2 TYPES OF NONLINEAR PRESSURE-DROP VERSUS FLOW-RATE RELATION OBSERVEDFOR SATURATED POROUS-MEDIA

Previous reports of experiments performed with water (Fand et al., 198 7 and Keceioglu and Jiang, 1994) indicated that beyond the Forchheimer regime the rate of change of the hydrostatic pressure gradient along a porous medium suddenly decreases. This abnormal behavior has been te rmed ''transition to turbulence in a porous medium.'' We investigate t he relationship between the hydrostatic pressure gradient of a fluid ( air) through a porous medium and the average seepage fluid velocity. O ur experimental results, reported here, indicate an increase in the hy drostatic pressure rate beyond a certain transition speed nor a decrea se. Physical arguments based on a consideration of internal versus ext ernal incompressible viscous flow are used to justify this distinct be havior, a consequence of the competition between a form dominated tran sition and a viscous dominated transition. We establish a criterion fo r the viscous dominated transition from consideration of the results o f three porous media with distinct hydraulic characteristics. A theore tical analysis based on the semivariance model validation principle in dicates that the pressure gradient versus fluid speed relation indeed departs from the quadratic Forchheimer-extended Darcy flow model, and can be correlated by a cubic function of fluid speed for the velocity range of our experiments.