Gas adsorption occurs when the dynamic adsorption equilibrium conditions of the local adsorptive sites are broken. In the overall process of unconventional natural gas generation, enrichment, storage, and production, this phenomenon plays a significant role. A double-distribution Lattice Boltzmann model for solving the coupled generalized Navier-Stokes equation and advection-diffusion equation with respect to the gas-solid dynamic adsorption process is proposed for multicomponent gas migration in the unconventional reservoir. The effective diffusion coefficient is introduced to the model of gas transport in the porous media. The Langmuir adsorption rate equation is employed to control the adsorption kinetic process of gas-solid adsorption/desorption. The model is validated in two steps through fluid flow without and with gas diffusion-adsorption between two parallel plates filled with porous media, respectively. Simulation results indicate that with other parameters being equal, the rate of gas diffusion in the porous material and the area of the dynamic adsorption equilibrium-associated region increase with the matrix porosity/permeability. Similar results will happen with a greater saturation adsorption amount or a lower Langmuir pressure. The geometric effect on adsorption is also studied, and it is found that a higher specific surface area or free flow region can enhance the gas transport and the rate of adsorption.

The occurrence of coalbed methane adsorption-desorption hysteresis has been widely observed, but a unified understanding of its mechanism is lacking, and the factors affecting its degree are unclear. This study introduces a microscale LB model for gas diffusion-adsorption-desorption in porous media that also accounts for the adsorption-desorption hysteresis effect. The accuracy of the model has been validated using previous experimental data, and the primary controlling factors of adsorption-desorption hysteresis were analyzed. The findings are as follows: (1) In the process of methane diffusion-adsorption-desorption, Knudsen diffusion dominates in micro- and mesopores, while viscous flow prevails in macropores; our model can adaptively adjust gas transport regimes across a broad range of pore sizes and pressures. (2) The desorption amount and rate are close relative to the correction factors α and β. A higher α value corresponds to greater initial adsorption as well as longer desorption time, whereas a lower β value implies weaker desorption capacity and a slower desorption rate. (3) Pore size can affect gas diffusion-adsorption-desorption kinetics, where larger pore size corresponds to efficient gas diffusivity; when r < 10 nm, the desorption process is mainly controlled by the desorption rate. Overall, this study has offered new insights into the mechanism behind methane adsorption-desorption hysteresis at the microscale, identified primary controlling factors of methane diffusion-adsorption-desorption process, and provided a foundation for numerical simulations and experiments related to the adsorption-desorption hysteresis.

Under specific conditions, moisture in natural coal seams can be adsorbed in the pores of the coal matrix, reducing the amount of methane adsorption sites and the effective area of the transport channels. This makes the prediction and evaluation of permeability in CBM exploitation more challenging. In this paper, we developed an apparent permeability model of coalbed methane coupling viscous flow, Knudsen diffusion, and surface diffusion which considers the effects of adsorbed gas and moisture in the pores of the coal matrix on the permeability evolution. The predicted data of the present model are compared with those of other models, and the results show good agreement, verifying the accuracy of the model. The model was employed to study the apparent permeability evolution characteristics of coalbed methane under different pressure and pore size distribution conditions. The main findings are as follows: (1) moisture content increases with saturation, with a slower increase for smaller porosities and an accelerated non-linear increase for porosities greater than 0.1. (2) Gas adsorption in pores decreases permeability, further weakened by moisture adsorption under high pressure but negligible at pressures below 1 MPa. (3) Higher water saturation weakens gas transport capacity, especially with pore sizes smaller than 10 nm. (4) The non-Darcy effect weakens with higher initial porosity, and neglecting moisture adsorption may significantly deviate from actual values in modeling methane transport in coal seams. The present permeability model can capture the transport characteristics of CBM in moist coal seams more realistically and is more applicable for predicting and evaluating the gas transport performance under dynamic variations of pressure, pore size, and moisture. The results in this paper can explain the transport behavior of gas in moist, tight, porous media and also provide a foundation for coalbed methane permeability evaluation.

The diffusion–adsorption behavior of methane in coal is an important factor that both affecting the decay rate of gas production and the total gas production capacity. In this paper, we established a pore-scale Lattice Boltzmann (LB) model coupled with fluid flow, gas diffusion, and gas adsorption–desorption in the bi-dispersed porous media of coalbed methane. The Knudsen diffusion and dynamic adsorption–desorption of gas in clusters of coal particles were considered. Firstly, the model was verified by two classical cases. Then, three dimensionless numbers, Re, Pe, and Da, were adopted to discuss the impact of fluid velocity, gas diffusivity, and adsorption/desorption rate on the gas flow–diffusion–adsorption process. The effect of the gas adsorption layer in micropores on the diffusion–adsorption–desorption process was considered, and a Langmuir isotherm adsorption theory-based method was developed to obtain the dynamic diffusion coefficient, which can capture the intermediate process during adsorption/desorption reaches equilibrium. The pore-scale bi-disperse porous media of coal matrix was generated based on the RCP algorithm, and the characteristics of gas diffusion and adsorption in the coal matrix with different Pe, Da, and pore size distribution were discussed. The conclusions were as follows: (1) the influence of fluid velocity on the diffusion–adsorption process of coalbed methane at the pore-scale is very small and can be ignored; the magnitude of the gas diffusivity in macropores affects the spread range of the global gas diffusion and the process of adsorption and determines the position where adsorption takes place preferentially. (2) A larger Fickian diffusion coefficient or greater adsorption constant can effectively enhance the adsorption rate, and the trend of gas concentration- adsorption is closer to the Langmuir isotherm adsorption curve. (3) The gas diffusion–adsorption–desorption process is affected by the adsorption properties of coal: the greater the p_L or V_m, the slower the global gas diffusivity decay. (4) The effect of the gas molecular adsorption layer has a great impact on the kinetic process of gas diffusion–adsorption–desorption. Coal is usually tight and has low permeability, so it is difficult to ensure that the gas diffusion and adsorption are sufficient, the direct use of a static isotherm adsorption equation may be incorrect.