Journal of Contaminant Hydrology ( IF 3.6 ) Pub Date : 2019-11-13 , DOI: 10.1016/j.jconhyd.2019.103578 Mohammad Amin Sadeghi 1 , Mehrez Agnaou 2 , Jake Barralet 3 , Jeff Gostick 4
Mass transfer in porous media resulting from dispersion occurs in a wide variety of applications such as water treatment, flow batteries, flow in aquifers, enhanced oil recovery, and packed-bed reactors. The underlying mechanisms of dispersion are the molecular diffusion superimposed on the advective transport induced by the fluid flow. Modeling dispersion in pore networks can be performed at a much lower computational cost compared to that in direct numerical simulations (DNS) such as finite element or the lattice Boltzmann methods, so it can be regarded as a suitable alternative provided its accuracy is sufficient. The most common approach to model dispersion in network models is based on the first-order upwind scheme, despite its known limitations in terms of accuracy for certain flow and transport regimes. In this study, three alternative pore-scale models for dispersion, which are more accurate than the existing ones, were derived and tested in pore network simulations. These models were adopted from the CFD literature and are based on a spatial discretization of the advection-diffusion equation using the hybrid and power-law finite difference schemes and the exact solution of the one-dimensional advection-diffusion equation. Finally, considering dispersion problems over arbitrary porous structures, consisting of stick-and-ball geometries, and different flow and mass transfer arrangements, the developed models were validated. Validation was carried-out through comparisons between results obtained with DNS, using a finite element solver, and those from pore network simulations. It is shown that under a wide range of dispersion regimes (up to the onset of the dispersion power-law regime), the relative error (with respect to DNS results) introduced by the power-law and exact solution-based models is consistently below 1%, whereas the use of the upwind scheme leads to >10% of relative error, depending on the dispersion regime. All the dispersion models developed in this study were implemented as part of the open-source network modeling package, OpenPNM.
中文翻译:
孔网络中的分散模型:常见孔尺度模型和替代方法的比较。
由分散引起的多孔介质中的传质发生在广泛的应用中,例如水处理,液流电池,含水层中的流动,提高的采油率和填充床反应器。分散的潜在机理是分子扩散叠加在由流体流动引起的对流输运上。与直接数值模拟(DNS)(例如有限元法或晶格Boltzmann方法)相比,可以在孔隙网络中对分散模型进行建模,而计算成本要低得多,因此,只要其精度足够,就可以将其视为合适的替代方法。尽管在某些流量和运输方式的准确性方面存在已知限制,但网络模型中最常用的模型分散方法是基于一阶迎风方案。在这个研究中,在孔隙网络模拟中推导并测试了三种替代的孔隙度模型,它们比现有模型更精确。这些模型是从CFD文献中采用的,并且基于对流扩散方程的空间离散化,使用了混合和幂律有限差分方案以及一维对流扩散方程的精确解。最后,考虑到在任意多孔结构上的分散问题,包括棒和球的几何形状以及不同的流量和传质布置,对开发的模型进行了验证。通过比较使用有限元求解器的DNS结果与孔隙网络模拟得到的结果,进行了验证。结果表明,在广泛的色散范围内(直到色散幂律范围的开始),幂律和基于精确解的模型引入的相对误差(相对于DNS结果)始终低于1%,而逆风方案的使用会导致相对误差> 10%,这取决于分散状态。本研究中开发的所有离散模型均作为开源网络建模软件包OpenPNM的一部分实施。