An Investigation of Dynamic Capillary Pressure in Two-Phase Porous Media Flows

多孔介质中的多相流模型通常包括毛细管压力（Pc）和饱和度（S）之间的平衡本构关系。 平衡关系的使用意味着这些变量之间的动态时间尺度相对于与其他系统动态相关的时间尺度是短的（快的）。 土壤科学文献中关于Pc和S之间平衡的时间尺度的实践指导表明，平衡关系可能是不合理的。 已经开发了一种替代制剂，其中引入了Pc和S之间的动态的、随时间变化的关系。 在文献中报道的数据的初步调查表明，在PC-S关系的动态存在，和相关的分析表明，这些动态可以捕捉到这个动态配方。 虽然这一提法是有前途的，有一些重要的方面，需要调查，从基本的动态的基本性质，以动态变化的方式作为空间平均尺度和异质性程度的函数。 为了解决这些动态的性质，提出了三个假设，这构成了所提出的工作的基础：假设1：在孔隙尺度的粘性效应导致动态毛细管压力。假设二：动态毛细管压力的影响是越来越重要的平均长度尺度的增加，并作为子尺度的异质性increasing.Hypothesis 3的程度：在新的配方中的动态系数不是常数，但饱和度Sw的一个明确的功能。这些假设将使用多相流的计算模型在一个范围内的长度尺度进行测试。如果这些假设是真的，那么50多年来描述和建模两相流问题的方式将需要修改，引入一个全新的参数，以及随之而来的思考这些系统的新方式。该项目将产生超出特定多孔介质研究的更广泛的影响。 除了通常培养研究生外，该项目还将包括与卑尔根大学（挪威）和德尔夫特技术大学（荷兰）的同事合作，包括这些机构与普林斯顿大学之间交换研究生。此外，在项目的第三年，将在普林斯顿召开一次国际研讨会，讨论多相流的新本构关系的具体专题，重点是动态毛细管压力。

Celia0309607Models of multi-phase flow in porous media typically include an equilibrium constitutive relationship between capillary pressure (Pc) and saturation (S). Use of an equilibrium relationship implies that time scales of dynamics between those variables are short (fast) relative to time scales associated with other system dynamics. Practical guidance in the soil science literature regarding time scales for equilibrium between Pc and S indicates that an equilibrium relationship may not be justified. An alternative formulation has been developed in which a dynamic, time-dependent relationship between Pc and S is introduced. Initial investigations of data reported in the literature indicate that dynamics in the Pc-S relationship exist, and associated analysis shows that those dynamics can be captured within this dynamic formulation. While this formulation is promising, there are a number of significant aspects that need to be investigated, from the fundamental nature of the underlying dynamics, to the ways in which the dynamics change as a function of spatial averaging scale and degree of heterogeneity. To address the nature of these dynamics, three hypotheses are posed, which form the basis for the proposed work:Hypothesis 1: Viscous Effects at the Pore Scale lead to a Dynamic Capillary Pressure. Hypothesis 2: Dynamic Capillary Pressure effects are progressively more important as averaging length scale increases and as the degree of subscale heterogeneity increases.Hypothesis 3: The dynamic coefficient in the new formulation is not constant but a well-defined function of saturation Sw.These hypotheses will be tested using computational models of multiphase flow across a range of length scales. If these hypotheses are true, then the way that two-phase flow problems have been described and modeled for more than 50 years will need to be modified, with a fundamentally new parameter introduced, and a concomitant new way of thinking about these systems. This project will have broader impacts beyond the specific porous media research. In addition to usual development of graduate students, the project will include collaborations with colleagues at the University of Bergen (Norway) and the Technical University of Delft (Netherlands), including exchanges of graduate students between those institutions and Princeton University. In addition, an international workshop will be convened at Princeton during the third year of the project, to discuss the specific topic of new constitutive relationships for multi-phase flow with a focus on dynamic capillary pressure.