Groundwater flow in karstic aquifer: analytic solution of dual-porosity fractional model to simulate groundwater flow

Abstract

Karst aquifers have a very complex flow system because of their high spatial heterogeneity of void distribution. In this manuscript, flow simulation has been used to investigate the flow mechanism in a fissured karst aquifer with double porosity, revealing how to connect exchange and storage coefficients to the volumetric density of the highly permeable form of media. The governing space-time differential equations of the dual-porosity model are modified by using the Caputo–Fabrizio fractional derivative operator for time memory. The sensitivity of exchange and storage coefficients has been demonstrated using numerical studies with theoretical karst systems in this hybrid system. When dealing with highly heterogeneous systems, it is demonstrated that porosity storage and exchange coefficients are required. The analytical model could possibly reveal some of the karstic network's essential structural features.