Mathematical model of permeability evolution of liquid CO₂ pressurized coal

To examine the permeability alterations in coal seams induced by liquid CO₂ injection, we employed COMSOL simulations to recreate the flow, force, and temperature fields, along with the corresponding physical parameters of the geological formation. We established a mathematical model to track the evolution of the coal body's permeability, enabling us to capture the phase distribution of CO₂, the dynamics of fluid transportation, and the coal body's mechanical responses during the liquid CO₂ injection process. Our findings revealed that the coal seam undergoes significant changes due to low-temperature freezing and shrinkage, gas-liquid phase transitions, and expansion impacts from solid-liquid phase changes. These factors collectively modify the pore structure, subsequently influencing the coal seam's permeability. Notably, the coal body's permeability, influenced by the pore structure and the Klinkenberg effect, increases logarithmically with rising injection pressure and falling temperatures. The structural changes in the coal body are markedly impacted by seepage and phase change pressures, with the permeability enhancement from secondary phase changes being 2.28 times greater than that from primary phase changes, and five times greater than in scenarios without phase change.