Study on gas transport behavior in coal matrix based on free gas density gradient diffusion: Comparison with fick model

Understanding the mechanism of gas transport in coal matrix is crucial for coalbed methane production and gas disaster prevention. The conventional Fick's law may have certain theoretical flaws because its content gradient includes both adsorbed and free gases, ignoring the fact that free gas dominate gas transport. In this study, enclosed isothermal adsorption tests with adsorbable methane (CH4) and non-adsorbable helium (He) were done first. Then, combined with Fick's law and free gas density gradient diffusion (FGDGD), the corresponding mathematical models of gas diffusion-adsorption were numerically established and solved with finite difference method (FDM). Finally, the numerical simulation results of these two models were validated. The results show that: 1) whether CH4 or He, the simulation curves based on the FGDGD model are always consistent with the experimental data, verifying the correctness of the FGDGD model; 2) the Fick model fits the experimental data with a substantial error when simulating the CH4 diffusion and adsorption process, but fits well when modeling He, demonstrating that the model's failure can be attributed to the misconception that adsorbed gas is involved in transport; and 3) the microchannel diffusion coefficient of free gas (Dm) shows that Dm (He) is greater than Dm (CH4), which can be attributed to the pore structure and gas adsorption-desorption. Consequently, the FGDGD model is reasonable in assuming that gas migration is mainly driven by free gas density gradient, and it also offers a novel method for further research into gas flow in coal matrix.