Unidirectional apparent diffusion-permeability model of gas in matrix micro-pores of low permeability coal seam

The traditional steady-state method and transient method are unable to measure the permeability in the matrix micropores of low-permeability coal seam, particle coal cannot be used as the object of measuring the matrix permeability under the loading condition, and the conventional theoretical model to describe the gas flow characteristics is unreasonable in the matrix pores of low-permeability coal seam under the loading condition. In order to solve above problems,the unidirectional apparent diffusion model of gas was established, and the analytical solution of the model was derived. Then, according to the principle of mass conservation, the relationship between permeability and diffusion coefficient was derived. An experimental method (apparent diffusion coefficient permeability) and a unidirectional apparent diffusion coefficient-permeability model were established to describe the permeability in the matrix micropores of low-permeability coal seams. In order to verify the rationality of the model, the unidirectional desorption flow experiment of gas under triaxial stress was carried out with a standard cylindrical coal core of phi 50 mm x 100 mm. At the same time, the comparative experiment of radial desorption flow of the same kind of columnar coal was performed. Under the same conditions, the steady-state permeability experiment was conducted. The experimental results of unidirectional desorption flow show that the apparent diffusion coefficient-permeability has a negative exponential relationship with the increase of confining pressure. The analysis indicates that the increase of confining pressure leads to the closure of pores and fractures, which makes the pore radius decrease. Therefore, the pore size and structure directly affect the apparent diffusion coefficient permeability, which results in the decrease of apparent diffusion coefficient permeability. Secondly, through the contrast testing, it was found that the desorption flow amount and desorption flow ratio are far less than those of the unidirectional desorption flow without loading, which indicates that the confining pressure has a great influence on the desorption flow characteristics of gas in coal seam, and the confining pressure conditions should be considered when we study the factors affecting the desorption flow characteristics of gas in coal seam. Under the same conditions, the permeability measured by the new method is at least two orders of magnitude lower than that measured by the steady-state method. Therefore, it is necessary to develop new permeability measurement methods. The verification shows that the unidirectional apparent diffusion coefficient-permeability model can effectively describe the flow characteristics of gas in the matrix pores of coal seams under loading conditions. As a result, the model was able to effectively provide theoretical guidance for measuring the matrix permeability of gas in matrix pores and describing the flow characteristics of gas in matrix pores well.