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The finite element method has been used to investigate mathematical models of idealized systems of vertical fractures in an effort to extend our understanding of the behavior of naturally fractured reservoirs. Regular systems of fractures have been chosen in such a way that the length of the fracture can be characterized in terms of the dimensions of a representative elemental area associated with that fracture. By changing the permeability of the fracture relate to the matrix, steady state solutions demonstrate how the effective permeability of the fractured system depends on both fracture conductivity and dimensionless parameters representing fracture density. Horizontal shale lenses, scattered through a reservoir can be modelled in the same way using finite elements of very low conductivity. Comparison of our results with those from a recent analytic solution for fractured systems indicate excellent agreement.
There are a significant number of petroleum reservoirs where discontinuities such as fractures or joints in the porous rock matrix are the main path transmitting fluids to the producing well. These naturally fractured systems producing well. These naturally fractured systems characteristically have a low matrix permeability and one or more well developed fracture systems.
The published reports on naturally fractured reservoirs show that vertical joint planes are a dominant feature. Daniel studied three fractured limestone reservoirs of the Middle East. He reports that in all three cases, vertical and near vertical fractures were widespread, and for the most part, there was a complete absence of low dipping fracture planes. Wilkinson's work on the Spraberry reservoir in Texas revealed that vertical joints are the largest, both in extent and width, and by far the most abundant type of fractures. This dominance of vertical fractures has also been reported by other authors.
Investigations of non-reservoir rocks have also revealed the same conclusions. Kelly and Clinton, Parker, and Hodgson have made extensive regional investigations on fractures and joints. They report that vertical joints constitute the most dominant mode of fracture systems. Furthermore, they report that in the areas studied, the fractures are not randomly oriented but are systematically arranged in sets. The same finding has also recently been reported by Louis and Perrot and Mahtab et al.
In all of these investigations more than one fracture system may be found. The area of an individual fracture plane may vary from a few square inches to several hundred square feet.