Modeling transport of charged species in pore networks: Solution of the Nernst-Planck equations coupled with fluid flow and charge conservation equations
Modeling transport of charged species in pore networks: Solution of the Nernst-Planck equations coupled with fluid flow and charge conservation equations
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DOI：
10.1016/j.cageo.2020.104505
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发表时间：
2020-07-01
影响因子：
4.4
通讯作者：
Gostick, Jeff T.
中科院分区：
文献类型：
--
作者：
Agnaou, Mehrez;Sadeghi, Mohammad Amin;Gostick, Jeff T.
提出了一种用于模拟带电物质（例如离子）在多孔介质中传输的孔隙网络建模（PNM）框架（1）。除了将物质浓度相互关联的电荷守恒方程之外，它还包括电解溶液中每种带电物质的 Nernst-Planck (NP) 方程。此外，采用动量和质量守恒方程，其解允许计算 NP 方程中平流对输运的贡献。所提出的框架是通过首先基于几种不同的时间和空间离散化方案推导与偏微分方程（PDE）相对应的数值模型方程（NME）而开发的，然后将其进行比较以评估解的准确性。该推导还考虑了各种电荷守恒场景，这些场景在速度和准确性方面也各有利弊。使用 PNM 和有限元法 (FEM) 求解器考虑并解决了任意孔隙网络中的离子传输问题。比较显示，就离子浓度而言，PNM 和 FEM 之间的平均偏差低于 5%，对于包含约 10(4) 个孔的介质，PNM 模拟比 FEM 模拟快 10(4) 倍以上。通过对平流项和迁移项采用更精确的离散化方案（取自 CFD 文献），可以提高精度。 NME 是在基于松弛迭代 Gummel 算法的开源包 OpenPNM 中实现的。这项工作提出了一种模拟带电物质传输的综合方法，适用于从电化学设备到地下纳米粒子运动的广泛应用。
A pore network modeling (PNM) framework(1) for the simulation of transport of charged species, such as ions, in porous media is presented. It includes the Nernst-Planck (NP) equations for each charged species in the electrolytic solution in addition to a charge conservation equation which relates the species concentration to each other. Moreover, momentum and mass conservation equations are adopted and there solution allows for the calculation of the advective contribution to the transport in the NP equations.The proposed framework is developed by first deriving the numerical model equations (NMEs) corresponding to the partial differential equations (PDEs) based on several different time and space discretization schemes, which are compared to assess solutions accuracy. The derivation also considers various charge conservation scenarios, which also have pros and cons in terms of speed and accuracy. Ion transport problems in arbitrary pore networks were considered and solved using both PNM and finite element method (FEM) solvers. Comparisons showed an average deviation, in terms of ions concentration, between PNM and FEM below 5% with the PNM simulations being over 10(4) times faster than the FEM ones for a medium including about 10(4) pores. The improved accuracy is achieved by utilizing more accurate discretization schemes for both the advective and migrative terms, adopted from the CFD literature. The NMEs were implemented within the open-source package OpenPNM based on the iterative Gummel algorithm with relaxation.This work presents a comprehensive approach to modeling charged species transport suitable for a wide range of applications from electrochemical devices to nanoparticle movement in the subsurface.