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 pL or Vm, 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.
Highlights
In recent years, the adsorption–desorption behavior of gases in porous media has gained wide attention, and many theories such as single-layer adsorption, multilayer adsorption, capillary condensation, and pore-filling have been successfully applied to many areas [1,2]
To consider the gas–solid dynamic adsorption process, we developed a Lattice Boltzmann (LB) model to realize the adaptive conversion of gas in porous media between adsorption and desorption based on the model proposed by He [38]
The fluid is driven by a pressure gradient, ∇p = 0.01, ignoring the fluid velocity inside the solid block (u = 0, v = 0), the four boundaries are all periodic boundaries; the initial concentration in the field is C0 = 0, the gas diffuses from the left, the concentration at the inlet is unity, the diffusion coefficient inside and outside the solid is consistent, the diffusion coefficient is 1/6, and the other boundaries are set to ∂C/∂n = 0
Summary
The adsorption–desorption behavior of gases in porous media has gained wide attention, and many theories such as single-layer adsorption, multilayer adsorption, capillary condensation, and pore-filling have been successfully applied to many areas [1,2]. For the UNG, including shale gas, coalbed methane, due to the involved complex pore geometries and multi-scale spatial distribution, which makes it difficult to reveal the underlying characteristics of the gas adsorption and storage in the reservoir. Since the wide distribution of pore size, it is difficult to characterize the pore structure of the coal matrix, which makes it complex to understand the behavior of gas flow in the reservoir. Gas flow in coal reservoirs usually involves multiple physical processes, including fluid dynamics, thermodynamics, chemical kinetics, and electrodynamics (because most natural media surfaces are charged), all of which are governed by interface phenomena at the pore-scale [23]. A multi-component gas flow–diffusion–adsorption coupled LB model was established to investigate the effects of fluid flow, gas transport, adsorption/desorption on adsorption, and adsorption-induced matrix diffusion coefficients and porosity
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