Response Surface Analysis on Multiple Parameter Effects on Borehole Gas Extraction Efficiency

To explore the impact of different factors on the effectiveness of borehole gas extraction, in situ stress tests were conducted in a test mining area. A theoretical model of gas migration within the coal matrix–fracture system was established. Based on field data, a numerical model was constructed to study the variation patterns of the effective extraction radius under different extraction conditions. Using the response surface methodology, the interactions of different factors and their impact on the effective extraction radius were analyzed, resulting in a response surface model for each factor and the effective extraction radius. The results indicate that the initial permeability of the coal seam has the greatest impact on the extraction radius, with a maximum range of 2.027 m. The influence of extraction time, extraction negative pressure, and borehole diameter decreases sequentially. The borehole diameter has the least impact, with a range of 0.608 m. The response surface model has good significance, with a coefficient of determination (R2) of 0.9957, and it can explain over 99.57% of the response values. The response surface between the initial permeability of the coal seam and extraction time shows the greatest degree of distortion, indicating a significant interaction effect on the extraction radius. In contrast, the response surface between extraction time and extraction negative pressure shows the least degree of distortion, indicating that their interaction effect is the least significant. These findings can provide a theoretical reference for improving borehole design and enhancing gas extraction efficiency.