Influence of sedimentary structure and pore-size distribution on upscaling permeability and flow enhancement due to liquid boundary slip: A pore-scale computational study

Abstract

Low-permeability sedimentary formations, such as tight sandstones, exhibit fluid flow and transport phenomena distinct from those in conventional porous systems due to the dominance of micro- to nanometer-sized pores and variable amounts of boundary slip. The widely used traditional no-slip boundary condition often fails to accurately describe fluid behavior in these formations. A knowledge gap exists in understanding how liquid slip influences fluid dynamics in complex, heterogeneous sedimentary structures, as previous studies have primarily focused on simplified, homogeneous pore geometries. In this study, we investigated the impact of boundary slip on low-Reynolds number fluid dynamics within synthetically designed two-dimensional graded and random pore networks with varying pore-size distributions to account for heterogeneity. Our results showed that velocity variance increased with increasing heterogeneity, following a power-law relationship. The power-law exponents decreased with boundary slip, quantifying how boundary slip mitigated the impact of heterogeneity on velocity variance. We developed a theoretical model to predict asymptotic flow enhancement and derived constitutive relations to estimate the coefficient C and maximum flow enhancement (ΔE) based on the pore-to-grain size ratio and porosity. Energy dissipation increased with both heterogeneity and boundary slip, which we identified as the primary mechanism contributing to asymptotic flow enhancement. This relationship was illustrated by a 1:1 linear correlation between maximum energy dissipation and maximum flow enhancement, regardless of heterogeneity, indicating that energy dissipation due to boundary slip entirely controls the emerging fluid dynamics. The presented theoretical model and constitutive equations offer practical applications for optimizing fluid dynamics in heterogeneous formations.