A Relative Permeability Model of Coal Based on Fractal Capillary Bundle Assumption

As the pore and fracture structure of coal significantly influence gas-water relative permeability (GWRP), it is crucial to study the GWRP in coal reservoirs for optimizing gas production. This paper provided parameters such as pore size range and capillary bundle porosity by referring to existing mercury intrusion porosimetry (MIP) experiments. The effective porosity coefficient and gas-water phase critical pore size were introduced to improve the GWRP model for coal based on the assumption of fractal capillary bundle. The GWRP model depends on changes in phase saturation, maximum and minimum capillary tube pore diameters, porosity, capillary size distribution dimension D_f, and fractal dimension of tortuosity D_t. It demonstrated that models for various coal samples from the southern Qinshui Basin exhibit good agreement with the GWRP experimental data. In addition, the improved GWRP model was used to simulate coalbed methane (CBM) production and water production. The findings suggested that as water and gas are continuously extracted, effective stress rises as reservoir pressure and water saturation decline, leading to a more even distribution of capillary diameter and an increase in capillary degree. Furthermore, the effect of structural parameters on CBM production was also discussed.