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Darcy flow only happens for relatively slow percolation:
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| LaTeX Math Block |
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{\bf u} = - M \cdot \nabla p = - \left< \frac{k}{\mu} \right > \cdot \nabla p |
where
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| LaTeX Math Inline |
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| body | \displaystyle M = \left< \frac{k}{\mu} \right> |
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In some practical cases the phases are moving in reservoir with similar velocities and have similar phase pressure which allows study of multiphase flow by aggregating them into a single-phase equivalent | LaTeX Math Block Reference |
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using the multi-phase mobility (see also Linear Perrine multi-phase diffusion @model).
See also
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Physics / Fluid Dynamics / Percolation
[ Forchheimer Equation ][ Linear Perrine multi-phase diffusion @model ]
References
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Jules Dupuit (1863). Etudes Théoriques et Pratiques sur le mouvement des Eaux dans les canaux découverts et à travers les terrains perméables (Second ed.). Paris: Dunod.
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