Pumping tests in fractal media

Abstract

The investigation of fractured rocks and their hydraulic properties has recently received growing attention as the result of plans to build nuclear waste repositories. Studies have shown the need to refine existing methods of measuring hydraulic parameters of fractured rocks, especially for contaminant transport problems. Traditional approaches have generally tried to model hydraulic tests in fractured media, first by conventional type curve analysis and then using more and more sophisticated models if the match of analytical predictions was poor with field data. In some instances it is possible to obtain a good match by, e.g., using a leaky aquifer model, even though the parameters obtained might not reflect the underlying geometric properties of the aquifer, leading to misleading interpretations.
This study focused on the combination of two novel approaches of hydraulic pumping tests in fractured media, using recently developed theories of flow in fractal media, and inverse modelling:1. A theoretical study investigating the properties of regular and stochastic fractal fracture networks. The main aim is to study functional relationships between fractal dimension measures of these networks, fractional flow dimensions, network connectivity and fracture probability in order to condition stochastic fracture networks. This is a first step to model the pumping response making use of the underlying fractal structure of fractured rocks.Computer codes and algorithms were developed and adapted to generate two-dimensional fracture networks with fractal properties using an iterated function system. Code was developed to prepare these networks for input into a finite element code so that the fractional flow dimension can be obtained. Results indicate that connectivity is related to flow dimension, and also to the network topology (“diffusion slowdown"). Calibration curves were generated that relate fractal dimension, flow dimension, fracture probability and connectivity.2. Another part of this study was to test the usefulness of a direct inverse modelling approach (“simulated annealing"). This method tries to fit existing pumping test data by altering the conductivity properties of a network input “template" (e.g. a generic 2-D regular mesh), without the intermediate step of parameter estimation using traditional type curves. A new approach was the combination of this method with the fractal fracture network generator mentioned above. Computer programmes were developed to inverse model synthetic pumping test data generated from fractal networks. It was revealed that inverse modelling runs generate networks with similar fractal properties as the one that was used to generate the pumping test data. The actual appearance of networks, however, can be radically different. Most importantly, by generating several instances of networks for the same input data it is possible to obtain a measure of uncertainty, with networks showing similar connectedness in regions of low uncertainty and large variations in other regions, enabling to determine how well different wells are connected, and where more data need to be collected to allow meaningful predictions.
In addition to the results obtained, the developed computer code will be of potential great use for the research group, enabling further work to study fractal media. The simulated annealing method and fractal network algorithms can be easily extended to 3-D and should be used in future work as soon as real data sets and enough computing power become available. A possible application of this method would be the interpretation of the NIREX RCF3 long term pumping test data set (requested data from NIREX did not arrive in time for this project).

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