{"title":"Thermodynamically Consistent Modeling of Compressible Two-Phase Flow in Porous Media","authors":"Junkai Wang, Xiaolin Zhou, Qiaolin He","doi":"10.1002/nme.70050","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>In this paper, we develop a thermodynamically consistent model for compressible two-phase flow in porous media according to the Reynolds transport theorem and the second law of thermodynamics. The Helmholtz free energy and saturation free energy are introduced to characterize fluid compressibility and capillary pressure effects, respectively. Especially, we use molar density instead of pressure as one of the primary variables and derive a Darcy-type momentum equation with chemical potential gradient as the main driving force. Furthermore, the discrete total free energy dissipation and prior error estimates of the proposed numerical scheme are derived. Numerical results are presented to validate the accuracy, stability, and effectiveness of our proposed method.</p>\n </div>","PeriodicalId":13699,"journal":{"name":"International Journal for Numerical Methods in Engineering","volume":"126 10","pages":""},"PeriodicalIF":2.7000,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal for Numerical Methods in Engineering","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/nme.70050","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
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Abstract
In this paper, we develop a thermodynamically consistent model for compressible two-phase flow in porous media according to the Reynolds transport theorem and the second law of thermodynamics. The Helmholtz free energy and saturation free energy are introduced to characterize fluid compressibility and capillary pressure effects, respectively. Especially, we use molar density instead of pressure as one of the primary variables and derive a Darcy-type momentum equation with chemical potential gradient as the main driving force. Furthermore, the discrete total free energy dissipation and prior error estimates of the proposed numerical scheme are derived. Numerical results are presented to validate the accuracy, stability, and effectiveness of our proposed method.
期刊介绍：
The International Journal for Numerical Methods in Engineering publishes original papers describing significant, novel developments in numerical methods that are applicable to engineering problems.
The Journal is known for welcoming contributions in a wide range of areas in computational engineering, including computational issues in model reduction, uncertainty quantification, verification and validation, inverse analysis and stochastic methods, optimisation, element technology, solution techniques and parallel computing, damage and fracture, mechanics at micro and nano-scales, low-speed fluid dynamics, fluid-structure interaction, electromagnetics, coupled diffusion phenomena, and error estimation and mesh generation. It is emphasized that this is by no means an exhaustive list, and particularly papers on multi-scale, multi-physics or multi-disciplinary problems, and on new, emerging topics are welcome.
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