This paper presents the theory, formulation, and correlation of the compressibility, porosity, and permeability of shale reservoirs by considering the effects of stress shock causing a slope discontinuity and loading/unloading hysteresis. The slope discontinuity occurs because the relative contributions of the matrix or fracture change at a critical effective stress depending on whether the process is loading or unloading. The hysteresis phenomenon occurs because of partially reversible and irreversible deformations of the various shale rock constituents by various processes during loading and unloading. Two successful modeling approaches are developed for describing the stress dependency of the petrophysical properties of porous rock formations. The first approach implements a kinetic model leading to a modified power–law equation, and the second approach applies an elastic cylindrical pore–shell model leading to a semianalytical equation. The primary advantage of the kinetic model is its applicability to any stress–dependent property, including strain, void ratio, porosity, pore compressibility, and permeability, thus making it a universal method. The semianalytical equation derived from an elastic cylindrical pore–shell model is applicable only for correlation of permeability. Both approaches are shown to yield high–quality correlations of the properties of porous rocks with effective stress by honoring the slope discontinuity observed at a critical effective stress.

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