...
The momentum balance equation relating a pressure gradient
in
porous medium with
the induced
fluid flow (
percolation) with velocity
:
LaTeX Math Block |
---|
|
{\bf u} = - M \cdot ( \nabla p - \rho \, {\bf g} ) |
where
In single-phase flow the Darcy flow equation takes a following form:
LaTeX Math Block |
---|
anchor | Darcy_single |
---|
alignment | left |
---|
|
{\bf u} = - \frac{k}{\mu} \cdot ( \nabla p - \rho \, {\bf g} ) |
...
where
Only valid 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 |
---|
body | --uriencoded--%7B\bf u%7D_\alpha |
---|
|
and Darcy flow equation is applicable for each phase independently:
LaTeX Math Block |
---|
|
{\bf u}_{\alpha} = - \frac{k_{\alpha}}{\mu_{\alpha}} \cdot ( \nabla p_{\alpha} - \rho_{\alpha} \, {\bf g} ) |
where
In some practical cases the phases are moving in reservoir with similar velocities and have similar phase pressure which allows study of multiphase flow by aggregating them into a single-phase equivalent LaTeX Math Block Reference |
---|
|
using the multi-phase mobility (see also Linear Perrine multi-phase diffusion @model).
See also
...
Physics / Fluid Dynamics / Percolation
[ Forchheimer Equation ][ Linear Perrine multi-phase diffusion @model ]
References
...
Jules Dupuit (1863). Etudes Théoriques et Pratiques sur le mouvement des Eaux dans les canaux découverts et à travers les terrains perméables (Second ed.). Paris: Dunod.