Gas transport model and numerical solution in roof rock based on the theory of free gas diffusion.

Accurately identifying the source of coalbed methane is of great practical significance in preventing gas concentration overruns and improving extraction efficiency. At present, it is widely believed that underground gas mainly comes from coal desorption, and the mechanism of gas flow inside the coal seam is explored in depth, while the gas released inside the rock is often neglected, and there is insufficient understanding of its internal transportation law. In this study, the density gradient theory (FGDGD) in the coal matrix was used as a guide to characterize the adsorption and transport properties of gases within the rock. The anthracite and mudstone from the same roadway in Yuxi mine were selected for the experiments, and coal rock samples with particle sizes of 0.425 mm–0.25 mm were ground. The adsorption constant test and adsorption process experiments were carried out under the constant volume condition, and the transport behavior of gas within the rock was simulated and numerically solved, and the content and flow behavior of gas in the rock were discussed in detail. The results are as follows: (i) The simulation curves based on the density gradient model fit well with the experimental data for both coal and rock downholes, indicating that the gas transport law inside the rock downhole is also in accordance with the density gradient theory, which broadens the scope of application of the theory. (ii) The free gas diffusion coefficients D ks (rock) are smaller than D ks (coal) for the gases in the rock matrix and coal matrix, which may be due to the difference in the pore structure of the rock matrix, resulting in lower adsorption sites than those of the coal. (iii) Although the gas content inside the rock is relatively low compared with that of coal, it is significant for reducing the prediction error of gas influx in engineering practice. Therefore, it is necessary to consider the storage of gas in rocks and its migration behavior when studying the sources of gas emissions in engineering fields. • Theoretical model of gas density gradient in roof mudstone matrix based on coal matrix. • Inversion of diffusion coefficient in roof mudstone based on empirical model. • In engineering practice, we cannot ignore the gas existing in the roof rock. [ABSTRACT FROM AUTHOR]