Adsorption Equilibrium and Kinetics of Methane and Nitrogen on

Article pubs.acs.org/IECR

Adsorption Equilibrium and Kinetics of Methane and Nitrogen on Carbon Molecular Sieve Ying Yang,†,‡ Ana M. Ribeiro,‡ Ping Li,† Jian-Guo Yu,† and Alirio E. Rodrigues*,‡ †

State Key Laboratory of Chemical Engineering, College of Chemical Engineering, East China University of Science and Technology (ECUST), Shanghai 20037, China ‡ Laboratory of Separation and Reaction Engineering (LSRE), Associated Laboratory LSRE/LCM, Department of Chemical Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias s/n, 4200-465 Porto, Portugal S Supporting Information *

ABSTRACT: Knowledge of adsorption equilibrium and kinetic data is essential for the design of an adsorption process. In this work, the adsorption equilibrium isotherms of methane and nitrogen are reported at 303, 323, and 343 K over the pressure range from 0 to 700 kPa by a gravimetric system on a carbon molecular sieve (CMS-131510). Methane is preferentially adsorbed. The adsorption capacity at 303 K and 700 kPa is 1.91 mol/kg for methane and 1.01 mol/kg for nitrogen. Experimental data obtained were fitted with the multisite Langmuir model and Toth model. The adsorption kinetics of pure gas was studied by a batch uptake experiment at several different surface coverages within the pressure range of 0−100 kPa and in the same temperature range covered by the equilibrium isotherm. The adsorption rate of both gases is found to be controlled by the surface barrier resistance at the mouth of the micropore and diffusion in the micropore interior. The dual resistance model employed in the simulation can successfully describe the uptake curves. The temperature and concentration dependences of kinetic parameters were also studied. A very high kinetic selectivity was observed. The effect of micropore distribution on the transport parameters is discussed in detail. Binary breakthrough curves were determined, and an enrichment of 50% for methane in the first few seconds was observed. The data reported in this work can be used for the future modeling of adsorption process for the separation of methane and nitrogen on this CMS material.

1. INTRODUCTION The increase of associated greenhouse gas (GHG) emissions and their implications for climate change attract extensive attention worldwide. After carbon dioxide, methane is the second most important GHG; its global warming potential is 25 times greater than that of carbon dioxide on a 100 year time scale.1 Any reduction in methane emissions is very important in the near-term atmosphere restoration and provides a number of important energy, safety, economic, and environmental benefits.2 The main anthropogenic sources of methane emission include landfill gas (LFG) and coal mine methane (CMM). The main components of LFG are methane, carbon dioxide, and nitrogen. To have a commercial heating value for methane, the removal of nitrogen along with carbon dioxide is needed.3 The concentration of N2 in CMM can be relatively high, especially in the low-concentration CMM and ventilation air methane.2,4 To capture and utilize methane from those sources, its separation from N2 is required. As the main component of natural gas, methane is also an important energy gas. The separation of CH4 and N2 is also the key point in the upgrading of natural gas.5−7 Traditionally, cryogenic distillation is used for the separation of CH4 and N2. However, the high energy requirements and cost intensity make this process less attractive, particularly in smallscale applications.5,6,8 Separation of gas mixtures by pressure swing adsorption (PSA) is a competitive alternative to other separation processes and has gained wide acceptance. In the application of PSA processes, appropriate adsorbents with high selectivity and good adsorption capacity are needed. Adsorption separation processes are based on adsorbents with selective © 2014 American Chemical Society

adsorption by different equilibrium capacities (equilibrium separation) or by differences in transport rate (kinetic separation).9 Kinetic separation has attracted considerable interest for separation of methane and nitrogen. A group of titanosilicate molecular sieves named ETS-4 and ETS-10 have been developed and patented by Engelhard Corporation.10−12 This kind of material possess a small pore network, the size of which can be controlled by heat treatment. It has the potential to separate methane and nitrogen based on kinetic difference.13−15 Carbon molecular sieves (CMS) are known to have significant kinetic selectivity between molecules with similar properties. The separations of N2/O2 and CH4/CO2 have been successfully achieved by kinetic separation on CMS.16,17 In many of the previous works, a great number of CMSs have been studied for methane and nitrogen separation.6,7,9,18−28 Qinglin et al.24,29 studied the unary and binary uptake of N2, O2, and CH4 on CMSs; three different models, namely, barrier model, pore model, and dual model, were used to analyze the experimental results. A strong concentration dependence of the transport parameters was also found. Cavenati7 and Fatehi22 investigated the performance of CMS for the separation of CH4/N2. As mentioned above, the adsorption kinetic and separation performance have been studied widely. However, the effect of the micropore size distribution on the mass transport of methane and nitrogen was not discussed. Received: Revised: Accepted: Published: 16840

July 22, 2014 September 27, 2014 October 9, 2014 October 9, 2014 dx.doi.org/10.1021/ie502928y | Ind. Eng. Chem. Res. 2014, 53, 16840−16850

Industrial & Engineering Chemistry Research

Article

In this work, a CMS sample with high kinetic selectivity from SHANLI Chemical Materials Co. Ltd. (China) was used. The adsorption isotherm of CO2 at 273 K was employed to analyze the micropore distribution. Adsorption equilibrium measurements of pure gases were performed on the CMS sample. Adsorption equilibrium data of CH4 and N2 at 303, 323, and 343 K with pressures ranging from 0 to 700 kPa on CMS is reported. The equilibrium data was analyzed with multisite Langmuir model and Toth model. Furthermore, adsorption kinetics of both gases was determined by batch uptake experiments using the dual resistance model. The temperature and concentration dependence of the kinetic parameters was also studied. The results of the dual resistance model are discussed in detail. The effect of micropore distribution on the transport parameters is discussed. This paper provides fundamental data to design a PSA process for kinetic separation for methane and nitrogen. Figure 1. Macropore size distribution of the CMS obtained by mercury intrusion.

2. EXPERIMENTAL SECTION 2.1. Materials. The commercial carbon molecular sieve (CMS-131510) used in this study was provided by SHANLI Chemical Materials Co. Ltd. (China). Some characteristic properties of the CMS are summarized in Table 1. The macroporous

Smic (m 2 g −1) =

2000V0 (cm 3 g −1) L (nm)

(3) 31

The method described by D. Cazorla et al. was employed to obtained the micropore size distribution by using the general adsorption isotherm (GAI). The results are shown in Table 1 and Figure 2.

Table 1. Physical Properties of the CMS and Parameters Used in the Dual Resistance Model

a

parameter

value

solid density (g/cm3) pellet density (g/cm3) porosity of the pellet (−) pellet diameter (cm) macropore volume (cm3/g) macropore radius (nm) micropore volume (cm3/g) micropore radius (nm) total surface area of micropores (cm2/g) shape factor of the macropore (−) shape factor of the micropore (−) tortuosity of the pellet (−)

2.13a 1.25 0.411 0.11−0.13 0.328 596 0.165 0.464 712 1 2 3

Determined by He pycnometry.

structure of the sample was assessed by mercury porosimetry. Macropore size distribution of the CMS obtained from mercury porosimetry is given in Figure 1. The micropore size was analyzed by the adsorption equilibrium isotherm of CO2 at 273 K. Because of the sound theoretical foundation and the ability to provide some information on the pore structure, the Dubinin−Radushkevich (DR) equation was employed to fit the CO2 isotherm. V = V0 exp( −(R gT ln(p0 /p))2 /(E0β)2 )

Figure 2. CO2 adsorption isotherm at 273 K on the CMS and obtained micropore size distribution.

All gases used in this work were supplied by Air Liquide: methane N35, nitrogen N45, and helium N50 with purities greater than 99.95%, 99.995%, and 99.999%, respectively. 2.2. Measurement of Adsorption Isotherm and Kinetics. Adsorption equilibrium and kinetic data were obtained by a magnetic suspension microbalance (Rubotherm, Germany). A detailed description of the gravimetric unit was given elsewhere.32 About 2 g of adsorbent sample were placed in a basket suspended by the permanent magnet of the balance. The balance was then closed with a jacketed cell, and the temperature inside this cell was controlled by a thermostatic oil bath (Huber, Germany). Prior to the first experiment, the activation of the sample was carried out under vacuum at 423 K overnight. Regeneration of the adsorbent for different experiments was performed only under vacuum at the desired temperature.

(1)

where V = qvm is the volume adsorbed, vm the molar volume which was used to transfer the adsorbed amount into volume adsorbed in adsorbed state, p0 the saturated vapor pressure, β the affinity coefficient, V0 the total micropore volume, and E0 the characteristic energy. V0 and E0 were obtained by fitting the DR equation to the experimental data. The mean micropore width, L, and the total surface area of micropores, Smic, were calculated by the following equations:30 L (nm) = 10.8/(E0 − 11.4)

(2) 16841

dx.doi.org/10.1021/ie502928y | Ind. Eng. Chem. Res. 2014, 53, 16840−16850


Article

Pure component equilibrium isotherms for methane and nitrogen were measured on a CMS sample up to about 700 kPa at 303, 323, and 343 K. Both adsorption and desorption experiments were performed. Differential adsorption uptakes of methane and nitrogen in the CMS sample were also measured at several different adsorbate loadings, within the pressure range of 0−100 kPa at 303, 323, and 343 K. When the initial equilibrium points were measured, a certain amount of adsorbate gas was introduced into the gravimetric unit. The adsorption uptakes for nitrogen and methane were recorded every 10 s and 1 min, respectively. The adsorption equilibrium measurements were performed for a sufficient length of time, that is, until there was no significant variation of weight and pressure. Then, a fresh supply of adsorbate gas was added into the gravimetric unit, and the remaining steps were repeated as described above. It is important to note that the amount of the adsorbate gas should be small enough to ensure the linearity of the segment of the adsorption isotherm so that the transport parameters could be assumed to be approximately constant. In this work, the pressure change for each uptake determination was less than 20 kPa. For all measurements in the Rubotherm microbalance, buoyancy correction was performed according to the following equation:32 q=

Δm + ρg (Vs + Vc)

ρl

msM w

ρl − ρg

Table 3. Operating Conditions for the Breakthrough Experiments

0.211 0.312 0.496 632 8238 500 20 80 73.2

P (bar)

QHe(SLPM)

QCH4(SLPM)

QN2(SLPM)

303 303

4 4

0.2 0.2

0.1 0.06

0.1 0.14

K ip [1 + (K ip)ni ]1/ ni

⎛ ΔH ⎞ i⎟ K i = K io exp⎜⎜ − ⎟ R T ⎝ g ⎠

(5)

(6)

where qi and qmi are the absolute amount adsorbed and the maximum amount adsorbed of component i; Koi is the adsorption constant at infinite temperature, (−ΔHi) the isosteric heat of adsorption at zero loading, and ni the heterogeneity parameter. An alternative model to fit the adsorption isotherm data is the multisite Langmuir model.35 This model is an extension of the Langmuir isotherm for localized monolayer adsorption. It is based on statistical thermodynamics and assumes that one adsorbate molecule can occupy more than one adsorption site on the surface. In the case of no adsorbate−adsorbate interaction, the model can be expressed as qi qmi

ai ⎛ qi ⎞ ⎜ ⎟ = aiK ip⎜1 − qmi ⎟⎠ ⎝

(7)

where ai is the number of neighboring sites occupied by component i and Ki is the equilibrium constant of the multisite Langmuir model, which has an exponential dependence with temperature in the same expression described by eq 6. In this model, the isosteric heat of adsorption is constant. The saturation capacity of each component is imposed by the thermodynamic constraint aiqmi = constant. This model works well with adsorption of hydrocarbons and carbon dioxide on activated carbon and carbon molecular sieve.33 Fitting of the Toth and multisite Langmuir isotherm models was done with MATLAB (The Mathworks, Inc.). The minimization routine uses the Nelder−Mead simplex method of direct search. The error function was defined as ⎛ qcal − qexp ⎞2 ⎟⎟ ERR = ∑ ∑ ⎜⎜ q ⎝ ⎠ T i cal

Table 2. Details of the Column Used in the Breakthrough Experiments column diameter (m) column length (m) porosity of the column (−) column density (kg/m3) column wall density (kg/m3) wall specific heat (J/kg K) wall heat transfer coefficient (W/m2 K) overall heat transfer coefficient (W/m2 K) weight of adsorbent (g)

T (K)

binary binary

qi = qmi

where q is the absolute amount adsorbed, Δm the difference of weight between one measurement and the previous one, ρl the density of the adsorbed phase, ρg the density of the gas, Vs the volume of the solid adsorbent, Vc the volume of the cell where the adsorbent is located, ms the mass of adsorbent used in the measurement, and Mw the molecular weight of the gas. To determine the volumes that contribute to the buoyancy effect (Vs + Vc), a calibration with helium was performed, under the assumption that helium is not adsorbed. 2.3. Fixed Bed Experiment: Breakthrough Curves. Binary breakthrough curves were measured in an already existing apparatus in our lab. The setup was described in detail in a previous paper.7 First, the adsorbent was activated at 423 K under a flow of helium for 10 h. For all the breakthrough experiments, helium was used to adjust the molar fraction of the feed mixture to the desired value. Before the experiments, the bed was filled with helium at the feed temperature and pressure. The details of the column and the operating conditions for the breakthrough experiments are shown in Table 2 and Table 3, respectively.

value

system

1 2

3. THEORETICAL SECTION 3.1. Adsorption Equilibrium. Various fundamental and empirical isotherm equations are available in the literature to describe the adsorption equilibria.33 The isotherm equations employed in this study are the Toth model and multisite Langmuir model. The Toth isotherm34 model is a semiempirical equation that is popularly used and can describe well many adsorption data. The equations corresponding to this model are

(4)

parameter

no.

(8)

where T is each experimental temperature, i the number of points of each isotherm, qcal the calculated amount adsorbed, and qexp is the experimental amount adsorbed. Isosteric heats of adsorption of pure components as a function of surface coverage were calculated from the following van’t Hoff equation:33 ⎡ ∂ lnp ⎤ ( −ΔH ) =⎢ ⎣ ∂T ⎥⎦q R gT 16842

(9)



Article

where (−ΔH) is the isosteric heat of adsorption and Rg is the ideal gas constant. 3.2. Adsorption Kinetics. For studying the kinetics of methane and nitrogen on CMS, differential adsorption uptake curves obtained from batch experiments were employed. To determine kinetic parameters from experimental data, an appropriate model is necessary. As we know, CMS has a bidisperse pore structure with clearly distinguishable macropore and micropore resistances to the transport of adsorbate. The latter is believed to be the limiting rate of the adsorption kinetics.36,37 Many researchers have studied the transport mechanism of gases in CMS micropores. A successful description of the transport mechanism is the dual resistance model, in which the transport is controlled by a barrier resistance at the mouth of the micropores followed by diffusion in its interior.7,21,22,24,38 The barrier resistance is based on the fact that CMS preparation involves a cracking process, which results in the narrowing of the micropore openings.28,38,39 In this work we have used the dual resistance model. Both the barrier resistance confined at the pore mouth and the pore diffusional resistance distributed in the micropore interior were considered. Although the transport of gases in the CMS is primarily controlled by micropore resistance, for the sake of generality, macropore diffusional resistance was taken into account in the model. This model was based on the following assumptions: (1) The gas phase follows the ideal gas law. (2) The temperature of the microbalance system is controlled by a thermostatic oil bath which is considered isothermal. (3) The transport in the macropores is represented by Knudsen diffusion and selfdiffusion40 described by the Bosanquet equation.19 (4) The shape of adsorbent particle is assumed to be an infinite cylinder and the micropore is spherical. (5) The kinetic parameters are assumed to remain constant over the incremental step change. Subject to these assumptions, the equations that describe the adsorption uptake are summarized in Table S1 (Supporting Information). To solve these partial differential equations, boundary and initial conditions are needed, which are presented in Table S2 (Supporting Information). Note that the batch experiment can be operated by having the microbalance cell initially free of any adsorbate and, at time t = 0+, an amount of adsorbate is introduced into the cell. Another condition is that the adsorbent is initially equilibrated with the adsorbate at pressure peq (the corresponding concentration is Ceq = peq/(RgT)), and at t = 0+, the pressure in the cell is increased from peq to pfeed. For the first case, qeq0 and peq in the initial conditions are equal to zero. The mathematical model described by eqs S1−S19 (Supporting Information) was numerically solved in gPROMS (PSE Enterprise, U.K.) using orthogonal collocation on finite elements. The radial domain of micropore and macropore were handled using third-order polynomials with 15 intervals.

Figure 3. Adsorption equilibrium isotherms of nitrogen on CMS at different temperatures. Symbols, experimental data (closed, adsorption; open, desorption); solid lines, multisite Langmuir model; dotted lines, Toth model.

Figure 4. Adsorption equilibrium isotherms of methane on CMS at different temperatures. Symbols, experimental data (closed, adsorption; open, desorption); solid lines, multisite Langmuir model; dotted lines, Toth model.

The solid lines in Figures 3 and 4 correspond to the fitting of the multisite Langmuir model, and the dotted lines to the Toth model. The parameters of multisite Langmuir model and Toth model are listed in Tables 4 and 5, respectively. As we can see from Figures 3 and 4, both models fit the experimental data quite well within the entire pressure and temperature range considered

4. RESULTS AND DISCUSSION 4.1. Adsorption Equilibrium. The adsorption equilibrium isotherms of CH4 and N2 on CMS were measured at 303, 323, and 343 K in the pressure range of 0−700 kPa. The results are shown in Figures 3 and 4. The closed symbols represent points determined by adsorption, while open symbols were obtained in desorption. It can be observed that all the isotherms are completely reversible. Each point takes some time to achieve adsorption equilibrium. In the case of nitrogen, it takes about 3 h, whereas for methane, around 4 days is needed. The experimental data of methane and nitrogen are listed in the Supporting Information.

Table 4. Fitting Parameters of Multisite Langmuir model gas

qmi (mol/kg)

Koi (kpa−1)

(−ΔHi) (kJ/mol)

ai

ERR

CH4 N2

7.186 7.252

1.369 × 10−7 7.909 × 10−8

20.21 17.51

6.329 6.271

1.01 1.13

Table 5. Fitting Parameters of Toth Model

16843

gas

qmi (mol/kg)

Koi (kpa−1)

(−ΔHi) (kJ/mol)

ni

ERR

CH4 N2

3.188 2.611

2.055 × 10−6 1.482 × 10−6

20.55 17.56

0.607 0.699

0.57 0.67



Article

in this work. As four-parameter models, they have a very good flexibility to fit experiment data. It is clear from Tables 4 and 5 that the saturation capacities of CH4 and N2 obtained from the multisite Langmuir model are much larger than those attained by the Toth model. In the multisite Langmuir model, each adsorbed molecule is assumed to occupy multiple sites, while in the Toth model each adsorbed molecule is assumed to occupy only one site. Therefore, the obtained values of saturation capacity for the multisite Langmuir model are always higher than those of the Toth model. Similar behavior has also been reported in the work of Qinglin et al.,29 in which the multisite Langmuir model could also describe the adsorption isotherm well. The multisite Langmuir model is preferred as it has a direct extension to multicomponent mixtures suitable for PSA modeling. Because of its sound theoretical basis, the multisite Langmuir model was widely employed to describe adsorption equilibrium isotherms of various adsorbates on activated carbons and CMS.29,33,41,42 The isosteric heat of adsorption is a measure of the interaction between the adsorbate molecules and the adsorbent.43 The knowledge of the isosteric heat is essential in the study of adsorption kinetics. When heat is released because of adsorption, the released energy is partly absorbed by the solid adsorbent, and this increases the particle temperature. This increase in temperature affects the adsorption kinetics.33 The isosteric heat of adsorption as a function of loading was calculated using the van’t Hoff equation (eq 9) with the equilibrium experimental data, and the results obtained are presented in Figure 5. It can be

Table 6. Comparison of Adsorption Equilibrium of CH4 and N2 on CMS q p T adsorbate (mol/kg) (kPa) (K)

adsorbent Takeda CMS 3K Takeda CMS 3A Takeda CMS 3A BF CMS BF CMS Air Products CMS CMS a

CH4 N2 CH4 N2 CH4 N2 CH4 N2 CH4 N2 CH4 N2

1.73 0.91 2.00 0.80 ∼1.87 ∼1.05

550 550 267 267 600 600

308 308 303 303 303 303

−ΔH (kJ/mol) 38.95 15.93 18.50 13.50

23.37 12.30 ∼1.51 ∼0.3 1.91 1.01

600 100 700 700

298 303 303 303

21.50 20.21 a 17.51 a

ref 7 7 20 20 25 25 21 21 9 23 this work

Multisite Langmuir model.

4.2. Adsorption Kinetics: Batch Uptake Experiment. Differential adsorption uptakes of methane and nitrogen in the CMS sample were measured at zero and several different surface coverages within the pressure range of 0−100 kPa at 303, 323, and 343 K. The kinetic parameters, namely, barrier masstransfer coefficient (kb) and micropore diffusivity (Dμ), for the dual model described by eqs S1−S19 (Supporting Information) at different adsorbent loadings were determined by fitting the model to experimental uptake curves. The fitting process was performed by using the “Parameter Estimation” function in gPROMS. 4.2.1. Uptake at Zero Surface Coverage. The experimental uptake results of N2 and CH4 in the CMS at zero surface coverage and at three different temperatures are shown in Figures 6 and 7,

Figure 5. Isosteric heat of adsorption for CH4 and N2 adsorption on CMS calculated from adsorption equilibrium isotherms at 303, 323, and 343 K. Solid lines correspond to the values obtained from multisite Langmuir model, while dotted lines are a result of the Toth model.

observed that the heat of adsorption predicted by the isotherm models was about 20 kJ/mol, which is in good agreement with the values obtained with the van’t Hoff equation. Adsorption equilibrium and the isosteric heat of adsorption for methane and nitrogen were compared with values previously reported in the literature.7,9,18,20,21,23−25,44 The results are summarized in Table 6. The obtained amounts of adsorbed methane and nitrogen are less than those previously reported by Yi et al.20 but compared well with those of other works.7,25 When heat of adsorption is analyzed, the reported values available in the literature7,20,21 show large deviations. For example, the values for methane range from 18.50 to 38.95 kJ/mol. The heats of adsorption for methane (20.21 kJ/mol) and nitrogen (17.51 kJ/mol) obtained in this work are within the reported values.7,20,21

Figure 6. Fractional uptakes of nitrogen on the CMS at zero surface coverage. Symbols, experimental data; solid lines, dual resistance model.

respectively. Solid lines in these graphics represent the fitting of the dual resistance model. As shown in Figures 6 and 7, the results predicted by the dual resistance model agree with experimental data very well. The temperature dependence of micropore diffusivity and barrier mass-transfer coefficient were described by the Arrhenius equation: Dμ0 rμ2 16844

=

D′μ0 rμ2

exp( −Ead /R gT )

(10)



Article

Figure 7. Fractional uptakes of methane on the CMS at zero surface coverage. Symbols, experimental data; solid lines, dual resistance model.

′ exp( −Eab /R gT ) k b0 = k b0

(11)

where Dμ0 and kb0 are micropore diffusivity and barrier masstransfer coefficient at zero surface coverage, which were obtained by fitting the dual resistance model with uptake experimental data. D′μ0 and k′b0 are pre-exponential factors, and Eda and Eba are activation energies. The two parameters for methane and nitrogen in CMS plotted against the reciprocal temperature are presented in Figure 8. The plots are linear as expected, which indicates that the Arrhenius equation can correctly describe the temperature dependency of the two parameters. From the correlation, the values of activation energy can be determined. A summary of the kinetic parameters determined from the fit of the uptake curves and correspondent activation energies are listed in Table 7. In this work, the activation energy of the micropore diffusivity was calculated as 39.27 kJ/mol for methane and 38.91 kJ/mol for nitrogen. Those values compare well with those obtained by Qinglin et al.24 and Cavenati et al.7 The activation energy of the barrier mass-transfer coefficient is 44.26 kJ/mol for methane and 27.31 kJ/mol for nitrogen. Those values are smaller than the 53.6 and 43.5 kJ/mol values reported by Reid et al.23,45 To determine the validity of the micropore diffusivity and barrier mass-transfer coefficient at zero surface coverage, the results are compared with the data obtained by different methods in previous works reported in the literature. The comparison results are summarized in Table 8. The kinetic parameters measured by different methods are different from each other. However, the order of magnitude of the values reported here is comparable to those obtained in previous works. It is clear that, both in this work as well as in others7,24 that used the dual resistance model, the barrier mass-transfer coefficient is about 1 order of magnitude larger than that of the micropore diffusivity. Because of the ink-bottle-like pore mouth of the CMS, the barrier mass-transfer resistance should be the main rate-controlling step. This might be caused by the assumptions of the dual resistance model. When developing the adsorption model, it was assumed that the adsorption of gases occurs only in the micropore (radius less than 0.464 nm in the case of our work). In other words, only transport pores (macropores) and uniform micropore system were assumed to be presented in the CMS.39 However, there are other bigger micropores where adsorption can also occur,

Figure 8. Temperature dependence of (a) micropore diffusivity and (b) barrier mass-transfer coefficient of the dual resistance model for methane and nitrogen in CMS.

as shown in Figure 2. Qinglin24 and Cavenati7 pointed out that the value of the barrier mass-transfer coefficient is mainly affected by the initial part of the uptake. It is expected that the larger pores, which have the smaller mass transport resistance (larger coefficient), are the first to be filled. Therefore, we believe that this can be the reason why the barrier mass-transfer coefficient has a value higher than the micropore diffusivity. In the case of this study, even though the values of the obtained kinetic parameters are smaller than that of other works, the kinetic selectivity of the CMS is 345, which is much higher, as shown in Table 8. The high kinetic selectivity indicates that the transport of CH4 is much slower than that of N2. As we know, in an equilibrium-based separation, the selectivity of the adsorbent is governed by the separation factor defined by19 αij =

Xi /Yi Xj /Yj

(12)

where Xi and Yi are the equilibrium mole fractions of component i in the adsorbed and gas phases, respectively. However, in a kinetically controlled separation process, the situation is different because the selectivity depends on both kinetic and equilibrium effects. The actual kinetic selectivity accounting for both kinetic and equilibrium effects in the linear range of the isotherms is given by46 SK = 16845

KHi KHj

kμi kμj

(13)



Article

Table 7. Kinetic Parameters of the Dual Resistance Model for CH4 and N2 Transport in the CMS at 303, 323, and 343 K Determined by Batch Uptake Experiments at Zero Surface Coverage adsorbate

T (K)

Dμo/rμ2 (× 107 s−1)

CH4

303.60 320.60 343.85 303.90 322.05 343.85

6.04 18.30 38.00 1210 3020 7250

N2

Dμ0 ′ /r2μ (s−1)

Eda (kJ/mol)

βp

kbo (× 106 s−1)

kb0 ′ (s−1)

Eba (kJ/mol)

βb

3.81

39.27

4.38

196.85

44.26

6.10

600.22

38.91

23.06

4.80 12.00 37.30 2720 4500 9540

129.55

27.31

10.14

Table 8. Comparison of the Kinetic Parameters of CH4 and N2 Adsorption in the CMS at Zero Surface Coverage adsorbent Takeda CMS 3A BF CMS Takeda CMS 5A BF CMS Takeda CMS 3K Takeda CMS 3A Takeda CMS 3R-162 CMS

gas CH4 N2 CH4 N2 CH4 N2 CH4 N2 CH4 N2 N2 N2 CH4 N2

method volumetric gravimetric chromatographic gravimetric volumetric gravimetric volumetric frequency response gravimetric

Dμo/rμ2 (s−1)

T (K)

kbo (s−1)

−6

−5

2.6 × 10 5.8 × 10−4 5.0 × 10−6 1.2 × 10−4 4.5 × 10−4 1.2 × 10−3 4.8 × 10−6b 1.0 × 10−3b 2.3 × 10−6 5.0 × 10−4

303 302 298 300 303 303 298 298 308 308 293 296 303 303

3.3 × 10 8.8 × 10−3

1.0 × 10−4 6.4 × 10−3 5.5 × 10−4 1.4 × 10−3 4.8 × 10−6 2.7 × 10−3

6.0 × 10−7 1.2 × 10−4

kμi/kμj

SK

ref

a

4.9

24 24 9 18 20 20 21 21 7 7 26 28 this work

262.8

2.67

0.6

207.5

3.2

133a

1.9

345.0a

5.3

a

For comparison, kinetic selectivity is calculated with overall mass-transfer coefficient. bOverall mass-transfer coefficient kμi = 1/[(1/kb,i) + (r2μ/15Dμ,i)]

Table 9. Micropore Diffusivity for N2 and CH4 Adsorption on the CMS in the Pressure Range of 0−100 kPa at 303, 323, and 343 K N2

N2

CH4

T = 303K

T = 323K

T = 343K

P (kPa)

θ (× 102)

Dμ/rμ2 (× 104 s−1)

θ (× 102)

Dμ/rμ2 (× 104 s−1)

θ (× 102)

Dμ/rμ2 (× 106 s−1)

5−10 10−20 20−40 40−60 60−80 80−100

0.24 0.54 0.94 1.79 2.64 3.35

1.44 1.50 1.62 1.98 2.29 2.56

0.34 0.63 1.22 1.79 2.33

3.68 3.86 4.17 4.80 5.44

0.97 1.89 3.18 4.62 5.69

4.25 4.81 5.51 5.69 6.71

Table 10. Barrier Mass-Transfer Coefficient for N2 and CH4 Adsorption on the CMS in the Pressure Range of 0−100 kPa at 303, 323, and 343 K N2

N2

T = 303K

CH4

T = 323K

T = 343K

P (kPa)

θ (× 102)

kb (× 103 s−1)

θ (× 102)

kb (× 103 s−1)

θ (× 102)

kb (× 105 s−1)

5−10 10−20 20−40 40−60 60−80 80−100

0.24 0.54 0.94 1.79 2.64 3.35

2.90 3.13 3.30 3.60 4.10 4.30

0.34 0.63 1.22 1.79 2.33

4.90 5.02 5.50 6.00 6.50

0.97 1.89 3.18 4.62 5.69

4.20 5.00 5.80 6.30 6.80

4.2.2. Variation of the Kinetic Parameters with Concentration. The kinetic parameters for the dual resistance model were also measured at different surface coverages by fitting the model to the experimental uptake curves. Representative results are listed in Tables 9 and 10. It can be seen that both the micropore diffusivity and barrier mass-transfer coefficient increase with the surface coverage. Similar results were also

where KHi is the Henry constant and kμi is the overall mass-transfer coefficient. In this work, the actual kinetic selectivity was calculated to be 5.3, which is higher than those obtained in previous works, as shown in Table 8. Because of this larger kinetic difference and relatively higher actual kinetic selectivity, it is expected that this CMS can be an appropriate adsorbent for the separation of methane and nitrogen. 16846



Article

observed in previous works.23,24,27,28,47 In adsorption systems, when the equilibrium isotherm is linear the kinetic parameter is generally independent of concentration. However, when the isotherm is nonlinear the kinetic parameter is generally concentration-dependent.47 Reid et al.23 pointed out that the increase of the kinetic parameters was associated with surface diffusion. At low surface coverage, adsorption occurs on the most energetic sites where the physisorption is stronger. As the surface coverage increases, the less energetic sites are occupied, the physisorption is weaker, and the surface diffusion is faster. The concentration dependence of micropore diffusivity is usually described by Darken’s equation,33,36,47,48 which for the multisite Langmuir isotherm is Dμ Dμo

=

1 + θ(ai − 1) d ln p = d ln q 1−θ

(14)

where θ = q/qm is the surface coverage; Dμo is the micropore diffusivity at zero surface coverage which is assumed to be independent of θ; and ai and qm are parameters already determined from the equilibrium isotherm fitting. Darken’s equation is derived from the chemical potential gradient as the driving force for diffusion. Similar to the micropore diffusivity, the barrier mass-transfer coefficient will also depend on concentration, as given by26,28,38 kb 1 + θ(ai − 1) d ln p = = k bo d ln q 1−θ

Figure 10. Concentration dependence of barrier mass-transfer coefficient of the dual resistance model for methane and nitrogen. The dotted lines are the plot of Darken’s equation, while the solid lines correspond to the predicted data described by the empirical correction equation with βb as the fitting parameter.

correction was presented by Qinglin et al.,24 which can be expressed as

(15)

where kbo is the barrier mass-transfer coefficient at zero surface which is also assumed to be independent of θ. The micropore diffusivity and barrier mass-transfer coefficient at zero surface coverage, which appear in Table 7, are the ones reported in the previous section. The dependence of the kinetic parameters upon the adsorbed phase concentration and the values predicted by eqs 14 and 15 at different temperatures are plotted in Figures 9 and 10, respectively. As shown in these figures, the concentration dependence of both kinetic parameters is much stronger than that predicted by Darken’s equation. To describe this stronger concentration dependence, an empirical

⎛ d ln p ⎞⎛ Dμ θ ⎞⎟ =⎜ ⎟⎜1 + βp 1 − θ⎠ Dμ*o ⎝ d ln q ⎠⎝

(16)

⎛ d ln p ⎞⎛ kb θ ⎞⎟ =⎜ ⎟⎜1 + β b ⎝ k bo 1 − θ⎠ ⎝ d ln q ⎠

(17)

where βp and βb are fitting parameters and k*bo and D*μo are limiting constraints which are independent of θ. When compared with Darken’s equation, eqs 16 and 17 indicate that Dμo and kbo change with surface coverage. This was assumed on the grounds that different pore sizes have different values of Dμo and kbo and that the pores are filled in the order of increasing pore size. Because the micropore size is fixed in the CMS model, the effect of the micropore size distribution on micropore diffusivity and barrier mass-transfer coefficient is described by this empirical correction. Under this hypothesis, kbo * and Dμo * are the barrier mass-transfer coefficient and micropore diffusivity of the smallest pore, respectively, and they are equal to the corresponding values at zero surface coverage. The predicted trends of micropore diffusivity and barrier mass-transfer coefficient given by eqs 16 and 17 are also plotted in Figures 9 and 10. βp and βb were determined by fitting eqs 16 and 17 to the experimental data appearing in Tables 9 and 10 and the values given in Table 7. In this work, the values of βp and βb obtained for nitrogen are larger than those of methane, which indicates that the micropore size distribution has a stronger effect on nitrogen diffusion. As was similarly observed by Qinglin et al.24 and Giesy et al.,28 the empirical modification fits the experimental data well. 4.3. Breakthrough Curves. The performance of the CH4/N2 separation on the CMS studied in this work was tested using binary breakthrough experiments. Two different molar fractions of methane in nitrogen (30% and 50% helium free basis) diluted in helium were used. Before the breakthrough experiments, helium at the desired pressure was introduced into the column to regenerate the adsorbent. Then the mixture of methane, nitrogen, and helium was fed to the column.

Figure 9. Concentration dependence of micropore diffusivity of the dual resistance model for methane and nitrogen. The dotted lines are the plot of Darken’s equation, while the solid lines correspond to the predicted data described by the empirical correction equation with βp as the fitting parameter. 16847



Article

Figure 11. Flow rate of methane from the column outlet (a) and the ratio between the outlet and inlet methane concentrations (b). Feed composition: CH4 = 50 mol %, N2 = 50 mol % (helium free basis).

Figure 12. Flow rate of methane from the column outlet (a) and the ratio between the outlet and inlet methane concentrations (b). Feed composition: CH4 = 30 mol %, N2 = 70 mol % (helium free basis).

The operating details are listed in Table 3. The flow rate and concentration of the outlet stream were measured. The experimental results are presented in Figures 11 and 12. As we can see, methane breaks through together with nitrogen. The methane was hardly adsorbed because of the very slow mass transport. From the concentration history of CH4 at the exit of the column, shown in Figures 11b and 12b, a high CH4 enrichment of 50% (C/C0) can be found. The concentration of methane was enhanced from 30% to 45% in the first few seconds. This behavior can be very useful in specific applications. For example, the low concentration coal mine methane, in which the composition of methane is less than 10%, is difficult to use. If the concentration is increased to 20%, the gas could be fed to the generator, thus avoiding methane release to the atmosphere.

The equilibrium of adsorption for methane and nitrogen on CMS was investigated at 303, 323, and 343 K in the pressure range from 0 to 700 kPa. CH4 is more adsorbed than N2 in all the conditions studied. The data was well-fitted with the multisite Langmuir model and Toth model. The equilibrium data reported here are consistent with other values published in previous works. Adsorption kinetics of the gases was studied at the same range of temperature over different surface coverage. The limiting rate of adsorption kinetics lies in the micropore resistance. A dual resistance model which was composed of barrier resistance at the micropore mouth and micropore diffusivity in the interior was employed to predict the uptake curves. The simulated results agree with the experimental data very well. The actual kinetic selectivity of this CMS sample at 303 K at zero surface coverage is 5.3, which is higher than that of other samples studied before, thus making it a promising adsorbent for kinetic separation of methane and nitrogen. The observed concentration dependence of barrier mass-transfer coefficient and micropore diffusivity is much stronger than that predicted by Darken’s equation (the form of the multisite Langmuir isotherm). An empirical correction of Darken’s equation in which the values of micropore diffusivity and barrier coefficient at zero surface change with different pore size was used to account for the stronger concentration dependence.

5. CONCLUSIONS In this study, a carbon molecular sieve with high kinetic selectivity was investigated. The macropore structure was measured by mercury intrusion; the porosity of the pellet is 0.411. The adsorption isotherm of CO2 at 273 K was employed to analyze the micropore distribution. The mean pore width was calculated to be 0.464 nm. The micropore volume assessed by the DR equation is 0.165 cm3/g. The micropore size distribution was obtained using the method of Cazorla et al.31 16848



Article

qi = absolute adsorbed phase concentration of component i, mol/kg qmi = maximum adsorbed phase concentration of component i, mol/kg qcal = calculated adsorbed phase concentration, mol/kg qeq0 = initial adsorbed phase concentration, mol/kg qexp = experimental adsorbed phase concentration, mol/kg Rg = ideal gas constant, J/(mol K) Sa = shape factor of the particle Si = shape factor of the micropore Sk = actual kinetic selectivity Smic = total surface area of micropore, m2/g t = time, s T = temperature, K Tc = critical temperature, K V = volume adsorbed, cm3/g V0 = total micropore volume, cm3/g vm = molar volume, cm3/mol Vs = volume of the solid adsorbent, m3 Vc = volume of the cell where the adsorbent is located, m3 Xi = equilibrium mole fraction of component i in the adsorbed phase Yi = equilibrium mole fraction of component i in the gas phase

Binary methane−nitrogen breakthrough curves were performed. An enrichment of 50% for methane in the first few seconds was observed. The data reported in this work can be used for the modeling and design of adsorption process like pressure swing adsorption for methane enrichment of natural gas, landfill gas, and coal mine methane.

■

ASSOCIATED CONTENT

* Supporting Information S

Mathematical model for the batch experiment, boundary and initial conditions for the model, and experimental data of adsorption equilibrium for methane and nitrogen. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +351 22 5081671. Fax: +351 22 5081674. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS Y.Y. is grateful for the fellowship from the China Scholarship Council (201306740026). This work was financed by the Program of International S&T Cooperation (S2015GR1004). This work was financed by FCT under the Cooperation Project FCT/CHINA 441.00. This work was cofinanced by FCT and FEDER under Programme COMPETE (Project PEst-C/EQB/ LA0020/2013). This work was cofinanced by QREN, ON2, and FEDER (Projects NORTE-07-0162-FEDER-000050 and NORTE-07-0124-FEDER-0000006).

Greek Letters

■

NOMENCLATURE ai = number of neighboring sites occupied by component i in MSL model Dμ = micropore diffusivity, m2/s Dμo = micropore diffusivity at zero surface coverage, m2/s D*μo = limiting micropore diffusivity of the smallest pore, m2/s Eba = activation energy of barrier mass-transfer coefficient, kJ/mol Eda = activation energy of micropore diffusivity, kJ/mol E0 = characteristic energy, kJ/mol L = mean micropore width, nm kb = barrier mass-transfer coefficient, 1/s kbo = barrier mass-transfer coefficient at zero surface coverage, 1/s k*bo = limiting barrier mass-transfer coefficient of the smallest pore, 1/s kμi = overall mass-transfer coefficient of component i, 1/s KHi = Henry constant of component i, mol/(kg kPa) Ki = equilibrium constant of component i, 1/Pa Kio = adsorption constant at infinite temperature of component i, 1/Pa ms = mass of adsorbent used, kg Mw = molecular weight of the gas, kg/mol ni = heterogeneity parameter of component i in the Toth model p = pressure, Pa pc = critical pressure, atm p0 = saturated vapor pressure, Pa q = absolute adsorbed phase concentration, mol/kg

■

αij = separation factor βp, βb = fitting parameters β = affinity coefficient εp = porosity of the particle τp = tortuosity of the particle θ = surface coverage Δm = difference of weight between one measurement and the previous one, kg ΔHi = isosteric heat of adsorption for component i, kJ/mol ρg = density of the gas, kg/m3 ρl = density of the adsorbed phase, kg/m3 ρp = density of the particle, kg/m3

REFERENCES

(1) Jager, T. K.; Manning, M.; Meyer, L. Safeguarding the Ozone Layer and the Global Climate System: Issues Related to Hydrofluorocarbons and Perfluorocarbons; IPCC: Cambridge, U.K., 2005. (2) Tanaka, N. Energy Sector Methane Recovery and Use. http:// www.iea.org/publications/freepublications/publication/methane_ brochure.pdf. (3) Rasi, S.; Läntelä, J.; Rintala, J. Upgrading landfill gas using a high pressure water absorption process. Fuel 2014, 115, 539−543. (4) Karakurt, I.; Aydin, G.; Aydiner, K. Mine ventilation air methane as a sustainable energy source. Renewable Sustainable Energy Rev. 2011, 15, 1042−1049. (5) Mulgundmath, V.; Tezel, F.; Hou, F.; Golden, T. Binary adsorption behaviour of methane and nitrogen gases. J. Porous Mater. 2012, 19, 455−464. (6) Ning, X.; Koros, W. J. Carbon molecular sieve membranes derived from Matrimid® polyimide for nitrogen/methane separation. Carbon 2014, 66, 511−522. (7) Cavenati, S.; Grande, C. A.; Rodrigues, A. E. Separation of methane and nitrogen by adsorption on carbon molecular sieve. Sep. Sci. Technol. 2005, 40, 2721−2743. (8) Yuan, B.; Wu, X.; Chen, Y.; Huang, J.; Luo, H.; Deng, S. Adsorptive separation studies of ethane−methane and methane−nitrogen systems using mesoporous carbon. J. Colloid Interface Sci. 2013, 394, 445−450. (9) Kapoor, A.; Yang, R. Kinetic separation of methanecarbon dioxide mixture by adsorption on molecular sieve carbon. Chem. Eng. Sci. 1989, 44, 1723−1733.

16849



Article

(33) Do Duong, D. Adsorption Analysis: Equilibria and Kinetics; Imperial College Press: London, 1998; Vol. 2. (34) Toth, J. State equations of the solid-gas interface layers. Acta Chim. Acad. Sci. Hung. 1971, 69, 311−328. (35) Nitta, T.; Shigetomi, T.; Kuro-Oka, M.; Katayama, T. An adsorption isotherm of multi-site occupancy model for homogeneous surface. J. Chem. Eng. Jpn. 1984, 17, 39−45. (36) Rutherford, S.; Do, D. Adsorption dynamics of carbon dioxide on a carbon molecular sieve 5A. Carbon 2000, 38, 1339−1350. (37) Farooq, S.; Qinglin, H.; Karimi, I. Identification of transport mechanism in adsorbent micropores from column dynamics. Ind. Eng. Chem. Res. 2002, 41, 1098−1106. (38) Srinivasan, R.; Auvil, S.; Schork, J. Mass transfer in carbon molecular sievesAn interpretation of Langmuir kinetics. Chem. Eng. J. (Amsterdam, Neth.) 1995, 57, 137−144. (39) Nguyen, C.; Do, D. Dual Langmuir kinetic model for adsorption in carbon molecular sieve materials. Langmuir 2000, 16, 1868−1873. (40) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena; John Wiley & Sons: New York, 2002. (41) Grande, C. A.; Blom, R.; Möller, A.; Möllmer, J. High-pressure separation of CH4/CO2 using activated carbon. Chem. Eng. Sci. 2013, 89, 10−20. (42) Lopes, F. V. S.; Grande, C. A.; Ribeiro, A. M.; Loureiro, J. M.; Evaggelos, O.; Nikolakis, V.; Rodrigues, A. E. Adsorption of H2, CO2, CH4, CO, N2 and H2O in activated carbon and zeolite for hydrogen production. Sep. Sci. Technol. 2009, 44, 1045−1073. (43) Liu, Z.; Grande, C. A.; Li, P.; Yu, J.; Rodrigues, A. E. Adsorption and desorption of carbon dioxide and nitrogen on zeolite 5A. Sep. Sci. Technol. 2011, 46, 434−451. (44) Jayaraman, A.; Chiao, A. S.; Padin, J.; Yang, R. T.; Munson, C. L. Kinetic separation of methane/carbon dioxide by molecular sieve carbons. Sep. Sci. Technol. 2002, 37, 2505−2528. (45) Reid, C.; Thomas, K. Adsorption kinetics and size exclusion properties of probe molecules for the selective porosity in a carbon molecular sieve used for air separation. J. Phys. Chem. B 2001, 105, 10619−10629. (46) Ruthven, D. M.; Farooq, S.; Knaebel, K. S. Pressure Swing Adsorption; VCH Publishers: New York, 1994; Vol. 480. (47) Ruthven, D. M. Sorption kinetics for diffusion-controlled systems with a strongly concentration-dependent diffusivity. Chem. Eng. Sci. 2004, 59, 4531−4545. (48) Ruthven, D. M. Principles of Adsorption and Adsorption Processes; John Wiley & Sons: New York, 1984.

(10) Kuznicki, S. M. Large-pored crystalline titanium molecular sieve zeolites. U.S. Patent 4,853,202, 1989. (11) Braunbarth, C.; Hillhouse, H. W.; Nair, S.; Tsapatsis, M.; Burton, A.; Lobo, R. F.; Jacubinas, R. M.; Kuznicki, S. M. Structure of strontium ion-exchanged ETS-4 microporous molecular sieves. Chem. Mater. 2000, 12, 1857−1865. (12) Bell, V. A.; Desai, B. T.; Kuznicki, S. M.; Petrovic, I., Small-pored crystalline titanium molecular sieve zeolites and their use in gas separation processes. U.S. Patent 6,068,682, 2000. (13) Marathe, R.; Mantri, K.; Srinivasan, M.; Farooq, S. Effect of ion exchange and dehydration temperature on the adsorption and diffusion of gases in ETS-4. Ind. Eng. Chem. Res. 2004, 43, 5281−5290. (14) Grande, C. A.; Cavenati, S.; Da Silva, F. A.; Rodrigues, A. E. Carbon molecular sieves for hydrocarbon separations by adsorption. Ind. Eng. Chem. Res. 2005, 44, 7218−7227. (15) Majumdar, B.; Bhadra, S.; Marathe, R.; Farooq, S. Adsorption and Diffusion of Methane and Nitrogen in Barium Exchanged ETS-4. Ind. Eng. Chem. Res. 2011, 50, 3021−3034. (16) Jee, J.-G.; Kim, M.-B.; Lee, C.-H. Pressure swing adsorption processes to purify oxygen using a carbon molecular sieve. Chem. Eng. Sci. 2005, 60, 869−882. (17) Kim, M.-B.; Bae, Y.-S.; Choi, D.-K.; Lee, C.-H. Kinetic separation of landfill gas by a two-bed pressure swing adsorption process packed with carbon molecular sieve: Nonisothermal operation. Ind. Eng. Chem. Res. 2006, 45, 5050−5058. (18) Ruthven, D.; Raghavan, N.; Hassan, M. Adsorption and diffusion of nitrogen and oxygen in a carbon molecular sieve. Chem. Eng. Sci. 1986, 41, 1325−1332. (19) Yang, R. T. Gas Separation by Adsorption Processes; Imperial College Press: London, 1986. (20) Yi, H. M.; Weiruo, S.; Maruti, B.; Jinqu, W.; Miller, G. W. Adsorption and diffusion of nitrogen, oxygen, argon, and methane in molecular sieve carbon at elevated pressures. Sep. Technol. 1991, 1, 90− 98. (21) Loughlin, K.; Hassan, M.; Fatehi, A.; Zahur, M. Rate and equilibrium sorption parameters for nitrogen and methane on carbon molecular sieve. Gas Sep. Purif. 1993, 7, 264−273. (22) Fatehi, A.; Loughlin, K.; Hassan, M. Separation of methane nitrogen mixtures by pressure swing adsorption using a carbon molecular sieve. Gas Sep. Purif. 1995, 9, 199−204. (23) Reid, C.; Thomas, K. Adsorption of gases on a carbon molecular sieve used for air separation: Linear adsorptives as probes for kinetic selectivity. Langmuir 1999, 15, 3206−3218. (24) Qinglin, H.; Sundaram, S.; Farooq, S. Revisiting transport of gases in the micropores of carbon molecular sieves. Langmuir 2003, 19, 393− 405. (25) Bae, Y.-S.; Lee, C.-H. Sorption kinetics of eight gases on a carbon molecular sieve at elevated pressure. Carbon 2005, 43, 95−107. (26) Rutherford, S.; Coons, J. Adsorption equilibrium and transport kinetics for a range of probe gases in Takeda 3A carbon molecular sieve. J. Colloid Interface Sci. 2005, 284, 432−439. (27) Campo, M.; Magalhaes, F.; Mendes, A. Comparative study between a CMS membrane and a CMS adsorbent: Part IMorphology, adsorption equilibrium and kinetics. J. Membr. Sci. 2010, 346, 15−25. (28) Giesy, T. J.; LeVan, M. D. Mass transfer rates of oxygen, nitrogen, and argon in carbon molecular sieves determined by pressure-swing frequency response. Chem. Eng. Sci. 2013, 90, 250−257. (29) Qinglin, H.; Farooq, S.; Karimi, I. Binary and ternary adsorption kinetics of gases in carbon molecular sieves. Langmuir 2003, 19, 5722− 5734. (30) Stoeckli, F.; Centeno, T. A. On the characterization of microporous carbons by immersion calorimetry alone. Carbon 1997, 35, 1097−1100. (31) Cazorla-Amorós, D.; Alcaniz-Monge, J.; De la Casa-Lillo, M.; Linares-Solano, A. CO2 as an adsorptive to characterize carbon molecular sieves and activated carbons. Langmuir 1998, 14, 4589−4596. (32) Cavenati, S.; Grande, C. A.; Rodrigues, A. E. Adsorption equilibrium of methane, carbon dioxide, and nitrogen on zeolite 13X at high pressures. J. Chem. Eng. Data 2004, 49, 1095−1101. 16850


Adsorption Equilibrium and Kinetics of Methane and Nitrogen on

Recommend Documents