A Study by the Finite-Element Method of the Influence of Fractures in Confined Aquifers
Authors: Gureghian A.B. 
Published: December 2007

Abstract
A treatment is presented of the effect of sandfilled fractures in a confined aquifer on the flow behavior, particularly flow to a fully penetrating well. The mathematical study was penetrating well. The mathematical study was based on the variational method and the computation was carried out using the finite-element method. A new governing equation was derived based on the variational principle applicable to the fracture problem and its form explained. Experimental checks problem and its form explained. Experimental checks were carried out using an electrolytic tank. The investigations determined the potential distribution and the borehole discharge in relation to the fracture flow capacity (that is, the ratio of the permeability of the fracture to the permeability of the surrounding formation), length, position, and orientation of fractures. The effect of horizontal and vertical anisotropy was also investigated.

Introduction
When limestone formations are subjected to pronounced folding, natural fractures occur. pronounced folding, natural fractures occur. Generally, the permeability of the limestone is very low, and the presence of a fracture, which in spite of its very small width has a very low flow resistance, can increase the flow to a well. Fractures and crevices also occur in oil reservoirs composed of ordinary consolidated sands (shale, sandstone, etc.). However, these fractures are not normally extensive and they are not likely to affect the producing capacity of an oil well except when they intersect the borehole. Artificial fractures are sometimes hydraulically produced to increase production for an oil reservoir. Similar fractures may result during the drilling of boreholes for water.
The work described here concerns the effect of fractures in rocks or soil on the properties of boreholes that may or may not intersect the fractures.
Earlier work has been concerned with the case of fractures intersecting the borehole. In the case of a homogeneous isotropic medium, fully penetrated by the borehole and confined between impermeable horizontal surfaces, an analytical solution has been given by Muskat and Prats and experimental studies of a more general geometry were reported by van Poollen and McGuire and Sikora.
The problem of nonintersecting fractures has been experimentally investigated by Huitt and Ollos, and mathematically by Warren and Root and Kazemi. However, the methods used in these earlier investigations are insufficient to treat the problem of anisotropy of the surrounding medium and can accept a limited degree of inhomogeneity only with difficulty.
To obtain a comprehensive picture of the effects of a fracture, solutions using the finite-element method were explored. This technique was first applied to porous-medium flow problems by Zienkiewicz and Cheung, porous-medium flow problems by Zienkiewicz and Cheung, and has been subsequently used by a great number of workers in the same field. Recently, Wilson and Witherspoon, using this numerical approach, presented a comprehensive study that describes the flow characteristics of rigid networks of planar fractures.
A suitable procedure is developed in this paper regarding the steady-state flow through fractured systems, and checked againstprevious work for a homogeneous and isotropic medium with a nonintersecting fracture intersecting the borehole andelectrolytic tank experiments for representative cases of a homogeneous isotropic medium with a nonintersecting fracture.
A comprehensive numerical investigation was then carried out to assess the influence of the system parameters of conductivity ratio, fissure length, orientation, and position for both isotropic and anisotropic media. position for both isotropic and anisotropic media. SPEJ
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