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

Celia0309607多孔介质中多相流模型通常包括毛细压力(Pc)和饱和度之间的平衡本构关系(S)。平衡关系的使用意味着这些变量之间的动力学时间尺度相对于与其他系统动力学相关的时间尺度是短(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。发展了一种替代公式，其中引入了Pc和S之间的动态、随时间变化的关系。对文献中报道的数据的初步调查表明，Pc-S关系中存在动力学，关联分析表明，这些动力学可以在这个动力学公式中捕捉到。虽然这一提法很有希望，但有许多重要的方面需要研究，从潜在动态的基本性质，到动态作为空间平均规模和异质性程度的函数变化的方式。为了解决这些动力学的本质，提出了三个假设，这三个假设构成了拟议工作的基础：假设1：孔隙尺度上的粘性效应导致动态毛细压力。假设2：随着平均长度尺度的增加和子尺度非均质性程度的增加，动态毛细压力效应逐渐变得更加重要。假设3：新公式中的动态系数不是恒定的，而是一个明确定义的饱和度S的函数。这些假设将使用跨越一定长度尺度的多相流计算模型来检验。如果这些假设是真的，那么50多年来描述和模拟两相流问题的方式将需要改变，引入一个根本新的参数，以及随之而来的思考这些系统的新方法。该项目将产生更广泛的影响，超出特定的多孔介质研究。除了研究生的常规培养外，该项目还将包括与卑尔根大学(挪威)和代尔夫特工业大学(荷兰)的同事合作，包括这些机构与普林斯顿大学之间的研究生交流。此外，在项目第三年期间，将在普林斯顿举办一次国际研讨会，讨论多相流新本构关系的具体专题，重点是动态毛细压力。

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.