Hydrology and Geochemistry Laboratory - LHyGeS, Strasbourg University - CNRS, 67000 Strasbourg, France.
Dipartimento di Ingegneria Civile e Ambientale (DICA), Politecnico di Milano, Piazza L. Da Vinci, 32, 20133 Milano, Italy; Department of Hydrology and Atmospheric Sciences, University of Arizona, Tucson, AZ, USA.
J Contam Hydrol. 2018 May;212:55-64. doi: 10.1016/j.jconhyd.2017.06.001. Epub 2017 Jun 7.
We present a combined experimental and numerical modeling study that addresses two principal questions: (i) is any particular Eulerian-based method used to solve the classical advection-dispersion equation (ADE) clearly superior (relative to the others), in terms of yielding solutions that reproduce BTCs of the kind that are typically sampled at the outlet of a laboratory cell? and (ii) in the presence of matches of comparable quality against such BTCs, do any of these methods render different (or similar) numerical BTCs at locations within the domain? To address these questions, we obtained measurements from carefully controlled laboratory experiments, and employ them as a reference against which numerical results are benchmarked and compared. The experiments measure solute transport breakthrough curves (BTCs) through a square domain containing various configurations of coarse, medium, and fine quartz sand. The approaches to solve the ADE involve Eulerian-Lagrangian and Eulerian (finite volume, finite elements, mixed and discontinuous finite elements) numerical methods. Model calibration is not examined; permeability and porosity of each sand were determined previously through separate, standard laboratory tests, while dispersivities are assigned values proportional to mean grain size. We find that the spatial discretization of the flow field is of critical importance, due to the non-uniformity of the domain. Although simulated BTCs at the system outlet are observed to be very similar for these various numerical methods, computed local (point-wise, inside the domain) BTCs can be very different. We find that none of the numerical methods is able to fully reproduce the measured BTCs. The impact of model parameter uncertainty on the calculated BTCs is characterized through a set of numerical Monte Carlo simulations; in cases where the impact is significant, assessment of simulation matches to the experimental data can be ambiguous.
我们提出了一项结合实验和数值建模的研究，旨在解决两个主要问题：（i）在求解经典的对流-弥散方程（ADE）时，是否存在任何特定的基于欧拉的方法在产生能够再现通常在实验室池出口处采样的 BTC 的解方面具有明显优势（相对于其他方法）？以及（ii）在存在与这些 BTC 匹配质量相当的情况下，这些方法中的任何一种在域内的位置会产生不同（或相似）的数值 BTC 吗？为了解决这些问题，我们从精心控制的实验室实验中获得了测量结果，并将其作为参考，以基准和比较数值结果。实验测量了通过包含粗、中、细石英砂各种配置的方形域的溶质传输突破曲线（BTC）。求解 ADE 的方法涉及欧拉-拉格朗日和欧拉（有限体积、有限元、混合和不连续有限元）数值方法。未检查模型校准；通过单独的标准实验室测试确定了每种砂的渗透率和孔隙度，而弥散度分配的值与平均粒径成正比。我们发现，由于域的非均匀性，流场的空间离散化至关重要。尽管这些各种数值方法在系统出口处观察到的模拟 BTC 非常相似，但计算出的局部（域内的点）BTC 可能非常不同。我们发现，没有一种数值方法能够完全再现测量的 BTC。通过一组数值蒙特卡罗模拟来表征模型参数不确定性对计算 BTC 的影响；在影响显著的情况下，对模拟与实验数据的匹配进行评估可能会模棱两可。
