A thermally sensitive permeability model for coal-gas interactions including thermal fracturing and volatilization

• A permeability model for coal-gas interactions under variable temperatures.
• Effects of thermal fracturing and thermal volatilization on permeability.
• Four stages and three sub-classes of permeability evolution with temperature.
• Verifications by experimental data from literature and our tests.

Experiments have observed that coal permeability experiences significant change when temperature varies from room temperature up to 100 °C. However, current permeability models have not well described this change so far. This paper proposes a thermally sensitive permeability model to describe the coal-gas interactions under variable temperatures. This model includes matrix permeability and fracture permeability. It describes the impacts of thermal expansion, thermal fracturing, the change of matrix sorption capacity, and the thermal volatilization of fracture surfaces on coal permeability. Particularly, the change of temperature in coal matrix may initiate, nucleate and grow up micro-pores and cracks, forming a crack cloud and changing the porosity of this matrix block. The fractal of cracks and pores is linearly evolved with temperature change. Second, the gas sorption capacity of coal matrix is modified by temperature change through an exponential function. Third, the thermal expansion of matrix is linearly related to temperature change but thermal volatilization occurs on the fracture surfaces and widens gas flow channels. Through the thickness change of volatile membrane, the change of fracture aperture is described by a quadratic function. This model is verified by three series of experimental data from either literature or our newly conducted tests. It is found that the permeability evolution with temperature has four stages which are dominated by one of four primary factors: thermal expansion, thermal volatilization, thermal fracturing and crack coalescence. In each stage, secondary factors may modify the evolution of permeability into sub-classes: linear curve, upward bending curve, or concave bending curve. These verifications confirm that this thermally sensitive permeability model can well describe the permeability evolution of different coals at either thermal expansion stage, or volatilization stage, or their transition.