Consiglio Nazionale delle Ricerche, Istituto di Ricerca Sulle Acque, Reparto di Chimica e Tecnologia delle Acque, 5 via Francesco De Blasio, 70132 Bari, Italy.
J Contam Hydrol. 2018 Aug;215:21-28. doi: 10.1016/j.jconhyd.2018.06.004. Epub 2018 Jun 30.
The theory for modeling non-equilibrium solute transport in porous media is still based on approximations to a model proposed by Lapidus and Amundson in 1952 that has not been updated. This Mobile-Immobile Model (MIM) is based on the definition of a mass-transfer coefficient (α), which has been proven subject to some severe limitations. Measurements at both laboratory and field scales have demonstrated the scale-dependency of α values. This means that the MIM theory fails in real applications, since α is not constant, as defined in the kinetic model theory, but is a time-residence (or distance) dependent coefficient. Multi-rate mass-transfer models have been proposed in recent literature to capture real-world solute transport with a multiple mass transfer. In this study, we propose a novel model, which implements the analytical solution of Fick's second law of diffusion directly in the nonequilibrium advection/dispersion equation of solute transport in porous media. New model solutions properly fitted data collected during tracer tests carried out at the CNR-IRSA Laboratory (Bari, Italy) in a horizontal sandbox, 2 m of length, by using sodium chloride as the conservative tracer. Selected breakthrough curves at specific positions were used to validate the proposed model solution and estimate both conventional and proposed coefficients of mass transfer. Results have shown a decreasing trend of α from 0.09 to 0.04 h after about 1.2 m of filtration for the investigated sand, whereas new solutions provide two scale-invariant tracer coefficients of rate of tracer mass-transfer (0.004 ± 0.005 h) and of tracer time delay (1.19 ± 0.01). The proposed model performs very well, since it provides a readily solved analytical solution with respect to the conventional MIM. Results of the proposed MIM are very similar to those provided by the conventional MIM. The new model solution can be implemented in particle tracking or random walk software in order to solve two-dimensional nonequilibrium solute transport in groundwater.
多孔介质中非平衡溶质运移的理论仍然基于 1952 年 Lapidus 和 Amundson 提出的模型的近似值，该模型尚未更新。这个移动-不移动模型（MIM）基于传质系数（α）的定义，该定义已被证明存在一些严重的局限性。实验室和现场尺度的测量都证明了α值的尺度依赖性。这意味着 MIM 理论在实际应用中失败了，因为α不是像动力学模型理论中定义的那样是常数，而是与时间停留（或距离）有关的系数。最近的文献中提出了多速率传质模型，以用多次传质来捕捉真实世界的溶质运移。在本研究中，我们提出了一种新模型，该模型直接在多孔介质中非平衡对流/弥散方程中实现了菲克第二定律扩散的解析解。新模型的解很好地拟合了在 CNR-IRSA 实验室（意大利巴里）进行的水平沙箱中进行的示踪剂试验中收集的数据，使用氯化钠作为保守示踪剂。在特定位置选择的突破曲线用于验证提出的模型解，并估计传统和提出的传质系数。结果表明，在所研究的沙中，过滤约 1.2 m 后，α从 0.09 减小到 0.04 h，而新的解提供了两个尺度不变的示踪剂传质速率（0.004 ± 0.005 h）和示踪剂时间延迟（1.19 ± 0.01）的示踪剂系数。提出的模型表现非常好，因为它提供了一个相对于传统 MIM 易于求解的解析解。提出的 MIM 的结果与传统 MIM 提供的结果非常相似。新的模型解可以在粒子跟踪或随机游走软件中实现，以解决地下水的二维非平衡溶质运移。
