Mathematical Modeling of Groundwater Flow and Solute Transport in Saturated Fractured Rock Using a Dual-Porosity Approach

Abstract

The present paper addresses critical issues that describe the transient transfer of stored rock-matrix flow into high-permeable fractures and rate-limited diffusive solute flux into low-permeable rock matrix using a typical dual-porosity approach. An improved mathematical model is suggested that better describes fluid flow through a coupled fracture-matrix system using a dual-porosity approach. The suggested model differs from a conventional model as the fracture flow equation contains a hyperbolic term in addition to the conventional dispersive term. The matrix flow equation contains the coupling term that controls the transient nature of fluid exchange from the stored rock matrix into the hydraulic conductors. The Langmuir sorption isotherm is suggested to describe the limited sorption sites available on fracture walls, while the Freundlich sorption isotherm is recommended to describe the unlimited sorption sites available within the rock matrix. The dispersion mechanism in a coupled fracture-matrix dual-porosity system becomes more complex as the convective longitudinal dispersion coefficient diverges resulting from huge variations in mean velocities of streamlines between the fracture and rock matrix.