# Optimization and Application of Drilling Parameters Based on Gas-Solid Coupling Simulation
## 1 Introduction  
With the continuous development of the economy, coal resources have long maintained a dominant position in China's energy system and remain central in the primary energy consumption structure [1, 2]. As shallow coal resources gradually deplete and mining depths continue to increase, coal mines are commonly confronted with complex \"three highs and one low\" geological conditions--specifically, high tectonic stress, high gas pressure, high formation temperature, and low permeability [3, 4, 5]. These conditions significantly increase the probability of coal-rock-gas dynamic disasters. The instantaneousrelease of enormous energy not only severely threatens the safety of underground workers but also tends to trigger chain reactions, such as mine ventilation system failures and equipment damage, making it the primary technical bottleneck restricting safe and efficient coal resource extraction [6]. The arrangement of directional high-level long boreholes in overlying strata for pressure-relief gas drainage enables coordinated coal and gas extraction, effectively addressing this challenge [7]. Directional high-level long boreholes demonstrate technical advantages, including rapid drilling speed, low construction costs, high drainage efficiency, and effective mitigation of mining succession tensions [8]. Therefore, research on the layout horizons and parameters of such boreholes holds significant importance for resolving gas overlimit issues and guiding subsequent working face arrangements. [PERSON] et al. [9] combined a gas pressure drop method with borehole gas flow analysis to determine the effective drainage radius of gas extraction boreholes in Tian'an Coal Mine through simultaneous measurement of gas pressure and flow in pressure-testing holes. [PERSON] et al. [10] derived the effective drainage radius and critical gas pressure in the Wudong mining area, analyzing gas pressure variations under different initial gas pressures, borehole diameters, and drainage negative pressures using COMSOL Multiphysics simulation. [PERSON] et al. [11] designed orthogonal experiments to analyze the influence of various borehole parameters on effective drainage radius, identifying optimal parameters validated through grey correlation analysis and a sulfur hexafluoride (SF\({}_{6}\)) tracer method. [PERSON] and [PERSON] [12] established a dynamic permeability model and employed FLAC3D numerical simulation to optimize borehole diameter and spacing, achieving a 29.7% improvement in gas concentration through their research outcomes. [PERSON] et al. [13] developed a gas-solid coupling model incorporating coal-rock deformation and matrix-fracture seepage-diffusion fields, demonstrating that equilateral triangular borehole arrangements effectively eliminate drainage blind zones. [PERSON] et al. [14] constructed a hydraulic fracturing gas-solid coupling model, revealing fracture development patterns in overlying strata and clarifying coal seam parameter impacts on fracturing-gas drainage processes. [PERSON] et al. [15] investigated a model considering matrix-fracture interactions and fluid exchanges. Through COMSOL simulations and field tests, [PERSON] et al. [16] optimized borehole spacing and negative pressure in Inner Mongolia mines while establishing a three-dimensional gas distribution model for goaf areas. [PERSON] et al. [17] identified enhanced initial permeability as the key factor for improving drainage radius. [PERSON]'s experiments [18] under confining pressure revealed decreasing coal permeability with increasing pore pressure during gas injection. [PERSON] et al. [19] developed a numerical simulation model considering viscous flow and Knudsen diffusion and investigated the effects of several factors, such as nanometer pore size, pressure-dependent viscosity, number of adsorbed gas layers, and temperature, on shale permeability. [PERSON] [20] proposed an equation for gas flow in nanopores based on Kundsen diffusion as well as a slip flow to study the influence of pore size on the variation in permeability.