Finite element techniques for modeling groundwater flow in fractured aquifers

Abstract

A mathematical description of groundwater flow in fractured aquifers is presented. Four alternative conceptual models are considered. The first three are based on the dual‐porosity approach with different representations of fluid interactions between the fractures and porous matrix blocks, and the fourth is based on the discrete fracture approach. Two numerical solution techniques are presented for solving the governing equations associated with the dual‐porosity flow models. In the first technique the Galerkin finite element method is used to approximate the equation of flow in the fracture domain and a convolution integral is used to describe the leakage flux between the fractures and porous matrix blocks. In the second the Galerkin finite element approximation is used in conjunction with a one‐dimensional finite difference approximation to handle flow in the fractures and matrix blocks, respectively. Both numerical techniques are shown to be readily amendable to the governing equations of the discrete fracture flow model. To verify the proposed numerical techniques and compare various conceptual models, four simulations of a problem involving flow to a well fully penetrating a fractured confined aquifer were performed. Each simulation corresponded to one of the four conceptual models. For the three simulated cases, where analytical solutions are available, the numerical and the analytical solutions were compared. It was found that both solution techniques yielded good results with relative coarse spatial and temporal discretizations. Greater accuracy was achieved by the combined finite element‐convolution integral technique for early time values at which steep hydraulic gradients occurring near the fracture‐matrix interface could not be accommodated by the linear finite difference approximation. Finally, the results obtained from the four simulations are compared and a discussion is presented on practical implications of these results and the utility of various flow models.