Flow dimensions corresponding to stochastic models of heterogeneous transmissivity

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.