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Experimental Investigation and Thermodynamic Modeling of CH4/N2 Adsorption on Zeolite 13X Masoud Mofarahi* and Ali Bakhtyari Chemical Engineering Department, Persian Gulf University, Bushehr, Iran ABSTRACT: To implement an experimental study of CH4/ N2 adsorption on Zeochem Co. zeolite 13X, a volumetric apparatus was utilized. In this regard, pure adsorption isotherms were measured at different temperatures [(273, 283, 303, 323, and 343) K] and pressures up to 10 bar, while binary data were collected at (303 and 323) K and different pressures and bulk gas phase molar fractions. Integral and differential thermodynamic consistency tests (TCT) were performed to validate the collected data and certify accuracy of the measurements. To have a thermodynamic view over the investigated system, thermodynamic functions such as enthalpy, entropy, surface potential, and Gibbs free energy were estimated numerically. Besides, the measured pure isotherms were regressed using different isotherm equations and the regressed parameters were applied to different models based on the thermodynamic theory of solutions, i.e., ideal adsorbed solution theory (IAST), vacancy solution models (VSM), and Peng− Robinson two-dimensional equation of state (PR 2D-EOS). All the models were applied in the predictive scheme. Experimental and predicted adsorption data were compared through the appropriate phase diagrams. Almost all the models could predict binary adsorption behavior of CH4 and N2 over zeolite 13X. zeolites. Na+ as the major cations, a 1.2 Si/Al ratio, and a 13.7 Å free diameter of central cavity are the characteristics of 13X zeolites. Approximately 7.4 Å 12-member oxygen ring apertures allow for transfer of molecules with kinetic diameter of 8.1 Å.12 Type X zeolites are highly selective for N2 in air separation due to interactions between Na+ cation sites and quadrupole moment of N2.13 Higher polarizability of CH4 than N2 causes stronger interactions of CH4 comparing N2 with polar adsorbents, e.g., 13X zeolites. Thus, it can be considered as a promising adsorbent for CH4 and N2 adsorptive separation.1,11 Accurate and reliable equilibrium data in a wide range of temperatures and pressures are essential information for optimum designing of the adsorptive separation processes. Multicomponent and single-component adsorption equilibrium data are necessary to evaluate the performance of an adsorption based separation process precisely. Measuring and publishing accurate multicomponent equilibrium data have an important role in development of the nonpredictive thermodynamic models e.g. real adsorbed solution theories (RAST).14−17 Besides, such data have significant effects on prediction of the multicomponent adsorption kinetics.18 Thus, some reliable and accurate multicomponent data must be collected experimentally. Adsorption isotherms of pure CH4 and N2 on zeolite 13X at temperatures from (273 to 318) K and pressures up to 20 MPa were previously reported by Salem et al.19 Cavenati et al. measured pure adsorption isotherms of CH4 and N2 on CECA zeolite 13X at temperatures from 298 to 323 K and pressures up

1. INTRODUCTION Currently, one-fourth of the required energy in domestic and industrial applications is supplied from natural gas. Nitrogen existent in methane-enriched natural gas streams is the main cause for low pipeline quality and high heating value. Maximum N2 content of natural gas streams cannot be more than 4% to meet the pipeline quality.1,2 Besides, global warming caused by the emission of CH4 as the most important non-CO2 greenhouse gas, landfill gas recovery for getting new resources of energy,3 improvement of Fischer−Tropsch synthesis process by a selective recycling of the tail gas4 and recovery of CH4 from coalmines with high N2 contamination5−7 are other applications of CH4 and N2 separation. Application of separation processes that are more cost-effective than cryogenic distillation for N2 removal from CH4 enriched gas streams is increasingly favorable. Adsorptive gas separation processes such as pressure swing adsorption (PSA) for N2 removal and upgrading CH4 enriched gas streams are currently state of the art. As a result, the knowledge of adsorption equilibria on a specific adsorbent is of great interest.5−10 The selected adsorbent for the particular adsorptive separation process has to ensure a good fractionation between molecules composing the bulk gas mixture. Separation on the basis of adsorption occurs due to difference in physical properties of adsorbates, e.g., molecular weight, shape, polarity, and dipole and quadrupole moments which makes it possible for the adsorbent particles to hold some molecules stronger than the others or to prevent the entrance of larger molecules.11 Zeolites e.g. type X zeolites are widely used for separation of gases. The framework of type X zeolites is the same as naturally occurring faujasites and has the largest cavity pore volume among any other known © XXXX American Chemical Society

Received: September 6, 2014 Accepted: January 7, 2015

A

DOI: 10.1021/je5008235 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

to 5 MPa.1 Adsorption of pure and binary mixtures of CH4 and N2 on CECA 13X zeolite at 313 and 373 K and 1 atm total pressure was studied by Mulgundmath et al. using a chromatographic technique.11 In the previous studies of our laboratory, O2/N2, C2H6/C2H4, CO2/CH4 and CH4/N2 adsorption were investigated both experimentally and thermodynamically.20−23 In the present study, to investigate adsorption characteristics of CH4 and N2 mixtures, adsorption equilibrium data of pure CH4 and N2 and their binary mixtures within a wide range of temperatures and pressures on Zeochem zeolite 13X are presented. Equilibrium selectivities curves and x-y diagrams were obtained experimentally at different pressures and gas phase molar fractions and compared with the calculated ones. Such data have never been previously published. In contrast to the refs 20 and 21, individual adsorbed amount, molar fractions of the adsorbates and equilibrium selectivity were measured experimentally. Comparing ref 23 (our previous paper that reported pure and binary equilibrium data of CH4/N2 on Zeolite 5A), in the present work, due to the measured data in a constant-pressure and constant-composition path, two different thermodynamic consistency tests (differential test and integral test) were performed. Besides, thermodynamic functions such as surface potential, Gibbs free energy, and entropy for adsorption of adsorbates were estimated. Thermodynamic modeling was implemented applying different models such as ideal adsorbed solution theory (IAST), Wilson vacancy solution model (W-VSM), Flory−Huggins vacancy solution model (FH-VSM), and Peng−Robinson (PR) two-dimensional equations of state (2D-EOS). The capability of these models against experimental data for this system was tested. Integral and differential thermodynamic consistency tests (TCT) were performed to validate the collected data and certify accuracy of the measurements.

and valves, and their volumes were determined using helium gas expansion in room temperature. To control temperature of the adsorption cell, a type K thermocouple with ± 0.1 K uncertainty was used. Controlling temperature of the loading cell was achieved using an RTD. Total mole of the injected gas into the system was determined by appropriate pressure, temperature, and volume measurements and a conventional equation of state. All the measured temperatures and pressures were recorded in constant time intervals via a recorder (Logoscreen 50, Jumo). About 12 g of the adsorbent particle weighted and loaded into the adsorption cell. After each measurement, particles were heated and reactivated in situ at 250 ◦C with helium purging under 0.25 bar vacuum supplied by a vacuumbrand RE6 model vacuum pump with 0.00005 bar vacuum levels for at least 6 h. A water bath (MC 12, Julabo Tech.) was applied to maintain temperature of the adsorption cell constant during the measurements. The temperature of water bath was controlled using a refrigeration circulator with 0.02 K uncertainties. Hence, the isothermal condition was achieved. In the binary experiments, the composition of bulk gas before and after equilibrium was analyzed using a gas chromatograph (GC) BEIFEN 3420 precalibrated with standard mixtures of known compositions. The thermal conductivity detector (TCD) with a packed column was initially calibrated under the injector temperature of 120 °C, detector temperature of 180 ◦C, column temperature of 35 °C and a 20 mL·min−1 helium flow rate. These operating conditions were kept fixed in all the further measurements. Gas phase molar fractions could be measured with 0.0001 uncertainties. Circulation of gas during measurements was implemented to ensure homogeneity and to reduce the time of equilibration. It was achieved using a homemade circulation pump. Performing the circulation caused no effect but homogeneity of the gas and reducing time of equilibration. A set of measurements were repeated with and without the mentioned pump. The obtained results such as pressure changes and isotherms were the same, but only in a relatively less time. The equilibrium state was considered to be reached when the temperature and the pressure of the system became constant for at least 1 and 2 h for each equilibrium data point in pure and binary measurements, respectively. On the other hand, at equilibrium state, changes of temperature and pressure did not exceed 0.1 K and 0.5 mbar, respectively. The quantity of adsorbed gas could be calculated from the recorded temperatures, pressures, and gas phase compositions before and after equilibrium state using a mole balance. SRK 3D-EOS was utilized to calculate the gas phase density before and after equilibrium state. In order to avoid errors in mole balance in binary measurements, the adsorption cell was evacuated and the adsorbent particles were reactivated after each equilibrium data point. Hence, reliable and accurate equilibrium data are obtained.24

2. MATERIALS AND EXPERIMENTAL METHOD 2.1. Materials. Zeolite 13X with the characteristics shown in Table 1 was supplied from Zeochem Co. (Switzerland). The gases used in this work and their purities and suppliers are shown in Table 2. Table 1. Details of the Adsorbent Used in This Study adsorbent

Zeolite 13X

supplier type particle size [cm] particle density [g·cm−3] heat capacity [cal·gr−1·K−1]

Zeochem Co. Sphere 0.15 0.93 0.42

Table 2. Details of Sample Gases Used in This Study gases

purity

supplier

N2 CH4 He

99.999 % 99.95 % 99.999 %

Bushehr Lian Oxygen (Iran) Technical Gas Services (U.A.E.) Technical Gas Services (U.A.E.)

3. MODEL DESCRIPTION Since it is costly and time-consuming to collect experimental data for mixtures, predicting multicomponent equilibrium data from single-component isotherms is preferable. In spite of the numerous models developed for this purpose, prediction of the multicomponent gas adsorption equilibria is still a challenge. It is often more complicated at the supercritical conditions, which is prevalent in the engineering interests. Various methods for predicting multicomponent gas adsorption equilibria have been proposed in the literature.25 Among them, models based on the thermodynamic theory of solutions are more favorable because

2.2. Apparatus and Procedure. Adsorption equilibrium measurements were implemented utilizing a static volumetric apparatus used in our previous works20−23 and shown in Figure 1. Main elements of the apparatus are adsorption cell, loading cell, circulation pump, and a pressure transmitter with ± 0.0005 bar uncertainty. All the elements are connected via 1/8 in. tubes B



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Figure 1. Schematic diagram of the volumetric adsorption apparatus.

component adsorption calculated by eq 1. The integrant (q/P) must be identified at the lower bond of integral of spreading pressure.28,29 Toth isotherm equation, which is useful in both low and high-pressure ranges, is as follows:25

of their simplicity and accuracy. Such models need only singlecomponent isotherms to predict multicomponent equilibrium data. 3.1. Ideal Adsorbed Solution Theory (IAST). A useful model for prediction of multicomponent gas adsorption equilibria is ideal adsorbed solution theory originally proposed by Myers and Prausnitz.26,27 This model was proposed on the basis of ideal behavior of adsorbates in the adsorbed phase as well as the bulk gas phase. Relation between the spreading pressure πi* and the equilibrium pressure of each species Pi can be obtained using Gibbs equation and a proper pure-substance adsorption isotherm equation: πi* =

πiA = RT

∫0

Pi0

πi* = π *

qi* Pi

dPi

q = qm

⎡ Q ⎛ T0 ⎞⎤ ⎜ − 1⎟⎥ b = b0 exp⎢ ⎠⎦ ⎣ RT0 ⎝ T

(1)

⎡ ⎛ T ⎞⎤ qm = qm0 exp⎢χ ⎜1 − ⎟⎥ ⎢⎣ ⎝ T0 ⎠⎥⎦

(3)

⎛ T⎞ t = t 0 + δ ⎜1 − 0 ⎟ ⎝ T⎠

NC

∑

qi = xiqT

(5)

is adsorbed amount of pure substances in the standard state pressure P0i . For solving the IAST equations simultaneously, the following constraints must be satisfied: NC i=1

NC i=1

(10)

where t0 is the exponent at the reference temperature and δ is a constant parameter. A six-parameter isotherm equation is obtained substituting eqs 8 to10 into eq 7. 3.2. Wilson Vacancy Solution Model (W-VSM). Suwanayuen and Danner proposed a vacancy solution model for describing single and multicomponent gas adsorption equilibria.30,31 Vacancy solution model considers osmotic equilibrium between two vacancy solutions involving adsorbates species and a hypothetical entity defined as a vacuum space acting as the solvent. Wilson activity coefficient model was utilized to account for nonideality of the adsorbed mixture. The following equation was obtained for single-component adsorption isotherms:

(4)

q0i

∑ xi = ∑ yi = 1

(9)

where qm0 is the maximum adsorbed amount at the reference temperature and χ is a constant parameter. Temperature dependency of the exponent t in Toth equation characterizing the system heterogeneity may take the following form:25

yi and xi are molar fractions in the bulk gas phase and the adsorbed phase, respectively. Total adsorbed amount qT and partial adsorbed amounts of the components qi can be obtained using the following equations: xi 0 0 q (Pi ) i=1 i

(8)

where T0 is the reference temperature and b0 is the affinity constant at T0. Q is the heat of adsorption and R is the universal gas constant. The following temperature dependency can be taken for the maximum adsorbed amount of Toth equation qm:25

where π* is reduced spreading pressure of the mixture, qi* is pure substance isotherm and P0i is the standard state pressure. Applying Rault’s law for equilibrium relation leads to the following equation for distribution of the components between the bulk gas phase and the adsorbed phase:

1 = qT

(7)

The temperature-dependent parameters are used to interpolate equilibrium data to the other temperatures as well as calculating the isosteric heat of adsorption. Temperature dependency of the affinity constant b in Toth isotherm equation may take the following form:25

(2)

Pyi = Pi0(π *)xi

bP [1 + (bP)t ]1/ t

(6)

Different isotherm equations can be used for adsorption of pure gases. Predicting multicomponent gas adsorption equilibria depends on precise evaluation of spreading pressure for singleC



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⎡ n ∞ θ ⎤⎡ 1 − (1 − Λ vi)θ ⎤ P=⎢ i ⎥⎢Λiv ⎥ ⎣ bi 1 − θ ⎦⎣ Λiv + (1 − Λiv)θ ⎦ ⎡ Λ (1 − Λ vi)θ (1 − Λiv)θ ⎤ exp⎢ − vi − ⎥ Λiv + (1 − Λiv)θ ⎦ ⎣ 1 − (1 − Λ vi)θ

θ=

ni ni∞

ln γv = 1 − ln(x1s Λ v1 + x 2s Λ v2 + xvs) ⎛ x1s Λ1v x 2s Λ 2v −⎜ s + s s x 2s + x1s Λ 21 + xvs Λ 2v ⎝ x1 + x 2 Λ12 + xv Λ1v (11)

+

where θ is the fractional loading and n∞ i , bi, Λiv, and Λvi are the model parameters. The parameter b is Henry’s law constant or affinity constant used for interaction at infinite dilution, i.e., lowpressure area. Temperature dependency of this parameter is as follows:32

(13)

Theoretically, qv,i could be taken as the heat of adsorption. n∞ i is the limiting adsorbed amount or saturation capacity with the following temperature dependency:32 ⎛ ri ⎞ ⎜ ⎟ ni∞ = ni∞ ,0 exp⎝ ⎠ T

⎛ α 2θ ⎞ ⎛ n∞ θ ⎞ ⎟ P=⎜ i ⎟ exp⎜ iv ⎝ bi 1 − θ ⎠ ⎝ 1 + αivθ ⎠

(14)

θ=

The following are temperature dependencies of Wilson parameters Λiv and Λvi:32 Λiv =

⎛ λ − λii ⎞ σi ⎟ exp⎜ − iv RT ⎠ σv ⎝

(15)

Λiv =

⎛ λ − λvv ⎞ σv ⎟ exp⎜ − vi ⎝ RT ⎠ σi

(16)

ni ni∞

(22)

⎛ ri ⎞ ⎜ ⎟ ni∞ = ni∞ ,0 exp⎝ ⎠ T

(24)

αiv = τini∞ − 1

(25)

Substituting eqs 22 to 25 into eq 21, a five-parameter model is obtained for describing single-component isotherms. Parameters are bi,0, qv,i, n∞ i,0 , ri, and τi. In the case of multicomponent adsorption, the following equilibrium relation for the distribution of components between two phases is obtained:33

⎧ ⎡ nm ni∞ n ∞ − ni∞ ⎤ yi ϕiP = γixi ∞ Λiv exp⎨(Λ vi − 1) − ⎢1 + m ⎥ nm bi nm ⎦ ⎣ ⎩

yi ϕiP = γixi

⎪

⎪

⎤ nm ni∞ ⎡ exp(αiv) ⎤⎡⎛ ni∞ − nm∞ ⎞ ⎢ ⎥⎢⎜ ⎟ − 1⎥ln γvxvs ∞ ⎥⎦ nm bi ⎣ 1 + αiv ⎦⎢⎣⎝ nm ⎠ (26)

where n∞ m is the same as eq 18 and ϕi and γi are fugacity coefficient

⎪

⎪

of the gas phase and activity coefficient of the adsorbed phase, respectively. Flory−Huggins activity coefficient model, which is applied to account for the nonideality of adsorbed mixture, is

(17)

NC

nm∞ =

∑ xini∞

NC

(18)

ln γi = −ln ∑

where ϕi and γi are fugacity coefficient of the gas phase and activity coefficient of the adsorbed phase, respectively. Wilson activity coefficient model, which is applied to account for the nonideality of the adsorbed mixture, is

j=1

i=1

NC

ln γk = 1 − ln ∑ xjs Λkj − j=1

(21)

where θ is the fractional loading and n∞ i , bi, and αiv are the model parameters. The following are the temperature dependencies of 32,33 affinity constant b, limiting adsorbed amount n∞ i and αiv: ⎛ qv , i ⎞ bi = bi ,0 exp⎜ − ⎟ ⎝ T ⎠ (23)

Substituting eqs 12 to 16 into eq 11, a seven-parameter model is obtained for describing single-component isotherms. Seven parameters are bi,0, qv,i, n∞ i,0 , ri, (σi/σv), ((λiv − λii)/R), and ((λvi − λvv)/R). In the case of multicomponent adsorption, using equality of the chemical potentials of the adsorbates in the bulk gas phase and the adsorbed phase, the following equilibrium relations for the distribution of components between two phases are obtained:31

⎫ ln γvxvs⎬ ⎭

(20)

A trial and error method must be applied to obtain a solution for calculating the total adsorbed amount of mixture nm and the molar fraction of adsorbed phase xi at a given bulk gas phase molar fraction yi. 3.3. Flory−Huggins Vacancy Solution Model (FH-VSM). The pairwise interaction parameters in W-VSM, Λiv, and Λvi, have been found to be highly correlated. Cochran et al.33 utilized Flory−Huggins activity coefficient model instead of the Wilson model to avoid this problem. The following equation for singlecomponent adsorption isotherms was obtained using the Flory− Huggins activity coefficient model combining vacancy solution definitions:

(12)

⎛ qv , i ⎞ bi = bi ,0 exp⎜ − ⎟ ⎝ T ⎠

⎞ xvs ⎟ s s s xv + x1 Λ v1 + x 2 Λ v2 ⎠

NC

(27)

+ [1 − ((1 + α1v)x1s + (1 + α2v)x 2s + xvs)−1] (28)

NC j=1

⎞−1⎤ ⎟ ⎥ 1 ⎟⎠ ⎥⎥ ⎦

ln γv = −ln[(1 + α1v)x1s + (1 + α2v)x 2s + xvs]

∑ [xjs Λik(∑ xjs Λij)−1] i=1

⎡ ⎛ NC x s j ⎢ + ⎢1 − ⎜⎜∑ αij + 1 ⎢ ⎝ j = 1 αij + ⎣ xjs

Total adsorbed amount of mixture nm and molar fraction of the adsorbed phase xi at a given bulk gas phase molar fraction yi are

(19) D



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Zaϕî ωi = kif ig

calculated utilizing a trial and error method. FH-VSM is a less complex model and involves less parameter than W-VSM. It should be mentioned that SRK three-dimensional equation of state (3D-EOS)34 was utilized to calculate fugacity coefficients of the gas phase in both W-VSM and FH-VSM models. Although, W-VSM and FH-VSM are widely applied for describing gas adsorption equilibria, they are thermodynamically inconsistent models as discussed by different authors.28,29,35 3.4. Peng−Robinson Two-Dimensional Equations of State (PR 2D-EOS). A general form of two-dimensional equations of state and the corresponding fugacity coefficient of adsorbed phase was proposed by Zhou et al.:36

ωi is the partial adsorbed amount of each species in the mixture, ki is the slope of isotherm at the origin, and f gi is the fugacity of components in the bulk gas phase calculated using conventional 3D-EOS such as SRK.34 Applying equilibrium relation and fugacity equations of adsorbed and bulk gas phase and supplied with adsorption isotherms of pure substances and a nonlinear regression algorithm, parameters of model αi, βi and ki can be determined. Parameters included in eqs 7, 11, 21, and 34 are determined by minimizing the following objective function:

⎤ ⎡ αω 2 [1 − (βω)m ] = ωRT ⎢A π + 2⎥ ⎣ 1 + Uβω + W (βω) ⎦

%AAD = (29)

A and π are surface area and surface pressure, respectively. ω is the adsorbed amount and α and β are the model parameters. PR 2D-EOS is obtained by setting m = 1, U = 2, and W = −1. Both single and multicomponent gas adsorption equilibria can be described using 2D-EOS. In the case of multicomponent adsorption, a proper mixing rule is required. Zhou et al.36 used the classical mixing rule and obtained fugacity coefficient of the adsorbed phase using conventional thermodynamic relations:

(30)

NC NC

∑ ∑ xixjβij

β=

(31)

i=1 j=1

∑

Xj

j=1

αi + αj

αij =

X jcal − X jex (39)

4. THERMODYNAMIC CONSISTENCY TEST (TCT) As discussed by Talu,37 because of the difficulties in collecting multicomponent gas adsorption equilibrium data, the accuracy of measurements must be checked and the validity of collected data must be verified. Pure and binary gas adsorption thermodynamics was studied by Sircar et al.38,39 using the definition of Gibbsian surface excess. Surface potential of Gibbs adsorbed phase Φ can be expressed in terms of Gibbsian surface excess nei variables using the following equation:34

NC NC i=1 j=1

NDP

100 NDP

where Xcal and Xex are the calculated and experimental adsorbed amounts, respectively when applied for eqs 7 and 34. They are the calculated and experimental equilibrium pressure, respectively when applied for eqs 11 and 21. NDP is number of data points used in the regression.

∑ ∑ xixjαij

α=

(38)

NC

d Φ = −s mdT −

(32)

2

∑ nie dμi

(40)

i=1

βij =

ββ i j

(33)

Corresponding fugacity coefficient of the adsorbed phase applying PR 2D-EOS and the classical mixing rule is

where sm is excess entropy and μi is the chemical potential of equilibrium gas phase at T, P and gas molar fraction yi. This equation can be differentiated or integrated to generate different consistency tests for pure and binary gas adsorption equilibria. Full details for derivation of integral and differential thermodynamic consistency tests are presented in the studies of Sircar et al.38,39 If eq 40 is integrated in a constant T and P path, following integral test is obtained for adsorption of an ideal binary gas mixture:

ϕ̂ ai

NC

a

ln(ϕî ) =

2 ∑ j = 1 βijωj − βω 1 − βω

− ln[1 − βω] − ln(Za) + T1

+ T2

(34) NC

T1 = −

2α ∑ j = 1 βijωj − αβω 2

RTβ[1 + 2βω − (βω) ] αβω +

T2 = −

NC 2β ∑ j = 1 αijωj

1 + (1 + ln 1 + (1 −

Za =

aπ Aπ = RT ωRT

−

(35)

NC 2α ∑ j = 1 βijωj

2 2 RTβ 2ω 2 )βω 2 )βω

n1e(1 − y1) − n2ey1

Φ*2 − Φ1* = RT

∫0

Φ*i =− RT

nie dP P

∫0

P

1

y1(1 − y1)

dy1

(41)

*

(42)

where ne1 and ne2 are the surface excess of component 1 and 2 in the binary system, nei * is the surface excess of pure substance i and Φi* is the surface potential of pure gas. The left-hand side (LHS) of eq 41 can be calculated using eq 42 and single-component isotherm data, while the right-hand side (RHS) is calculated at constant T and P using binary adsorption data. Thus, the integral consistency between pure and binary data is checked in this way. Equation 40 can be differentiated with respect to P at constant T and y1 to generate the following differential consistency test:

(36)

(37)

Za and a are adsorbed phase compressibility factor and specific molar area, respectively. According to the thermodynamic treatment of Zhou et al.,36 the following equilibrium relation was obtained: E



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Table 3. Pure Adsorption Isotherms of CH4 on Zeolite 13X 273 Ka

283 K

b

P

q

bar

mol·kg

0.0481 0.2025 0.3921 0.5708 0.7928 0.9945 1.2913 1.566 1.9348 2.9819 4.0931 5.0356 6.0062 6.9301 8.0282 9.0511 10.006 a

303 K

P −1

q

bar

0.05728 0.20018 0.36478 0.51454 0.68805 0.82983 1.03476 1.20317 1.4378 1.87047 2.18487 2.39706 2.57032 2.71883 2.87965 3.00791 3.0979

P

mol·kg

0.044 0.191 0.372 0.573 0.786 0.999 1.276 1.579 2.015 2.985 3.983 5.031 6.048 7.041 8.097 9.083 10.019

−1

bar

0.03533 0.14173 0.27504 0.40896 0.54767 0.67914 0.85974 1.02806 1.22863 1.60769 1.94206 2.21588 2.43715 2.60993 2.75204 2.88224 2.95562

323 K q mol·kg

0.0487 0.1894 0.3764 0.5836 0.7851 1.0204 1.2794 1.5974 1.9588 2.897 3.9116 4.9093 5.98 7.0328 8.0633 9.042 10.044

P −1

bar

0.02806 0.09255 0.18224 0.27696 0.36474 0.46275 0.58188 0.70209 0.8692 1.22149 1.51958 1.8062 2.04752 2.25732 2.42239 2.55129 2.70334

0.0501 0.1897 0.3924 0.5934 0.7937 1.0141 1.3285 1.5882 2.0081 3.0197 4.0107 5.0255 5.9711 7.0439 8.1165 9.1031 10.041

q

P

343 K q

P

q

bar

mol·kg−1

0.02285 0.06992 0.13475 0.20642 0.26795 0.34571 0.43671 0.51125 0.63441 0.91449 1.16615 1.41313 1.60895 1.82082 2.00944 2.16778 2.30159

0.0535 0.1884 0.3853 0.598 0.7881 1.0263 1.2931 1.6161 2.0579 3.0237 4.0062 5.0306 6.0355 7.0214 8.0476 9.1082 10.055

0.01569 0.05654 0.10571 0.15489 0.19984 0.25332 0.31663 0.38338 0.48408 0.66142 0.86503 1.05171 1.22787 1.39469 1.58249 1.72786 1.87148

q

P

q

bar

mol·kg−1

0.052 0.193 0.403 0.595 0.790 0.996 1.321 1.622 2.051 3.071 4.090 5.176 6.176 6.996 8.013 9.070 10.033 -

0.00845 0.02438 0.04641 0.06804 0.09182 0.11557 0.14898 0.18728 0.23541 0.33209 0.42317 0.52863 0.61814 0.68815 0.76768 0.85693 0.93046 -

mol·kg

−1

Measured with 0.1 K uncertainty. bMeasured with 0.5 mbar uncertainty.

Table 4. Pure Adsorption Isotherms of N2 on Zeolite 13X 273 Ka P

q

bar

303 K

P

mol·kg

0.049 0.186 0.389 0.580 0.807 1.009 1.320 1.606 2.061 2.964 4.022 5.051 6.059 7.059 8.061 9.067 10.023 a

283 K

b

−1

bar

0.02845 0.09109 0.17680 0.25165 0.34202 0.41016 0.51217 0.60137 0.75031 0.97910 1.19985 1.39852 1.55914 1.70135 1.82190 1.93845 2.05569 -

0.052 0.200 0.387 0.583 0.784 1.006 1.319 1.593 1.971 2.975 4.033 5.040 5.939 7.007 8.009 8.917 9.982 -

q mol·kg

P −1

bar

0.02436 0.07776 0.14253 0.20791 0.27203 0.33930 0.42729 0.50047 0.60296 0.84690 1.05374 1.23791 1.38789 1.55281 1.68602 1.80187 1.93003 -

323 K

mol·kg

0.047 0.196 0.394 0.609 0.794 1.035 1.320 1.601 2.006 2.993 3.965 4.996 5.961 6.965 7.979 9.042 10.016 -

−1

0.01651 0.05303 0.11316 0.16159 0.20086 0.25223 0.30849 0.37637 0.44425 0.61511 0.75734 0.89704 1.01750 1.14490 1.27753 1.40148 1.51589 -

bar 0.058 0.192 0.393 0.589 0.791 0.988 1.196 1.392 1.600 1.973 2.473 2.972 3.971 4.935 5.972 6.951 7.980 8.964 9.975

343 K

mol·kg

−1

0.01520 0.03906 0.07734 0.11751 0.14747 0.18112 0.21429 0.24362 0.27117 0.32077 0.39219 0.45229 0.57861 0.68359 0.78665 0.87916 0.97314 1.06660 1.14602

Measured with 0.1 K uncertainty. bMeasured with 0.5 mbar uncertainty. *

n2e = ne − P

∂ ⎡⎢ ∂P ⎢⎣

y1

∫0

n1e(1 − y1) − n2ey1 y1(1 − y1)

⎤ dy1⎥ ⎥⎦ T, y

1

*

n1e = ne − P

∂ ⎡⎢ ∂P ⎢⎣

∫y

1

1

n1e(1 − y1) − n2ey1 y1(1 − y1)

⎤ dy1⎥ ⎥⎦ T, y

1

The quantities on the LHS of eqs 43 and 44 can be calculated from single-component adsorption isotherms at any T and P. The quantities on the RHS of eqs 43 and 44 can be evaluated using binary adsorption equilibrium data at constant T and yi. Thus, the differential consistency between pure and binary data is checked in this way.

(43)

5. THERMODYNAMIC OF ADSORPTION To have a thermodynamic analysis on the adsorption phenomena, we usually discuss about Gibbs free energy (ΔG), entropy (ΔS) and enthalpy (ΔH). Each property has a specific physical meaning used to understand adsorption behavior. Gibbs

(44)

NC

ne =

∑ nie i=1

(45) F



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free energy (or surface potential) indicates minimum necessary work to load the adsorbents to a certain level in an isothermal path. Entropy is the criterion of disorder or the ways in which a thermodynamic system can be rearranged. On the other hand, entropy is a balance between vibration, rotation and translation freedoms of the molecules inside the adsorbent particles. Enthalpy elucidates the heat effect of adsorption, which makes us understand the way adsorbed molecules packed inside the adsorbent. Besides, heats of adsorption for mixture ingredients determine the temperature change caused by adsorption and desorption during a process in the energy balance. Hence, information on heats is important in kinetic studies. Gibbs free energy, entropy and isosteric heat (i.e., enthalpy) of adsorption for pure CH4 and N2 were estimated by numerical analysis of the following functions:40−42 Φ* q

(46)

1 ⎡ ∂Φ* ⎤ ΔS = − ⎢ ⎥ q ⎣ ∂T ⎦ P

(47)

ΔG =

ΔH =

⎛ ∂Φ* ⎞ ⎤ 1⎡ ⎟ ⎥ ⎢Φ* − T ⎜ ⎝ ∂T ⎠P⎦ q⎣

(48)

Φ* is the surface potential calculated using eq 42 and q is the equilibrium loading.

6. RESULT AND DISCUSSION 6.1. Pure Adsorption Isotherms. Adsorption isotherms of pure CH4 and N2 on Zeochem zeolite 13X were measured at five temperatures [(273, 283, 303, 323, and 343) K] and pressures up to 10 bar. The collected data are tabulated in Tables 3 and 4. The adsorption isotherm data were correlated by the Toth model and pure-substance schemes of W-VSM, FH-VSM, and PR 2D-EOS. Experimental adsorption isotherms of CH4 and N2 are plotted in Figure 2 and compared against PR 2D-EOS and Toth equations, respectively. Both CH4 and N2 isotherms are type I isotherms according to BET classification in the range of measurements indicating adsorption of gases in microporous adsorbents.25 Obtained isotherms conform to the previously reported experimental isotherms especially at low-pressure region. Amount adsorbed differs slightly at high-pressure region.1,11 Such differences may be due to different sample preparation, different Si/Al ratios of the 13X samples, and differences in the methods of measurement. Measured isotherms of CH4 and N2 at 323 K are compared with those reported by Cavenati et al.1 in Figure 3. Equilibrium loading of CH4 is higher than that of N2 in all the temperatures due to the higher polarizability of CH4 and stronger interactions with polar nature of 13X zeolites. The correlated parameters and the corresponding errors of different models are tabulated in Tables 5 to 8. As shown in these tables, the isotherm data are well correlated by all the proposed models. Obtained percentage average absolute deviations (%AADs) exhibit the optimum ability of the proposed models to describe the pure isotherms of CH4 and N2. The obtained %AADs of all models are less than 5% for pure CH4 and less than 10% for pure N2 according to correlation results. 6.2. Thermodynamic of Adsorption. Estimated heats of adsorption and entropy for CH4 and N2 are shown in Figure 4. As can be seen in Figure 4a, the isosteric heats of adsorption of both gases are practically independent of loading at lower degree of

Figure 2. Pure adsorption isotherms of CH4 and PR 2D-EOS correlation (a), N2 and Toth equation correlation (b).

Figure 3. Comparing pure adsorption isotherms of CH4 and N2 at 323 K with the isotherms reported by Cavnati et al.1

G



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CH4 results in higher surface potential.40−42 Surface potential indicates the minimum work required to load the adsorbent to a certain level in an isothermal path. Accordingly, lower equilibrium capacity results in lower (less negative) surface potential than higher equilibrium capacity. The surface potential of both gases show a remarkable decrease upon a temperature increase from (273 to 323) K. This decline follows from the lower adsorption capacity at 323 K compared to that at 273 K. A monotonically decreases in surface potential with respect to pressure (i.e., loading) to reach a limit at higher pressures is observed. This may be regarded as the surface potential at saturation capacity of the cavity pores at each temperature. Surface potential of adsorption versus loading shows a quick reduction upon further packing of molecules in cavity pores. In such conditions, higher isothermal work is required to pack more molecules into the spaces of cavity pores than at the initial stages (fresh adsorbent). Such a behavior is due to screened active sites of the adsorbent.40−42 Estimated Gibbs free energies of CH4 and N2 are shown in Figure 6. A monotonically decrease in ΔG of both gases with equilibrium pressure is observed. In such a case, packing more molecules into the cavity pores needs isothermal work higher than at the initial stages. Such a manner is due to screened active sites. Estimated ΔG of CH4 are higher than N2 which means CH4 needs a higher pressure and chemical potential to adsorb in the cavities of zeolite 13X.40−42 6.3. Binary Adsorption. Because of the extra degrees of freedom in binary gas adsorption, controlling the equilibrium pressure and gas phase composition in volumetric method are often difficult and need lots of experiments to obtain the specified points in the phase diagrams. Hence, equilibrium data points with relatively equal pressures and gas phase compositions are considered in a data set. Besides, performing TCT is practical in this way. Various equilibrium data of CH4 and N2 binary adsorption on Zeochem Co. zeolite 13X were measured volumetrically. Binary equilibrium data and adsorbed phase properties, i.e., total adsorbed amounts, partial adsorbed amounts, molar fraction of substances, and equilibrium selectivity at (303 and 323) K are tabulated in Tables 9 and 10. Selectivity of adsorption was obtained using equilibrium molar fraction of the bulk gas phase measured directly utilizing GC and molar fraction of the adsorbed phase determined applying mole balance:

Table 5. Regression Results for Pure CH4 and N2 on Zeolite 13X Using PR 2D-EOS parameters

273 K

283 K

303 K

323 K

α β k %AAD

2717.41 0.15728 0.95698 2.066

α β k %AAD

−2989.77 0.09657 0.52180 3.672

343 K

2274.81 0.14244 0.75763 0.939

1389.61 0.11275 0.49733 1.327

504.41 0.08307 0.34393 2.962

−380.79 0.05338 0.24830 4.526

N2 −2674.43 0.09763 0.40269 2.993

−2043.75 0.09975 0.25246 5.535

−1413.06 0.10187 0.16770 9.002

−782.38 0.10399 0.11684 3.356

CH4

coverage and a slight decrease in the heats of both gases is observed at higher degree of coverage. Variation of heats for both gases does not exceed 16%. Zeolites are energetically homogeneous to adsorption if the isosteric heat is independent of loading and they are energetically heterogeneous when the isosteric heat decreases with loading. The observed decrease in the heat of adsorption may be considered as interplay between the interaction energy of adsorbate−adsorbent and adsorbate− adsorbate pairs. In the initial state of adsorption, molecules are located on the fresh cavity pores and their lateral interaction energy (adsorbate−adsorbate interaction) is lower than the effect of the surface heterogeneity. Increasing loading causes occupying more cavities by adsorbed molecules. Accordingly, the adsorbate−adsorbent interaction energy inside pores becomes smaller than the adsorbate−adsorbate interaction energy. Hence, the heat of adsorption decreases with increasing loading.43 It can be concluded that this system is slightly heterogeneous. Similar behavior was reported by Park et al. for the adsorption of N2 at low pressures on zeolite 13X produced by Baylith Co.44 and for adsorption of CH4 on zeolite 13X by Salem at al.19 Isosteric heats at infinite dilution reported by Salem et al. were (17.53 and 13.91) kJ mol−1 for adsorption of CH4 and N2 on zeolite 13X, respectively.19 While, Cavenati et al. reported these quantities (15.3 and 12.8) kJ mol−1 for adsorption of CH4 and N2 on CECA zeolite 13X.1 Therefore, obtained isosteric heats in this study are in the range of the heats reported previously in the literature. The observed discrepancies may be caused by different sample preparations or various Si/Al ratios in the zeolite 13X produced by different brands. As clear in Figure 4b, at lower degrees of coverage, TΔS quantities of CH4 are more than those of N2, indicating higher degree of freedom of N2. While at higher degrees of coverage, observed results are contrariwise. On the other hand, at higher degrees of coverage, the entropy of CH4 is higher, thus it has higher degree of disorder. Increasing temperature causes a slight increase in the TΔS quantities of the adsorbates, but the trend of curves with respect to loading are the same. Figure 5 shows the estimated surface potential of CH4 and N2 on zeolite 13X. As clear, surface potential of both gases decrease with equilibrium pressure. Besides, the surface potentials of CH4 are higher than N2. Surface potential is a criterion of work required to reach the equilibrium state. Hence, higher loading of

xCH4 /yCH

SCH4 /N2 =

4

x N2 /yN

(49)

2

Equilibrium selectivities of this system are 1.8 to 2.2 according to Tables 9 and 10. No steric mechanism occurs in coadsorption of CH4 and N2, because kinetic diameters of CH4 and N2 are smaller than diameter of zeolite 13X apertures.11,17,45 Hence, different adsorption capacities of CH4 and N2 are due to different interactions with cationic sites of zeolite 13X. Thus, zeolite 13X is selective to CH4 because of higher polarizability of CH4 molecules.

Table 6. Regression Results for Pure CH4 and N2 on Zeolite 13X Using the Toth Isotherm gases

qm0

χ

b0

Q/R

t0

δ

T0

%AAD

CH4 N2

4.3115 9.0791

−1.7948 0.0555

0.18418 0.05151

2583.7 2111.3

1.1162 0.5747

0.6576 0.7491

283 283

3.255 3.984

H



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Table 7. Regression Results for Pure CH4 and N2 on Zeolite 13X Using the W-VSM Isotherm gases

b0,i·104

qv,i

n∞ i,0

r

σi/σv

(λiv − λii)/R

(λvi − λvv)/R

%AAD

CH4 N2

8.239 8.120

−1947.02 −1743.17

3.694 4.829

32.175 45.604

0.0222 45.141

−1180.19 405.56

1306.39 235.51

3.553 5.840

Table 8. Regression Results for Pure CH4 and N2 on Zeolite 13X Using the FH-VSM Isotherm gases

b0,i·104

qv,i

n∞ i,0

ri

τi

%AAD

CH4 N2

7.003 11.206

−2019.99 −1630.16

39.982 86.590

−586.674 −834.621

0.110455 0.332092

4.396 6.947

Figure 5. Surface potential of CH4 (a) and N2 (b) on zeolite 13X.

Figure 4. Heat of adsorption (a) and entropy (b) of CH4 and N2 on zeolite 13X.

comparison with typical models are shown in Figure 7. As can be seen, all the predictions are highly consistent with the experimental data. Both experimental and calculated curves are close to 45° line indicating difficult equilibrium separation of CH4 and N2 using zeolite 13X. Complete characterization of binary adsorption equilibria is implemented via diagrams showing adsorbed amounts of mixture ingredients beside the x−y diagrams. Binary adsorption of mixtures versus gas phase molar fraction of CH4 at different temperatures and pressures are shown in Figures 8. More differences between predictions and experimental data are observed at 3 bar shown in Figure 8b. Two different reasons could be found for such a result. First, weakness of W-VSM in the prediction of data in the region of higher molar fractions, second, inconsistency of the measured data at higher molar fractions, as the error if integral consistencies at higher molar fractions were obtained % 20.

Table 11 shows the obtained %AADs of the proposed models in predicting various equilibrium data of binary adsorption of CH4 and N2 on zeolite 13X. Clearly, all the proposed models are able to predict data very well and results obtained using modeling on the basis of the thermodynamic theory of solutions are highly consistent with experimental data. As clear, predictions for xCH4 are close. Difference between errors of predictions by different model for xCH4 do not exceed % 1.5. However, at 303 K, IAST and at 323 K, W-VSM models have less error than the others do. The x−y diagrams giving quick overview of binary adsorption behavior are shown in Figure 7. Unlike the vapor−liquid equilibria, the x−y diagram of gas−solid equilibria is a function of both temperature and pressure due to the extra degrees of freedom.24 x−y diagrams of the binary adsorption of CH4 and N2 on zeolite 13X at different pressures and temperatures and I



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Table 9. Binary Adsorption Equilibrium Data of CH4 and N2 on Zeolite 13X at 303 Ka Pb

qtot c

bar

yCH4

7.0473 5.0146 3.0738 1.0889 6.9785 5.0356 3.0659 1.0484 6.9602 5.0479 2.9376 6.1984 4.9414 3.0412 1.0852 6.9501 5.0187 3.0472

0.3001 0.3005 0.2997 0.2995 0.4664 0.4652 0.4654 0.4652 0.8322 0.8319 0.8317 0.8857 0.8856 0.8851 0.8845 0.9391 0.9390 0.9388

mol·kg

qCH4 −1

1.4449 1.1607 0.8049 0.3244 1.5679 1.3314 0.7853 0.3530 1.9296 1.5710 1.0139 1.7942 1.5757 1.0403 0.4823 1.9989 1.5897 1.0778

mol·kg

qN2 −1

0.6816 0.5421 0.3738 0.1456 1.0348 0.8724 0.5589 0.2138 1.7712 1.4362 0.9920 1.6966 1.4870 0.9743 0.4534 1.9430 1.5434 1.0446

mol·kg−1

xCH4

SCH4/N2

0.7633 0.6186 0.4311 0.1788 0.5331 0.4590 0.3164 0.1347 0.1584 0.1348 0.0919 0.0976 0.0888 0.0660 0.0289 0.0559 0.0463 0.0332

0.4717 0.4671 0.4643 0.4489 0.6600 0.6553 0.6386 0.6183 0.9179 0.9143 0.9094 0.9456 0.9437 0.9366 0.9399 0.9720 0.9709 0.9692

2.083 2.040 2.026 1.905 2.221 2.185 2.030 1.863 2.255 2.154 2.032 2.243 2.165 1.918 2.044 2.254 2.167 2.053

a Measured with 0.1 K uncertainty. bMeasured with 0.5 mbar uncertainty. cMeasured with 0.0001 uncertainty.

Table 10. Binary Adsorption Equilibrium Data of CH4 and N2 on Zeolite 13X at 323 Ka Pb

Figure 6. Gibbs free energy of CH4 and N2 on zeolite 13X at 273 K (a) and 343 K (b).

Symmetric x−y diagrams and strictly ascending adsorbed amount versus gas phase molar fraction are the characteristics of relatively ideal adsorptive systems. As shown in Figure 7, x−y diagrams of CH4 and N2 binary adsorption on zeolite 13X are totally symmetric at different temperatures and pressures and Figure 8 shows strictly ascending adsorbed amounts with increasing gas molar fraction. Hence, CH4 and N2 form ideal adsorptive mixtures on zeolite 13X. Variations of equilibrium selectivity with total pressure for a mixture with gas phase molar fraction of 0.466 at 303 K and for a mixture with a gas phase molar fraction of 0.301 at 323 K are shown in Figure 9. Almost all models describe the trend of selectivity curves well. As it can be seen, equilibrium selectivity increases with increasing total pressure at constant gas phase molar fraction. Adsorption on energetically homogeneous adsorbents has such a characteristic. On the other hand, such an unusual behavior is a characteristic of adsorption of binary mixtures on energetically homogeneous adsorbents, in which the component with smaller size (number of adsorption sites occupied per molecule) adsorbs stronger than the component with larger size.46 The same behavior was observed for the adsorption of CH4 and N2 binary mixtures on 4A and 5A zeolites.23,47,48 As previously shown in Figure 4a, heats of

qtot

qCH4

qN2

bar

yCH4

mol·kg−1

mol·kg−1

mol·kg−1

xCH4

SCH4/N2

7.0251 4.9952 3.0937 1.0892 7.0112 5.0961 3.0509 1.0544 7.0178 5.0571 3.0636 5.7820 7.0252 5.0225 3.0014

0.3015 0.3010 0.3009 0.3007 0.4665 0.4667 0.4663 0.4664 0.8335 0.8334 0.8333 0.8865 0.9406 0.9405 0.9404

1.0357 0.8679 0.5555 0.2245 1.2052 0.9596 0.6340 0.2321 1.4650 1.1503 0.7679 1.3435 1.5379 1.2119 0.8044

0.5045 0.4117 0.2621 0.1023 0.7841 0.6219 0.3964 0.1427 1.3372 1.0458 0.6947 1.2661 1.4939 1.1765 0.7802

0.5312 0.4562 0.2934 0.1222 0.4211 0.3477 0.2376 0.0894 0.1278 0.1045 0.0732 0.0774 0.0440 0.0354 0.0242

0.4871 0.4744 0.4719 0.4559 0.6506 0.6481 0.6252 0.6145 0.9128 0.9092 0.9047 0.9424 0.9714 0.9708 0.9700

2.199 2.096 2.076 1.949 2.129 2.105 1.910 1.824 2.089 2.001 1.900 2.097 2.147 2.104 2.048

c

a

Measured with 0.1 K uncertainty. bMeasured with 0.5 mbar uncertainty. cMeasured with 0.0001 uncertainty.

adsorption for CH4 and N2 on zeolite 13X changes slightly with loading. Besides, the exponent t in the Toth equation, which is close to unity in the range of measurements, confirms relatively homogeneous behavior of CH4 and N2 adsorption on 13X zeolite. Mulgundmath et al. investigated binary adsorption behavior of CH4 and N2 gases on CECA 13X zeolite at 313 and 373 K and 1 atm total pressure using a chromatographic technique.11 They obtained selectivities higher than the obtained results in the present study. They claimed that CECA 13X zeolite could find application in CH4 and N2 separation in the region of yCH4 > 0.4, i.e., landfill gas, coal bed gas, and natural gas. In our previous study, we investigated CH4/N2 adsorption on Zeochem Co. zeolite 5A.23 Equilibrium selectivity of CH4/N2 J



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close at lower pressures, while at higher pressures, the selectivity is promoted using 13X. It might be due to difference between adsorbent−adsorbate interactions at higher pressures and stronger force field of 13X induced by Na+ cation sites. 6.4. Thermodynamic Consistency Test (TCT). Accuracy of obtained binary equilibrium data was checked utilizing integral and differential TCT. The error of data was obtained using the following equation:

Table 11. Comparison of Predictions Error of Models for Binary Adsorption of CH4 and N2 quantities

NDP

qtot qCH4

18 18

qN2

18

3.431

3.282

8.587

3.555

xCH4

18

0.928

1.536

2.939

1.460

xN2

18

2.805

2.489

7.120

4.053

SCH4/N2

18

3.852

4.152

10.205

5.782

CH4 + N2 at 323 K, %AAD 9.509 6.871 9.863 10.132 7.441 11.737

5.258 6.898

qtot qCH4

15 15

IAST

W-VSM

FH-VSM

CH4 + N2 at 303 K, %AAD 5.992 2.497 6.286 6.955 3.887 8.979

PR 2D-EOS 3.013 3.698

qN2

15

5.861

6.549

9.931

3.630

xCH4

15

0.841

0.611

1.962

1.781

xN2

15

3.642

2.024

5.312

6.104

SCH4/N2

15

4.729

2.621

7.288

8.525

error =

|RHS − LHS| ·100 LHS

(48)

where RHS and LHS are right-hand side and left-hand side of eqs 41 and 43. In each equation, RHS and LHS have to be equal, but due to experimental errors, there is a difference between them. Nevertheless, the observed differences are acceptable and comparable with those of previous reported TCT results.38,39 As shown in Table 12, binary adsorption data of CH4 and N2 on zeolite 13X obey the integral TCT well. Obtained errors are more at 323 K, and the most errors are for the pressure of 7 bar. As clear, errors of the integral TCT in almost all cases are higher at higher pressures, which may be due to the assumption of ideal gas in derivation of TCT.38,39 Table 13 shows the error of data in differential TCT. As can be seen there are differences between

adsorption on zeolite 13X and 5A at 303 K are compared in Figure 10. As clear, equilibrium selectivity of both adsorbents is

Figure 7. x−y diagrams for CH4 and N2 binary adsorption on zeolite 13X at 303 K and 5 bar (a), 303 K and 3 bar (b), 323 K and 7 bar (c), and 323 K and 5 bar (d). K



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Figure 8. Binary adsorption isotherms of CH4 and N2 on zeolite 13X at 5 bar (a) and 3 bar (b).

Figure 9. Equilibrium selectivity for CH4 and N2 binary adsorption on zeolite 13X at 303 K and yCH4 = 0.466 (a) and 323 K and yCH4 = 0.301 (b).

adsorbed amounts of pure substance isotherms and corresponding adsorbed amount obtained using differential TCT. The most error is for a mixture with molar fraction of 0.9388 at 3 bar and 303 K. Almost all errors are less than 20 %. However, relative deviations of more than 50 % are common in data published in the literature as mentioned by Talu.37

namic models were compared with experimental ones through various phase diagrams. 1. According to the measured pure adsorption isotherms, CH4 is adsorbed more than N2 on zeolite 13X due to its higher polarizability. 2. Good fits were obtained using the temperature-dependent Toth equation and pure-substance schemes of W-VSM, FH-VSM, and PR 2D-EOS for single-component adsorption isotherms. FH-VSM showed the most deviations in correlating pure isotherms of both gases. Maximum %AAD for correlation of pure adsorption isotherms of CH4 and N2 using the proposed models do not exceed %5 and %10, respectively. 3. Integral and differential TCT using the definition of Gibbsian surface excess were performed to check the accuracy of data. Obtained errors of less than %20 in almost all data sets show the adequate accuracy of the experiments. More inconsistencies between pure and binary data and between measurements and calculations were observed at higher molar fractions of CH4, as shown by the errors of differential TCT.

7. CONCLUSION In the present study, adsorption isotherms of pure CH4 and N2 and their binary mixtures on Zeochem Co. zeolite 13X were collected experimentally using a static volumetric apparatus. Pure isotherms were measured at (273, 283, 303, 323, and 343) K and pressures up to 10 bar, while binary measurements were performed at (303 and 323) K and different total pressures and gas phase molar fractions. Pure isotherms were measured in the range of pressures and temperatures that are suitable and applicable in the adsorptive separation processes such as PSA. Thermodynamic functions such as enthalpy, entropy, surface potential, and Gibbs free energy were estimated numerically. Correlated parameters of pure isotherms were applied to predict binary adsorption equilibria. Predicted results via thermodyL



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Table 13. Differential TCT for CH4 and N2 Equilibrium Adsorption Data on Zeolite 13X Using eq 43 P (bar)

y1

7 7 7 7 5 5 5 5 5 3 3 3 3 3

0.3001 0.4664 0.8322 0.9391 0.3005 0.4652 0.8319 0.8856 0.939 0.2997 0.4654 0.8317 0.8851 0.9388

7 7 7 7 5 5 5 5 3 3 3 3

0.3015 0.4665 0.8335 0.9406 0.3010 0.4667 0.8334 0.9405 0.3009 0.4663 0.8333 0.9404

Figure 10. Equilibrium selectivity for CH4 and N2 binary adsorption at 303 K on zeolite 13X with yCH4 = 0.466, (this work) and zeolite 5A (ref 23) wilt yCH4 = 0.485.

Table 12. Integral TCT for CH4 and N2 Equilibrium Adsorption Data on Zeolite 13X Using eq 41 P (bar)

LHS of eq 39

3 5 7

0.6195 0.9946 1.1899

3 5 7

0.4535 0.7459 1.0164

RHS of eq 39

error

0.5749 0.9369 1.3239

7.201 5.807 10.118

0.4126 0.6559 0.8695

9.016 12.080 14.454

303 K

323 K

■

LHS of eq 41 303 K 1.1495 1.1495 1.1495 1.1495 0.8976 0.8976 0.8976 0.8976 0.8976 0.6161 0.6161 0.6161 0.6161 0.6161 323 K 0.8836 0.8836 0.8836 0.8836 0.6900 0.6900 0.6900 0.6900 0.4558 0.4558 0.4558 0.4558

RHS of eq 41

error

1.1668 1.2546 1.1856 1.3085 0.8676 0.9027 0.9488 0.9926 1.0575 0.5348 0.5518 0.5565 0.6326 0.7395

1.508 9.147 3.139 13.836 3.344 0.568 5.711 10.588 17.818 13.197 10.430 9.678 2.679 20.037

0.8343 0.8224 0.8510 0.9311 0.6746 0.6617 0.6432 0.7808 0.4612 0.4569 0.4542 0.4959

5.580 6.930 3.698 5.371 2.234 4.114 6.787 13.155 1.18 0.238 0.36 8.7985

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: +98 7733441495.

4. To have an entire overview of the binary adsorption, predicted x−y diagrams and binary adsorbed amounts of various mixtures were plotted against experimental data. Symmetric x−y diagrams and ascending adsorbed amounts versus gas phase molar fraction show the ideal behavior of CH4 and N2 binary adsorption on zeolite 13X. 5. Practically predictions of all the proposed models were in good agreement with the experimental data. In almost all cases, FH-VSM was the less precise model in prediction of the different equilibrium data. 6. Experimental selectivities were compared with the predicted ones. The most deviations in predicting selectivities at 303 K obtained using FH-VSM and at 323 obtained using PR 2D-EOS models. Increasing equilibrium selectivities with increasing total pressure indicate the energetically homogeneous nature of this system. Although, a slight heterogeneity was observed according to isosteric heats of adsorption. 7. FH-VSM totally failed to predict the trend of selectivity curves with total pressure. 8. Equilibrium selectivity of this system obtained 1.8 to 2.2 at different total pressures. Although it is capable of separating CH4 and N2, application of Zeochem Co. zeolite 13X causes high operating costs in the adsorption separation processes such as pressure swing adsorption due to low recovery and productivity.

Notes

The authors declare no competing financial interest.

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