Pore-scale understandings for steady-state two-phase flow in porous sandstone from full-range pore connectivity quantification

Fluid/chemical transport in the connected pore network of porous sandstone with variable permeability governs numerous subsurface energetic, environmental, and industrial activities. In this work, we compile a multi-scale pore connectivity evaluation by integrated pore structure characterization involving casting thin section, scanning electron microscope, nuclear magnetic resonance, X-ray computed tomography, and mercury intrusion porosimetries. The pore connected pattern, connective ratio, and connected full-range pore size distribution (CPSD) are obtained by the determination of full-range pore size distribution and empirical correlations between pore size and connective ratio, upon which the across-scale steady-state multiphase flow physics are further explored incorporating physical simulation experiment and numerical analyses. The scale-invariant connective ratio of conventional sandstone with reticular connection pattern stays at around 0.60, that of low-permeability sandstone ranges from 0.53 to 0.60, exhibiting branch-like connection, and it is avg. 0.31 in tight sandstone with local chain-like pattern, of which the ratio can be predicted by its strong dependence on porosity, permeability, and connected median pore radius. With decreasing pore connectivity, the fractional flow of non-wetting phase in steady-state two-phase flow turns from linear deviated flow to power-law flows. The pore-scale interpretations of multiphase mobility and interaction dynamic by incorporating DLVO theory, augmented Young-Laplace equation, and effective hydraulic radius model suggest that the connected full-range pore size distribution determines the wetting phase mobility and non-wetting phase accessibility, controlling the dynamic of multiphase interaction and build of non-wetting phase pathways. Preferential flow path expansions in the connected pores < 1000 nm, leading to strong differences in the resistance for non-wetting phase flow, are the primary reasons for distinctions in flow regimes. The increasing pores of 30-50 nm in the non-wetting phase flow paths are responsible for the TPG, pressure disorders, and fluid snap-offs, resulting in the power-law flow deviations. A dynamic fractional flux prediction model for non-wetting phase is proposed by modifying the fractal-based Hagen-Poiseuille equation considering flow physics, pore heterogeneity, and critical percolation length scale variations along with flow path expansion in the connected pore system. Comparative analysis indicates that the determination of hydraulic flow diameter  should follow the percolation threshold theory and reliable of porous sandstone is at round R₄₀ of the connected flow pathway.