ANALYTICAL SOLUTION FOR THE UNSTEADY-STATE RADIAL FLOW MODEL OF GAS IN CROSS-MEASURE BOREHOLE

Accurate characterization of the radial transient gas flow in cross-measure boreholes is a fundamental theoretical basis for the prevention and control of coal mine gas disasters as well as for efficient coalbed methane extraction. However, analytical investigations of this process remain limited. In this study, a novel gas flow model was established based on cylindrical coordinates and constant-pressure boundary conditions. By employing Laplace transforms and Bessel functions, an analytical solution for this model was derived, which was further validated through comparisons with numerical solutions and traditional exponential integral functions. The sensitivity of key parameters to gas extraction efficiency was systematically analyzed. The study demonstrates that the analytical solution, numerical solution, and traditional exponential integral function exhibit highly consistent temporal evolution, validating the accuracy and reliability of the analytical solution. The agreement between the analytical and numerical solutions significantly outperforms that of the exponential integral function. High permeability significantly enhances initial extraction efficiency, while high adsorption exhibits an inhibitory effect. Higher initial gas pressure aids in increasing initial extraction rate and pressure drop magnitude but reduces overall pressure drop efficiency, leading to more pronounced rate decay in the later extraction phase. Increasing drawdown pressure enhances suction but yields limited gains in extraction rate and efficiency. Increasing the borehole radius enhances the extraction rate and cumulative extraction volume per borehole but reduces the extraction efficiency per unit area. The influence of each parameter on extraction efficiency is ranked as follows: initial gas pressure is greater than adsorption properties, which is greater than or equal to permeability, followed by borehole radius, and extraction negative pressure is the smallest. The findings provide deeper theoretical insight into the transient radial flow behavior of gas in cross-seam boreholes and offer an analytical framework for optimizing gas drainage strategies, improving extraction efficiency, and ensuring safe coal mine production.