On the Validity of Darcy's Law In Subsurface Flow Regimes.

Water flow in porous media is traditionally described using Darcy’s law. The linear relationship between the specific discharge and the gradient, as described by Darcy’s law has been well documented to be valid only under certain conditions (e.g., Dullien, 1992; Bear, 1988). It is clear that Darcy’s law is a close approximation of the underlying physical process. Given the fact that Darcy’s law has been ascribed to be an experimentally-derived than a fundamental law, the limitations of its use in porous media have been not well understood. For example, the threshold value (as represented by the highest Reynolds number) where Darcy’s law may not be violated is not very clearly described. It is however, hypothesized to be dependent on the relative effects of viscous force and inertial forces in the porous media. . Although a Reynolds number of 1-10 has been indicated to be the upper limit, the range is too wide to be used as a pointer in reality. Also, for subsurface hydrology purposes, it would be more intuitive to express this upper limit as a function of hydraulic gradient and porous media. Specific discharge-hydraulic gradient relationships are essentially non-linear across all values of hydraulic gradient. This is especially the case for coarser soils. We propose that the gradients (or Reynolds number) up to which Darcy’s law is valid should be statistically defined rather than on a purely physical basis.  The objective of this paper is to understand the limitations of Darcy’s law as a function of porous media. We develop criterion which ca be potentially used to estimate the upper limit of hydraulic gradient after which the Darcy's law is invalid.