Telegraphic double porosity models for head transient behavior in naturally fractured aquifers

We present a general phenomenological formalism for the modeling of hydraulic head behavior in naturally fractured aquifers. A nonlocal in time version of the double porosity model is developed for Euclidean and fractal reservoirs. In the fractal case, time nonlocality allows to find the geometric and topological factors responsible for subdiffusive behavior in such heterogeneous environments. Opposite to other fractal models presented in the literature, ours include dead-ends-backbone interactions instead of matrix-fracture interactions with clear and well-defined scaling exponents, thus giving a better characterization of the reservoir after such parameters are estimated. Applications to field tests are discussed. In particular, a distinctive short time head behavior during well tests is found.