Numerical modeling of gas extraction from coal seam combined with a dual-porosity model: Finite difference solution and multi-factor analysis

Abstract Gas extraction from coal seams is an extremely significant technical measure for preventing gas hazards and predicting coalbed methane (CBM) reservoir. Gas diffusion and seepage properties during the extraction process jointly dominate the CBM migration and production. How to integrate diffusion and seepage theories to construct numerical models of coalbed methane flow and evaluate extraction performance has become one of the hot spots of competitive research. In this work, we developed an integrated mathematical model of seepage and diffusion during borehole gas extraction combined with a dual-porosity model. Emphatically, the gas diffusion driver in coal matrix is no longer the concentration gradient (CG) associated with Fick's Law, but the innovative free gas density gradient (FGDG). The driving force for gas seepage in fractures remains the pressure gradient (PG) with respect to Darcy's law. Here, seepage and diffusion were coupled by a gas source term equation. Subsequently, a numerical simulator based on finite difference method (FDM) was programmed to compute the mathematical equations of gas extraction. Finally, the simulation results were validated by field gas extraction data and the contribution of some key parameters to the gas flow rate was discussed. The findings indicate that: (i) the simulation results are generally consistent with field data, and the developed model as well as simulator both have the capability to predict methane gas extraction. (ii) The gas diffusion process in coal matrix can be considered to be dominated by the FGDG. (iii) The gas permeability coefficient in fractures mainly controls the gas flow rate in the early extraction stages, while the coal matrix radius and microchannel diffusion coefficient contribute more in the later periods of gas extraction. (iv) Fracture porosity is positively correlated with gas flow rate and negatively correlated with the magnitude of flow rate decay. (v) The higher the original gas pressure or the lower the extraction pressure, the greater the pressure gradient between the borehole and the coal seam, contributing to an increase in gas flow. This work is expected to provide some support in modelling the gas flow in coal seam and assessing the dynamic CBM production.