The optimum design of gas drainage boreholes is crucial for energy security and sustainability in coal mining. Therefore, the construction of fluid−solid coupling models and numerical simulation analyses are key problems for gas drainage boreholes. This work is based on the basic theory of fluid−solid coupling, the correlation definition between coal porosity and permeability, and previous studies on the influence of adsorption expansion, change in pore free gas pressure, and the Klinkenberg effect on gas flow in coal. A mathematical model of the dynamic evolution of coal permeability and porosity is derived. A fluid−solid coupling model of gas-bearing coal and the related partial differential equation for gas migration in coal are established. Combined with an example of the measurement of the drilling radius of the bedding layer in a coal mine, a coupled numerical solution under negative pressure extraction conditions is derived by using COMSOL Multiphysics simulation software. Numerical simulation results show that the solution can effectively guide gas extraction and discharge during mining. This study provides theoretical and methodological guidance for energy security and coal mining sustainability.