Fractal permeability model for dual-porosity media embedded with natural tortuous fractures

Abstract

Coal is a dual-porosity medium with an internal pore-fracture structure that serves as a channel for the migration of coalbed methane. Understanding the relationship between permeability and pore-fracture structure characteristics is therefore of great significance to accurately predict coalbed methane productivity. In this work, we analyze the pore-fracture structure characteristics of real coal samples and establish a new fractal permeability model of dual-porosity media embedded with natural tortuous fractures. Compared with the traditional dual-porosity medium model with embedded parallel plane fractures, this model not only considers the characteristics of pore tortuosity but also those of fracture tortuosity. The results show that the predicted permeability values obtained from the proposed model are 1–2 orders of magnitude lower than those of the traditional model, which implies that the latter overestimates coal seam permeability. The coal matrix permeability is approximately 13 orders of magnitude lower than the fracture permeability, and the latter mainly controls the overall coal seam permeability. Gas flow analysis of the coal seam is conducted in COMSOL Multiphysics, in which a fracture structure image is transformed to the computational domain. We use the results to discuss the relationships between coal permeability and fracture geometric characteristic parameters. The results show that the porosity ϕf and fractal dimension Dl of the fracture substantially affect coal seam permeability and follow a strong power-law relationship. The numerical simulation results are in good agreement with the theoretical predicted values (the average error is about 11.97%), which verifies the accuracy of the proposed model.