The Forchheimer Number, the Reynolds Number, and Non-Darcy Flow In Porous Media: An Experimental Investigation

A series of experiments were conducted in packed porous media with different grain diameters under relatively high velocity conditions. The experimental results show that relationships between the hydraulic gradient (i) and the specific discharge (q) deviate from Darcy's law. The change of the ratio of the hydraulic gradient and the specific discharge (i/q) with q is analyzed to determine different flow regimes. The experimental results indicate that both the power-type Izbash and the Forchheimer equations fit the experimental data equally well. In terms of the Forchheimer equation, the Forchheimer number (F0) is calculated and recommended as an alternative criterion to identify non-Darcy flow. Such a criterion is compared with another conventionally used criterion of the Reynolds number. Some advantages of using the Forchheimer number have been discussed and compared with those of using the Reynolds number. We have proposed a new relationship between the friction factor and the Forchheimer number. This new relationship may be used to predict the critical specific discharge or hydraulic gradient for non-Darcy flow to start.