Representative Element Modeling of Fracture Systems Based on Stochastic Analysis

Abstract

An important task associated with reservoir simulation is the development of a technique to model a large number of fractures with a single description. Representative elements must be developed before reservoirs c a l e simulations can adequately address the effects of intersecting fracture systems on fluid migration. An effective element model will sharply reduce the cost and complexity of large scale simulations to bring these to manageable levels. Stochastic analysis is a powerful tool which can determine the hydrau l t c and transport characteristics of intersecting sets of statistically defined fractures. Hydraulic and t r a n s port characteristic s are required to develop representative e l em en t s. Given an assumption of fully developed laminar flow, the net fracture conductivities and hence flow velocities can b e determined from d e script i v e statistics of fractur e spacing, o r t e n t at i o n, aperture, and extent. The distribution of physical character is t i c s about the t r mean leads to a d l s t r i bution of the associated conduct i v i t i e s. The variance of hydraulic conductivity induces dispersion Into the transport process. The simple s to f frac t u r e systems, a single set of parallel fractures, I s treated to demonstrate the usefulness of stochastic a n a1 y s i s. Explicit equations for conduc t i v t t y of an element are developed and the d is pers i o n characteristics are shown. The analysis reveals the dependence of the represent at i v e element properties on the various parameters used to d e s c r l b e the fracture system. N 0 T AT IO N a depth of fracture system.