Intra-pore tortuosity and diverging-converging pore geometry controls on flow enhancement due to liquid boundary slip

The liquid boundary slip, in contrast to the conventional no-slip boundary condition, exists due to a less wetting or the non-wetting nature of sediment grains, which can significantly control fluid hydraulics of porous media, specifically which consists of smaller pore-throats, e.g., siltstones and mudstones. Most studies to date presume a no-slip boundary condition and a few who have investigated the aspects of slip-boundary presume a simplified straight tube or a non-tortuous pore shape. Therefore, how the degree of tortuosity and pore-geometry control flow enhancement in porous media remains underexplored. In this computational study, we design a set of diverging-converging staggered tortuous (DCST) pores, which account for a variable amount of intra-pore tortuosity. To compare, a set of capillary pores are designed that can account for tortuosity by taking the form of sinusoidal and helical shapes. Our results quantify how the diverging-converging nature of pore geometry and its intra-pore tortuosity alone have a significant impact on modifying the microscopic flow behavior -accounting of which is a key in upscaling these effects to a macroscopic continuum or the Darcy-scale. We find, DCST pores contribute to an asymptotic flow enhancement behavior in response to boundary slip. In comparison, capillary pores lead to a linearly 'unlimited' flow enhancement. This unlimited nature of flow enhancement can lead to differences over several orders in magnitude. We test theoretical models to predict flow enhancement from all pores. We determine constitutive relations that can predict flow enhancement as a function of intra-pore tortuosity and hydraulic shape factor. We examine the physical mechanisms of energy dissipation and find that the microscopic fluid-structure interactions can contribute to significant variation in how intra-pore geometry and boundary slip manifest as the flow enhancement factor relevant to the continuum-scale. We find that the `asymptote' in the flow enhancement factor of DCST pores manifests as a result of an equilibrium between energy dissipation and enhancing flow due to boundary slip, at least in the laminar flow regime.

Automated summary

The study reveals that the microscopic flow behavior in porous media is significantly influenced by pore geometry and intra-pore tortuosity, affecting boundary slip reaction and flow enhancement factor.