COLABORATIVE RESEARCH: Closure of Thermodynamically Constrained Models for Multiphase Systems

传统的多孔介质多相流模型建立在实验数据的经验性和关联性基础上。在过去的二十年里，在发展基于守恒原则的多相流模型的理论基础方面付出了巨大的努力。这些方法既揭示了当前模型中隐含的假设，也揭示了通向更严格和稳健模型的途径。最优雅和概念上令人满意的方法之一是热力学约束平均理论方法(TCATA)。最近与TCATA的工作导致了一套多孔介质中两相流动模型的形成。然而，要全面发展TCATA，还需要采取额外的步骤。当前提案的目标是超越纯粹的理论和理想化的多孔介质来描述真实的系统，以证明TCATA在描述多孔介质中多相流物理方面的可行性、重要性和必要性。为了满足本项目的目标，我们将结合使用理论、孔隙尺度的形态和建模、连续介质尺度的建模和实验室实验的方法。这项工作将在北卡罗来纳大学的卡斯·T·米勒教授的团队和圣母大学的威廉·G·格雷教授的团队之间现有合作的基础上并继续进行，以完成这项工作。这份提案描述了两个小组的联合工作，每个机构直接向NSF提交完成其工作份额所需的资源。这项工作将对自然和工程系统中的任何多相多孔介质系统阵列具有额外的适用性。我们期望从这项工作中获得几个重要的成果：(1)发展包括膜流动和分离压力的理论框架；(2)将毛细压力表述为饱和度和界面面积的函数，从而减少或消除当毛细压力仅表示为饱和度的函数时的滞后；(3)发展包括动态几何参数的本构关系，以表达相对渗透率的函数依赖性；(4)建立和实施数值算法来求解扩展的模型方程组；以及(5)将实验数据与模型结果进行比较，以揭示我们方法的优点和缺点，以及进一步改进解释多相流物理的方法的必要性。

9901660MillerTraditional models of multiphase flow in porous media are based in empiricism and correlation of experimental data. Over the past two decades significant effort has been expended in developing a theoretical basis for multiphase flow models grounded in conservation principles. These approaches both reveal assumptions implicit in the current models and paths to more rigorous and robust models. One of the most elegant and conceptually satisfying approaches is the thermodynamically constrained averaging theory approach (TCATA). Recent work with the TCATA has led to the formulation of a set of models for two-phase flow in porous media. Additional steps, however, are required to develop the TCATA fully. The goals of the current proposal are to move beyond pure theory and idealized porous media to the description of real systems to demonstrate the viability, importance, and necessity of the TCATA for describing the physics of multiphase flow in porous media.To meet the goals of this project, we will use a combination of theoretical, pore scale morphology and modeling, continuum scale modeling, and laboratory experimental approaches. This work will be accomplished by building upon and continuing an existing collaboration between Professor Cass T. Miller's group at the University of North Carolina and Professor William G. Gray's group at the University of Notre Dame. This proposal describes the joint work of both groups, with each institution submitting directly to NSF requesting the resources needed to accomplish their share of the work.This work will have additional applicability to any array of multiphase porous media systems in both natural and engineered systems. We expect several significant accomplishments from this work: (1) the development of a theoretical framework that includes film flow and disjoining pressures; (2) the formulation of capillary pressure as a function of both saturation and interfacial area, thereby reducing or eliminating the hysteresis found when capillary pressure is represented as a function of saturation only; (3) the development of constitutive relations that include dynamic geometric parameters in expressing the functional dependence of relative permeability; (4) formulation and implementation of a numerical algorithm to solve the extended set of model equations; and (5) comparison of experimental data with model results to reveal the strengths and weaknesses of our approaches and the needs for further advancement of methods that account for the physics of multiphase flow.