Molecular Investigation on the Displacement Characteristics of CH 4 by CO 2 , N 2 and Their Mixture in a Composite Shale Model

: The rapid growth in energy consumption and environmental pollution have greatly stimulated the exploration and utilization of shale gas. The injection of gases such as CO 2 , N 2 , and their mixture is currently regarded as one of the most effective ways to enhance gas recovery from shale reservoirs. In this study, molecular simulations were conducted on a kaolinite–kerogen IID composite shale matrix to explore the displacement characteristics of CH 4 using different injection gases, including CO 2 , N 2 , and their mixture. The results show that when the injection pressure was lower than 10 MPa, increasing the injection pressure improved the displacement capacity of CH 4 by CO 2 . Correspondingly, an increase of formation temperature also increased the displacement efﬁciency of CH 4 , but an increase of pore size slightly increased this displacement efﬁciency. Moreover, it was found that when the proportion of CO 2 and N 2 was 1:1, the displacement efﬁciency of CH 4 was the highest, which proved that the simultaneous injection of CO 2 and N 2 had a synergistic effect on shale gas production. The results of this paper will provide guidance and reference for the displacement exploitation of shale gas by injection gases. revealed that CO 2 -N 2 gas injection recovery to understanding of the


Introduction
The consumption of traditional energy such as oil and coal induces increasingly severe environmental pollution and the greenhouse effect. Therefore, it is urgent to improve the energy consumption structure and reduce the consumption of oil and coal. The environmental pollution and greenhouse gas emission problems can be alleviated once traditional energy is replaced by shale gas, which is a type of clean low-carbon energy [1,2]. The main component of shale gas is methane (CH 4 ), which is generally stored in a shale reservoir in three states (i.e., adsorbed state, free state, and dissolved state) [3]. Among them, CH 4 with an adsorbed state plays a dominant role [4]. Therefore, transforming adsorbed-state CH 4 to a free state is the critical process in shale gas exploitation. Unfortunately, the low porosity and permeability of shale reservoirs significantly inhibit the desorption and diffusion processes of adsorbed CH 4 molecules, increasing the difficulty of shale gas recovery.
Currently, hydraulic fracturing is the most commonly used method to improve the productivity of shale gas recovery by dramatically enhancing the shale porosity and permeability [5]. However, this method faces the shortcomings of waste production and water pollution [6,7]. By contrast, these disadvantages could be avoided by replacing water with supercritical carbon dioxide (CO 2 ) during the fracturing process. Apart from this, injecting CO 2 into shale reservoirs as a means of reducing greenhouse gas emissions is regarded as one of the promising strategies for CO 2 sequestration. Thus, the use of CO 2 as an alternative fluid to enhance shale gas recovery has attracted increasing attention and has recently stimulated many research efforts [8][9][10][11]. Nitrogen has proved to be another potential fracturing fluid for efficiently enhancing shale gas recovery, owing to its low viscosity and price [4,12,13]. Meanwhile, experiments conducted by the authors of [14] revealed that CO 2 -N 2 mixed gas injection exhibits improved shale gas recovery performance compared to CO 2 injection alone. Therefore, an understanding of the displacement behaviors between CH 4 and CO 2 , N 2 , and the mixture of CO 2 -N 2 , from a micro-scale perspective, is immensely valuable in guiding the efficiency of shale gas recovery and CO 2 sequestration.
Many efforts by different research groups have been devoted to the experimental investigation of the effects of injection gases on shale gas recovery [15,16]. For instance, nuclear magnetic resonance (NMR) was adopted by the authors of [17] to explore the effect of CO 2 pressure on the efficiency of shale gas recovery. Their results indicated that the desorption efficiency of the adsorbed CH 4 was improved by 27% and 26% when the CO 2 was kept at ambient pressure and abandonment pressure, respectively. Moreover, the effects of shale reservoir temperature, pressure, and particle size, CO 2 flow rate, and pressure on the efficiency of shale gas recovery were studied in [18]. They found that a high injection pressure of CO 2 had the benefit of enhancing the efficiency of shale gas recovery, whereas the effects of CO 2 flow rate and shale reservoir temperature could be ignored. Furthermore, the effect of gas injection composition, including CO 2 , N 2 , and CO 2 -N 2 mixed gas, on the efficiency of shale gas recovery were investigated in [19][20][21]. In summary, the presence of N 2 has the benefit of prolonging the breakthrough time of CO 2 and achieving the goal of CO 2 storage over the long term, and the ratio of CO 2 /N 2 is an important parameter for optimizing shale gas recovery and CO 2 storage. Although many scholars [17,19] tried to experimentally reveal the displacement mechanism between the injection gases and CH 4 , a microscopic mechanism has not yet been reported due to the limitations of measurement techniques.
As alternatives, molecular simulation methods, including density functional theory (DFT), grand canonical Monte Carlo (GCMC), and molecular dynamics (MD), are effective approaches to explore the interactional characteristics between the gases and shale reservoirs as well as the displacement behaviors between injection gases and CH 4 [22]. For instance, the authors of [23] proved that the adsorption energy of CO 2 was much larger than that of CH 4 using a DFT model. The authors of [24] indicated that the van der Waals' force plays a dominant role in the interactions between CH 4 and the kerogen surface. In [25], the authors explored the competitive adsorption behavior between CO 2 and CH 4 using a GCMC model. Their results indicated that the adsorption capacity of CO 2 was much higher than that of CH 4 under various conditions. Similarly, the authors of [26,27] investigated the effect of pore size on the adsorption behaviors of CH 4 in kaolinite and quartz, respectively, using the GCMC mothed. They found that the adsorption performance of the shale matrix on CH 4 was exponentially reduced with an increase in pore size. The authors of [28] studied the diffusion characteristics of CH 4 and CO 2 in the shale matrix based on MD. Their results showed that the diffusion coefficient of CH 4 and CO 2 in nanoscale pores of the montmorillonite slit decreased with increasing pressure, and the diffusion coefficient of CH 4 was larger than that of CO 2 .
Moreover, the authors of [29] proved that the displacement performance of CH 4 decreased gradually once CO 2 , N 2 , and H 2 O were successively injected in carbon nanotubes. In [30], the authors investigated the displacement of shale gas by CO 2 and the sequestration of CO 2 simultaneously in a shale matrix at different geological depths using the GCMC method. They pointed out that pore size played a significant role in the displacement of CH 4 by CO 2 , and the optimum geological depth for the displacement of CH 4 by CO 2 was about 1.0 km. Besides, the authors of [4] used the MD method to simulate the displacement process of CH 4 by CO 2 and N 2 in a composite model of quartz and methylnaphthalene. They found that the displacement efficiency of a small pore (30 Å) was the highest and the displacement efficiencies of CH 4 by different gases were larger than 50% when the injection pressure was greater than 30 MPa. Although extensive studies on the displacement characteristics of CH 4 by single-component gas (CO 2 , N 2 , and H 2 O) in various shale models were conducted, limited studies have been performed to explore the mechanism of shale gas displacement by mixed gas CO 2 -N 2 from a microscopic perspective. The synergistic Energies 2021, 14, 2 3 of 13 effect of the simultaneous injection of N 2 and CO 2 on the displacement efficiency of CH 4 was observed experimentally [19], while the microscale mechanism of this phenomenon has not been made clear yet, and few studies have tried to explore it from the molecular level. Besides, the optimal N 2 /CO 2 ratio at which the displacement efficiency reaches its maximum has not been reported. However, this value was regarded as one of the most important parameters to enhance shale gas recovery. On the other hand, thorough research on the displacement process of CH 4 in a realistic organic-inorganic composite shale model under a complex environment, such as a humid environment, is still lacking.

Model Description
In this study, a composite shale model consisting of two inorganic layers (kaolinite) and two organic layers (kerogen IID, which belongs to the over-mature stage of kerogen II), as shown in Figure 1, was established for numerical simulations. The reason for choosing the kaolinite and kerogen IID as the inorganic and organic layers, respectively, was that these two materials are the typical components of actual shale. This composite shale model establishment process can be described as follows: 50% when the injection pressure was greater than 30 MPa. Although extensive studies on the displacement characteristics of CH 4 by single-component gas (CO 2 , N 2 , and H 2 O) in various shale models were conducted, limited studies have been performed to explore the mechanism of shale gas displacement by mixed gas CO 2 -N 2 from a microscopic perspective. The synergistic effect of the simultaneous injection of N 2 and CO 2 on the displacement efficiency of CH 4 was observed experimentally [19], while the microscale mechanism of this phenomenon has not been made clear yet, and few studies have tried to explore it from the molecular level. Besides, the optimal N 2 /CO 2 ratio at which the displacement efficiency reaches its maximum has not been reported. However, this value was regarded as one of the most important parameters to enhance shale gas recovery. On the other hand, thorough research on the displacement process of CH 4 in a realistic organicinorganic composite shale model under a complex environment, such as a humid environment, is still lacking.

Model Description
In this study, a composite shale model consisting of two inorganic layers (kaolinite) and two organic layers (kerogen IID, which belongs to the over-mature stage of kerogen II), as shown in Figure 1, was established for numerical simulations. The reason for choosing the kaolinite and kerogen IID as the inorganic and organic layers, respectively, was that these two materials are the typical components of actual shale. This composite shale model establishment process can be described as follows: (1) The inorganic kaolinite layered model box was first established as shown in Figure  1a, in which the parameters of the kaolinite cell structure were obtained from the data in [31]; (2) A single kerogen IID molecule was built based on the data from [32] (Figure 1b), and then the corresponding kerogen IID box with 11 kerogen IID molecules was established according to the size of the layered inorganic mineral lattice; (3) The kaolinite box in Figure 1a and two kerogen IID boxes were combined to form a composite shale model (Figure 1c).
Density is one of the most important physical properties of organic materials. Figure  2 shows the density of the present kerogen IID box as a function of a relaxation time. It can be seen that when the density of the kerogen IID box reached stability, its average value was about 1.28 g/cm 3 , which is in good agreement with the value of 1.1 g/cm 3 - (1) The inorganic kaolinite layered model box was first established as shown in Figure 1a, in which the parameters of the kaolinite cell structure were obtained from the data in [31]; (2) A single kerogen IID molecule was built based on the data from [32] (Figure 1b), and then the corresponding kerogen IID box with 11 kerogen IID molecules was established according to the size of the layered inorganic mineral lattice; (3) The kaolinite box in Figure 1a and two kerogen IID boxes were combined to form a composite shale model ( Figure 1c).
Density is one of the most important physical properties of organic materials. Figure 2 shows the density of the present kerogen IID box as a function of a relaxation time. It can be seen that when the density of the kerogen IID box reached stability, its average value was about 1.28 g/cm 3 , which is in good agreement with the value of 1.1 g/cm 3 -1.4 g/cm 3 for kerogen IID in real shale reservoirs [33], indicating the this kerogen IID model is reliable. The adsorption process of CH 4 in kerogen boxes at T = 338 K was also conducted, and the calculated adsorption isotherm was compared with that in [34], as shown in Figure 3. The compared result in Figure 3 further validates the present kerogen IID box model and shows the reliability of the adsorption model used in the present paper. 1.4 g/cm 3 for kerogen IID in real shale reservoirs [33], indicating the this kerogen IID model is reliable. The adsorption process of CH 4 in kerogen boxes at T = 338 K was also conducted, and the calculated adsorption isotherm was compared with that in [34], as shown in Figure 3. The compared result in Figure 3 further validates the present kerogen IID box model and shows the reliability of the adsorption model used in the present paper.  Once the composite shale matrix model ( Figure 1c) was established, CH 4 was preadsorbed on this model at a certain temperature and pressure using the GCMC method, as shown in Figure 4. The red region on the left side of the composite shale model is the injection gas, which could be CO 2 , N 2 , or CO 2 -N 2 mixed gas.  1.4 g/cm 3 for kerogen IID in real shale reservoirs [33], indicating the this kerogen IID model is reliable. The adsorption process of CH 4 in kerogen boxes at T = 338 K was also conducted, and the calculated adsorption isotherm was compared with that in [34], as shown in Figure 3. The compared result in Figure 3 further validates the present kerogen IID box model and shows the reliability of the adsorption model used in the present paper.  Once the composite shale matrix model ( Figure 1c) was established, CH 4 was preadsorbed on this model at a certain temperature and pressure using the GCMC method, as shown in Figure 4. The red region on the left side of the composite shale model is the injection gas, which could be CO 2 , N 2 , or CO 2 -N 2 mixed gas.  Once the composite shale matrix model ( Figure 1c) was established, CH 4 was preadsorbed on this model at a certain temperature and pressure using the GCMC method, as shown in Figure 4. The red region on the left side of the composite shale model is the injection gas, which could be CO 2 , N 2 , or CO 2 -N 2 mixed gas. 1.4 g/cm 3 for kerogen IID in real shale reservoirs [33], indicating the this kerogen IID model is reliable. The adsorption process of CH 4 in kerogen boxes at T = 338 K was also conducted, and the calculated adsorption isotherm was compared with that in [34], as shown in Figure 3. The compared result in Figure 3 further validates the present kerogen IID box model and shows the reliability of the adsorption model used in the present paper.  Once the composite shale matrix model ( Figure 1c) was established, CH 4 was preadsorbed on this model at a certain temperature and pressure using the GCMC method, as shown in Figure 4. The red region on the left side of the composite shale model is the injection gas, which could be CO 2 , N 2 , or CO 2 -N 2 mixed gas.

Simulation Details
In this study, the GCMC method was adopted to simulate the adsorption process of CH 4 in the above composite model. In the GCMC simulations, the van der Waals interaction and electrostatic interaction between molecules were calculated by the Atom and Ewald summation methods, respectively. The adsorption equilibrium and adsorption production of CH 4 were set as 5 × 10 6 and 1 × 10 7 , respectively. We used the condensed-phase optimized molecular potentials for atomistic simulation studies (COMPASS) force field, which can effectively simulate molecular systems including organic polymers and inorganic molecules, and the non-bond cutoff radius was set as 1.9 nm. After obtaining the preadsorption configuration of CH 4 in the composite shale model (Figure 4), the MD method was employed to investigate the displacement characteristics of CH 4 under different conditions. The force field parameters and interaction parameters used in the MD simulations were set as those in the above GCMC method. The canonical ensemble (NVT) and a Nose-Hoover thermostat were used to control the temperature, and the total calculation time was set as 1.0 ns with the time step of 1.0 fs.
To evaluate the displacement capacity efficiency of CH 4 by the injection gas, the displacement efficiency R dis is defined as follows: where N ad mmol·g −1 is the amount of pre-adsorbed CH 4 in the composite model, and N dis (mmol·g −1 ) is the residual amount of CH 4 in the composite shale after the displacement process.

Results and Discussion
As mentioned in the introduction, there are many factors, including formation conditions and gas species, that influence shale gas displacement efficiency. Thus, in the following sections, different physical models with different pore size and water content are presented. Then, the influence of different factors, such as the formation temperature, pressure, pore size, gas composition, and water content, on the displacement characteristics and displacement efficiency of CH 4 is discussed.

The Influence of Pressure on the Displacement Characteristics
In order to examine the influence of gas pressure on the displacement characteristics of CH 4 , the displacement processes of CH 4 by CO 2 at different pressures, including p = 6, 10, 15, 20 MPa, were investigated. Figure 5 plots the displacement capacity of CH 4 as a function of time under different pressures. In the figure, when the displacement process reaches a steady-state, the displacement capacity increases with the increase in the injection pressure. However, the growth rate of the displacement capacity gradually slows down with the increase in pressure (Figure 5b), which indicates that properly increasing the injection pressure is beneficial to the displacement of CH 4 .  Figure 6 shows the displacement process with p = 20 MPa and T = 323 K at different times. The figure indicates that as time goes by, the CO 2 molecules on the left side gradually enter the slit and are gradually absorbed in the pores and the surface of the kerogen matrix. CO 2 molecules occupy the adsorption sites of CH 4 , and the adsorbed CH 4 molecules are replaced from the shale reservoir. Then, the free-state CO 2 molecules displace   Figure 6 shows the displacement process with p = 20 MPa and T = 323 K at different times. The figure indicates that as time goes by, the CO 2 molecules on the left side gradually enter the slit and are gradually absorbed in the pores and the surface of the kerogen matrix. CO 2 molecules occupy the adsorption sites of CH 4 , and the adsorbed CH 4 molecules are replaced from the shale reservoir. Then, the free-state CO 2 molecules displace the desorbed CH 4 molecules from the nanoscale pores.  Figure 6 shows the displacement process with p = 20 MPa and T = 323 K at different times. The figure indicates that as time goes by, the CO 2 molecules on the left side gradually enter the slit and are gradually absorbed in the pores and the surface of the kerogen matrix. CO 2 molecules occupy the adsorption sites of CH 4 , and the adsorbed CH 4 molecules are replaced from the shale reservoir. Then, the free-state CO 2 molecules displace the desorbed CH 4 molecules from the nanoscale pores.  Figure 7 plots the displacement efficiency as a function of pressure. It can be seen that as the injection pressure increases from 6 MPa to 10 MPa, the displacement efficiency increases by 44.4%. However, when the injection pressure is larger than 10 MPa, the increasing tendency of the displacement slows down. The displacement efficiency only increases by 7.0%, as the pressure increases from 10 MPa to 20 MPa. That means a further increase in the injection pressure is of little significance for enhancing shale gas recovery.  Figure 7 plots the displacement efficiency as a function of pressure. It can be seen that as the injection pressure increases from 6 MPa to 10 MPa, the displacement efficiency increases by 44.4%. However, when the injection pressure is larger than 10 MPa, the increasing tendency of the displacement slows down. The displacement efficiency only increases by 7.0%, as the pressure increases from 10 MPa to 20 MPa. That means a further increase in the injection pressure is of little significance for enhancing shale gas recovery.  Figure 8 plots the displacement capacity of CH 4 by CO 2 at different temperatures under p = 20 MPa, as a function of time. It can be seen that, as time goes by, the displacement capacity of CH 4 at higher temperatures climbs faster, and a higher temperature ultimately leads to a greater displacement capacity. This is because the activity of gas molecules increases with the increase in temperature. From Figure 9, it can be seen that with the same pore size of d = 2 nm, when the displacement process achieves a steady-state, and as the temperature of the reservoir increases from 298 K to 383 K, the displacement capacity of CH 4 increases by 9.4%. Interestingly, when the injection temperature is low (T < 353 K), the displacement capacity increases linearly as temperature increases; however, as the injection temperature further increases, the increase of the displacement capacity is not obvious. Besides, Figure 10 shows that as the temperature increases, the displacement   It can be seen that, as time goes by, the displacement capacity of CH 4 at higher temperatures climbs faster, and a higher temperature ultimately leads to a greater displacement capacity. This is because the activity of gas molecules increases with the increase in temperature. From Figure 9, it can be seen that with the same pore size of d = 2 nm, when the displacement process achieves a steady-state, and as the temperature of the reservoir increases from 298 K to 383 K, the displacement capacity of Energies 2021, 14, 2 7 of 13 CH 4 increases by 9.4%. Interestingly, when the injection temperature is low (T < 353 K), the displacement capacity increases linearly as temperature increases; however, as the injection temperature further increases, the increase of the displacement capacity is not obvious. Besides, Figure 10 shows that as the temperature increases, the displacement efficiency increases monotonously, indicating that increasing the injection or formation temperature is beneficial to the exploitation of shale gas. Figure 8 plots the displacement capacity of CH 4 by CO 2 at different temperatures under p = 20 MPa, as a function of time. It can be seen that, as time goes by, the displacement capacity of CH 4 at higher temperatures climbs faster, and a higher temperature ultimately leads to a greater displacement capacity. This is because the activity of gas molecules increases with the increase in temperature. From Figure 9, it can be seen that with the same pore size of d = 2 nm, when the displacement process achieves a steady-state, and as the temperature of the reservoir increases from 298 K to 383 K, the displacement capacity of CH 4 increases by 9.4%. Interestingly, when the injection temperature is low (T < 353 K), the displacement capacity increases linearly as temperature increases; however, as the injection temperature further increases, the increase of the displacement capacity is not obvious. Besides, Figure 10 shows that as the temperature increases, the displacement efficiency increases monotonously, indicating that increasing the injection or formation temperature is beneficial to the exploitation of shale gas.    Figure 11 plots the displacement capacity of CH 4 by CO 2 as a function of pore size. It can be seen that at the early stage of the displacement process, the displacement capacity in different pores increases sharply as time increases. In addition, as the pores size in-   Figure 11 plots the displacement capacity of CH 4 by CO 2 as a function of pore size. It can be seen that at the early stage of the displacement process, the displacement capacity   Figure 11 plots the displacement capacity of CH 4 by CO 2 as a function of pore size. It can be seen that at the early stage of the displacement process, the displacement capacity in different pores increases sharply as time increases. In addition, as the pores size increases, the time required to reach steady-state decreases. This is because the larger pore size is conducive to the replacement of adsorbed CH 4 from the reservoir and is also beneficial to the diffusion of CH 4 in nanoscale pores. When the pore size increases from 1 nm to 3 nm, the displacement capacity increases by 11.8%. Figure 12 presents the displacement efficiency of CH 4 as a function of the aperture. When the pore size increases from 1 nm to 3 nm, the displacement efficiency only increases by 2.6%, which is smaller than the increment of the displacement capacity. This can be attributed to the fact that the preadsorbed CH 4 in larger pores is relatively larger than that in smaller pores.   Figure 13 shows the displacement capacity of CH 4 by gas with different proportions over time. It shows that at the early stage of the displacement process, the higher the nitrogen content, the larger amount of CH 4 that is displaced from the composite shale reservoir. This is because compared with CO 2 , N 2 is not easily adsorbed on the composite shale reservoir (Figure 14), and the free-state N 2 can displace CH 4 from the shale pores in the early stage of the process. Moreover, the free-state N 2 can also reduce the partial pressure of CH 4 in the shale pores and promote the self-desorption process of CH 4 . From Figure 15, it can be seen that when the displacement process reaches a steady-state, the displacement capacity of CH 4 by N 2 is the least. This is because the adsorption capacity of the shale reservoir to nitrogen is slightly lower, and thus the amount of absorbed CH 4 replaced by pure N 2 from the shale reservoir is less. Interestingly, the displacement capacity and displacement efficiency (Figure 16) reach the maximum when the ratio of CO 2 and N 2 is 1:1, with displacement capacity and displacement efficiency up to 2.2 mmol •   Figure 13 shows the displacement capacity of CH 4 by gas with different proportions over time. It shows that at the early stage of the displacement process, the higher the nitrogen content, the larger amount of CH 4 that is displaced from the composite shale reservoir. This is because compared with CO 2 , N 2 is not easily adsorbed on the composite shale reservoir (Figure 14), and the free-state N 2 can displace CH 4 from the shale pores in the early stage of the process. Moreover, the free-state N 2 can also reduce the partial pressure of CH 4 in the shale pores and promote the self-desorption process of CH 4 . From Figure 15, it can be seen that when the displacement process reaches a steady-state, the displacement capacity of CH 4 by N 2 is the least. This is because the adsorption capacity of the shale reservoir to nitrogen is slightly lower, and thus the amount of absorbed CH 4 replaced by pure N 2 from the shale reservoir is less. Interestingly, the displacement capacity and displacement efficiency (Figure 16) reach the maximum when the ratio of CO 2  Figure 13 shows the displacement capacity of CH 4 by gas with different proportions over time. It shows that at the early stage of the displacement process, the higher the nitrogen content, the larger amount of CH 4 that is displaced from the composite shale reservoir. This is because compared with CO 2 , N 2 is not easily adsorbed on the composite shale reservoir (Figure 14), and the free-state N 2 can displace CH 4 from the shale pores in the early stage of the process. Moreover, the free-state N 2 can also reduce the partial pressure of CH 4 in the shale pores and promote the self-desorption process of CH 4 . From Figure 15, it can be seen that when the displacement process reaches a steady-state, the dis-Energies 2021, 14, 2 9 of 13 placement capacity of CH 4 by N 2 is the least. This is because the adsorption capacity of the shale reservoir to nitrogen is slightly lower, and thus the amount of absorbed CH 4 replaced by pure N 2 from the shale reservoir is less. Interestingly, the displacement capacity and displacement efficiency (Figure 16) reach the maximum when the ratio of CO 2 and N 2 is 1:1, with displacement capacity and displacement efficiency up to 2.2 mmol·g −1 and 81.5%, respectively. This is because the appropriate amount of CO 2 can replace the absorbed CH 4 from the shale reservoir, and free-state N 2 has the benefit of displacing the desorbed CH 4 from the shale pores. As the proportion of CO 2 increases, more CO 2 will be absorbed on the shale reservoir, which makes it possible to block the shale pores and prevent the desorption of CH 4 .        Figure 17 shows the displacement capacity of CH 4 with different water contents over time. It indicates that with the increase in water content, the displacement capacity decreases. When the displacement process reaches a steady-state, the displacement capacity of CH 4 decreases from 2.04 mmol · g −1 to 1.68 mmol · g −1 as the water content increases from 0 wt.% to 1.6 wt.%. This can be explained as follows: (1) water molecules prevent CO 2 molecules from entering the shale matrix and replacing the absorbed CH 4 ; (2) the water content can reduce the connectivity of the shale matrix ( Figure 18)-that is, with the increase of water content, the free volume and surface area of shale gradually decrease; and (3) the existence of water molecules reduces the amount of pre-adsorbed CH 4 in the shale reservoir ( Figure 19). The reason for the low adsorption of CH 4 with high water content can be attributed to the fact that water molecules occupy the adsorption sites of CH 4 . Besides, the displacement efficiency of CH 4 decreases as the water content increases, as presented in Figure 20, which means that the water content in the shale reservoir is not conducive to shale exploitation.   Figure 17 shows the displacement capacity of CH 4 with different water contents over time. It indicates that with the increase in water content, the displacement capacity decreases. When the displacement process reaches a steady-state, the displacement capacity of CH 4 decreases from 2.04 mmol·g −1 to 1.68 mmol·g −1 as the water content increases from 0 wt.% to 1.6 wt.%. This can be explained as follows: (1) water molecules prevent CO 2 molecules from entering the shale matrix and replacing the absorbed CH 4 ; (2) the water content can reduce the connectivity of the shale matrix ( Figure 18)-that is, with the increase of water content, the free volume and surface area of shale gradually decrease; and (3) the existence of water molecules reduces the amount of pre-adsorbed CH 4 in the shale reservoir ( Figure 19). The reason for the low adsorption of CH 4 with high water content can be attributed to the fact that water molecules occupy the adsorption sites of CH 4 . Besides, the displacement efficiency of CH 4 decreases as the water content increases, as presented in Figure 20, which means that the water content in the shale reservoir is not conducive to shale exploitation.  Figure 17 shows the displacement capacity of CH 4 with different water contents over time. It indicates that with the increase in water content, the displacement capacity decreases. When the displacement process reaches a steady-state, the displacement capacity of CH 4 decreases from 2.04 mmol · g −1 to 1.68 mmol · g −1 as the water content increases from 0 wt.% to 1.6 wt.%. This can be explained as follows: (1) water molecules prevent CO 2 molecules from entering the shale matrix and replacing the absorbed CH 4 ; (2) the water content can reduce the connectivity of the shale matrix ( Figure 18)-that is, with the increase of water content, the free volume and surface area of shale gradually decrease; and (3) the existence of water molecules reduces the amount of pre-adsorbed CH 4 in the shale reservoir ( Figure 19). The reason for the low adsorption of CH 4 with high water content can be attributed to the fact that water molecules occupy the adsorption sites of CH 4 . Besides, the displacement efficiency of CH 4 decreases as the water content increases, as presented in Figure 20, which means that the water content in the shale reservoir is not conducive to shale exploitation.

Conclusions
In this paper, the displacement characteristics of CH 4 by CO 2 , N 2 , and their mixture were investigated by molecular simulations based on a kaolinite-kerogen IID composite shale model. The influence of some factors, including injection pressure, formation temperature, pore size, water content, and gas proportion on the displacement characteristics were examined, and the main results are as follows:

Conclusions
In this paper, the displacement characteristics of CH 4 by CO 2 , N 2 , and their mixture were investigated by molecular simulations based on a kaolinite-kerogen IID composite shale model. The influence of some factors, including injection pressure, formation temperature, pore size, water content, and gas proportion on the displacement characteristics were examined, and the main results are as follows:

Conclusions
In this paper, the displacement characteristics of CH 4 by CO 2 , N 2 , and their mixture were investigated by molecular simulations based on a kaolinite-kerogen IID composite shale model. The influence of some factors, including injection pressure, formation temperature, pore size, water content, and gas proportion on the displacement characteristics were examined, and the main results are as follows: (1) When the injection pressure is smaller than 10 MPa, an effective way to improve the displacement capacity of CH 4 is to increase the injection pressure; the displacement efficiency increased by 44.4% with a pressure increase from 6 MPa to 10 MPa. However, when p > 10 MPa, the growth of the displacement efficiency was not apparent with the further increase of pressure, and the displacement efficiency only increased by 7.0% as the pressure increased from 10 MPa to 20 MPa. Formation temperature was one of the crucial factors affecting displacement efficiency, and as the formation temperature increased, the displacement efficiency increased monotonically. (2) When the process reached a steady-state, the displacement efficiency increased by 2.6% as the pore size increased from 1 nm to 3 nm. The water content decreased the pre-adsorption capacity and the displacement capacity of CH 4 by decreasing the volume fraction of shale pores. (3) Compared with N 2 , CO 2 showed better displacement capacity on CH 4 . The displacement ability of CO 2 -N 2 mixed gas was greater than that of CO 2 and N 2 alone, and the optimal gas ratio of CO 2 /N 2 at which the displacement efficiency reached the maximum of 81.5% was about 1:1.
In the present study, only the displacement characteristics of CH 4 in a shale reservoir slit with an aperture smaller than 3 nm was investigated. However, the pores of a real shale reservoir may be very different from the present model. Thus, it is necessary to investigate the influence of pore morphology and injection gases on the transport properties of CH 4 in future research.

Data Availability Statement:
The authors declare that the data presented in this study are available within the article.

Conflicts of Interest:
The authors declare no conflict of interest.