The Theis solution for subdiffusive flow in rocks

Abstract

The central contribution of this work is the development of a “master” solution similar to the Theis solution to evaluate well responses under subdiffusive flow. Models based on subdiffusion employ fractional constitutive laws, a redefinition of Darcy’s law. Subdiffusive models discussed here are particularly useful to address situations where the internal architecture of the geological medium, such as fluvial and fractured systems, matters and where the existence of topological, geometrical and spatial influences result in distorted flow paths and a loss in connectivity. The developed solution provides the means for addressing these ends.