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Pure and Binary Adsorption Equilibria of Methane and Nitrogen on Zeolite 5A Ali Bakhtyari and Masoud Mofarahi* Chemical Engineering Department, Persian Gulf University, Bushehr, Iran

ABSTRACT: Adsorption isotherms of pure methane and nitrogen and their binary mixtures on Zeochem Co. zeolite 5A were measured 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 data were measured at (303 and 323) K and different pressures and bulk gas phase compositions. Experimentally measured data were validated using the integral thermodynamic consistency test. In contrast to the aforementioned binary measurements, predictions of different thermodynamic models utilizing pure adsorption isotherms were used to describe binary adsorption behavior of methane and nitrogen over zeolite 5A. Models based on the thermodynamic theory of solutions such as ideal adsorbed solution theory, vacancy solution models, and two-dimensional equations of state were used for this purpose. Experimental and predicted equilibrium data were compared through the appropriate phase diagrams. Predicted selectivity curves were compared against experimental data. All the proposed models are capable to describe adsorption equilibria of the investigated system. Results of the present study show that methane and nitrogen form an ideal and energetically homogeneous adsorptive system on Zeochem Co. zeolite 5A. technology developed by Engelhard using ETS-4,5 for nitrogen removal and upgrading methane enriched gas streams are currently state of the art. Consequently, the knowledge of pure and multicomponent adsorption equilibria over a specific adsorbent is of great interest.5−9 The difference in physical properties of the gaseous mixture ingredients such as molecular weight, shape, polarity, dipole and quadrupole moments are the basis of adsorptive separation processes. These differences make the adsorbent particles hold some molecules stronger than the others or prevent the entrance of larger molecules.10 Thus, the selected adsorbent for a desired adsorptive separation process has to ensure a good fractionation between molecules composing the bulk gas mixture. Zeolites, for example, type A and X zeolites are the most widely utilized adsorbents for the separation of gases such as air separation and olefin/paraffin separation.11−14 The structural unit in type A zeolites is a truncated octahedron called the sodalite cage and has a 11.4 Å central cavity pore. Na+ cations exchanged with Ca2+ or Mg2+ cations form the commercial 5A

1. INTRODUCTION Natural gas as the cleanest source of energy among fossil fuels supplies one-fourth of required energy in domestic and industrial applications. Methane enriched natural gas streams containing large amounts of nitrogen as the main contamination must be upgraded in order to have the minimum heating value specifications. To meet pipeline quality, the typical contamination predominantly containing nitrogen cannot exceed 4%.1,2 The reduction of methane emission as the most significant non-CO2 greenhouse gas, recovery of landfill gas to provide new resources of energy,3 selective recycling of the tail gas in Fischer−Tropsch synthesis process to have a better performance,4 and recovery of methane from coal mines with high nitrogen contamination5,6 are the other applications of methane and nitrogen separation. Currently, most of the commercial nitrogen removal facilities utilize cryogenic distillation, which is not always economical because it is highly energy-intensive and costly especially in small-scale separations. Developing new adsorbents and highly efficient adsorption cycles with low cost and low energy consumption make the adsorptive separation technologies as the most attractive alternatives for gas separation. Pressure swing adsorption (PSA) processes such as the so-called Molecular Gate © 2014 American Chemical Society

Received: May 24, 2013 Accepted: February 3, 2014 Published: February 13, 2014 626

dx.doi.org/10.1021/je4005036 | J. Chem. Eng. Data 2014, 59, 626−639

Journal of Chemical & Engineering Data

Article

2. MATERIALS AND EXPERIMENTAL METHOD 2.1. Materials. Zeolite 5A particles were supplied from Zeochem Co. (Switzerland). Characteristics of 5A adsorbent used in this study are shown in Table 1. Gases used in this work and their purities and suppliers are shown in Table 2.

zeolites having larger apertures as compared to commercial 4A zeolites. An approximately 1 Si/Al ratio and 4.2 Å eightmember oxygen ring apertures allowing transport of molecules with a kinetic diameter of 4.9 Å are the characteristics of 5A zeolites.15 Type A zeolites are found to be highly selective for nitrogen in air separation due to interactions between cation sites and the quadrupole moment of nitrogen.13 5A zeolite can be considered as a promising adsorbent for methane and nitrogen separation because of the higher polarizability of methane molecules than nitrogen molecules which causes stronger interactions of methane as compared to nitrogen with polar adsorbents such as 5A zeolites.16 Effective application of adsorptive separation processes depends on suitable development of adsorption cycles and accurate adsorption equilibrium data. Single and multicomponent adsorption equilibrium data over a wide range of temperature and pressure are necessary tools for designing practical adsorption cycles. To evaluate the performance of an adsorption-based separation process precisely, multicomponent adsorption data besides single-component isotherms are required. Since experimental data for mixtures are costly and time-consuming to collect, predictions using thermodynamic models are preferable. In addition, the capability of the predicting models to represent adsorption equilibrium of the considered system must be checked using a set of experimental multicomponent equilibrium data. Thus, some reliable and accurate multicomponent data must be collected experimentally. Over the years, various researchers have studied pure and binary adsorption of methane and nitrogen on different molecular sieves such as 4A,17−19 ZSM-5 with different Si/Al ratio,4,20,21 13X,1,10 silicalite,3 and activated alumina10 both experimentally and theoretically. Nam et al. measured pure adsorption isotherms of methane and nitrogen on zeolites 5A produced by Grace & Davision Co. at 293 K, 303 K, and 313 K and pressures up to 1800 kPa volumetrically.16 Adsorption isotherms of pure methane and nitrogen on 5A crystals at 303 K to 363 K and pressures up to 30 atm were measured by Sievers and Mersmann. Besides, they measured binary adsorption at different pressures and gas phase compositions.22−25 Pelletized adsorbents produced using binders are common in industrial applications. Adsorption characteristics of crystals may be different in the presence of binder. In the previous works published from our laboratory, pure and binary adsorption equilibria of oxygen and nitrogen26 and ethane and ethylene on Zeochem Co. zeolite 5A was studied.27 As a subsequent study, we present adsorption equilibrium data of nitrogen and methane and their binary mixtures over a wide range of temperature and pressure on Zeochem Co. zeolite 5A. Equilibrium selectivities and x−y diagrams as criteria for evaluation of methane and nitrogen separation using zeolite 5A were obtained experimentally at different pressures and gas phase compositions. Such data have never been previously published. Pure adsorption isotherms were utilized to predict binary adsorption of methane and nitrogen using different thermodynamic models such as ideal adsorbed solution theory (IAST) of Myers and Prausnitz, Wilson vacancy solution model (W-VSM), Flory−Huggins vacancy solution model (FH-VSM), and various two-dimensional equations of state (2D-EOS). Experimentally collected data for binary adsorption of nitrogen and methane were compared against predicted results. The accuracy of experimentally collected data was verified by thermodynamic consistency test (TCT).

Table 1. Details of the Adsorbent Used in This Study adsorbent

Zeolite 5A

supplier type particle size [cm] particle density [g·cm−3] heat capacity [cal·g−1·K−1] BET surface area [m2·g−1]

Zeochem Co. sphere 0.3 1.16 0.22 457 to 600

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

purity

supplier

He CH4 N2

99.999 % 99.95 % 99.999 %

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

2.2. Apparatus and Procedure. Equilibrium measurements of pure and binary adsorption of methane and nitrogen on Zeochem Co. zeolite 5A was performed in a static volumetric apparatus. Details of the apparatus were previously described26,27 and are shown in Figure 1. Stainless steel made adsorption and loading cells and a circulation pump were connected using 1/8 in. tubes and 1/8 in. valves to minimize the dead volume. On the basis of the volumetric method, appropriate pressure, temperature, and volume measurements were performed to determine the total amount of gas introduced into the system. A K type thermocouple with ± 0.1 K uncertainty and a pressure transmitter with ± 0.5 mbar uncertainty were used to measure the temperature and the pressure of the system. Adsorption and loading cells and dead volumes were measured using helium gas expansion at room temperature. A recorder (Logoscreen 50, Jumo) was used to record temperature and pressure of the system at constant time intervals. Constant temperature of the adsorption cell to provide isothermal conditions during measurements was supplied utilizing a water bath (MC 12, Julabo Tech.). The temperature of the water bath was controlled using a refrigeration circulator with 0.02 K uncertainties. Initially weighed and activated adsorbent particles at 573 K were loaded to the adsorption cell. The loaded adsorbents were heated and regenerated after each measurement in situ at 523 K with helium purging under 250 mbar provided by a Vacuumbrand RE6 model vacuum pump with 0.05 mbar vacuum levels for 6 h. A BEIFEN 3420 gas chromatograph (GC) containing a thermal conductivity detector (TCD) with a packed column was used for the analysis of introduced and equilibrium gas compositions in binary measurements. To ensure accurate measurements, the GC was initially calibrated with standard mixtures of known compositions under the injector temperature of 393 K, detector temperature of 453 K, column temperature of 308 K, and a 20 mL·min−1 helium flow rate. Such circumstances were kept fixed in all further measurements. Gas was circulated during measurements to reduce the time of equilibration, and the homogeneity of the gas sample was guaranteed in this way. To avoid errors in mole balance in binary measurements, the adsorption cell was 627



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Figure 1. Schematic diagram of the volumetric adsorption apparatus. NC

evacuated and the adsorbent particles were regenerated after each equilibrium data point. Reliable and accurate equilibrium data can be obtained in this way.43

i=1

πi* =

πiA = RT

πi* = π *

∫0

qi* Pi

dPi

i = 1, 2, ..., NC

q (bP)1/ n = qm 1 + (bP)1/ n

1 = qT

(1) (2)

(8)

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

(9)

(10)

where T0 is reference temperature and b0, qm0, and n0 are affinity constant, saturation capacity, and the exponent at the reference temperature, respectively. Q is the heat of adsorption and R is the universal gas constant. χ and α are the model constants. A six-parameter model is obtained by substituting eqs 8 and 10 into eq 7. The application of Sips equation in IAST leads to analytical solutions. 3.2. Two-Dimensional Equations of State. Zhou et al. investigated pure and multicomponent gas adsorption equilibria using 2D-EOS and proposed a general form of 2D-EOS and the corresponding fugacity coefficient for the adsorbed phase:33

(3)

∑

qi = xiqT

(7)

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

⎛ T⎞ 1 1 = + α ⎜1 − 0 ⎟ ⎝ n n0 T⎠

NC

xi 0 0 q (Pi ) i=1 i

(6)

The temperature dependence of the parameters may take the following forms:28

Where qi* is pure substance isotherm, Pi0 is hypothetical pressure, and π* is the spreading pressure of the adsorbed mixture. Distribution of the components can be expressed using the well-known Raoult’s equation: Pyi = Pi0(π *)xi

i=1

Accurate multicomponent predictions rely on precise evaluation of spreading pressure. The utilized single-component adsorption equation must have identified values of q/p32. The six-parameter Sips isotherm equation, which is applicable in both low and high-pressure areas, is as follows:28

3. MODEL DESCRIPTION Among different models proposed in the literature for prediction of multicomponent adsorption equilibria,28,29 models based on the thermodynamic theory of solutions are more preferable because of the necessity of only a singlecomponent isotherm and accurate and simple calculations. 3.1. Ideal Adsorbed Solution Theory (IAST). IAST is one of the simplest models for prediction of the multicomponent adsorption equilibria.30,31 In the IAST, Gibbs transform incorporating with a pure substance isotherm equation, relates the spreading pressure of the ideal adsorbed phase πi*, and the equilibrium pressure of the ideal bulk gas phase Pi: Pi0

NC

∑ xi = ∑ yi = 1

(4) (5)

where yi and xi are molar fractions in the bulk gas phase and adsorbed phase, respectively, qT is total adsorbed amount, qi is the partial adsorbed amounts of the components, and qi0 is adsorbed amount of pure substances in the hypothetical pressure Pi0. IAST equations must be solved under the following constraints:

⎤ ⎡ αω 2 [1 − (βω)m ] = ωRT ⎢A π + 2⎥ ⎣ 1 + Uβω + W (βω) ⎦ (11) 628



Article

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

where A and π are surface area and surface pressure, respectively, ω is the adsorbed amount, and α and β are model parameters. By identification of the model coefficients U, W, and m, specific forms of the 2D-EOS can be obtained. Model coefficients are assigned as following: U = 0, W = 0, and m = 1 for VDW; U = 0, W = 0, and m = 0.5 for Eyring; U = 1, W = 0, and m = 1 for SRK; and U = 2, W = −1 and m = 1 for PR 2D-EOS. Applying 2D-EOS for multicomponent systems requires a proper mixing rule such as the classical mixing rule:33

⎡ Λ (1 − Λ vi)θ (1 − Λiv)θ ⎤ × exp⎢ − vi − ⎥ Λiv + (1 − Λiv)θ ⎦ ⎣ 1 − (1 − Λ vi)θ (21)

θ=

NC NC

where θ is fractional loading and bi, Λiv, and Λvi are model parameters. The following temperature dependencies were considered for the parameters in the W-VSM isotherm:37 ⎛ qv , i ⎞ bi = bi ,0 exp⎜ − ⎟ ⎝ T ⎠ (23)

(12)

i=1 j=1

NC NC

∑ ∑ xixjβij

β=

(13)

i=1 j=1

(14)

⎛ ri ⎞ ⎜ ⎟ ni∞ = ni∞ ,0 exp⎝ ⎠ T

(15)

Λiv =

⎛ λ − λii ⎞ ai ⎟ exp⎜ − iv ⎝ av RT ⎠

(25)

Λ vi =

⎛ λ − λvv ⎞ av ⎟ exp⎜ − vi ⎝ ai RT ⎠

(26)

(αi + αj)

αij =

2

βij =

ββ i j

The corresponding fugacity coefficient of the adsorbed phase ϕ̂ ai is33 NC

a

ln(ϕî ) =

2 ∑ j = 1 βijωj − βω (βω)1 − m − βω

−

1 ln[1 − (βω)m ] m

− ln(Za) + T1 + T2

(16)

2α ∑ j = 1 βijωj − αβω RTβ[1 + Uβω + W (βω)2 ] NC

T2 = −

nm ni∞ Λiv nm∞ bi ⎧ ⎫ ⎡⎛ n ∞ − n ∞ ⎞ ⎤ ⎪ ⎪ m ⎢⎜ i ⎥ln γvxvs⎬ × exp⎨ ( Λ − 1) + − 1 ⎟ vi ⎪ ⎪ ⎢⎣⎝ ⎥⎦ nm ⎠ ⎭ ⎩

yi ϕiP = γixi

(17) NC

αβω + 2β ∑ j = 1 αijωj − 2α ∑ j = 1 βijωj

× ln

RTβ 2ω(U 2 − 4W )1/2

(27)

2 + (U + (U 2 − 4W )1/2 )βω 2 + (U − (U 2 − 4W )1/2 )βω

aπ Aπ = Za = RT ωRT

NC

nm∞ =

(18)

a

∑ xini∞

(28)

i=1

where ϕi and γi are the fugacity coefficient of the gas phase and activity coefficient of the adsorbed phase, respectively. The Wilson activity coefficient model for accounting nonideality of the adsorbed mixture is

(19)

Za and a are adsorbed phase compressibility factor and specific molar area, respectively. Furthermore, the following equation holds at the adsorption and distribution of species between two phases:

Zaϕî ωi = kifi ̂

(24)

Substituting eqs 22 to 26 into eq 21, a seven-parameter model is obtained. The following equations describe multicomponent adsorption and distribution of components between two phases:36

NC

T1 = −

(22)

ni∞,

∑ ∑ xixjαij

α=

ni ni∞

NC

ln γk = 1 − ln ∑ xjs Λkj −

g

j=1

(20)

NC

NC

∑ [xjs Λik(∑ xjs Λij)−1] i=1

j=1

(29)

The total adsorbed amount of mixture nm and the molar fractions of adsorbed phase xi are calculated using a trial and error method and specifying total pressure P and gas phase molar fractions yi. 3.4. Flory−Huggins Vacancy Solution Model. Because of correlative pairwise interaction parameters in W-VSM, Λiv, and Λvi, Cochran et al.38 utilized the Flory−Huggins activity coefficient model instead of the Wilson model to avoid such a problem. The following equation for single-component adsorption was obtained using the Flory−Huggins model:

where ωi is the partial adsorbed amount of the species in the mixture, ki is the slope of isotherm at the origin, and fgî is the fugacity of components in the bulk gas phase calculated using a conventional three-dimensional equation of state (3D-EOS).34 3.3. Wilson Vacancy Solution Model. The VSM model for predicting single and multicomponent gas adsorption was proposed by Suwanayuen and Danner based on the vacancy solution definitions combined with the Wilson activity coefficient model.35,36 This model treats the adsorption equilibrium as an osmotic equilibrium between two vacancy solutions with different compositions of adsorbates and vacancies. The following equation was obtained for singlecomponent adsorption isotherms:

⎛ α 2θ ⎞ ⎛ n∞ θ ⎞ iv ⎟ P=⎜ i ⎟ exp⎜ − θ + αivθ ⎠ b 1 1 ⎝ i ⎠ ⎝ 629

(30)



Article

Table 3. Pure Adsorption Isotherms of Methane on Zeolite 5A 273 Ka

283 K

b

P

bar

mol·kg

0.0499 0.1344 0.2338 0.3671 0.5686 0.7653 0.9823 1.1745 1.5694 1.9954 2.9629 4.0481 4.9842 6.0289 7.0272 8.0080 9.0215 10.036 a

303 K

Pb

n −1

0.06842 0.16422 0.26225 0.40746 0.58861 0.74602 0.90172 1.02110 1.22424 1.40577 1.68756 1.95384 2.10230 2.22729 2.32559 2.40964 2.49230 2.55472

Pb

n

bar

mol·kg

0.0511 0.1421 0.2466 0.4001 0.5811 0.7689 0.9839 1.2518 1.5792 2.1392 3.1073 4.0736 5.1711 6.0368 7.0199 7.9975 8.9654 10.065

−1

0.05878 0.13580 0.22196 0.33777 0.46882 0.58837 0.71391 0.84909 0.99638 1.19153 1.46554 1.65258 1.80622 1.93094 2.04672 2.14584 2.22362 2.29279

323 K Pb

n

bar

mol·kg

0.0438 0.1423 0.2476 0.3933 0.5817 0.8025 0.9904 1.2102 1.5690 1.9881 2.9466 3.9648 5.0044 5.9371 7.0317 7.9781 9.0795 10.066

−1

bar

0.03291 0.08598 0.13707 0.20758 0.29804 0.39010 0.46611 0.55292 0.67863 0.82029 1.06739 1.31989 1.50010 1.62991 1.76565 1.87704 1.96202 2.00226

343 K n mol·kg

0.0485 0.1349 0.2393 0.4001 0.5865 0.7921 1.0541 1.1901 1.5878 1.9643 2.9792 3.9615 4.9816 5.9830 6.9618 7.9965 8.9981 10.029

−1

0.02637 0.04987 0.08028 0.13010 0.18631 0.24588 0.31889 0.35468 0.45083 0.53625 0.74716 0.92306 1.08165 1.20442 1.34307 1.47338 1.57416 1.66481

Pb

n

bar

mol·kg−1

0.0536 0.1459 0.2613 0.4013 0.5878 0.7844 0.9864 1.1888 1.5856 2.0007 2.9457 3.9930 4.9640 5.9580 6.9301 7.9724 8.9653 9.9982

0.01553 0.03688 0.05949 0.08809 0.11277 0.15545 0.19323 0.23333 0.30148 0.38068 0.53457 0.67196 0.82227 0.94577 1.06777 1.18143 1.28668 1.38629

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

θ=

ni ni∞

%AAD =

(31)

ni∞,

where θ is fractional loading and bi, and αiv are model parameters. The following are temperature dependencies of the model parameters:37,38 ⎛ qv , i ⎞ bi = bi ,0 exp⎜ − ⎟ ⎝ T ⎠

(32)

⎛ ri ⎞ ⎜ ⎟ ni∞ = ni∞ ,0 exp⎝ ⎠ T

(33)

αiv = mini∞ − 1

(34)

dΦ = − s m dT −

ln γi = −ln ∑ j=1

X jexp

(37)

∑ nie dμi

(38)

i=1

(35)

where sm is excess entropy and μi is the chemical potential of equilibrium gas phase at T, P, and gas molar fraction yi. Differentiation and integration of eq 38 lead to different consistency tests for pure and binary gas adsorption data. By integrating eq 38 in a constant T and P path, an integral test is generated for adsorption of an ideal binary gas mixture:

The Flory−Huggins model, which is applied to account nonideality of adsorbed mixture, is ⎡ ⎛ NC x s j ⎢ + ⎢1 − ⎜⎜∑ αij + 1 ⎢ α + ⎝ j = 1 ij ⎣

j=1

X jcal − X jexp

NC

⎧⎡⎛ n ∞ − n ∞ ⎞ ⎫ ⎤ ⎪ m ⎨⎢⎜ i × exp⎪ ⎟ − 1⎥ln γvxvs⎬ ⎪ nm ⎠ ⎦⎥ ⎭ ⎩⎢⎣⎝ ⎪

xjs

∑

4. THERMODYNAMIC CONSISTENCY TEST As discussed by Talu et al.,39 because of the difficulties in multicomponent measurements due to higher degrees of freedom, the accuracy of measurements must be checked and the validity of collected data must be verified using TCT; on the other hand, we can trust in the measured data that obeys consistency test. The thermodynamics of pure and binary gas adsorption using the definition of Gibbsian surface excess was studied by Sircar et al.40,41 The surface potential of Gibbs adsorbed phase Φ expressed in terms of Gibbsian surface excess nie variables is as follows:34

nm ni∞ ⎡ exp(αiv) ⎤ ⎢ ⎥ nm∞ bi ⎣ 1 + αiv ⎦

NC

NDP

where Xcal and Xexp are calculated and experimental adsorbed amounts, respectively, when applied for eqs 7 and 16 (and they are calculated) and experimental equilibrium pressure, respectively, when applied for eqs 21 and 30. NDP is the number of data points used in regression.

A substitution of eqs 31 to 34 into eq 30 gives a five-parameter model for-single-component isotherms. In the case of multicomponent adsorption, the following equation holds at the equilibrium between two phases:38 yi ϕiP = γixi

100 NDP

⎞−1⎤ ⎟ ⎥ 1 ⎟⎠ ⎥⎥ ⎦

(36)

The total adsorbed amount of mixture nm and molar fraction of adsorbed phase xi at a given total pressure P and bulk gas phase molar fraction yi is calculated utilizing a trial and error method. Parameters included in eqs 7, 16, 21, and 30 are determined by minimizing the following objective function: 630

n1e(1 − y1) − n2ey1

Φ*2 − Φ1* = RT

∫0

Φ*i =− RT

nie dP P

∫0

P

1

y1(1 − y1)

dy1

(39)

*

(40)



Article

Table 4. Pure Adsorption Isotherms of Nitrogen on Zeolite 5A 273 Ka P

b

bar 0.0414 0.1821 0.3720 0.5661 0.7800 0.9740 1.1789 1.3771 1.6001 1.9697 2.4559 2.9936 3.9495 4.9794 5.9802 6.9771 7.9853 8.9727 10.126 a

283 K Pb

n mol·kg

−1

0.04499 0.13562 0.24214 0.33664 0.43360 0.50672 0.58035 0.64404 0.71296 0.81097 0.94790 1.05889 1.22580 1.35815 1.47421 1.56603 1.66824 1.73413 1.79762

bar 0.0477 0.1843 0.3774 0.5762 0.7759 0.9783 1.1771 1.3813 1.5806 1.9655 2.5123 2.9610 3.3942 4.9320 5.5091 6.4456 7.4731 8.4275 9.8971

303 K Pb

n mol·kg

−1

0.03668 0.10593 0.19278 0.27401 0.34877 0.41329 0.47145 0.53052 0.58692 0.67970 0.80479 0.89609 1.06962 1.20067 1.26914 1.37180 1.47780 1.56748 1.66605

323 K Pb

n

bar

mol·kg

0.0554 0.1883 0.3873 0.5911 0.7911 0.9883 1.1867 1.3878 1.5902 1.9705 2.4772 2.9602 3.8410 4.9362 5.9618 6.9192 7.9530 8.9673 9.9349

−1

0.02490 0.06112 0.11528 0.15696 0.20249 0.24648 0.31346 0.34613 0.40156 0.47674 0.56941 0.64634 0.78281 0.94415 1.06590 1.16802 1.25977 1.35311 1.40258

bar 0.0579 0.1917 0.3931 0.5887 0.7908 0.9881 1.1963 1.3916 1.6001 1.9732 2.4729 2.9721 3.9714 4.9351 5.9720 6.9510 7.9801 8.9637 9.9750

343 K n mol·kg

−1

0.01528 0.03939 0.07802 0.11853 0.14889 0.18291 0.21649 0.24621 0.27419 0.32458 0.39702 0.45820 0.58667 0.69380 0.79924 0.89402 0.99041 1.08616 1.16802

Pb

n

bar

mol·kg−1

0.0479 0.1944 0.3935 0.5919 0.7963 1.0025 1.1854 1.3903 1.5921 2.0560 2.5050 2.9750 3.9410 4.9420 5.9710 6.9685 7.9730 8.8493 10.163

0.00891 0.02652 0.04778 0.07474 0.09570 0.12406 0.14883 0.17399 0.20083 0.25012 0.30252 0.35148 0.44270 0.53648 0.63166 0.70990 0.79242 0.86944 0.94845

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

where n1e and n2e are surface excess of component 1 and 2 in the binary system, nei * is surface excess of pure substance i, and Φi* is the surface potential of pure gas. The left-hand side (LHS) of eq 39 is calculated using eq 40 and single-component isotherms, while the right-hand side (RHS) is calculated at constant T and P using binary adsorption data. Thus, integral consistency between pure and binary data is checked in this way.

selected so that data are suitable for separation processes such as PSA. The Sips model as well as pure substance schemes of 2D-EOS, W-VSM, and FH-VSM were applied to correlate data. Experimentally collected adsorption isotherms of methane and nitrogen are plotted against the Sips equation in Figures 2 and

5. HEAT OF ADSORPTION The equilibrium of a typical adsorption system is described by adsorption isotherms as well as heats of adsorption, because heats of adsorption of components determine the temperature change induced by adsorption and desorption during an adsorption cycle in the energy balance. Hence, knowledge of heats of adsorption is necessary in kinetic studies. Besides, a variation of heat of adsorption with respect to adsorption loading is the most direct evidence of energetic heterogeneity.42 Because of difficulty in experimental methods, the estimation of heat of adsorption using adsorption isotherms is of great interest. Isosteric heat of adsorption of pure methane and nitrogen were estimated using the Clausius−Clapeyron equation applied to the measured isotherm data at the five temperatures. Linear dependency of ln P on the inverse of absolute temperature (1/T) at constant loading was used for this purpose.28 ⎡ ∂ ln P ⎤ ΔH − 2 =⎢ ⎣ ∂T ⎥⎦n RT

Figure 2. Measured and correlated adsorption isotherms of pure methane on zeolite 5A: the points are experimental data and the curves are Sips isotherms.

(41)

3, respectively. As per Figures 2 and 3, in the range of measurements, both methane and nitrogen isotherms have type I behavior according to BET classification indicating adsorption of gases in microporous adsorbents.28 Reported isotherms in the present study conform pretty well to the previously obtained experimental isotherms especially at low pressure area. Slight discrepancies were observed at high pressure area, which

6. RESULTS AND DISCUSSION 6.1. Adsorption of Pure Methane and Nitrogen. Pure adsorption isotherms of methane and nitrogen on Zeochem Co. zeolite 5A tabulated in Tables 3 and 4, were obtained at five temperatures (273, 283, 303, 323, and 343) K and pressures up to 10 bar volumetrically. Temperature and pressure ranges were 631



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Table 6. Regression Results for Pure Nitrogen on Zeolite 5A Using 2D-EOS 2D-EOS

Figure 3. Measured and correlated adsorption isotherms of pure nitrogen on zeolite 5A: the points are experimental data and the curves are Sips isotherms.

may be due to different sample preparation.16,22−25 In all temperatures, equilibrium loading of methane was observed to be higher than nitrogen caused by higher polarizability of methane molecules and stronger interactions with the polar nature of 5A zeolites. The regressed parameters of the proposed models for describing pure adsorption isotherms and corresponding errors are tabulated in Tables 5 to 9. As can be seen, all the proposed models describe pure adsorption of methane and nitrogen on zeolite 5A quite well. According to

NDP

α

PR Eyring VDW SRK

18 18 18 18

2615.71 11098.97 724.24 648.71

PR Eyring VDW SRK

18 18 18 18

2589.29 12148.61 928.17 1119.10

PR Eyring VDW SRK

18 18 18 18

2536.46 14247.91 1336.03 2059.89

PR Eyring VDW SRK

18 18 18 18

2483.63 16347.20 1743.88 3000.68

PR Eyring VDW SRK

18 18 18 18

2430.80 18446.49 2151.74 3941.47

β 273 K 0.21160 0.19094 0.20507 0.20101 283 K 0.21036 0.19406 0.20355 0.20204 303 K 0.20787 0.200310 0.20052 0.2041 323 K 0.20537 0.20655 0.19748 0.20615 343 K 0.20288 0.21280 0.19445 0.20821

k

% AAD

1.19508 2.17165 1.31350 1.31639

1.978 3.379 3.522 1.827

0.89293 1.57777 0.95801 0.95228

3.821 2.569 2.750 2.799

0.52810 0.88720 0.54249 0.53135

4.327 1.822 3.761 4.100

0.33333 0.53576 0.32961 0.31869

4.232 4.210 4.146 4.996

0.22199 0.34313 0.21225 0.20288

5.681 5.113 4.702 4.727

α

PR Eyring VDW SRK

19 19 19 19

−2143.67 10819.44 −2198.92 −3879.08

PR Eyring VDW SRK

19 19 19 19

−1565.10 10596.70 −2301.42 −2473.90

PR Eyring VDW SRK

19 19 19 19

−407.96 10151.22 −2506.42 336.46

PR Eyring VDW SRK

19 19 19 19

749.17 9705.74 −2711.41 3146.83

PR Eyring VDW SRK

19 19 19 19

1906.31 9260.26 −2916.43 5957.19

β 273 K 0.23442 0.21614 0.20232 0.18370 283 K 0.22595 0.20139 0.18390 0.19483 303 K 0.20902 0.17189 0.14707 0.21707 323 K 0.19208 0.14239 0.11024 0.23931 343 K 0.17515 0.11289 0.07341 0.26156

k

% AAD

0.79283 1.17415 0.71209 0.74046

4.140 1.219 3.204 3.046

0.56772 0.85102 0.53011 0.54018

3.871 1.092 3.320 3.089

0.31101 0.47649 0.31146 0.30600

4.418 4.161 3.970 4.355

0.18356 0.28666 0.19545 0.18599

4.779 2.219 3.549 4.884

0.11521 0.18298 0.12951 0.11980

9.756 4.932 3.566 5.300

correlation results, the obtained % AADs of all models do not exceed 7 % for pure methane and 10 % for pure nitrogen. It should be mentioned that in correlation of data using Sips, WVSM, and FH-VSM models, all data points were correlated simultaneously using temperature-dependent parameters, while in the application of 2D-EOS, data points of each single temperature were used individually. 6.2. Isosteric Heat of Adsorption. The isosteric heats for pure adsorption of methane and nitrogen on zeolite 5A obtained by applying Clausius−Clapeyron equation to the measured isotherms are shown in Figure 4. Neglecting the steep decrease in the infinite dilute region, the isosteric heats of adsorption of both gases are practically independent of loading. Constant heat of adsorption with respect to adsorption loading indicates the homogeneous surface and lack of interaction between the adsorbed molecules. In the presence of different levels of surface energy or interaction between adsorbed molecules, the isosteric heat of adsorption varies with respect to adsorption loading.44 Thus, obtained results indicate energetically homogeneous behavior of methane and nitrogen adsorption on zeolite 5A. The heat of adsorption of methane is higher than that of nitrogen reflecting polarizability interaction energy. Isosteric heats evaluated using reported isotherms by Nam et al. on zeolites 5A produced by Grace & Davision Co.16 confirm obtained results for isosteric heat of nitrogen adsorption in this study, while the isosteric heat of methane adsorption differs slightly at higher degrees of surface coverage, which may be due to different sample preparation methods and different cations used in the synthesis of 5A samples. As declared by Ruthven, heats of adsorption of nitrogen and methane in the 5A are practically the same.45 Evaluated quantities of heats for both gases in this study are close to each other. Loughlin et al. presented different heats of

Table 5. Regression Results for Pure Methane on Zeolite 5A Using 2D-EOS 2D-EOS

NDP

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Table 7. Regression Results for Pure Methane and Nitrogen on Zeolite 5A Using Sips Isotherm gases

NDP

qm0

χ

b0

Q/R

n0

α

T0

% AAD

CH4 N2

90 95

3.2806 2.8315

0.3885 −1.3252

0.35253 0.18367

1935.4 2452.8

1.0648 1.1229

0.63109 0.38181

273 273

4.285 2.547

Table 8. Regression Results for Pure Methane and Nitrogen on Zeolite 5A Using W-VSM Isotherm gases

NDP

b0,i × 104

qv,i

ni,0∞

ri

(ai/av) × 102

(λiv − λii)/R

(λvi − λvv)/R

% AAD

CH4 N2

90 95

3. 5125 2. 3880

−2250.04 −2187.11

32.504 534.923

−453.89 −1180.11

16. 018 10.625

−1543.99 −2198.42

526.15 459.1

6.341 5.539

Table 9. Regression Results for Pure Methane and Nitrogen on Zeolite 5A Using FH-VSM Isotherm gases

NDP

b0,i × 104

qv,i

ni,0∞

ri

mi

% AAD

CH4 N2

90 95

3.7644 3.3251

−2209.6 −2062.6

5.3916 8.8426

−93.627 −290.996

0.092214 0.125479

6.756 6.604

Table 10. Binary Adsorption Equilibrium Data of Methane and Nitrogen on Zeolite 5A at 303 K Pa

Figure 4. Heat of adsorption of methane (blue ) and nitrogen (pink ···) on zeolite 5A as a function of adsorption loading.

nt

nCH4

n N2

bar

yCH4

mol·kg−1

mol·kg−1

mol·kg−1

xCH4

SCH4/N2

8.9451 7.055 5.082 3.02 0.993 7.036 5.0475 3.0197 0.9802 9.1555 6.9991 5.0051 3.0008 1.0104 7.0914 5.0001 3.0145 0.9922

0.2724 0.272 0.2715 0.2712 0.2709 0.4868 0.4855 0.4841 0.4818 0.5369 0.7144 0.7141 0.7123 0.7113 0.8933 0.893 0.8923 0.8914

1.407 1.264 1.0372 0.7626 0.3282 1.3438 1.1524 0.8528 0.3579 1.6059 1.4398 1.2109 0.9741 0.4308 1.539 1.3104 1.0236 0.453

0.5457 0.4852 0.3955 0.2793 0.1146 0.8723 0.7459 0.5452 0.2245 1.0925 1.1966 0.9929 0.7974 0.3469 1.4488 1.23 0.9598 0.4238

0.8613 0.7788 0.6417 0.4833 0.2136 0.4715 0.4065 0.3076 0.1334 0.5134 0.2432 0.2179 0.1767 0.0839 0.0902 0.0804 0.0638 0.0292

0.3879 0.3839 0.3813 0.3662 0.3491 0.6492 0.6472 0.6393 0.6273 0.6803 0.8311 0.82 0.8186 0.8051 0.9414 0.9386 0.9376 0.9354

1.693 1.668 1.654 1.553 1.444 1.951 1.944 1.889 1.81 1.835 1.967 1.824 1.823 1.677 1.919 1.832 1.814 1.764

b

a

Measured with 0.5 mbar uncertainty. uncertainty.

adsorption of methane on zeolite 5A reported by other authors. The obtained isosteric heat for methane in this study is close to the average of quantities reported by Loughlin et al.46 6.3. Binary Adsorption. It is difficult to obtain desired points in a phase diagram in a binary gas adsorption equilibria using the volumetric method. This is because of higher degrees of freedom than vapor−liquid equilibria. In fact, equilibrium pressure and gas phase composition in the volumetric method get out of hand and they are difficult to accurately control due to the aforementioned degrees of freedom. Hence, many experiments are required to obtain specified points in the phase diagrams. Therefore, equilibrium data points with relatively equal pressures and gas phase compositions are considered in a data set. Besides, in this way it is practical to perform TCT. Volumetrically collected equilibrium data of methane and nitrogen binary adsorption on Zeochem Co. zeolite 5A containing total adsorbed amounts, partial adsorbed amounts, molar fraction of substances in gas, and adsorbed phases and equilibrium selectivity at 303 K and 323 K are tabulated in Tables 10 and 11, respectively. Equilibrium selectivity was calculated using the equilibrium molar fraction of the bulk gas phase measured directly utilizing GC, and molar fraction of the

b

Measured with 0.0001

Table 11. Binary Adsorption Equilibrium Data of Methane and Nitrogen on Zeolite 5A at 323 K Pa

a

nt b

bar

yCH4

7.0593 5.0654 2.9921 1.0443 7.0532 4.9807 3.0181 1.0391

0.7240 0.7234 0.7228 0.7219 0.8849 0.8846 0.8845 0.8841

mol·kg

nCH4 −1

1.1513 0.9734 0.6975 0.3027 1.2572 1.0366 0.7203 0.3115

mol·kg

n N2 −1

mol·kg−1

xCH4

SCH4/N2

0.2081 0.1769 0.1296 0.0573 0.0868 0.0737 0.0524 0.0234

0.8192 0.8182 0.8142 0.8109 0.931 0.9289 0.9274 0.9248

1.728 1.721 1.681 1.652 1.755 1.704 1.668 1.612

0.9432 0.7965 0.5679 0.2454 1.1704 0.9629 0.6679 0.2881

Measured with 0.5 mbar uncertainty. uncertainty.

b

Measured with 0.0001

adsorbed phase determined by applying a mole balance before and after equilibrium: 633



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Table 12. Comparison of Predictions Errors of Models for Binary Adsorption of Methane and Nitrogen quantities

NDP

IAST

W-VSM

FH-VSM

VDW

SRK

PR

Eyring

CH4+N2 at 303 K, % AAD nt nCH4

18 18

5.851 8.614

5.292 11.287

3.27 5.547

3.545 6.129

3.343 5.709

3.046 5.406

3.679 6.946

n N2

18

4.859

3.852

4.856

6.446

4.213

4.084

6.107

xCH4

18

3.163

5.891

3.338

3.308

3.152

3.104

3.961

x N2

18

3.334

6.047

3.441

3.399

3.316

3.231

4.706

SCH4/N2

18

6.81

13.106

7.127

7.088

6.796

6.64

9.292

nt nCH4

8 8

4.489 5.766

3.42 3.85

CH4+N2 at 323 K, % AAD 7.727 3.319 8.13 3.204

3.531 3.446

2.802 2.685

2.957 2.619

n N2

8

3.52

2.168

6.171

5.121

5.308

9.139

6.663

xCH4

8

0.346

0.455

0.712

0.378

0.449

1.169

0.749

x N2

8

2.251

2.273

4.904

2.664

3.193

8.038

5.079

SCH4/N2

8

2.615

2.835

5.954

3.149

3.784

10.051

6.216

xCH4

SCH4 / N2 =

yCH

4

x N2 yN

2

(42)

According to Tables 10 and 11, measured equilibrium selectivities of the methane and nitrogen binary adsorption on zeolite 5A vary in the range of 1.4 to 1.95. Because of a smaller kinetic diameter of adsorbates rather than apertures of the adsorbent particles, no size exclusion occurs in coadsorption of methane and nitrogen on zeolite 5A.47,48 Hence, different interactions with cationic sites of zeolite 5A cause different adsorption capacities of methane and nitrogen and observed equilibrium selectivity. Thus, zeolite 5A is selective to methane because of a higher polarizability of methane molecules. However, such quantities of equilibrium selectivity are not adequate for an adsorptive separation process based on the equilibrium selectivity. Performance of different thermodynamic models in describing methane and nitrogen binary adsorption equilibria on zeolite 5A are shown in Table 12. The ability of the proposed models in predicting various equilibrium data of this system has been compared in term of % AAD errors. Clearly, all the proposed models predict data very well and a high consistency between results obtained using modeling based on the thermodynamic theory of solutions and experimental data are observed. To have a quick overview of binary gas adsorption, the x−y diagrams are used. x−y diagrams of methane and nitrogen binary adsorption are shown in Figures 5 and 6 for 7 and 5 bar total pressures, respectively. Because of extra degrees of freedom in gas−solid equilibria, the x−y diagram is a function of both temperature and pressure, unlike the vapor−liquid equilibria.43 Experimental x−y diagrams of binary adsorption of methane and nitrogen on zeolite 5A at 303 K and 7 bar and predictions of IAST, W-VSM, FH-VSM, and VDW 2D-EOS are shown in Figure 5. As shown, binary adsorption behavior of methane and nitrogen adsorption is predicted well by all the proposed models. The x−y diagram at 303 K and 5 bar is shown in Figure 6. Obviously, predictions of IAST, W-VSM, FH-VSM, and SRK 2D-EOS are highly consistent with experimental data. Predictions of all models cross the experimental data points once for all experimental conditions

Figure 5. x−y diagram for methane and nitrogen binary adsorption on zeolite 5A at 303 K and 7 bar: experimental data (red ●) against IAST (), W-VSM (blue ---), FH-VSM (purple -·-·) and SRK 2D-EOS (pink -··-) predictions.

reflecting consistency between predictions and experimental results.32 To evaluate binary adsorption of gases and have a complete characterization of it, beside x−y diagrams, total and partial adsorbed amounts of mixtures must be investigated. Total and partial adsorbed amounts of binary mixtures versus gas phase molar fraction of methane at 303 K and 5 bar are shown in Figure 7. Predictions of IAST, W-VSM, FH-VSM, and SRK 2DEOS against experimental data are shown in this figure. As can be seen, almost all models predict total and partial adsorbed amounts well. IAST and W-VSM predictions have more deviations than those of FH-VSM and SRK 2D-EOS. Corresponding % AADs shown in Table 12 coincide such statements. Experimental data and predictions have less difference at 303 K and 3 bar as shown in Figure 8. To satisfy the consistency condition between pure and binary measured data, binary adsorption isotherms must have continuity with pure isotherms. On the other hand, at a fixed temperature and 634



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Figure 8. Total and partial adsorbed amounts for methane and nitrogen binary adsorption on zeolite 5A at 303 K and 3 bar: experimental data of total (red ●), methane (blue ▲) and nitrogen (purple ◆) adsorption against IAST (green ···), W-VSM (blue ---), FH-VSM (purple -·-·) and SRK 2D-EOS () predictions.

Figure 6. x-y diagram for methane and nitrogen binary adsorption on zeolite 5A at 303 K and 5 bar: experimental data (red ●) against IAST (), W-VSM (blue ---), FH-VSM (purple -·-·) and SRK 2D-EOS (pink -··-) predictions.

fraction are the characterizations of ideal adsorbed mixtures. As shown in Figures 5 and 6, x−y diagrams of methane and nitrogen binary adsorption on zeolite 5A are totally symmetric, and Figures 7 and 8 show strictly ascending total adsorbed amounts with respect to gas molar fraction. Hence, methane and nitrogen form ideal adsorptive mixtures on zeolite 5A. Equilibrium selectivities of methane and nitrogen binary mixtures versus total pressure are shown in Figures 9 to 11. Variation of equilibrium selectivity with respect to total pressure for a mixture with methane molar fraction of 0.893 in the bulk gas phase at 303 K is shown in Figure 9. Besides,

Figure 7. Total and partial adsorbed amounts for methane and nitrogen binary adsorption on zeolite 5A at 303 K and 5 bar: experimental data of total (red ●), methane (blue ▲) and nitrogen (purple ◆) adsorption against IAST (green ···), W-VSM (blue ---), FH-VSM (purple -·-·) and SRK 2D-EOS () predictions.

total pressure, the total adsorbed amount of a binary mixture must approach the respective pure component values at the infinite dilution regions (i.e., when the gas phase molar fraction approaches unity).32 Such a condition is observed at 3 bar as shown in Figure 8. As per Figure 7, more deviation is observed at 5 bar at the end point where the gas phase molar fraction of methane approaches unity. Gaseous mixtures that form ideal adsorptive systems have symmetric x−y diagrams and ascending total adsorbed amount versus gas phase molar fraction. On the one hand, symmetric x−y diagrams and ascending total adsorbed amount versus gas phase molar

Figure 9. Equilibrium selectivity for methane and nitrogen binary adsorption on zeolite 5A at 303 K and yCH4 = 0.893: experimental data (red ●) against IAST (green ···), W-VSM (blue ---), FH-VSM (purple -·-·) and PR 2D-EOS () predictions. 635



Article

with methane molar fraction of 0.884 in bulk gas phase at 323 K against predicted results of IAST, W-VSM, FH-VSM, and VDW 2D-EOS are shown in Figure 11. Predictions of IAST and W-VSM are in very good agreement with experimental data. According to % AAD values presented in Table 12, performance of all models but PR 2D-EOS are better in the prediction of equilibrium selectivity at 323 K than that of 303 K. Experimental and predicted results show that equilibrium selectivity of binary adsorption of methane and nitrogen on zeolite 5A increases with increasing pressure at constant gas phase molar fraction showing the homogeneity of adsorbent. In fact, in adsorption on energetically homogeneous adsorbents in which the component with smaller size (number of adsorption sites occupied per molecule) adsorbs stronger than the one with larger size, equilibrium selectivity increases with respect to total pressure.49 Different authors for the adsorption of methane and nitrogen binary mixtures on zeolite 4A and zeolite 5A crystals reported the same trend.18,22,41 Independent heats of adsorption shown in Figure 4 and the exponent n in Sips equation, which is close to unity in the range of measurements, confirm such a statement about heterogeneity of this system. Sievers and Mersmann reported binary adsorption of methane and nitrogen on zeolite 5A crystals at 303 K and 323 K and pressures of 0.1, 0.6, and 3 MPa.22−25 Obtained results for equilibrium selectivity of methane and nitrogen binary adsorption on Zeochem Co. zeolite 5A are in the range of the equilibrium selectivity reported by Sievers and Mersmann. Total adsorbed amounts of various mixtures versus total pressure at 303 K and 323 K are shown in Figures 12 and 13, respectively. Predictions of typical models are compared in these figures. A good agreement between experimental data and predictions can be seen in these figures. 6.4. Thermodynamic Consistency Test (TCT). Integral TCT on the basis of Gibbs definition of adsorption equilibria was applied in order to increase the confidence in the accuracy

Figure 10. Equilibrium selectivity for methane and nitrogen binary adsorption on zeolite 5A at 303 K and yCH4 = 0.271: experimental data (red ●) against IAST (), W-VSM (blue ---), FH-VSM (purple -·-·) and VDW 2D-EOS (purple -··-) predictions.

Figure 11. Equilibrium selectivity for methane and nitrogen binary adsorption on zeolite 5A at 323 K and yCH4 = 0.884: experimental data (red ●) against IAST (), W-VSM (blue ---), FH-VSM (purple -·-·) and VDW 2D-EOS (purple -··-) predictions.

predictions of IAST, W-VSM, FH-VSM, and PR 2D-EOS are shown in this figure. Almost all predictions are in good agreement with experimental points, although FH-VSM fails to predict an increasing trend of the selectivity with increasing total pressure. In Figure 10, the effect of total pressure on equilibrium selectivity for adsorption of a mixture with methane molar fraction of 0.271 in bulk gas phase at 303 K have been compared with predictions of IAST, W-VSM, FH-VSM, and VDW 2D-EOS. As shown in this figure, more differences between predictions and experimental data are observed. WVSM has the most deviation and FH-VSM fails to evaluate the effect of total pressure on equilibrium selectivity. Effect of total pressure on equilibrium selectivity for adsorption of a mixture

Figure 12. Total adsorbed amounts for methane and nitrogen binary adsorption on zeolite 5A at 303 K: experimental data of mixtures with yCH4 = 0.893 (red ●), yCH4 = 0.485 (blue ▲) and yCH4 = 0.271 (pink ◆) against Eyring 2D-EOS (purple ---) predictions, pure methane (green ) and pure nitrogen (····). 636



Article

isotherms were measured at 273 K, 283 K, 303 K, 323 K, and 343 K and pressures up to 10 bar. Sips isotherm equation and pure substance schemes of W-VSM, FH-VSM, and 2DEOS were utilized to describe pure adsorption isotherms, and excellent fits were observed using these models. Obtained % AAD does not exceed 7 % and 10 % for correlating pure adsorption isotherms of methane and nitrogen, respectively. Binary adsorption data of methane and nitrogen on zeolite 5A containing total and partial adsorbed amounts, adsorbed phase molar fraction, and equilibrium selectivity were measured at 303 K and 323 K and pressures up to 7 bar volumetrically. Integral TCT using the definition of Gibbsian surface excess were performed to increase the confidence in the accuracy of measured data. Obtained consistency errors of less than 19 % in all data sets show the adequate accuracy of the measurements. Higher inconsistencies were observed in the measured data at higher pressures. The best-fit parameters of pure adsorption isotherms were utilized to predict binary adsorption equilibrium data using Sips-IAST, W-VSM, FH-VSM, and different 2DEOS. Obtained results of thermodynamic models were compared against measured binary adsorption data. Besides, performance of the proposed models in describing adsorption behavior of this system was compared in term of % AAD. All the proposed models describe adsorption behavior of this system pretty well. Predicted x−y diagrams used to describe binary adsorption were plotted against experimental data. Total and partial adsorbed amounts of binary mixtures versus methane molar gas fraction were plotted to describe binary behavior of methane and nitrogen adsorption entirely. Symmetric x−y diagrams and ascending total adsorbed amounts versus gas phase molar fraction show the ideal behavior of methane and nitrogen binary adsorption on zeolite 5A. Thus, a simple predictive model such as IAST is sufficient to describe the binary adsorption equilibrium of this system. Experimental equilibrium selectivities were compared with predicted ones. The most deviations in predicting selectivities at 303 K were obtained using W-VSM and at 323 K were obtained using PR 2D-EOS models. Increasing equilibrium selectivities with total pressure reflects the energetically homogeneous nature of this system. The same results were obtained using loading-independent isosteric heats of adsorption. Equilibrium selectivity of this system was 1.45 to 1.97 at different pressures. Although Zeochem Co. zeolite 5A is capable of separating methane and nitrogen, its application causes high operating costs in adsorptive separation processes such as PSA processes.

Figure 13. Total adsorbed amounts for methane and nitrogen binary adsorption on zeolite 5A at 323 K: experimental data of mixtures with yCH4 = 0.884 (red ●) and yCH4 = 0.723 (blue ◆) against FH-VSM (purple ---) predictions, pure methane (green ) and pure nitrogen (····).

of experimentally collected binary equilibrium data in this study. The error of consistency was calculated using the following equation and shown in Table 13: error =

|RHS − LHS| 100 LHS

(43)

Table 13. Integral TCT for Methane and Nitrogen Equilibrium Adsorption Data on Zeolite 5A at 303 K P (bar)

LHS of eq 39

RHS of eq 39

% error

1 3 5 7

0.2011 0.5486 0.8024 0.9934

0.1913 0.4868 0.6585 0.8139

4.87 11.28 17.94 18.06

where RHS and LHS are right-hand side and left-hand sides of eq 39. Integral TCT was applied on the measured data at 303 K. Owing to the imperfect set of data at 323 K, precise evaluation of the numerical integral on the RHS of the eq 39 is not possible. As can be seen in Table 13, methane and nitrogen binary adsorption data on Zeochem Co. zeolite 5A obey the integral TCT fairly well. Obtained consistency errors are more at higher pressures and the most errors are observed in the pressure of 7 bar. As previously discussed and shown in Figures 7 and 8, more uncertainty between binary data and pure data were observed at higher pressures in the infinite dilution region reflecting lower consistency of data in this region at higher pressures. Obtained errors are rarely more than 18 % showing reasonably good consistency of pure and binary measured data. However, relative deviations of more than 50 % are common in the data published in the literature as mentioned by Talu.39

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Fax: +98 7714541495. Funding

We thank the Persian Gulf University research office for financial support, for providing various facilities, and for necessary approval under Contract No. 19-1781. Notes

The authors declare no competing financial interest.

■

REFERENCES

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7. CONCLUSION Pure and binary adsorption equilibrium data of methane and nitrogen on Zeochem Co. zeolite 5A were collected experimentally using a static volumetric apparatus. Pure 637



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