Mathematical model and numerical solution of constant pressure adsorption of gas in coal particles

In order to study the flow mechanism of gas in coal particles, four groups of constant pressure adsorption experiments were carried out at different initial pressures, and the experimental data of cumulative gas adsorption volume content with time were extracted. Based on Darcy theory driven by pressure gradient and new diffusion model driven by the density gradient of free gas, two kinds of mathematical models of gas adsorption at constant pressure were established, and the adsorption process was numerically solved by VB program code, and the simulation data of cumulative adsorption volume content inside coal particles were obtained. By comparing and analyzing the two kinds of simulation results with the experimental data, it is found that numerical calculation results are consistent with the experimental data, thus verifying the accuracy of the numerical simulation. In addition, the key proportional coefficients in the two models with the change of pressure are different. The permeability coefficient is negatively correlated with the pressure, and the microchannel diffusion coefficient does not change with the pressure. It is concluded that the diffusion model driven by the density gradient of free gas is more suitable to describe the gas migration law in coal particles than Darcy's law and Fick's law.