We examine the temporal evolution of the maximum concentration of a dissolved inert solute in spatially heterogeneous subsurface flows. The maximum concentration of a given substance is at the basis of most of environmental regulatory practices where maximum tolerable levels of concentration are typically prescribed for a variety of known contaminants. Through the use of the Lagrangian framework, we elaborate over a physically based, semi-analytical model for the maximum concentration. Specifically, we address how the maximum concentration is affected by key geostatistical parameters (i.e., logconductivity variance), local-scale dispersion processes and engineering design variables such as the dimensions of the solute injection zone. The model will help in identifying the major components that determine the maximum concentration, which is important in order to better allocate resources toward site characterization and reduce uncertainty in predictions. The ultimate scope is to provide a theoretical framework that is application-oriented to estimate the maximum concentration in natural aquifers and provide some guidance in applications. It also provides an useful tool for preliminary, screening analysis and testing scenarios. We test the performance of the model against the MADE transport experiment, with reasonably good agreement.

我们研究了在空间上非均质的地下流动中溶解的惰性溶质的最大浓度的时间演变。给定物质的最大浓度是大多数环境法规实践的基础，在这些实践中，通常为各种已知污染物规定了最大可容许的浓度水平。通过使用拉格朗日框架，我们详细说明了基于物理的最大浓度半分析模型。具体而言，我们解决了最大浓度如何受到关键地统计学参数（即对数电导率方差），局部尺度分散过程和工程设计变量（例如溶质注入区的尺寸）的影响。该模型将有助于识别确定最大浓度的主要成分，为了更好地分配资源进行站点表征并减少预测的不确定性，这一点很重要。最终范围是提供一个面向应用的理论框架，以估算天然含水层中的最大浓度并为应用提供一些指导。它还为初步，筛选分析和测试方案提供了有用的工具。我们以合理的良好协议对照MADE运输实验测试了模型的性能。筛选分析和测试方案。我们以合理的良好协议对照MADE运输实验测试了模型的性能。筛选分析和测试方案。我们以合理的良好协议对照MADE运输实验测试了模型的性能。