Characterization of gas flow in backfill mining-induced coal seam using a fractional derivative-based permeability model

Backfill mining technique has become more and more popular in Chinese coal enterprises in recent years. When it is applied in high gassy mines, a modeling approach to gas flow in backfill mining-induced coal seam plays an important role in assessment of safety of the technological system. In order to establish an intrinsic relationship between post-peak damage of coal and its permeability, a fractional derivative permeability model based on the classic model is proposed by incorporating a damage variable into fractional derivative order. Since the coal body is damaged, its permeability increases rapidly, which can be represented by a increasing trend in the value of fractional order, indicating that the proposed model can effectively reflect the dramatic change in permeability caused by post-peak damage. By testing permeability during the loading and unloading process of coal samples, key parameters of the fractional permeability model were obtained to enter specific values into the model to represent in-situ conditions. Then, based on the Mazars damage evolution criterion and the fractional permeability model, stress field equations and seepage field equations of mining-induced coal are established and applied in a generalized numerical model to characterize gas flow in backfill mining-induced coal seam under different elastic foundation coefficients of filling body. The result shows that the damage scale and degree at coal seam in front of the longwall face, as well as its permeability, appear to be smaller with increase of filling body's elastic foundation coefficient. Along the direction of gas flow, as the elastic foundation coefficient increases, the gas flow velocity reduces, while the gas pressure and content go up correspondingly at the same position of the front coal body. It indicates that the ability for gas to flow is negatively correlated with the elastic foundation coefficient of filling body in backfill mining-induced coal seam.