The momentum balance equation relating a pressure gradient \nabla p in subsurface reservoir with the induced fluid flow {\bf u}::
| (1) | {\bf u} = - \frac{k}{\mu} \ \nabla p |
where
{\bf u} | flow velocity vector |
|---|---|
\nabla p | pressure gradient |
k | formation permeability |
\mu | fluid viscosity |
Only valid for the slow flow: { \rm Re} < 1
For a wider range of flow regimes see Forchheimer equation.