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Innovative Application of the Ritz Method to Oil-Gas Seepage Problems: A Novel Variational Approach for Solving Underground Flow Equations.

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Title: Innovative Application of the Ritz Method to Oil-Gas Seepage Problems: A Novel Variational Approach for Solving Underground Flow Equations.
Authors: Liu, Xiongzhi1,2 (AUTHOR), Yang, Hao1,2 (AUTHOR), Dong, Lifei3 (AUTHOR), Lei, Ming2,4 (AUTHOR), Han, Jie2,5 (AUTHOR), Kang, Hao1,4,5 (AUTHOR) haokang@hebtu.edu.cn
Source: Energies (19961073). Jun2025, Vol. 18 Issue 12, p3207. 15p.
Subjects: Ritz method, Oil seepage, Finite differences, Gas reservoirs, Petroleum reservoirs
Abstract: State-of-the-art commercial simulators (e.g., Eclipse, CMG) predominantly employ finite difference schemes, which face persistent challenges in modeling strongly nonlinear seepage dynamics. This study explores the application of the Ritz method, grounded in variational theory, to solve underground oil seepage problems in reservoir engineering. The research focuses on deriving the variational form of steady-state seepage equations and presents a systematic procedure for solving these equations in finite domains. Using a one-dimensional steady-state seepage problem as a case study (which can effectively represent a wide range of typical flow regimes), the study compares the approximate solutions obtained by the Ritz method (both monomial and binomial forms) with exact solutions. The results demonstrate that the binomial approximate solution achieves high accuracy, with an average deviation of only 0.30% from the exact solution, significantly outperforming the monomial solution. The findings validate the Ritz method as an effective tool for addressing seepage problems and highlight its potential for broader applications in oil and gas reservoir modeling. [ABSTRACT FROM AUTHOR]
Copyright of Energies (19961073) is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: Innovative Application of the Ritz Method to Oil-Gas Seepage Problems: A Novel Variational Approach for Solving Underground Flow Equations.
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  Data: <searchLink fieldCode="DE" term="%22Ritz+method%22">Ritz method</searchLink><br /><searchLink fieldCode="DE" term="%22Oil+seepage%22">Oil seepage</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+differences%22">Finite differences</searchLink><br /><searchLink fieldCode="DE" term="%22Gas+reservoirs%22">Gas reservoirs</searchLink><br /><searchLink fieldCode="DE" term="%22Petroleum+reservoirs%22">Petroleum reservoirs</searchLink>
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  Data: State-of-the-art commercial simulators (e.g., Eclipse, CMG) predominantly employ finite difference schemes, which face persistent challenges in modeling strongly nonlinear seepage dynamics. This study explores the application of the Ritz method, grounded in variational theory, to solve underground oil seepage problems in reservoir engineering. The research focuses on deriving the variational form of steady-state seepage equations and presents a systematic procedure for solving these equations in finite domains. Using a one-dimensional steady-state seepage problem as a case study (which can effectively represent a wide range of typical flow regimes), the study compares the approximate solutions obtained by the Ritz method (both monomial and binomial forms) with exact solutions. The results demonstrate that the binomial approximate solution achieves high accuracy, with an average deviation of only 0.30% from the exact solution, significantly outperforming the monomial solution. The findings validate the Ritz method as an effective tool for addressing seepage problems and highlight its potential for broader applications in oil and gas reservoir modeling. [ABSTRACT FROM AUTHOR]
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  Label:
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  Data: <i>Copyright of Energies (19961073) is the property of MDPI and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.3390/en18123207
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        Text: English
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        Type: general
      – SubjectFull: Oil seepage
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      – SubjectFull: Finite differences
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              Text: Jun2025
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