# Laws of fluid flow in porous medium

What are the equations that describe the flow of a fluid in a porous medium? Is there a variation of the Navier-Stokes equations?

I would like to model the flow of air through a sponge-like structure. Instead of modelling the structure of the sponge, I would like to treat it like a homogenous area, where I solve appropriate equations for conservation of momentum, mass and energy.

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Situationes where Stokes (without Navier) rules, are well known, eg hydrogeology (ground water) or oil geology (secondary or tertiaty recovery)

A word which might be usefull to search for: percolation.

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$$\vec{q}=-K\nabla p$$
$\vec{q}:=\vec{u} \cdot \text{porosity}$, so it is equivalent to normal flow only for homogeneous media.