Modeling Of Fractured Reservoirs Using TheBoundary Element Method

Abstract

Many commercial gas and oil reservoirs are composed of fractured reservoir rock. The fractures provide high flow channels through the reservoir and can add significantly to the reservoir conductivity. However, the inclusion of the fracture effects is a very difficult modeling task. One of the current methods for modeling fractured reservoirs is the so-called dual porosity model. In this model the reservoir rock is represented by blocks of low conductivity material regularly spaced within a higher conductivity matrix, which represents the fractures. The regular nature of the model and the high connectivity of the fracture components results in a highly nonphysical model. Another popular model ignores the conductivity effects of the matrix rock and only examines the flow through the fracture system. The disadvantage of this model is that it leads to predictions of zero conductivity over length scales where there is a loss in fracture connectivity. We propose a formulation of the problem that accounts for the matrix flow, the fracture flow and the mutual interaction of the two. One of the principal complications associated with constructing a model is that each fracture is characterized by two length scales; the thickness which is very short, and the length or breadth which is significantly longer. We use this fact and assume that the fractures are thin enough, so that the flow in each fracture can be represented as two dimensional flow in a plane. Additionally, we assume that the effect of the fracture-matrix interaction can be represented as a planar source distribution within the matrix and a corresponding sink distribution within the fracture. The boundary element method provides a natural and efficient way for solving this novel formulation of the problem. Linear elements are used in the boundary element method, which allows all the boundary integrals to be computed analytically. The end result is an extremely efficient tool for Transactions on Modelling and Simulation vol 9, © 1995 WIT Press, www.witpress.com, ISSN 1743-355X