A BOUNDARY VALUE PROBLEM IN GROUNDWATER MOTION ANALYSIS — COMPARISON OF PREDICTIONS BASED ON DARCY’S LAW AND THE CONTINUUM THEORY OF MIXTURES

Abstract

The classical problem of the radial flow to a well in a confined horizontal aquifer is solved using two theories: (1) when the flow is based on Darcy’s law, and (2) when the flow is based on equations of the Continuum Theory of Mixtures. The latter reduce to Darcy’s law when the inertia of the fluid can be neglected, and when the viscosity of the fluid does not enter into the expression for the partial stress for the fluid. A comparison of the two solutions shows that there are conditions when Mixture Theory could predict results that provide a significant departure from those predicted by Darcy’s Law. In this paper we delineate the extent of validity of Darcy’s law, within the context of a more general theoretical framework. The results of our work indicate that Darcy’s law is indeed quite good for low flow rates for a fluid like water. However this is not the case for dense fluids, say oils or effluents, due to the inclusion of inertial effects in the equations of motions.