Theoretical model and numerical solution of gas desorption and flow mechanism in coal matrix based on free gas density gradient

Understanding the gas migration mechanism is of vital significance to predict gas production from Coal-Bed Methane (CBM) wellbores. At present, the widely used Fick?s law of diffusion in coal matrix has been questioned by more and more researchers. In this paper, a new diffusion theory with Free Gas Density Gradient (FGDG) as driving force is put forward and the corresponding key parameter is named microchannel diffusion coefficient (Dm). Then, mathematical model was established and solved numerically by the Finite Difference Method (FDM), and the numerically calculated data were compared with the experimental data of gas desorption amount of eight coal samples. Finally, the rationality of the FGDG model and the TID (Time-Independent Diffusivity) and TDD (Time-Dependent Diffusivity) models based on Fick?s law were analyzed and discussed. The numerical solution of the FGDG model matches well with the relevant experimental result during the entire desorption period. Compared with the TID and TDD models based on Fick diffusion theory, the FGDG model is more reasonable and accurate, and can be considered for predicting the gas migration behavior. Furthermore, Dm can eliminate its dependence on time while it exhibits an asymmetric U-shaped distribution with respect to coal rank. This research aims to provide some new ideas for the promotion of gas migration theory.