# Mechanism and Characteristics of CH4/CO2/H2O Adsorption in Lignite Molecules

Authors: Zhihui Wen; Yunpeng Yang; Qi Wang; Banghua Yao
Journal: Geofluids
 (2021)

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## Abstract

Adsorption characteristics of coalbed methane (CBM) are significant to investigate the absorption of coal, shale, and porous media. In particular, adsorption characteristics of CH4, CO2, and H2O play an important role in predicting CBM output and geologic sequestration potentials of CO2 in research fields of CO2-enhanced CBM recovery (CO2-ECBM) and sequestration of CO2. In this work, adsorption characteristics of CH4, CO2, and H2O in lignite molecules were simulated through the grand canonical Monte Carlo (GCMC) method and molecular dynamics (MD) method. Research results demonstrated that given the same temperature and pressure, the ultimate adsorption capacity of lignite per unit to H2O is the highest, followed by those of CO2 and CH4 successively. All isothermal adsorption curves conform to the “I-type” characteristics. In the saturated molecular configuration, gas molecules show different distribution patterns at two sides of the lignite molecule chain. Lignite has typical physical adsorption to CH4 and CO2, with adsorption energy provided by nonbonding energy. However, lignite has both physical adsorption and chemical adsorption to H2O, with adsorption energy provided by both nonbonding energy and hydrogen bond energy. High temperature is against adsorption of CH4, CO2, and H2O. Temperature might inhibit adsorption of gas molecules. Research conclusions lay foundations for the exploitation and development of CBM and relevant studies on sequestration of CO2.


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## Body

## 1. Introduction

Recently, the energy problem has become an important global research field. With the increasing exhaustion of fossil fuels, it is crucial to find new energies [1, 2]. Coalbed methane (CBM), a high-efficiency, environmental-friendly, and rich energy source, has been highly concerned by scholars and experts [3–7]. It is the best substitute for fossil fuels at present. CBM is mainly composed of CH4, CO2, H2O, O2, and some other trace gases, and 80%-90% of CBM are adsorbed on the surface of the coal matrix [8, 9]. According to estimations, the global CBM resources are higher than 200,000 billion m3. China also possesses abundant CBM reserves, and it is the third-largest CBM reserve in the world. There are about 35,000 billion m3 of CBM resources in more than 2,000 m of buried depth, including about 12,000 m3 of explored reserves and 23,000 m3 of future reserves. There is a great development potential of CBM resources in China [10, 11]. Meanwhile, exploiting CBM before coal mining can avoid the occurrence of outburst of gas and gas explosion effectively. Injecting CO2 to enhance coalbed methane (CO2-ECBM) has been widely concerned by many scholars because it can not only displace the methane in coal but also reduce the greenhouse gas effect by geological storage [12, 13]. Many studies have demonstrated that the total pore volume of coals is mainly determined by micropores (<2 nm) and mesopores (2-50 nm) [14–16]. Therefore, elaborating the microscale adsorption characteristics and mechanism of coals is critical to adopt effective CO2-ECBM measures and gas disaster control technologies. Therefore, it is very necessary to carry out molecular simulation on adsorption of CH4, CO2, and H2O in coal matrix molecules.With the development of scientific technology, the molecular adsorption mechanism between adsorbent and adsorbate can be discussed through computer molecular simulation. Microscopic technology is very suitable to study adsorption behavior of nanometer and submicron pores of coals [17]. Matranga et al. [18] simulated the adsorption behavior of CH4, CO2, and N2 on activated carbons by the grand canonical Monte Carlo (GCMC) method, finding that the adsorption capacity and adsorption heats of CO2 are higher than those of CH4 and N2. Narkiewicz and Mathews [19] introduced an adsorption position corresponding to the CO2 adsorption of low-volatile soft coals and methane molecular capacity and model through molecular simulation. Zhang et al. [20] discussed adsorption effects of benzene ring and side chains of coal surface molecules to CH4, CO2, N2, and O2 through molecular simulation. Xiang et al. [21] concluded adsorption capacities of CH4, CO2, and H2O, molecular configuration, and effects of oxygen-containing functional groups on adsorption performance of Yanzhou coal through GCMC and MD methods. Mosher et al. [14] carried out a molecular simulation to explore competitive adsorption behaviors of CH4 and CO2 in micropores and middle pore structures of coals. Dang et al. [22] and Song et al. [23] studied adsorption behaviors of CH4, CO2, and H2O in low-rank coals by using density functional theory (DFT) and MD, finding that high temperature is against adsorption of CH4, CO2, and H2O in coal matrix and oxygen-functional groups and nitrogen-containing functional groups of coal can influence adsorption greatly. Xu et al. [24] studied molecular behaviors that CO2 promotes CH4 desorption in coals. You et al. [25] simulated the interaction between subbituminous coals and water through MD simulation and found that water molecules are easy to be adsorbed by carboxyls. Li et al. [26] calculated and discussed adsorption capacities of CH4, CO2, and N2 in coal silt models, finding a relationship in adsorption capacities of three gases with the increase of silt width: H2O>CH4>N2. Gao et al. [27] simulated adsorption characteristics of lignite through GCMC and MD methods. Results showed that the adsorption isotherm of single gas conformed to the Langmuir equation and the CO2 enjoys obvious advantages in the competitive adsorption of multiple gases. Hu et al. [28] and You et al. [29] studied self-diffusion and mutual diffusion of CH4, CO2, and multicomponent gases through the MD method.Although many works have been reported, only few concentrate on adsorption characteristics of CH4, CO2, and H2O in lignite. Besides, lignite reserves account for 47% of total coal reserves, indicating that lignite has great potentials in CBM development and sequestration of CO2. In this study, adsorption characteristics of CH4, CO2, and H2O in lignite which possesses a great reserve were discussed with the classical GCMC and MD method. Moreover, the stable configuration of lignite molecules was discussed, and the saturated adsorption capacity and saturated molecular configuration of lignite molecules were simulated. The variation law of adsorption energy of different adsorbates in lignite molecules was analyzed, and the microscopic mechanism of CH4, CO2, and H2O adsorption in lignite molecules was elaborated. Research conclusions provide theoretical supports to study adsorption performances of different adsorbates in lignite molecules.


## 2. Methodology

### 2.1. Brown Coal Structure Construction

Coal is a type of porous heterogeneous solids with complicated physical and chemical structures. The basic structural unit of coals includes a regular part and irregular part. The regular part is composed of benzene rings, heterocyclic rings, alicyclic rings, and hydroaromatic rings, and it forms the core part of the structural unit of coals. The irregular part is composed of functional groups which are connected to the regular part and side chains of alkyls. Among studies of the molecular structure of coals, more than 130 molecular structures have been proposed yet [30]. Among them, the Given model [31], Wiser model [32], and Solomon model [33] are representative ones. In particular, the Wiser model is regarded as a relatively comprehensive and reasonable model to describe lignite with a low degree of metamorphism, and this model can reflect the modern concept of the molecular structure of coals. The Wiser model can explain surface chemical and other reactive properties of lignite. Therefore, it is widely applied in simulation studies related to lignite molecules [17, 26, 33]. The Wiser model (C184H155N3O20S3) has basic features of lignite, including a single aromatic ring which is linked and cross-linked through the aliphatic side chain. It is applicable to the molecular simulation study of gas adsorption of lignite. The plane molecular structure of the Wiser model is shown in Figure 1.Figure 1
Molecular plane structure of the Wiser model [28].In this work, Materials Studio (MS) was used to carry out the simulation calculation. In the MS, 3D lignite molecular structural units were constructed according to the molecular formula (C184H155N3O20S3), and they were defined as a molecular fragment. The initial 3D space structure of lignite molecules was gained by adding hydrogen until saturation. In the Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS), the smart technique was chosen to optimize the initial 3D spatial structure of lignite molecules. The number of iteration steps, convergent standard accuracy, and energy deviation were set as 100,000, fine, and 0.0001 kcal/mol, respectively. The acting energies of Coulomb electrostatic force and Van der Waals (VDW) force were set at the atomic state, and charges carried on the lignite molecular structure were distributed automatically by a force field. Potential energy surfaces were searched through annealing added with energy disturbance to recognize the point with the lowest energy in the system. The frame with the lowest energy was chosen as the stable structure of the molecular structural model of lignite. The optimized 3D structure of lignite molecules is shown in Figure 2.Figure 2
Stable molecular model of lignite. Color scheme: C: black; H: gray; O: red; N: blue; S: yellow.In order to verify the accuracy of the constructed molecular model of lignite, unit cells were added through setting of density to the stable molecular model of lignite in Figure2 by using the Amorphous Cell module. The constructed unit cells were processed by MD optimization and annealing, thus getting stable configuration and energy distribution of unit cells under different densities. The molecular structure at the lowest system energy is the most stable. At this moment, the density corresponding to the system energy is the optimal density after adding periodic boundary conditions. The variation laws of unit cell system energy of lignite with density are shown in Figure 3.Figure 3
Variation of energy with density in unit cell system of lignite.
(a)
Density change during annealing kinetics(b)
System energy change with densityIt can be seen from Figure3(b) that with the increase in system density, system energy of lignite molecules presents a “V-shaped” variation after unit cells are added in. The system energy of unit cells of lignite fluctuates when the molecular density is between 1.20 g/cm3 and 1.26 g/cm3 (Figure 3(a)). When the molecular system density of lignite is 1.23 g/cm3, the system energy of unit cells reaches the minimum. Besides, the system energy of unit cells shows an upward trend with the increase and decrease of system density. In other words, the system energy of unit cells of lignite reaches the lowest when the system density is 1.23 g/cm3. Under this circumstance, the molecular structure of lignite is the most stable and the molecular configuration of lignite is the optimal one when periodic boundary conditions are added in. This conforms to the mean lignite density (1.21 g/cm3) which is calculated in References [34, 35]. Therefore, the constructed model can be used to investigate the adsorption characteristics in lignite molecules. At this moment, the unit cell size of lignite molecules is 1.5745695nm×1.5745695nm×1.5745695nm.


### 2.2. Force Field

In molecular simulation calculations, various types of force fields are used, including (a) the classic fields, such as the MM force field, AMBER force field, CHARMM force field, and CVFF force field, and (b) the second generation fields, such as the COMPASS force field. The existing force field has been highly applicable to description of macromolecular substances and biomacromolecules [26, 36–38]. The molecular force field is formed by a set of potential functions and dynamic constant. The total molecular energy is the sum of kinetic energies and potential energies. Potential energy of molecules can be expressed in a simple geometric coordinate function.The force field used in this study is a second-generation field. The force field is designed to accurately calculate various properties, structures, spectra, thermodynamic properties, and other expected parameters of a molecule. Thus, in addition to incorporating an enormous amount of experimental data, the derivation of the force-field constant refers to the exact quantum calculation results. Due to the use of varying parameters, second-generation force fields can be divided into various types: CFF91, CFF95, PCFF, and MMFF93.An appropriate force field should be able to reproduce experimental results quantitatively. We have used different force fields, such as polymer-consistent force field (PCFF), Dreiding, condensed phase optimized molecular potential for atomistic simulation studies (COMPASS), and universal force field, to calculate the density of the lignite molecule model. The results indicated that the density computed through Dreading force field was the closest to the experimental values. The PCFF force field selected for this study was derived from the CFF91 force field, which is suitable for the study of polymers and organic matter. In addition to the parameters of the force field of CFF91, PCFF contains the force-field parameters of inert gas atoms, such as He, Kr, and metal atoms. These parameters could be used to reckon the molecular system containing these atoms.The total energy of a molecule was considered to be the sum of the kinetic and potential energies. The bonding energy includes energy of slip keys (Eb), bending energy of bond angle Eθ, torsion energy of the bond dihedron Eφ, bending energy of bond angle surface Eχ, and crossing energy Ecross. The nonbonding energy covers Coulomb electrostatic force Ec and VDW force Ev. The total energy of the molecular simulation system Etotal can be expressed as
(1)Etotal=Eb+Eθ+Eφ+Eχ+Ecross+Ev+Ec.Eb of atoms can be expressed as
(2)Eb=∑bK2b−b02+K3b−b03+K4b−b04,where K2, K3, and K4 are the elastic constant of chemical bonds, respectively. b and b0 are the chemical bond length and bond length at the equilibrium state, respectively. With the decrease of the elastic constant, the vibrational frequency and vibration amplitude slow down and decrease, respectively. Eθ can be expressed as
(3)Eθ=∑θH2θ−θ02+H3θ−θ03+H4θ−θ04,where θ and θ0 are the bond angle and bond angle at the equilibrium state, respectively. H2, H3, and H4 are the bending elastic constants of the bond angle, respectively. Eφ can be expressed as
(4)Eφ=∑φV11−cosφ−φ10+V21−cos2φ−φ20+V31−cos3φ−φ30,where V2, V3, and V4 are the torsion elastic constant of the dihedral angle. φ refers to four adjacent dihedral angles which are not formed by atoms on the same plane. φ0 can be used to reflect the dihedral angle in the initial stage. Eχ can be expressed as
(5)Eχ=∑χKχχ2,where Kχ is the bending elastic constant of the bond angle out of the plane. χ denotes the bending angle out of the plane. Ecross of bonds, bond angles, and dihedral angles can be expressed as
(6)Ecross=∑b∑b′Fbb′b−b0b′−b0′+∑θ∑θ′Fθθ′θ−θ0θ′−θ0′+∑b∑θFbθb−b0θ−θ0+∑b∑φb−b0V1cosφ+V2cos2φ+V3cos3φ+∑b′∑φb′−b0′V1cosφ+V2cos2φ+V3cos3φ+∑θ∑φθ−θ0V1cosφ+V2cos2φ+V3cos3φ+∑φ∑θ∑θ′Kθφφ′cosφθ−θ0θ′−θ0′,where Fbb′ is an extended coupling elastic constant, Fθθ′ denotes the bending coupling elastic constant, Fbθ refers to the coupling elastic constant of extended bending, and Kθφφ′ refers to the coupling elastic constant of torsional bending. Ec can be expressed as
(7)Ec=∑i,jqiqjrij,where qi and qj are the quantity of electric charge of atoms. rij refers to the distance between two atoms. The nonbonded VDW forces (Ev) can be expressed as
(8)Ev=4εijσijrij12−σijrij6,where εij is the effective dielectric constant between two atoms and σij is the potential parameter which changes according to the atom type.


### 2.3. Implementation of Simulation

#### 2.3.1. Optimization of Adsorbate

Molecular structures of adsorbates CH4, CO2, and H2O are plotted by Skirt in MS, and a 3D atom document of gas molecules is constructed. The plotted molecular structures of adsorbates were cleaned, followed by optimization of molecular mechanical structures and annealing processing under the Focite module. In this process, parameters were set consistent with those in Section 2 for molecular optimization of coals.


#### 2.3.2. Simulation Scheme and Parameter Setting

This study is a GCMC simulation based on the Sorption module in MS software. During simulation, the number of gas molecules is added to the coal surface one by one. The coal surface will release heats after adsorption with gas molecules, leading to the energy of the system declining gradually. The system energy reaches the minimum at saturated adsorption of gas molecules in coal structures. Under this circumstance, the number of gas molecules adsorbed on the coal surface is the maximum adsorption capacity of the coal surface to the gas molecule.During GCMC simulation of adsorption behaviors based on the Sorption module, the task term chose “adsorption isotherm,” and the interaction force between lignite molecules and gas molecules chose “Ewald” and “atom-based.” The electrostatic force was calculated by Ewald, and the VDW force was calculated by the atom-based method. The interaction between lignite molecules and gas molecules was described by the Lennard-Jones (LJ) 12-6 electric potentials [39]. Meanwhile, classical Metropolis rules were used to accept or reject production, disappear, translation, and rotation of gas micromolecules to assure that the system is at the lowest energy state [40]. The temperature in simulation was cycled five times automatically. Step length was adjusted and calculated automatically. The whole simulation involved 2×107 Monte Carlo steps. The first 107 steps were set to reach the adsorption equilibrium of the system, while the rest 107 steps were for sampling and statistics of relevant thermodynamic parameters.This work is to construct an optimized stable configuration of lignite for adsorbent, and the adsorbates are CH4, CO2, and H2O molecules. The simulation adopted 0.00 MPa~10.00 MPa pressure and periodic boundary conditions. Two situations were involved in the simulation:
(1)
The adsorption characteristics of CH4, CO2, and H2O in lignite molecules under the temperature of 303.15 K were simulated. The saturated adsorption configuration was analyzed, and the evolution laws of energies in the adsorption process were discussed(2)
Effects of simulation temperatures (283.15 K, 303.15 K, and 323.15 K) on CH4, CO2, and H2O in lignite were analyzedThe adsorption capacity gained in the simulation refers to the number of gas molecules adsorbed in a single unit cell. Its unit is moleculars/u.c., but the unit of adsorption capacity in a conventional experiment is cm3/g. These adsorption capacities in different units can be converted according to the following formula:
(9)1moleculars/u.c.=1/N×103÷M=1/N÷M×Vmol,where N is the Avogadro’s constant which values 6.02×1023. M refers to the mass of a single unit cell, and it is 4.08017×10−21 g. Vmol refers to the molar volume of gas under standard conditions, and it is 22.4×103 cm3/mol.


## 2.1. Brown Coal Structure Construction

Coal is a type of porous heterogeneous solids with complicated physical and chemical structures. The basic structural unit of coals includes a regular part and irregular part. The regular part is composed of benzene rings, heterocyclic rings, alicyclic rings, and hydroaromatic rings, and it forms the core part of the structural unit of coals. The irregular part is composed of functional groups which are connected to the regular part and side chains of alkyls. Among studies of the molecular structure of coals, more than 130 molecular structures have been proposed yet [30]. Among them, the Given model [31], Wiser model [32], and Solomon model [33] are representative ones. In particular, the Wiser model is regarded as a relatively comprehensive and reasonable model to describe lignite with a low degree of metamorphism, and this model can reflect the modern concept of the molecular structure of coals. The Wiser model can explain surface chemical and other reactive properties of lignite. Therefore, it is widely applied in simulation studies related to lignite molecules [17, 26, 33]. The Wiser model (C184H155N3O20S3) has basic features of lignite, including a single aromatic ring which is linked and cross-linked through the aliphatic side chain. It is applicable to the molecular simulation study of gas adsorption of lignite. The plane molecular structure of the Wiser model is shown in Figure 1.Figure 1
Molecular plane structure of the Wiser model [28].In this work, Materials Studio (MS) was used to carry out the simulation calculation. In the MS, 3D lignite molecular structural units were constructed according to the molecular formula (C184H155N3O20S3), and they were defined as a molecular fragment. The initial 3D space structure of lignite molecules was gained by adding hydrogen until saturation. In the Condensed-phase Optimized Molecular Potentials for Atomistic Simulation Studies (COMPASS), the smart technique was chosen to optimize the initial 3D spatial structure of lignite molecules. The number of iteration steps, convergent standard accuracy, and energy deviation were set as 100,000, fine, and 0.0001 kcal/mol, respectively. The acting energies of Coulomb electrostatic force and Van der Waals (VDW) force were set at the atomic state, and charges carried on the lignite molecular structure were distributed automatically by a force field. Potential energy surfaces were searched through annealing added with energy disturbance to recognize the point with the lowest energy in the system. The frame with the lowest energy was chosen as the stable structure of the molecular structural model of lignite. The optimized 3D structure of lignite molecules is shown in Figure 2.Figure 2
Stable molecular model of lignite. Color scheme: C: black; H: gray; O: red; N: blue; S: yellow.In order to verify the accuracy of the constructed molecular model of lignite, unit cells were added through setting of density to the stable molecular model of lignite in Figure2 by using the Amorphous Cell module. The constructed unit cells were processed by MD optimization and annealing, thus getting stable configuration and energy distribution of unit cells under different densities. The molecular structure at the lowest system energy is the most stable. At this moment, the density corresponding to the system energy is the optimal density after adding periodic boundary conditions. The variation laws of unit cell system energy of lignite with density are shown in Figure 3.Figure 3
Variation of energy with density in unit cell system of lignite.
(a)
Density change during annealing kinetics(b)
System energy change with densityIt can be seen from Figure3(b) that with the increase in system density, system energy of lignite molecules presents a “V-shaped” variation after unit cells are added in. The system energy of unit cells of lignite fluctuates when the molecular density is between 1.20 g/cm3 and 1.26 g/cm3 (Figure 3(a)). When the molecular system density of lignite is 1.23 g/cm3, the system energy of unit cells reaches the minimum. Besides, the system energy of unit cells shows an upward trend with the increase and decrease of system density. In other words, the system energy of unit cells of lignite reaches the lowest when the system density is 1.23 g/cm3. Under this circumstance, the molecular structure of lignite is the most stable and the molecular configuration of lignite is the optimal one when periodic boundary conditions are added in. This conforms to the mean lignite density (1.21 g/cm3) which is calculated in References [34, 35]. Therefore, the constructed model can be used to investigate the adsorption characteristics in lignite molecules. At this moment, the unit cell size of lignite molecules is 1.5745695nm×1.5745695nm×1.5745695nm.


## 2.2. Force Field

In molecular simulation calculations, various types of force fields are used, including (a) the classic fields, such as the MM force field, AMBER force field, CHARMM force field, and CVFF force field, and (b) the second generation fields, such as the COMPASS force field. The existing force field has been highly applicable to description of macromolecular substances and biomacromolecules [26, 36–38]. The molecular force field is formed by a set of potential functions and dynamic constant. The total molecular energy is the sum of kinetic energies and potential energies. Potential energy of molecules can be expressed in a simple geometric coordinate function.The force field used in this study is a second-generation field. The force field is designed to accurately calculate various properties, structures, spectra, thermodynamic properties, and other expected parameters of a molecule. Thus, in addition to incorporating an enormous amount of experimental data, the derivation of the force-field constant refers to the exact quantum calculation results. Due to the use of varying parameters, second-generation force fields can be divided into various types: CFF91, CFF95, PCFF, and MMFF93.An appropriate force field should be able to reproduce experimental results quantitatively. We have used different force fields, such as polymer-consistent force field (PCFF), Dreiding, condensed phase optimized molecular potential for atomistic simulation studies (COMPASS), and universal force field, to calculate the density of the lignite molecule model. The results indicated that the density computed through Dreading force field was the closest to the experimental values. The PCFF force field selected for this study was derived from the CFF91 force field, which is suitable for the study of polymers and organic matter. In addition to the parameters of the force field of CFF91, PCFF contains the force-field parameters of inert gas atoms, such as He, Kr, and metal atoms. These parameters could be used to reckon the molecular system containing these atoms.The total energy of a molecule was considered to be the sum of the kinetic and potential energies. The bonding energy includes energy of slip keys (Eb), bending energy of bond angle Eθ, torsion energy of the bond dihedron Eφ, bending energy of bond angle surface Eχ, and crossing energy Ecross. The nonbonding energy covers Coulomb electrostatic force Ec and VDW force Ev. The total energy of the molecular simulation system Etotal can be expressed as
(1)Etotal=Eb+Eθ+Eφ+Eχ+Ecross+Ev+Ec.Eb of atoms can be expressed as
(2)Eb=∑bK2b−b02+K3b−b03+K4b−b04,where K2, K3, and K4 are the elastic constant of chemical bonds, respectively. b and b0 are the chemical bond length and bond length at the equilibrium state, respectively. With the decrease of the elastic constant, the vibrational frequency and vibration amplitude slow down and decrease, respectively. Eθ can be expressed as
(3)Eθ=∑θH2θ−θ02+H3θ−θ03+H4θ−θ04,where θ and θ0 are the bond angle and bond angle at the equilibrium state, respectively. H2, H3, and H4 are the bending elastic constants of the bond angle, respectively. Eφ can be expressed as
(4)Eφ=∑φV11−cosφ−φ10+V21−cos2φ−φ20+V31−cos3φ−φ30,where V2, V3, and V4 are the torsion elastic constant of the dihedral angle. φ refers to four adjacent dihedral angles which are not formed by atoms on the same plane. φ0 can be used to reflect the dihedral angle in the initial stage. Eχ can be expressed as
(5)Eχ=∑χKχχ2,where Kχ is the bending elastic constant of the bond angle out of the plane. χ denotes the bending angle out of the plane. Ecross of bonds, bond angles, and dihedral angles can be expressed as
(6)Ecross=∑b∑b′Fbb′b−b0b′−b0′+∑θ∑θ′Fθθ′θ−θ0θ′−θ0′+∑b∑θFbθb−b0θ−θ0+∑b∑φb−b0V1cosφ+V2cos2φ+V3cos3φ+∑b′∑φb′−b0′V1cosφ+V2cos2φ+V3cos3φ+∑θ∑φθ−θ0V1cosφ+V2cos2φ+V3cos3φ+∑φ∑θ∑θ′Kθφφ′cosφθ−θ0θ′−θ0′,where Fbb′ is an extended coupling elastic constant, Fθθ′ denotes the bending coupling elastic constant, Fbθ refers to the coupling elastic constant of extended bending, and Kθφφ′ refers to the coupling elastic constant of torsional bending. Ec can be expressed as
(7)Ec=∑i,jqiqjrij,where qi and qj are the quantity of electric charge of atoms. rij refers to the distance between two atoms. The nonbonded VDW forces (Ev) can be expressed as
(8)Ev=4εijσijrij12−σijrij6,where εij is the effective dielectric constant between two atoms and σij is the potential parameter which changes according to the atom type.


## 2.3. Implementation of Simulation

### 2.3.1. Optimization of Adsorbate

Molecular structures of adsorbates CH4, CO2, and H2O are plotted by Skirt in MS, and a 3D atom document of gas molecules is constructed. The plotted molecular structures of adsorbates were cleaned, followed by optimization of molecular mechanical structures and annealing processing under the Focite module. In this process, parameters were set consistent with those in Section 2 for molecular optimization of coals.


### 2.3.2. Simulation Scheme and Parameter Setting

This study is a GCMC simulation based on the Sorption module in MS software. During simulation, the number of gas molecules is added to the coal surface one by one. The coal surface will release heats after adsorption with gas molecules, leading to the energy of the system declining gradually. The system energy reaches the minimum at saturated adsorption of gas molecules in coal structures. Under this circumstance, the number of gas molecules adsorbed on the coal surface is the maximum adsorption capacity of the coal surface to the gas molecule.During GCMC simulation of adsorption behaviors based on the Sorption module, the task term chose “adsorption isotherm,” and the interaction force between lignite molecules and gas molecules chose “Ewald” and “atom-based.” The electrostatic force was calculated by Ewald, and the VDW force was calculated by the atom-based method. The interaction between lignite molecules and gas molecules was described by the Lennard-Jones (LJ) 12-6 electric potentials [39]. Meanwhile, classical Metropolis rules were used to accept or reject production, disappear, translation, and rotation of gas micromolecules to assure that the system is at the lowest energy state [40]. The temperature in simulation was cycled five times automatically. Step length was adjusted and calculated automatically. The whole simulation involved 2×107 Monte Carlo steps. The first 107 steps were set to reach the adsorption equilibrium of the system, while the rest 107 steps were for sampling and statistics of relevant thermodynamic parameters.This work is to construct an optimized stable configuration of lignite for adsorbent, and the adsorbates are CH4, CO2, and H2O molecules. The simulation adopted 0.00 MPa~10.00 MPa pressure and periodic boundary conditions. Two situations were involved in the simulation:
(1)
The adsorption characteristics of CH4, CO2, and H2O in lignite molecules under the temperature of 303.15 K were simulated. The saturated adsorption configuration was analyzed, and the evolution laws of energies in the adsorption process were discussed(2)
Effects of simulation temperatures (283.15 K, 303.15 K, and 323.15 K) on CH4, CO2, and H2O in lignite were analyzedThe adsorption capacity gained in the simulation refers to the number of gas molecules adsorbed in a single unit cell. Its unit is moleculars/u.c., but the unit of adsorption capacity in a conventional experiment is cm3/g. These adsorption capacities in different units can be converted according to the following formula:
(9)1moleculars/u.c.=1/N×103÷M=1/N÷M×Vmol,where N is the Avogadro’s constant which values 6.02×1023. M refers to the mass of a single unit cell, and it is 4.08017×10−21 g. Vmol refers to the molar volume of gas under standard conditions, and it is 22.4×103 cm3/mol.


## 2.3.1. Optimization of Adsorbate

Molecular structures of adsorbates CH4, CO2, and H2O are plotted by Skirt in MS, and a 3D atom document of gas molecules is constructed. The plotted molecular structures of adsorbates were cleaned, followed by optimization of molecular mechanical structures and annealing processing under the Focite module. In this process, parameters were set consistent with those in Section 2 for molecular optimization of coals.


## 2.3.2. Simulation Scheme and Parameter Setting

This study is a GCMC simulation based on the Sorption module in MS software. During simulation, the number of gas molecules is added to the coal surface one by one. The coal surface will release heats after adsorption with gas molecules, leading to the energy of the system declining gradually. The system energy reaches the minimum at saturated adsorption of gas molecules in coal structures. Under this circumstance, the number of gas molecules adsorbed on the coal surface is the maximum adsorption capacity of the coal surface to the gas molecule.During GCMC simulation of adsorption behaviors based on the Sorption module, the task term chose “adsorption isotherm,” and the interaction force between lignite molecules and gas molecules chose “Ewald” and “atom-based.” The electrostatic force was calculated by Ewald, and the VDW force was calculated by the atom-based method. The interaction between lignite molecules and gas molecules was described by the Lennard-Jones (LJ) 12-6 electric potentials [39]. Meanwhile, classical Metropolis rules were used to accept or reject production, disappear, translation, and rotation of gas micromolecules to assure that the system is at the lowest energy state [40]. The temperature in simulation was cycled five times automatically. Step length was adjusted and calculated automatically. The whole simulation involved 2×107 Monte Carlo steps. The first 107 steps were set to reach the adsorption equilibrium of the system, while the rest 107 steps were for sampling and statistics of relevant thermodynamic parameters.This work is to construct an optimized stable configuration of lignite for adsorbent, and the adsorbates are CH4, CO2, and H2O molecules. The simulation adopted 0.00 MPa~10.00 MPa pressure and periodic boundary conditions. Two situations were involved in the simulation:
(1)
The adsorption characteristics of CH4, CO2, and H2O in lignite molecules under the temperature of 303.15 K were simulated. The saturated adsorption configuration was analyzed, and the evolution laws of energies in the adsorption process were discussed(2)
Effects of simulation temperatures (283.15 K, 303.15 K, and 323.15 K) on CH4, CO2, and H2O in lignite were analyzedThe adsorption capacity gained in the simulation refers to the number of gas molecules adsorbed in a single unit cell. Its unit is moleculars/u.c., but the unit of adsorption capacity in a conventional experiment is cm3/g. These adsorption capacities in different units can be converted according to the following formula:
(9)1moleculars/u.c.=1/N×103÷M=1/N÷M×Vmol,where N is the Avogadro’s constant which values 6.02×1023. M refers to the mass of a single unit cell, and it is 4.08017×10−21 g. Vmol refers to the molar volume of gas under standard conditions, and it is 22.4×103 cm3/mol.


## 3. Results and Discussion

### 3.1. Adsorption Isotherms and Adsorption Capacity

The adsorption performance of coal is usually expressed by the adsorption isotherm of coal. The adsorption isotherm refers to the curve of the change of coal’s adsorption gas volume with gas pressure at a certain fixed temperature. A large number of research results at home and abroad show that when coal adsorbs gas, the adsorption isotherm conforms to the Langmuir adsorption equation expressed as(10)V=abp1+bp,where V is adsorption capacity (cm3/g), a is Langmuir adsorption constant (cm3/g), b is Langmuir adsorption constant (1/MPa), and p is gas pressure (MPa).Firstly, GCMC molecular simulation on adsorption isotherm of single pure CH4, CO2, or H2O was carried out under 303.15 K and 0.00 MPa~10.00 MPa. Results are shown in Figure 4.Figure 4
Adsorption isotherms of lignite on CH4, CO2, and H2O.Evident differences in adsorption capacities of CH4, CO2, and H2O in lignite are observed in Figure 4. In particular, with the increase in adsorption pressure, the adsorption capacity soars up in the low-pressure stage. However, such growth rate declines significantly when the adsorption pressure reaches a fixed value. This indicates that the pressure can promote adsorption behavior. In view of the upward trend of adsorption capacity of lignite per unit mass, the H2O adsorption in lignite is significantly faster than those of CO2 and CH4 in the low-pressure stage. The CO2 adsorption in lignite is the second fast, and the CH4 adsorption is the slowest. In the high-pressure stage, the adsorption rates of CH4, CO2, and H2O in lignite tend to be stable. The simulation results could describe adsorption characteristics of CH4, CO2, and H2O on the lignite surface well by using the Langmuir equation. The gained isothermal curves show good “I-type” characteristics [41], which conform to previous research results [21, 22, 42]. It can be seen from Figure 4 that given the same temperature and pressure, the ultimate adsorption capacities of CH4, CO2, and H2O in lignite per unit mass observe the laws of H2O>CO2>CH4. This was consistent with previous research results based on simulation [16, 17, 21, 26].


### 3.2. Adsorption Saturation Configuration

The saturated molecular configuration of lignite molecules cannot be displayed clearly due to the influences of a single unit cell. The molecular configuration of the unit cell was extended for one time along the directionAB through the task term “supercell” in the Build module of MS software. The molecular configuration of CH4, CO2, and H2O in lignite molecular cells was observed from a different perspective.The saturated molecular configurations of CH4, CO2, and H2O adsorption in lignite molecules are shown in Figure 5. Distributions of the adsorbed CH4, CO2, and H2O molecules in lignite molecules can be seen clearly, and all adsorbate molecules distribute at two sides of the lignite molecular chain. Specifically, CH4 molecules are in clustering distribution and present the conformation of pairwise crossing ethane. CO2 molecules are in parallel or crossing and even vertical arrangement. For the H2O molecules, the hydrogen atoms point to the coal molecules or oxygen atoms in surrounding H2O molecules as a response to the hydrogen bond energy.Figure 5
Saturated adsorption configuration of CH4, CO2, and H2O adsorbed on lignite. Color scheme: C: black; H: gray; O: red; N: blue; S: yellow.
(a)
Saturated adsorption configuration of CH4(b)
Saturated adsorption configuration of CO2(c)
Saturated adsorption configuration of H2OUnder the same condition, the adsorbed quantities of CH4, CO2, and H2O in the saturated configuration of lignite vary. The adsorbed quantity of H2O is far higher than those of CH4 and CO2, and the adsorbed quantity of CO2 is higher than that of CH4, indicating that CO2 adsorption is more advantageous than CH4 adsorption in lignite. With respect to the adsorbed quantity of CH4, CO2, and H2O, there is a law of H2O>CO2>CH4, which conforms to the variation law of isothermal adsorption curves gained from simulation.For coal molecules with fixed pore diameter distributions, the MD diameters of adsorbates (0.38 nm, 0.33 nm, and 0.265 nm for CH4, CO2, and H2O molecules) determine their adsorption behaviors in coals. Only when coals with pore diameter larger than the diameter of adsorbates can the adsorbates be absorbed effectively [26]. When lignite adsorbs CH4, CO2, and H2O, it is found that molecular diameter is inversely proportional to adsorption capacity. This proves that the adsorption capacity of H2O in lignite is higher than those of CH4 and CO2. In fact, the interaction between lignite molecules and H2O molecules is stronger in the adsorption process, which is mainly caused by different interaction energies during gas molecular adsorption in lignite.


### 3.3. Adsorption Energy

During the simulation process, the energy of the unit cell system after every adding of adsorbate molecules can be recorded. This energy is the difference between energy of the adsorption composite structure and energies of adsorbents and adsorbates. The adsorption energy can be calculated according to(11)ΔEads=Eadsorbent/adsorbate−Eadsorbent−Eadsorbate,where ΔEads is the adsorption energy of adsorbates after the occurrence of adsorption; Eadsorbent/adsorbate is the total energy of the whole adsorption system after the occurrence of adsorption behaviors; Eadsorbent is the energy of adsorbent before adsorption, that is, energy of lignite cell model; and Eadsorbate is the energy of adsorbates before adsorption, which refers to energies of CH4, CO2, and H2O molecular models.Heats are released during gas molecule adsorption, thus resulting in the decreasing energy of the whole system. With the increase in the number of adsorbate molecules, the total system energy after adsorption presents a downward trend until reaching the minimum. Subsequently, no adsorption occurs by adding adsorbate molecules. Instead, there are molecular repulsions and the total system energy increases gradually. The number of adsorbate molecules when the total system energy is the lowest refers to the saturated adsorption capacity of the adsorbate.


#### 3.3.1. Energy Change of Adsorbed CH4 Gas Molecules

It can be seen from Figure6 that Ec and Ev play positive roles in the adsorption process of CH4 before saturated adsorption in lignite molecular cells. However, Ec makes a tiny contribution, and Ev takes the dominant role in the adsorption of CH4. The total system energy reaches the lowest, and the system achieves the saturation state after the unit cell adsorbs 7 CH4 molecules. Subsequently, the adsorption system begins to repel CH4 molecules after adding gas molecules.Figure 6
Energy changes during unit cell adsorption of different amounts of CH4 molecules.


#### 3.3.2. Energy Change of Adsorbed CO2 Gas Molecules

It can be seen from Figure7 that Ec, Ev, and Eb‐H play positive roles in the adsorption process of CO2 before saturated adsorption in lignite molecular cells. However, Eb‐H makes a tiny contribution, while Ec and Ev take the dominant role in the adsorption of CO2. The total system energy reaches the lowest and the system achieves the saturation state after the unit cell adsorbs 9 CO2 molecules. Subsequently, the adsorption system begins to repel CO2 molecules after adding gas molecules.Figure 7
Energy changes during unit cell adsorption of different amounts of CO2 molecules.


#### 3.3.3. Energy Change of Adsorbed H2O Gas Molecules

It can be seen from Figure8 that the changes of system energy during H2O adsorption in lignite molecular cells are more complicated. Ec is the primary contributor to system energy, followed by Eb‐H. The contribution of Ev is basically zero before the adsorbed quantity of H2O molecules is lower than 12. After the adsorbed quantity of H2O is higher than 12, Ev becomes negative energy against adsorption of H2O molecules. Such repulsion effect increases with the increase of adsorbed quantity of H2O molecules until reaching saturated adsorption. Although Ev hinders adsorption, the growth amplitude of the sum of Ec and Eb−H which are positive to the adsorption is higher than the growth amplitude of Ev, thus keeping the adsorption. The total system energy reaches the lowest, and the system achieves the saturation state after the unit cell adsorbs 27 H2O molecules. Subsequently, the adsorption system begins to repel H2O molecules after adding gas molecules. During the repulsive interaction stage, Ec and Eb‐H are major repulsive energies, while Ev turns to be the energy that consumes repulsion effect.Figure 8
Energy changes during unit cell adsorption of different amounts of H2O molecules.According to system energy changes during CH4, CO2, and H2O adsorption in lignite molecules, it can be seen that
(1)
system energies after CH4, CO2, and H2O adsorption in lignite molecules drop significantly. With respect to the reduction amplitudes, there is a law of H2O>CO2>CH4, indicating that H2O adsorption capacity in coals is the highest, followed by adsorption capacities of CO2 and CH4 [14, 17, 21, 23, 26](2)
single ignite molecular cells reach the saturated adsorption state and the system energy is the lowest after adsorbing 7 CH4 molecules, 9 CO2 molecules, or 27 H2O molecules. With continuous adding of adsorbate molecules, the adsorption system begins to repel gas molecules and the total system energy increases gradually [21](3)
in the process of CH4, CO2, and H2O adsorption in lignite molecules, adsorption of CH4 and CO2 is typical physical adsorptions. The adsorption energy of CH4 is provided by Ev in the nonbonding energy, while the adsorption energy of CO2 is provided by Ec and Ev in the nonbonding energy together. Adsorption of H2O involves both chemical and physical adsorptions, and the adsorption energy of H2O is attributed to both nonbonding energy and Eb‐H. This conforms to previous research conclusions [23, 43–45]


### 3.4. Effects of Temperature on Adsorption Behaviors

Isothermal curves of CH4, CO2, and H2O adsorptions in lignite under 0.00~10.00 MPa and at different temperatures (283.15 K, 303.15 K, and 323.15 K) are shown in Figure 9.Figure 9
The lignite adsorption isotherms of CH4, CO2, and H2O at different temperatures.
(a)
The lignite adsorption isotherms of CH4 at different temperatures(b)
The lignite adsorption isotherms of CO2 at different temperatures(c)
The lignite adsorption isotherms of H2O at different temperaturesBased on single-gas adsorption in lignite molecules, it can be seen clearly that temperature can inhibit adsorption. This can be explained as follows. CH4, CO2, and H2O adsorptions in coals which are porous media belong to physical adsorption, and thermal movement of gas molecules is intensified with the increase of system temperature, thus increasing kinetic energy of adsorbate molecules. Under this circumstance, the probability for gas molecules to get rid of binding of adsorption energy increases. In particular, the probability of VDW force which promotes desorption increases, and the difficulties of capturing adsorbed gas molecules on the coal surface are increased, thus reducing adsorbing capacity [44, 46, 47]. Meanwhile, the gas molecular adsorption on the coal surface is a heat-releasing process, and temperature rise is against the heat releasing, which is the reason for decreasing adsorption capacity of lignite [48, 49].


## 3.1. Adsorption Isotherms and Adsorption Capacity

The adsorption performance of coal is usually expressed by the adsorption isotherm of coal. The adsorption isotherm refers to the curve of the change of coal’s adsorption gas volume with gas pressure at a certain fixed temperature. A large number of research results at home and abroad show that when coal adsorbs gas, the adsorption isotherm conforms to the Langmuir adsorption equation expressed as(10)V=abp1+bp,where V is adsorption capacity (cm3/g), a is Langmuir adsorption constant (cm3/g), b is Langmuir adsorption constant (1/MPa), and p is gas pressure (MPa).Firstly, GCMC molecular simulation on adsorption isotherm of single pure CH4, CO2, or H2O was carried out under 303.15 K and 0.00 MPa~10.00 MPa. Results are shown in Figure 4.Figure 4
Adsorption isotherms of lignite on CH4, CO2, and H2O.Evident differences in adsorption capacities of CH4, CO2, and H2O in lignite are observed in Figure 4. In particular, with the increase in adsorption pressure, the adsorption capacity soars up in the low-pressure stage. However, such growth rate declines significantly when the adsorption pressure reaches a fixed value. This indicates that the pressure can promote adsorption behavior. In view of the upward trend of adsorption capacity of lignite per unit mass, the H2O adsorption in lignite is significantly faster than those of CO2 and CH4 in the low-pressure stage. The CO2 adsorption in lignite is the second fast, and the CH4 adsorption is the slowest. In the high-pressure stage, the adsorption rates of CH4, CO2, and H2O in lignite tend to be stable. The simulation results could describe adsorption characteristics of CH4, CO2, and H2O on the lignite surface well by using the Langmuir equation. The gained isothermal curves show good “I-type” characteristics [41], which conform to previous research results [21, 22, 42]. It can be seen from Figure 4 that given the same temperature and pressure, the ultimate adsorption capacities of CH4, CO2, and H2O in lignite per unit mass observe the laws of H2O>CO2>CH4. This was consistent with previous research results based on simulation [16, 17, 21, 26].


## 3.2. Adsorption Saturation Configuration

The saturated molecular configuration of lignite molecules cannot be displayed clearly due to the influences of a single unit cell. The molecular configuration of the unit cell was extended for one time along the directionAB through the task term “supercell” in the Build module of MS software. The molecular configuration of CH4, CO2, and H2O in lignite molecular cells was observed from a different perspective.The saturated molecular configurations of CH4, CO2, and H2O adsorption in lignite molecules are shown in Figure 5. Distributions of the adsorbed CH4, CO2, and H2O molecules in lignite molecules can be seen clearly, and all adsorbate molecules distribute at two sides of the lignite molecular chain. Specifically, CH4 molecules are in clustering distribution and present the conformation of pairwise crossing ethane. CO2 molecules are in parallel or crossing and even vertical arrangement. For the H2O molecules, the hydrogen atoms point to the coal molecules or oxygen atoms in surrounding H2O molecules as a response to the hydrogen bond energy.Figure 5
Saturated adsorption configuration of CH4, CO2, and H2O adsorbed on lignite. Color scheme: C: black; H: gray; O: red; N: blue; S: yellow.
(a)
Saturated adsorption configuration of CH4(b)
Saturated adsorption configuration of CO2(c)
Saturated adsorption configuration of H2OUnder the same condition, the adsorbed quantities of CH4, CO2, and H2O in the saturated configuration of lignite vary. The adsorbed quantity of H2O is far higher than those of CH4 and CO2, and the adsorbed quantity of CO2 is higher than that of CH4, indicating that CO2 adsorption is more advantageous than CH4 adsorption in lignite. With respect to the adsorbed quantity of CH4, CO2, and H2O, there is a law of H2O>CO2>CH4, which conforms to the variation law of isothermal adsorption curves gained from simulation.For coal molecules with fixed pore diameter distributions, the MD diameters of adsorbates (0.38 nm, 0.33 nm, and 0.265 nm for CH4, CO2, and H2O molecules) determine their adsorption behaviors in coals. Only when coals with pore diameter larger than the diameter of adsorbates can the adsorbates be absorbed effectively [26]. When lignite adsorbs CH4, CO2, and H2O, it is found that molecular diameter is inversely proportional to adsorption capacity. This proves that the adsorption capacity of H2O in lignite is higher than those of CH4 and CO2. In fact, the interaction between lignite molecules and H2O molecules is stronger in the adsorption process, which is mainly caused by different interaction energies during gas molecular adsorption in lignite.


## 3.3. Adsorption Energy

During the simulation process, the energy of the unit cell system after every adding of adsorbate molecules can be recorded. This energy is the difference between energy of the adsorption composite structure and energies of adsorbents and adsorbates. The adsorption energy can be calculated according to(11)ΔEads=Eadsorbent/adsorbate−Eadsorbent−Eadsorbate,where ΔEads is the adsorption energy of adsorbates after the occurrence of adsorption; Eadsorbent/adsorbate is the total energy of the whole adsorption system after the occurrence of adsorption behaviors; Eadsorbent is the energy of adsorbent before adsorption, that is, energy of lignite cell model; and Eadsorbate is the energy of adsorbates before adsorption, which refers to energies of CH4, CO2, and H2O molecular models.Heats are released during gas molecule adsorption, thus resulting in the decreasing energy of the whole system. With the increase in the number of adsorbate molecules, the total system energy after adsorption presents a downward trend until reaching the minimum. Subsequently, no adsorption occurs by adding adsorbate molecules. Instead, there are molecular repulsions and the total system energy increases gradually. The number of adsorbate molecules when the total system energy is the lowest refers to the saturated adsorption capacity of the adsorbate.


### 3.3.1. Energy Change of Adsorbed CH4 Gas Molecules

It can be seen from Figure6 that Ec and Ev play positive roles in the adsorption process of CH4 before saturated adsorption in lignite molecular cells. However, Ec makes a tiny contribution, and Ev takes the dominant role in the adsorption of CH4. The total system energy reaches the lowest, and the system achieves the saturation state after the unit cell adsorbs 7 CH4 molecules. Subsequently, the adsorption system begins to repel CH4 molecules after adding gas molecules.Figure 6
Energy changes during unit cell adsorption of different amounts of CH4 molecules.


### 3.3.2. Energy Change of Adsorbed CO2 Gas Molecules

It can be seen from Figure7 that Ec, Ev, and Eb‐H play positive roles in the adsorption process of CO2 before saturated adsorption in lignite molecular cells. However, Eb‐H makes a tiny contribution, while Ec and Ev take the dominant role in the adsorption of CO2. The total system energy reaches the lowest and the system achieves the saturation state after the unit cell adsorbs 9 CO2 molecules. Subsequently, the adsorption system begins to repel CO2 molecules after adding gas molecules.Figure 7
Energy changes during unit cell adsorption of different amounts of CO2 molecules.


### 3.3.3. Energy Change of Adsorbed H2O Gas Molecules

It can be seen from Figure8 that the changes of system energy during H2O adsorption in lignite molecular cells are more complicated. Ec is the primary contributor to system energy, followed by Eb‐H. The contribution of Ev is basically zero before the adsorbed quantity of H2O molecules is lower than 12. After the adsorbed quantity of H2O is higher than 12, Ev becomes negative energy against adsorption of H2O molecules. Such repulsion effect increases with the increase of adsorbed quantity of H2O molecules until reaching saturated adsorption. Although Ev hinders adsorption, the growth amplitude of the sum of Ec and Eb−H which are positive to the adsorption is higher than the growth amplitude of Ev, thus keeping the adsorption. The total system energy reaches the lowest, and the system achieves the saturation state after the unit cell adsorbs 27 H2O molecules. Subsequently, the adsorption system begins to repel H2O molecules after adding gas molecules. During the repulsive interaction stage, Ec and Eb‐H are major repulsive energies, while Ev turns to be the energy that consumes repulsion effect.Figure 8
Energy changes during unit cell adsorption of different amounts of H2O molecules.According to system energy changes during CH4, CO2, and H2O adsorption in lignite molecules, it can be seen that
(1)
system energies after CH4, CO2, and H2O adsorption in lignite molecules drop significantly. With respect to the reduction amplitudes, there is a law of H2O>CO2>CH4, indicating that H2O adsorption capacity in coals is the highest, followed by adsorption capacities of CO2 and CH4 [14, 17, 21, 23, 26](2)
single ignite molecular cells reach the saturated adsorption state and the system energy is the lowest after adsorbing 7 CH4 molecules, 9 CO2 molecules, or 27 H2O molecules. With continuous adding of adsorbate molecules, the adsorption system begins to repel gas molecules and the total system energy increases gradually [21](3)
in the process of CH4, CO2, and H2O adsorption in lignite molecules, adsorption of CH4 and CO2 is typical physical adsorptions. The adsorption energy of CH4 is provided by Ev in the nonbonding energy, while the adsorption energy of CO2 is provided by Ec and Ev in the nonbonding energy together. Adsorption of H2O involves both chemical and physical adsorptions, and the adsorption energy of H2O is attributed to both nonbonding energy and Eb‐H. This conforms to previous research conclusions [23, 43–45]


## 3.3.1. Energy Change of Adsorbed CH4 Gas Molecules

It can be seen from Figure6 that Ec and Ev play positive roles in the adsorption process of CH4 before saturated adsorption in lignite molecular cells. However, Ec makes a tiny contribution, and Ev takes the dominant role in the adsorption of CH4. The total system energy reaches the lowest, and the system achieves the saturation state after the unit cell adsorbs 7 CH4 molecules. Subsequently, the adsorption system begins to repel CH4 molecules after adding gas molecules.Figure 6
Energy changes during unit cell adsorption of different amounts of CH4 molecules.


## 3.3.2. Energy Change of Adsorbed CO2 Gas Molecules

It can be seen from Figure7 that Ec, Ev, and Eb‐H play positive roles in the adsorption process of CO2 before saturated adsorption in lignite molecular cells. However, Eb‐H makes a tiny contribution, while Ec and Ev take the dominant role in the adsorption of CO2. The total system energy reaches the lowest and the system achieves the saturation state after the unit cell adsorbs 9 CO2 molecules. Subsequently, the adsorption system begins to repel CO2 molecules after adding gas molecules.Figure 7
Energy changes during unit cell adsorption of different amounts of CO2 molecules.


## 3.3.3. Energy Change of Adsorbed H2O Gas Molecules

It can be seen from Figure8 that the changes of system energy during H2O adsorption in lignite molecular cells are more complicated. Ec is the primary contributor to system energy, followed by Eb‐H. The contribution of Ev is basically zero before the adsorbed quantity of H2O molecules is lower than 12. After the adsorbed quantity of H2O is higher than 12, Ev becomes negative energy against adsorption of H2O molecules. Such repulsion effect increases with the increase of adsorbed quantity of H2O molecules until reaching saturated adsorption. Although Ev hinders adsorption, the growth amplitude of the sum of Ec and Eb−H which are positive to the adsorption is higher than the growth amplitude of Ev, thus keeping the adsorption. The total system energy reaches the lowest, and the system achieves the saturation state after the unit cell adsorbs 27 H2O molecules. Subsequently, the adsorption system begins to repel H2O molecules after adding gas molecules. During the repulsive interaction stage, Ec and Eb‐H are major repulsive energies, while Ev turns to be the energy that consumes repulsion effect.Figure 8
Energy changes during unit cell adsorption of different amounts of H2O molecules.According to system energy changes during CH4, CO2, and H2O adsorption in lignite molecules, it can be seen that
(1)
system energies after CH4, CO2, and H2O adsorption in lignite molecules drop significantly. With respect to the reduction amplitudes, there is a law of H2O>CO2>CH4, indicating that H2O adsorption capacity in coals is the highest, followed by adsorption capacities of CO2 and CH4 [14, 17, 21, 23, 26](2)
single ignite molecular cells reach the saturated adsorption state and the system energy is the lowest after adsorbing 7 CH4 molecules, 9 CO2 molecules, or 27 H2O molecules. With continuous adding of adsorbate molecules, the adsorption system begins to repel gas molecules and the total system energy increases gradually [21](3)
in the process of CH4, CO2, and H2O adsorption in lignite molecules, adsorption of CH4 and CO2 is typical physical adsorptions. The adsorption energy of CH4 is provided by Ev in the nonbonding energy, while the adsorption energy of CO2 is provided by Ec and Ev in the nonbonding energy together. Adsorption of H2O involves both chemical and physical adsorptions, and the adsorption energy of H2O is attributed to both nonbonding energy and Eb‐H. This conforms to previous research conclusions [23, 43–45]


## 3.4. Effects of Temperature on Adsorption Behaviors

Isothermal curves of CH4, CO2, and H2O adsorptions in lignite under 0.00~10.00 MPa and at different temperatures (283.15 K, 303.15 K, and 323.15 K) are shown in Figure 9.Figure 9
The lignite adsorption isotherms of CH4, CO2, and H2O at different temperatures.
(a)
The lignite adsorption isotherms of CH4 at different temperatures(b)
The lignite adsorption isotherms of CO2 at different temperatures(c)
The lignite adsorption isotherms of H2O at different temperaturesBased on single-gas adsorption in lignite molecules, it can be seen clearly that temperature can inhibit adsorption. This can be explained as follows. CH4, CO2, and H2O adsorptions in coals which are porous media belong to physical adsorption, and thermal movement of gas molecules is intensified with the increase of system temperature, thus increasing kinetic energy of adsorbate molecules. Under this circumstance, the probability for gas molecules to get rid of binding of adsorption energy increases. In particular, the probability of VDW force which promotes desorption increases, and the difficulties of capturing adsorbed gas molecules on the coal surface are increased, thus reducing adsorbing capacity [44, 46, 47]. Meanwhile, the gas molecular adsorption on the coal surface is a heat-releasing process, and temperature rise is against the heat releasing, which is the reason for decreasing adsorption capacity of lignite [48, 49].


## 4. Conclusions

In this work, adsorption characteristics of CH4, CO2, and H2O molecules in lignite are discussed through a simulation. The selection optimization and simulation methods of the lignite molecular models are elaborated thoroughly. Moreover, adsorption capacities of CH4, CO2, and H2O in lignite molecules, saturated molecular configuration, evolutions of adsorption energies, and influences of temperature on adsorption behavior are analyzed. Some major conclusions could be drawn:
(1)
The classical Wiser model can reflect the basic features of low-metamorphism lignite comprehensively. After molecular dynamics optimization and annealing process, the lignite molecular structure becomes more compacted and has stronger stereo perception. Based on a density energy simulation, the constructed lignite molecular model is proved applicable to simulation of adsorption characteristics(2)
Adsorption capacities of CH4, CO2, and H2O in lignite are significantly different. Given the same temperature and pressure, H2O shows the highest ultimate adsorption capacity of these three gases in unit mass of lignite, followed by CO2 and CH4 successively. The isothermal curves present well “I-type” characteristics(3)
A single lignite molecular cell reaches saturated adsorption upon 7 CH4 molecules, 9 CO2 molecules, or 27 H2O molecules. The molecular configurations of lignite molecules to CH4, CO2, and H2O gases are extracted, finding that all gas molecules distribute at two sides of the lignite molecular chain. Specifically, CH4 molecules are in clustering distributions and form a pairwise crossing ethane conformation. CO2 molecules are in parallel or crossing and even vertical arrangement. H2O molecules point to the coal molecules or oxygen atoms in surrounding H2O molecules as a response to the hydrogen bond energies(4)
The CH4 and CO2 adsorptions in lignite are typical physical adsorption, and adsorption energies are provided by nonbonding energies. However, H2O adsorption involves both physical and chemical adsorptions, with adsorption energies provided by both nonbonding energy and hydrogen bond energy(5)
Temperature can inhibit adsorption of lignite since CH4 CO2 and H2O adsorptions in lignite are physical adsorptions. With the increase of temperature, thermal movement of gas molecules is intensified. As a result, kinetic energy of adsorbate molecules increases, and the difficulties of adsorbed gas molecules are increased. Temperature rise is not in favor of the adsorption-induced heat releasing



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*Source: 5535321-2021-03-20.xml*