14-17 May 2018
New Orleans
US/Central timezone

Macroscale modeling of immiscible two-phase flows in highly permeable porous media

14 May 2018, 14:25
New Orleans

New Orleans

Oral 20 Minutes MS 1.08: Non-linear flows in porous media: impact of inertia and non-linear rheologies on pore scale processes and applications Parallel 2-G


Dr Yohan Davit (Institut de Mécanique des Fluides de Toulouse)


Multiphase flows in porous media play an important role in many natural and industrial processes, such as transport mechanisms in the vadose zone, CO2 sequestration in saline aquifers or oil recovery in petroleum applications. The traditional picture for such flows is one at low Reynolds number where the distribution and flow of the different phases is controlled by interfacial energies of fluid/fluid and fluid/solid interfaces, with a major influence of wettability and capillarity \cite{Muskat1946,Whitaker1986}. While this is accurate for creeping flows in relatively low permeability porous media, highly permeable porous structures --such as those found in trickle bed reactors, fuel bundles in nuclear cores or distillation columns used in chemical engineering applications-- challenge the relevance of this represention. In those, the relative importance of interfacial energies may be reduced, with much larger inertial effects and exchanges of momentum between fluid phases.

Here, we discuss whether the continuum models used for flows in low permeability porous media, such as generalized Darcy's laws, are adequate for highly permeable porous structures (high Re, Bo and We numbers). We first propose an alternative representation for mass and momentum transport of two-phase immiscible flow at the continuum-scale, which is based on a multiscale analysis starting from the flow problem at the pore-scale. Compared to the generalized Darcy's law, our representation contains additional drag and cross terms that account for inertial effects and exchanges between fluid phases. We then go on to determine constitutive relationships for the effective parameters using experimental data on co- and counter-current flows from recent water/air experimental data \cite{ClavierChikhiFichotEtAl2017,Wang_thesis}. Results show that the macroscale model allows us to capture important physical aspects of the flow that the generalized Darcy's law fails to describe. We further find that the impact of the cross and inertial terms increases with the Reynolds numbers of the phases.


Title = {The flow of homogeneous fluids through porous media.},
Author = {M. Muskat},
Journal = {International series in physics, York The Mapple Press Company},
Year = {1946}

Title = {Flow in porous media II: The governing equations for immiscible, two-phase flow},
Author = {S. Whitaker},
Journal = {Transport in Porous Media},
Year = {1986},

author = {R. Clavier and N. Chikhi and F. Fichot and M. Quintard},
title = {Modeling of Inertial Multi-Phase Flows through High Permeability Porous Media: Friction Closure Laws},
journal = {International Journal of Multiphase Flow},
year = {2017},
volume = "91",
pages = "243 - 261",

Title = {{Mass Transfer Coefficients and Effective Area of Packing}},
Author = {C. Wang},
School = {University of Texas, Austin},
Year = {201},
Month = may

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Primary authors

Sylvain Pasquier Michel Quintard (Institut de Mécanique des Fluides de Toulouse) Dr Yohan Davit (Institut de Mécanique des Fluides de Toulouse)

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