This paper puts forward a new mathematical model, which is a coal damage-heat-fluid-solid multi-field coupling theory, in order to reveal the mechanical mechanism of the increase of coal-bed methane recovery through thermal stimulation, and to evaluate its effect. The strain field is introduced to define the damage of coal by considering of the effects of temperature, gas pressure, and mining stress of the coal seam. It is used to quantitatively describe the degree of coal rupture and damage. Additionally, the elastic and damage constitutive equation of coal and rock mass, the governing equation of the temperature field, and the coupling equation of gas diffusion and seepage are established. Based on these equations, the finite element source program is redeveloped by using the FORTRAN language, and a multi-field coupling analysis program is compiled. This program takes the temperature, the gas seepage, and the damage and deformation of coal and rock mass into consideration. The effect of heat injection temperature on gas production efficiency, gas pressure distribution, and effective extraction radius during coal-bed methane mining process is analyzed. The results show that the injection of heat can significantly improve the desorption and diffusion of gas, as well as the gas production rate and the production efficiency of coal-bed methane.

The fracture field of coal and rock mass is the main channel for gas migration and accumulation. Exploring the evolution law of fracture field of coal and rock mass under the condition of drilling and slitting construction has important theoretical significance for guiding efficient gas drainage. The generation and evolution process of coal and rock fissures is also the development and accumulation process of its damage. Therefore, based on damage mechanics and finite element theory, the mathematical model is established. The damage variable of coal mass is defined by effective strain, the elastoplastic damage constitutive equation is established and the secondary development of finite element program is completed by FORTRAN language. Using this program, the numerical simulation of drilling and slitting construction of the 15-14120 mining face of Pingdingshan No. 8 Mine is carried out, and the effects of different single borehole diameters, different kerf widths and different kerf heights on the distribution area of surrounding coal fracture field and the degree of damage are studied quantitatively. These provide a theoretical basis for the reasonable determination of the slitting and drilling arrangement parameters at the engineering site.