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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2026, Vol. 43 ›› Issue (3): 470-478.doi: 10.3969/j.issn.1005-3085.2026.03.006cstr: 32411.14.cjem.CN61-1269/O1.2026.03.006

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多孔介质两相流耦合地应力问题的混合有限元分析

李彦超1,  沈建国1,  李俊翔1,  马  强2,  张亚东2,  罗振东2   

  1. 1. 中国石油川庆钻探工程有限公司，成都  610051

    2. 四川大学数学学院，成都 610064

  • 收稿日期:2023-07-17 接受日期:2023-09-28 出版日期:2026-04-15 发布日期:2026-08-15
  • 通讯作者: 罗振东 E-mail: zhdluo@163.com
  • 基金资助:
    国家自然科学基金(11801387; 11871413; 11971336; 11971337).

The Mixed Finite Element Analysis for Coupled Geostress with Two-phase Flow Problem in Porous Media

LI Yanchao1,  SHEN Jianguo1,  LI Junxiang1,  MA Qiang2,  ZHANG Yadong2,  LUO Zhendong2   

  1. 1. Chuanqing Drilling Engineering Company Limited, Chengdu 610051
    2. School of Mathematics, Sichuan University, Chengdu 610064
  • Received:2023-07-17 Accepted:2023-09-28 Online:2026-04-15 Published:2026-08-15
  • Contact: Z. Luo. E-mail address: zhdluo@163.com
  • Supported by:
    The National Natural Science Foundation of China (11801387; 11871413; 11971336; 11971337).

摘要：

研究地质储层中包含流体饱和度、压力、速度、地应力及结构位移为未知物理量的两相流体流动与地应力耦合的非线性模型的数值方法，为该非线性模型建立Crank-Nicolson(CN)混合有限元解，证明该格式的CN混合有限元解的存在性、无条件稳定性和无条件收敛性，并分析CN混合有限元解的误差。因此，该研究为包含流体饱和度、压力、速度、地应力及结构位移为未知物理量的两相流体流动与地应力耦合的非线性模型数值解法的存在性和稳定性提供理论依据，具有重要理论意义和应用价值。

关键词: 两相流耦合地应力模型, Crank-Nicolson混合有限元解, 稳定性和收敛性及误差估计

Abstract:

The numerical method of the nonlinear model for the two-phase flow coupled with the geostress in the geologic reservoir with unknown physical quantities of fluid saturation, pressure, velocity, geostress, porosity, and structural displacement is studied. The Crank-Nicolson (CN) mixed finite element (CNMFE) formulation is established for the nonlinear model. The unconditional stability and unconditional convergence for the CNMFE solutions are proved. The errors of CNMFE solutions are analyzed. Therefore, this study provides a theoretical foundation for the existence and stability of the nonlinear model numerical solutions for the nonlinear model. It has significant theoretical significance and application value.

Key words: two-phase flow coupled with geostress, Crank-Nicolson mixed finite element format, stability and convergence as well as error estimate

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