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 (D_m). 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, D_m 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.

理解天然气运移机制对于预测煤层气（CBM）井筒的天然气产量具有至关重要的意义。目前，在煤基质中广泛使用的菲克扩散定律已受到越来越多研究者的质疑。提出了一种以自由气体密度梯度（FGDG）为驱动力的扩散理论，并将其对应的关键参数称为微通道扩散系数（D _m）。然后，建立了数学模型，并通过有限差分法（FDM）进行了数值求解，并将数值计算结果与8个煤样的气体脱附量实验数据进行了比较。最后，分析和讨论了基于Fick定律的FGDG模型以及TID（时间无关扩散率）和TDD（时间相关扩散率）模型的合理性。在整个解吸期间，FGDG模型的数值解与相关的实验结果非常吻合。与基于Fick扩散理论的TID和TDD模型相比，FGDG模型更合理，更准确，可用于预测气体迁移行为。此外，D _m可以消除其对时间的依赖性，而相对于煤阶却表现出不对称的U形分布。本研究旨在为推广天然气运移理论提供一些新思路。