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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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{\bf u} = - \frac{k}{\mu} \cdot ( \nabla p - \rho \, {\bf g} ) |
where
M = / \mufluid mobilityrho density
In multiphase flow the different phases
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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
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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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