@wikipedia
The momentum balance equation relating a pressure gradient
in
porous medium with induced
fluid flow (
percolation) with velocity
:
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{\bf u} = - M \cdot ( \nabla p - \rho \, {\bf g} ) |
where
In single-phase flow the Darcy flow equation takes a following form:
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{\bf u} = - \frac{k}{\mu} \cdot ( \nabla p - \rho \, {\bf g} ) |
where
Darcy flow only happens for relatively slow percolation:
.
For a wider range of flow regimes see Forchheimer Equation.
In multiphase flow the different phases move with different velocities | LaTeX Math Inline |
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| body | --uriencoded--%7B\bf u%7D_\alpha |
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and Darcy flow equation is applicable for each phase independently:
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{\bf u}_{\alpha} = - \frac{k_{\alpha}}{\mu_{\alpha}} \cdot ( \nabla p_{\alpha} - \rho_{\alpha} \, {\bf g} ) |
where
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
Physics / Fluid Dynamics / Percolation
[ Forchheimer Equation ][ Linear Perrine multi-phase diffusion @model ]
References
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.
