Modelling Groundwater Flow in a Confined Aquifer with Dual Layers

Abstract

Fractal-fractional derivatives are used to solve a complex physical problem and are found to be effective in modelling anomalous diffusion. In order to include in the mathematical formulation some complexities of the geological formation, the concept of fractal-fractional differential and integral operators are used. These new differential operators are able to depict scenarios that are able to depict certain non-local behaviour: long-range dependence, fading memory, and/or crossover behaviours with or without self-similarities. In this study, the Theis groundwater flow model was extended by replacing the time classical differentiation with three different types of fractal-fractional operators. The modified models are solved numerically using the newly introduced numerical scheme. For each case, a detailed stability and convergence analysis is presented. The obtained numerical solutions are used to depict numerical simulations showing different values of fractional order and fractal dimension. The obtained figures present a new class of flow different from the normal flow. The fractal dimension brings new flow trends that can be observed in fractured rock aquifers. The application of these differential operators opens a new way to capture heterogeneity associated with geological formation. Keywords: Heterogeneity, non-local behaviour, self-similarity, flow in confined aquifer