One-phase and Two-phase Flow In Highly Permeable Porous Media

Many industrial and natural processes involve flow in highly permeable media, such as heat and mass exchangers, canopy, networks of urban canyons, etc. For these systems, the traditional assumptions made prior to upscaling pore-flow equations do not hold anymore. Reynolds numbers may be high enough so Darcy’s law is no longer valid, Capillary and Bond numbers may be also sufficiently large to invalidate the quasi-static assumptions used when upscaling multiphase flows. Several time-scales of very different order of magnitudes may be at play. Based on new experimental data and upscaling results, this paper reviews several approaches that have been developed to handle such cases. The case of one-phase flow has been largely studied from various point of views. This led to various forms of the macroscale momentum equation: generalized Forchheimer equation, macro-scale turbulent models. The case of two-phase flow is more complicated and largely remains an open problem. The possibility of deriving macro-scale models from the pore-scale equations is discussed and potential macro-scale models are introduced: generalized Darcy’s laws, model with various form of inertia terms, cross terms accounting for the viscous interaction between the two flowing phases, dynamic models. Classes of models suitable for describing flow in structured media like, for instance, chemical exchangers made with structured packings, are also introduced. Finally, hybrid models are presented involving the coupling between two-different scale modeling, for instance a network approach coupled with dynamic rules coming from pore-scale numerical simulations or experiments. This is useful, for example, in describing the apparent diffusion of impinging jets in packed beds which often cannot be described properly by capillary diffusion