Heat treatment on shale reservoirs can promote the development of secondary fractures in a matrix on the basis of hydraulic fracturing, forming multi-scale gas–water seepage channels and strengthening the gas desorption. Experimental evidence shows that heat treatment can enhance gas recovery in the same mining life. Heat treatment on a shale gas reservoir is a multi-physical and multi-phase coupling process. However, how the thermal stimulation interacts with nonlinear two-phase flow in heterogeneous shale volume fracturing has not been clear. In this paper, a fully coupled THGM model for heating-enhanced shale-gas recovery in heterogeneous shale reservoirs is proposed. First, the governing equations are formulated for the shale-reservoir deformation involving both gas adsorption and thermal expansion, the permeability evolution model for the cracking process of fractured shale, the gas–water two-phase continuity equation considering the effects of gas solubility and the heat transfer equation for heat conduction and convection. The interactions among stress, temperature and seepage in a heterogeneous shale reservoir were studied. Secondly, a test on shale permeability after 50 °C temperature treatment was conducted. The evolution of temperature, capillary pressure, water and gas saturation and the permeability of shale during the heat treatment of the reservoir were numerically analyzed. Finally, the gas production from a shale gas reservoir was numerically simulated with this THGM model. The numerical results indicated that the thermal-induced fracturing, gas desorption and separation from water make predominant contributions to the evolution of permeability. The heat treatment can enhance cumulative gas production by 58.7% after 27.4 years of heat injection through promoting gas desorption and matrix diffusion.
