JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (8): 25-34.doi: 10.6040/j.issn.1671-9352.0.2017.040

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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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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

CLC Number: 

  • O241.82
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