Miller Cass T, Gray William G
Department of Environmental Sciences and Engineering, University of North Carolina, Chapel Hill, North Carolina 27599-7431, USA.
Adv Water Resour. 2008 Mar;31(3):577-597. doi: 10.1016/j.advwatres.2007.11.004.
This work is the fourth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. The general TCAT framework and the mathematical foundation presented in previous works are built upon by formulating macroscale models for conservation of mass, momentum, and energy, and the balance of entropy for a species in a phase volume, interface, and common curve. In addition, classical irreversible thermodynamic relations for species in entities are averaged from the microscale to the macroscale. Finally, we comment on alternative approaches that can be used to connect species and entity conservation equations to a constrained system entropy inequality, which is a key component of the TCAT approach. The formulations detailed in this work can be built upon to develop models for species transport and reactions in a variety of multiphase systems.
这项工作是关于热力学约束平均理论（TCAT）方法的系列论文中的第四篇，该方法用于对多尺度多孔介质系统中的流动和传输现象进行建模。通过为相体积、界面和公共曲线中的质量、动量和能量守恒以及物种的熵平衡制定宏观模型，在前作中提出的通用TCAT框架和数学基础得以进一步构建。此外，实体中物种的经典不可逆热力学关系从微观尺度平均到宏观尺度。最后，我们对可用于将物种和实体守恒方程与约束系统熵不等式相连接的替代方法进行了评论，这是TCAT方法的关键组成部分。基于本文详细阐述的公式，可以进一步开发各种多相系统中物种传输和反应的模型。
