@wikipedia
The momentum balance equation equation relating a pressure gradient
in porous medium with induced fluid flow (percolation) with velocity : LaTeX Math Block |
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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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anchor | Darcy_single |
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alignment | left |
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{\bf u} = - \frac{k}{\mu} \cdot ( \nabla p - \rho \, {\bf g} ) |
where
{\bf u} | flow velocity vector
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
pressure gradientformation visocity
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.Only valid for the slow flow: LaTeX Math Inline |
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body | { \rm Re} < 1