka P 1 + bP The Henry constant is low T
The parameter, b=ka/kd, is called affinity constant obtained by taking the q
& related to the heat of adsorption (Q) by limit p → 0:
b = b0 exp(Q / RT ) (5) ⎛ q⎞ high T
K' = lim ⎜ ⎟ = bq s (7)
where b0 is a constant, R is the gas constant and p→0 ⎝ p ⎠

T the temperature in Kelvin. Since adsorption is p


exothermic (Q = - ΔH > 0) b should decrease By rearrangement of
with increasing temperature. The higher value of equation (6) we get
b, the stronger the adsorption.

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CENG 371 Environmental Control CENG 371 Environmental Control

1 1 1 1 1/q By taking logarithm on


= + (8)
q q s bq s p both sides of equation lnq
Therefore if we plot 1 (10), we have
slope=
1/q vs. 1/p, a linear
1/q s bqs ln q = n ln p + ln K
line should be (10) slope=n
-b 0 1/p So by plotting ln(q) vs. lnK
obtained with a slope
1 1 ln(p) we should obtain
of , an intersect on y-axis of , a linear line with the 0 lnp
bq s qs
slope being the
and an intersect on x-axis of -b. exponential constant n, and the intersect on y-axis
being lnK.
• Freundlich isotherm
If the adsorption sites are not identical, the total • Sips (Langmuir-Freundlich) isotherm
adsorbed amount is summed over all types of sites.
This is the hybrid Langmuir-Freundlich isotherm,
When an exponentially decaying energy distribution
is assumed, the Freundlich isotherm is obtained, it takes into account the fragmentation of the
which was originally an empirical equation: molecule so one molecule occupies 1/t sites.
q = Kp n or q = Kp1 / m bp t
q = qs (11)
(9) 1 + bp t
n<1
where K and n are q n=1 It is a three parameter isotherm (qs, b, t).
constants determined
experimentally. The • Unilan isotherm (UNIform energy distribution
isotherm is favorable & local LANgmuir equation)
when n<1, linear if n=1, n>1
0 p q ⎡ 1 + bes p ⎤
and unfavorable if n>1. q = s ln ⎢ ⎥ (12)
2s ⎣1 + be −s p ⎦
Three parameters are qs, b, s.

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CENG 371 Environmental Control CENG 371 Environmental Control

p
• Toth isotherm
b1/ t p
q(p s-p)
q = qs (13)
(1 + bp ) t 1/ t

Three parameters are qs, b, t. 1 c-1


slope= q
q monoc monoc

• BET (Brunauer-Emmett-Teller) isotherm 0 p/p s


This is a multilayer adsorption isotherm
P 1 c −1 ⎛ P ⎞
= + ⎜ ⎟ (14) Surface area from the BET equation
0
q( P − P) qmono c qmono c ⎝ P 0 ⎠
where qmono is the monolayer saturation when qmono is obtained, we can calculate the
concentration and P0 is the vapor pressure. By specific surface area of the adsorbent by the
using experimental data in the range of P/P0 = following equation:
0.05 to 0.35, the left-hand side of equation (14) is q (g / g solid)N 0 A
S t (m 2 / g solid) = mono (15)
plotted against the relative pressure (P/P0), the M w (g / mol)
values of qmono and c can be obtained from the where Mw is the molecular weight, N0 is
slope and intercept of the linear line. Knowing Avogadro’s number (6.023x1023/mol), and A is
o
the molecular area (eg., 16.2 A 2 /molecule for the surface area of one molecule, which is
nitrogen at 77K), the value of the surface area can 16.2x10-20m2, for N2 at 77K.
be calculated directly from qmono.

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CENG 371 Environmental Control CENG 371 Environmental Control

The BET isotherm is only valid in the range of Heat of adsorption


P/P0 = 0.05 to 0.35, beyond this region, BET is The isosteric heat of adsorption (-ΔH) is
not a good model because of the capillary determined from the Clausius-Clapeyron
condensation (P/P0 > 0.3) or the system fails to equation applied to adsorption isotherm:
form multilayer adsorption (P/P0 < 0.05). ⎛ ∂ ln p ⎞ − ΔH
⎜ ⎟ = (16)
⎝ ∂T ⎠ q RT 2
Similarly a Langmuir surface area can be defined Integrate assuming ΔH independent of T,
by replacing qmono in Eq. (15) by qs used in the ΔH
Langmuir isotherm. As Langmuir equation ln p = + cons tan t (17)
RT
assumes monolayer adsorption, the surface area A plot of lnp vs 1/T at constant q gives a linear
calculated from Langmuir isotherm is always line with a slope of ΔH/R.
larger than that obtained by BET equation.
For the Langmuir isotherm, we have
− ΔH Q dqs (1 + bp )
2
= 2
− (18)
RT RT dT qs
where we allow the maximum adsorbed capacity,
(qs) to vary with temperature.
RT 2 dqs (1 + bp )
− ΔH = Q − (19)
dT qs
However, the isosteric heat of adsorption (-ΔH) is
constant for the Langmuir equation if the
saturation capacity is independent of temperature,
but changes with the surface loading for other
isotherms.

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CENG 371 Environmental Control CENG 371 Environmental Control

Measurement of adsorption isotherm Example: A wastewater solution having a


(Batch adsorption) volume of 1.0 m3 contains 0.21 kg phenol/ m3 of
solution (0.21 g/L). A total of 1.40 kg of fresh
The adsorption isotherm is often obtained by granular activated carbon is added to the solution,
using a batch reactor. In liquid adsorption, this is which is then mixed thoroughly to reach
conducted in a stirred tank. A certain volume of equilibrium. The isotherm data are shown in the
liquid (V) with known concentration (c0) is fed Table and plotted in the figure below.
into the tank, then a known mass of adsorbent
particles (m) is added to the solution. After c (kg/m3) 0.0011 0.0061 0.039 0.117 0.322
sometime (usually overnight to a few days, q (kg/kg) 0.045 0.059 0.094 0.122 0.150
depending on the particle size) the system
becomes steady state. The final concentrations in what are the final equilibrium values, and what
the liquid phase (cf) and in the solid phase (qf) are percent of phenol is extracted?
in equilibrium. By taking a material balance we
have
q f m + cf V = q 0 m + c0V (20)
So qf can be calculated as
q m + c0V − cf V
qf = 0 (21)
m
Now we get one isotherm point (cf, qf), more
isotherm data can be obtained by changing
relative amount of solution and solid, or the
initial liquid concentration and repeat the above
procedure.

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CENG 371 Environmental Control CENG 371 Environmental Control

Solution 1: The given values are c0=0.21 kg Solution 2: From the mass balance equation (eq.
phenol/ m3, V=1.0 m3, m=1.40 kg carbon, and q0 20), we have
is assumed zero. Substituting into eq. (20) qf(1.40) + cf(1.0) = 0(1.40) + 0.21(1.0)
qf(1.40)+ cf(1.0)=0(1.40)+0.21(1.0) 1.4qf + cf = 0.21
This is a linear line, which is plotted in the figure Fitting the Freundlich equation to the isotherm
below together with the isotherm. The equilibrium data, we obtain
values are obtained from the intersection: qf = 0.194cf1/4.4848
cf=0.062 kg phenol/ m3
qf=0.106 kg phenol/kg carbon Solving the mass balance and isotherm equations
The percent of phenol extracted is together, we get the solution.
% extracted
c − cf 0.210 − 0.062 cf=0.062 kg phenol/ m3
= 0 (100) = (100) = 70.5
c0 0.210 qf=0.106 kg phenol/kg carbon

The percent of phenol extracted is


% extracted
c − cf 0.210 − 0.062
= 0 (100) = (100) = 70.5
c0 0.210

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CENG 371 Environmental Control CENG 371 Environmental Control

Volumetric measurement rig for gas Before an equilibrium experiment starts, a


adsorption isotherm molecular drag pump is used to evacuate the
It has two separate chambers. One has a supply system to 10-5 mmHg. The operation procedure is
bomb and the other contains an adsorption cell. described below.
Each chamber has a transducer & a thermocouple
to record the pressure & temperature. The
1. Activated carbon was crushed to about
volume of each chamber is also known.
0.1 mm and dried in an oven at 200oC for three
hours to remove excess moisture. The carbon was
then weighted and loaded into the adsorption cell.
2. The whole system was first evacuated to
vacuum using an Alcatel molecular drag pump
and the activated carbon particles in the
adsorption cell were heated up to 300oC and kept
at this temperature and under vacuum for
overnight to degas any possible adsorbed species.
3. Pure gas was then dosed into the supply
bomb and the pressure and temperature were
recorded when constant readings were reached.

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CENG 371 Environmental Control CENG 371 Environmental Control

4. A small amount of pure gas was dosed Multicomponent Langmuir isotherm


from the supply bomb into the adsorption cell
For species i, the multicomponent Langmuir
which was kept isothermal by using a water bath. isotherm equation is
After the pressure in the adsorption cell becomes bici
q i = q i,max NC
(22)
constant (typically about two hours), the pressures 1 + ∑ b jc j
j=1
and temperatures in both supply bomb and
where NC is the number of components.
adsorption cell were recorded.
5. The amount adsorbed which was in The derivation follows the same assumptions of
equilibrium with the pressure in the gas phase of single-component Langmuir isotherm. The
system is defined as containing partial pressure
the cell was calculated from the amount supplied p1, p2, ..., pNC in the gas phase, which is in
from the supply bomb via the ideal P-V-T equilibrium with coverages θ1, θ2, ..., θNC on the
relationship. surface. The rate of condensation for gas i, ri, is
given by:
6. Steps 4 and 5 were repeated to get the
⎛ NC ⎞
equilibrium isotherm data at higher pressures until ri = k ai p i ⎜1 − ∑ θ j ⎟ (23)
⎝ j=1 ⎠
a full isotherm curve was obtained. The rate of evaporation for gas i is kdiθi.
At equilibrium,
⎛ NC ⎞
k ai p i ⎜1 − ∑ θ j ⎟ = k diθ i (24)
⎝ j=1 ⎠
By defining b=ka/kd, we have

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CENG 371 Environmental Control CENG 371 Environmental Control

⎛ NC ⎞ The extended Langmuir equation is


b i p i ⎜1 − ∑ θ j ⎟ = θ i (25)
⎝ j=1 ⎠ thermodynamically consistent only when the
Summing Eq. (25) over all components (NC) maximum adsorption capacities (qsi) are the same
gives for all species. If the maximum adsorption
NC ⎛ NC ⎞ NC capacity differs significantly between different
∑ b j p j ⎜1 − ∑ θ j ⎟ = ∑ θ j (26) component, the usage of extended Langmuir
j=1 ⎝ j=1 ⎠ j=1
isotherm may cause errors.
so
NC
NC
∑ b jp j • Loading Ratio Correlation
j=1
∑θj = NC (27) As in the extended Langmuir equation, the hybrid
j=1 1 + ∑ b jp j Langmuir-Freundlich equation can also be
j=1
extended to an m-component mixture.
substituting Eq. (27) into (25) to give 1 / mi
bi pi bi pi
θi = (28) qi = qsi NC
(29)
NC 1/ m j
1 + ∑ b jp j 1+ ∑ bj p j
j=1 j =1
which is the extended Langmuir isotherm The ratio qi/qsi is referred to as loading ratio,
( θ i=qi/qsi). It can also be used for liquid hence the term loading ratio correlation (LRC).
adsorption.

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