Fractional flow equation in fractured aquifer using dual permeability model with non-singular kernel

Ritu Agarwal,Ravi P Agarwal,Mahaveer Prasad Yadav

doi:10.1007/s40065-020-00293-y

Abstract

In this paper, a finite fractured aquifer, bounded by a stream and impervious layers on the other sides, has been considered. Variation in the level of groundwater is analyzed in confined aquifer for the unsteady flow. The governing differential equation for piezometric head involves the Caputo–Fabrizio fractional derivative operator with respect to time and is based on dual-porosity model with the assumption that the flow from fracture to block is in pseudo steady state. The obtained solutions can be used to anticipate the fluctuations in the waterlevels of the confined aquifer and for the numerical validation of a model in an aquifer.

Highlights

An aquifer is a geological formation of underground layer of permeable rocks, rock fractures or unconsolidated materials which can contain and transmit the groundwater
Fractures are important for groundwater flow, whereas blocks act as a source or sink to the fractures
The dual-porosity model has been recognized as a powerful tool to simulate flow and transport phenomena in fractured aquifer [10,12,16,19,21,22,23,24]

Summary

Introduction

An aquifer is a geological formation of underground layer of permeable rocks, rock fractures or unconsolidated materials which can contain and transmit the groundwater. The dual-porosity model has been recognized as a powerful tool to simulate flow and transport phenomena in fractured aquifer [10,12,16,19,21,22,23,24] In this approach, the porous medium consists of two continua, one associated with the fractured system and other with a less permeable pore system of matrix block. Since we consider a finite fractured aquifer, bounded by a stream and impervious layers and variation in the level of groundwater is analyzed in confined aquifer for the unsteady flow All these physical observations and facts cannot be described with more accuracy via the local derivative and the well-known derivative with fractional order. Where 0 < α ≤ 1, 0 < β ≤ 1 along with initial and boundary conditions (16) and (17)

Mathematical preliminaries

Flow in fractured confined aquifer

Flow rate

Numerical simulation

Conclusion