Precomputing upscaled hydraulic conductivity for complex geological structures

3D geological models are built to capture the geological heterogeneity at a fine scale. However groundwater modellers are often interested in the hydraulic conductivity (K) values at a much coarser scale to reduce the numerical burden. Upscaling is used to assign conductivity to large volumes, which necessarily causes a loss of information. Recent literature has shown that the connectivity in the channelized structures is an important feature that needs to be taken into account for accurate upscaling. In this work we study the effect of channel parameters, e.g. width, sinuosity, connectivity etc. on the upscaled values of the hydraulic conductivity and the associated uncertainty. We devise a methodology that derives correspondences between a lithological description and the equivalent hydraulic conductivity at a larger scale. The method uses multiple-point geostatistics simulations (MPS) and parameterizes the 3D structures by introducing continuous rotation and affinity parameters. Additional statistical characterization is obtained by transition probabilities and connectivity measures. Equivalent hydraulic conductivity is then estimated by solving a flow problem for the entire heterogeneous domain by applying steady state flow in horizontal and vertical directions. This is systematically performed for many random realisations of the small scale structures to enable a probability distribution for the equivalent upscaled hydraulic conductivity. This process allows deriving systematic relationships between a given depositional environment and precomputed equivalent parameters. A modeller can then exploit the prior knowledge of the depositional environment and expected geological heterogeneity to bypass the step of generating small-scale models, and directly work with upscaled values.