REPRESENTATIVE HYDRAULIC CONDUCTIVITY OF MODEL UNITS: INSIGHTS FROM AN EXPERIMENTAL STRATIGRAPHY

A critical issue facing groundwater flow models is the estimation of representative hydraulic conductivity for the model units. A high-resolution fully heterogeneous hydraulic conductivity map is created based on an experimental stratigraphy. It offers a geologically realistic test case to evaluate this parameter. Various hydrogeological units are distinguished, each is of irregular shape with distinct heterogeneity patterns corresponding to physical sedimentation processes. The total ln(K) variance is 4.07, large compared to other synthetic stratified aquifers. A noval numerical upscaling method is developed to estimate an equivalent conductivity for each model unit. The equivalent conductivity is then compared with direct averages (arithmetic, geometric, harmonic means) and an effective conductivity predicted by a well-known stochastic theory.

Results suggest that for all units, the maximum principal component (Kmax) of the equivalent conductivity is closely matched by the arithmetic mean of the within-unit conductivity. The minimum principal component (Kmin) lies between the harmonic and geometric means. Significantly, using Kmax (or arithmetic mean), geometric mean, and ln(K) variance, the stochastic theory predicts a Kmin that is consistent with the up-scaled conductivity. Similarly, knowing Kmin, Kmax predicted by theory is also consistent with the up-scaled value. This suggests the potential of using theory to predict representative conductivities for geologically realistic heterogeneities, without the need for detailed upscaling. However, error using the theory increases for units of higher variance. For most units (some with variance greater than 1), a low-variance version of the theory is more accurate than a high-variance version, consistent with the experimental study of Fernandez-Garcia et al (2005). Finally, the equivalent conductivity changes with the domain area of up-scaling, indicating "scale effect". In this case, the "scale effect" is controlled by the global non-stationarity in the mean local conductivity, a result of depositional variability. Thus, upscaling (either numerical or analytical) the entire model unit is necessary to obtain the representative conductivity.