Evolution Model of Gas Pressure Around Coal Seam Boreholes and Determination of the Effective Drainage Radius

The effective drainage radius is a key parameter for borehole layout and gas drainage performance evaluation, and it is determined by the spatiotemporal evolution of gas pressure around drainage boreholes. Taking the M4–5 coal seam of a Xinjiang coal mine as the study case, the residual gas-content criterion was converted into a site-specific equivalent pressure criterion using Langmuir adsorption parameters, and 0.58 MPa was adopted as the working pressure threshold for effective drainage. A transient radial gas pressure evolution model was then established based on mass conservation, Darcy seepage, and Langmuir adsorption and evaluated against field measurements. For 62 paired measured–calculated data points at radial distances of 1.0 and 1.5 m, the overall MAE, RMSE, and MAPE were 0.0204 MPa, 0.0265 MPa, and 2.86%, respectively, with an R2 of 0.9756 and a maximum absolute relative error of 8.67%. Decreasing the borehole boundary pressure, increasing the coal-seam gas permeability coefficient, and increasing the borehole radius could promote gas pressure reduction, while the additional benefit of further reducing the boundary pressure gradually diminished at lower pressure levels. Increasing the coal-seam gas permeability coefficient from 0.015 to 0.090 m2·MPa−2·d−1 reduced the gas pressure at 1.0 m by 35.63% and increased the effective drainage radius from 0.65 to 2.01 m over 15–90 d. Field measurements showed that, after 90 d, the residual gas pressure and gas content at 2.0 m were 0.39 MPa and 3.95 m3/t, respectively, providing preliminary field support for the calculated drainage range. An empirical relationship among initial gas content, drainage duration, and effective drainage radius was further established, with an overall MAPE of 7.50% and an R2 of 0.9562 within the fitted range. For an initial gas content of 8.3 m3/t and a drainage duration of 300 d, long-term mathematical extrapolation yielded an effective drainage radius of 2.80 m; after conservative engineering correction, 2.30 m was adopted, corresponding to a geometrically estimated upper-limit borehole spacing of 4.60 m. The results provide a reference for effective drainage radius prediction and borehole layout optimization under gas-geological conditions similar to those of the test area.