@wikipedia

The momentum balance equation relating a pressure gradient  in porous medium with induced fluid flow (percolation) with velocity 

-  \nabla p = \frac{\mu}{k} \, {\bf u} + \beta \, \rho \,  | {\bf u} | \, {\bf u}

where

Forchheimer coefficient depends on flow regime and formation permeability as:

\beta = \frac{C_E}{\sqrt{k}}

where   is dimensionless quantity called Ergun constant accounting for inertial (kinetic) effects and depending on flow regime only.

  is small for slow percolation (thus reducing Forchheimer equation to Darcy equation) and grows quickly with high flow velocities.

Forchheimer equation can be approximated by non-linear permeability model as:

{\bf u} =  - \frac{k}{\mu} \, k_f \, \nabla p

k_f(|\nabla p|) =  \frac{2}{w} \big[ 1- \sqrt{1-w}   \big]

w = 4 \, \left(\frac{k}{\mu} \right)^2 \, \beta \, \rho \,  |\nabla p| \, < \, 1

See also

Physics /  Fluid Dynamics / Percolation

[ Darcy Flow Equation ]

Reference

 Philipp Forchheimer (1886). "Über die Ergiebigkeit von Brunnen-Anlagen und Sickerschlitzen". Z. Architekt. Ing.-Ver. Hannover. 32: 539–563.