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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 ›› 2021, Vol. 38 ›› Issue (6): 845-855.doi: 10.3969/j.issn.1005-3085.2021.06.007

• • 上一篇    下一篇

多孔介质两相流耦合地应力问题的非线性混合有限元方法

刘子平1,   李俊翔1,   刘  琦1,   马  强2,   魏华祎3   

  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
    3. 湘潭大学数学与计算科学学院，湘潭 411105
  • 出版日期:2021-12-15 发布日期:2022-02-15
  • 通讯作者: 马 强 E-mail: maqiang809@scu.edu.cn
  • 基金资助:
    国家自然科学基金 (11801387; 11871413; 11971336; 11971337)；中央高校基本科研业务费专项资金 (YJ201811).

Nonlinear Mixed Finite Element Method for Coupled Two-phase Flow and Geomechanics Problem in Porous Media

LIU Ziping1,   LI Junxiang1,   LIU Qi1,   MA Qiang2,   WEI Huayi3   

  1. 1. CNPC Chuanqing Drilling Engineering Company Limited, Chengdu 610051
    2. School of Mathematics, Sichuan University, Chengdu 610064
    3. School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105
  • Online:2021-12-15 Published:2022-02-15
  • Contact: Q. Ma. E-mail address: maqiang809@scu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (11801387; 11871413; 11971336; 11971337); the Fundamental Research Funds for the Central Universities (YJ201811).

PDF (PC)

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摘要：

研究了一种描述地质储层中两相流体流动与地应力耦合的非线性模型，推导了以流体饱和度、压力、速度与结构位移为未知量的耦合控制方程，结合混合有限元与标准线弹性有限元，建立了两相流耦合地应力模型的非线性有限元离散格式，保证了流体在局部单元中的质量守恒，提出了相应的算法流程。通过对均匀地质区域水驱油模型的数值实验，验证了算法的正确性，并进一步给出了带裂缝区域的模拟计算，得到了流体饱和度的高分辨率分布，这表明所提出的方法能准确捕捉带裂缝非均匀地质区域中流体的复杂物理力学行为。

关键词: 非均匀裂缝储层, 多孔介质, 两相流耦合地应力模型, 混合有限元

Abstract:

A fully coupled two-phase flow and geomechanics in a reservoir system is considered. The governing equation is derived in terms of the saturation, pressure, velocity for the flow and displacement for the structure. A nonlinear computational scheme is constructed by incorporating the mixed finite element with the conforming element, and the corresponding finite element procedure is proposed, which guarantees the local conservation of mass within the element. The effectiveness and correctness are verified by performing the numerical experiment for the water flooding in a homogeneous reservoir. Moreover, the water flooding in a heterogeneous reservoir with cross fracture is simulated and the high resolution of saturation solution is obtained, showing that the complex multiphysics of the reservoir system can be well captured by the proposed method.

Key words: heterogeneous reservoir with fracture, porous media, geomechanics coupled with two-phase flow, mixed finite element

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