Effects of vortices trapped in a dead end on resistance to pore-scale flow

Abstract

There are numerous dead ends in micro-scale porous media and their special expansion-contraction structure incurs vortices in pore-scale flow. These vortices involve energy dissipation and thus cause extra flow resistance. Since there are no methods available for calculating this extra resistance, this work presents an innovative method for this purpose. It involves two steps including theoretical calculation and numerical simulation. Based on the well-known Hagen-Poiseuille equation, theoretical models are established for capillary tubes with different dead ends, both for calculating intrinsic flow resistance and Reynolds number. Computational fluid dynamics (CFD) simulation, based on the well-known Naiver-Stokes equations, is employed to characterize a pore-scale flow with vortices and to obtain the total flow resistance. The extra vortex-induced resistance can be further calculated by subtracting the theoretical intrinsic resistance from the simulated total resistance. This method is performed for five base cases, including a straight one without a dead end, a square-dead-end one, a quarter-circle-dead-end one, a triangle-dead-end one and one with combination of three dead ends. CFD simulations reveal that main and secondary vortices obviously exist in dead ends. Energy dissipation caused by vortices induces extra flow resistance. The extra resistance shows significant dependence on dead end shape and size as well as number. One possible reason is that a larger space of a dead end may promote the formation of more complex vortices thus causing larger extra resistance. The existence of numerous dead ends in a real micro-scale porous medium means formation of substantial numbers of shear-driven vortices and thus induction of huge increase in flow resistance. As a result, a real Q~Δp relationship may lie far away below the theoretical Q~Δp relationship determined by the Darcy's Law, thus undermining its dominance in characterizing pressure-driven pore-scale laminar flow. This work sheds light on insight of pore-scale flow and drops a hint that we may need corrections to this law in order to improve its characterization quality.