A fractal model for gas-water relative permeability in inorganic shale considering water occurrence state

Gas-water relative permeability in inorganic shale plays a crucial role in fluid transfer efficiency, therefore it is of paramount importance for modelling shale gas recovery. This study introduces a novel theoretical model to determine gas–water relative permeability in inorganic shale under various water saturations. For the first time, this model integrates the water occurrence state in inorganic shale with the fractal characteristics of pore structures. In particular, three distinct states of water occurrence in inorganic shale pores and two corresponding critical pore sizes are defined in the model based on nuclear magnetic resonance (NMR) testing. The validity and accuracy of the new model have been corroborated by multiple sets of experimental data for shale and other porous rocks. Additionally, the model discussion focus on the water occurrence state in inorganic shale is conducted, and the following results are innovatively obtained: (1) Ignoring pores with only irreducible water results in a 6–26 % overestimation of gas relative permeability (GRP) and approximately 4 % overestimation of water relative permeability (WRP). (2) Omitting pores with both irreducible and movable water leads to a 2–13 % overestimation of GRP and a 1.1 to 21 times overestimation of WRP at various water saturations. (3) Disregarding pores with only movable water causes an approximately 23 % underestimation of GRP and a 13–100 % underestimation of WRP at different water saturations. Furthermore, based on the proposed model, the impact of fractal dimension of pore size distribution, fractal dimension of pore tortuosity, irreducible water saturation, and critical pore sizes are also comprehensively analyzed.