The Apparent Permeability Model of Gas in Micro-Nano Pore in Coal Seam Considering Multi-Layer Adsorption and Effective Stress and its Application

Abstract

Gas, as a clean energy source, is an integral part of the global energy market structure. The permeability is a crucial parameter determining the gas extraction efficiency. However, the current studies about the permeability models of micro-nano pores in coal seams are insufficient, and many models were not fitted accurately with field gas extraction data. To solve above issues, the gas apparent permeability model of micro-nano 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 is 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 the increasing the Kn, in view of effective stress and multilayer adsorption, while gas pressure primarily influences the Kn by altering mean molecular free path. Furthermore, an increase of both effective stress and adsorption layer thickness affects 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.

Keywords: Different flow states, Knudsen number, Apparent permeability model, coalbed methane, Multilayer adsorption