Efficient upscaling of hydraulic conductivity in heterogeneous alluvial aquifers

An efficient method to upscale hydraulic conductivity (K) from detailed three-dimensional geostatistical models of hydrofacies heterogeneity to a coarser model grid is presented. Geologic heterogeneity of an alluvial fan system was characterized using transition-probability-based geostatistical simulations of hydrofacies distributions. For comparison of different hydrofacies architecture, two alternative models with different hydrofacies structures and geometries and a multi-Gaussian model, all with the same mean and variance in K, were created. Upscaling was performed on five realizations of each of the geostatistical models using the arithmetic and harmonic means of the K-values within vertical grid columns. The effects of upscaling on model domain equivalent K were investigated by means of steady-state flow simulations. A logarithmic increase in model domain quivalent K with increasing upscaling, was found for all fields. The shape of that upscaling function depended on the structure and geometry of the hydrofacies bodies. For different realizations of one geostatistical model, however, the upscaling function was the same. From the upscaling function a factor could be calculated to correct the upscaled K-fields for the local effects of upscaling.