1 Department of Geotechnical Engineering and Geosciences, Technical University of Catalonia, Jordi Girona 1-3, E-08034 Barcelona, Spain

2 D.I.I.A.R., Politecnico di Milano, Piazza L. Da Vinci, 32, I-20133 Milano, Italy

Abstract One of the most crucial decisions to properly model transport is the choice of upscaled transport parameters (dispersivities and porosity) to be used in a numerical model for a given grid size and problem scale. Here we study block-upscaling of transport parameters of the classical advection–dispersion equation (ADE) to describe the spreading of a nonreactive solute migrating within a single realization of a heterogeneous transmissivity field. We start by assuming that solute transport can be modelled by a local scale ADE, which we employ to solve a concentration field on a finely discretized grid. The latter is taken as the ground truth against which we compare results from an upscaling procedure. The effect of increasing size of (constant, upscaled) transmissivity blocks is assessed upon employing an inverse transport model, the outputs of which are the (constant, upscaled) dispersivities providing a best fit against sampled concentrations at given observation times. Our results provide a set of rules-of-thumb to be used in order to obtain meaningful upscaled parameters.

Keywords heterogeneous media; inverse modelling; numerical modelling; transport; upscaling