Introduction

Unconventional gas reservoirs, including shale and coalbed reservoirs, have drawn much attention these years, attributed to the high demand for natural fossil resources and the clean characteristics of unconventional reservoirs1,2,3. However, shale reservoirs are typically associated with connate water, the high content of which usually forms a water bridge that significantly impacts gas adsorption, transportation, and recovery processes4,5,6,7. Hence, understanding the effect of water bridges in shale reservoirs is crucial and essential for the industrial exploration of shale gas, estimation of in-place reserves, and CO2 sequestration potential. Therefore, this work focuses on the gas adsorption and transportation behaviors in the encroached subsurface environment, which has been studied at a shallow depth and needs to be noticed or addressed in previous studies, and reveals the water bridge’s impacting mechanisms behind the gas movement.

In shale gas-bearing gas reservoirs, the pore size ranges from angstrom to micrometer, with micro and mesopores comprising the prominent pores that possess primary gas adsorption capacity. To observe the mechanisms of water bridge impacts on gas adsorption in small-scale pores is a great challenge in the laboratory. Therefore, molecular dynamics (MD) simulation has emerged as a practical approach for examining gas flow behaviors in shale formation8,9,10. The MD method allows visualization of molecular movement and computation interactions among particles by determining the intermolecular and intramolecular interactions, accordingly providing a practical method for examining and clarifying gas adsorption and diffusion performances11,12,13.

Shale reservoirs generally comprise organic and inorganic substances, with the primary gas adsorption attributed to the organic matter. Moreover, the organic matter is fundamentally composed of kerogen6,8, 14. Due to its physical and chemical nature, type II-D kerogen, falling in the thermogenic gas window range, is usually utilized as the predominant unit in established shale models. Li and Sun investigated the CH4 and CO2 adsorption properties with various moisture contents in the type II-D kerogen matrix. They discovered that H2O molecules predominantly occupy superior adsorption sites on the shale surface and inside the shale matrix. As a result, water molecules drive CH4 and CO2 to reside in the bulk pore space, and H2O distribution in shale reservoirs restricts the CH4 and CO2 adsorption6,7, 14. Liu et al. probed the stability of the water bridge during the shale gas diffusion. They observed that CH4 merely diffuses at the interface of the water phase, whereas partial CO2 could penetrate the liquid water phase, owing to the high solubility of CO2 in water. High pressure restricted the diffusion process and enhanced CO2 solubility in the water bridge by strengthening the interactions between CO2 and H2O molecules4. Therefore, CO2 was a dominant factor influencing water bridge stability over CH4, due to the soluble process4. Tuan et al. observed that the water distribution in shale organic pores is essential for hydrocarbon adsorption and crucial in hydraulic fracture15. Tuan constructed three kerogen models by MD simulation and observed that the organic-pore systems exhibited mixed-wet characteristics, which might lead to a high potential for water entrapment and hinder gas adsorption and desorption processes15. Furthermore, another study by Tuan demonstrated that the contact angle and wettability of water on shale were influenced by gas injection pressure; the growing CO2 injection pressure increases the water contact angle and makes the water more hydrophobic on the organic surface, favoring gas recovery16. However, despite these findings, there still needs to be more understanding regarding the impact of water bridges on gas behavior and the additional ions in the water-bridge systems on efficient shale gas extraction and development.

This work uses MD simulation to construct a kerogen model representing the shale gas reservoir. Subsequently, the adsorption and density distribution profiles of CH4 and CO2 with a water bridge are investigated and examined within the established shale model. Furthermore, ions are introduced into the water system to mimic the mineralized formation water, enhancing the reliability and accuracy of simulation results for future gas extraction and recovery.

Methodology

Adsorbent model and construction

The type II-D kerogen unit at top and side views are depicted in Fig. 1a,b, and the unit is employed for establishing a realistic organic shale model, which ties the meso-slit and micropores characteristics in one, presenting the primary physical and chemical properties of shale gas-bearing reservoirs. The detailed physical and chemical information regarding type II-D kerogen is shown in Table 1. In order to generate this shale model, 100 units of C175H102N4O9S2 are employed to structure the organic matrix, as shown in Fig. 1c. The model generation and simulation processes, including gas adsorption determination and diffusion calculation, are conducted in the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS)17.

Figure 1
figure 1

The (a) top view and (b) side view of atomic structure for the type II-D kerogen unit with chemical formula of C175H102N4O9S2, (c) the constructed shale matrix with meso-slit and nanopores rendered by the pore surface (purple color). (Atom representation: grey color for C, white color for H, red color for O, blue color for N, and yellow color for S.).

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Table 1 Structural parameters of type ii-d kerogen18.
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The initial step was establishing the organic model by relaxing the single kerogen fragment at 338 K until the geometry was optimized. Subsequently, 100 units were placed in a 2003 Å3 box, with each region containing 50 units in the upper and lower regions to obtain the initial configuration of the shale matrix. During this step, two helium slabs are input into the system to maintain the height of the 30 Å meso-slit embedded in the shale model. The Constant Isobaric-Isothermic Ensemble (NPT) was then employed to achieve the shale system's final target temperature and pressure. NPT cycles were implemented with the pressure increases from 0.1 to 20 MPa while simultaneously controlling temperature drops from 1000 to 338 K. Each NPT cycle consisted of 2,000,000 steps to reach an equilibrium state. Following this, a Canonical Ensemble (NVT) was employed for another 2,000,000 steps to obtain the final stabilized configuration at 338 K and a pressure of 20 MPa. Therefore, the equilibrium density was determined as 1.36 g/cm3, lying in the range of 1.15–1.65 g/cm3 for shale kerogen density19,20,21. Moreover, the surface area was 570.45 m2/g, consistent with previous studies by Peng22 and shales in Eagle Fold Play and Marcellus Play23. The porosity calculated in the two pieces of software, namely, Ovito and PoreBlazer24,25, was determined to be 27.41%, falling in the range of 26–34% for the kerogen matrices26,27. This study combines the micropores and mesopores as a union to extract multi-scale physical characteristics of natural shale reservoirs, making the simulation environment more approach to the realistic geological condition and the simulation results more reliable.

Adsorbate models

This work employs the Optimized Potentials for Liquid Simulations All-Atom (OPLS-AA) force field to describe CH4, which characterizes each atom thoroughly without sacrificing the intramolecular interactions to promote simulation efficiency, demonstrating a high accuracy in predicting hydrocarbon physical properties28. The elementary physical model (EPM2) force field is adopted to represent CO2. The extended simple point charge (SPC/E) model describes H2O molecules with charges assigned to each atom, ensuring precise results for further analysis. The consistent valence force field (CVFF) force field defines the kerogen matrix. Saline environments with a concentration of 3 mol/L NaCl are modeled using the clay force field (CLAYFF), incorporating Na+ and Cl− ions to investigate their effect on gas adsorption and distribution behavior surrounding the water bridge. A generic force field, the DREIDING force field, is used to compute intramolecular interactions among the shale model, H2O molecules, ions, and gas particles. The detailed force field information is presented in Table S1 of the Supplementary information. Validation of the developed models can be found in Fig. S1 of the Supplementary information, which has successfully reproduced the macroscopic properties of fluids from the National Institute of Standards and Technology (NIST) database5,6,7, 14.

The DREIDING force field potential consists of two essentials, i.e., the bonding and non-bonding factors. The bonding part includes the bond stretch term (Eb), the angle-bend term (Ea), the torsion term (Et), the out-of-plane angle term (Eo), and the cross-coupling term (Ec), which are expressed as follows29,

$$E_{potential} = \, E_{bond} + \, E_{{non{ - }bonded}}$$
(1)
$$E_{bond} = \, E_{b} + \, E_{a} + \, E_{t} + \, E_{o} + \, E_{c}$$
(2)

The non-bonding part includes the van der Waals (vdW) interaction represented by the Lennard–Jones 12-6 potential, and the Coulombic potential, described as follows29,

$$E_{non - bonded} = 4\varepsilon_{XY} \left[ {\left( {\frac{{\sigma_{XY} }}{{r_{ij} }}} \right)^{12} - \left( {\frac{{\sigma_{XY} }}{{r_{ij} }}} \right)^{6} } \right] + k_{e} \frac{{q_{X} q_{Y} }}{{r_{ij} }}$$
(3)

where εXY stands for the Lennard–Jones potential well depth, and σXY represents the zero-potential distance. rij corresponds to the distance between particles of i and j, and q is the charge of particles. In addition, the cross term is computed by applying the Lorentz–Berthelot mixing rule as below,

$$\sigma_{ij} = \frac{1}{2} \left( {\sigma_{ii} + \sigma_{jj} } \right)$$
(3)
$$\varepsilon_{ij} = \sqrt {\varepsilon_{ii} \times \varepsilon_{jj} }$$
(4)

Results and discussion

The density distributions of CH4 and CO2 are examined and discussed in this section to highlight water bridge’s impact and explore the water bridge’s stability from a visualized perspective, providing a molecular-scale analysis of the water bridge’s influence in shale reservoirs. In addition, the effects of temperature, pressure, and salinity on the adsorption and diffusion performances of CH4 and CO2 are investigated in this work.

Density distribution of gas molecules

The gas density distribution is computed under various geological conditions, including the temperatures of 308 K, 338 K, and 368 K at pressures of 10 MPa and 20 MPa for pure CH4 and CO2. The amount of pre-absorbed water molecules needed to form a water bridge can be determined by the equation below,

$$\varpi = \frac{{N_{{H_{2} O}} *W_{{H_{2} O}} }}{{N_{{H_{2} O}} *W_{{H_{2} O}} + W_{skeleton} }}$$
(5)

where N represents the molecule number, and W represents the molar weight (g/mol). This work sets the moisture content as 11.15% of the matrix mass to enhance the water bridge effect. The quantity of H2O molecules was calculated as 1720. The introduced H2O molecules decreased the micropore volume by 44.96%, similar to that of a 44.1% reduction in a type II-D kerogen matrix with a 2 nm embedded slit by Stevens19, indicating the rationality and reliability of this study.

The density profiles of the water bridge and gas molecules are determined by chunking the simulation system along three axes using the chunking command built into the LAMMPS software. The water density distribution profiles in three axes are plotted in Fig. 2 for better understanding. Based on the molecular distribution description in Fig. 2a,b, the water bridge distribution is in line with the observation in previous studies30,31. The increasing moisture content contributes to a water bridge formation between the shale slit. The density profile in Fig. 2c–e shows that the water bridge exhibits a narrow waist region, indicating weaker potential energy in this area, as seen in the center light blue area in the z direction, which lies between -12.5 Å and 12 Å.5 in Fig. 2e, presenting poor interactions between H2O molecules and the kerogen matrix. In contrast, the left light blue regions in Fig. 2e show a stronger connection between the water bridge and the kerogen surface, suggesting high potential energy and strengthened interaction between them, aligning with the findings by Sun and Liu4,32. This adsorption distribution suggests H2O molecules preferentially adsorb on the kerogen surface other than residing within the void slit in shale.

Figure 2
figure 2

The (a) side view and (b) front view of water bridge atomic structure, (c–e) density distribution profiles of water bridge (H2O number of 1720), blueberry color for H atoms of H2O and navy color for O atoms of H2O.

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The density profiles of CH4 in three axes with the presence of water molecules at 10 MPa under temperatures of 308 K, 338 K, and 368 K are depicted in Fig. 3. The CH4 absolute adsorption under 10 MPa is 6.0 mmol/g, 5.4 mmol/g, and 4.6 mmol/g, respectively, 308 K, 338 K, and 368 K, with a water bridge. This adsorption pattern is in line with previous experimental studies by Billemont, and Ottiger33,37,35 conducted on Eagle Ford Play shale and Marcellus Play, of which are 5.8 mmol/g and 5.5 mmol/g at 318 K. The determined values in this work also algin with Sui, Heidari, and other simulation studies36,40,38 presented 5.2 mmol/g, 5.6 mmol/g, 6.1 mmol/g, and 5.5 mmol/g of absolute CH4 adsorption in shale gas reservoir, the adsorption deviations are negligible compared with this study. According to the density distribution in the z-axis, it is evident that CH4 exhibits a two-layer adsorption pattern in the shale model. The first adsorption peak shows up within the micropores featured kerogen matrix, while the secondary adsorption layer is observed near the kerogen surface inside the kerogen slit. The secondary adsorption layer is more noticeable than the first peak due to the micropores restraining the gas particles accumulation than that in meso-slit. Figure 3a–c demonstrate a decrease in CH4 adsorption across all directions with the increasing temperature and CH4 density distribution consistent with the outcomes by Huang34. Figure 3d presents an overview of the CH4 adsorption pattern with H2O. As the temperature increases, CH4 adsorption decreases insignificantly within the kerogen matrix but dramatically within the slit as the bulk phase as well as in the regions adjacent to the kerogen surface. This noticeable reduction in slit is attributed to the tremendous energy brought by the high temperature, allowing gas particles to be more energetic and wander around. The neglectable decrease within micropores of the kerogen matrix is attributed to the micropores having a more significant overlapping effect on gas adsorption, the increasing temperature enhances the collisions between gas molecules and the kerogen wall, thereby increasing the attachment potential, hence canceling the negative impact brought by the rising temperature to some extent.

Figure 3
figure 3

The (a–c) density distribution profiles of CH4 adsorption at 10 MPa under 308 K, 338 K, and 368 K, (d) front view of CH4 adsorption atomic structure with the presence of water bridge at 308 K and 10 MPa, lime color for C atoms of CH4 and green color for O atoms of CH4.

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The computed density profiles of CO2 in three axes with the water bridge at 10 MPa under temperatures of 308 K, 338 K, and 368 K are presented in Fig. 4. The CO2 absolute adsorption under 10 MPa is 8.6 mmol/g, 7.4 mmol/g, and 6.7 mmol/g at respectively 308 K, 338 K, and 368 K. This computed adsorption amount is in line with the observations by Raza, Ottiger, and other studies35,39,37, 39, 40, presenting 10.5 mmol/g in simulation, and 9.0 mmol/g by simulation under the same conditions. Figure 4a–c demonstrate a decreasing trend in CO2 adsorption amount with increasing temperature in all directions. Figure 4d presents an overview of CO2 adsorption behavior with H2O. Similar to CH4, the density profile of CO2 exhibits a two-layer adsorption structure in the direction of z-axis. The first adsorption is observed within the kerogen matrix, and the secondary adsorption layer lies adjacent to the kerogen surface. As the temperature grows, CO2 adsorption mildly shrinks in the kerogen matrix but significantly decreases within the slit as a bulk phase. Unlike CH4, there is no significant decrease in CO2 density next to the kerogen surface in the direction of z-axis, which is attributing to a stronger affinity between CO2 and shale than that of CH4 and shale.

Figure 4
figure 4

The (a–c) density distribution profiles of CO2 adsorption at 10 MPa under 308 K, 338 K, and 368 K, (d) front view of CO2 adsorption atomic structure with a water bridge at 308 K and 10 MPa, pink color for C atoms of CO2 and magenta color for O atoms of CO2.

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Figure 5 illustrates a water bridge presenting density profiles of CH4 and CO2 under 308 K and 10 MPa. Both CH4 and CO2 exhibit a two-layered adsorption shape within the kerogen matrix, showing the significant gas adsorption potential for the kerogen matrix; however, a higher CO2 adsorption amount within the kerogen matrix, suggesting more intense interactions between CO2 molecules and kerogen than that of CH4. Furthermore, CO2 shows higher density distribution in the bulk phase than CH4, indicating the preferential competitive adsorption performance of CO2 over CH4 within the matrix. CO2 has high sequestration potential in shale reservoirs, which suggests high capability in CO2 storage.

Figure 5
figure 5

Density distribution of CH4, CO2, and H2O in direction of z-axis at 308 K and 10 MPa.

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According to the analysis of the density distribution of CH4 and CO2 at 338 K under 10 MPa and 20 MPa, as shown in Fig. 6, the gas adsorption is enhanced in all directions with the rising pressure. The deviation is that CH4 has higher adsorption at high pressure in both the matrix surface region and in the kerogen slit as the bulk phase, as depicted in Fig. 6a–c. From Fig. 6d–f, CO2 density properties are similar to those of CH4 with pressure. On the contrary, the density profile of CO2 in the direction of the z-axis, as seen in Fig. 6f, shifts insignificantly on the matrix surface due to the almost fulfillment of the surface adsorption sites, but a noticeable increase in the matrix slit as the bulk phase.

Figure 6
figure 6

Density distribution in 3-axes of (a–c) CH4, and (d–f) CO2 at 338 K under 10 MPa and 20 MPa.

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Saline effect in density distribution

Saline aquifers are abundant and geographically widespread worldwide41,42. Thereby, Na+ and Cl− are introduced into the system to model the saline environment, as NaCl is considered the primary component of many formation brines43. The introduced H2O–NaCl system is usually employed to represent the fluid inclusions in various geological settings, such as hydrothermal mineral deposits, to quantify the salinity effect on gas adsorption inside the kerogen matrix.

The density profiles of H2O molecules with the presence of NaCl were computed in three directions, as depicted in Fig. 7. Figure 7a–c demonstrate the dynamic process of the water bridge shifting in the yz plane, which moves towards the center of the slit with the increasing NaCl concentration. In addition, the increasing concentration leads to a more uniform water distribution, which expands across the kerogen surface. This observation aligns with the simulation studies by Zhao, Xiong44,45, and the experimental works by Teklu and Wang46,47. This observation is evident in three axes, as shown in Fig. 7d,e. Furthermore, density distribution increases adjacent to the matrix surface, whereas, decreasing within the bulk phase with the concentration along the z-axis. This observation suggests that ions enhance the potential between H2O molecules and the matrix surface, resulting in preferential attachment of H2O molecules onto the kerogen surface. The scenario is attributed to negative and positive charges distributed on the shale surface; extra ions are introduced into the kerogen–water–gas system with the increasing concentration, H2O molecules enlarge along the shale surface, and the hydrophilicity of the kerogen surface increases with the growing concentration. This observation indicates an alternation in the shale surface wettability resulting from the contact angle reduction. Moreover, the amount of H2O molecules inside the matrix slits is reduced, implying ion weakens the potential energy at the water waist. In contrast, there is negligible H2O distribution variation within kerogen nanopores, owing to the adsorption sites within the matrix being almost filled with H2O molecules. The increasing concentration cannot further enhance H2O adsorption inside the nanopores of the matrix.

Figure 7
figure 7

The (a–c) side view of pure, 3 mol/L, and 6 mol/L NaCl water bridge structure, (d–f) density distribution profiles of water bridge under different salinity in 3 axes, pink color for Na+ ions and yellow color for Cl− ions.

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According to the density distributions of CH4 and CO2 in Fig. 8a–c, CH4 exhibits a decreasing trend at the matrix surface with concentration. This observation is in line with the experimental study by Zhang. Coal samples from the Baode block underwent a noticeable CH4 reduction with increasing salinity from 1000 to 2200 mg/L48. This CH4 reduction consists of the simulation outcomes on a type II-D kerogen matrix that experienced a NaCl encroachment from 2.5 to 6 mol/L by Zhou49. Figure 8a,b depict insignificant CH4 adsorption decreases at the boundaries of the x and y axes, whereas a particular reduction along the z-axis in Fig. 8c, attributed to the increased salinity promoting the interaction between H2O and kerogen, causes H2O to occupy the adsorption sites previously held by CH4. On the contrary, CO2 presents a distinct adsorption pattern, as depicted in Fig. 8d,e, CO2 demonstrates a slight adsorption increase on the kerogen surface with increasing salinity due to its favorable solubility in H2O, neutralizing the negative impact of H2O preferential adsorption. These observations provide evidence for the dynamic response of CO2 influence on H2O penetration into the kerogen matrix, suggesting that CO2 alters shale surface wettability.

Figure 8
figure 8

(a–c) CH4, and (d–f) CO2 density profiles in 3 axes under 0 mol/L, 3 mol/L, and 6 mol/L NaCl water bridge environment.

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Gas diffusion behavior and mean square distance

Gas diffusion plays a crucial role during industrial gas flow, the organic nanopores restrain the gas diffusion process in shale, profoundly impacting both CH4 recovery and CO2 storage processes. The mean square distance (MSD) indicator is usually adopted to compute the diffusivity of gas transport and investigate the gas diffusion process. Previous studies50,56,57,58,54 have simplified this determination by considering Ds as the slope divided by six from linear regression analysis of MSD curves; however, this approach may lead to unexpected deviations in self-diffusivity results. This study combines the MSD and Einstein methods for a more precise self-diffusion coefficient estimation. The Einstein equation is expressed as follows50:

$$D_{s} = \frac{1}{6N}\mathop {\lim }\limits_{t \to \infty } \frac{d}{dt}\left\langle {\mathop \sum \limits_{k = 1}^{N} \left[ {r_{k} (t) - r_{k} (0)} \right]^{2} } \right\rangle$$
(6)

where Ds is the self-diffusion coefficient, representing the random motions or mixing of particles in the thermodynamic equilibrium. N is the gas molecular number, and k is the simulation time. rk(t) and rk(0) are the position vectors at t time and initial time. This section investigates the gas diffusion behavior for CH4 and CO2 in the water bridge system under 10 MPa and 20 MPa with and without ions.

Figure 9 depicts the MSD plots for CH4 and CO2. An initial unstable stage at the early timesteps is observed for both gases, particularly at low pressure. Then, the MSD profile stabilized at an equilibrium stage. A noticeable MSD reduction is observed at 20 MPa compared to 10 MPa for CH4 and CO2, indicating that high pressure restricts gas diffusion. CH4 in Fig. 9a presents a steeper MSD slope than CO2 in Fig. 9b, suggesting CO2 preferentially tends to attach to the adsorption sites, whereas CH4 predominantly resides within the slit as the bulk phase under the same condition. CO2 acts out a preferential adsorption behavior on shale over CH4, even with the presence of the water bridge.

Figure 9
figure 9

MSD of (a) CH4, and (b) CO2 under 338 K at 10 and 20 MPa.

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Figure 10a illustrates the MSD variation with the temperature conducted at 308 K, 338 K, and 368 K under 10 MPa. The MSD slope exhibits significant growth with increasing temperature, from 0.088 cm2/s at 308 K to 1.02 cm2/s at 338 K and further to 1.24 cm2/s at 368 K, which aligns the observation by Sun and Zhou50,55. This scenario is attributing to the high temperature providing more energy and facilitating the more intense particles’ movement transporting along the passing channel. Different NaCl concentrations are added into the water system to probe the encroachment effect on gas diffusion, the computed results of which are illustrated in Fig. 10b. As salinity increased, MSD increased a little from 1.02 cm2/s in pure water bridge to 1.08 cm2/s and 1.1 cm2/s at NaCl 3 mol/L and 6 mol/L concentrations, respectively. This enhancement can be attributed to the above-flattened water bridge attachment on the shale surface with increasing salinity, making a thinner waist and leaving more void space for CH4 to traverse.

Figure 10
figure 10

(a) MSD of CH4 under 10 MPa at 308 K, 338 K, and 368 K, (b) MSD of CH4 at 338 K with the presence of a water bridge of concentration of 0 mol/L, 3 mol/L, and 6 mol/L.

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The Einstein determination comprises two stages, the anomalous diffusion represents the undersaturated gas state where molecules under full adsorption attempt to occupy vacant sites. In contrast, Einstein diffusion characterizes the saturated gas state where molecules attach to available sites and achieve a stable diffusion state. Figure 11 yields consistent findings that the increasing pressure restricts the self-diffusion coefficient in anomalous and Einstein stages for CH4 and CO2. Under saturation conditions, the CH4 self-diffusivity slope in Fig. 11 is 0.99 × 10−9 m2/s (orange line), which aligns with the previous results of 0.97 × 10−9 m2/s by Dawass et al.56,57,58,59. The thermodynamic properties of CO2 are illustrated in Fig. 11b, exhibiting a higher self-diffusion coefficient than CH4, indicating that the smaller aerodynamic diameter holder CO2 passes through kerogen meso-slit faster to get saturated conditions. The self-diffusion coefficient curves at two Einstein stages at 20 MPa are below 10 MPa, suggesting that increasing pressure makes gas diffusion challenging.

Figure 11
figure 11

Self-diffusion of (a) CH4, and (b) CO2 under 338 K at 10 MPa and 20 MPa.

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Figure 12a demonstrates an increase in self-diffusion coefficient with rising temperature, consistent with the above-mentioned observations depicted in Fig. 10a. During the anomalous stage, a more pronounced deviation in self-diffusion coefficient as CH4 molecules tend to occupy available adsorption sites. Followed by a reduced deviation scale during the Einstein stage, CH4 almost saturated and travels as the bulk phase. In addition, CH4 shows minor shifting with ions despite the concentration increases from 0 to 6 mol/L in Fig. 12b, owing to the non-polarity characteristic of CH4 weakening the interactions between CH4 and kerogen. However, the more flattened water bridges distribution on the kerogen surface enables more space for CH4 molecules to wander inside.

Figure 12
figure 12

Self-diffusion coefficients of (a) CH4 under 10 MPa at 308 K, 338 K, and 368 K, (b) CH4 at 338 K with the presence of a water bridge of concentration of 0 mol/L, 3 mol/L, and 6 mol/L.

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Conclusions

This work has novelty investigated the gas adsorption and transportation behavior in shale gas reservoir with formation water, which has usually been neglected or overlooked in previous studies. Notably, this work induced various salinity approaches to a more reliable subsurface environment. Based on the discussion in section “Results and discussion”, the water bridge formed inside the shale reservoir negatively works on gas distribution, particularly water-contained ions inside the underground system, further impeding the gas transport and adsorption pattern. This study has probed and discussed gas adsorption characteristics, distribution profile, and diffusion behavior under 308 K, 338 K, and 368 K at 10 MPa and 20 MPa with a water bridge. Furthermore, 3–6 mol/L NaCl are added into the system, the effect of the ion on the water bridge pattern on the shale surface and interaction with gas particles. This approach is more suitable for modeling underground environments and can enhance the realism of gas exploration and extraction. The conclusions are drawn as follows,

  1. 1.

    CH4 and CO2 adsorption on the kerogen and slit decreases with the presence of a water bridge, owing to the preferential interaction between H2O and kerogen enhancing the H2O capture of the available adsorption sites, thereby leaving CH4 and CO2 less favorable adsorption environment.

  2. 2.

    The increasing salinity of NaCl weakens CH4 and CO2 adsorption on the kerogen surface added into the water system, attributed to the ions enhancing the interaction between H2O and kerogen, thereby reducing available adsorption sites for gas particles and resulting in a diminished adsorption pattern.

  3. 3.

    The diffusivities of CH4 and CO2 are constrained by the increasing pressure in this work, attributed to the external force that restricts the movement of gas particles. Conversely, increasing temperature enhances gas diffusivity by providing more energy. Moreover, the growing salinity has an insignificant influence on gas diffusivity.