Turbulent Flow Through Porous Media

The pressure driving flow through porous media must be equal to the viscous resistance plus the inertial resistance. Formulas are developed for both the viscous resistance and the inertial resistance. The expression for the coefficient of permeability consists of parameters which describe the characteristics of the porous medium and the permeating fluid and which, for unconsolidated isotropic granular media, are all measurable. A procedure is proposed for testing for the occurrence of turbulence and calculating the effective permeability when it occurs. The formulas are applied to a set of data from 588 permeameter runs ranging from laminar to highly turbulent. The equations fit the data from the permeameter closely through the laminar flow conditions and quite closely through the turbulent conditions. In the turbulent range, the plotting of the data separates into three distinct lines for each of the three shapes of particles used in the tests. For the porous medium and fluid of these tests, turbulence begins at a head gradient of about 0.1.