组份多相混合物平衡问题的统一公式分析

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

摘要

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