[1] The generalized radial flow approach to hydraulic test interpretation uses the flow dimension to describe the change in flow area versus radial distance from the borehole. The flow dimension of a hydraulic test may reflect several characteristics of the hydrogeologic system, including heterogeneity, boundaries, and leakage. We show that a radial flow system with a linear, constant-head boundary asymptotically reaches a flow dimension of four, while the flow dimension of a leaky aquifer is a function of time and the leakage factor. We use numerical techniques to show that a stationary transmissivity field with a modest level of heterogeneity has a flow dimension that stabilizes at two. We also show that the flow dimension for a nonstationary transmissivity field depends on the form and magnitude of the nonstationarity. The flow dimension observed during hydraulic tests helps identify admissible conceptual models for the tested system, and places hydraulic testing in its full hydrogeologic context.
Traditional approaches to characterization and modeling of highly heterogeneous aquifers face many technical challenges. One nontraditional approach begins with the Generalized Radial Flow interpretation of hydraulic tests, which infers an additional parameter, the flow dimension, to describe flow geometry. The flow dimension is examined for three stochastic models of heterogeneous transmissivity, T(x), via Monte Carlo analysis of numerical models. For lognormal T(x) of low variance, the ensemble average of the apparent flow dimensions is two regardless of the test duration, and if the test duration is sufficiently long, the apparent flow dimension converges to two even for individual tests. The variability of the apparent flow dimension depends on the variance and integral scale of ln T(x), suggesting that these parameters might be estimated from a set of aquifer tests. Results suggest that the flow dimension may be useful for selecting models of heterogeneity and their parameters.
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