Upscaling of radionuclide transport and retention in crystalline rocks exhibiting micro-scale heterogeneity of the rock matrix

•We assess the impact of micro-scale matrix heterogeneity on radionuclide retention.•We use upscaling approaches to propagate the signal of heterogeneous retention.•At small scale the medium behaves as a composite system.•At large scale the breakthrough curves are well described by homogeneous solutions. In different in-situ diffusion experiments carried out in fractured crystalline rocks, sorbing radionuclides have shown a behaviour that strongly differs from what is predicted by homogeneous-based models. Their breakthrough curves are in fact often characterised by a fast first-arrival and these radionuclides can penetrate surprisingly long distances deep into the matrix. The heterogeneous structure of mineral distribution and porosity geometry had been offered as an explanation for these discrepancies. Here, we use reactive transport simulations to investigate the effect of the sparse distribution of sorption sites on the breakthrough curves of sorbing radionuclides. At small scale, the computed breakthrough curves significantly differ from those predicted using homogeneous models. For instance, the early part of these curves does not show any clear separation with the corresponding part of the curve of a non-sorbing tracer and a long transition zone is observed, with a very smooth slope of the tailing. Two different upscaling strategies, aimed at propagating the signal of heterogeneous retention over larger scales, are proposed and demonstrated against independent solutions computed at intermediate scales. The upscaling strategies are also used to show that at large scales (e.g. the scale of interest in a safety assessment study for a deep geological repository for nuclear waste) the signature of mineralogical heterogeneity is smoothed out and the heterogeneous breakthrough curve is well approximated by a homogeneous solution where the radionuclide distribution coefficient for the pure mineral phase is scaled by the mineral volume fraction. However, the spatial persistence of the heterogeneous signature is significant when the sorbing mineral is present in a low amount.