How boundary slip controls emergent Darcy flow of liquids in tortuous and in capillary pores

Abstract

Fundamental investigations of how boundary slip relative to the no-slip condition for liquid flow in a set of two distinct idealized pore geometries, i.e., a diverging-converging tortuous pore, in contrast to a straight tube capillary pore, contribute to emergent Darcy flow and flow enhancement are presented. Using steady-state solutions to Navier-Stokes equations, a sensitivity study investigates the role of (a) a large variation in boundary slip reported in the literature, and (b) a large variation in pore-throat sizes found in geologic porous media. Results show that both the pore geometry and their pore-throat sizes contribute to differences over several orders of magnitude in the emergent Darcy flow behavior and the flow enhancement. Tortuous pores contribute to a lower flow enhancement relative to the capillary pores, and while the larger pore throats (i.e., ≥10μm) negligibly enhance flow, it increasingly becomes significant for the micron-size pore throats. From capillary pores, flow enhancement is found to increases linearly in an unlimited manner with an increment in boundary slip relative to the no-slip condition. In contrast, flow enhancement from diverging-converging tortuous pores is found to get limited defined by an asymptote for flows with a larger boundary slip. Capillary pores offer no change in resistance to flow due to boundary slip. In contrast, the very nature of diverging-converging tortuous pore geometry offers growth in drag forces and energy dissipation rate, i.e., an increase in resistance to flow, which contributes to the asymptote or the limited flow enhancement. A set of theoretical models are presented, which can be used to predict the flow enhancement as a function of boundary slip and spatial-scale of pore throats. This study may have implications for predicting flow enhancement and pressure loss during fluid injection or recovery from low permeability geologic reservoirs, and relevant to other engineering applications, e.g., hydraulics in corrugated channels or design of carbon nanotube membranes for desalinization purposes.