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.
Highlights
Coal seams are typical dual porosity media consisting of the cleats and matrix blocks, which differ significantly from conventional gas reservoirs in that most methane in coal seams is originally adsorbed on the surface area of coal matrix rather than stored as a free gas.[1]
In this letter, taking into account the heterogeneity of pore structure and the adsorption effect of coal on methane, we propose an anomalous subdiffusion model with fractional derivatives for methane desorption in coal matrix, which includes the diffusional flux based on anomalous time and space subdiffusion in the pore volume, the concentration variation due to accumulation in the pore volume and on the pore surface as follows
This study presents an anomalous subdiffusion model with fractional time and space derivatives to describe the methane desorption process in heterogeneous coal matrix
Summary
Coal seams are typical dual porosity media consisting of the cleats and matrix blocks, which differ significantly from conventional gas reservoirs in that most methane in coal seams is originally adsorbed on the surface area of coal matrix rather than stored as a free gas.[1]. The adequacy of those models for describing the methane diffusion in coal matrix with a highly heterogeneous pore structure is debated.[4] There exist significant deviations between theoretical predictions of current Fickian diffusion-based models and experimental values over the full timescale of desorption, and it is difficult to obtain a reasonable representation of the multi-scale pore structure for numerical modelling.[5,6,7,8] It is argued whether the methane diffusion in heterogeneous coal matrix obeys Fickian diffusion theory, and whether any theory can describe the mechanism of methane diffusion. An increasing number of natural phenomena no longer fit into the relatively simple description of Fick diffusion, but the anomalous diffusion, so that it is announced “anomalous is normal”.11
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