Apparent Permeability Model of Gas in Micronano Pores in Coal Seam Considering Multilayer Adsorption, Effective Stress, and Application

Gas plays an important role in environmental protection and energy transformation. Rational development and use of gas resources can effectively reduce environmental pressure and promote sustainable development. Permeability is a key index to measure the characteristics of coal seams and is related to the speed and flow of natural gas and affects the efficiency, recovery rate, and cost of mining. However, current studies on the permeability models of micronano pores in coal seams are insufficient, and many models were not fitted accurately with field gas extraction data. To solve these issues, the gas apparent permeability model of micronano pores, including dynamic changes in pore size, is constructed and validated based on the impacts through effective stress, multilayer adsorption, and surface diffusion in this paper. The mechanisms of the Knudsen number (Kn) and apparent permeability are discussed, and it is applied to interpret field gas extraction laws. The results indicate that this model is verified by matching experimental data. The reduction of the effective pore radius causes an increase in Kn in view of effective stress and multilayer adsorption, whereas gas pressure primarily influences Kn by altering the mean molecular free path. Furthermore, an increase of both effective stress and adsorption layer thickness causes a change of the pore radius, causing a reduction in apparent permeability, and apparent permeability also decreases as gas pressure increases. Accurate prediction of methane content in coal seams can be achieved by taking into account adsorption layer thickness. Gas production will improve through measures aimed at reducing effective stress. Combining this model with field data, it is found that increasing the persistence and proportion of viscous and slip flow can effectively improve gas extraction rates. The findings presented in this paper establish a theoretical foundation for enhancing the efficiency of coalbed methane extraction.