Fractional flow equation in fractured aquifer using dual permeability model with non-singular kernel
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Arabian Journal of Mathematics
Ritu Agarwal · Mahaveer Prasad Yadav
· Ravi P. Agarwal
Fractional flow equation in fractured aquifer using dual permeability model with non-singular kernel
Received: 24 July 2019 / Accepted: 21 August 2020 © The Author(s) 2020
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. Mathematics Subject Classfication
34A08 · 26A33
1 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. Aquifer may occur at various depths in ground, close to surface are used to water supply and irrigation. Many desert areas having limestones hills or mountains can be exploited as groundwater resources. The fractured rocks are the type of an aquifer which contains groundwater. The fractured aquifer having two overlapping medium in which one represent the fracture and other representing the blocks. These formations are the type of heterogeneous medium in which blocks have very low permeability and containing large amount of storage comparing to fractures which have high permeability. Groundwater is transferred between fractures to blocks, but in any two blocks, there is no flow, because of its low permeability [15,29]. Therefore, 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 [10,12,16,19,21–24]. 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. For saturated and unsaturated flows, the continuum approach is good unless the porous media has very high heterogeneity. Heterogeneous porous media give rise to non-uniform flow with widely different velocity distributions. Such flow often referred as preferential or bypass flow [27]. The continuum approach cannot provide realistic R. Agarwal · M. P. Yadav (B) Department of Mathematics, Malaviya National Institute of Technology, Jaipur 302017, India E-mail: [email protected] R. Agarwal E-mail: [email protected] R. P. Agarwal Department of Mathematics, Texas A&M University, Kingsville, 700 University Blvd., Kingsville, TX 78363-8202, USA E-mail: [email protected]
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Arab. J. Math.
predictions for the flow in porous media which contains
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