**5. Conclusions**

In this paper, we established the pore-scale LB model coupled with fluid flow, gas di ffusion, and gas adsorption–desorption in the bi-dispersed porous media of coalbed methane. The Knudsen di ffusion 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 di ffusivity, and adsorption/desorption rate on the gas flow–di ffusion–adsorption process. The e ffect of the gas adsorption layer in micropores on the di ffusion–adsorption–desorption process was considered, and a Langmuir isotherm adsorption theory-based method was developed to obtain the dynamic di ffusion coe fficient, which can capture the intermediate process when 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 di ffusion and adsorption in the coal matrix with di fferent *Pe*, *Da*, and pore size distribution were discussed. The conclusions were as follows:


In the research, many key parameters of coalbed methane, such as Langmuir pressure and volume, cover a relatively wide range. Moreover, due to many characteristics, including geological environment, complex components, fractures, etc., of coal are excluded at pore-scale, the results obtained can be widely applied in the coalbed methane exploitation.

**Author Contributions:** Funding acquisition, Z.P., Z.D., and H.F.; methodology, Z.D.; supervision, Y.L.; validation, H.F.; writing—original draft, Z.P.; writing—review and editing, S.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Project of Hunan Education Department (Grant No. 19C0370), and the General project of Hunan Natural Science Foundation (Grant No. 2020JJ4156), and the Outstanding Youth Project of Hunan Provincial Education Department (Grant No. 18B437).

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

**Data Availability:** The data used to support the findings of this study are included in the article.
