An Alternative Parameterization of Relative Permeability and Capillary Pressure Curves

This paper presents a theoretically rigorous correlation of the performance of capillary pressure and relative permeability of naturally fractured sandstone and carbonate reservoirs involving saturation shocks and loading/unloading hysteresis under various stress and thermal conditions. The proposed modeling approach accounts for the combined effects of the porous-rock alteration by various processes, including deformation, transformation, deterioration, and collapse of pore structure, under prevailing temperature and stress conditions during loading and unloading processes, and their effect on the capillary pressure and relative permeability of naturally fractured reservoirs. A saturation shock causing a slope discontinuity in the capillary pressure and relative permeability is shown to occur during saturation change in some sandstone- and carbonate-reservoir formations at a critical saturation condition. This phenomenon can be triggered by alteration of fluid-percolation pathways as a result of the transition from open to closed natural or induced fractures and the deformation of pore structure. The effect of the saturation shock and loading/unloading hysteresis on the capillary pressure and relative permeability of reservoir-rock formations is formulated by means of a phenomenological kinetics model and its applicability is demonstrated by analyzing and correlating the available experimental data. In this paper, the proven comprehensive model developed from a kinetics equation is shown to lead to a theoretically meaningful, universal, and practical constitutive equation in the form of a modified power law. This kinetics equation expresses the probability of dependence of a petrophysical property of porous rocks on a variable, such as saturation for capillary pressure and relative permeability, based on the value of the property relative to its low- and high-end limit values. The applicability of the modified power-law equation is validated by means of the experimental data of the capillary pressure and relative permeability gathered by testing of representative samples from various sandstone and carbonate reservoirs. The phenomenological parameters of the core samples obtained from sandstone and carbonate reservoirs are determined for best match of the experimental data with the modified power-law equation. The value of the critical fluid saturation is determined by the observance of a slope discontinuity occurring in the measured experimental data of the variation of the capillary pressure and relative permeability with saturation. The scenarios presented in this study indicate that loading/unloading hysteresis and saturation shock have significant effects on the stress- and temperature-dependent capillary pressure and relative permeability of the porous reservoir-rock formations. The data-inferred physics-based model presented in this paper is proved to describe the stress- and temperature-dependent capillary pressure and relative permeability of sandstone and carbonate rocks with high accuracy while meeting the endpoint-limit conditions satisfactorily.