An analysis of the unified formulation for the equilibrium problem of compositional multiphase mixtures

IF 1.9 3区 数学 Q2 Mathematics
Ibtihel Ben Gharbia, M. Haddou, Quang Huy Tran, Duc Thach Son Vu
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引用次数: 1

Abstract

In this paper , we conduct a thorough mathematical analysis of the unified formulation advocated by Lauser et al . [ Adv . Water Res . 34 (2011), 957-966] for compositional multiphase flows in porous media . The interest of this formulation lies in its potential to automatically handle the appearance and disappearance of phases. However , its practical implementation turned out to be not always robust for realistic fugacity laws associated with cubic equations of state , as shown by Ben Gharbia and Flauraud [ Oil & Gas Sci . Technol . 74 (2019), 43]. By focusing on the subproblem of phase equilibrium , we derive sufficient conditions for the existence of the corresponding system of equations. We trace back the difficulty of cubic laws to a deficiency of the Gibbs functions that comes into play due to the `` unifying '' feature of the new formulation. We propose a partial remedy for this problem by extending the domain of definition of these functions in a natural way . Besides , we highlight the crucial but seemingly unknown fact that the unified formulation encapsulates all the properties known to physicists on phase equilibrium , such as the tangent plane criterion and the minimization of the Gibbs energy of the mixture.
组份多相混合物平衡问题的统一公式分析
本文对Lauser等人倡导的统一表述进行了深入的数学分析。[副词]水资源[34](2011), 957-966]。这种配方的有趣之处在于它有可能自动处理相的出现和消失。然而,正如Ben Gharbia和Flauraud[石油与天然气科学]所表明的那样,对于与三次状态方程相关的实际逸性律,其实际实施并不总是鲁棒的。抛光工艺。[74](2019), 43。通过对相平衡子问题的研究,得到了相应方程组存在的充分条件。我们将三次定律的困难归结为由于新公式的“统一”特征而起作用的吉布斯函数的缺陷。通过自然地扩展这些函数的定义域,提出了解决这一问题的部分方法。此外,我们强调了一个关键但看似未知的事实,即统一公式包含了物理学家已知的相平衡的所有性质,如切平面准则和混合物的吉布斯能量最小化。
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
CiteScore
2.70
自引率
5.30%
发文量
27
审稿时长
6-12 weeks
期刊介绍: M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.
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