Computing Relative Permeability and Capillary Pressure of Heterogeneous Rocks Using Realistic Boundary Conditions

IF 2.7 3区 工程技术 Q3 ENGINEERING, CHEMICAL Transport in Porous Media Pub Date : 2024-06-19 DOI:10.1007/s11242-024-02092-x
AbdAllah A. Youssef, Qi Shao, S. K. Matthäi
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Abstract

Relative permeability and capillary pressure are key parameters in multiphase flow modelling. In heterogeneous porous media, flow direction- and flow-rate dependence result from non-uniform saturation distributions that vary with the balance between viscous, gravitational, and capillary forces. Typically, relative permeability is measured using constant inlet fractional-flow—constant outlet fluid pressure conditions on samples mounted between permeable porous plates to avoid capillary end-effects. This setup is replicated in numeric experiments but ignores the extended geologic context beyond the sample size, impacting the saturation distribution and, consequently, the upscaled parameters. Here, we introduce a new workflow for measuring effective relative permeability and capillary pressure at the bedform scale while considering heterogeneities at the lamina scale. We harness the flexibility of numeric modelling to simulate continuum-REV-scale saturation distributions in heterogeneous rocks eliminating boundary artefacts. Periodic fluid flux boundary conditions are applied in combination with arbitrarily oriented, variable-strength pressure gradient fields. The approach is illustrated on a periodic model of cross-bedded sandstone. Stepping saturation while applying variable-strength pressure-gradient fields with different orientations, we cover the capillary-viscous force balance spectrum of interest. The obtained relative permeability and capillary pressure curves differ from ones obtained with traditional approaches highlighting that the definition of force balances needs consideration of flow direction as an additional degree of freedom. In addition, we discuss when the common viscous and the capillary limits are applicable and how they vary with flow direction in the presence of capillary interfaces.

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利用现实边界条件计算异质岩石的相对渗透率和毛细管压力
相对渗透率和毛细管压力是多相流建模的关键参数。在异质多孔介质中,流动方向和流速取决于非均匀的饱和度分布,而饱和度分布会随着粘滞力、重力和毛细力之间的平衡而变化。通常情况下,相对渗透率的测量是在安装在透水多孔板之间的样品上,使用恒定入口分流-恒定出口流体压力条件,以避免毛细管末端效应。这种设置可在数值实验中复制,但忽略了样本尺寸以外的扩展地质背景,影响了饱和度分布,进而影响了放大参数。在此,我们介绍一种新的工作流程,用于测量床形尺度的有效相对渗透率和毛细管压力,同时考虑层状尺度的异质性。我们利用数值建模的灵活性来模拟异质岩石中的连续-REV 尺度饱和度分布,消除了边界假象。周期性流体通量边界条件与任意方向、可变强度的压力梯度场相结合。该方法在交叉层砂岩的周期模型上进行了说明。在应用不同方向的可变强度压力梯度场的同时,逐步提高饱和度,从而涵盖了所关注的毛细管-粘性力平衡谱。所获得的相对渗透率和毛细管压力曲线与传统方法所获得的曲线不同,突出表明力平衡的定义需要考虑流动方向作为额外的自由度。此外,我们还讨论了普通粘性极限和毛细极限何时适用,以及在存在毛细界面的情况下它们如何随流动方向而变化。
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来源期刊
Transport in Porous Media
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).
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