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LaTeX Math Block |
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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
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:
LaTeX Math Block |
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{\bf u}_{\alpha} = - \frac{k_{\alpha}}{\mu_{\alpha}} \cdot ( \nabla p_{\alpha} - \rho_{\alpha} \, {\bf g} ) |
where
In most popular case of a 3-phase Oil + Gas + Water fluid model with relatively homogeneous flow (phases may move at different velocities but occupy the same reservoir space and have the same phase pressure) the Darcy flow equation can be approximated with Perrine model of Multi-phase Mobility:
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Darcy flow only happens for relatively slow percolation:
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See also
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Physics / Fluid Dynamics / Percolation
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