Flow and transport in hierarchically fractured rock

We construct multiple realizations of hierarchical fracture networks with fractal dimensions between one and two, then simulate single-well pumping tests and natural-gradient tracer tests on them. We calculate averages and standard deviations of test results over the multiple realizations, and show individual results for selected cases to highlight key features of flow and transport through hierarchically fractured rock. These studies are intended to illustrate the range of possible behavior that can be obtained during fracture-dominated hydraulic and tracer tests, and provide insights into how to interpret field responses. The fractal dimension of the fracture network itself is generally larger than the fractal dimension of the flow field arising during a well test. The performance measures of the natural-gradient tracer tests, including the total flow through the fracture network, tracer travel time, front width, and maximum breakthrough concentration, can all be correlated to fractal dimension. Although some of the features observed in the flow and transport behavior within the hierarchically fractured rock have been observed by other authors using non-fractal fracture network concepts (e.g. channelized flow with early breakthrough times, crossing breakthrough curves), others arise directly from the fractal nature of the fracture network, in which variability occurs on all scales (e.g. front width and maximum breakthrough concentration that are constant over a wide range of fractal dimensions). Generally, transport simulations show large variability within a given realization and among realizations with the same fractal dimension, even in networks whose dimension is close to two. This finding is consistent with the large variability in experimental results observed at fractured rock field sites.