Conditional simulations of fluid flow in three‐dimensional networks of discrete fractures

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Abstract
How to predict flow through a network of discrete fractures in a three‐dimensional domain is investigated. Fractures are modeled as circular discs of arbitrary size, orientation, transmissivity, and location. A fracture network is characterized by the statistical distributions of these quantities. Fracture traces observed on a wall form the basis for estimates of mean fracture radius, fracture orientation parameters, and fracture density. Fracture trace lengths are estimated with the scanline method and from areal sampling on circular regions. The traces observed on the wall can also be used to condition the network. This trace conditioning is achieved by forcing the network generator to always reproduce the observed traces. Conditioning might be a means of decreasing the variability of the fracture networks. A numerical simulation model has been developed which is capable of generating a fracture network of desired statistical properties and solving for the steady state flow. On each fracture disc the flow is discretized with the boundary element method. A series of hypothetical examples are analyzed. These examples consist of sets of Monte‐Carlo simulations of flow through a series of networks generated from the same statistical distributions. The examples lead to the following conclusions. Large fractures and high fracture density implies good connectivity in the networks. A high fracture density implies a small variance in the flow through the network. Trace conditioning decreases estimation variance only when the fracture network consists of large fractures. Fracture statistics can be estimated reasonably well from fracture traces observed on a wall.