Having a clear understanding of the permeability variation mechanism is important for controlling the process of displacement of CH4 with CO2 in deep coal seams. Based on the stress-strain equation of porous elastic media and horizontal strain variations of coal, a mathematical model predicting permeability variation after CO2 injection into gas saturated coal seams was established. The model shows that, during the displacement of CH4 with CO2, the shrinkage strain of the coal matrix increases logarithmically with the decrease of pore pressure. With a decrease in the reservoir pressure, permeability rebound occurs with the influence of matrix shrinkage and gas slippage. Under low confining pressures, the rebounded permeability is high, and its associated rebound pore pressure is also high. For coals with a high cleat compression coefficient, the permeability decreases range is obvious. And permeability rebound only happens under low reservoir pressures. Coal properties, e.g., Poisson's ratio and Langmuir volume, show obvious influences in permeability variation during gas production. The model was also extended to predict permeability variation for a well-control area. During gas drainage process, the permeability in the well-controlled area first increases, then decreases, and then slowly returns to the original state with the lengthening of well-controlled radius. Under high confining pressures, the permeability decline range is more obvious. Also, correspondingly, the attenuation range of permeability increases and the rebound range decreases. The proposed model is beneficial in predicting permeability variations during the displacement of CH4 with CO2, as well as guiding CO2 injection into coal seams.
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