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Comparison of Pore-scale Capillary Pressure to Macroscale Capillary Pressure using Direct Numerical Simulations of Drainage under Dynamic and Quasi-static Conditions
Advances in Water Resources ( IF 4.7 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.advwatres.2020.103792
Santosh Konangi , Nikhil K. Palakurthi , Nikolaos K. Karadimitriou , Ken Comer , Urmila Ghia

Abstract Conventional macroscale two-phase flow equations for porous media (such as Darcy's law and Richards Equation) require a constitutive relation for capillary pressure (Pc). The capillary pressure relation significantly impacts the behavior and prediction of fluid flow in porous media, and needs to accurately characterize the capillary forces. In a typical laboratory experiment, a functional macroscopic capillary pressure-saturation (Pc-Sw) relationship is measured as the difference between the pressures of the non-wetting-phase reservoir at the inlet (Pnw) and wetting-phase reservoir at the outlet (Pw) of a porous medium. It is well-known that this traditional macroscopic capillary pressure definition is valid only at equilibrium conditions and if the phases are connected. Under non-equilibrium (dynamic) conditions, when the fluids are moving, the macroscopic capillary pressure measured in experiments implicitly includes the pressure head caused by viscous effects. The goal of the present effort is to understand how well the traditional macroscopic capillary pressure definition represents the pore-scale capillary forces under different flow conditions. Using direct numerical simulations (DNS) of two-phase flow in a porous medium, we evaluate the capillary pressure at the pore-scale, and compare it to the macroscopic capillary pressure, Pc(Sw), that is typically measured in experiments using pressure transducers. The pore-scale capillary pressure is the pressure difference across the interface between two fluids as the fluids move through a porous medium; the interface pressure differences at fluid-fluid invasion front are averaged across all the pores of the porous medium to yield a representative pore-scale capillary pressure curve, referred to as the interface capillary pressure. The pore-scale interface capillary pressure represents the “true” capillary forces in the system, since depends only on the pore morphology (shape) and interfacial energy of the two fluids, and does not account for the viscous dissipation. In experiments it is difficult to measure the interface capillary pressure jump without accounting for the viscous pressure head, which is at least an order of magnitude larger. Upscaling the pore-scale capillary pressure is an essential step for complete characterization of capillary-dominant two-phase flow in a porous medium at the laboratory scale. Drainage is simulated under equilibrium (quasi-static) and non-equilibrium (dynamic) conditions for various capillary numbers. The Navier–Stokes (NS) equations are solved in the pore space using the open-source finite-volume computational fluid dynamics (CFD) code, OpenFOAM. The Volume-of-Fluid (VOF) method is employed to track the evolution of the fluid–fluid interfaces, and a contact angle is used to account for the effect of wall adhesion. The simulations are first validated with published experimental data for dynamic and quasi-static drainage in a micromodel. From the microscale simulations, the interface capillary pressure is determined, and compared to the macroscopic capillary pressure under equilibrium and non-equilibrium conditions. Our results show the traditionally-measured macroscopic capillary pressure curves exhibit a strong dependence on the capillary number under dynamic flow conditions. In contrast, the interface capillary pressure-saturation relation, which relies on pore-scale pressure differences at the invasion front, is almost invariant of flow conditions (dynamic and quasi-static).

中文翻译:

使用动态和准静态条件下排水的直接数值模拟比较孔隙尺度毛细管压力与宏观毛细管压力

摘要 多孔介质的常规宏观两相流动方程(如达西定律和理查兹方程)需要毛细管压力 (Pc) 的本构关系。毛细管压力关系显着影响多孔介质中流体流动的行为和预测,需要准确表征毛细管力。在典型的实验室实验中,功能宏观毛细管压力饱和度 (Pc-Sw) 关系被测量为入口处非湿相储层 (Pnw) 和出口处湿相储层的压力之差 (Pc-Sw)。 Pw) 的多孔介质。众所周知,这种传统的宏观毛细管压力定义仅在平衡条件下和相连接时才有效。在非平衡(动态)条件下,当流体运动时,实验中测量的宏观毛细管压力隐含地包括由粘性效应引起的压头。目前努力的目标是了解传统的宏观毛细管压力定义如何很好地代表不同流动条件下的孔隙尺度毛细管力。使用多孔介质中两相流的直接数值模拟 (DNS),我们评估孔隙尺度的毛细管压力,并将其与宏观毛细管压力 Pc(Sw) 进行比较,后者通常在使用压力的实验中测量换能器。孔隙尺度毛细管压力是流体通过多孔介质时两种流体界面上的压力差;流体-流体侵入前沿的界面压力差在多孔介质的所有孔隙上取平均值,以产生具有代表性的孔隙尺度毛细管压力曲线,称为界面毛细管压力。孔隙尺度界面毛细管压力代表系统中“真实”的毛细管力,因为仅取决于两种流体的孔隙形态(形状)和界面能,而不考虑粘性耗散。在实验中,如果不考虑粘性压头,就很难测量界面毛细管压力跳跃,粘性压头至少要大一个数量级。提高孔隙尺度的毛细管压力是在实验室规模的多孔介质中完全表征毛细管主导的两相流的必要步骤。在平衡(准静态)和非平衡(动态)条件下模拟各种毛细管数下的排水。Navier-Stokes (NS) 方程使用开源有限体积计算流体动力学 (CFD) 代码 OpenFOAM 在孔隙空间中求解。流体体积 (VOF) 方法用于跟踪流体 - 流体界面的演变,并使用接触角来解释壁粘附的影响。模拟首先使用已发布的微模型中动态和准静态排水的实验数据进行验证。根据微观模拟,确定界面毛细管压力,并与平衡和非平衡条件下的宏观毛细管压力进行比较。我们的结果表明,传统测量的宏观毛细管压力曲线在动态流动条件下表现出对毛细管数的强烈依赖性。相比之下,界面毛细管压力-饱和度关系依赖于入侵前沿的孔隙尺度压力差,几乎不受流动条件(动态和准静态)的影响。
更新日期:2021-01-01
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