This paper delves into the key factors governing contaminant retardation and the scaling of retardation factor for contaminant transport in naturally fractured media. It employs a geostatistical approach, utilizing hierarchical transition probability and covariance models, to characterize multimodal reactive mineral facies. Subsequently, scale-dependent models are developed to illustrate the transport behaviors of reactive contaminants under equilibrium sorption conditions and quantify the spatial and temporal variations of the effective retardation factor. These models incorporate various factors, including the structural characteristics of reactive minerals (the volume proportions and lengths of different facies types), fracture characteristics (the means and variances of fracture apertures), and the adsorption capacity of contaminants on minerals (sorption coefficients (ln )). The results from these Lagrangian-based models are compared and validated against experimental data of solute transport in a single natural fracture. These findings underscore the remarkable agreement between the derived scale-dependent analytical expressions and the experimental results. Additionally, a global sensitivity analysis was performed using the Monte Carlo-based Sobol’ indices method to understand the influential factors governing contaminant retardation. The study reveals that the primary influential factor is the sorption capacity of contaminants on minerals, while fracture and reactive mineral structural characteristics play a secondary role. These insights provide significant information for understanding the reactive transport processes and the environmental impact of transport parameters in fractured media.

中文翻译：

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裂缝介质中污染物传输的延迟因子缩放

本文深入研究了控制污染物延迟的关键因素以及自然裂缝介质中污染物传输的延迟因子的缩放。它采用地质统计方法，利用分层转移概率和协方差模型来表征多峰反应矿物相。随后，开发了与尺度相关的模型，以说明平衡吸附条件下活性污染物的传输行为，并量化有效延迟因子的空间和时间变化。这些模型综合了多种因素，包括活性矿物的结构特征（不同相类型的体积比例和长度）、裂缝特征（裂缝孔径的均值和方差）以及污染物对矿物的吸附能力（吸附系数（ln ））。这些基于拉格朗日模型的结果与单个天然裂缝中溶质迁移的实验数据进行了比较和验证。这些发现强调了导出的尺度相关分析表达式与实验结果之间的显着一致性。此外，使用基于蒙特卡罗的 Sobol' 指数方法进行了全局敏感性分析，以了解控制污染物延迟的影响因素。研究表明，主要影响因素是污染物对矿物的吸附能力，而裂隙和活性矿物结构特征起着次要作用。这些见解为理解断裂介质中的反应输运过程和输运参数对环境的影响提供了重要信息。