A fractal model for two-phase flow in rough pores with immobile water film effects

The seepage characteristics of multiphase flow in unsaturated porous media hold significant application value in industrial fields such as natural gas hydrate exploitation and oil–gas migration in tight reservoirs. However, the pore walls in actual formations are often uneven. Existing models mostly assume smooth pore walls or fail to simultaneously account for the differential sensitivity of roughness and immobile water film to various physical parameters, which limits the accurate prediction of fluid transport behavior in complex formations. To address this issue, this paper establishes an effective aperture model for circular cross section pores based on the real fluid distribution, considering the coupled effects of roughness and immobile water film thickness. Analytical expressions for the flow rate and relative permeability of the wetting and non-wetting phases in a single pore and in fractal capillary bundles are derived. The validity of the model is verified through comparison with experimental data. The study reveals that the influence of roughness on the relative permeability of the wetting phase is significantly greater than that on the non-wetting phase. Furthermore, its impact decreases with increasing wetting phase saturation and increases with the increasing maximum pore diameter. This research elucidates the physical limitations of roughness on two-phase flow and provides theoretical support for enhancing the efficiency of subsurface energy extraction.