Derivation of a groundwater flow model within leaky and self-similar aquifers: Beyond Hantush model

Scientists conducted researches on leaky aquifers, developed groundwater models and equations for this type of aquifer. These equations are developed from classical formulas like Darcy's Law. The classical equations cannot be used to assess heterogeneous and porous aquifers. A fractal differential operator is then defined for fractal geometry and it is now widely used by many scientists to allow better understanding of such aquifers, which cannot be based on Euclid geometry or assessed using classical formulas. Fractals have a property called self-similarity and there are examples in nature like fractured aquifers. A self-similar leaky aquifer is visualized as a heterogeneous media, which cannot be solved or assessed using the classical equation. This article entails a new groundwater equation derived for flow within a self-similar leaky aquifer. We provided in this paper new models of groundwater flowing within a leaky aquifers with self-similarities. The new model is more representative that one suggested by Hantush as it includes in the mathematical formulation the scaling effect of a geological formation. Thus the solution is not only function of time-space and the well-known aquifer's parameters including the transmissivity, storativity and leaky factor, but there is a new factor that takes into account the scaling of the aquifer. We presented the existence and uniqueness of the solutions. We used a newly established numerical scheme to solve the new equations. We presented some numerical simulations and observed very interesting features that are observed in real world problems.