Static and Dynamic Simulation of Single and Binary Component Adsorption of CO 2 and CH 4 on Fixed Bed Using Molecular Sieve of Zeolite 4A

: The simulation of carbon dioxide (CO 2 )-methane (CH 4 ) mixed gas adsorption and the selectivity on zeolite 4A using Aspen Adsorption were studied. The inﬂuence of temperature ranging from 273 to 343 K, pressure up to 10 bar and various compositions of CO 2 in the binary system were simulated. The ﬁndings of the study demonstrate that the models are accurate. In addition, the effects of various key parameters such as temperature, pressure, and various compositions of binary gases were investigated. The highest CO 2 and CH 4 adsorption are found at 273 K and 10 bar in the Langmuir isotherm model with 5.86 and 2.88 mmol/g, respectively. The amount of CO 2 adsorbed and the selectivity of the binary mixture gas depends on the composition of CO 2 . The kinetics of adsorption for pure components of CO 2 at high temperatures can reach saturation faster than CH 4 . The inﬂuence of the physical properties of zeolite 4A on kinetic adsorption were also studied, and it was observed that small adsorbent particles, large pore diameter, and large pore volume would enter saturation quickly. The prediction of CO 2 -CH 4 mixed gas adsorption and selectivity on zeolite 4A were developed for further use for commercial gas separation.


Introduction
Carbon dioxide (CO 2 ) and methane (CH 4 ) are the main components of greenhouse gases that affect global warming. CO 2 emissions primarily involve the burning of fossil fuels [1]. Therefore, carbon dioxide trapping and storage also reduces CO 2 emissions into the atmosphere, and the stored CO 2 can be used for various benefits. The purity of CO 2 is often used directly in the food industry and enhanced oil recovery. There are new chemical and biological transformations of CO 2 into a feedstock for the manufacturing of chemicals and materials such as organic chemistry, minerals, and polymers. Conversion of CO 2 into polymers is one of the added value methods for CO 2 applications, CO 2 is used to copolymerize with various monomers [2]. Therefore, improving the purity of CO 2 from the burning of fossil fuels through various processes is important. Improving of CH 4 purity produced from natural gas, fermenting organic matter, and coal and natural gas refining by removing contaminant gases such as CO 2 , O 2 , N 2 , H 2 S, and H 2 O is also important. Pure CH 4 is important for industries such as pulp and paper manufacturing, food processes, and petroleum refineries. In addition, CH 4 is an ingredient in various materials such as, fabric, antifreeze, and fertilizer [3]. The purity of CO 2 and CH 4 can be accomplished effectively through pressure swing adsorption (PSA) or temperature swing adsorption (TSA).
The CO 2 and CH 4 gas separation process can be performed through various methods, including distillation, extraction, membrane separation, and adsorption [4][5][6][7]. The chemical Table 1. Physical properties of the zeolite 4A adsorbent and column used in simulation of adsorption.

Parameters Value
Packing length (mm) 97.5 Internal bed diameter (mm) 9.1 Particle size (cm) 0.2 (average diameter) Pellet density (kg/m 3 ) 1109 Solid density of adsorbent (kg/m 3 ) 2429 Total intrusion volume (cm 3 /g) 0.3147 BET surface area (m 2 /g) 501.4 The zeolite 4A diameter was in the range of 0.16-0.25 cm in granular form as shown in Table 1. The pellet density and total intrusion volume were obtained by mercury intrusion and the solid density was obtained by helium picnometry. The BET surface area was measured from the N 2 adsorption at 77 K in granule form [19].

Dynamic Simulation of Adsorption Experiments
Dynamic adsorption experiments were simulated by the Aspen Adsorption V11 program. The flow sheet including adsorbent characteristics (gas bed), feed gas, and product streams is shown in Figure 1. The internal diameter bed was 9.1 mm and the packing length was 97.5 mm in the column. The gas bed model configuration allowed for specifying the number of layers, labels for each component and setting the geometry of the bed. There were a set of assumptions for all layers, constant variables, and initial conditions. General assumptions of Aspen Adsorption including partial differential equation (PDE) discretization method were used to approximate spatial derivatives and number PDE nodes with 20 nodes. Material balance was assumed with convection only, momentum balance was laminar, and turbulent flow conditions during operation used the Ergun equation. The kinetic model was set as linear lumped resistance (LDF) and the mass transfer coefficient was constant. The isotherm for the pure components was determined using the Langmuir isotherm. The simulation model was calculated in the multicomponent with an extended Langmuir model based on partial pressure. Energy balance for this research was defined for non-isothermal conditions with no conduction. The heat transfer to the environment was set as adiabatic (no external heat transfer) [20,21].

Pure Component Adsorption Isotherm
Isotherms of pure CO2 and CH4 at 273, 283, 303, 323 and 343 K and pressure ranging from 1 to 10 bar were studied using the Langmuir isotherm model. This simulation was compared to the results of Seabra and coworkers [19]. The Langmuir isotherm model is a replica of the easiest and most popular isotherm model as shown in Equation (1). This model was used for monolayer adsorption and

Pure Component Adsorption Isotherm
Isotherms of pure CO 2 and CH 4 at 273, 283, 303, 323 and 343 K and pressure ranging from 1 to 10 bar were studied using the Langmuir isotherm model. This simulation was compared to the results of Seabra and coworkers [19]. The Langmuir isotherm model is a replica of the easiest and most popular isotherm model as shown in Equation (1). This model was used for monolayer adsorption and physical adsorption [22].
where q (mmol/g) is the amount adsorbed, q m (mmol/g) is the maximum adsorption capacity of the adsorbent, P (bar) is the pressure and b (bar −1 ) is the Langmuir constant. The Langmuir constant depends on the temperature of the system, represented by Equation (2).
where b 0 (bar −1 ) is the adsorption constant at an infinite temperature, −∆H (J/mmol) is the heat of adsorption, R (J·K −1 ·mol −1 ) is the universal gas constant, and T (K) is the temperature of the system.

Binary Component Adsorption Isotherm
Adsorption equilibrium for the binary gas mixture between CO 2 and CH 4 was predicted. The temperatures were at 273, 283, 303, 323, and 343 K with pressure ranging from 1 to 10 bars. The compositions of CO 2 to CH 4 were 10:90, 30:70, 40:60, 50:50, 60:40, and 80:20 using an extended Langmuir (EL) isotherm model and the ideal adsorbed solution theory (IAST). The extended Langmuir isotherm model for a binary component or multicomponent adsorption was developed from the Langmuir model. In pure components, EL used the information of adsorption from Equation (3) [23].
where q i (mmol/g) is the amount adsorbed of component i, q m (mmol/g) is the maximum adsorption capacity of the adsorbent of component i, P i (bar)is the partial pressure of component i and b (bar −1 ) is the Langmuir constant of component i. Therefore, the EL model for binary components is shown in Equations (4) and (5). For binary component: IAST is used to predict the adsorption capacity of binary mixed gas using pure component data. IAST is a thermodynamic method based on the adsorption equilibrium with Raoult's law for vapor-liquid equilibrium. The equilibrium between adsorbed phase and ideal gas phase can be specified by Equation (6) [24][25][26].
where y i and x i are the molar fractions of component i in the gas phase and adsorbed phase, respectively. P (bar) is the total pressure of the mixture, and P 0 i (π * ) (bar) is the equilibrium gas phase pressure of pure component i corresponding to solution temperature and solution spreading pressure, π*.
For a pure component i, the spreading pressure using Equations (7) and (8) was followed: where π i * is the reduced spreading pressure of component i in the adsorbed phase, π i is the spreading pressure of component i in the adsorbed phase, A is the specific surface area of the adsorbent, q i is the pure component adsorption isotherm equation, and P 0 i is At the standard state, reduced spreading pressure of the mixture (π*) is the same as the reduced spreading pressure of a single component according to Equation (8).
where q T (mmol/g) is the total amount adsorbed.

Modeling of Mass Transfer Coefficient
Mass transfer coefficients (MTC) were shown in Equation (12) which was assumed to be constant. MTC included the effects of micropore, macropore and film resistances [27]. The effect of macropore was considered using the following equation.
where k i (s −1 ) is the overall mass transfer coefficient of species i, D pi (cm 2 /s) is the macropore diffusivity of species i, and R p (cm) is the particle radius and ε p is the porosity of adsorbent particle or intraparticle. The effective macropore diffusivity can be determined using the Bosanquet equation [28]: where τ is the pore tortuosity factor, D ki (cm 2 /s) is the Knudsen diffusivity and D mi (cm 2 /s) is the molecular diffusivity. Estimation of the molecular diffusivity of binary gas mixtures with the best method calculated from the Lennard-Jones equation represented using Equation (14) [28]. The molecular diffusivity was determined using the following equation.
where M i (g/mol) is the molecular weight of species i, Ω D is the collision integral and σ 12 (Å) is the collision diameter of the binary pair of species A and B. Knudsen diffusion is gas diffusion through small pores, which can be calculated using Equation (15).
where R P (cm) is pore radius.

Selectivity of CO 2 over CH 4 in Binary Mixture Gas
Selectivity represents the ratio of the amount of adsorption of the two gases. It can also be called separation coefficient. If the selectivity of CO 2 /CH 4 is high, it means that the adsorption amount of CO 2 is greater than CH 4 [10]. The adsorption selectivity of CO 2 over CH 4 in binary mixtures was defined in Equation (16). (16) where q CO 2 and q CH 4 (mmol/g) are the amount adsorbed of CO 2 and CH 4, and P CO 2 and P CH 4 (bar) are the partial pressures of CO 2 and CH 4 , respectively.

Breakthrough Curves Modeling
To assess the performance of the fixed-bed adsorption column and measure the breakthrough curves, it is necessary to design and utilize the lab-scale experimental setup. By optimizing the mathematical models to the measured experimental data, the useful information can be used to design large-scale industrial columns and to predict the practical conditions. The model used in this work are the Thomas model and the Yoon-Nelson model.

Thomas Model
The Thomas model [29] is one of the most commonly used in the prediction of the breakthrough curve and the describing of the column performance. This model was developed based on the Langmuir kinetics of adsorption that assumed negligible axial dispersion in the column adsorption. The rate of the driving force carries out the secondorder reversible reaction kinetics [30]. The Thomas model is shown in Equation (17): where q 0 is the equilibrium adsorbate uptake in adsorbent (mg/g), Q is the flow rate (mL/min), M is the mass of the adsorbent (g), C is effluent concentration (mg/L), C 0 is influent concentration (mg/L), t is time (min), and k Th is the Thomas model constant (mL/min·mg).

Yoon-Nelson Model
The Yoon-Nelson model [31] is based on the assumption that the rate of decrease in the probability of adsorption for each adsorbate is proportional to the probability of adsorbate breakthrough on the adsorbent [32]. The Yoon-Nelson model was used for the following equation.
where k YN is the Yoon-Nelson constant (min −1 ) and τ is the time required to reach the effluent concentration to 50% of the influent concentration (min).

Pure Component Adsorption Isotherm
Adsorption isotherm of pure CO 2 and pure CH 4 at different temperatures and pressures are shown in Figure 2. The experimental data for pure CO 2 and CH 4 adsorption at 303 and 343 K were from Seabra [19]. The experimental results are fitted with the Langmuir isotherm model in Equations (1) and (2).
The adsorption capacity of CO 2 and CH 4 decreased with the rising temperature, indicating the adsorption of CO 2 and CH 4 are exothermic physical. The type of physical and chemical adsorption depends on the amount of heat in the adsorption. For heat of adsorption with 80 kJ·mol −1 or more, the adsorption process indicates chemisorption, while lower values represent a physical adsorption [33]. Values of the isosteric heat of adsorption in zeolite 4A of 47.8 kJ mol −1 for the adsorption of CO 2 [34] and 16.72 kJ·mol −1 for CH 4 [35] were found. Thus, the adsorption of CO 2 and CH 4 on zeolite 4A was physical adsorption; it could adsorb well when the temperature is decreased. In fact, as temperature decreases, gas molecules have less kinetic energy because the bond between gas and adsorbent is increased [36,37]. Moreover, the effect of pressure on the adsorption capacity is shown in Figure 2. The adsorption capacity increased rapidly as the pressure increased due to an increase in the gas molecules hitting the surface. Therefore, the increase in pressure caused the adsorption rate to increase linearly. However, when the pressure became high and almost the entire surface of the adsorbent received saturated gas, the pressure had little effect on the adsorption capacity. Ultimately, it could reach a point where the pressure did not affect the adsorption capacity because the number of adsorption sites was fixed, and no more adsorption occurred in those sites. At the same pressure and temperature conditions, the adsorption capacity of CO 2 is much higher than CH 4 because CO 2 has a quadrupole moment and polarizability greater than CH 4 , and it also has a high critical temperature as shown in Table 2 [38,39].

Pure Component Adsorption Isotherm
Adsorption isotherm of pure CO2 and pure CH4 at different temperatures and pressures are shown in Figure 2. The experimental data for pure CO2 and CH4 adsorption at 303 and 343 K were from Seabra [19]. The experimental results are fitted with the Langmuir isotherm model in Equations (1) and (2). The adsorption capacity of CO2 and CH4 decreased with the rising temperature, indicating the adsorption of CO2 and CH4 are exothermic physical. The type of physical and chemical adsorption depends on the amount of heat in the adsorption. For heat of adsorption with 80 kJ·mol −1 or more, the adsorption process indicates chemisorption, while lower values represent a physical adsorption [33]. Values of the isosteric heat of adsorption in zeolite 4A of 47.8 kJ mol −1 for the adsorption of CO2 [34] and 16.72 kJ·mol −1 for CH4 [35] were found. Thus, the adsorption of CO2 and CH4 on zeolite 4A was physical adsorption; it could adsorb well when the temperature is decreased. In fact, as temperature decreases, gas molecules have less kinetic energy because the bond between gas and adsorbent is increased [36,37]. Moreover, the effect of pressure on the adsorption capacity is shown in Figure 2. The adsorption capacity increased rapidly as the pressure increased due to an increase in the gas molecules hitting the surface. Therefore, the increase in pressure caused the adsorption rate to increase linearly. However, when the pressure became high and almost the entire surface of the adsorbent received saturated gas, the pressure had little effect on the adsorption capacity. Ultimately, it could reach a point where the pressure did not affect the adsorption capacity because the number of adsorption sites was fixed, and no more adsorption occurred in those sites. At the same pressure and temperature conditions, the adsorption capacity of CO2 is much higher than CH4 because CO2 has a quadrupole moment and polarizability greater than CH4, and it also has a high critical temperature as shown in Table 2 [38,39].   Table 3 shows the parameters of the Langmuir isotherm model for CO 2 and CH 4 adsorption on zeolite 4A. Where q m,0 is maximum adsorption capacity, b 0 is Henry law constant, Q/R is adsorption heat and X is empirical constant. The constant values in Table 3 were used in the Langmuir isotherm model in Equations (1) and (2).  Parameters of the previously mentioned equations were determined by minimizing the root-mean-square (RMS) in Equation (19): (19) where N is the number of data points and q cal i and q exp i are calculated and experimental adsorbed amounts, respectively. Low RMS value indicates that the Langmuir isotherm model is suitable.
The Langmuir isotherm model depends on pressure, maximum adsorption capacity of the adsorbent, and the Langmuir constant. Maximum adsorption capacity and the Langmuir constant depend on temperature. Therefore, the amount of adsorption for each pressure and temperature could be determined [22].
The crystal structure of zeolite 4A with sodium cation distribution as shown in Figure 3. There are three sites for sodium cation distribution including site I (S1) at the center of the 6-rings of sodalite cages, site II (S2) at the center of the 8-ring window of α cages and site III (S3) at opposite the 4-rings on the interior of α cages. Sodium ions in zeolite 4A contains 12 ions per unit cell (S1:S2:S3 = 8:3:1) [40,41]. Figure 3. The crystal structure of zeolite 4A.

REVIEW
The adsorption mechanism of the CO2 molecule on zeolite 4A show teracts with the sodium cations in the adsorption site. Interaction between rupole and sodium cations was electrostatic interaction. Sites of CO2 ads tion with the sodium cation were shown in a single cation site. CO2 inter sodium cations at dual cation sites. Moreover, CO2 could interact with mo dium cations and was denoted as multiple cation sites [42,43]. For insta between CO2 and zeolite 4A was shown in Figure 4. The CO2 molecule inte The adsorption mechanism of the CO 2 molecule on zeolite 4A showed that CO 2 interacts with the sodium cations in the adsorption site. Interaction between the CO 2 quadrupole and sodium cations was electrostatic interaction. Sites of CO 2 adsorption interaction with the sodium cation were shown in a single cation site. CO 2 interacted with two sodium cations at dual cation sites. Moreover, CO 2 could interact with more than two sodium cations and was denoted as multiple cation sites [42,43]. For instance, interaction between CO 2 and zeolite 4A was shown in Figure 4. The CO 2 molecule interacted with the sodium cation in S1 perpendicular to the plane of the 6-rings of sodalite cages along the body diagonal. If the distance between the CO 2 molecule and sodium cation is long distance, it indicates a weak interaction. tion with the sodium cation were shown in a single cation site. CO2 interacted with two sodium cations at dual cation sites. Moreover, CO2 could interact with more than two sodium cations and was denoted as multiple cation sites [42,43]. For instance, interaction between CO2 and zeolite 4A was shown in Figure 4. The CO2 molecule interacted with the sodium cation in S1 perpendicular to the plane of the 6-rings of sodalite cages along the body diagonal. If the distance between the CO2 molecule and sodium cation is long distance, it indicates a weak interaction. Likewise, CH4 interacted with sodium cation the same as CO2. However, the distance or molecular arrangement may differ due to the different properties of CO2 and CH4 as shown in Table 2. The CH4 has zero quadrupole moment and polarizability less than CO2. Therefore, the electrostatic affinity and adsorption capacity for CH4 were less than CO2. For the distance between the gas molecule and the cation, the longer distance indicated a weak interaction. In addition, CO2 and CH4 molecules could interact with oxygen atoms of the framework as well.

Binary Component Adsorption Isotherm
The simulation was predicted for a binary gas mixture using extended Langmuir Equations (4) and (5) and the ideal adsorbed solution theory models used in Equations Likewise, CH 4 interacted with sodium cation the same as CO 2 . However, the distance or molecular arrangement may differ due to the different properties of CO 2 and CH 4 as shown in Table 2. The CH 4 has zero quadrupole moment and polarizability less than CO 2 . Therefore, the electrostatic affinity and adsorption capacity for CH 4 were less than CO 2 . For the distance between the gas molecule and the cation, the longer distance indicated a weak interaction. In addition, CO 2 and CH 4 molecules could interact with oxygen atoms of the framework as well.

Binary Component Adsorption Isotherm
The simulation was predicted for a binary gas mixture using extended Langmuir Equations (4) and (5) and the ideal adsorbed solution theory models used in Equations (9)- (11). The composition of CO 2 and CH 4 in the gas mixture affected the amount of adsorption. The predictions of the adsorption of the binary gas mixture between CO 2 and CH 4 on zeolite 4A with the EL isotherm model were shown in Figure 5a,b.
Processes 2021, 9, x FOR PEER REVIEW 10 of 19 (9)- (11). The composition of CO2 and CH4 in the gas mixture affected the amount of adsorption. The predictions of the adsorption of the binary gas mixture between CO2 and CH4 on zeolite 4A with the EL isotherm model were shown in Figure 5a,b.
(a) (b) The results showed that the total amount of adsorbed gas mixture increased with the amount of CO2 adsorption. In other words, the higher the composition of CO2 received the greater the amount of total gas adsorption. Thus, the adsorption capacity of the mixed gas was between the two pure gases due to gas mixture had competition and was a hinderance between CO2 and CH4 molecules in the adsorption. It was indicated that the quadrupole moment of CO2 could result in strong interactions between CO2 molecules and the surface of zeolite 4A. The effect of pressure and temperature on the adsorption of the binary gas mixture showed the same tendency as the pure component [44][45][46]. Therefore, the adsorption of the mixed gas was also a physical adsorption because the total amount The results showed that the total amount of adsorbed gas mixture increased with the amount of CO 2 adsorption. In other words, the higher the composition of CO 2 received the greater the amount of total gas adsorption. Thus, the adsorption capacity of the mixed gas was between the two pure gases due to gas mixture had competition and was a hinderance between CO 2 and CH 4 molecules in the adsorption. It was indicated that the quadrupole moment of CO 2 could result in strong interactions between CO 2 molecules and the surface of zeolite 4A. The effect of pressure and temperature on the adsorption of the binary gas mixture showed the same tendency as the pure component [44][45][46]. Therefore, the adsorption of the mixed gas was also a physical adsorption because the total amount adsorbed decreased with the rising temperature.
Zeolite 4A has a cubic structure as shown in Figure 3. The effective size of its windows depends on the sodium cation of zeolite 4A, which has a pore window size of approximately 0.38 nm. The kinetic diameter affected the separation of CO 2 from CH 4 as observed in theory. These pores of zeolite have dimensions very close to the kinetic diameters of CO 2 and CH 4 , allowing CO 2 to diffuse through the adsorbent faster than CH 4 . Therefore, CO 2 can be separated from CH 4 while CO 2 diffuses more quickly in narrow pores than CH 4 with a kinetic diameter effect. For the molecular sieve effect, both CO 2 and CH 4 have different kinetic diameters inside a zeolite as shown in Table 2. CO 2 has the smallest kinetic diameter at 0.33 nm, and CH 4 at 0.38 nm. Zeolite 4A showed pore window apertures that are similar to the kinetic diameter of CH 4 . Therefore, CO 2 could enter the zeolite 4A freely, but CH 4 was blocked [47]. Figure 6 showed the comparison between the EL and IAST models of the CO 2 -CH 4 mixture in different CO 2 and CH 4 ratios. The total adsorption of IAST is a little higher than the EL model. The total adsorption between IAST and EL models was approximately the same. The IAST model showed better adsorption of the CO 2 -CH 4 gas mixture than the EL model compared to the experimental results according to the study of Rios [48]. In Wu's research [39], IAST could be used to predict the behavior of a binary mixture with very high accuracy. The IAST model was able to work very well when the adsorbates were similar sizes. On the other hand, the EL model was able to predict sorption behavior with acceptable precision. ocesses 2021, 9, x FOR PEER REVIEW similar sizes. On the other hand, the EL model was able to predict sorption b acceptable precision.

Selectivity for Separating of CO2-CH4 Mixture
The selectivity of binary gas mixtures can be calculated from Equation lectivity at different compositions of CO2:CH4 and pressures shown in Figur If the composition of CO2 increased, the selectivity also increased because th of CO2 molecules with the atoms of the zeolite 4A structure was stronger th CH4 molecules. In addition, CO2 molecules particularly adsorbed well in the olite 4A and hindered the diffusion of the weaker adsorbing CH4 molecules.

Selectivity for Separating of CO 2 -CH 4 Mixture
The selectivity of binary gas mixtures can be calculated from Equation (16). The selectivity at different compositions of CO 2 :CH 4 and pressures shown in Figure 7a at 303 K. If the composition of CO 2 increased, the selectivity also increased because the interaction of CO 2 molecules with the atoms of the zeolite 4A structure was stronger than that with CH 4 molecules. In addition, CO 2 molecules particularly adsorbed well in the pores of zeolite 4A and hindered the diffusion of the weaker adsorbing CH 4 molecules.
The obtained selectivity from IAST and EL models for different compositions are shown in Figure 7a. It was indicated that the EL selectivity of CO 2 /CH 4 was constant for all gas compositions and pressures. On the other hand, the IAST selectivity showed various results for both total pressure and composition. From this prediction of IAST, the composition of CO 2 would affect selectivity when the pressure was increased. Figure 7b shows the different temperatures on selectivity of 50:50 of CO 2 :CH 4 ratio, at 1 bar. The selectivity increased with rising temperature [49] which is the same in both models. For this reason, the pressure and temperature had a positive impact on the adsorption selectivity of CO 2 over CH 4 . Therefore, to predict the selectivity of CO 2 -CH 4 , the IAST calculation was based on Langmuir and EL calculations. As mentioned above, the use of an adsorbent must be considered for high efficiency separation. Therefore, the comparison of the adsorption capacity in each adsorbent can be used as analytical data for improving the adsorbent. Table 4 shows the adsorption capacity for the CO2-CH4 binary gas mixture with zeolite compared to others. It can be seen that the adsorption values of both CO2 and CH4 from zeolite 4A showed similar trends to those of 13 X and 5A zeolites at the same conditions. The BET specific surface area of zeolite 4A was close to that of zeolite 13X. Therefore, the adsorption capacities of CO2 were similar to CH4. There were no different adsorption effects in each zeolite in Table 4. The adsorption capacity of CO2 showed greater than CH4. The selectivity of the binary gas mixture has an important parameter because it can form zeolite into an ideal material adsorbent for CO2 and CH4 mixture gas separation.  Figure 8 shows the kinetic adsorption of CO2 and CH4 on zeolite 4A at different temperatures (273, 303, 343 K) and pressures (1, 5, 10 bar). As mentioned above, the use of an adsorbent must be considered for high efficiency separation. Therefore, the comparison of the adsorption capacity in each adsorbent can be used as analytical data for improving the adsorbent. Table 4 shows the adsorption capacity for the CO 2 -CH 4 binary gas mixture with zeolite compared to others. It can be seen that the adsorption values of both CO 2 and CH 4 from zeolite 4A showed similar trends to those of 13 X and 5A zeolites at the same conditions. The BET specific surface area of zeolite 4A was close to that of zeolite 13X. Therefore, the adsorption capacities of CO 2 were similar to CH 4 . There were no different adsorption effects in each zeolite in Table 4. The adsorption capacity of CO 2 showed greater than CH 4 . The selectivity of the binary gas mixture has an important parameter because it can form zeolite into an ideal material adsorbent for CO 2 and CH 4 mixture gas separation.  Figure 8 shows the kinetic adsorption of CO 2 and CH 4 on zeolite 4A at different temperatures (273, 303, 343 K) and pressures (1, 5, 10 bar). It was observed that at the beginning of the adsorption, the amount of CO2 adsorbed on the adsorbent was slightly fast and then slowly decreased until it reached equilibrium. In the initial stages, CO2 molecules directly contacted with the adsorbent, resulting in great interaction between adsorbate and adsorbent [50]. After total pores were adsorbed without any further adsorption of CO2 molecules, the process of adsorption went to saturation. In addition, when the temperature increased, faster saturation was observed due to the exothermic process for CO2 adsorption. In the exothermic process, increasing temperature caused adsorption to decrease because of the decreased of the attraction between the adsorbate and the adsorbent [37,39,44].

Dynamic Simulation of Adsorption Experiment
The mass transfer coefficient was increased with increased temperature as shown in Table 5. This is caused by CO2 and CH4 molecules moving faster with higher temperature from the increased kinetic energy [28,51]. From the simulation adsorption model, it was found that pressure affected the adsorption capacity and mass transfer coefficient. The mass transfer coefficient decreased with the rising pressure because of effective diffusivity decreased from decreased molecular diffusion [28,51]. The relation of mass transfer coefficient, effective diffusivity and molecular diffusivity are shown in Equations (12)-(14), respectively. Equation (15) shows Knudsen diffusion which depends on temperature. Figure 8b shows that CH4 adsorption It was observed that at the beginning of the adsorption, the amount of CO 2 adsorbed on the adsorbent was slightly fast and then slowly decreased until it reached equilibrium. In the initial stages, CO 2 molecules directly contacted with the adsorbent, resulting in great interaction between adsorbate and adsorbent [50]. After total pores were adsorbed without any further adsorption of CO 2 molecules, the process of adsorption went to saturation. In addition, when the temperature increased, faster saturation was observed due to the exothermic process for CO 2 adsorption. In the exothermic process, increasing temperature caused adsorption to decrease because of the decreased of the attraction between the adsorbate and the adsorbent [37,39,44].
The mass transfer coefficient was increased with increased temperature as shown in Table 5. This is caused by CO 2 and CH 4 molecules moving faster with higher temperature from the increased kinetic energy [28,51]. From the simulation adsorption model, it was found that pressure affected the adsorption capacity and mass transfer coefficient. The mass transfer coefficient decreased with the rising pressure because of effective diffusivity decreased from decreased molecular dif-fusion [28,51]. The relation of mass transfer coefficient, effective diffusivity and molecular diffusivity are shown in Equations (12)- (14), respectively. Equation (15) shows Knudsen diffusion which depends on temperature. Figure 8b shows that CH 4 adsorption took a long time to adsorb, due to the decrease in the polarizability and kinetic diameter of CH 4 , which was larger than CO 2 as shown in Table 2. 3.4.1. The Effect of the Physical Properties of Zeolite 4A on Kinetic Adsorption The physical properties of various zeolite 4A with different particle size, pore volume and pore diameter are shown in Table 6. Three types of zeolites were compared in this study: zeolite 4A-0.2 cm, zeolite 4A (HSD, high bulk density)-0.2 cm and zeolite 4A-0.4 cm. To study the physical properties of the zeolite 4A adsorbents, the model developed to predict the breakthrough curves of CO 2 and CH 4 adsorptions on zeolite 4A was shown in Figure 9. It was found that small particle sizes of zeolite went into saturation and balance more quickly than large ones because of long diffusion inside the pores [52]. For different pore volumes with the same particle size, at large pore volumes could go into saturation quickly because the adsorption capacity was greater for larger pore volumes. Moreover, after all the pores were occupied by the adsorbate, the adsorbent could no longer adsorb CO 2 molecules. The efficiency was high if the amount of porosity was large. Less pore diameter affects the kinetic adsorption on fast diffusion. The effect of pore diameter on the adsorption is mentioned in Section 3.2.
Processes 2021, 9, x FOR PEER REVIEW 14 of 19 took a long time to adsorb, due to the decrease in the polarizability and kinetic diameter of CH4, which was larger than CO2 as shown in Table 2. 3.4.1. The effect of the Physical Properties of Zeolite 4A on Kinetic Adsorption The physical properties of various zeolite 4A with different particle size, pore volume and pore diameter are shown in Table 6. Three types of zeolites were compared in this study: zeolite 4A-0.2 cm, zeolite 4A (HSD, high bulk density)-0.2 cm and zeolite 4A-0.4 cm. To study the physical properties of the zeolite 4A adsorbents, the model developed to predict the breakthrough curves of CO2 and CH4 adsorptions on zeolite 4A was shown in Figure 9. It was found that small particle sizes of zeolite went into saturation and balance more quickly than large ones because of long diffusion inside the pores [52]. For different pore volumes with the same particle size, at large pore volumes could go into saturation quickly because the adsorption capacity was greater for larger pore volumes. Moreover, after all the pores were occupied by the adsorbate, the adsorbent could no longer adsorb CO2 molecules. The efficiency was high if the amount of porosity was large. Less pore diameter affects the kinetic adsorption on fast diffusion. The effect of pore diameter on the adsorption is mentioned in Section 3.2. The mass transfer coefficient of large particles was smaller than the small ones as shown in Table 7. From Equation (12), the mass transfer coefficient was inverse to the particle radius. Therefore, the particle radius was large; the mass transfer coefficient was reduced. The mass transfer coefficient of large particles was smaller than the small ones as shown in Table 7. From Equation (12), the mass transfer coefficient was inverse to the particle radius. Therefore, the particle radius was large; the mass transfer coefficient was reduced.    When CO2 composition increased, the saturation of the breakthrough curve was decreased, representing the faster kinetics of the adsorption process with a high CO2 content [53]. It was predicted that CO2 had a higher adsorption with zeolite 4A than CH4. As a result, when CO2 composition was high, competition of CO2 and CH4 for adsorption was less than with less composition of CO2 [54,55].

Modeling of Breakthrough Curves
Modeling of the breakthrough curves were obtained from experiments using the Thomas and Yoon-Nelson model. The experimental data of the adsorption of CO2 on zeolite 4A at 573.15 K and flow rate of 5 L/h were obtained from Tobarameekul [56]. Figure 11 shows the ability of the Thomas and Yoon-Nelson model to predict the experimental breakthrough curves. The prediction of the Yoon-Nelson model is better than Thomas's model. Both models were formed according to the experimental data. The parameters from fitting the different models to experimental breakthrough curves were shown in Table 8. The correlation coefficient (R 2 ) of the Yoon-Nelson model is greater than that of Thomas. When CO 2 composition increased, the saturation of the breakthrough curve was decreased, representing the faster kinetics of the adsorption process with a high CO 2 content [53]. It was predicted that CO 2 had a higher adsorption with zeolite 4A than CH 4 . As a result, when CO 2 composition was high, competition of CO 2 and CH 4 for adsorption was less than with less composition of CO 2 [54,55].

Modeling of Breakthrough Curves
Modeling of the breakthrough curves were obtained from experiments using the Thomas and Yoon-Nelson model. The experimental data of the adsorption of CO 2 on zeolite 4A at 573.15 K and flow rate of 5 L/h were obtained from Tobarameekul [56]. Figure 11 shows the ability of the Thomas and Yoon-Nelson model to predict the experimental breakthrough curves. The prediction of the Yoon-Nelson model is better than Thomas's model. Both models were formed according to the experimental data. The parameters from fitting the different models to experimental breakthrough curves were shown in Table 8. The correlation coefficient (R 2 ) of the Yoon-Nelson model is greater than that of Thomas. Processes 2021, 9, x FOR PEER REVIEW 16 of 19 Figure 11. Comparison of the prediction of the Thomas and Yoon-Nelson model with the experimental breakthrough curve.

Conclusions
Adsorption isotherms of pure CO2 and pure CH4 on zeolite 4A with 273 to 343 K, and pressure up to 10 bar using the Langmuir model were performed. Adsorption generally depended on the temperature. Adsorption decreased with increasing temperature because adsorption processes were exothermic reaction. On the other hand, at a constant temperature, the adsorption capacity increased with pressure. Therefore, the highest CO2 and CH4 adsorption from this study was found at 273 K and 10 bar. The properties of CO2 and CH4 affected on the adsorption capacity so that the adsorption capacity of CO2 was much higher than CH4. The effect of temperature and pressure on the binary gas mixture had the same effect on the pure component of adsorption. However, the adsorption of the mixed gas increased with the amount of CO2 entered. The effect of pore size on adsorption showed that CO2 with a smaller kinetic diameter could be separated from CH4 with a larger kinetic diameter as CO2 diffuses more quickly in narrow pores than CH4. In addition, Zeolite 4A has pore window apertures that are similar to the kinetic diameter of CH4, then CO2 could enter the zeolite 4A freely, but CH4 was blocked. Simulation models for gas mixtures were IAST and EL models. The amount of adsorption of the IAST model was greater than the EL model and the selectivity also increased with the amount of CO2 entered, and the results showed that selectivity rose with the temperature. Moreover, the amount of CO2 adsorbed from dynamic adsorption simulation increased with increasing pressure because of effective diffusivity decreased from decreased molecular diffusion. At the same time, CH4 showed the same trend as CO2, but its adsorption capacity was less than CO2. In addition, the rising temperature could reach the equilibrium faster than the low temperature. Small adsorbent particles and large pore volume could enter the saturation fast. For the kinetic adsorption simulation of the CO2-CH4 binary mixture gas adsorp-

Conclusions
Adsorption isotherms of pure CO 2 and pure CH 4 on zeolite 4A with 273 to 343 K, and pressure up to 10 bar using the Langmuir model were performed. Adsorption generally depended on the temperature. Adsorption decreased with increasing temperature because adsorption processes were exothermic reaction. On the other hand, at a constant temperature, the adsorption capacity increased with pressure. Therefore, the highest CO 2 and CH 4 adsorption from this study was found at 273 K and 10 bar. The properties of CO 2 and CH 4 affected on the adsorption capacity so that the adsorption capacity of CO 2 was much higher than CH 4 . The effect of temperature and pressure on the binary gas mixture had the same effect on the pure component of adsorption. However, the adsorption of the mixed gas increased with the amount of CO 2 entered. The effect of pore size on adsorption showed that CO 2 with a smaller kinetic diameter could be separated from CH 4 with a larger kinetic diameter as CO 2 diffuses more quickly in narrow pores than CH 4 . In addition, Zeolite 4A has pore window apertures that are similar to the kinetic diameter of CH 4 , then CO 2 could enter the zeolite 4A freely, but CH 4 was blocked. Simulation models for gas mixtures were IAST and EL models. The amount of adsorption of the IAST model was greater than the EL model and the selectivity also increased with the amount of CO 2 entered, and the results showed that selectivity rose with the temperature. Moreover, the amount of CO 2 adsorbed from dynamic adsorption simulation increased with increasing pressure because of effective diffusivity decreased from decreased molecular diffusion. At the same time, CH 4 showed the same trend as CO 2 , but its adsorption capacity was less than CO 2 . In addition, the rising temperature could reach the equilibrium faster than the low temperature. Small adsorbent particles and large pore volume could enter the saturation fast. For the kinetic adsorption simulation of the CO 2 -CH 4 binary mixture gas adsorption, the increased composition of CO 2 would greatly benefit the efficiency of CO 2