Pure and Mixture Gas Adsorption of Light Hydrocarbon on ETS-10 Zeolite
Nadhir A. Al-Baghli 1 and Kevin F. Loughlin 2,3
1 Chemical Engineering Department, King Fahd University of Petroleum & Minerals,
Dhahran, Saudi Arabia 3126, nabaghli@kfupm.edu.sa
2 Chemical Engineering Department, King Fahd University of Petroleum & Minerals,
Dhahran, Saudi Arabia 3126, loughkf@kfupm.edu.sa
3 To whom correspondence should be addressed to.
1
Abstract
Pure, binary and ternary equilibrium adsorption data are reported for methane, ethane
and ethylene on ETS-10 zeolite for pressures up to 1000 kPa in a 280-425 K temperature
span. The data is modeled using ten different pure isotherm equations (Toth, Unilan,
Radke-Prausnitz, Mathews-Weber, Volmer, Virial with 2 or 3 constants, Freundlich,
Langmuir-Freundlich and the Loading Ratio Correlation). Unconstrained and constrained
optimization techniques have been applied to optimize the model parameters. Henry's
constant values and limiting heat of adsorption are deduced from the Virial three constant
model and compared to the values derived for the other models. The saturation
concentration is deduced based on the assumptions of complete occupancy of the free
voidage with adsorbed state molecular volumes estimated from liquid densities and Van der
Waals volume. The actual values derived are a little less than the theoretical value due to
steric effects.
The multicomponent data is modeled by the Ideal Adsorbed Solution Theory (IAST)
employing Toth, Unilan and Virial three constant model as the relevant isotherm model.
The fit is satisfactory with these isotherms.
Keywords: ETS-10 zeolite, Henry's constant, isosteric heat of adsorption, isotherm models,
mixture models.
2
Introduction
ETS-10, an experimental titanium silicate was first synthesized in 1989.1 It is a
microporous crystalline solid consisting mainly of an assemblage of titanium oxide (TiO 2 )
and silicate ( SiO 2 ). The pore sizes in ETS-10 are uniform and similar in dimension to large
pore classical zeolites. Titanium is octahedrally coordinated in the framework and requires
two counterbalancing cations per titanium. The structure of ETS-10 is somewhat different
from classical aluminosilicate zeolite. This material is composed of chains of octahedrally
coordinated zeolites type rings.2,3,4 The effective pore size of ETS-10 is about 8 Å and it is
thermally stable in air up to 600 o C . The properties of ETS-10 are given in Table 1.5
Titanium zeolites such as ETS-4 and ETS-10 are extensively used in ion exchange, gas
separation or purification and in catalytic studies. These studies have been reported by
Bianchi et al.,6,7 Gervasini et al.3,4 The properties of these adsorbents were originally
expounded by Kuzuicki1 and have being further examined by Pavel et al.8,9 X-ray
diffraction, UV-VIS, NMR, EPR and Ramon studies have been used to characterize these
zeolites in original or ion-exchanged forms by Zibrowius et al10, Otero Arean et al.11,
Anderson et al.12, Grillo and Carraza13,14, Yang, et al.15, Kishiman and Okubo16, Sankar et
al.17, and Ashtekar et al.18 The limited adsorption studies reported involve adsorption of H2,
N2, CO, NO and O2 on sodium and potassium titanosilicates19, pure component adsorption
on ETS-1020 and use of methane as a probe molecule for basic site determination.21 Unlike
other zeolites, strong framework deformations occur on adsorption of guest molecules.17
Kuznicki et al.22 have used this property to adjust the pore sizes of ETS-4 through
systematic dehydration at elevated temperatures to ‘tune’ the effective pores of the crystal.
This can be successfully applied to tailor these adsorbents to give size-selective adsorbents
for commercially important separations of gas mixtures with similar size in the 3Å-4Å
range, such as N2/CH4, Ar/O2 and N2/O2.
The objective of the current study is to examine the performance of ETS-10 zeolite as a
separation tool. Equilibrium data both for single, binary and multicomponent form of
methane, ethane and ethylene are reported and analyzed using various model isotherms.
3
Theoretical Background
The equilibrium relationship in physical adsorption is highly affected by the
characteristics of the adsorbents and adsorbates. For a specified adsorbent this relation is
governed by the system temperature, pressure and compositions.
It is convenient to
represent this equilibrium relation as:
q i  f (T , P , y i )
(1)
where q i is the solid or adsorbed phase loading of species i, T is the system temperature, P
is the system pressure and y i is the bulk phase composition vector.
The total solid phase loading q is the sum of the loadings of all species present in the
system:
N
q   qi
(2)
i 1
and the solid phase xi composition of species i is given by:
xi 
qi
q
(3)
For pure species the loading is a function of the system pressure at a fixed temperature.
At low pressure the loading is linearly related to the system pressure:
lim q  K H  P
P 0
(4)
The coefficient KH is known as Henry's constant and is related to temperature by an
Arheneus-type equation:
 H 
K H  K  exp 

 RT 
where K
is a constant and
 H 
is the isosteric heat of adsorption.
(5)
Any
thermodynamically consistent model should satisfy equation (4) at very low pressure.
In the upper limit, the pressure at which the pores are completely filled is the saturation
pressure Ps and the corresponding loading is the saturation concentration q s :
lim q  q s
P Ps
4
(6)
The saturation concentration and Henry's constant are important parameters which
characterize most of the adsorption models. The fraction of surface covered with adsorbed
molecules  is defined as:

q
qs
(7)
The saturation concentration can be theoretically calculated for microporous zeolites by:
qs 

v
(8)
where  is the voidage of the adsorbent, 119.5 cc/kg for ETS-10 zeolite (Tables 1), and v 
is the molar volume at the system temperature T given by:
 T T b 
v  v b  
 b v b 
T c T b 
(9)
where T c and T b are the critical and boiling temperatures respectively, and vb and b are
respectively the molar volume at Tb and the van der Waal's volume. Above the critical
temperature, v* is assumed equal to b. The value of the saturation concentration calculated
from the above expressions are based on the assumption of complete occupancy of the free
voidage and that the adsorbed state molecules behave analogous to a highly compressed
liquid state under the same conditions. However, the actual value is a little less due to steric
effects.
An important system variable in adsorption is the spreading pressure  . It corresponds
to the difference in surface tension between a clean surface and a surface covered with
adsorbate. Hence, it represents the change in internal energy per mass of adsorbent (U) due
to the spreading of the adsorbate over the surface of the adsorbent (A) at constant adsorbed
phase entropy ( S ), volume (v ) and adsorbed quantity ( q )
  U 
 

  A S ,v ,q
(10)
The spreading pressure can be calculated from the equilibrium adsorption data using the
integrated form of Gibbs equation:
5
A
P
q
dP
P
0

RT
(11)
Several models have been developed to describe the equilibrium relationship between the
amount adsorbed ( q ) and the pressure (P) for pure components. These models are based
on assumptions which are appropriate only for limited systems. The derivation of most
models is based on theoretical foundations. On the other hand, some models are based on
experimental data and may be thermodynamically meaningless.
The simplest model, developed by Langmuir in 191823 is in general not applicable to
zeolitic adsorption. However, it is frequently employed in column studies on adsorption due
to its simplicity and thermodynamic consistency. The Langmuir model can be written as:
q
K Lqs P
1 K L P
(12)
where K L is an equilibrium parameter. Henry's constant can be determined from the above
equation by applying equation 4:
K H  K L qs
(13)
The Langmuir model is very ideal and is applicable only at low pressures. However, this
model has provided the basis of several other models.
Toth,24 has derived a model based on monolayer adsorption considering the
heterogeneity of the adsorbent where the energy of the sites are no longer equivalent :
q
qs P
b  P 
t 1/ t
(14)
where b is an equilibrium parameter and t is a heterogeneity parameter. This model reduces
to the Langmuir model for t = 1 which refers to a homogeneous surface. Applying equation
(4) to Toth model we get:
K H  q s b 1/t
(15)
Honig and Reyerson25 have developed a model based on a uniform distribution of
energies of adsorption. The model is a modified version of the Langmuir model :
q
q s  c  P exp(s ) 
ln
2s  c  P exp(s ) 
6
(16)
where c is an equilibrium parameter and s is a constant related to the heterogeneity of the
surface. Equation 16 is commonly known as the Unilan model. For a homogeneous surface,
s vanishes and the Unilan model reduces to the Langmuir model. Henry's constant can be
obtained from:
KH 
qs
sinh  s 
cs
(17)
Mathews and Weber26 extended the Langmuir model by adding a dimensionless
constant ( n MW ) which corrects for deviation of the experimental data in the systems they
studied:
q
q s b MW P
1  b MW P 
n MW
(18)
where the subscript MW refers to Mathews-Weber. Henry's constant can be found from:
K H  q s bMW
(19)
Radke and Prausnitz27 have derived a model based on the principles of dilute solution
thermodynamics:
q
b RP q s P
 b P 
1  b RP P   RP n RP 
 c RP P 
(20)
where bRP , c RP are equilibrium parameters and nRP is a dimensionless constant. This model
has been derived to make the Langmuir-Freundlich model thermodynamically consistent
and is found to be suitable for weakly adsorbed components. The Henry's constant can be
obtained from the Radke-Prausnitz model by :
K H  q s bRP
(21)
Volmer28 derived a model based on the Gibbs adsorption isotherm:
qRT
  
A
 
P
  P T
(22)
in conjunction with the equation of state:
 A 1     qRT
to obtain:
7
(23)
P
qs
KH
  
  

 exp 

 1 
 1 
(24)
The Gibbs adsorption isotherm may also be used in conjunction with an equation of
state of Virial form:
A
qRT
 1  B1q  B 2q 2 
(25)
to obtain the Virial adsorption isotherm:
P
q
exp  A1q  A 2q 2 
KH

(26)
This isotherm does not give information about the nature of the adsorbed phase; therefore,
it is considered as a correlation. However, the values of Henry's constant calculated from
this model are deemed the most accurate as it omits the constraint of the saturation
concentration.
The models based on theoretical foundation, sometimes fail to represent accurately the
experimental data for polar gases adsorbed in varying pore size-adsorbents. Hence, several
correlations with weak theoretical basis have been developed and used satisfactorily. These
correlations include Freundlich model28:
q  k F P nF
(27)
Langmuir-Freundlich model28:
q
q s K LF P nLF
1  K LF P nLF
(28)
and the loading ratio correlation (LRC) model28:
q
q s (K LRC P )1/ nLRC
1  (K LRC P )1/ nLRC
(29)
These three models do not reduce to Henry's Law as the pressure approaches zero which is
the main disadvantage of these models. On the other hand, the fit obtained for various data
using these models has been found reasonable especially for the Langmuir-Freundlich and
the LRC models. The above mentioned isotherms are used to model the data in this work.
Other published models such as the one published by Nitta et al.
but were not deemed necessary in this study.
8
29,30
could also been used
Some pure component models can be extended to describe the equilibrium adsorption
behavior of multicomponent systems. For instance, the amount adsorbed for the ith
component in a mixture ( qi ) can be written using the Langmuir model as :
qi 
K Li q s i Pi
(30)
N
1   K Li Pi
i 1
For the Langmuir-Freundlich model, q i is given by :
qi 
K LFi q s i Pi
N
n LFi
1   K LFi Pi
(31)
n LFi
i 1
where the subscript i refers to the ith component in the mixture.
The multicomponent equilibrium behavior can also be predicted from knowledge of the
pure component equilibrium corresponding to the mixture using the ideal adsorbed solution
theory (IAST). This theory28 presents a relationship between the bulk and the adsorbed
phase for the mixtures assuming ideal behavior. Thus, the relationship between the two
phases can be described by an analogous form of Raoult's law :
Py i  Pi x i
(32)
where Pi is the pressure of pure component i which it would exert as a pure component at
the same temperature and spreading pressure as those of the mixture. At equilibrium, the
spreading pressure for each component is constant:
A
RT
 
P1

0
q1
dP1 
P1
P2
q2
dP2 
P2

0

Pi
qi
 P dP
i
0
(33)
i
The summation of the adsorbed phase mole fraction is unity:
N
x
i 1
i
1
(34)
Therefore, if an appropriate pure component model is used in equation 33, the values of
Pi o's corresponding to each component in the mixture can be calculated. The mole fraction
of each component in the mixture can be calculated from:
9
xi 
Py i
Pi
(35)
The total amount adsorbed can then be obtained from:
q
1
xi

i 1 q i
N
(36)
where q i is the amount adsorbed for component i in the pure state at Pi . Valenzuela and
Myers28 present a general algorithm for solving the IAST equation. This algorithim was
adopted in this paper to predict the mixture behavior using the pure models of Toth, Unilan
and Virial three constant models.
Experimental Setup and Procedure
The volumetric method is used to collect the adsorption data for all the systems studied.
The apparatus used and the experimental procedure are similar to these reported by by
Abdul Rehman et al31 and Loughlin et al.32
Data Regression
Model parameters are obtained using the nonlinear least square method of Margules.
The parameters are optimized based on the minimum sum of square error given by:
2
q
 NP
2
ss    mod  1   q mod  q exp 

 i 1
i 1  q exp

NP
(37)
where ss is the sum of squares error, NP is the number of data points, and qmod and qexp
are respectively the amount adsorbed per unit mass of adsorbent calculated from model and
experiment.
Both constrained and unconstrained optimizations have been applied for each model. In
the unconstrained regression the saturation concentration parameter q s is forced to be
greater than the highest experimental concentration obtained at the highest pressure and
lowest temperature while the remaining parameters are left to relax to their optimum
values. However, in the constrained regression, the saturation concentration parameter is
10
forced to be equal to 95% of the theoretical value calculated from equation 8 taking into
consideration the steric effect. In addition, the parameters for each model which are found
to give similar values at different temperatures, have been forced to be constant at values
which minimize the total sum of squares error. In the virial model, only the virial first
constant has been forced to be constant.
Results and Discussion
The unconstrained optimization parameters for the sorption of methane, ethane and
ethylene on ETS-10 zeolite are presented in Tables 2, 3 and 4 respectively. The fits of the
ten models used to the methane adsorption data, is excellent with the exception of
Freundlich model as indicated by a very large sum of squares. The fit of the models to the
ethylene adsorption data is comparable to methane's. On the other hand, the fits to the
ethane adsorption data is relatively the weakest of the three sets. From examination of the
total sum of squares error, the Radke-Prausnitz and the virial three constant models appear
best. This is expected since the number of constants for each model is four.
Comparing the saturation concentration parameter obtained from the fit of each model
to the methane data indicates that the values obtained from Toth, Unilan, LRC., LangmuirFreundlich and Mathews-Weber models are too low when compared to the theoretical value
calculated from equation 8 (2.66 mole/kg). The values obtained from Radke-Prausnitz
model are too high at 315, 325 and 350 K and low at 280 and 300 K. However, the values
obtained from Volmer model are comparable to the theoretical value. Values of Henry's
constant extracted from all models are comparable to the values obtained from the virial
three constant model.
The values of the saturation concentration obtained from the fits of Volmer and RadkePrausnitz models to the ethane adsorption data are too high in comparison to the theoretical
value (1.75 mole/kg). However, the values obtained from the remaining models are all very
close to the theoretical values.
The x-ray diffraction analysis of the extruded ETS-10 sample indicated that the
amount of non crystalline material is negligible. This conclusion was also supported by the
11
experimental values of qs obtained for methane, ethane and ethylene which were very close
to the theoretical values calculated for pure ETS-10 zeolite using equation 8.
Henry's constant values calculated from the Radke-Prausnitz and the Volmer models
are comparable to the values obtained from the virial three constant model. The values
obtained from Mathews-Weber appear too low, while the values obtained from the
remaining models appear too high relative to the virial isotherm.
For ethylene adsorption data, the values of q s obtained from all models except Unilan
are comparable to the theoretical value (2.00 mole/kg). The values obtained from the
Unilan model are almost twice the theoretical value. The values of Henry's constant
extracted from all models except the Mathews-Weber appear too high when compared to
the values calculated from the virial three constant model (Toth and Unilan values are at
least thirty times the virial's). The values given by the Mathews-Weber model appear too
low.
In the constrained regression, the saturation concentration for methane, ethane and
ethylene have been fixed at 2.66, 1.75 and 2.00 mole per kg of ETS-10 respectively. These
values correspond to 95% of the theoretical values calculated from equation 8. Other model
parameters which exhibit no trend in the unconstrained regression have been optimized
between the minimum and maximum values obtained from the unconstrained regression
corresponding to each parameter till a minimum sum of squares error is reached. The
constrained regression results are given in Tables 5, 6 and 7 for methane, ethane, and
ethylene respectively.
As a result of constraining the model parameters, the total sum of squares error obtained
from each model increases. However, the values of K H become more consistent.
12
The vant Hoff equation parameters for the sorption of methane, ethane and ethylene on
ETS-10 zeolite are given in Table 8 for all the models. The isosteric heat of adsorption
parameters calculated for methane data using all models except the Radke-Prausnitz are
consistent at approximately 21 kJ/mole. Values of K
determined from the Radke-
Prausnitz, the Mathews-Weber and the Volmer models appear too low when compared to
the value obtained from the virial model. The corresponding K values obtained from Toth
and Unilan models are consistent with those of the virial model.
The value of heat of adsorption of Toth and Unilan models for ethane data are
comparable to virial's. However, the values obtained by other models differ. Only the pre
exponential factor for the Toth model approaches the value obtained for the virial three
constant model.
The vant Hoff parameters obtained by all models for ethylene data deviate significantly
from the values extracted for the virial three constant model. This is of course attributed to
the large deviation of Henry's constant values.
Plots of the isotherms of methane, ethane and ethylene data on ETS-10 zeolite have
been constructed together with the fit of Toth, Unilan and virial three constant models using
the constrained parameters. The plots are shown in Figures 1, 2, and 3 respectively.
Three different experiments were carried out to examine the adsorption behavior of the
binary system methane-ethane on ETS-10 zeolite at various temperatures and pressures.
Two runs were performed at 280 K and at a pressures of 150 kPa and 500 kPa and the third
run was conducted at 325 K and 150 kPa. The experimental data are all symmetrical and
consistent. In addition, an excellent fit has been obtained using the IAST in conjunction
13
with with Toth, Unilan and Virial three constant isotherms for the four runs. Plots of the
adsorbed phase mole fraction of methane versus the gas phase mole fraction of methane are
presented in Figures 4-a, 4-b, and 4-c. These plots indicate that the IAST-Toth combination
appears the best among the models used. In addition, the three models support the
experimental data that the separation of methane from ethane on ETS-10 is possible at any
conditions and it is best at low temperature and pressure. The x-q fit for this system is
presented in Figure 4-d. Comparing the results obtained for this system on ETS-10 to those
obtained by Abdul Rehman et al.31 and Loughlin et al.32 on 13X and 5A zeolites indicates
that the separation of methane from ethane is more practical on ETS-10 zeolite.
The methane-ethylene system has been examined at three different conditions, namely,
280 K-150 kPa, 280 K-250 kPa, and 325 K-150 kPa. The x-y fits to the data are presented
in Figures 5-a, 5-b, and 5-c while the x-q plots are shown in Figure 5-c. The results
indicate that methane is very weakly adsorbed in the presence of ethylene and a separation
can be achieved easily at any conditions but is best at low temperature and pressure.
Three experiments at the same conditions of the previous system were obtained for the
binary system ethane-ethylene. The data and the fits are presented in Figures 6-a, 6-b, 6-c,
and 6-d. The results indicate that ethane adsorption on ETS-10 is weak in the presence of
ethylene which indicates that ETS-10 is a highly appropriate adsorbent for the separation of
ethane from ethylene. This conclusion is supported by the three models used to fit the
experimental data for this system (IAST-Toth, IAST-Unilan and IAST-Virial).
The adsorption behavior of the ternary system methane-ethane-ethylene has been
examined in four experiments at two different temperatures 280 and 325 K and at a
pressure of 200 kPa at different loading of ethylene and ethane. The data obtained are
14
compared to the fit of IAST model in conjunction with Toth, Unilan and Virial pure
component models at the same conditions. Sample results are tabulated as x-y comparison
in Table 9 and x-q comparison in Table 10. The results obtained from the three cases are
comparable to the data. From consideration of the amount adsorbed at different loading,
the concentration of ethane in the adsorbed phase does not vary significantly at low loading
of ethane suggesting that methane molecules replace only ethylene molecules in the
adsorbed phase as the partial pressure of methane increases. This conclusion is supported
by the three models.
Conclusions
With the exception of the Freundlich model, the fits of the other nine models to the pure
adsorption equilibrium data of methane, ethane, and ethylene on ETS-10 zeolite are
reasonable. The Radke-Prausnitz model is the most appropriate for the methane and ethane
data. However, virial three constant model is best for the ethylene data.
The ideal adsorbed solution theory model (IAST) is used to fit all the multicomponent
data obtained on ETS-10 zeolite. The constrained optimized parameters of Toth, Unilan and
virial three constant isotherms are used in the IAST equations. Similar results have been
obtained from the three isotherms. The fit of IAST to the multicomponent systems
methane-ethane, ethane-ethylene, methane-ethylene, methane-ethane-ethylene on ETS-10
zeolite are satisfactory.
The separation of methane from ethane on ETS-10 zeolite is possible and is better than
the separation on 13X and 5A adsorbents. The separation of ethane from ethylene is easy
15
on ETS-10 zeolite especially at low temperatures. The effect of pressure on the separation
of ethane-ethylene on ETS-10 is not significant.
Acknowledgments
The authors wish to acknowledge the support of King Fahd University of Petroleum &
Minerals (KFUPM), Dhahran, Saudi Arabia during the course of this work.
Acknowledgements are also extended to S. M. Kasnicki of Engelhard who provided the
samples of ETS-10 and to the research institute at KFUPM for assistance in extrusion of the
ETS-10 samples.
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