The momentum balance equation relating a pressure gradient \nabla p in porous medium with induced fluid flow (percolation) with velocity {\bf u}:
| (1) | {\bf u} = - M \cdot \nabla p = - \left< \frac{k}{\mu} \right> \cdot \nabla p |
where
\displaystyle M = \left< \frac{k}{\mu} \right> | fluid mobility |
|---|---|
k | formation permeability |
\mu | fluid viscosity |
In multiphase flow the
Darcy flow only happens for relatively slow percolation: { \rm Re} < 2,000
For a wider range of flow regimes see Forchheimer Equation.
See also
Physics / Fluid Dynamics / Percolation