A Heuristic Insight on End-Point Calculation and a New Phase Interference Parameter in Two-Phase Relative Permeability Curves for Horizontal Fracture Flow

Relative permeability curves of two-phase flow in a fracture have been a subject of study in recent years. The importance of these curves have been widely observed in multidisciplines, such as water subsurface resources, geothermal energy and underground hydrocarbon resources, especially fractured oil and gas reservoirs. Extensive experimental studies have been cited alongside the numerical studies in this area. However, simple analytical and practical solutions are still attractive. In the current study, wettability effects and phase interference explicitly were tried to be implemented in a simple analytical formula. The wettability effects are represented by residual saturations which resulted in direct calculation of relative permeability end points. In addition, the phase interference part affected the shape of the curves that allowed to quantify the degree of phase interference from no phase interference, assigned as zero, to ultimate phase interference, assigned as infinity. The results were compared and validated with the available experimental data in the literature. The proposed formulation is applicable for both smooth and rough fracture assemblies.