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Description
At present, groundwater flow and contaminant transport in fractured aquifers are commonly simulated using models designed for porous media. The continuum method replaces a fractured medium with a porous medium which is theoretically equivalent in average aquifer parameters. The theories governing flow through fractured rock and homogeneous isotropic porous media are used to determine when flow through a fractured rock behaves as a porous medium. The first portion of the study examines the distribution of fracture occurrence in two field areas. In both areas the number of fractures in a given interval can be modeled using a negative binomial distribution and the spacing between these fractures can be modeled using a truncated exponential distribution. This information was used as an aid in developing a random fracture network generator. A model was developed to generate fractures in a two dimensional region. These fractures are randomly generated according to the distributions of field data currently available in the literature for various fracture parameters, including orientation, aperture, length and spacing. Since the input parameters of the model are random variables, it is important to realize the output will also be random and should be described as such. With this model a Monte Carlo determination of the distribution of hydraulic conductivity in the direction of the gradient was found for several fracture network geometries. In the simulations where the distribution of fracture length was fixed, exponential, or lognormal a normal distribution of hydraulic conductivity was observed. The choice of the lognormal or exponential distribution for fracture length does not seem to affect the average hydraulic conductivity or average network characteristics significantly. Unless field observations indicate otherwise, it appears that either length model can be utilized with little effect on the result. In the cases where the distribution of aperture was lognormal the distribution of hydraulic conductivity was observed to be lognormal. In these simulations a range of hydraulic conductivities through three orders of magnitude was observed. Once the hydraulic conductivity distribution for a given set of network parameters has been determined the probability that a fracture network will have a hydraulic conductivity in a specified range can be calculated. The mean number of intersections per fracture and the product of fracture density (N) with the average fracture length (r) squared (N(r2)) were used to determine when a network might conduct flow (i.e., will be above the percolation threshold) and when a fracture network might be considered an equivalent porous medium. These characteristic values were determined using stochastically generated fracture networks. The mean number of intersections per fracture for networks classified as equivalent porous media is determined to be approximately 4.03. For networks not behaving as equivalent porous media approximately 2.94 intersections per fracture are observed. Observed networks were more likely to behave as equivalent porous media if the value of N(r2) was approximately 2.5 or above. The mean value of intersections per fracture and N(r2) were also calculated to determine the percolation threshold of random networks. The value of N(r2) at the percolation threshold is shown to be 1.1. The mean number of intersections per fracture required for flow to occur is shown to be in the range 2.4 to 3.4. The results of this work are limited to the study of low fracture density networks in a single size flow region with two identical orthogonal fracture sets.
