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Pré-Publication, Document De Travail Année : 2024

Flows of two slightly miscible fluids in porous media: two scale numerical modelling

Résumé

We address the two-scale homogenization of the Navier-Stokes and Cahn-Hilliard equations in the case of a weak miscibility of a two-component fluid. To this end a notion of the miscibility strength is formulated on the basis of a corre- lation between the upscaling parameter and the surface tension. As a result, a two-scale model is derived. Macro-equations turn out to be a generalization of the Darcy law enjoying cross-coupling permeability tensors. It implies that the Darcy velocity of each phase depends on pressure gradients of both the phases. Micro-equations serve for determination both of the permeability tensors and the capillary pressure. An example is constructed by analytical tools to describe cap- illary displacement of oil by mixture of water with Carbon dioxide in a system of hydrophobic parallel channels.
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Dates et versions

hal-04538089 , version 1 (09-04-2024)

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Paternité

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  • HAL Id : hal-04538089 , version 1

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Youcef Amirat, Vladimir Shelukhin, Konstantin Trusov. Flows of two slightly miscible fluids in porous media: two scale numerical modelling. 2024. ⟨hal-04538089⟩
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