A fractal model for gas-water relative permeability curve in shale rocks

Initial water content and subsequent fracturing fluid injection lead to gas-water flow in shale nanopores, especially the water-wet pores. But there is few research and experiment to introduce relative permeability curves governing multiphase transport behaviors in shale nanopores. With the consideration of water true slippage and gas slippage, an analytical model illustrating gas-water relative permeability curve in fractal-like tree pore structures has been constructed, aiming to explain gas-water two phase flow behaviors and further evaluate the effects of pore size distributions and water films on gas-water transport. Sensitivity analysis verifies that smaller pore radius, more branching levels and less branching number tend to increase the gas relative flow capacity. Also, ignoring the existence of high-viscosity water molecules has been discovered to reduce water flow resistance. But if the high-viscosity water film loses its mobility, water relative permeability drops slightly. In contrast, mobile bulk water molecules are mainly conducive to increase the gas molecules relative movements. Besides, the analysis of pore size distribution confirms that the fractal-like tree network possesses a more significant gas dominancy compared with log-normal pore network.