Macroscopic properties of porous media containing two immiscible fluids, such as capillary pressure, relative permeabilities, and resistivity index, are fundamental to petroleum engineering. In this work we present a methodology for obtaining a priori understanding of hysteresis in these macroscopic properties. The approach is based on the mechanistic modeling of fluid displacement processes at the grain scale in a random dense packing of equal spheres. The method allows computing pore-level fluid configurations, which, in turn, allows direct calculation of macroscopic properties. Meniscus motion at the grain scale is entirely mechanistic, so any hysteresis that emerges does so exclusively from the interaction between the mechanics and the grain space geometry. Our model predicts that hysteresis during the fluid displacement cycle (drainage then imbibition of the wetting phase) has a significant effect on relative permeability and resistivity index. In particular, the usual assumption that the electrical parameter n in Archie's equation, determined by a drainage experiment, is equally applicable to imbibition is unwarranted. The results for electrical properties are also presented as electrical efficiency, which was developed specifically to account for the effects of pore-level geometry.

The predictions made in this work are compared with existing experimental data and found consistent with them. The methodology allows quantifying the influence of hysteresis in other conditions (consolidated rocks, varying wettability).

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