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山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (8): 25-34.doi: 10.6040/j.issn.1671-9352.0.2017.040

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可压多孔介质流的扩展混合元解法

于金彪1,任永强2,3,曹伟东1,鲁统超2,程爱杰2,戴涛1   

  1. 1.中国石化股份胜利油田分公司勘探开发研究院, 山东 东营 257015;2.山东大学数学学院, 山东 济南 250100;3. 齐鲁工业大学理学院, 山东 济南 250353
  • 收稿日期:2017-02-10 出版日期:2017-08-20 发布日期:2017-08-03
  • 作者简介:于金彪(1970—),男,高级工程师,研究方向为油藏数值模拟. E-mail:yjbxx@slof.com
  • 基金资助:
    国家科技重大专项资助基金(2011ZX05011-004,2011ZX05052)

Expanded mixed finite element method for compressible miscible displacement in heterogeneous porous media

YU Jin-biao1, REN Yong-qiang2,3, CAO Wei-dong1, LU Tong-chao2, CHENG Ai-jie2, DAI tao1   

  1. 1. Research Institute of Petroleum Exploration &
    Development, Shengli Oilfield Company Ltd., Dongying 257015, Shandong, China;
    2. School of Mathematics, Shandong University, Jinan 250100, Shandong, China;
    3. School of Mathematial and Physical Sciences, Qilu University of Technology, Jinan 250353, Shandong, China
  • Received:2017-02-10 Online:2017-08-20 Published:2017-08-03

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摘要： 讨论多孔介质中两种可压缩流体混溶驱动问题数值方法,假定介质是各向异性的,渗透率系数为张量形式。压力方程采用扩展混合元方法求解压力变量、梯度变量,以及速度变量;浓度方程采用标准有限元方法求解,这一方法对各向异性渗透率多孔介质流可以获得更可靠的数值解。构造了半离散数值格式,通过理论分析得到了压力、速度以及浓度等变量的最优L2模误差估计,对浓度变量获得了H1模最优误差估计。

关键词: 扩展混合元, 渗透率张量, 混溶驱动问题, 多孔介质, 可压缩, 误差估计

Abstract: We consider the numerical methods for the mathematical model describing the transport and diffusion process of porous media flow. There are two kinds of fluids, one is displaced by another, which are compressible and miscible. The media is supposed to be heterogeneous, so the permeability is of full tensor form. For the pressure equation, an expanded mixed finite element method is introduced to solve the variables of pressure, gradient, and velocity. For the concentration equation, a Galerkin finite element formulation is constructed to solve the variable of concentration. This approach aims at obtaining more reliable numerical solutions for porous media flow with heterogenous permeability. By means of theoretical analysis, optimal error estimates in L2-norm for pressure and in H1-norm for concentration are derived.

Key words: porous media, compressibility, error analysis, tensor permeability, miscible displacement, expanded mixed finite element method

中图分类号: 

  • O241.82
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