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

Xiongzhi Liu, Hao Yang, Lifei Dong, Ming Lei, Jie Han and Hao Kang ()
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Xiongzhi Liu: School of Engineering and Technology, China University of Geosciences (Beijing), Beijing 100083, China
Hao Yang: School of Engineering and Technology, China University of Geosciences (Beijing), Beijing 100083, China
Lifei Dong: School of Civil Engineering, Chongqing Three Gorges University, Chongqing 404100, China
Ming Lei: Research Institute of Petroleum Exploration & Development-Northwest, PetroChina, Lanzhou 730020, China
Jie Han: Research Institute of Petroleum Exploration & Development-Northwest, PetroChina, Lanzhou 730020, China
Hao Kang: Polytechnic Institute, Hebei Normal University, Shijiazhuang 050024, China

Energies, 2025, vol. 18, issue 12, 1-15

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.

Keywords: variational theory; ritz method; oil flow; approximate solution; analytical solution (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2025
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