Analytical Solution for Fractional Well Flow in a Double‐ Porosity Aquifer with Fractional Transient Exchange between Matrix and Fractures

Abstract

An analytical solution is presented for groundwater flow to a well in an aquifer with double‐porosity behavior and transient transfer between fractures and matrix. The solution is valid for fractional flow dimensions including linear, cylindrical or spherical flow to the well and for fractional inter‐porosity diffusive transfer including release from storage in infinite slabs, infinite cylinders or spherical matrix blocks. Approximations are also presented for small and large times that are easy to evaluate in practice. The solution can be used to analyze pumping tests via coupling with a parameter estimation code. The utility of the method is demonstrated by a practical example using data from a pumping test performed in a fractured chalk aquifer. The analytical solution allows the accurate modeling of pumping tests and the estimation of aquifer parameters that are statistically significant and physically relevant.