Numerical modeling and experimental validation of anomalous time and space subdiffusion for gas transport in porous coal matrix

Abstract

Accurate description of gas transport in porous coal matrix is one critical issue for coalbed methane production. However, the adequacy of existing Fickian diffusion-based models for gas transport in heterogeneous coal matrix is debated. In this study, taking into account the basic topological complexity inherent to porous coal matrix and the strong adsorption effect of coal on gas molecules, an anomalous subdiffusion model with fractional time and space derivatives is proposed to characterize the mechanism of gas transport in heterogeneous coal matrix. The fractional diffusion equation is discretized and solved by using an implicit numerical scheme which is based on the generalization of standard finite-difference method. Furthermore, gas adsorption and desorption experiments with two coal samples collected from China were carried out to validate the anomalous subdiffusion model. It is revealed that the anomalous subdiffusion model with merely three parameters can reproduce the dynamic process of gas transport with better accuracy than existing Fickian diffusion-based models, suggesting the anomalous time and space subdiffusion to be the governing process of gas transport in coal matrix. Finally, the parametric sensitivity analysis shows that the introduction of fractional parameters in the present model is essential to accurate description of gas transport in heterogeneous coal matrix.