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. 2011 Jun;34(6):770-778. doi: 10.1016/j.advwatres.2011.04.001.
Standard models of flow of two immiscible fluids in a porous medium make use of an expression for the dependence of capillary pressure on the saturation of a fluid phase. Data to support the mathematical expression is most often obtained through a sequence of equilibrium experiments. In addition to such expressions being hysteretic, recent experimental and theoretical studies have suggested that the equilibrium functional forms obtained may be inadequate for modeling dynamic systems. This situation has led to efforts to express relaxation of a system to an equilibrium capillary pressure in relation to the rate of change of saturation. Here, based on insights gained from the thermodynamically constrained averaging theory (TCAT) we propose that dynamic processes are related to changes in interfacial area between phases as well as saturation. A more complete formulation of capillary pressure dynamics is presented leading to an equation that is suitable for experimental study.
多孔介质中两种不混溶流体流动的标准模型利用了毛细压力与流体相饱和度之间依赖关系的表达式。支持该数学表达式的数据通常是通过一系列平衡实验获得的。除了这些表达式具有滞后性外，最近的实验和理论研究表明，所获得的平衡函数形式可能不足以对动态系统进行建模。这种情况促使人们努力将系统向平衡毛细压力的松弛表示为与饱和度变化率相关的形式。在此，基于从热力学约束平均理论（TCAT）获得的见解，我们提出动态过程与相界面面积以及饱和度的变化有关。本文给出了毛细压力动力学更完整的公式，得出了一个适合实验研究的方程。
