多孔网络中带电物质输运的模拟：与流体流动和电荷守恒方程耦合的能斯特-普朗克方程的解
Modeling transport of charged species in pore networks: solution of the Nernst-Planck equations coupled with fluid flow and charge conservation equations
摘要：
提出了一种模拟多孔介质中带电物质（如离子）输运的孔隙网络模型（PNM）框架。它包括能斯特-普朗克（NP）方程的电解质溶液中的每一个带电的物种，除了一个电荷守恒方程，其中涉及的物种浓度彼此。此外，采用动量和质量守恒方程，并在NP方程中计算对流对输送的贡献。所提出的框架是通过首先推导出相应的偏微分方程（PDE）的数值模型方程（NME）的基础上几个不同的时间和空间离散方案，比较评估解决方案的精度。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有优缺点。考虑了离子在任意孔隙网络中的输运问题，并用PNM和有限元法求解。比较表明，在离子浓度方面，PNM和FEM之间的平均偏差低于$5\%$，对于包括约${10}^{4}$孔的介质，PNM模拟比FEM模拟快${10}^{4}$倍以上。通过对对流项和迁移项采用更精确的离散化方案，提高了计算精度，这些离散化方案来自CFD文献。NME是在开源软件包OpenPNM中基于松弛迭代Gummel算法实现的。这项工作提出了一个全面的方法来模拟带电物质的运输适合于广泛的应用，从电化学设备的纳米粒子在地下的运动。
英文摘要：
A pore network modeling (PNM) framework 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.
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