Study on Gas Pre-Extraction Law of Along-Layer Boreholes Based on Thermo-Hydro-Mechanical-Damage Coupled Model

Modeling the pre-extraction of coalbed methane presents a significant mathematical challenge due to the complex interplay of multiple physical fields. This paper presents a robust mathematical model based on a thermo-hydro-mechanical damage (THMD) framework to describe this process. The model is formulated as a system of coupled, non-linear partial differential equations (PDEs) that integrate governing equations for heat transfer, fluid seepage, and solid mechanics with a damage evolution law derived from continuum damage mechanics. A key contribution of this work is the integration of this multi-physics model, solved numerically using the Finite Element Method (FEM), with a statistical modeling approach using Response Surface Methodology (RSM) and Analysis of Variance (ANOVA). This integrated framework allows for a systematic analysis of the model’s parameter space and a rigorous quantification of sensitivities. The ANOVA results reveal that the model’s damage output is most sensitive to the borehole diameter (F = 2531.51), while the effective extraction radius is predominantly governed by the initial permeability (F = 4219.59). This work demonstrates the power of combining a PDE-based multi-physics model with statistical metamodeling to provide deep, quantitative insights for optimizing gas extraction strategies in deep, low-permeability coal seams.