An anomalous subdiffusion model with fractional derivatives for methane desorption in heterogeneous coal matrix

Abstract

Methane desorption in coal matrix is one of the fundamental gas transport processes during coalbed methane extraction, the mechanism of which is commonly described by Fickian diffusion theory. Here, an anomalous subdiffusion model with fractional derivatives is developed to explore the methane desorption in coal matrix with a highly heterogeneous pore structure. Numerical simulations reproduce the volume fraction of gas desorbed over the entire timescale of experimental desorption. It is suggested that the diffusion of methane in heterogeneous coal matrix may obey the anomalous time and space subdiffusion, rather than Fickian second law. The physical reason is perhaps due to the basic topological complexity inherent to porous coal matrix and the strong adsorption effect of coal on methane molecules.