Linearity of the Co-moving Velocity

IF 2.7 3区工程技术 Q3 ENGINEERING, CHEMICAL Transport in Porous Media Pub Date : 2024-08-28 DOI:10.1007/s11242-024-02121-9

Alex Hansen

引用次数: 0

Abstract

The co-moving velocity is a new variable in the description of immiscible two-phase flow in porous media. It is the saturation-weighted average over the derivatives of the seepage velocities of the two immiscible fluids with respect to saturation. Based on analysis of relative permeability data and computational modeling, it has been proposed that the co-moving velocity is linear when plotted against the derivative of the average seepage velocity with respect to the saturation, the flow derivative. I show here that it is enough to demand that the co-moving velocity is characterized by an additive parameter in addition to the flow derivative to be linear. This has profound consequences for relative permeability theory as it leads to a differential equation relating the two relative permeabilities describing the flow. I present this equation together with two solutions.

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同向运动速度的线性度

共渗速度是描述多孔介质中不相溶两相流的一个新变量。它是两种不相溶流体的渗流速度相对于饱和度的导数的饱和加权平均值。根据对相对渗透率数据和计算模型的分析，有人提出，当与平均渗流速度相对于饱和度的导数（即流动导数）作图时，共渗速度是线性的。我在这里指出，要使同向运动速度具有线性，只需在流动导数之外再加上一个附加参数即可。这对相对渗透率理论有着深远的影响，因为它导致了一个与描述流动的两个相对渗透率相关的微分方程。我将介绍这个方程以及两个解决方案。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Transport in Porous Media 工程技术-工程：化工

CiteScore

5.30

自引率

7.40%

发文量

155

审稿时长

4.2 months

期刊介绍： -Publishes original research on physical, chemical, and biological aspects of transport in porous media- Papers on porous media research may originate in various areas of physics, chemistry, biology, natural or materials science, and engineering (chemical, civil, agricultural, petroleum, environmental, electrical, and mechanical engineering)- Emphasizes theory, (numerical) modelling, laboratory work, and non-routine applications- Publishes work of a fundamental nature, of interest to a wide readership, that provides novel insight into porous media processes- Expanded in 2007 from 12 to 15 issues per year. Transport in Porous Media publishes original research on physical and chemical aspects of transport phenomena in rigid and deformable porous media. These phenomena, occurring in single and multiphase flow in porous domains, can be governed by extensive quantities such as mass of a fluid phase, mass of component of a phase, momentum, or energy. Moreover, porous medium deformations can be induced by the transport phenomena, by chemical and electro-chemical activities such as swelling, or by external loading through forces and displacements. These porous media phenomena may be studied by researchers from various areas of physics, chemistry, biology, natural or materials science, and engineering (chemical, civil, agricultural, petroleum, environmental, electrical, and mechanical engineering).