InterPore2022

Some analytical results about countercurrent capillary imbibition.

30 May 2022, 11:20

15m

Oral Presentation (MS21) Non-linear effects in flow and transport through porous media MS21

Speaker

Dr benoit Noetinger

Description

Capillary imbibition is a major process that controls many transport phenomena in porous media for many applications. In the countercurrent case, the process may be represented as the solution of a strongly non-linear diffusion equation $\partial S(x, t)/\partial t = \nabla . [D(S(x, t)) \nabla S (x, t)]$ in which S(x, t) denotes the wetting fluid saturation at position x at time t. The function D(S) depends non linearly on S through an expression involving relative permeabilities and capillary pressure. D(S) vanishes as a power law near the extreme saturations, leading to a singular boundary problem that was investigated by many authors. Considering a finite block, two time regimes can be observed: a short time regime involving the Boltzmann variable x/t, and a long time asymptotic regime that remains to be elucidated. We found an ansatz was proposed that yields a complete analytical determination of the spatial part of the asymptotic long time behavior of S(x, t). The corresponding flux at the boundary of the block exhibits a two regimes that may be represented as a non-linear exchange term involving the average saturation on the block, weighted by a shape factor. This feature is well-suited for setting-up a macroscopic dual porosity description.

Selected references.

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Braconnier, Douarche, Momeni, Quintard and Noetinger, About non-linear diffusion in porous and fractured media: Early- and late-time regimes, submitted

References

Braconnier, Douarche, Momeni, Quintard and Noetinger, About non-linear diffusion in porous and fractured media: Early- and late-time regimes, submitted