One-Phase and Two-Phase Flow in Highly Permeable Porous Media.

Abstract

Many industrial and natural processes involve flow in highly permeable media, such as exchangers, canopies, urban canyons. Traditional assumptions used for modeling flow equations in low permeability structures may not hold for these systems with very large pores. Reynolds numbers may be too large so that Darcy’s law is no longer valid. Large Capillary and Bond numbers may also invalidate the quasistatic assumptions implicit in many empirical formulations and upscaling results. In this paper, we review several approaches developed to handle such cases, basing our analysis on new experimental data and results from upscaling methods. For one-phase flow this has led to various formulations of macro-scale momentum transport including generalized Forchheimer equations and macro-scale turbulent models. For two-phase flows, we discuss possible ways toward deriving macro-scale models from the pore-scale equations and introduce several macro-scale models: generalized Darcy’s laws, models with cross terms accounting for the viscous interaction between the flowing phases, formulations capturing inertial, or dynamic effects. Models suitable for describing flow in structured media like chemical exchangers containing structured packings are also introduced. Finally, we present hybrid representations that couple approaches at two different scales, for instance, a meso-scale network approach coupled with dynamic rules obtained from pore-scale numerical simulations or experiments. This approach proved useful in describing the diffusion of impinging jets in packed beds, which is not described properly by capillary diffusion.