Porta G M, Ceriotti G, Thovert J-F
Dipartimento di Ingegneria Civile ed Ambientale, Politecnico di Milano, Piazza L. Da Vinci 32, 20133 Milano, Italy.
Dipartimento di Ingegneria Civile ed Ambientale, Politecnico di Milano, Piazza L. Da Vinci 32, 20133 Milano, Italy.
J Contam Hydrol. 2016 Feb-Mar;185-186:1-13. doi: 10.1016/j.jconhyd.2015.12.003. Epub 2015 Dec 28.
We compare the ability of various continuum-scale models to reproduce the key features of a transport setting associated with a bimolecular reaction taking place in the fluid phase and numerically simulated at the pore-scale level in a disordered porous medium. We start by considering a continuum-scale formulation which results from formal upscaling of this reactive transport process by means of volume averaging. The resulting (upscaled) continuum-scale system of equations includes nonlocal integro-differential terms and the effective parameters embedded in the model are quantified directly through computed pore-scale fluid velocity and pore space geometry attributes. The results obtained through this predictive model formulation are then compared against those provided by available effective continuum models which require calibration through parameter estimation. Our analysis considers two models recently proposed in the literature which are designed to embed incomplete mixing arising from the presence of fast reactions under advection-dominated transport conditions. We show that best estimates of the parameters of these two models heavily depend on the type of data employed for model calibration. Our upscaled nonlocal formulation enables us to reproduce most of the critical features observed through pore-scale simulation without any model calibration. As such, our results clearly show that embedding into a continuum-scale model the information content associated with pore-scale geometrical features and fluid velocity yields improved interpretation of typically available continuum-scale transport observations.
我们比较了各种连续介质尺度模型再现与在流体相中发生的双分子反应相关的输运设置关键特征的能力，该反应在无序多孔介质的孔隙尺度水平上进行了数值模拟。我们首先考虑一种连续介质尺度公式，它是通过体积平均对这种反应输运过程进行形式上的粗化而得到的。由此产生的（粗化后的）连续介质尺度方程组包括非局部积分 - 微分项，并且模型中嵌入的有效参数直接通过计算得到的孔隙尺度流体速度和孔隙空间几何属性进行量化。然后将通过这种预测模型公式获得的结果与通过可用的有效连续介质模型提供的结果进行比较，这些有效连续介质模型需要通过参数估计进行校准。我们的分析考虑了文献中最近提出的两个模型，它们旨在嵌入在平流主导的输运条件下由快速反应导致的不完全混合。我们表明，这两个模型参数的最佳估计严重依赖于用于模型校准的数据类型。我们的粗化非局部公式使我们能够在不进行任何模型校准的情况下再现通过孔隙尺度模拟观察到的大多数关键特征。因此，我们的结果清楚地表明，将与孔隙尺度几何特征和流体速度相关的信息内容嵌入到连续介质尺度模型中，能够改进对通常可用的连续介质尺度输运观测结果的解释。
