Modification of Darcy's law for turbulent flow in saturated porous media

Abstract

"Darcy's law is an essential equation in determining the permeability of porous media which is vital tool in seepage and drainage control in soils. However, whenever the aggregate sizes of the porous media and hydraulic gradient are large, the flow in drains will be semi-turbulent to turbulent. This research aims at modifying the true Darcy's permeability determined under small hydraulic gradients that ensure laminar or nearly laminar flow to allow for reduced efficiency caused by turbulence at greater hydraulic gradient and provide a relation between the maximum gradient for laminar flow and porosity of the porous media. A modeled experiment was set up using sand samples of different porosities from riverbed as porous media, which were packed in a vertical transparent cylinder tube of diameter 1.85x102m and relative permeabilities were determined for gradient ranging from 1.15-15.00. The result of the experiment shows that relative permeability increases with increasing porosity but decreases with increasing gradient. The maximum (or limiting) hydraulic gradient for laminar flow decreases with increasing porosity. Also, the vertical fluid flow in any porous medium is laminar or nearly laminar as much as hydraulic gradient is less than or equal to 1.04.

"