Performance assessment of solute transport upscaling methods in the context of nuclear waste disposal

Stochastic simulations of solute transport in heterogeneous log10 K random fields were conducted at two different support scales to assess solute transport upscaling methods in the context of nuclear waste disposal. A very fine grid-scale is used to obtain a reference solution of the real problem, which is based on data from the Sellafield site. A coarse-scale model is obtained by upscaling the heterogeneous grid-blocks onto equivalent homogeneous hydraulic conductivity tensors calculated using the Simple Laplacian Technique. Random fields were designed with different degrees of heterogeneity such that the standard deviation of log10 K ranged between 0 and 1. It is shown that the early arrival time of particles at a control location, reflected in the lower limit of the 95% confidence interval of the mass flux cumulative density function stochastic process, associated with the upscaled model is strikingly similar to the one associated with the real solution for all heterogeneities. This is encouraging for the application of upscaled stochastic models to the design of nuclear waste repositories where the design of a nuclear waste disposal facility relies on the estimation of the early travel time of radionuclides arriving at a control location. On the contrary, the late arrival time of particles at the control location is largely underestimated by the upscaled model.