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. INTRODUCTION Literature ReviewFlow in fractured porous media has been and still continues to be an important concern in areas such as petroleum and mining engineering and karst hydrology. Increased interest in fractured porous media has resulted from terminal waste storage programs, especially those associated with high-level radioactive waste. Characterization of the media, as well as development of related methodologies for predicting flow behavior, are of primary importance to these programs. This paper, the first in a series of three, deals with the latter problem of predicting flow behavior. In particular, we focus attention on areal flow in fractured aquifers and discuss four alternative conceptual models, as well as present the mathematical formulation and finite element solution algorithms. The second paper makes use of results from the first paper and extends our predictive capabilities by incorporating singlespecies solute transport. In the final paper of the series, multiple-species solute transport with chain reactions is discus...

Karst Aquifer evolution in fractured, porous rocks

“…Therefore a leakage term has to be introduced to couple flow between rock matrix and fractures. In contrast, the discrete fracture approach incorporates fractures directly into the medium [e.g., Gureghian, 1975;Huyakorn et al, 1983], accounting for the geometry of the fractures directly as well as the flow in the combined matrix-fracture medium. We adopt the latter approach for our numerical simulations.…”

“…In this approach, two different conductivities are introduced to characterize the permeability of the rock matrix and the fractures [e.g., Barenblatt et al, 1960;Streltsova-Adams, 1978;Huyakorn et al, 1983]. It is commonly assumed that flow is directed from the rock matrix toward the fractures.…”

“…The aim of this paper is to adopt the discrete fracture approach [Huyakorn et al, 1983] to simulate flow and evolution in a fractured, porous karst aquifer. We have developed a new method based on the finite-element approach, which simultaneously solves for flow in the fractured, porous medium and dissolutional widening of the fissures.…”

Survival, transport and dissemination of Escherichia coli and enterococcci in a fissured environment. Study of a flood in a karstic aquifer

“…The primary aim of this study is to describe the transport combined with those of the fissures separating the blocks (Warren and Root 1963;Wilson and Witherspoon 1974; and dissemination of bacteria, especially during a rising phase, through a fissured medium. The ultimate goal is to confirm Huyakorn et al 1983;Shapiro and Andeson 1983;Moench 1984). The matrix porosity of karstic rock is frequently almost the vulnerability of groundwater in karst to pollution.…”

Control‐volume method for numerical simulation of two‐phase immiscible flow in two‐ and three‐dimensional discrete‐fractured media

“…[12] The FU-FEM, first proposed by Dalen [1979], gives a physically correct result for two-phase immiscible flow in 2-D porous media [Dalen, 1979;Huyakorn et al, 1983;Rabbani, 1994;Helmig and Huber, 1998]. (An analysis of the FU-FEM is given by Helmig [1997].)…”