Layout optimization of long horizontal boreholes to improve gas extraction efficiency through mathematical models and numerical simulations

Abstract Coal mining causes strata fractures and emissions of coal seam gas, posing a serious threat to mining safety along with gas migration within the fractures. Layout of long horizontal boreholes (LHBs) for gas extraction can reduce safety hazards and enhance gas utilization. However, the optimal layout of LHBs is crucial for extraction efficiency. Currently, there is more research on LHB layout based on on-site situations and numerical simulation experiments, and rare theoretical analysis. In this study, the theory of complex functions and the mirror principle were used to establish three mathematical models of LHBs for gas extraction based on three types of layouts: single-row linear layout, nonlinear layout, and double-row parallel layout (divided into aligned and staggered layout). Under various LHB layouts, extraction efficiencies were analyzed and compared through theoretical analysis and numerical simulations. The results showed that when three boreholes were arranged, the individual borehole had a relatively balanced extraction efficiency under single-row linear layout, and exhibited stronger extraction capacity under nonlinear layout, which is preferable. When six boreholes were arranged, there was no significant difference in the total extraction capacity of boreholes under double-row aligned layout and staggered layout. The latter is recommended due to its reduced shielding effect and more balanced extraction efficiency. However, double-row parallel layout had a significant shielding effect, approximately 0.7379, leading to a significant reduction in extraction efficiency, so it should be adopted as little as possible. The research results can provide theoretical reference for LHB layout and thus improve gas extraction efficiency.