Geometry‐Imbedded Darcy's Law and Transient Subsurface Flow

Abstract

The traditional interpretation of Darcy's experiment views it as a valuable means for setting up the partial differential equation of transient or steady state subsurface fluid flow. In the present work, Darcy's observations are viewed from a different perspective, enabling the statement of transient subsurface fluid flow in terms of an equation defined over finite domains of space and time. Two new notions, namely, geometry imbedding and location of average, are introduced. The equation describes transient flow along a flow tube with arbitrarily varying cross section, consisting of materials with properties dependent on fluid potential. This equation, based on its own postulates, is fully consistent within itself and exists independently of the classical partial differential equation. This technical note presents preliminary ideas on what appears to be a promising new line of inquiry that departs from the traditional approach based on continuum mechanics. Further work is in progress.