Gray William G, Miller Cass T
Department of Environmental Sciences and Engineering, University of North Carolina, Chapel Hill, North Carolina 27599-7431, USA.
Adv Water Resour. 2009 May 1;32(5):681-711. doi: 10.1016/j.advwatres.2008.10.013.
This work is the fifth 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 used to develop models that describe species transport and single-fluid-phase flow through a porous medium system in varying physical regimes. Classical irreversible thermodynamics formulations for species in fluids, solids, and interfaces are developed. Two different approaches are presented, one that makes use of a momentum equation for each entity along with constitutive relations for species diffusion and dispersion, and a second approach that makes use of a momentum equation for each species in an entity. The alternative models are developed by relying upon different approaches to constrain an entropy inequality using mass, momentum, and energy conservation equations. The resultant constrained entropy inequality is simplified and used to guide the development of closed models. Specific instances of dilute and non-dilute systems are examined and compared to alternative formulation approaches.
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五篇，该方法用于对多尺度多孔介质系统中的流动和输运现象进行建模。利用先前工作中提出的通用TCAT框架和数学基础，来开发描述不同物理状态下多孔介质系统中物质输运和单流体相流动的模型。推导了流体、固体和界面中物质的经典不可逆热力学公式。提出了两种不同的方法，一种是对每个实体使用动量方程以及物质扩散和弥散的本构关系，另一种方法是对实体中的每个物质使用动量方程。通过依赖不同的方法来利用质量、动量和能量守恒方程约束熵不等式，从而开发出替代模型。对由此产生的约束熵不等式进行简化，并用于指导封闭模型的开发。研究了稀溶液和非稀溶液系统的具体实例，并与其他公式化方法进行了比较。
