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Investigation of methane adsorption on chlorite by grand canonical Monte Carlo simulations

Investigation of methane adsorption on chlorite by grand canonical Monte Carlo simulations Pet. Sci. (2017) 14:37–49 DOI 10.1007/s12182-016-0142-1 ORIGINAL PAPER Investigation of methane adsorption on chlorite by grand canonical Monte Carlo simulations 1 1 1 2 • • • Jian Xiong Xiang-Jun Liu Li-Xi Liang Qun Zeng Received: 8 April 2016 / Published online: 7 January 2017 The Author(s) 2017. This article is published with open access at Springerlink.com Abstract In this paper, the methane adsorption behaviours adsorption space of the methane, leading to a reduction in in slit-like chlorite nanopores were investigated using the the methane excess adsorption capacity. The excess grand canonical Monte Carlo simulation method, and the adsorption capacity of gas on chlorite decreased in the influences of the pore sizes, temperatures, water, and following order: carbon dioxide [ methane [ nitrogen. If compositions on methane adsorption on chlorite were dis- the mole fraction of nitrogen or carbon dioxide in the cussed. Our investigation revealed that the isosteric heat of binary gas mixture increased, the mole fraction of methane adsorption of methane in slit-like chlorite nanopores decreased, methane adsorption sites changed, and methane decreased with an increase in pore size and was less than adsorption space was reduced, resulting in the decrease in 42 kJ/mol, suggesting that methane adsorbed on chlorite the methane excess adsorption capacity. through physical adsorption. The methane excess adsorp- tion capacity increased with the increase in the pore size in Keywords Chlorite  Methane  Nanopores  Grand micropores and decreased with the increase in the pore size canonical Monte Carlo  Adsorption capacity in mesopores. The methane excess adsorption capacity in chlorite pores increased with an increase in pressure or decrease in pore size. With an increase in temperature, the 1 Introduction isosteric heats of adsorption of methane decreased and the methane adsorption sites on chlorite changed from lower- The study ‘‘Technically Recoverable Shale Oil and Shale energy adsorption sites to higher-energy sites, leading to Gas Resources: An Assessment of 137 Shale Formations in the reduction in the methane excess adsorption capacity. 41 Countries outside the United States’’ conducted by the Water molecules in chlorite pores occupied the pore wall in US DOE’s Energy Information Administration (EIA) in a directional manner, which may be related to the van der 2013, indicated that technically the shale gas resource in 12 3 Waals and Coulomb force interactions and the hydrogen the world was approximately 220 9 10 m , suggesting bonding interaction. It was also found that water molecules that there was a significant developmental potential for existed as aggregates. With increasing water content, the shale gas resources in the world (EIA 2013). Free, adsor- water molecules occupied the adsorption sites and bed, and dissolved gases exist in shale formations. Adsorbed gas is found on the surface of the mineral grains or in the micropore structure of organic matter in shale gas & Jian Xiong reservoirs. However, free gas is mainly contained in 361184163@qq.com microfractures or larger pores in organic matter as well as State Key Laboratory of Oil and Gas Reservoir Geology and in mineral grains in shale gas reservoirs. In 2002, Curtis Exploitation, Southwest Petroleum University, studied the characteristics of American shale gas reser- Chengdu 610500, Sichuan, China voirs, drawing the conclusion that adsorbed gas accounts Institute of Chemical Materials, Engineering Physical for approximately 20%–85% of the total gas content and Academy of China, Mianyang 621999, Sichuan, China suggesting that adsorbed gas played an important role in the shale gas resource. Therefore, it is important to Edited by Jie Hao 123 38 Pet. Sci. (2017) 14:37–49 investigate the methane adsorption capacity of organic-rich types of clay minerals (montmorillonite, illite and kaolinite) shales to evaluate shale gas resources. Both the physico- and also studied the effects of different temperatures on the chemical properties of shales and environmental factors methane adsorption behaviours. Sui et al. (2015) studied the could have an impact on the methane adsorption capacity microscopic structural properties and diffusion behaviours of shales, illustrating that the mineralogical compositions of methane in slit-like montmorillonite pores using the are key factors that affect the methane adsorption capacity GCMC and MD methods. Xiong et al. (2016) studied the of shales. According to previous research (Liang et al. microscopic adsorption mechanism of methane in slit-like 2015; Liu et al. 2015; Xiong et al. 2015a), clay minerals are montmorillonite pores using the GCMC method. These the essential mineralogical components of the shales from studies generated knowledge on methane adsorption on the Yanchang Formation of the Ordos Basin as well as the montmorillonite, illite and kaolinite. However, the detailed Longmaxi Formation and Wufeng Formation of the microscopic adsorption mechanism of methane in chlorite Sichuan Basin, the contents of which were comparatively pores has not been well studied. higher. Therefore, it is important to investigate the methane Hence, this article regarded chlorite as an object of study adsorption capacity on chlorite, which is an important type and used the computer molecular simulation technique to of clay mineral. Currently, studies aimed at evaluating the construct skeleton patterns of slit-like chlorite pores. Then, methane adsorption capacity on chlorite mainly focused on the impacts of pore sizes, temperatures, water and gas isothermal adsorption experiments. Ji et al. (2012a, b) compositions on the methane adsorption behaviours in slit- investigated the influences of pressure, temperature, and like chlorite pores and the microscopic adsorption mecha- grain size on the methane adsorption capacity of chlorite. nism of methane in chlorite pores were studied using the Fan et al. (2014) studied the influences of pressure and GCMC simulations. Finally, the influence of the tempera- temperature on the methane adsorption capacity of chlorite. tures, water contents and compositions on the adsorption Tang and Fan (2014) studied the methane adsorption behaviours of methane on chlorite and their interaction capacity of chlorite at different temperatures under a mechanisms were discussed, which can provide important pressure of 20 MPa. Liang et al. (2016) investigated the theoretical and instructional significance for the explo- methane adsorption capacity of chlorite under a pressure of ration and development of shale gas reservoirs. 20 MPa. All of the above studies were based on isothermal adsorption experiments, that is, the value of the adsorption amount under equilibrium pressure can be used to evaluate 2 Molecular model the methane adsorption capacity of chlorite. However, this value comprehensively reflects the specific surface area of The parameters of the chlorite crystal cell can be found in chlorite and the value of the adsorption amount per unit the literature (Joswig et al. 1980). The following parame- surface area and cannot fundamentally reflect the essence ters from this crystal cell are listed: a = 0.5327 nm, of microscopic adsorption mechanisms of the methane b = 0.9232 nm, c = 1.440 nm, a = c = 90, b = 97.16. adsorption on the chlorite owing to the results obtained for According to the 9a 9 4b super-cell structure constructed the macroscopic behaviour. in the x and y directions of the chlorite unit crystal cell Computational molecular simulations have recently structure, the size of this super-cell structure in the attracted much attention as a theoretical research method that x 9 y direction is 4.794 nm 9 3.693 nm. Based on this, a can be used to study the adsorption properties of the adsor- space can be added in the z direction between the two bent and could therefore be used to investigate the adsorption super-cell structures to construct pores with different sizes mechanism of fluid molecules on porous material. Titiloye in the chlorite super-cell structure. Figure 1 shows the and Skipper (2005) used the grand canonical Monte Carlo configuration of the slit-like chlorite pore, and Table 1 (GCMC) and molecular dynamics (MD) methods to study presents their basic parameters. the adsorption behaviours and structural properties of The Lennard–Jones (L–J) potential parameters and methane in slit-like montmorillonite pores. Using MD sim- charges of the sites in the unit cell of chlorite are presented in ulations, the microscopic structural properties and diffusion Table 2 and are taken from the work of Cygan et al. (2004) behaviours of carbon dioxide in slit-like montmorillonite and Jin and Firoozabadi (2013, 2014). Methane and nitrogen pores were studied by Yang and Zhang (2005). Jin and molecules were modelled using a TraPPE force field (Martin Firoozabadi (2013, 2014) used GCMC to investigate the and Siepmann 1998; Potoff and Siepmann 2001), the water adsorption behaviours of methane and carbon dioxide in slit- molecule was modelled using an SPC-E force field like montmorillonite pores as well as the influence of water (Berendsen et al. 1987), and the carbon dioxide molecule on the adsorption behaviours of methane and carbon dioxide. was simulated by using the EPM2 model (Harris and Yung Using the GCMC method, Sun et al. (2015) performed 1995). All fluid molecules retain electric neutrality. The L–J research on the methane adsorption behaviours of different potential parameters and charges of each atom in the liquids 123 Pet. Sci. (2017) 14:37–49 39 -12 dielectric constant, 8.854 9 10 F/m; and r and e are ij ij the L–J potential parameters. According to the Lorentz– Botherlot mixed rules these are set as: pffiffiffiffiffiffiffiffiffiffiffiffi r ¼ r þ r 2 e ¼ e  e ð2Þ ij i j ij i j where r ; r are the collision diameters of the atoms or i j molecules i; j in nm and e ; e are the potential well depths i j in kJ/mol. 3 Simulation method 3.1 Grand canonical Monte Carlo (GCMC) Monte Carlo simulations have been widely used to study Fig. 1 Schematic representation of the slit-like chlorite pore (H rep- the adsorption properties of materials, while GCMC has resents different pore sizes) (red circle is oxygen atom, white circle is been widely applied in the investigation of the adsorption hydrogen atom, yellow circle is silicon atom, purple circle is behaviours of an adsorbate on an adsorbent. In this work, aluminium atom, green circle is magnesium atom) we use GCMC simulation to investigate the adsorption behaviours of methane in a slit-like chlorite pore. In the are also shown in Table 2 and can be found in the above grand canonical ensemble, the chemical potential, volume, references. During the simulation, the force fields are based and temperature are the independent variables. Among on the Dreiding force field, and chlorite is supposed to be a these, the chemical potential is a function of the fugacity rigid body. Furthermore, owing to the lack of force fields for instead of the pressure. In this research, the Soave, Redlich magnesium, we assign the same L–J parameters for mag- and Kwong (SRK) state equation was used to calculate the nesium as for aluminium in the Dreiding force field (Zeng fugacity (Soave 1972). The fugacity coefficients of pure et al. 2003; Jin and Firoozabadi 2013). In addition, the methane at different temperatures and pressures in the charges of magnesium and aluminium are ?2 and ?3, simulations are shown in Fig. 2a, and the fugacity coeffi- respectively. In the simulation, the interactions consist of the cients of the mole fraction of methane in the binary gas van der Waals force and Coulomb force. The L–J (12–6) mixture at different pressures in the simulations are potential model was used to describe the van der Waals force. described in Fig. 2b, c. Simulation of the methane The model to represent the Coulomb force and van der Waals isothermal adsorption by the GCMC method was per- force is given by: "# formed mainly using Sorption Module of the Materials 12 6 r r q q ij ij i j Studio 6.0. The temperature in this simulation varied from E ¼ e  þ : ð1Þ ij r r 4pe r ij ij 0 ij 313 to 373 K, and the temperature interval was 20 K. The maximum simulated pressure was 40 MPa, and the simu- where q ; q are the charges of atoms in the system in C; r i j ij lation was under constant pressure, point by point, divided is the distance between the atoms i and j in nm; e is the into a total of 15 points. The force field type used in this Table 1 Parameters of the slit-like chlorite pore of different pore sizes -17 2 -20 3 3 -19 H,nm x,nm y,nm z,nm ab c Surface area, 9 10 m Volume, 9 10 cm Density, g/cm Mass, 9 10 g 1 4.794 3.693 5.227 90 97.16 90 1.77 9.727 2.292 2.23 1.5 4.794 3.693 5.727 90 97.16 90 1.77 10.61 2.101 2.23 2 4.794 3.693 6.227 90 97.16 90 1.77 11.50 1.940 2.23 3 4.794 3.693 7.227 90 97.16 90 1.77 13.27 1.681 2.23 4 4.794 3.693 8.227 90 97.16 90 1.77 15.04 1.483 2.23 6 4.794 3.693 10.227 90 97.16 90 1.77 18.58 1.200 2.23 8 4.794 3.693 12.227 90 97.16 90 1.77 22.12 1.008 2.23 10 4.794 3.693 14.227 90 97.16 90 1.77 25.66 0.869 2.23 15 4.794 3.693 19.227 90 97.16 90 1.77 34.51 0.646 2.23 20 4.794 3.693 24.227 90 97.16 90 1.70 43.36 0.514 2.23 123 40 Pet. Sci. (2017) 14:37–49 Table 2 L–J potential parameters and charges of each atom Atoms e=k ,K r,nm q, e References Chlorite O(t) 78.18 0.3166 -0.800 Cygan et al. (2004), Jin and Firoozabadi (2013, 2014) O(a) 78.18 0.3166 -1.000 O(o) 78.18 0.3166 -1.7175 O(OH) 78.18 0.3166 -1.7175 H(OH) 0.00 0.0000 0.7175 Si 9.26 9 10 0.3302 1.200 Al 4.54 9 10 0.5086 3.000 Mg 4.54 9 10 0.5086 2.000 Methane C 148.10 0.3730 0 Martin and Siepmann (1998) Water O 78.18 0.3166 -0.8476 Berendsen et al. (1987) H 0 0 0.4238 Carbon dioxide C 28.129 0.2757 0.6512 Harris and Yung (1995) O 80.507 0.3033 -0.3256 Nitrogen N 36 0.331 -0.482 Potoff and Siepmann (2001) COM 0 0 0.964 Notes: (t) tetrahedron oxygen, (o) octahedral oxygen, (a) terminal oxygen, COM at the centre of the nitrogen–nitrogen bond (a) 1.00 1.3 (b) y y =80 % =20 % 313 K 333 K CH N 4 2 353 K 373 K y y =60 % =40 % CH N 4 2 0.95 1.2 y y =40 % =60 % CH N 4 2 y =20 % y =80 % CH N 4 2 0.90 1.1 0.85 1.0 0.80 0.9 0.75 0.8 0 5 10 15 20 25 30 35 40 0 8 16 24 32 40 p, MPa p, MPa (c) 1.0 y y 0.8 =80 % =20 % CH CO 4 2 y y =60 % =40 % CH CO 4 2 y y =40 % =60 % CH CO 4 2 0.6 y y =20 % =80 % CH CO 4 2 0.4 0 8 16 24 32 40 p, MPa Fig. 2 Methane fugacity coefficient at different temperatures and pressures φ Pet. Sci. (2017) 14:37–49 41 simulation was the Dreiding force field, with the Coulomb q V þ V represents the total area of b and c, as shown a g force and van der Waals force interactions calculated by in Fig. 2. Then, the excess adsorption amount can be the Ewald & Group method and the atom interaction-based expressed as follows: method with an L–J potential cutoff distance of 1.55 nm. n ¼ N  q V þ V ¼N  q V ð4Þ ex a g p g g The maximum number of load steps in each simulation was 6 6 6 3 9 10 , including 1.5 9 10 balance steps and 1.5 9 10 where N is the total amount of gas in mol/g, V is the gas 3 3 process steps. The related statistics were obtained using the phase volume in g/cm , and V is the free volume in g/cm . later 1.5 9 10 configurations. The free volume in the pore can be determined by the method that uses He as the probe (Talu and Myers 2001). 3.2 Excess adsorption amount Therefore, the gas amount obtained from the results of the simulation is the total amount of gas, and based on the free The isothermal adsorption experiments of the chlorite volume in the pore, the total amount of gas can be con- exceed the critical temperature of methane (191 K), sug- verted into the excess adsorption amount of the gas gesting that the methane adsorption behaviour on chlorite according to Eq. (4). belongs to supercritical adsorption. For supercritical adsorption, Gibbs proposed that an adsorbate molecule in the adsorbed phase on the surface of the adsorbent cannot 4 Results and discussions be used as the total adsorption amount. Additionally, the distribution of adsorbate molecules in the adsorbed phase 4.1 Influences of different pore sizes based on the gas phase density was independent of the gas/solid molecule inter-atomic forces (Xiong et al. Figure 4 presents the total amount and excess adsorption 2015b). According to this view, Gibbs introduced the capacity isotherms of methane in chlorite pores for dif- concept of the excess adsorption amount: ferent pore sizes. Examination of Fig. 4a shows that the total amount of methane increased with the increment of n ¼ n  q V ; ð3Þ ex ab g a the pore size and first increased rapidly and then increased where n is the excess adsorption amount in mol/g, n is slowly with the increase in pressure. At the same time, ex ab the absolute adsorption amount in mol/g, V is the adsorbed a from Fig. 4b, it can be seen that the differences among the 3 3 phase volume in cm , and q is the vapour density in g/cm excess adsorption capacity of methane on chlorite in micropores were small. However, it also showed that the calculated by the SRK state equation (Soave 1972). Figure 3 shows a schematic representation of the excess methane excess adsorption capacity gradually decreased as the pore size increased in the mesopores, and the excess adsorption amount and absolute adsorption amount in which the area of a represents the excess adsorption adsorption capacity of methane in mesopores is signifi- cantly smaller than that in micropores. This may be amount and the total area of a and b expresses the absolute adsorption amount. We assume that the total amount of because the potential superimposed effect of the pore wall can significantly affect the adsorption of methane mole- adsorbate in the adsorption system is N, corresponding to the total area of a, b, and c, as shown in Fig. 3, which is cules in micropores, and the methane adsorption capacity in the pore would therefore be limited by the pore volume, equal to the expression (n þ q V ). Therefore, ab g that is, the pore volume increases with the increase in the pore size and methane adsorption capacity. However, the adsorption of methane molecules in mesopores was mainly Adsorbed affected by the surface potential effect of the two sides of phase the pore wall; the interactions between the methane molecules and the chlorite decrease, and movement space Gas phase of the methane molecules increases, which makes the force Solid phase a to escape from the chlorite pore wall easy to overcome. Then, the methane adsorption capacity decreases with increasing pore size. In addition, the excess adsorption capacity of methane first increased after the pressure drop. That is, there is a maximum value of the excess adsorption s capacity (n ), and the corresponding pressure is exc–max z z known as the maximum pressure (p ). This conclusion is max in line with that of previous studies of organic-rich shales Fig. 3 Schematic representation of the excess adsorption amount and (Rexer et al. 2013; Gasparik et al. 2014; Yang et al. 2015). absolute adsorption amount 123 42 Pet. Sci. (2017) 14:37–49 (a) (b) 0.004 1 nm 1.5 nm 0.12 2 nm 3 nm 4 nm 6 nm 8 nm 10 nm 0.003 15 nm 20 nm 0.08 0.002 1 nm 1.5 nm 0.04 0.001 2 nm 3 nm 4 nm 6 nm 8 nm 10 nm 15 nm 20 nm 0.00 0.000 0 10203040 0 10203040 p, MPa p, MPa Fig. 4 Total amount isotherms of methane (a) and the excess adsorption isotherms of methane (b) in chlorite pores for different pore sizes (temperature of 333 K) Table 3 shows the maximum values of the methane excess the methane isosteric heat decreased gradually with an adsorption capacity and its corresponding pressure for increase in pore size. The isosteric heat for a pore size of different pore sizes. Examination of the data in Table 3 1 nm was the maximum value (13.6 kJ/mol), and the shows that the maximum pressure corresponding to the average isosteric heat for a pore size of 20 nm was the maximum value of the excess adsorption capacity was minimum value (6.12 kJ/mol). Experimentally, Ji et al. different and that the range of the maximum pressure was (2012a, b) found that the average isosteric heat of methane between 14 MPa and 18 MPa. This finding is in agreement adsorption on chlorite was 9.4 kJ/mol. Although there are with previous studies on organic-rich shales (Rexer et al. differences between the simulated and experimental 2013; Gasparik et al. 2014; Yang et al. 2015), suggesting results, they also showed similarities to a certain extent. that the maximum pressure (p ) was between 10 and This result may be related to the differences of research max 19 MPa, as was concluded from the experimental data. methods and samples. The pore size in the experiments is This result indicates that, to a certain extent, our simulation distributed continuously between 20 nm and 100 nm (Ji results are in reasonable agreement with the experimental et al. 2012a, b), and the methane isosteric heat obtained results. Meanwhile, the maximum value of the excess from the experiment reflects the synthesis results obtained adsorption capacity decreased with an increase in pore size for the sample with a continuous distribution of pore sizes. in mesopores. The maximum value of the excess adsorp- However, the pore skeletons of chlorite in the simulation tion capacity reached a peak value of 0.00372 mmol/m have a single pore size, and the methane isosteric heat when the pore size was 2 nm, while the minimum value of obtained from the simulation reflects the results for a single the excess adsorption capacity was 0.00239 mmol/m pore and changes with pore size. In addition, the isosteric when the pore size was 20 nm. The conclusions illustrate heat of adsorption of methane in chlorite pores with dif- that the methane adsorption capacity in chlorite micropores ferent pore sizes was less than 42 kJ/mol, demonstrating increased with an increase in pore size, whereas that in that the methane adsorption on chlorite is of the physical chlorite mesopores decreased with an increase in the pore adsorption type. This conclusion is in accord with previous size. studies that suggested the methane is adsorbed on chlorite The average isosteric heat of methane in chlorite pores by physical adsorption (Ji et al. 2012a, b; Fan et al. 2014; with different pore sizes is shown in Fig. 5. It is seen that Tang and Fan 2014; Liang et al. 2016). 2 2 Table 3 Simulation results of H,nm n , mmol/m p , MPa H,nm n , mmol/m p , MPa exc-max max exc-max max methane adsorption on chlorite for different pore sizes 1 0.003276 18 6 0.002839 16 1.5 0.003417 18 8 0.002614 14 2 0.003505 18 10 0.002496 16 3 0.003199 18 15 0.002340 14 4 0.003016 16 20 0.002178 14 -2 Total amount, mmol·m -2 Excess adsorption, mmol·m Pet. Sci. (2017) 14:37–49 43 under low pressure is not as stable as that under high- pressure conditions. In addition, the potential energy dis- tribution curves of methane and chlorite with different pore sizes under a pressure of 20 MPa are presented in Fig. 6b. Examination of Fig. 6b shows that the potential energy distribution curves of methane and chlorite gradually 9 moved to the right with the increase in pore size and the most probable potential energy of methane and chlorite gradually increased, that is, the most probable potential energy changed from -11.92 to -3.56 kJ/mol when the 6 pore size increased from 1 nm to 20 nm. This suggests that methane adsorption occurring in chlorite pores gradually 0 5 10 15 20 changed from lower-energy adsorption sites to higher-en- H, nm ergy adsorption sites as the pore size increased, and the methane adsorption capacity in chlorite micropores was Fig. 5 Average methane isosteric heat in a chlorite pore with stronger than that in macropores. different pore sizes According to the simulation results, we obtained the 4.2 Influence of different temperatures potential energy distribution of methane and chlorite. The methane and chlorite potential energy distribution curves The excess adsorption isotherms of methane for different temperatures (pore size of 4 nm) are listed in Fig. 7. It can be for different pressures (pore size of 4 nm) are presented in Fig. 6a. It can be noted that the curve transforms the twin seen that the methane excess adsorption capacity decreased with increasing temperature under the same pressure; this peaks into a unimodal distribution with the increase in the pressure. At the same time, as the pressure is increased, the may be due to methane adsorption on chlorite being of the potential energy distribution curves of methane and chlo- physical adsorption type. When the temperature increases, rite gradually moved to the left. Additionally, the most the thermal motion of methane molecules would increase, probable potential energy of methane and chlorite gradu- resulting in an increase in the mean kinetic energy of methane molecules, generating a sufficiently large force to ally decreased, that is, the most probable potential energy changed from -0.209 to -6.485 kJ/mol as the pressure escape from the chlorite pore wall easily, thus causing a reduction in the methane adsorption capacity. This conclu- increased from 2 to 36 MPa. This indicates that methane adsorption occurring in chlorite pores gradually changes sion is in accord with the results of the isothermal adsorption experiments performed by Ji et al. (2012a, b), suggesting that from higher-energy adsorption sites to lower-energy adsorption sites with the increase in pressure and that the the methane adsorption capacity on chlorite decreased with adsorption state of methane molecules in chlorite pores increasing temperature. 1.2 1.2 (a) (b) 2 MPa 6 MPa 1 nm 1.5 nm 2 nm 3 nm 10 MPa 14 MPa 4 nm 6 nm 20 MPa 28 MPa 8 nm 10 nm 36 MPa 15 nm 20 nm 0.8 0.8 0.4 0.4 0.0 0.0 -20 -15 -10 -5 0 5 -20 -15 -10 -5 0 5 -1 -1 Energy, kJ·mol Energy, kJ·mol Fig. 6 Potential energy distribution curves of methane and chlorite for different pressures (pore size of 4 nm) (a) and different pore sizes (pressure of 20 MPa) (b) -1 Poisson distribution of energy (E) Average isosteric heats, kJ·mol Poisson distribution of energy (E) 44 Pet. Sci. (2017) 14:37–49 0.004 moved to the right. Furthermore, the most probable potential energy of methane and chlorite gradually increased, that is, the most probable potential energy 0.003 changed from -4.393 to -3.138 kJ/mol when the tem- perature increased from 313 to 373 K. This finding sug- gests that the adsorption sites of methane molecules in 0.002 chlorite pores gradually change from lower-energy adsorption sites to higher-energy adsorption sites with increasing temperature, causing the reduction in the 0.001 313 K 333 K methane adsorption capacity. 353 K 373 K 0.000 4.3 Influence of different water contents 0 1020 3040 p, MPa To investigate the influence of water on the methane adsorption in chlorite pores, three simulation projects Fig. 7 Excess adsorption isotherms of methane for different temper- atures (pore size of 4 nm) considering three water contents (wt% = the water mole- cules mass/the chlorite mass) were carried out. First the Figure 8 shows the average methane isosteric heat in adsorption sites of water molecules in the slit-like chlorite chlorite pores for different temperatures (pore size of pores need to be determined by using the annealing sim- 4 nm). We observe that the average isosteric heat of ulation method. The distribution of the different water methane decreased with increasing temperature, indicating contents in the chlorite pores is given in Fig. 10. In addi- that the interactions between methane molecules and tion, the size of the chlorite pores is 4 nm and the tem- chlorite became weaker with increasing temperature, perature is 333 K in simulation. resulting in a decrease in the methane adsorption capacity. Examination of Fig. 10 shows that water molecules In the range of the simulated temperatures, the value of the occupied the chlorite pore walls in a directional manner, average isosteric heat of methane in a chlorite pore with the and the oxygen atoms of the water molecules were close to pore size of 4 nm is between 7.59 and 8.21 kJ/mol (less or pointed to the surface of the chlorite pore wall or than 42 kJ/mol), illustrating that the adsorption of methane hydrogen atoms of the surrounding water molecules, with in the chlorite pores is due to physical adsorption. These the hydrogen atoms located at a distance from the surface findings indicate that methane adsorption on chlorite is of the chlorite pore wall. This may be due to the positive exothermic and the increase in temperature is not con- charges of the aluminium and silicon atoms on the surface ducive for methane adsorption on chlorite. The potential of the chlorite pore wall and the negative charge of the energy distribution curves between methane and chlorite at oxygen atoms of the water molecule, causing a pattern in different temperatures (pore size of 4 nm) are shown in which the oxygen atoms of the water molecules are close to Fig. 9. When the temperature increased, the potential or point to the surface of the chlorite pore wall. This energy distribution curve of methane and chlorite gradually phenomenon arises from the Coulomb and van der Waals 1.2 8.1 313 K 333 K 353 K 373 K 0.8 7.8 0.4 7.5 0.0 7.2 -20 -15 -10 -5 0 5 320 340 360 380 -1 T, K Energy, kJ·mol Fig. 8 Average isosteric heats of methane for different temperatures Fig. 9 Potential energy distribution curves of methane and chlorite at (pore size of 4 nm) different temperatures (pore size of 4 nm) -1 -2 Average isosteric heats, kJ·mol Excess adsorption, mmol·m Poisson distribution of energy (E) Pet. Sci. (2017) 14:37–49 45 that the curves have two peaks, with the main peak lying in the higher-energy area and the secondary peak located in the lower-energy area. The most probable potential energy of methane and chlorite did not change significantly with the increase in the water contents, indicating that the methane molecules in the higher-energy adsorption sites could not be occupied with the change of water contents. However, the secondary peak of the potential energy dis- tribution curve gradually became broad, implying that the water molecules occupy the lower-energy adsorption sites of methane molecules. It can be deduced that water molecules mainly occupied lower-energy adsorption sites on the chlorite pore walls instead of higher-energy Fig. 10 Distribution of different water contents in chlorite pores (the adsorption sites, illustrating that the water molecules and number in parentheses represents the number of water molecules) methane molecules compete with each other for adsorption space and adsorption sites. Therefore, the adsorption space force interactions between water molecules and chlorite, and adsorption sites occupied by water molecules resulting in the aggregation of water molecules in the decreased the adsorption space and adsorption sites of chlorite pore. In addition, due to the hydrogen bonding methane molecules, leading to a decrease in the methane interaction, the oxygen atoms of the water molecules point adsorption capacity. to the hydrogen atoms of surrounding water molecules. All of the data indicate that the water molecules are adsorbed 4.4 Influence of different mole fractions of nitrogen on the surface of the pore walls and occupy the adsorption space of the methane molecules in the form of aggregation. To investigate the influence of mole fraction of nitrogen on Figure 11 shows the methane excess adsorption iso- competitive adsorption of nitrogen and methane in the therms for different water contents. It can be seen that the chlorite pores, five simulation projects considering five methane excess adsorption capacity on chlorite is reduced mole fractions of nitrogen in the methane/nitrogen binary when the water contents increased under the same tem- gas mixture (y = 80% means that the mole fraction of CH4 perature and pressure, implying that water molecules methane is 80% while the mole fraction of nitrogen is 20%) inhibit methane adsorption on chlorite. This conclusion is would be carried out. The size of the chlorite pores is 4 nm in agreement with a previous study of methane adsorption and the temperature is 333 K in the simulation. on montmorillonite (Jin and Firoozabadi 2013, 2014), The excess adsorption isotherms of methane for differ- indicating that water reduced the methane adsorption ent mole fractions of nitrogen are shown in Fig. 13. The capacity on montmorillonite. The potential energy distri- methane excess adsorption capacity decreased with the bution curves of methane and chlorite for different water increase in the nitrogen mole fraction at the same tem- contents are shown in Fig. 12. Inspection of Fig. 12 shows perature and pressure, indicating that a lower mole fraction 1.2 0.0036 0 % 2 % 4 % 8 % 0.0027 0.8 0.0018 0.4 0.0009 0 % 2 % 4 % 8 % 0.0 0.0000 010 20 30 40 -20 -15 -10 -5 0 5 -1 p, MPa Energy, kJ·mol Fig. 11 Excess adsorption isotherms of methane for different water Fig. 12 Potential energy distribution curves of methane and chlorite contents for different water contents -2 Excess adsorption, mmol·m Poisson distribution of energy (E) 46 Pet. Sci. (2017) 14:37–49 1.5 of the methane in the methane/nitrogen binary gas mixture y y =80 % =20 % CH N 4 2 leads to a smaller methane adsorption capacity on chlorite. y =60 % y =40 % In the adsorption system of the methane/nitrogen binary CH N 4 2 gas mixture, the potential energy distribution curves for y y =40 % =60 % CH N 4 2 1.0 different mole fractions of nitrogen are presented in y y =20 % =80 % CH N 4 2 Fig. 14. It can be seen that the most probable potential energy of methane and chlorite under different nitrogen mole fractions was smaller than that of the nitrogen, 0.5 demonstrating that the potential energy distribution between methane and chlorite was different from that between nitrogen and chlorite, that is, the methane adsorption occurring on the chlorite pore walls was due to 0.0 the lower-energy adsorption sites, whereas nitrogen -20 -15 -10 -5 0 5 -1 adsorption occurred in higher-energy adsorption sites, Energy, kJ·mol illustrating that nitrogen adsorption on chlorite in the Fig. 14 Potential energy distribution curves for different mole adsorption system of the methane/nitrogen binary gas fractions of nitrogen mixture was less stable than that of methane. Figure 15 (the distributions of methane and nitrogen on the surface of chlorite) also illustrates this conclusion. Figure 15 shows Methane that the methane molecules and nitrogen molecules on the chlorite surface were distributed among different adsorp- tion sites. Furthermore, we found that the interactions between methane and nitrogen led to a change of the potential energy distribution curves of methane and chlorite. At the Nitrogen same time, the potential energy distribution curve of methane and chlorite gradually moved to the right and the most probable potential energy of methane and chlorite Fig. 15 Distributions of methane and nitrogen on the surface of gradually increased with increasing nitrogen mole fraction. chlorite (right does not include the chlorite cell) Namely, the methane adsorption gradually changed from lower-energy adsorption sites to higher-energy adsorption space for methane molecules. Hence, in the adsorption sites with the increase in the nitrogen mole fraction, system of the methane/nitrogen binary gas mixture, the resulting in a decrease in the methane adsorption capacity methane adsorption capacity on chlorite is greater than that on chlorite, implying that the nitrogen adsorption occurring of nitrogen. According to the previous analysis, the in the chlorite pores led to the change of the adsorption site methane adsorption capacity decreased with the increase in of methane molecules and the reduction of the adsorption the mole fraction of nitrogen due to the decrease in the methane mole fraction in the gas phase, the change of the 0.004 y y y =100 % =80 % =60 % CH CH CH adsorption sites of the methane molecules and the reduc- 4 4 4 y y =40 % =20 % tion in the adsorption space of the methane molecules. CH CH 4 4 0.003 4.5 Influence of different mole fractions of carbon dioxide 0.002 To investigate the influence of the mole fraction of carbon dioxide on competitive adsorption of carbon dioxide and 0.001 methane in the chlorite pores, simulations with five mole fractions of carbon dioxide in the carbon dioxide/methane binary gas mixture (y = 80% means that the mole CH4 0.000 0 1020 3040 fraction of methane is 80% while the mole fraction of p, MPa carbon dioxide is 20%) were carried out. The size of the chlorite pores is 4 nm, and the temperature is 333 K in Fig. 13 Excess adsorption isotherms of methane on chlorite for these simulations. different mole fractions of nitrogen -2 Excess adsorption, mmol·m Poisson distribution of energy (E ) Pet. Sci. (2017) 14:37–49 47 0.9 Excess adsorption isotherms of methane for different y y =80 % =20 % CH CO mole fractions of carbon dioxide are shown in Fig. 16.It 2 y =60 % y can be seen that the methane excess adsorption capacity =40 % CH CO decreased as the carbon dioxide mole fraction increased at y y =40 % =60 % CH CO 4 2 0.6 the same pressure and temperature, indicating that the y y =20 % =80 % CH CO 4 2 smaller methane mole fraction in the carbon dioxide/ methane binary gas mixture led to lower methane adsorp- tion capacity. 0.3 In the adsorption system of the carbon dioxide/methane binary gas mixture, the potential energy distribution curves for different mole fractions of carbon dioxide are shown in Fig. 17. It can be seen that the most probable potential 0.0 energy of methane and chlorite for different carbon dioxide -40 -36 -32 -28 -24 -20 -16 -12 -8 -4 0 4 -1 mole fractions was higher than that of carbon dioxide, Energy, kJ·mol suggesting that the potential energy distribution between Fig. 17 Potential energy distribution curves for different mole methane and chlorite was different from that between fractions of carbon dioxide carbon dioxide and chlorite. That is, carbon dioxide adsorption on the chlorite pore walls occurred in the lower- energy adsorption sites, whereas methane adsorption was Methane located in higher-energy adsorption sites, implying that methane adsorption on chlorite in the adsorption system of the carbon dioxide/methane binary gas mixture was less stable than that of carbon dioxide. Figure 18 (the distri- butions of methane and carbon dioxide on the chlorite surface) also illustrates this conclusion. Figure 18 shows that methane and carbon dioxide molecules on the chlorite Carbon dioxide surface were distributed among different adsorption sites. Furthermore, we also observed that the interactions Fig. 18 Distributions of methane and carbon dioxide on the surface between methane and carbon dioxide could change the of chlorite (right does not include the chlorite cell) potential energy distribution curves of methane and chlo- rite. At the same time, the potential energy distribution higher-energy adsorption sites with the increasing carbon curve of methane and chlorite gradually moved to the right dioxide mole fraction, leading to a reduction in the and the most probable potential energy of methane and methane adsorption capacity on chlorite. This phenomenon chlorite gradually increased with increasing carbon dioxide demonstrates that carbon dioxide adsorption occurring in mole fraction, meaning that the methane adsorption sites chlorite pores results in a change of the adsorption site of gradually changed from lower-energy adsorption sites to methane molecules and a reduction in their adsorption space. Thus, the carbon dioxide adsorption capacity on chlorite is greater than that of methane in the carbon y y y =100 % =80 % =60 % CH CH CH 4 4 4 0.0032 y y dioxide/methane binary gas mixture adsorption system. =20 % =40 % CH CH 4 Based on the previous analysis, the methane adsorption capacity decreased with the increase in the carbon dioxide 0.0024 mole fraction, resulting in a reduction in the methane mole fraction in the gas phase, a change of the adsorption sites of 0.0016 the methane molecules and a reduction in the methane adsorption space. 0.0008 5 Conclusions 0.0000 0 1020 3040 p, MPa First, the average methane isosteric heat decreased with increasing pore size, which was smaller than 42 kJ/mol in Fig. 16 Excess adsorption isotherms of methane in chlorite pores for the chlorite–methane adsorption system, suggesting that different carbon dioxide mole fractions -2 Excess adsorption, mmol·m Poisson distribution of energy (E) 48 Pet. Sci. (2017) 14:37–49 systems. Energy Explor Exploit. 2014;32(6):927–42. doi:10. methane adsorbed on the chlorite through a physical 1260/0144-5987.32.6.927. adsorption. Gasparik M, Bertier P, Gensterblum Y, et al. Geological controls on Second, the methane adsorption capacity in chlorite the methane storage capacity in organic-rich shales. Int J Coal pores increased with the increase in pressure or decrease in Geol. 2014;123:34–51. doi:10.1016/j.coal.2013.06.010. Harris JG, Yung KH. Carbon dioxide’s liquid-vapor coexistence the pore size. In chlorite micropores, the methane adsorp- curve and critical properties as predicted by a simple molecular tion capacity increased with the increase in pore size, model. J Phys Chem. 1995;99(31):12021–4. doi:10.1021/ showing an opposite trend to the findings for mesopores. j100031a034. In addition, the isosteric heat of methane decreased with Ji LM, Qua JL, Zhang TW, Xia YQ. Relationship between methane adsorption capacity of clay minerals and micropore volume. the increase in temperature. At that time, the methane Earth Sci (J China Univ Geosci). 2012a;37(5):1043–50. doi:10. adsorption site changed from lower-energy adsorption sites 3799/dqkx.2012.111 (in Chinese). to higher-energy adsorption sites, leading to the decline of Ji LM, Zhang TW, Milliken KL, Qua JL, Zhang XL. Experimental the methane adsorption capacity. Water molecules in the investigation of main controls to methane adsorption in clay-rich rocks. Appl Geochem. 2012b;27:2533–45. doi:10.1016/j.apgeo chlorite pores occupied the pore wall in a directional chem.2012.08.027. manner and occupied the adsorption sites and adsorption Jin ZH, Firoozabadi A. Methane and carbon dioxide adsorption in space of methane molecules, causing a decrease in the clay-like slit pores by Monte Carlo simulations. Fluid Phase methane adsorption capacity. Equilib. 2013;360:456–65. doi:10.1016/j.fluid.2013.09.047. 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Investigation of methane adsorption on chlorite by grand canonical Monte Carlo simulations

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Earth Sciences; Mineral Resources; Industrial Chemistry/Chemical Engineering; Industrial and Production Engineering; Energy Economics
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Pet. Sci. (2017) 14:37–49 DOI 10.1007/s12182-016-0142-1 ORIGINAL PAPER Investigation of methane adsorption on chlorite by grand canonical Monte Carlo simulations 1 1 1 2 • • • Jian Xiong Xiang-Jun Liu Li-Xi Liang Qun Zeng Received: 8 April 2016 / Published online: 7 January 2017 The Author(s) 2017. This article is published with open access at Springerlink.com Abstract In this paper, the methane adsorption behaviours adsorption space of the methane, leading to a reduction in in slit-like chlorite nanopores were investigated using the the methane excess adsorption capacity. The excess grand canonical Monte Carlo simulation method, and the adsorption capacity of gas on chlorite decreased in the influences of the pore sizes, temperatures, water, and following order: carbon dioxide [ methane [ nitrogen. If compositions on methane adsorption on chlorite were dis- the mole fraction of nitrogen or carbon dioxide in the cussed. Our investigation revealed that the isosteric heat of binary gas mixture increased, the mole fraction of methane adsorption of methane in slit-like chlorite nanopores decreased, methane adsorption sites changed, and methane decreased with an increase in pore size and was less than adsorption space was reduced, resulting in the decrease in 42 kJ/mol, suggesting that methane adsorbed on chlorite the methane excess adsorption capacity. through physical adsorption. The methane excess adsorp- tion capacity increased with the increase in the pore size in Keywords Chlorite  Methane  Nanopores  Grand micropores and decreased with the increase in the pore size canonical Monte Carlo  Adsorption capacity in mesopores. The methane excess adsorption capacity in chlorite pores increased with an increase in pressure or decrease in pore size. With an increase in temperature, the 1 Introduction isosteric heats of adsorption of methane decreased and the methane adsorption sites on chlorite changed from lower- The study ‘‘Technically Recoverable Shale Oil and Shale energy adsorption sites to higher-energy sites, leading to Gas Resources: An Assessment of 137 Shale Formations in the reduction in the methane excess adsorption capacity. 41 Countries outside the United States’’ conducted by the Water molecules in chlorite pores occupied the pore wall in US DOE’s Energy Information Administration (EIA) in a directional manner, which may be related to the van der 2013, indicated that technically the shale gas resource in 12 3 Waals and Coulomb force interactions and the hydrogen the world was approximately 220 9 10 m , suggesting bonding interaction. It was also found that water molecules that there was a significant developmental potential for existed as aggregates. With increasing water content, the shale gas resources in the world (EIA 2013). Free, adsor- water molecules occupied the adsorption sites and bed, and dissolved gases exist in shale formations. Adsorbed gas is found on the surface of the mineral grains or in the micropore structure of organic matter in shale gas & Jian Xiong reservoirs. However, free gas is mainly contained in 361184163@qq.com microfractures or larger pores in organic matter as well as State Key Laboratory of Oil and Gas Reservoir Geology and in mineral grains in shale gas reservoirs. In 2002, Curtis Exploitation, Southwest Petroleum University, studied the characteristics of American shale gas reser- Chengdu 610500, Sichuan, China voirs, drawing the conclusion that adsorbed gas accounts Institute of Chemical Materials, Engineering Physical for approximately 20%–85% of the total gas content and Academy of China, Mianyang 621999, Sichuan, China suggesting that adsorbed gas played an important role in the shale gas resource. Therefore, it is important to Edited by Jie Hao 123 38 Pet. Sci. (2017) 14:37–49 investigate the methane adsorption capacity of organic-rich types of clay minerals (montmorillonite, illite and kaolinite) shales to evaluate shale gas resources. Both the physico- and also studied the effects of different temperatures on the chemical properties of shales and environmental factors methane adsorption behaviours. Sui et al. (2015) studied the could have an impact on the methane adsorption capacity microscopic structural properties and diffusion behaviours of shales, illustrating that the mineralogical compositions of methane in slit-like montmorillonite pores using the are key factors that affect the methane adsorption capacity GCMC and MD methods. Xiong et al. (2016) studied the of shales. According to previous research (Liang et al. microscopic adsorption mechanism of methane in slit-like 2015; Liu et al. 2015; Xiong et al. 2015a), clay minerals are montmorillonite pores using the GCMC method. These the essential mineralogical components of the shales from studies generated knowledge on methane adsorption on the Yanchang Formation of the Ordos Basin as well as the montmorillonite, illite and kaolinite. However, the detailed Longmaxi Formation and Wufeng Formation of the microscopic adsorption mechanism of methane in chlorite Sichuan Basin, the contents of which were comparatively pores has not been well studied. higher. Therefore, it is important to investigate the methane Hence, this article regarded chlorite as an object of study adsorption capacity on chlorite, which is an important type and used the computer molecular simulation technique to of clay mineral. Currently, studies aimed at evaluating the construct skeleton patterns of slit-like chlorite pores. Then, methane adsorption capacity on chlorite mainly focused on the impacts of pore sizes, temperatures, water and gas isothermal adsorption experiments. Ji et al. (2012a, b) compositions on the methane adsorption behaviours in slit- investigated the influences of pressure, temperature, and like chlorite pores and the microscopic adsorption mecha- grain size on the methane adsorption capacity of chlorite. nism of methane in chlorite pores were studied using the Fan et al. (2014) studied the influences of pressure and GCMC simulations. Finally, the influence of the tempera- temperature on the methane adsorption capacity of chlorite. tures, water contents and compositions on the adsorption Tang and Fan (2014) studied the methane adsorption behaviours of methane on chlorite and their interaction capacity of chlorite at different temperatures under a mechanisms were discussed, which can provide important pressure of 20 MPa. Liang et al. (2016) investigated the theoretical and instructional significance for the explo- methane adsorption capacity of chlorite under a pressure of ration and development of shale gas reservoirs. 20 MPa. All of the above studies were based on isothermal adsorption experiments, that is, the value of the adsorption amount under equilibrium pressure can be used to evaluate 2 Molecular model the methane adsorption capacity of chlorite. However, this value comprehensively reflects the specific surface area of The parameters of the chlorite crystal cell can be found in chlorite and the value of the adsorption amount per unit the literature (Joswig et al. 1980). The following parame- surface area and cannot fundamentally reflect the essence ters from this crystal cell are listed: a = 0.5327 nm, of microscopic adsorption mechanisms of the methane b = 0.9232 nm, c = 1.440 nm, a = c = 90, b = 97.16. adsorption on the chlorite owing to the results obtained for According to the 9a 9 4b super-cell structure constructed the macroscopic behaviour. in the x and y directions of the chlorite unit crystal cell Computational molecular simulations have recently structure, the size of this super-cell structure in the attracted much attention as a theoretical research method that x 9 y direction is 4.794 nm 9 3.693 nm. Based on this, a can be used to study the adsorption properties of the adsor- space can be added in the z direction between the two bent and could therefore be used to investigate the adsorption super-cell structures to construct pores with different sizes mechanism of fluid molecules on porous material. Titiloye in the chlorite super-cell structure. Figure 1 shows the and Skipper (2005) used the grand canonical Monte Carlo configuration of the slit-like chlorite pore, and Table 1 (GCMC) and molecular dynamics (MD) methods to study presents their basic parameters. the adsorption behaviours and structural properties of The Lennard–Jones (L–J) potential parameters and methane in slit-like montmorillonite pores. Using MD sim- charges of the sites in the unit cell of chlorite are presented in ulations, the microscopic structural properties and diffusion Table 2 and are taken from the work of Cygan et al. (2004) behaviours of carbon dioxide in slit-like montmorillonite and Jin and Firoozabadi (2013, 2014). Methane and nitrogen pores were studied by Yang and Zhang (2005). Jin and molecules were modelled using a TraPPE force field (Martin Firoozabadi (2013, 2014) used GCMC to investigate the and Siepmann 1998; Potoff and Siepmann 2001), the water adsorption behaviours of methane and carbon dioxide in slit- molecule was modelled using an SPC-E force field like montmorillonite pores as well as the influence of water (Berendsen et al. 1987), and the carbon dioxide molecule on the adsorption behaviours of methane and carbon dioxide. was simulated by using the EPM2 model (Harris and Yung Using the GCMC method, Sun et al. (2015) performed 1995). All fluid molecules retain electric neutrality. The L–J research on the methane adsorption behaviours of different potential parameters and charges of each atom in the liquids 123 Pet. Sci. (2017) 14:37–49 39 -12 dielectric constant, 8.854 9 10 F/m; and r and e are ij ij the L–J potential parameters. According to the Lorentz– Botherlot mixed rules these are set as: pffiffiffiffiffiffiffiffiffiffiffiffi r ¼ r þ r 2 e ¼ e  e ð2Þ ij i j ij i j where r ; r are the collision diameters of the atoms or i j molecules i; j in nm and e ; e are the potential well depths i j in kJ/mol. 3 Simulation method 3.1 Grand canonical Monte Carlo (GCMC) Monte Carlo simulations have been widely used to study Fig. 1 Schematic representation of the slit-like chlorite pore (H rep- the adsorption properties of materials, while GCMC has resents different pore sizes) (red circle is oxygen atom, white circle is been widely applied in the investigation of the adsorption hydrogen atom, yellow circle is silicon atom, purple circle is behaviours of an adsorbate on an adsorbent. In this work, aluminium atom, green circle is magnesium atom) we use GCMC simulation to investigate the adsorption behaviours of methane in a slit-like chlorite pore. In the are also shown in Table 2 and can be found in the above grand canonical ensemble, the chemical potential, volume, references. During the simulation, the force fields are based and temperature are the independent variables. Among on the Dreiding force field, and chlorite is supposed to be a these, the chemical potential is a function of the fugacity rigid body. Furthermore, owing to the lack of force fields for instead of the pressure. In this research, the Soave, Redlich magnesium, we assign the same L–J parameters for mag- and Kwong (SRK) state equation was used to calculate the nesium as for aluminium in the Dreiding force field (Zeng fugacity (Soave 1972). The fugacity coefficients of pure et al. 2003; Jin and Firoozabadi 2013). In addition, the methane at different temperatures and pressures in the charges of magnesium and aluminium are ?2 and ?3, simulations are shown in Fig. 2a, and the fugacity coeffi- respectively. In the simulation, the interactions consist of the cients of the mole fraction of methane in the binary gas van der Waals force and Coulomb force. The L–J (12–6) mixture at different pressures in the simulations are potential model was used to describe the van der Waals force. described in Fig. 2b, c. Simulation of the methane The model to represent the Coulomb force and van der Waals isothermal adsorption by the GCMC method was per- force is given by: "# formed mainly using Sorption Module of the Materials 12 6 r r q q ij ij i j Studio 6.0. The temperature in this simulation varied from E ¼ e  þ : ð1Þ ij r r 4pe r ij ij 0 ij 313 to 373 K, and the temperature interval was 20 K. The maximum simulated pressure was 40 MPa, and the simu- where q ; q are the charges of atoms in the system in C; r i j ij lation was under constant pressure, point by point, divided is the distance between the atoms i and j in nm; e is the into a total of 15 points. The force field type used in this Table 1 Parameters of the slit-like chlorite pore of different pore sizes -17 2 -20 3 3 -19 H,nm x,nm y,nm z,nm ab c Surface area, 9 10 m Volume, 9 10 cm Density, g/cm Mass, 9 10 g 1 4.794 3.693 5.227 90 97.16 90 1.77 9.727 2.292 2.23 1.5 4.794 3.693 5.727 90 97.16 90 1.77 10.61 2.101 2.23 2 4.794 3.693 6.227 90 97.16 90 1.77 11.50 1.940 2.23 3 4.794 3.693 7.227 90 97.16 90 1.77 13.27 1.681 2.23 4 4.794 3.693 8.227 90 97.16 90 1.77 15.04 1.483 2.23 6 4.794 3.693 10.227 90 97.16 90 1.77 18.58 1.200 2.23 8 4.794 3.693 12.227 90 97.16 90 1.77 22.12 1.008 2.23 10 4.794 3.693 14.227 90 97.16 90 1.77 25.66 0.869 2.23 15 4.794 3.693 19.227 90 97.16 90 1.77 34.51 0.646 2.23 20 4.794 3.693 24.227 90 97.16 90 1.70 43.36 0.514 2.23 123 40 Pet. Sci. (2017) 14:37–49 Table 2 L–J potential parameters and charges of each atom Atoms e=k ,K r,nm q, e References Chlorite O(t) 78.18 0.3166 -0.800 Cygan et al. (2004), Jin and Firoozabadi (2013, 2014) O(a) 78.18 0.3166 -1.000 O(o) 78.18 0.3166 -1.7175 O(OH) 78.18 0.3166 -1.7175 H(OH) 0.00 0.0000 0.7175 Si 9.26 9 10 0.3302 1.200 Al 4.54 9 10 0.5086 3.000 Mg 4.54 9 10 0.5086 2.000 Methane C 148.10 0.3730 0 Martin and Siepmann (1998) Water O 78.18 0.3166 -0.8476 Berendsen et al. (1987) H 0 0 0.4238 Carbon dioxide C 28.129 0.2757 0.6512 Harris and Yung (1995) O 80.507 0.3033 -0.3256 Nitrogen N 36 0.331 -0.482 Potoff and Siepmann (2001) COM 0 0 0.964 Notes: (t) tetrahedron oxygen, (o) octahedral oxygen, (a) terminal oxygen, COM at the centre of the nitrogen–nitrogen bond (a) 1.00 1.3 (b) y y =80 % =20 % 313 K 333 K CH N 4 2 353 K 373 K y y =60 % =40 % CH N 4 2 0.95 1.2 y y =40 % =60 % CH N 4 2 y =20 % y =80 % CH N 4 2 0.90 1.1 0.85 1.0 0.80 0.9 0.75 0.8 0 5 10 15 20 25 30 35 40 0 8 16 24 32 40 p, MPa p, MPa (c) 1.0 y y 0.8 =80 % =20 % CH CO 4 2 y y =60 % =40 % CH CO 4 2 y y =40 % =60 % CH CO 4 2 0.6 y y =20 % =80 % CH CO 4 2 0.4 0 8 16 24 32 40 p, MPa Fig. 2 Methane fugacity coefficient at different temperatures and pressures φ Pet. Sci. (2017) 14:37–49 41 simulation was the Dreiding force field, with the Coulomb q V þ V represents the total area of b and c, as shown a g force and van der Waals force interactions calculated by in Fig. 2. Then, the excess adsorption amount can be the Ewald & Group method and the atom interaction-based expressed as follows: method with an L–J potential cutoff distance of 1.55 nm. n ¼ N  q V þ V ¼N  q V ð4Þ ex a g p g g The maximum number of load steps in each simulation was 6 6 6 3 9 10 , including 1.5 9 10 balance steps and 1.5 9 10 where N is the total amount of gas in mol/g, V is the gas 3 3 process steps. The related statistics were obtained using the phase volume in g/cm , and V is the free volume in g/cm . later 1.5 9 10 configurations. The free volume in the pore can be determined by the method that uses He as the probe (Talu and Myers 2001). 3.2 Excess adsorption amount Therefore, the gas amount obtained from the results of the simulation is the total amount of gas, and based on the free The isothermal adsorption experiments of the chlorite volume in the pore, the total amount of gas can be con- exceed the critical temperature of methane (191 K), sug- verted into the excess adsorption amount of the gas gesting that the methane adsorption behaviour on chlorite according to Eq. (4). belongs to supercritical adsorption. For supercritical adsorption, Gibbs proposed that an adsorbate molecule in the adsorbed phase on the surface of the adsorbent cannot 4 Results and discussions be used as the total adsorption amount. Additionally, the distribution of adsorbate molecules in the adsorbed phase 4.1 Influences of different pore sizes based on the gas phase density was independent of the gas/solid molecule inter-atomic forces (Xiong et al. Figure 4 presents the total amount and excess adsorption 2015b). According to this view, Gibbs introduced the capacity isotherms of methane in chlorite pores for dif- concept of the excess adsorption amount: ferent pore sizes. Examination of Fig. 4a shows that the total amount of methane increased with the increment of n ¼ n  q V ; ð3Þ ex ab g a the pore size and first increased rapidly and then increased where n is the excess adsorption amount in mol/g, n is slowly with the increase in pressure. At the same time, ex ab the absolute adsorption amount in mol/g, V is the adsorbed a from Fig. 4b, it can be seen that the differences among the 3 3 phase volume in cm , and q is the vapour density in g/cm excess adsorption capacity of methane on chlorite in micropores were small. However, it also showed that the calculated by the SRK state equation (Soave 1972). Figure 3 shows a schematic representation of the excess methane excess adsorption capacity gradually decreased as the pore size increased in the mesopores, and the excess adsorption amount and absolute adsorption amount in which the area of a represents the excess adsorption adsorption capacity of methane in mesopores is signifi- cantly smaller than that in micropores. This may be amount and the total area of a and b expresses the absolute adsorption amount. We assume that the total amount of because the potential superimposed effect of the pore wall can significantly affect the adsorption of methane mole- adsorbate in the adsorption system is N, corresponding to the total area of a, b, and c, as shown in Fig. 3, which is cules in micropores, and the methane adsorption capacity in the pore would therefore be limited by the pore volume, equal to the expression (n þ q V ). Therefore, ab g that is, the pore volume increases with the increase in the pore size and methane adsorption capacity. However, the adsorption of methane molecules in mesopores was mainly Adsorbed affected by the surface potential effect of the two sides of phase the pore wall; the interactions between the methane molecules and the chlorite decrease, and movement space Gas phase of the methane molecules increases, which makes the force Solid phase a to escape from the chlorite pore wall easy to overcome. Then, the methane adsorption capacity decreases with increasing pore size. In addition, the excess adsorption capacity of methane first increased after the pressure drop. That is, there is a maximum value of the excess adsorption s capacity (n ), and the corresponding pressure is exc–max z z known as the maximum pressure (p ). This conclusion is max in line with that of previous studies of organic-rich shales Fig. 3 Schematic representation of the excess adsorption amount and (Rexer et al. 2013; Gasparik et al. 2014; Yang et al. 2015). absolute adsorption amount 123 42 Pet. Sci. (2017) 14:37–49 (a) (b) 0.004 1 nm 1.5 nm 0.12 2 nm 3 nm 4 nm 6 nm 8 nm 10 nm 0.003 15 nm 20 nm 0.08 0.002 1 nm 1.5 nm 0.04 0.001 2 nm 3 nm 4 nm 6 nm 8 nm 10 nm 15 nm 20 nm 0.00 0.000 0 10203040 0 10203040 p, MPa p, MPa Fig. 4 Total amount isotherms of methane (a) and the excess adsorption isotherms of methane (b) in chlorite pores for different pore sizes (temperature of 333 K) Table 3 shows the maximum values of the methane excess the methane isosteric heat decreased gradually with an adsorption capacity and its corresponding pressure for increase in pore size. The isosteric heat for a pore size of different pore sizes. Examination of the data in Table 3 1 nm was the maximum value (13.6 kJ/mol), and the shows that the maximum pressure corresponding to the average isosteric heat for a pore size of 20 nm was the maximum value of the excess adsorption capacity was minimum value (6.12 kJ/mol). Experimentally, Ji et al. different and that the range of the maximum pressure was (2012a, b) found that the average isosteric heat of methane between 14 MPa and 18 MPa. This finding is in agreement adsorption on chlorite was 9.4 kJ/mol. Although there are with previous studies on organic-rich shales (Rexer et al. differences between the simulated and experimental 2013; Gasparik et al. 2014; Yang et al. 2015), suggesting results, they also showed similarities to a certain extent. that the maximum pressure (p ) was between 10 and This result may be related to the differences of research max 19 MPa, as was concluded from the experimental data. methods and samples. The pore size in the experiments is This result indicates that, to a certain extent, our simulation distributed continuously between 20 nm and 100 nm (Ji results are in reasonable agreement with the experimental et al. 2012a, b), and the methane isosteric heat obtained results. Meanwhile, the maximum value of the excess from the experiment reflects the synthesis results obtained adsorption capacity decreased with an increase in pore size for the sample with a continuous distribution of pore sizes. in mesopores. The maximum value of the excess adsorp- However, the pore skeletons of chlorite in the simulation tion capacity reached a peak value of 0.00372 mmol/m have a single pore size, and the methane isosteric heat when the pore size was 2 nm, while the minimum value of obtained from the simulation reflects the results for a single the excess adsorption capacity was 0.00239 mmol/m pore and changes with pore size. In addition, the isosteric when the pore size was 20 nm. The conclusions illustrate heat of adsorption of methane in chlorite pores with dif- that the methane adsorption capacity in chlorite micropores ferent pore sizes was less than 42 kJ/mol, demonstrating increased with an increase in pore size, whereas that in that the methane adsorption on chlorite is of the physical chlorite mesopores decreased with an increase in the pore adsorption type. This conclusion is in accord with previous size. studies that suggested the methane is adsorbed on chlorite The average isosteric heat of methane in chlorite pores by physical adsorption (Ji et al. 2012a, b; Fan et al. 2014; with different pore sizes is shown in Fig. 5. It is seen that Tang and Fan 2014; Liang et al. 2016). 2 2 Table 3 Simulation results of H,nm n , mmol/m p , MPa H,nm n , mmol/m p , MPa exc-max max exc-max max methane adsorption on chlorite for different pore sizes 1 0.003276 18 6 0.002839 16 1.5 0.003417 18 8 0.002614 14 2 0.003505 18 10 0.002496 16 3 0.003199 18 15 0.002340 14 4 0.003016 16 20 0.002178 14 -2 Total amount, mmol·m -2 Excess adsorption, mmol·m Pet. Sci. (2017) 14:37–49 43 under low pressure is not as stable as that under high- pressure conditions. In addition, the potential energy dis- tribution curves of methane and chlorite with different pore sizes under a pressure of 20 MPa are presented in Fig. 6b. Examination of Fig. 6b shows that the potential energy distribution curves of methane and chlorite gradually 9 moved to the right with the increase in pore size and the most probable potential energy of methane and chlorite gradually increased, that is, the most probable potential energy changed from -11.92 to -3.56 kJ/mol when the 6 pore size increased from 1 nm to 20 nm. This suggests that methane adsorption occurring in chlorite pores gradually 0 5 10 15 20 changed from lower-energy adsorption sites to higher-en- H, nm ergy adsorption sites as the pore size increased, and the methane adsorption capacity in chlorite micropores was Fig. 5 Average methane isosteric heat in a chlorite pore with stronger than that in macropores. different pore sizes According to the simulation results, we obtained the 4.2 Influence of different temperatures potential energy distribution of methane and chlorite. The methane and chlorite potential energy distribution curves The excess adsorption isotherms of methane for different temperatures (pore size of 4 nm) are listed in Fig. 7. It can be for different pressures (pore size of 4 nm) are presented in Fig. 6a. It can be noted that the curve transforms the twin seen that the methane excess adsorption capacity decreased with increasing temperature under the same pressure; this peaks into a unimodal distribution with the increase in the pressure. At the same time, as the pressure is increased, the may be due to methane adsorption on chlorite being of the potential energy distribution curves of methane and chlo- physical adsorption type. When the temperature increases, rite gradually moved to the left. Additionally, the most the thermal motion of methane molecules would increase, probable potential energy of methane and chlorite gradu- resulting in an increase in the mean kinetic energy of methane molecules, generating a sufficiently large force to ally decreased, that is, the most probable potential energy changed from -0.209 to -6.485 kJ/mol as the pressure escape from the chlorite pore wall easily, thus causing a reduction in the methane adsorption capacity. This conclu- increased from 2 to 36 MPa. This indicates that methane adsorption occurring in chlorite pores gradually changes sion is in accord with the results of the isothermal adsorption experiments performed by Ji et al. (2012a, b), suggesting that from higher-energy adsorption sites to lower-energy adsorption sites with the increase in pressure and that the the methane adsorption capacity on chlorite decreased with adsorption state of methane molecules in chlorite pores increasing temperature. 1.2 1.2 (a) (b) 2 MPa 6 MPa 1 nm 1.5 nm 2 nm 3 nm 10 MPa 14 MPa 4 nm 6 nm 20 MPa 28 MPa 8 nm 10 nm 36 MPa 15 nm 20 nm 0.8 0.8 0.4 0.4 0.0 0.0 -20 -15 -10 -5 0 5 -20 -15 -10 -5 0 5 -1 -1 Energy, kJ·mol Energy, kJ·mol Fig. 6 Potential energy distribution curves of methane and chlorite for different pressures (pore size of 4 nm) (a) and different pore sizes (pressure of 20 MPa) (b) -1 Poisson distribution of energy (E) Average isosteric heats, kJ·mol Poisson distribution of energy (E) 44 Pet. Sci. (2017) 14:37–49 0.004 moved to the right. Furthermore, the most probable potential energy of methane and chlorite gradually increased, that is, the most probable potential energy 0.003 changed from -4.393 to -3.138 kJ/mol when the tem- perature increased from 313 to 373 K. This finding sug- gests that the adsorption sites of methane molecules in 0.002 chlorite pores gradually change from lower-energy adsorption sites to higher-energy adsorption sites with increasing temperature, causing the reduction in the 0.001 313 K 333 K methane adsorption capacity. 353 K 373 K 0.000 4.3 Influence of different water contents 0 1020 3040 p, MPa To investigate the influence of water on the methane adsorption in chlorite pores, three simulation projects Fig. 7 Excess adsorption isotherms of methane for different temper- atures (pore size of 4 nm) considering three water contents (wt% = the water mole- cules mass/the chlorite mass) were carried out. First the Figure 8 shows the average methane isosteric heat in adsorption sites of water molecules in the slit-like chlorite chlorite pores for different temperatures (pore size of pores need to be determined by using the annealing sim- 4 nm). We observe that the average isosteric heat of ulation method. The distribution of the different water methane decreased with increasing temperature, indicating contents in the chlorite pores is given in Fig. 10. In addi- that the interactions between methane molecules and tion, the size of the chlorite pores is 4 nm and the tem- chlorite became weaker with increasing temperature, perature is 333 K in simulation. resulting in a decrease in the methane adsorption capacity. Examination of Fig. 10 shows that water molecules In the range of the simulated temperatures, the value of the occupied the chlorite pore walls in a directional manner, average isosteric heat of methane in a chlorite pore with the and the oxygen atoms of the water molecules were close to pore size of 4 nm is between 7.59 and 8.21 kJ/mol (less or pointed to the surface of the chlorite pore wall or than 42 kJ/mol), illustrating that the adsorption of methane hydrogen atoms of the surrounding water molecules, with in the chlorite pores is due to physical adsorption. These the hydrogen atoms located at a distance from the surface findings indicate that methane adsorption on chlorite is of the chlorite pore wall. This may be due to the positive exothermic and the increase in temperature is not con- charges of the aluminium and silicon atoms on the surface ducive for methane adsorption on chlorite. The potential of the chlorite pore wall and the negative charge of the energy distribution curves between methane and chlorite at oxygen atoms of the water molecule, causing a pattern in different temperatures (pore size of 4 nm) are shown in which the oxygen atoms of the water molecules are close to Fig. 9. When the temperature increased, the potential or point to the surface of the chlorite pore wall. This energy distribution curve of methane and chlorite gradually phenomenon arises from the Coulomb and van der Waals 1.2 8.1 313 K 333 K 353 K 373 K 0.8 7.8 0.4 7.5 0.0 7.2 -20 -15 -10 -5 0 5 320 340 360 380 -1 T, K Energy, kJ·mol Fig. 8 Average isosteric heats of methane for different temperatures Fig. 9 Potential energy distribution curves of methane and chlorite at (pore size of 4 nm) different temperatures (pore size of 4 nm) -1 -2 Average isosteric heats, kJ·mol Excess adsorption, mmol·m Poisson distribution of energy (E) Pet. Sci. (2017) 14:37–49 45 that the curves have two peaks, with the main peak lying in the higher-energy area and the secondary peak located in the lower-energy area. The most probable potential energy of methane and chlorite did not change significantly with the increase in the water contents, indicating that the methane molecules in the higher-energy adsorption sites could not be occupied with the change of water contents. However, the secondary peak of the potential energy dis- tribution curve gradually became broad, implying that the water molecules occupy the lower-energy adsorption sites of methane molecules. It can be deduced that water molecules mainly occupied lower-energy adsorption sites on the chlorite pore walls instead of higher-energy Fig. 10 Distribution of different water contents in chlorite pores (the adsorption sites, illustrating that the water molecules and number in parentheses represents the number of water molecules) methane molecules compete with each other for adsorption space and adsorption sites. Therefore, the adsorption space force interactions between water molecules and chlorite, and adsorption sites occupied by water molecules resulting in the aggregation of water molecules in the decreased the adsorption space and adsorption sites of chlorite pore. In addition, due to the hydrogen bonding methane molecules, leading to a decrease in the methane interaction, the oxygen atoms of the water molecules point adsorption capacity. to the hydrogen atoms of surrounding water molecules. All of the data indicate that the water molecules are adsorbed 4.4 Influence of different mole fractions of nitrogen on the surface of the pore walls and occupy the adsorption space of the methane molecules in the form of aggregation. To investigate the influence of mole fraction of nitrogen on Figure 11 shows the methane excess adsorption iso- competitive adsorption of nitrogen and methane in the therms for different water contents. It can be seen that the chlorite pores, five simulation projects considering five methane excess adsorption capacity on chlorite is reduced mole fractions of nitrogen in the methane/nitrogen binary when the water contents increased under the same tem- gas mixture (y = 80% means that the mole fraction of CH4 perature and pressure, implying that water molecules methane is 80% while the mole fraction of nitrogen is 20%) inhibit methane adsorption on chlorite. This conclusion is would be carried out. The size of the chlorite pores is 4 nm in agreement with a previous study of methane adsorption and the temperature is 333 K in the simulation. on montmorillonite (Jin and Firoozabadi 2013, 2014), The excess adsorption isotherms of methane for differ- indicating that water reduced the methane adsorption ent mole fractions of nitrogen are shown in Fig. 13. The capacity on montmorillonite. The potential energy distri- methane excess adsorption capacity decreased with the bution curves of methane and chlorite for different water increase in the nitrogen mole fraction at the same tem- contents are shown in Fig. 12. Inspection of Fig. 12 shows perature and pressure, indicating that a lower mole fraction 1.2 0.0036 0 % 2 % 4 % 8 % 0.0027 0.8 0.0018 0.4 0.0009 0 % 2 % 4 % 8 % 0.0 0.0000 010 20 30 40 -20 -15 -10 -5 0 5 -1 p, MPa Energy, kJ·mol Fig. 11 Excess adsorption isotherms of methane for different water Fig. 12 Potential energy distribution curves of methane and chlorite contents for different water contents -2 Excess adsorption, mmol·m Poisson distribution of energy (E) 46 Pet. Sci. (2017) 14:37–49 1.5 of the methane in the methane/nitrogen binary gas mixture y y =80 % =20 % CH N 4 2 leads to a smaller methane adsorption capacity on chlorite. y =60 % y =40 % In the adsorption system of the methane/nitrogen binary CH N 4 2 gas mixture, the potential energy distribution curves for y y =40 % =60 % CH N 4 2 1.0 different mole fractions of nitrogen are presented in y y =20 % =80 % CH N 4 2 Fig. 14. It can be seen that the most probable potential energy of methane and chlorite under different nitrogen mole fractions was smaller than that of the nitrogen, 0.5 demonstrating that the potential energy distribution between methane and chlorite was different from that between nitrogen and chlorite, that is, the methane adsorption occurring on the chlorite pore walls was due to 0.0 the lower-energy adsorption sites, whereas nitrogen -20 -15 -10 -5 0 5 -1 adsorption occurred in higher-energy adsorption sites, Energy, kJ·mol illustrating that nitrogen adsorption on chlorite in the Fig. 14 Potential energy distribution curves for different mole adsorption system of the methane/nitrogen binary gas fractions of nitrogen mixture was less stable than that of methane. Figure 15 (the distributions of methane and nitrogen on the surface of chlorite) also illustrates this conclusion. Figure 15 shows Methane that the methane molecules and nitrogen molecules on the chlorite surface were distributed among different adsorp- tion sites. Furthermore, we found that the interactions between methane and nitrogen led to a change of the potential energy distribution curves of methane and chlorite. At the Nitrogen same time, the potential energy distribution curve of methane and chlorite gradually moved to the right and the most probable potential energy of methane and chlorite Fig. 15 Distributions of methane and nitrogen on the surface of gradually increased with increasing nitrogen mole fraction. chlorite (right does not include the chlorite cell) Namely, the methane adsorption gradually changed from lower-energy adsorption sites to higher-energy adsorption space for methane molecules. Hence, in the adsorption sites with the increase in the nitrogen mole fraction, system of the methane/nitrogen binary gas mixture, the resulting in a decrease in the methane adsorption capacity methane adsorption capacity on chlorite is greater than that on chlorite, implying that the nitrogen adsorption occurring of nitrogen. According to the previous analysis, the in the chlorite pores led to the change of the adsorption site methane adsorption capacity decreased with the increase in of methane molecules and the reduction of the adsorption the mole fraction of nitrogen due to the decrease in the methane mole fraction in the gas phase, the change of the 0.004 y y y =100 % =80 % =60 % CH CH CH adsorption sites of the methane molecules and the reduc- 4 4 4 y y =40 % =20 % tion in the adsorption space of the methane molecules. CH CH 4 4 0.003 4.5 Influence of different mole fractions of carbon dioxide 0.002 To investigate the influence of the mole fraction of carbon dioxide on competitive adsorption of carbon dioxide and 0.001 methane in the chlorite pores, simulations with five mole fractions of carbon dioxide in the carbon dioxide/methane binary gas mixture (y = 80% means that the mole CH4 0.000 0 1020 3040 fraction of methane is 80% while the mole fraction of p, MPa carbon dioxide is 20%) were carried out. The size of the chlorite pores is 4 nm, and the temperature is 333 K in Fig. 13 Excess adsorption isotherms of methane on chlorite for these simulations. different mole fractions of nitrogen -2 Excess adsorption, mmol·m Poisson distribution of energy (E ) Pet. Sci. (2017) 14:37–49 47 0.9 Excess adsorption isotherms of methane for different y y =80 % =20 % CH CO mole fractions of carbon dioxide are shown in Fig. 16.It 2 y =60 % y can be seen that the methane excess adsorption capacity =40 % CH CO decreased as the carbon dioxide mole fraction increased at y y =40 % =60 % CH CO 4 2 0.6 the same pressure and temperature, indicating that the y y =20 % =80 % CH CO 4 2 smaller methane mole fraction in the carbon dioxide/ methane binary gas mixture led to lower methane adsorp- tion capacity. 0.3 In the adsorption system of the carbon dioxide/methane binary gas mixture, the potential energy distribution curves for different mole fractions of carbon dioxide are shown in Fig. 17. It can be seen that the most probable potential 0.0 energy of methane and chlorite for different carbon dioxide -40 -36 -32 -28 -24 -20 -16 -12 -8 -4 0 4 -1 mole fractions was higher than that of carbon dioxide, Energy, kJ·mol suggesting that the potential energy distribution between Fig. 17 Potential energy distribution curves for different mole methane and chlorite was different from that between fractions of carbon dioxide carbon dioxide and chlorite. That is, carbon dioxide adsorption on the chlorite pore walls occurred in the lower- energy adsorption sites, whereas methane adsorption was Methane located in higher-energy adsorption sites, implying that methane adsorption on chlorite in the adsorption system of the carbon dioxide/methane binary gas mixture was less stable than that of carbon dioxide. Figure 18 (the distri- butions of methane and carbon dioxide on the chlorite surface) also illustrates this conclusion. Figure 18 shows that methane and carbon dioxide molecules on the chlorite Carbon dioxide surface were distributed among different adsorption sites. Furthermore, we also observed that the interactions Fig. 18 Distributions of methane and carbon dioxide on the surface between methane and carbon dioxide could change the of chlorite (right does not include the chlorite cell) potential energy distribution curves of methane and chlo- rite. At the same time, the potential energy distribution higher-energy adsorption sites with the increasing carbon curve of methane and chlorite gradually moved to the right dioxide mole fraction, leading to a reduction in the and the most probable potential energy of methane and methane adsorption capacity on chlorite. This phenomenon chlorite gradually increased with increasing carbon dioxide demonstrates that carbon dioxide adsorption occurring in mole fraction, meaning that the methane adsorption sites chlorite pores results in a change of the adsorption site of gradually changed from lower-energy adsorption sites to methane molecules and a reduction in their adsorption space. Thus, the carbon dioxide adsorption capacity on chlorite is greater than that of methane in the carbon y y y =100 % =80 % =60 % CH CH CH 4 4 4 0.0032 y y dioxide/methane binary gas mixture adsorption system. =20 % =40 % CH CH 4 Based on the previous analysis, the methane adsorption capacity decreased with the increase in the carbon dioxide 0.0024 mole fraction, resulting in a reduction in the methane mole fraction in the gas phase, a change of the adsorption sites of 0.0016 the methane molecules and a reduction in the methane adsorption space. 0.0008 5 Conclusions 0.0000 0 1020 3040 p, MPa First, the average methane isosteric heat decreased with increasing pore size, which was smaller than 42 kJ/mol in Fig. 16 Excess adsorption isotherms of methane in chlorite pores for the chlorite–methane adsorption system, suggesting that different carbon dioxide mole fractions -2 Excess adsorption, mmol·m Poisson distribution of energy (E) 48 Pet. Sci. (2017) 14:37–49 systems. 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J Nat Gas Sci Eng. 2016;33:1107–18. doi:10.1016/j.jngse.2016.05.024. adsorption sites as well as a reduction in the methane Liang LX, Xiong J, Liu XJ. Mineralogical, microstructural and adsorption space and the mole fraction of methane in the physiochemical characteristics of organic-rich shales in the gas phase, resulting in a decrease in the methane adsorption Sichuan Basin, China. J Nat Gas Sci Eng. 2015;26:1200–12. capacity. doi:10.1016/j.jngse.2015.08.026. Liu XJ, Xiong J, Liang LX. Investigation of pore structure and fractal characteristics of organic-rich Yanchang Formation shale in Acknowledgements This research was supported by the United Fund central China by nitrogen adsorption/desorption analysis. J Nat Project of National Natural Science Foundation of China (Grant No. Gas Sci Eng. 2015;22:62–72. doi:10.1016/j.jngse.2014.11.020. U1262209) and the National Natural Science Foundation of China Martin MG, Siepmann JI. 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Published: Jan 7, 2017

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