Abstract 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.

中文翻译：

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显示岩石基质微尺度非均质性的结晶岩中放射性核素输运和滞留的放大

摘要 在裂隙结晶岩中进行的不同原位扩散实验中，吸附放射性核素表现出的行为与均质模型预测的行为截然不同。事实上，它们的突破曲线通常以快速到达为特征，并且这些放射性核素可以穿透到基质深处的惊人长距离。矿物分布的异质结构和孔隙度几何结构已被提供作为对这些差异的解释。在这里，我们使用反应输运模拟来研究吸附位点的稀疏分布对吸附放射性核素的穿透曲线的影响。在小范围内，计算出的突破曲线与使用均质模型预测的那些有显着差异。例如，这些曲线的前半部分与非吸附示踪剂曲线的相应部分没有显示出任何明显的分离，并且观察到一个长的过渡区，尾矿的斜率非常平滑。针对在中间尺度计算的独立解决方案，提出并证明了两种不同的放大策略，旨在在更大尺度上传播异质保留信号。升级策略也用于表明在大规模（例如 核废料深层地质处置库安全评估研究中感兴趣的尺度）平滑了矿物学异质性的特征，并且非均质突破曲线被均质解很好地近似，其中纯矿物相的放射性核素分布系数被缩放由矿物体积分数。然而，当吸附矿物的含量较低时，异质特征的空间持久性很重要。