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{\bf u} = - M \cdot \nabla p = - \left< \frac{k}{\mu} \right> \cdot \nabla p |
where
In multiphase flow the Darcy flow equation is applicable for each phase independently.
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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{\bf u} = - M \cdot \nabla p = - \left< \frac{k}{\mu} \right > \cdot \nabla p |
where
Darcy flow only happens for relatively slow percolation:
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