Solving of coal seam gas seepage based on Crank-Nicolson difference method

In the process of drainage and natural emission of coal mine gas, Darcy seepage is the main pattern of gas transport in coal seam. The presence of adsorption makes the seepage control equations more complicated. The oversimplification had to be performed for this equations. Based on the seepage theory, the normalized form of governing equations of gas Darcy seepage in coal seams for various coordinate systems are derived. Aiming at the problem of unidirectional gas flow after sudden exposure of coal wall, an unconditionally stable seepage governing finite difference equation with second-order accuracy is derived by using Crank-Nicolson difference method without too much simplification. Using Python's SciPy package and a variant of Powell hybrid method for solving nonlinear equations, numerical solving of the constructed difference equations is implemented through programming. The results show that at different times, both gas content and pressure at different distances from the coal wall, exhibit an arc-tangent function relationship with distance. Therefore, a comprehensive fitting equation for gas content calculation at any position and time could be provided. It is also concluded that the gas emission rate of coal wall decreases as a power function over time.