# Adsorption Equilibrium and Thermodynamic Analysis of CO2 and CH4 on Qinshui Basin Anthracite

Authors: Xidong Du; Tengfei Wu; Fulong Sun; Zhenkun Hou; Zhenjian Liu; Liang Huo; Yu Hao; Yuan Zhao
Journal: Geofluids
 (2019)

---

## Abstract

Adsorption isotherms of CH4 and CO2 on Qinshui Basin anthracite were obtained at the temperatures of 283 K, 303 K, and 323 K using the gravimetric method. The feasibility of the displacement of CH4 by injecting CO2 on this anthracite was verified by calculating the selectivity factor of CO2 over CH4 (αCO2/CH4), adsorption affinities, and thermodynamic properties of CH4 and CO2. Results show that the values of αCO2/CH4 are more than 4.0. Henry’s constant (KH) of CH4 is smaller than that of CO2, and CH4 has a weaker affinity with coal surface. As temperature improves, KH of CO2 and CH4 decrease. Gibbs free energy change (ΔG) and surface potential (Ω) of CO2 are more negative than those of CH4, indicating that CO2 adsorption on anthracite is more spontaneous and favorable. The absolute values of Ω and ΔG of CH4 and CO2 increase with pressure rises. Isosteric heat of adsorption (Qst) of CH4 is lower than that of CO2. With increasing loading, Qst and entropy loss (ΔS) of CH4 decrease, while Qst and ΔS of CO2 increase. The higher ΔS of CO2 reveals that the adsorbed CO2 molecules constitute a more stable rearrangement than CH4 molecules. High temperature reduces ΔS of CH4 and CO2.


---

## Body

## 1. Introduction

In the last few decades, coalbed methane has gradually grown in significance as an alternative to conventional natural gas resource due to its low pollution, abundant reserves, and wide distribution [1]. Meanwhile, coalbed methane is deemed as a dangerous gas for the underground coal mining activity, as the release of CH4 during coal mining process can potentially result in the risk of gas explosion and coal and gas outburst [2]. The effective exploitation and disposition of coalbed methane is essential for the safe mining of coal. With the worsening of the global greenhouse effect, the sequestration of anthropogenic CO2 into deep geological formations, such as deep unmineable coal seams, saline aquifers, depleted oil and gas reservoirs, and shale gas sediments, has received lots of attention [3–6]. Based on the higher adsorption affinity of CO2 over CH4 on coal surface, injected CO2 can competitively displace the preadsorbed CH4 out of micropores and subsequently stay in the fracture and coal matrix [4], which is a promising technology that has the benefits of enhanced coal methane recovery and CO2 sequestration in a geological time scale.The underlying principle of the technology of enhanced coal methane recovery by CO2 injection (CO2-ECBM) is the competitive adsorption between injected CO2 and preadsorbed CH4. More than 80% of coalbed methane is stored in the form of adsorbed gas [7]. Investigation about the adsorption performances of CH4 and CO2 on coal could provide useful information to understand the adsorption mechanisms of CH4 and CO2 and verify the feasibility of the technology of CO2-ECBM. To date, many studies have addressed the adsorption behaviors of CH4 and CO2 on different rank coals by the means of laboratory experiment and numerical simulation analysis [2, 8–17]. Their results indicate that the adsorption amount and adsorption rate of CO2 on coal are larger than those of CH4 [2, 13, 16]. The adsorption abilities of CH4 and CO2 on coal are tightly related to the reservoir condition (pressure, temperature, and effective stress) and the physical-chemical property of coal (mineral composition, total organic carbon content, ash content, pore structure, surface functional group, and moisture content) [8–12, 14, 16, 17]. Various adsorption models including the Langmuir model, Brunauer-Emmett-Teller (BET) model, and pore-filling model are capable of dealing with the adsorption data of CH4 and CO2 on coal [2, 14, 15, 17, 18]. The values of selectivity factor of CO2 over CH4, which is a key indicator to assess the displacement efficiency of CO2, are all higher than one on different rank coals [8, 13, 15–18].Adsorption processes are often accompanied by heat generation and changes in the entropy and enthalpy of the adsorption system. Research about the interaction between coal matrix surface and adsorbate molecule from the thermodynamic point of view is conducive to comprehending the intrinsic adsorption mechanisms of CH4 and CO2 on coal. The adsorption thermodynamic properties viz., isosteric heat of adsorption (Qst), surface potential (Ω), Gibbs free energy change (ΔG), enthalpy change (ΔH), and entropy change (ΔS), have specific physical meaning to illustrate the adsorption phenomenon. At present, the thermodynamics of adsorption of CH4 and CO2 on porous materials, such as shale, carbon molecular sieves, activated carbon fiber, and zeolite 13X, have been analyzed [19–22]. Duan et al. [19] investigated the thermodynamics of CH4 and CO2 on Sichuan Basin marine shale. They found that the absolute values of entropy loss, Gibbs free energy change, and surface potential of CO2 are bigger than those of CH4, and CO2 molecules constitute a more stable and ordered arrangement on matrix surface. Song et al. [20] conducted the thermodynamic analysis of CH4 and CO2 on three carbon molecular sieves. Their results indicated that with increasing surface coverage, the absolute value of entropy change rises, while the absolute value of Gibbs free energy reduces. Zhou et al. [21] discussed the thermodynamic characteristic of CO2 on activated carbon fiber and suggested that the Gibbs free energy change of CO2 increases smoothly over the whole pressure range, whereas the entropy loss decreases continuously. Mofarahi and Bakhtyari [22] estimated the thermodynamic parameters of CH4 on zeolite 13X. They observed that adsorption loading has no influence on the isosteric adsorption heat of CH4 at lower degree of coverage, and the absolute values of Gibbs free energy and surface potential increase with enhancing equilibrium pressure.There are also some studies on the thermodynamic behaviors of CH4 and CO2 on coal [13, 14, 23, 24]. Busch and Gensterblum [14] revealed that the isosteric adsorption heats of CH4 and CO2 on coal both gradually reduce with the increase of moisture content. Zhou et al. [23] discovered that the change of Gibbs free energy after CO2 adsorption on coal is higher than that after CH4 adsorption, and the initial isosteric adsorption heats of CO2 and CH4 are 48.2 and 33.4 kJ/mol, respectively. Dong et al. [24] performed a molecular simulation study about the adsorption of CH4 and CO2 on middle-rank coal, and reported that with the increase of sorption loading, Qst of CO2 and CH4 reduce at first, and then slowly rise. In addition, Qst of CH4 is lower than that of CO2 at the same adsorbed density. You et al. [13] researched the adsorption behaviors of CH4, CO2, and their mixtures on bituminous coal by the means of numerical simulation. Their results showed that Qst of CH4 and CO2 both decrease with increasing adsorption amount, and this decline is due to the presence of heteroatom functional groups. Apparently, the thermodynamic characteristics of CH4 and CO2 on coal, especially the surface potential and entropy change, require further study. Therefore, it is of fundamental importance to perform the detailed thermodynamic analysis of CO2 and CH4 on coal.In this paper, the adsorption isotherms of CH4 and CO2 on anthracite were measured using the accurate gravimetric method at the temperatures of 283 K, 303 K, and 323 K and pressures up to 1.80 MPa. The Langmuir-Freundlich model was adopted to fit the adsorption data. The selectivity factor of CO2 over CH4 on anthracite was predicted based on the single component adsorption isotherm using ideal adsorbed solution theory. Henry’s constant was estimated and used to analyze the affinity between adsorbate and coal matrix surface. Adsorption thermodynamic parameters of CH4 and CO2 on coal were calculated and discussed. This research will lay the foundation for the better understanding of the adsorption mechanisms of CH4 and CO2 on coal and provide guide for the future application of the technology of CO2-ECBM.


## 2. Material and Method

### 2.1. Material Preparation and Characterization

#### 2.1.1. Material Preparation

The Qinshui (QS) anthracite adopted in this study was sampled from the southern district of Qinshui Basin of China at the depth of 350 m. Before measurement and characterization, the bulk coal was crushed and sieved into 0.85 to 0.425 mm particles.


#### 2.1.2. Characterization of Coal Sample

(1) Mesopore and Macropore Morphology Analysis. The mesopore and macropore structures of this anthracite were analyzed with an ASAP 2020M system (Micromeritics Instruments, USA), using a low-pressure N2 adsorption at 77 K. The BET surface area (SBET), macropore volume (Vmac), mesopore volume (Vmes), micropore volume (Vmic), total volume (Vt), and pore size distribution (PSD) were obtained based on N2 adsorption isotherm data.The desorption and adsorption isotherm data of N2 at 77 K are shown in Figure 1(a). The PSD of QS sample determined by N2 adsorption is depicted in Figure 1(b). The estimated mesopore and macropore parameters are listed in Table 1.Figure 1
N2 adsorption and desorption isotherms at 77 K (a) and the pore size distribution of mesopore and macropore (b).
(a)
(b)Table 1
Pore structure parameters of QS sample determined from N2 and CO2 adsorption.
N2 adsorption
CO2 adsorption
SBET (m2/g)
Vmic (cm3/g)
Vmes (cm3/g)
Vmac (cm3/g)
Vt (cm3/g)
SDR (m2/g)
VDR (cm3/g)
0.62
0
0.0018
0.0005
0.0023
58.59
0.023The hysteresis loop between adsorption and desorption curves belongs to type H2 based on the definition of International Union of Pure and Applied Chemistry (IUPAC). The type of this hysteresis loop indicates that the pore of QS anthracite is slit shape. The PSD shown in Figure1(b) indicates that QS anthracite has continuous wide meso/macropore size distribution from 13 nm to 60 nm. In addition, it can be found from Table 1 that QS anthracite has a lot of mesopores (pore size of 2-50 nm) whose volume (Vmes) is much larger than the volume of macropore (Vmac of pore size larger than 50 nm).(2) Micropore Morphology Analysis. The micropore structure of QS sample was also obtained using ASAP 2020M system by CO2 adsorption at 273.15 K. The micropore surface area (SDR) and micropore volume (VDR) were calculated by the Dubinin-Radushkevich (DR) model based on CO2 adsorption data. The micropore size distribution was determined by the nonlocal density functional theory (NLDFT) model.The adsorption isotherm of CO2 at 273.15 K is shown in Figure 2(a). The estimated micropore parameters are listed in Table 1. The micropore size distribution of QS sample determined by CO2 adsorption is depicted in Figure 2(b). We can find that QS anthracite has a broad micropore distribution with major peak at around 0.55 nm.Figure 2
CO2 adsorption isotherm at 273.15 K (a) and micropore size distribution (b).
(a)
(b)It is noticeable that the value ofSDR of 58.59 m2/g is much higher than that of SBET of 0.62 m2/g. Meanwhile, the value of VDR of 0.023 cm3/g is bigger than those of Vmes of 0.0018 cm3/g and Vmac of 0.0005 cm3/g. Therefore, the surface and pore volume of QS anthracite are mainly contributed by micropore, and micropore will provide a large number of adsorption sites for the adsorption of CH4 and CO2 on this anthracite.(3) Ultimate and Proximate Analyses. Ultimate and proximate analyses were used to characterize coal chemical composition. Ultimate analysis was performed by Flash EA2000 elemental analyzer, Thermo Fisher Scientific. The results of ultimate and proximate analyses of this anthracite are given in Table 2. It is clear that carbon, hydrogen, oxygen, and nitrogen are the main elements in coal reservoir, accounting for more than 95% of the total element content.Table 2
Results of ultimate and proximate analyses of QS anthracite.
Sample
Coal rank
Ultimate analysis (wt% daf)
Proximate analysis (wt%)
C
H
N
O
Cfix
Vdaf
Aad
Mad
QS
Anthracite
90.01
3.75
0.94
2.01
70.73
10.42
18.55
3.62
Note:Cfix: fixed carbon; Vdaf: volatile matters; Aad: ash; Mad: moisture.


### 2.2. Adsorption Isotherm Measurement and Simulation

A high-resolution intelligent gravimetric analyzer (IGA-100B, U.K.) was employed to measure the adsorption isotherms of CH4 and CO2 at pressure up to 1.80 MPa and at temperatures of 283 K, 303 K, and 323 K.Adsorption isotherm can offer useful information about the surface property of porous material and the interaction between adsorbent and adsorbate [25]. Meanwhile, adsorption isotherm simulation is of great importance for the prediction of adsorption capacity and the interpretation of adsorption mechanism. In this study, the Langmuir-Freundlich (L-F) model was applied to simulate the adsorption data of CH4 and CO2. The L-F model is described in the following form [26]:
(1)q=qmbPc1+bPc,where q is the adsorption amount at pressure P; qm is the saturation adsorption capacity of adsorption sites; b is the affinity coefficient of adsorption sites; and c is equal to 1/n, where n is the deviation from an ideal homogenous surface.


### 2.3. Ideal Adsorbed Solution Theory

The adsorption of binary gas mixtures can be directly predicted from pure component adsorption data using ideal adsorbed solution theory (IAST) proposed by Myers and Prausnitz [27]. Many studies have confirmed the effectiveness of IAST to predict the adsorption of mixture gases on a variety of porous materials [28–30].When the adsorption equilibrium of mixture gases is reached, the chemical potential of each component in the adsorbed phase is equal to that of the corresponding component in the gas phase [31]. Based on this criterion of thermodynamics equilibrium, it can be concluded that
(2)Ptyi=Pi0πxi,where Pt is total pressure of adsorption system; yi and xi are the mole fractions of pure component i in the bulk gas phase and the adsorbed phase, respectively; Pi0 is the equilibrium gas phase pressure of component i at the mixture temperature and spreading pressure (π).For the binary mixture gases, the following equations are satisfied [32]:
(3)Pty1=P10x1,Pt1−y1=P201−x1,where y1 and x1 are the mole fractions of component 1 in the bulk phase and adsorbed phase, respectively; P10 and P20 are the equilibrium gas phase pressures of component 1 and component 2 at the mixture temperature and spreading pressure, respectively.The spreading pressureπ and the reduced spreading pressure π∗ are defined by [31]:
(4)π=RTA∫0Pi0qPdP,(5)π∗=AπRT=∫0Pi0qPdP,where T is the temperature, R is the universal gas constant, and A is the surface area of adsorbent per unit mass.Substituting Equation (1) into Equation (5), it can be found that
(6)π∗=1cqmln1+bPi0c.When the adsorption of binary mixture gases reaches equilibrium, the reduced spreading pressures of component 1 and component 2 are equal.(7)π1∗=π2∗,π1∗=1c1qm1ln1+b1P10c1,π2∗=1c2qm2ln1+b2P20c2,where π1∗ and π2∗ are the reduced spreading pressures of component 1 and component 2, respectively; c1 and c2 are the L-F coefficients of component 1 and component 2, respectively; qm1 and qm2 are the saturation adsorption capacities of component 1 and component 2, respectively; b1 and b2 are the affinity coefficients of component 1 and component 2, respectively.Combing Equations (3–7) and (8) leads to:
(8)1c1qm1ln1+b1Pty1x1c1−1c2qm2ln1+b2Pt1−y11−x1c2=0.For the givenPt and y1, the value of x1 can be obtained by Equation (8).The selectivity factorα can be decided by:
(9)α=x1/y1x2/y2,where y2 and x2 are the mole fractions of component 2 in the bulk gas phase and adsorbed phase, respectively.


### 2.4. Henry’s Law Constant

Henry’s constant (KH) can be applied to calculate the affinity between adsorbent surface and adsorbate molecule. Molecule-surface forces predominate at low pressure, and Henry’s constant is directly related to the interaction of matrix surface with adsorbate molecule [33]. A larger KH reflects the stronger affinity between adsorption pair.In order to calculateKH, the relationship between adsorption amount and equilibrium pressure can be expressed by a virial equation [34]:
(10)lnqP=A0+A1q+A2q2+⋯,where A0, A1, and A2 are the virial coefficients. The first virial coefficient A0 is related to Henry’s constant, as KH=expA0. At the low-pressure range, q is small, and the high-order terms in Equation (10) can be neglected. Thus, Equation (10) can be written as follows:
(11)lnPq=−A0−A1q.By fitting the linear region oflnP/q vs. the loading q, A0 and KH can be obtained.


### 2.5. Thermodynamics of Adsorption

The thermodynamic parameters in this paper are calculated using the following equations [19, 22, 35, 36]:
(12)Qst=RT2∂lnP∂Tq,lnP=−QstRT+C,Ω=−RT∫0PqdlnP,ΔG=Ωq=−RT∫0PqdlnPq,ΔH=−Qst,ΔS=ΔH−ΔGT,where C is the integration constant.


## 2.1. Material Preparation and Characterization

### 2.1.1. Material Preparation

The Qinshui (QS) anthracite adopted in this study was sampled from the southern district of Qinshui Basin of China at the depth of 350 m. Before measurement and characterization, the bulk coal was crushed and sieved into 0.85 to 0.425 mm particles.


### 2.1.2. Characterization of Coal Sample

(1) Mesopore and Macropore Morphology Analysis. The mesopore and macropore structures of this anthracite were analyzed with an ASAP 2020M system (Micromeritics Instruments, USA), using a low-pressure N2 adsorption at 77 K. The BET surface area (SBET), macropore volume (Vmac), mesopore volume (Vmes), micropore volume (Vmic), total volume (Vt), and pore size distribution (PSD) were obtained based on N2 adsorption isotherm data.The desorption and adsorption isotherm data of N2 at 77 K are shown in Figure 1(a). The PSD of QS sample determined by N2 adsorption is depicted in Figure 1(b). The estimated mesopore and macropore parameters are listed in Table 1.Figure 1
N2 adsorption and desorption isotherms at 77 K (a) and the pore size distribution of mesopore and macropore (b).
(a)
(b)Table 1
Pore structure parameters of QS sample determined from N2 and CO2 adsorption.
N2 adsorption
CO2 adsorption
SBET (m2/g)
Vmic (cm3/g)
Vmes (cm3/g)
Vmac (cm3/g)
Vt (cm3/g)
SDR (m2/g)
VDR (cm3/g)
0.62
0
0.0018
0.0005
0.0023
58.59
0.023The hysteresis loop between adsorption and desorption curves belongs to type H2 based on the definition of International Union of Pure and Applied Chemistry (IUPAC). The type of this hysteresis loop indicates that the pore of QS anthracite is slit shape. The PSD shown in Figure1(b) indicates that QS anthracite has continuous wide meso/macropore size distribution from 13 nm to 60 nm. In addition, it can be found from Table 1 that QS anthracite has a lot of mesopores (pore size of 2-50 nm) whose volume (Vmes) is much larger than the volume of macropore (Vmac of pore size larger than 50 nm).(2) Micropore Morphology Analysis. The micropore structure of QS sample was also obtained using ASAP 2020M system by CO2 adsorption at 273.15 K. The micropore surface area (SDR) and micropore volume (VDR) were calculated by the Dubinin-Radushkevich (DR) model based on CO2 adsorption data. The micropore size distribution was determined by the nonlocal density functional theory (NLDFT) model.The adsorption isotherm of CO2 at 273.15 K is shown in Figure 2(a). The estimated micropore parameters are listed in Table 1. The micropore size distribution of QS sample determined by CO2 adsorption is depicted in Figure 2(b). We can find that QS anthracite has a broad micropore distribution with major peak at around 0.55 nm.Figure 2
CO2 adsorption isotherm at 273.15 K (a) and micropore size distribution (b).
(a)
(b)It is noticeable that the value ofSDR of 58.59 m2/g is much higher than that of SBET of 0.62 m2/g. Meanwhile, the value of VDR of 0.023 cm3/g is bigger than those of Vmes of 0.0018 cm3/g and Vmac of 0.0005 cm3/g. Therefore, the surface and pore volume of QS anthracite are mainly contributed by micropore, and micropore will provide a large number of adsorption sites for the adsorption of CH4 and CO2 on this anthracite.(3) Ultimate and Proximate Analyses. Ultimate and proximate analyses were used to characterize coal chemical composition. Ultimate analysis was performed by Flash EA2000 elemental analyzer, Thermo Fisher Scientific. The results of ultimate and proximate analyses of this anthracite are given in Table 2. It is clear that carbon, hydrogen, oxygen, and nitrogen are the main elements in coal reservoir, accounting for more than 95% of the total element content.Table 2
Results of ultimate and proximate analyses of QS anthracite.
Sample
Coal rank
Ultimate analysis (wt% daf)
Proximate analysis (wt%)
C
H
N
O
Cfix
Vdaf
Aad
Mad
QS
Anthracite
90.01
3.75
0.94
2.01
70.73
10.42
18.55
3.62
Note:Cfix: fixed carbon; Vdaf: volatile matters; Aad: ash; Mad: moisture.


## 2.1.1. Material Preparation

The Qinshui (QS) anthracite adopted in this study was sampled from the southern district of Qinshui Basin of China at the depth of 350 m. Before measurement and characterization, the bulk coal was crushed and sieved into 0.85 to 0.425 mm particles.


## 2.1.2. Characterization of Coal Sample

(1) Mesopore and Macropore Morphology Analysis. The mesopore and macropore structures of this anthracite were analyzed with an ASAP 2020M system (Micromeritics Instruments, USA), using a low-pressure N2 adsorption at 77 K. The BET surface area (SBET), macropore volume (Vmac), mesopore volume (Vmes), micropore volume (Vmic), total volume (Vt), and pore size distribution (PSD) were obtained based on N2 adsorption isotherm data.The desorption and adsorption isotherm data of N2 at 77 K are shown in Figure 1(a). The PSD of QS sample determined by N2 adsorption is depicted in Figure 1(b). The estimated mesopore and macropore parameters are listed in Table 1.Figure 1
N2 adsorption and desorption isotherms at 77 K (a) and the pore size distribution of mesopore and macropore (b).
(a)
(b)Table 1
Pore structure parameters of QS sample determined from N2 and CO2 adsorption.
N2 adsorption
CO2 adsorption
SBET (m2/g)
Vmic (cm3/g)
Vmes (cm3/g)
Vmac (cm3/g)
Vt (cm3/g)
SDR (m2/g)
VDR (cm3/g)
0.62
0
0.0018
0.0005
0.0023
58.59
0.023The hysteresis loop between adsorption and desorption curves belongs to type H2 based on the definition of International Union of Pure and Applied Chemistry (IUPAC). The type of this hysteresis loop indicates that the pore of QS anthracite is slit shape. The PSD shown in Figure1(b) indicates that QS anthracite has continuous wide meso/macropore size distribution from 13 nm to 60 nm. In addition, it can be found from Table 1 that QS anthracite has a lot of mesopores (pore size of 2-50 nm) whose volume (Vmes) is much larger than the volume of macropore (Vmac of pore size larger than 50 nm).(2) Micropore Morphology Analysis. The micropore structure of QS sample was also obtained using ASAP 2020M system by CO2 adsorption at 273.15 K. The micropore surface area (SDR) and micropore volume (VDR) were calculated by the Dubinin-Radushkevich (DR) model based on CO2 adsorption data. The micropore size distribution was determined by the nonlocal density functional theory (NLDFT) model.The adsorption isotherm of CO2 at 273.15 K is shown in Figure 2(a). The estimated micropore parameters are listed in Table 1. The micropore size distribution of QS sample determined by CO2 adsorption is depicted in Figure 2(b). We can find that QS anthracite has a broad micropore distribution with major peak at around 0.55 nm.Figure 2
CO2 adsorption isotherm at 273.15 K (a) and micropore size distribution (b).
(a)
(b)It is noticeable that the value ofSDR of 58.59 m2/g is much higher than that of SBET of 0.62 m2/g. Meanwhile, the value of VDR of 0.023 cm3/g is bigger than those of Vmes of 0.0018 cm3/g and Vmac of 0.0005 cm3/g. Therefore, the surface and pore volume of QS anthracite are mainly contributed by micropore, and micropore will provide a large number of adsorption sites for the adsorption of CH4 and CO2 on this anthracite.(3) Ultimate and Proximate Analyses. Ultimate and proximate analyses were used to characterize coal chemical composition. Ultimate analysis was performed by Flash EA2000 elemental analyzer, Thermo Fisher Scientific. The results of ultimate and proximate analyses of this anthracite are given in Table 2. It is clear that carbon, hydrogen, oxygen, and nitrogen are the main elements in coal reservoir, accounting for more than 95% of the total element content.Table 2
Results of ultimate and proximate analyses of QS anthracite.
Sample
Coal rank
Ultimate analysis (wt% daf)
Proximate analysis (wt%)
C
H
N
O
Cfix
Vdaf
Aad
Mad
QS
Anthracite
90.01
3.75
0.94
2.01
70.73
10.42
18.55
3.62
Note:Cfix: fixed carbon; Vdaf: volatile matters; Aad: ash; Mad: moisture.


## 2.2. Adsorption Isotherm Measurement and Simulation

A high-resolution intelligent gravimetric analyzer (IGA-100B, U.K.) was employed to measure the adsorption isotherms of CH4 and CO2 at pressure up to 1.80 MPa and at temperatures of 283 K, 303 K, and 323 K.Adsorption isotherm can offer useful information about the surface property of porous material and the interaction between adsorbent and adsorbate [25]. Meanwhile, adsorption isotherm simulation is of great importance for the prediction of adsorption capacity and the interpretation of adsorption mechanism. In this study, the Langmuir-Freundlich (L-F) model was applied to simulate the adsorption data of CH4 and CO2. The L-F model is described in the following form [26]:
(1)q=qmbPc1+bPc,where q is the adsorption amount at pressure P; qm is the saturation adsorption capacity of adsorption sites; b is the affinity coefficient of adsorption sites; and c is equal to 1/n, where n is the deviation from an ideal homogenous surface.


## 2.3. Ideal Adsorbed Solution Theory

The adsorption of binary gas mixtures can be directly predicted from pure component adsorption data using ideal adsorbed solution theory (IAST) proposed by Myers and Prausnitz [27]. Many studies have confirmed the effectiveness of IAST to predict the adsorption of mixture gases on a variety of porous materials [28–30].When the adsorption equilibrium of mixture gases is reached, the chemical potential of each component in the adsorbed phase is equal to that of the corresponding component in the gas phase [31]. Based on this criterion of thermodynamics equilibrium, it can be concluded that
(2)Ptyi=Pi0πxi,where Pt is total pressure of adsorption system; yi and xi are the mole fractions of pure component i in the bulk gas phase and the adsorbed phase, respectively; Pi0 is the equilibrium gas phase pressure of component i at the mixture temperature and spreading pressure (π).For the binary mixture gases, the following equations are satisfied [32]:
(3)Pty1=P10x1,Pt1−y1=P201−x1,where y1 and x1 are the mole fractions of component 1 in the bulk phase and adsorbed phase, respectively; P10 and P20 are the equilibrium gas phase pressures of component 1 and component 2 at the mixture temperature and spreading pressure, respectively.The spreading pressureπ and the reduced spreading pressure π∗ are defined by [31]:
(4)π=RTA∫0Pi0qPdP,(5)π∗=AπRT=∫0Pi0qPdP,where T is the temperature, R is the universal gas constant, and A is the surface area of adsorbent per unit mass.Substituting Equation (1) into Equation (5), it can be found that
(6)π∗=1cqmln1+bPi0c.When the adsorption of binary mixture gases reaches equilibrium, the reduced spreading pressures of component 1 and component 2 are equal.(7)π1∗=π2∗,π1∗=1c1qm1ln1+b1P10c1,π2∗=1c2qm2ln1+b2P20c2,where π1∗ and π2∗ are the reduced spreading pressures of component 1 and component 2, respectively; c1 and c2 are the L-F coefficients of component 1 and component 2, respectively; qm1 and qm2 are the saturation adsorption capacities of component 1 and component 2, respectively; b1 and b2 are the affinity coefficients of component 1 and component 2, respectively.Combing Equations (3–7) and (8) leads to:
(8)1c1qm1ln1+b1Pty1x1c1−1c2qm2ln1+b2Pt1−y11−x1c2=0.For the givenPt and y1, the value of x1 can be obtained by Equation (8).The selectivity factorα can be decided by:
(9)α=x1/y1x2/y2,where y2 and x2 are the mole fractions of component 2 in the bulk gas phase and adsorbed phase, respectively.


## 2.4. Henry’s Law Constant

Henry’s constant (KH) can be applied to calculate the affinity between adsorbent surface and adsorbate molecule. Molecule-surface forces predominate at low pressure, and Henry’s constant is directly related to the interaction of matrix surface with adsorbate molecule [33]. A larger KH reflects the stronger affinity between adsorption pair.In order to calculateKH, the relationship between adsorption amount and equilibrium pressure can be expressed by a virial equation [34]:
(10)lnqP=A0+A1q+A2q2+⋯,where A0, A1, and A2 are the virial coefficients. The first virial coefficient A0 is related to Henry’s constant, as KH=expA0. At the low-pressure range, q is small, and the high-order terms in Equation (10) can be neglected. Thus, Equation (10) can be written as follows:
(11)lnPq=−A0−A1q.By fitting the linear region oflnP/q vs. the loading q, A0 and KH can be obtained.


## 2.5. Thermodynamics of Adsorption

The thermodynamic parameters in this paper are calculated using the following equations [19, 22, 35, 36]:
(12)Qst=RT2∂lnP∂Tq,lnP=−QstRT+C,Ω=−RT∫0PqdlnP,ΔG=Ωq=−RT∫0PqdlnPq,ΔH=−Qst,ΔS=ΔH−ΔGT,where C is the integration constant.


## 3. Results and Discussion

### 3.1. Adsorption Isotherms of CO2 and CH4 on Anthracite

The adsorption isotherms of CO2 and CH4 at three temperatures are shown in Figure 3. We can find that the adsorption amounts of CO2 and CH4 increase monotonically with increasing equilibrium pressure. For the adsorption of CO2 on coal, the adsorption rate is faster at low-pressure range. As pressure enhances, CO2 adsorption rate gradually decreases. For the adsorption of CH4 on coal, the adsorption rate is almost the same over the whole pressure range. The adsorption amounts of both gases at three temperatures are as follows: 283 K > 303 K > 323 K. High temperature will be detrimental to gas adsorption on anthracite, especially for the adsorption of CO2. This is mainly because increasing temperature will give the adsorbate molecules more energy to overcome the van der Waals force and electrostatic interaction and stay in the gas phase [21]. On the shale organic nanochannels, the effect of temperature on CH4 adsorption is more remarkable [37]. Meanwhile, the adsorption isotherms of both gases belong to type I according to the IUPAC classification, which indicates that the adsorbent sample is typically microporous material conforming to the result of the characterization of pore structure of this anthracite.Figure 3
Adsorption isotherms of CO2 and CH4 at different temperatures on anthracite.At the same condition, the adsorption quantity of CO2 on anthracite is much higher than that of CH4. The ratios of adsorption amount of CO2 relative to CH4 (qCO2/qCH4) at three temperatures are displayed in Figure 4. We can find that the values of qCO2/qCH4 range from 1.8 to 6.1, and these values are in coincidence with previous reports [1, 9, 10, 12, 38]. More than 1.8 of the value of qCO2/qCH4 verifies the possibility of the displacement of adsorbed CH4 by injecting CO2. With elevating equilibrium pressure, qCO2/qCH4 declines. It seems that the continuous decrease of the adsorption rate of CO2 and the minor change of the adsorption rate of CH4 can account for the downward trend of qCO2/qCH4. At pressure lower than 0.2 MPa, qCO2/qCH4 is the biggest at 323 K, while at 303 K qCO2/qCH4 is the smallest. When the pressure is higher than 0.2 MPa, low temperature is beneficial to obtaining bigger qCO2/qCH4.Figure 4
Ratios of adsorption amount of CO2 relative to CH4 at different temperatures.The larger adsorption capacity of CO2 than CH4 on coal is attributed to the different characteristics of CH4 and CO2. Table 3 summarizes the physical and chemical properties of CO2 and CH4 molecules. The smaller kinetic diameter and the linear shape of CO2 molecule allow CO2 to diffuse into the more restricted inner pore spaces where the entry of CH4 is not permitted. Relevant research has shown that CO2 molecule can diffuse into an additional 40% of the organic pore structure compared with CH4 molecule [39]. Besides, CH4 is nonpolar, while CO2 has a permanent quadrupole moment. This quadrupole moment can lead to the intensive electrostatic interaction between CO2 molecule and porous adsorbent surface [20] and thereby the larger adsorption quantity. Meanwhile, the boiling point of CH4 is lower than that of CO2. The fluid with higher boiling point is easily adsorbed to porous material, as the fluid with higher boiling point has the larger intermolecular attraction and is liable to liquefaction [40].Table 3
Physical and chemical characteristics of CO2 and CH4 molecules.
Adsorbate
CO2
CH4
Kinetic diameter (nm)
0.33
0.38
Shape
Linear
Tetrahedron
Quadrupole moment (10-26 esu·cm2)
4.30
0
Dipole moment (10-26 esu·cm2)
0
0
Polarizability (10-25 cm3)
29.1
25.9
Boiling point (K)
216.55
111.65


### 3.2. Simulation of Adsorption Isotherms of CO2 and CH4

The simulated results of the adsorption curves of CH4 and CO2 using the L-F model are presented in Figures 5(a) and 5(b), respectively. It is obvious that the simulated results agree well with the experimental results, revealing that the adopted L-F model is able to describe the adsorption curves of CH4 and CO2 on anthracite.Figure 5
Simulated results of the adsorption isotherms using the L-F model: (a) CO2 and (b) CH4.
(a)
(b)Table4 lists the parameters of CH4 and CO2 in the L-F model. As given in Table 4, qm for CO2 and CH4 both decrease with increasing temperature, implying that low temperature helps to achieve higher coalbed methane content and sequestrate large amounts of CO2. Meanwhile, the values of b of both gases also decrease with the improvement of temperature. In addition, the values of n for the adsorption of CH4 and CO2 all deviate from the unity, which reveals that the anthracite is heterogeneous sedimentary rock. For the naturally occurring carbonaceous organic-rich materials, such as coal and shale, the most prominent feature of these solid surfaces is its inhomogeneity [41]. On the one hand, the inhomogeneity comes from lattice defects, vacancies, and dislocations in crystals. On the other hand, the presence of chemical impurities can also cause the inhomogeneity of solid surface.Table 4
Fitting parameters of the L-F model of the isotherms of CO2 and CH4.
Gas
T (K)
qm (mmol/g)
b (MPa-1)
c
n
Rnrc2
CO2
283
2.629
2.346
1.102
0.907
0.9995
303
2.354
2.250
1.065
0.939
0.9998
323
2.044
2.116
1.124
0.890
0.9998
CH4
283
2.671
0.361
1.089
0.918
0.9996
303
2.498
0.343
1.072
0.933
0.9997
323
2.318
0.323
1.136
0.880
0.9994
Note:Rnrc2: the nonlinear regression coefficient.


### 3.3. Adsorption Selectivity of CO2 over CH4 on Anthracite

The predicted adsorption selectivity factors of CO2 over CH4 (αCO2/CH4) on anthracite are illustrated in Figure 6. For an equimolar CO2/CH4 mixture system, αCO2/CH4>1infers that CO2 is preferentially adsorbed in the binary mixture [37]. High selectivity implies the enrichment in the adsorbed phase of CO2 over CH4 compared with the ratio in gas phase [8]. It is noticeable that mole fraction of CO2 (yCO2) in mixture gases has significant influence on αCO2/CH4. Meanwhile, the variation trends of αCO2/CH4 at three temperatures are different.Figure 6
Predicted adsorption selectivity of CO2 over CH4 at different temperatures: (a) 283 K, (b) 303 K, and (c) 323 K.
(a)
(b)
(c)At 283 K, with the increase of pressure,αCO2/CH4 quickly increases to the maximum and then slowly declines. In the low-pressure range, αCO2/CH4 improves with the increase of CO2 mole fraction in mixture gases. In the high-pressure range, αCO2/CH4 decreases with increasing CO2 mole fraction in mixture gases. At 303 K, the change pattern of αCO2/CH4 is similar to that of αCO2/CH4 at 283 K. The difference is that the inflection point of variation curve of αCO2/CH4 is delayed at 303 K. It should be noted that at 323 K, the change pattern of αCO2/CH4 is different from those of αCO2/CH4 at 283 K and 303 K. At 323 K, αCO2/CH4 continuously reduces as pressure increases. Meanwhile, the lower CO2 mole fraction in mixture gases is helpful to obtain bigger αCO2/CH4 at 323 K. Zhang et al. [8] and You et al. [13] also observed that the adsorption selectivity of CO2 over CH4 declines gradually with the increase of the bulk CO2 mole fraction.The comparison ofαCO2/CH4 at different temperatures for the adsorption of different CO2/CH4 mixture gases (yCO2=0.1, yCO2=0.5, and yCO2=0.9) are depicted in Figure 7. It can be found that αCO2/CH4 at 283 K is higher than that at 303 K for the adsorption of three selected CO2/CH4 mixture gases. When equilibrium pressure is bigger than 0.20 MPa, αCO2/CH4 at 283 K is the highest for the adsorption of mixture gases of 10 : 90/CO2 : CH4. For the adsorption of mixture gases of 50 : 50/CO2 : CH4, αCO2/CH4 at 283 K is the highest when equilibrium pressure is bigger than 0.10 MPa. For the adsorption of mixture gases of 90 : 10/CO2 : CH4, αCO2/CH4 at 283 K is the highest when equilibrium pressure is bigger than 0.05 MPa. Generally, the technology of CO2-ECBM is applied in deep unmineable coal seams with reservoir pressure higher than 0.5 MPa. Therefore, low temperature is beneficial for injected CO2 to displace preadsorbed CH4.Figure 7
Comparison of predicted adsorption selectivity of CO2 over CH4 at three temperatures for the adsorption of different CO2/CH4 mixture gases: (a) yCO2=0.1, (b) yCO2=0.5, and (c) yCO2=0.9.
(a)
(b)
(c)As shown in Figure7, the values of αCO2/CH4 are more than 4.0, revealing that the adsorbed CH4 on coal surface can be directly displaced by injected CO2. The higher the αCO2/CH4 is, the higher the displacement efficiency of CO2 is. Hence, the further application of the technology of CO2-ECBM in this anthracite seam is feasible.Comparison ofαCO2/CH4 on different coals and shales is listed in Table 5. It is clear that the values of αCO2/CH4 in studied anthracite are within the range of the values of αCO2/CH4 in other coals reported by previous researchers [8, 13, 15, 18, 42]. This confirms that using the IAST model to calculate the values of αCO2/CH4 is reliable. In addition, the values of αCO2/CH4 on coals are comparable to those of αCO2/CH4 on shales, which shows that the technology of enhanced shale gas recovery by CO2 injection is also feasible.Table 5
Comparison ofαCO2/CH4 on different coals and shales.
Coal
PressureP (MPa)
TemperatureT (K)
αCO2/CH4
Reference
Anthracite
0-1.80
283-323
4.00-5.30
This study
Lignite
0-1.80
288-328
4.84-5.27
Liu [18]
Bituminous
0-1.80
288-328
4.43-4.95
Liu [18]
Anthracite
0-1.80
288-328
5.03-7.97
Liu [18]
Bituminous coal model
3.04-32.25
295.70-370.20
2.00-9.00
Zhang et al. [8]
Coal molecular model
3.04-14.82
295.70-325.70
1.25-5.00
Brochard et al. [42]
Bituminous coal model
0-15
300-340
3.20-6.80
You et al. [13]
Coal surface model
0-10
298
2.20-14.50
Liu et al. [15]
Sichuan Basin shale
0-2
278-318
2.72-7.87
Duan [43]
Barnett shale
0-27.50
313
2.42
Duan [43]
Marcellus shale
0-27.50
313
4.76
Duan [43]


### 3.4. Henry’s Law Constants of CO2 and CH4 on Anthracite

The calculated results of Henry’s constant for CH4 and CO2 on anthracite are given in Table 6. KH for CO2 and CH4 both decrease with increasing experiment temperature. High temperature can reduce the adsorption affinity of two gases on anthracite surface. Accordingly, the adsorption capacity decreases with temperature increases as shown in Figure 3. Under same condition, KH of CH4 is much smaller than that of CO2, and CO2 has stronger adsorption affinity with anthracite. The permanent quadrupole moment of CO2 molecule, which causes stronger electrostatic interaction between CO2 and adsorbent, brings about greater affinity of CO2 on porous material surface [21]. As a result, the adsorption amount of CO2 is much higher than that of CH4 on anthracite.Table 6
Results of Henry’s constant for CO2 and CH4 at different temperatures on anthracite.
Gases
283 K
303 K
323 K
CH4
0.66
0.60
0.35
CO2
4.45
3.87
2.92


### 3.5. Thermodynamic Analysis of Adsorption of CO2 and CH4 on Anthracite

#### 3.5.1. Surface Potential

The minimum isothermal work, which is necessary to load the adsorbent to a given level, is defined as surface potentialΩ [36]. The calculated results of surface potential for CH4 and CO2 as a function of pressure are illustrated in Figures 8(a) and 8(b), respectively. At all experiment temperatures, the absolute values of Ω of CO2 and CH4 rise monotonically with increasing system pressure. This is mainly because higher isotherm work is needed to fill more adsorbate molecules into cavity pores than at the initial stage of adsorption [19]. This phenomenon is also found for gas adsorption on other porous materials, such as zeolite 13X, shale, and chabazite zeolite [19, 22, 36]. Meanwhile, with the elevation of temperature, the decrease of Ω in the negative value takes place. Surface potential is a criterion of necessary work to achieve the equilibrium of system. Thus, a lower equilibrium capacity leads to smaller (less negative) surface potential [33], and high temperature can reduce the absolute values of Ω of CO2 and CH4. It should be noted that under the same condition, the absolute value of Ω of CO2 is much bigger than that of CH4, revealing that CO2 adsorption on anthracite is more favorable.Figure 8
Surface potentials of CO2 (a) and CH4 (b) on anthracite at different temperatures.
(a)
(b)


#### 3.5.2. Gibbs Free Energy Change

Gibbs free energy refers to the increment of free energy of system with increasing adsorbent unit area at constant temperature and pressure [23]. The calculated results of Gibbs free energy change ΔGof CO2 and CH4 on anthracite are displayed in Figures 9(a) and 9(b), respectively. We can note that the values of ΔG of both gases are negative, implying that the adsorption processes of both gases on anthracite are spontaneous. The absolute values of ΔG of both gas rise gradually with the increase of pressure, which indicates that the degree of spontaneity of gas adsorption is larger at high pressure. Therefore, the adsorptions of CO2 and CH4 are more likely to occur under high pressure condition. The absolute value of ΔG of CO2 is apparently bigger than that of ΔG of CH4, and the degree of spontaneity of CO2 adsorption is greater. According to the minimum energy principle, any interface has the tendency to spontaneously reduce the energy of interface. The solid interface is difficult to shrink due to the immobility of molecule or atom on interface. Thus, the surface free energy can only be reduced by adsorbing other molecule. The greater free energy change results in the bigger motivation to adsorb gas and the larger adsorption quantity [23]. This is one reason why the adsorption amount of CH4 is much smaller than that of CO2 on anthracite.Figure 9
Gibbs free energy changes of CO2 (a) and CH4 (b) on anthracite at different temperatures.
(a)
(b)


#### 3.5.3. Isosteric Heat of Adsorption

The heat effect of adsorption can be quantified by isosteric heat of adsorptionQst (−ΔH, enthalpy change). Adsorption heat can result in the change in temperature [19]. This temperature variation will cause the localized changes in the kinetic and equilibrium properties, which ultimately influences the adsorption behavior and displacement efficiency [44]. When the adsorbent surface is energetically homogeneous and the lateral adsorbate-adsorbate interaction can be neglected, Qst is independent of adsorbate loading. When the adsorbent is energetically heterogeneous, Qst becomes a function of adsorbate loading [45]. The degree of adsorbent heterogeneity has a strong effect on Qst. The means of indirect estimation from temperature-dependent adsorption equilibrium data or direct measurement by dosing calorimetry can be adopted to acquire Qst [44]. In this paper, the values of Qst for CO2 and CH4 were obtained by the indirect estimation approach based on the adsorption isotherm data at three temperatures.The calculated results ofQst for CO2 and CH4 are plotted in Figure 10. The values of ΔH (−Qst) for both gas are negative, indicating that the adsorption processes of CO2 and CH4 on anthracite are exothermic. Therefore, low temperature can enhance the adsorption amounts of CO2 and CH4. In addition, Qst for CO2 and CH4 are not constant with the increase of adsorption amount, confirming that the studied anthracite is inherently heterogeneous. As the adsorption quantity enhances, Qst of CO2 increases consistently, whereas Qst of CH4 declines monotonously.Figure 10
Isosteric heat of adsorption of CO2 and CH4 on anthracite.At the initial stage of adsorption, the available sorption sites are abundant and the lateral adsorbate-adsorbate interaction energy is lower. As adsorption loading increases, more and more cavities are occupied by adsorbate. Thus, the decrease inQst with adsorption loading takes place [46]. For the adsorption of CH4 on anthracite, the continuous reduction of Qst suggests that the interaction energy among CH4 molecules is much weaker at higher surface coverage. With the increase of pressure (i.e., loading), more CH4 molecules are in a free state within the pore structure of anthracite. For the adsorption of CH4 on shale, the isosteric heat of adsorption also reduces with adsorption loading increases [19].For CO2 adsorption on anthracite, the intermolecular force among CO2 molecules is gradually strengthened in the cavity pores with enhancing pressure. Compared with CH4 molecule, CO2 molecule with higher boiling point has the larger intermolecular attraction and is liable to liquefaction. At higher surface coverage, the stronger lateral interaction between CO2 molecules results in the increase of Qst. Similar changing trend of Qst was reported by Zhou et al. for CO2 adsorption on coal matrix [23].Meanwhile, the value ofQst of CH4 is lower than that of CO2. He et al. [47] have found that the hindering effect of spherical molecules caused by pore wall is smaller than that of nonspherical molecules for the same size. Contrary to regular tetrahedral CH4 molecule, the diffusion of claviform CO2 molecule into micropores is more influenced by inner pore walls, thereby releasing more energy and heat. During the displacement coalbed methane process, the release of heat from CO2 adsorption will improve the temperature of coal reservoir. The rising temperature is beneficial to CH4 desorption and the enhancement of coalbed methane recovery. Nevertheless, the increase of temperature is harmful for the sequestration of injected CO2.


#### 3.5.4. Entropy Change

Entropy is the measurement of disorder or patterns in which the thermodynamic system is rearranged [22]. The entropy change ΔS is a net of balance between rotation, vibration, and translation freedoms of adsorbate molecule within matrix [33]. Research about the behavior of entropy change as a function of adsorption loading helps to understand the packing manner of adsorbed molecules. The calculated results of ΔS of CO2 and CH4 on anthracite are shown in Figures 11(a) and 11(b), respectively. It can be seen that the values of ΔS of CO2 and CH4 are negative, which elucidates that the adsorption of CO2 and CH4 on coal surface are from a random phase to an order phase. The adsorption progress involves the reduction in the degree of freedom and the formation of a more stable rearrangement in adsorbent surface.Figure 11
Entropy changes of CO2 (a) and CH4 (b) on anthracite at different temperatures.
(a)
(b)Relevant literature has observed that for the adsorption of CH4 molecule, the entropy loss is between -82 and -87 J/mol/K at temperature ranging from 273 to 423 K [48]. For CH4 adsorption on this anthracite, the value of ΔS is from -4.96 to -14.51 J/mol/K over the temperature range of 283-323 K, which is very bigger than -82 J/mol/K. The smaller entropy loss of CH4 on anthracite implies that injected CH4 is not completely adsorbed on coal matrix but free gas stayed in the inner pores. As illustrated in Figure 11(b), the entropy loss of CH4 reduces as adsorption amount increases. Therefore, more injected CH4 molecules are trapped in the coal pore volume rather than adsorbed on matrix surface with increasing surface coverage, and the degree of orderliness the system becomes lower.As illustrated in Figure11(a), for CO2 adsorption on anthracite, the entropy loss enhances with increasing surface coverage, inferring that the orderliness degree of the whole system becomes bigger. The increase in entropy loss is mainly because the free space in the cavity reduces, and the freedom of the adsorbate molecule becomes severely limited [21]. Hence, the adsorbed CO2 is in a more stable state at higher surface coverage. The value of ΔS of CO2 is from -12.97 to -45.76 J/mol/K at temperature ranging from 283 to 323 K. The value of ΔS of CO2 on anthracite is smaller than those of ΔSof CO2 on 5A and 13X zeolites [33], which indicates that the orderliness of adsorbed CO2 on 5A and 13X zeolites is higher than that on anthracite.It is obvious that the entropy loss of CH4 on anthracite is lower than that of CO2 at the same condition. Barrer [49] has found that the interaction between permanent quadrupole moment of molecule and electrostatic field can result in a more efficient packing. If the molecule packing is more effective, the larger adsorption heat will be released [33]. Due to the existence of quadrupole moment, the packing manner of CO2 molecule on anthracite is more efficient, and Qst of CO2 is greater as shown in Figure 10. Meanwhile, the bigger entropy loss of CO2 reveals that the adsorbed CO2 molecules form a more stable configuration, which is also one reason why the sorption amount of CO2 on coal is larger than that of CH4. In addition, the entropy losses of both gases decline slightly with the increase of temperature. High temperature will be not conducive to forming a more ordered and stable configuration for adsorbed CH4 and CO2, and thus, the sorption quantities of both gases decrease as temperature rises.


## 3.1. Adsorption Isotherms of CO2 and CH4 on Anthracite

The adsorption isotherms of CO2 and CH4 at three temperatures are shown in Figure 3. We can find that the adsorption amounts of CO2 and CH4 increase monotonically with increasing equilibrium pressure. For the adsorption of CO2 on coal, the adsorption rate is faster at low-pressure range. As pressure enhances, CO2 adsorption rate gradually decreases. For the adsorption of CH4 on coal, the adsorption rate is almost the same over the whole pressure range. The adsorption amounts of both gases at three temperatures are as follows: 283 K > 303 K > 323 K. High temperature will be detrimental to gas adsorption on anthracite, especially for the adsorption of CO2. This is mainly because increasing temperature will give the adsorbate molecules more energy to overcome the van der Waals force and electrostatic interaction and stay in the gas phase [21]. On the shale organic nanochannels, the effect of temperature on CH4 adsorption is more remarkable [37]. Meanwhile, the adsorption isotherms of both gases belong to type I according to the IUPAC classification, which indicates that the adsorbent sample is typically microporous material conforming to the result of the characterization of pore structure of this anthracite.Figure 3
Adsorption isotherms of CO2 and CH4 at different temperatures on anthracite.At the same condition, the adsorption quantity of CO2 on anthracite is much higher than that of CH4. The ratios of adsorption amount of CO2 relative to CH4 (qCO2/qCH4) at three temperatures are displayed in Figure 4. We can find that the values of qCO2/qCH4 range from 1.8 to 6.1, and these values are in coincidence with previous reports [1, 9, 10, 12, 38]. More than 1.8 of the value of qCO2/qCH4 verifies the possibility of the displacement of adsorbed CH4 by injecting CO2. With elevating equilibrium pressure, qCO2/qCH4 declines. It seems that the continuous decrease of the adsorption rate of CO2 and the minor change of the adsorption rate of CH4 can account for the downward trend of qCO2/qCH4. At pressure lower than 0.2 MPa, qCO2/qCH4 is the biggest at 323 K, while at 303 K qCO2/qCH4 is the smallest. When the pressure is higher than 0.2 MPa, low temperature is beneficial to obtaining bigger qCO2/qCH4.Figure 4
Ratios of adsorption amount of CO2 relative to CH4 at different temperatures.The larger adsorption capacity of CO2 than CH4 on coal is attributed to the different characteristics of CH4 and CO2. Table 3 summarizes the physical and chemical properties of CO2 and CH4 molecules. The smaller kinetic diameter and the linear shape of CO2 molecule allow CO2 to diffuse into the more restricted inner pore spaces where the entry of CH4 is not permitted. Relevant research has shown that CO2 molecule can diffuse into an additional 40% of the organic pore structure compared with CH4 molecule [39]. Besides, CH4 is nonpolar, while CO2 has a permanent quadrupole moment. This quadrupole moment can lead to the intensive electrostatic interaction between CO2 molecule and porous adsorbent surface [20] and thereby the larger adsorption quantity. Meanwhile, the boiling point of CH4 is lower than that of CO2. The fluid with higher boiling point is easily adsorbed to porous material, as the fluid with higher boiling point has the larger intermolecular attraction and is liable to liquefaction [40].Table 3
Physical and chemical characteristics of CO2 and CH4 molecules.
Adsorbate
CO2
CH4
Kinetic diameter (nm)
0.33
0.38
Shape
Linear
Tetrahedron
Quadrupole moment (10-26 esu·cm2)
4.30
0
Dipole moment (10-26 esu·cm2)
0
0
Polarizability (10-25 cm3)
29.1
25.9
Boiling point (K)
216.55
111.65


## 3.2. Simulation of Adsorption Isotherms of CO2 and CH4

The simulated results of the adsorption curves of CH4 and CO2 using the L-F model are presented in Figures 5(a) and 5(b), respectively. It is obvious that the simulated results agree well with the experimental results, revealing that the adopted L-F model is able to describe the adsorption curves of CH4 and CO2 on anthracite.Figure 5
Simulated results of the adsorption isotherms using the L-F model: (a) CO2 and (b) CH4.
(a)
(b)Table4 lists the parameters of CH4 and CO2 in the L-F model. As given in Table 4, qm for CO2 and CH4 both decrease with increasing temperature, implying that low temperature helps to achieve higher coalbed methane content and sequestrate large amounts of CO2. Meanwhile, the values of b of both gases also decrease with the improvement of temperature. In addition, the values of n for the adsorption of CH4 and CO2 all deviate from the unity, which reveals that the anthracite is heterogeneous sedimentary rock. For the naturally occurring carbonaceous organic-rich materials, such as coal and shale, the most prominent feature of these solid surfaces is its inhomogeneity [41]. On the one hand, the inhomogeneity comes from lattice defects, vacancies, and dislocations in crystals. On the other hand, the presence of chemical impurities can also cause the inhomogeneity of solid surface.Table 4
Fitting parameters of the L-F model of the isotherms of CO2 and CH4.
Gas
T (K)
qm (mmol/g)
b (MPa-1)
c
n
Rnrc2
CO2
283
2.629
2.346
1.102
0.907
0.9995
303
2.354
2.250
1.065
0.939
0.9998
323
2.044
2.116
1.124
0.890
0.9998
CH4
283
2.671
0.361
1.089
0.918
0.9996
303
2.498
0.343
1.072
0.933
0.9997
323
2.318
0.323
1.136
0.880
0.9994
Note:Rnrc2: the nonlinear regression coefficient.


## 3.3. Adsorption Selectivity of CO2 over CH4 on Anthracite

The predicted adsorption selectivity factors of CO2 over CH4 (αCO2/CH4) on anthracite are illustrated in Figure 6. For an equimolar CO2/CH4 mixture system, αCO2/CH4>1infers that CO2 is preferentially adsorbed in the binary mixture [37]. High selectivity implies the enrichment in the adsorbed phase of CO2 over CH4 compared with the ratio in gas phase [8]. It is noticeable that mole fraction of CO2 (yCO2) in mixture gases has significant influence on αCO2/CH4. Meanwhile, the variation trends of αCO2/CH4 at three temperatures are different.Figure 6
Predicted adsorption selectivity of CO2 over CH4 at different temperatures: (a) 283 K, (b) 303 K, and (c) 323 K.
(a)
(b)
(c)At 283 K, with the increase of pressure,αCO2/CH4 quickly increases to the maximum and then slowly declines. In the low-pressure range, αCO2/CH4 improves with the increase of CO2 mole fraction in mixture gases. In the high-pressure range, αCO2/CH4 decreases with increasing CO2 mole fraction in mixture gases. At 303 K, the change pattern of αCO2/CH4 is similar to that of αCO2/CH4 at 283 K. The difference is that the inflection point of variation curve of αCO2/CH4 is delayed at 303 K. It should be noted that at 323 K, the change pattern of αCO2/CH4 is different from those of αCO2/CH4 at 283 K and 303 K. At 323 K, αCO2/CH4 continuously reduces as pressure increases. Meanwhile, the lower CO2 mole fraction in mixture gases is helpful to obtain bigger αCO2/CH4 at 323 K. Zhang et al. [8] and You et al. [13] also observed that the adsorption selectivity of CO2 over CH4 declines gradually with the increase of the bulk CO2 mole fraction.The comparison ofαCO2/CH4 at different temperatures for the adsorption of different CO2/CH4 mixture gases (yCO2=0.1, yCO2=0.5, and yCO2=0.9) are depicted in Figure 7. It can be found that αCO2/CH4 at 283 K is higher than that at 303 K for the adsorption of three selected CO2/CH4 mixture gases. When equilibrium pressure is bigger than 0.20 MPa, αCO2/CH4 at 283 K is the highest for the adsorption of mixture gases of 10 : 90/CO2 : CH4. For the adsorption of mixture gases of 50 : 50/CO2 : CH4, αCO2/CH4 at 283 K is the highest when equilibrium pressure is bigger than 0.10 MPa. For the adsorption of mixture gases of 90 : 10/CO2 : CH4, αCO2/CH4 at 283 K is the highest when equilibrium pressure is bigger than 0.05 MPa. Generally, the technology of CO2-ECBM is applied in deep unmineable coal seams with reservoir pressure higher than 0.5 MPa. Therefore, low temperature is beneficial for injected CO2 to displace preadsorbed CH4.Figure 7
Comparison of predicted adsorption selectivity of CO2 over CH4 at three temperatures for the adsorption of different CO2/CH4 mixture gases: (a) yCO2=0.1, (b) yCO2=0.5, and (c) yCO2=0.9.
(a)
(b)
(c)As shown in Figure7, the values of αCO2/CH4 are more than 4.0, revealing that the adsorbed CH4 on coal surface can be directly displaced by injected CO2. The higher the αCO2/CH4 is, the higher the displacement efficiency of CO2 is. Hence, the further application of the technology of CO2-ECBM in this anthracite seam is feasible.Comparison ofαCO2/CH4 on different coals and shales is listed in Table 5. It is clear that the values of αCO2/CH4 in studied anthracite are within the range of the values of αCO2/CH4 in other coals reported by previous researchers [8, 13, 15, 18, 42]. This confirms that using the IAST model to calculate the values of αCO2/CH4 is reliable. In addition, the values of αCO2/CH4 on coals are comparable to those of αCO2/CH4 on shales, which shows that the technology of enhanced shale gas recovery by CO2 injection is also feasible.Table 5
Comparison ofαCO2/CH4 on different coals and shales.
Coal
PressureP (MPa)
TemperatureT (K)
αCO2/CH4
Reference
Anthracite
0-1.80
283-323
4.00-5.30
This study
Lignite
0-1.80
288-328
4.84-5.27
Liu [18]
Bituminous
0-1.80
288-328
4.43-4.95
Liu [18]
Anthracite
0-1.80
288-328
5.03-7.97
Liu [18]
Bituminous coal model
3.04-32.25
295.70-370.20
2.00-9.00
Zhang et al. [8]
Coal molecular model
3.04-14.82
295.70-325.70
1.25-5.00
Brochard et al. [42]
Bituminous coal model
0-15
300-340
3.20-6.80
You et al. [13]
Coal surface model
0-10
298
2.20-14.50
Liu et al. [15]
Sichuan Basin shale
0-2
278-318
2.72-7.87
Duan [43]
Barnett shale
0-27.50
313
2.42
Duan [43]
Marcellus shale
0-27.50
313
4.76
Duan [43]


## 3.4. Henry’s Law Constants of CO2 and CH4 on Anthracite

The calculated results of Henry’s constant for CH4 and CO2 on anthracite are given in Table 6. KH for CO2 and CH4 both decrease with increasing experiment temperature. High temperature can reduce the adsorption affinity of two gases on anthracite surface. Accordingly, the adsorption capacity decreases with temperature increases as shown in Figure 3. Under same condition, KH of CH4 is much smaller than that of CO2, and CO2 has stronger adsorption affinity with anthracite. The permanent quadrupole moment of CO2 molecule, which causes stronger electrostatic interaction between CO2 and adsorbent, brings about greater affinity of CO2 on porous material surface [21]. As a result, the adsorption amount of CO2 is much higher than that of CH4 on anthracite.Table 6
Results of Henry’s constant for CO2 and CH4 at different temperatures on anthracite.
Gases
283 K
303 K
323 K
CH4
0.66
0.60
0.35
CO2
4.45
3.87
2.92


## 3.5. Thermodynamic Analysis of Adsorption of CO2 and CH4 on Anthracite

### 3.5.1. Surface Potential

The minimum isothermal work, which is necessary to load the adsorbent to a given level, is defined as surface potentialΩ [36]. The calculated results of surface potential for CH4 and CO2 as a function of pressure are illustrated in Figures 8(a) and 8(b), respectively. At all experiment temperatures, the absolute values of Ω of CO2 and CH4 rise monotonically with increasing system pressure. This is mainly because higher isotherm work is needed to fill more adsorbate molecules into cavity pores than at the initial stage of adsorption [19]. This phenomenon is also found for gas adsorption on other porous materials, such as zeolite 13X, shale, and chabazite zeolite [19, 22, 36]. Meanwhile, with the elevation of temperature, the decrease of Ω in the negative value takes place. Surface potential is a criterion of necessary work to achieve the equilibrium of system. Thus, a lower equilibrium capacity leads to smaller (less negative) surface potential [33], and high temperature can reduce the absolute values of Ω of CO2 and CH4. It should be noted that under the same condition, the absolute value of Ω of CO2 is much bigger than that of CH4, revealing that CO2 adsorption on anthracite is more favorable.Figure 8
Surface potentials of CO2 (a) and CH4 (b) on anthracite at different temperatures.
(a)
(b)


### 3.5.2. Gibbs Free Energy Change

Gibbs free energy refers to the increment of free energy of system with increasing adsorbent unit area at constant temperature and pressure [23]. The calculated results of Gibbs free energy change ΔGof CO2 and CH4 on anthracite are displayed in Figures 9(a) and 9(b), respectively. We can note that the values of ΔG of both gases are negative, implying that the adsorption processes of both gases on anthracite are spontaneous. The absolute values of ΔG of both gas rise gradually with the increase of pressure, which indicates that the degree of spontaneity of gas adsorption is larger at high pressure. Therefore, the adsorptions of CO2 and CH4 are more likely to occur under high pressure condition. The absolute value of ΔG of CO2 is apparently bigger than that of ΔG of CH4, and the degree of spontaneity of CO2 adsorption is greater. According to the minimum energy principle, any interface has the tendency to spontaneously reduce the energy of interface. The solid interface is difficult to shrink due to the immobility of molecule or atom on interface. Thus, the surface free energy can only be reduced by adsorbing other molecule. The greater free energy change results in the bigger motivation to adsorb gas and the larger adsorption quantity [23]. This is one reason why the adsorption amount of CH4 is much smaller than that of CO2 on anthracite.Figure 9
Gibbs free energy changes of CO2 (a) and CH4 (b) on anthracite at different temperatures.
(a)
(b)


### 3.5.3. Isosteric Heat of Adsorption

The heat effect of adsorption can be quantified by isosteric heat of adsorptionQst (−ΔH, enthalpy change). Adsorption heat can result in the change in temperature [19]. This temperature variation will cause the localized changes in the kinetic and equilibrium properties, which ultimately influences the adsorption behavior and displacement efficiency [44]. When the adsorbent surface is energetically homogeneous and the lateral adsorbate-adsorbate interaction can be neglected, Qst is independent of adsorbate loading. When the adsorbent is energetically heterogeneous, Qst becomes a function of adsorbate loading [45]. The degree of adsorbent heterogeneity has a strong effect on Qst. The means of indirect estimation from temperature-dependent adsorption equilibrium data or direct measurement by dosing calorimetry can be adopted to acquire Qst [44]. In this paper, the values of Qst for CO2 and CH4 were obtained by the indirect estimation approach based on the adsorption isotherm data at three temperatures.The calculated results ofQst for CO2 and CH4 are plotted in Figure 10. The values of ΔH (−Qst) for both gas are negative, indicating that the adsorption processes of CO2 and CH4 on anthracite are exothermic. Therefore, low temperature can enhance the adsorption amounts of CO2 and CH4. In addition, Qst for CO2 and CH4 are not constant with the increase of adsorption amount, confirming that the studied anthracite is inherently heterogeneous. As the adsorption quantity enhances, Qst of CO2 increases consistently, whereas Qst of CH4 declines monotonously.Figure 10
Isosteric heat of adsorption of CO2 and CH4 on anthracite.At the initial stage of adsorption, the available sorption sites are abundant and the lateral adsorbate-adsorbate interaction energy is lower. As adsorption loading increases, more and more cavities are occupied by adsorbate. Thus, the decrease inQst with adsorption loading takes place [46]. For the adsorption of CH4 on anthracite, the continuous reduction of Qst suggests that the interaction energy among CH4 molecules is much weaker at higher surface coverage. With the increase of pressure (i.e., loading), more CH4 molecules are in a free state within the pore structure of anthracite. For the adsorption of CH4 on shale, the isosteric heat of adsorption also reduces with adsorption loading increases [19].For CO2 adsorption on anthracite, the intermolecular force among CO2 molecules is gradually strengthened in the cavity pores with enhancing pressure. Compared with CH4 molecule, CO2 molecule with higher boiling point has the larger intermolecular attraction and is liable to liquefaction. At higher surface coverage, the stronger lateral interaction between CO2 molecules results in the increase of Qst. Similar changing trend of Qst was reported by Zhou et al. for CO2 adsorption on coal matrix [23].Meanwhile, the value ofQst of CH4 is lower than that of CO2. He et al. [47] have found that the hindering effect of spherical molecules caused by pore wall is smaller than that of nonspherical molecules for the same size. Contrary to regular tetrahedral CH4 molecule, the diffusion of claviform CO2 molecule into micropores is more influenced by inner pore walls, thereby releasing more energy and heat. During the displacement coalbed methane process, the release of heat from CO2 adsorption will improve the temperature of coal reservoir. The rising temperature is beneficial to CH4 desorption and the enhancement of coalbed methane recovery. Nevertheless, the increase of temperature is harmful for the sequestration of injected CO2.


### 3.5.4. Entropy Change

Entropy is the measurement of disorder or patterns in which the thermodynamic system is rearranged [22]. The entropy change ΔS is a net of balance between rotation, vibration, and translation freedoms of adsorbate molecule within matrix [33]. Research about the behavior of entropy change as a function of adsorption loading helps to understand the packing manner of adsorbed molecules. The calculated results of ΔS of CO2 and CH4 on anthracite are shown in Figures 11(a) and 11(b), respectively. It can be seen that the values of ΔS of CO2 and CH4 are negative, which elucidates that the adsorption of CO2 and CH4 on coal surface are from a random phase to an order phase. The adsorption progress involves the reduction in the degree of freedom and the formation of a more stable rearrangement in adsorbent surface.Figure 11
Entropy changes of CO2 (a) and CH4 (b) on anthracite at different temperatures.
(a)
(b)Relevant literature has observed that for the adsorption of CH4 molecule, the entropy loss is between -82 and -87 J/mol/K at temperature ranging from 273 to 423 K [48]. For CH4 adsorption on this anthracite, the value of ΔS is from -4.96 to -14.51 J/mol/K over the temperature range of 283-323 K, which is very bigger than -82 J/mol/K. The smaller entropy loss of CH4 on anthracite implies that injected CH4 is not completely adsorbed on coal matrix but free gas stayed in the inner pores. As illustrated in Figure 11(b), the entropy loss of CH4 reduces as adsorption amount increases. Therefore, more injected CH4 molecules are trapped in the coal pore volume rather than adsorbed on matrix surface with increasing surface coverage, and the degree of orderliness the system becomes lower.As illustrated in Figure11(a), for CO2 adsorption on anthracite, the entropy loss enhances with increasing surface coverage, inferring that the orderliness degree of the whole system becomes bigger. The increase in entropy loss is mainly because the free space in the cavity reduces, and the freedom of the adsorbate molecule becomes severely limited [21]. Hence, the adsorbed CO2 is in a more stable state at higher surface coverage. The value of ΔS of CO2 is from -12.97 to -45.76 J/mol/K at temperature ranging from 283 to 323 K. The value of ΔS of CO2 on anthracite is smaller than those of ΔSof CO2 on 5A and 13X zeolites [33], which indicates that the orderliness of adsorbed CO2 on 5A and 13X zeolites is higher than that on anthracite.It is obvious that the entropy loss of CH4 on anthracite is lower than that of CO2 at the same condition. Barrer [49] has found that the interaction between permanent quadrupole moment of molecule and electrostatic field can result in a more efficient packing. If the molecule packing is more effective, the larger adsorption heat will be released [33]. Due to the existence of quadrupole moment, the packing manner of CO2 molecule on anthracite is more efficient, and Qst of CO2 is greater as shown in Figure 10. Meanwhile, the bigger entropy loss of CO2 reveals that the adsorbed CO2 molecules form a more stable configuration, which is also one reason why the sorption amount of CO2 on coal is larger than that of CH4. In addition, the entropy losses of both gases decline slightly with the increase of temperature. High temperature will be not conducive to forming a more ordered and stable configuration for adsorbed CH4 and CO2, and thus, the sorption quantities of both gases decrease as temperature rises.


## 3.5.1. Surface Potential

The minimum isothermal work, which is necessary to load the adsorbent to a given level, is defined as surface potentialΩ [36]. The calculated results of surface potential for CH4 and CO2 as a function of pressure are illustrated in Figures 8(a) and 8(b), respectively. At all experiment temperatures, the absolute values of Ω of CO2 and CH4 rise monotonically with increasing system pressure. This is mainly because higher isotherm work is needed to fill more adsorbate molecules into cavity pores than at the initial stage of adsorption [19]. This phenomenon is also found for gas adsorption on other porous materials, such as zeolite 13X, shale, and chabazite zeolite [19, 22, 36]. Meanwhile, with the elevation of temperature, the decrease of Ω in the negative value takes place. Surface potential is a criterion of necessary work to achieve the equilibrium of system. Thus, a lower equilibrium capacity leads to smaller (less negative) surface potential [33], and high temperature can reduce the absolute values of Ω of CO2 and CH4. It should be noted that under the same condition, the absolute value of Ω of CO2 is much bigger than that of CH4, revealing that CO2 adsorption on anthracite is more favorable.Figure 8
Surface potentials of CO2 (a) and CH4 (b) on anthracite at different temperatures.
(a)
(b)


## 3.5.2. Gibbs Free Energy Change

Gibbs free energy refers to the increment of free energy of system with increasing adsorbent unit area at constant temperature and pressure [23]. The calculated results of Gibbs free energy change ΔGof CO2 and CH4 on anthracite are displayed in Figures 9(a) and 9(b), respectively. We can note that the values of ΔG of both gases are negative, implying that the adsorption processes of both gases on anthracite are spontaneous. The absolute values of ΔG of both gas rise gradually with the increase of pressure, which indicates that the degree of spontaneity of gas adsorption is larger at high pressure. Therefore, the adsorptions of CO2 and CH4 are more likely to occur under high pressure condition. The absolute value of ΔG of CO2 is apparently bigger than that of ΔG of CH4, and the degree of spontaneity of CO2 adsorption is greater. According to the minimum energy principle, any interface has the tendency to spontaneously reduce the energy of interface. The solid interface is difficult to shrink due to the immobility of molecule or atom on interface. Thus, the surface free energy can only be reduced by adsorbing other molecule. The greater free energy change results in the bigger motivation to adsorb gas and the larger adsorption quantity [23]. This is one reason why the adsorption amount of CH4 is much smaller than that of CO2 on anthracite.Figure 9
Gibbs free energy changes of CO2 (a) and CH4 (b) on anthracite at different temperatures.
(a)
(b)


## 3.5.3. Isosteric Heat of Adsorption

The heat effect of adsorption can be quantified by isosteric heat of adsorptionQst (−ΔH, enthalpy change). Adsorption heat can result in the change in temperature [19]. This temperature variation will cause the localized changes in the kinetic and equilibrium properties, which ultimately influences the adsorption behavior and displacement efficiency [44]. When the adsorbent surface is energetically homogeneous and the lateral adsorbate-adsorbate interaction can be neglected, Qst is independent of adsorbate loading. When the adsorbent is energetically heterogeneous, Qst becomes a function of adsorbate loading [45]. The degree of adsorbent heterogeneity has a strong effect on Qst. The means of indirect estimation from temperature-dependent adsorption equilibrium data or direct measurement by dosing calorimetry can be adopted to acquire Qst [44]. In this paper, the values of Qst for CO2 and CH4 were obtained by the indirect estimation approach based on the adsorption isotherm data at three temperatures.The calculated results ofQst for CO2 and CH4 are plotted in Figure 10. The values of ΔH (−Qst) for both gas are negative, indicating that the adsorption processes of CO2 and CH4 on anthracite are exothermic. Therefore, low temperature can enhance the adsorption amounts of CO2 and CH4. In addition, Qst for CO2 and CH4 are not constant with the increase of adsorption amount, confirming that the studied anthracite is inherently heterogeneous. As the adsorption quantity enhances, Qst of CO2 increases consistently, whereas Qst of CH4 declines monotonously.Figure 10
Isosteric heat of adsorption of CO2 and CH4 on anthracite.At the initial stage of adsorption, the available sorption sites are abundant and the lateral adsorbate-adsorbate interaction energy is lower. As adsorption loading increases, more and more cavities are occupied by adsorbate. Thus, the decrease inQst with adsorption loading takes place [46]. For the adsorption of CH4 on anthracite, the continuous reduction of Qst suggests that the interaction energy among CH4 molecules is much weaker at higher surface coverage. With the increase of pressure (i.e., loading), more CH4 molecules are in a free state within the pore structure of anthracite. For the adsorption of CH4 on shale, the isosteric heat of adsorption also reduces with adsorption loading increases [19].For CO2 adsorption on anthracite, the intermolecular force among CO2 molecules is gradually strengthened in the cavity pores with enhancing pressure. Compared with CH4 molecule, CO2 molecule with higher boiling point has the larger intermolecular attraction and is liable to liquefaction. At higher surface coverage, the stronger lateral interaction between CO2 molecules results in the increase of Qst. Similar changing trend of Qst was reported by Zhou et al. for CO2 adsorption on coal matrix [23].Meanwhile, the value ofQst of CH4 is lower than that of CO2. He et al. [47] have found that the hindering effect of spherical molecules caused by pore wall is smaller than that of nonspherical molecules for the same size. Contrary to regular tetrahedral CH4 molecule, the diffusion of claviform CO2 molecule into micropores is more influenced by inner pore walls, thereby releasing more energy and heat. During the displacement coalbed methane process, the release of heat from CO2 adsorption will improve the temperature of coal reservoir. The rising temperature is beneficial to CH4 desorption and the enhancement of coalbed methane recovery. Nevertheless, the increase of temperature is harmful for the sequestration of injected CO2.


## 3.5.4. Entropy Change

Entropy is the measurement of disorder or patterns in which the thermodynamic system is rearranged [22]. The entropy change ΔS is a net of balance between rotation, vibration, and translation freedoms of adsorbate molecule within matrix [33]. Research about the behavior of entropy change as a function of adsorption loading helps to understand the packing manner of adsorbed molecules. The calculated results of ΔS of CO2 and CH4 on anthracite are shown in Figures 11(a) and 11(b), respectively. It can be seen that the values of ΔS of CO2 and CH4 are negative, which elucidates that the adsorption of CO2 and CH4 on coal surface are from a random phase to an order phase. The adsorption progress involves the reduction in the degree of freedom and the formation of a more stable rearrangement in adsorbent surface.Figure 11
Entropy changes of CO2 (a) and CH4 (b) on anthracite at different temperatures.
(a)
(b)Relevant literature has observed that for the adsorption of CH4 molecule, the entropy loss is between -82 and -87 J/mol/K at temperature ranging from 273 to 423 K [48]. For CH4 adsorption on this anthracite, the value of ΔS is from -4.96 to -14.51 J/mol/K over the temperature range of 283-323 K, which is very bigger than -82 J/mol/K. The smaller entropy loss of CH4 on anthracite implies that injected CH4 is not completely adsorbed on coal matrix but free gas stayed in the inner pores. As illustrated in Figure 11(b), the entropy loss of CH4 reduces as adsorption amount increases. Therefore, more injected CH4 molecules are trapped in the coal pore volume rather than adsorbed on matrix surface with increasing surface coverage, and the degree of orderliness the system becomes lower.As illustrated in Figure11(a), for CO2 adsorption on anthracite, the entropy loss enhances with increasing surface coverage, inferring that the orderliness degree of the whole system becomes bigger. The increase in entropy loss is mainly because the free space in the cavity reduces, and the freedom of the adsorbate molecule becomes severely limited [21]. Hence, the adsorbed CO2 is in a more stable state at higher surface coverage. The value of ΔS of CO2 is from -12.97 to -45.76 J/mol/K at temperature ranging from 283 to 323 K. The value of ΔS of CO2 on anthracite is smaller than those of ΔSof CO2 on 5A and 13X zeolites [33], which indicates that the orderliness of adsorbed CO2 on 5A and 13X zeolites is higher than that on anthracite.It is obvious that the entropy loss of CH4 on anthracite is lower than that of CO2 at the same condition. Barrer [49] has found that the interaction between permanent quadrupole moment of molecule and electrostatic field can result in a more efficient packing. If the molecule packing is more effective, the larger adsorption heat will be released [33]. Due to the existence of quadrupole moment, the packing manner of CO2 molecule on anthracite is more efficient, and Qst of CO2 is greater as shown in Figure 10. Meanwhile, the bigger entropy loss of CO2 reveals that the adsorbed CO2 molecules form a more stable configuration, which is also one reason why the sorption amount of CO2 on coal is larger than that of CH4. In addition, the entropy losses of both gases decline slightly with the increase of temperature. High temperature will be not conducive to forming a more ordered and stable configuration for adsorbed CH4 and CO2, and thus, the sorption quantities of both gases decrease as temperature rises.


## 4. Conclusions

In this paper, the adsorption isotherms of CH4 and CO2 on Qinshui Basin anthracite were obtained at the temperatures of 283 K, 303 K, and 323 K. The adsorption selectivity factor of CO2 over CH4 on anthracite was predicted. The affinities and thermodynamic properties of CH4 and CO2 on anthracite were investigated. The main conclusions are as follows:
(1)
The sorption ability of CO2 on anthracite is much larger than that of CH4. At the temperatures of 283 K and 303 K, αCO2/CH4 quickly increases to the maximum and then slowly declines with the increase of pressure. At 323 K, αCO2/CH4 monotonously reduces as pressure enhances. CO2 mole fraction in mixture gases has obvious effect on αCO2/CH4. The values of αCO2/CH4 are more than 4.0, revealing that the technology of CO2-ECBM is feasible. In actual coal reservoir, low temperature is helpful for injected CO2 to displace preadsorbed CH4. Henry’s constant of CH4 is smaller than that of CO2, and CH4 has a weaker adsorption affinity with matrix surface
(2)
The values ofΩ of both gases are more negative with the increase of pressure. The absolute value of Ωof CO2 is much bigger than that of CH4, revealing that CO2 adsorption is more favorable. As pressure increases, the absolute values of ΔG of CO2 and CH4 rise. The larger absolute value of ΔG of CO2 indicates that the degree of spontaneity of CO2 adsorption is higher
(3)
As adsorption loading enhances,Qst of CO2 increases, while Qst of CH4 declines. The value of Qst of CO2 is larger than that of CH4. With increasing surface coverage, the entropy loss of CH4 decreases, while the entropy loss of CO2 enlarges. Improving temperature will reduce the entropy losses of both gases. The higher entropy loss of CO2 suggests that the adsorbed CO2 molecules constitute a more ordered configuration than adsorbed CH4 molecules



---

*Source: 8268050-2019-12-21.xml*