de Barros F P J, Fiori A, Boso F, Bellin A
Sonny Astani Dept. of Civil and Environmental Engineering, University of Southern California, Los Angeles, USA.
Dip. di Ingegneria, Universita di Roma Tre, Rome, Italy.
J Contam Hydrol. 2015 Apr-May;175-176:72-83. doi: 10.1016/j.jconhyd.2015.01.004. Epub 2015 Feb 14.
Spatial heterogeneity of the hydraulic properties of geological porous formations leads to erratically shaped solute clouds, thus increasing the edge area of the solute body and augmenting the dilution rate. In this study, we provide a theoretical framework to quantify dilution of a non-reactive solute within a steady state flow as affected by the spatial variability of the hydraulic conductivity. Embracing the Lagrangian concentration framework, we obtain explicit semi-analytical expressions for the dilution index as a function of the structural parameters of the random hydraulic conductivity field, under the assumptions of uniform-in-the-average flow, small injection source and weak-to-mild heterogeneity. Results show how the dilution enhancement of the solute cloud is strongly dependent on both the statistical anisotropy ratio and the heterogeneity level of the porous medium. The explicit semi-analytical solution also captures the temporal evolution of the dilution rate; for the early- and late-time limits, the proposed solution recovers previous results from the literature, while at intermediate times it reflects the increasing interplay between large-scale advection and local-scale dispersion. The performance of the theoretical framework is verified with high resolution numerical results and successfully tested against the Cape Cod field data.
地质多孔地层水力性质的空间非均质性会导致溶质云形状不规则，从而增加溶质体的边缘面积并提高稀释速率。在本研究中，我们提供了一个理论框架，用于量化稳态流中受水力传导率空间变异性影响的非反应性溶质的稀释情况。采用拉格朗日浓度框架，在平均流均匀、注入源小且非均质性弱至中等的假设下，我们得到了稀释指数作为随机水力传导率场结构参数函数的显式半解析表达式。结果表明，溶质云的稀释增强如何强烈依赖于多孔介质的统计各向异性比和非均质性水平。显式半解析解还捕捉了稀释速率的时间演化；对于早期和晚期极限，所提出的解恢复了文献中的先前结果，而在中间时间，它反映了大尺度平流和局部尺度弥散之间日益增强的相互作用。该理论框架的性能通过高分辨率数值结果得到验证，并成功地针对科德角现场数据进行了测试。
