**Pore-Scale Lattice Boltzmann Simulation of Gas Di**ff**usion–Adsorption Kinetics Considering Adsorption-Induced Di**ff**usivity Change**

#### **Zhigao Peng 1,2,\*, Shenggui Liu 3, Yingjun Li 4, Zongwei Deng 1 and Haoxiong Feng 1**


Received: 13 August 2020; Accepted: 17 September 2020; Published: 20 September 2020

**Abstract:** 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 grea<sup>t</sup> 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.

**Keywords:** coalbed methane; Lattice Boltzmann method; gas diffusion; adsorption–desorption; pore-scale
