裂缝多孔介质中达西流动的有限差分方法

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英文篇名：Finite Difference Methods for Darcy Flow in Fracture Porous Media 作者：陈国灿 ; 罗贤兵 ; 张校域 英文作者：CHEN Guo-can;LUO Xian-bing;ZHANG Xiao-Yu;College of Mathematics and Statistics, Guizhou University; 关键词：偏微分方程 ; 有限差分 ; 降维模型 ; 达西定律 ; 渗透率 英文关键词：partial differential equation;;finite difference;;reduced model;;Darcy's law;;permeability 中文刊名：XNZK 英文刊名：Journal of Southwest China Normal University(Natural Science Edition) 机构：贵州大学数学与统计学院; 出版日期：2019-05-20 出版单位：西南师范大学学报(自然科学版) 年：2019 期：v.44;No.266 基金：国家自然科学基金项目(11461013) 语种：中文; 页：XNZK201905007 页数：6 CN：05 ISSN：50-1045/N 分类号：34-39

摘要

用差分方法来模拟二维裂缝多孔介质中的单相达西流动问题.采用降维模型对二维区域内的裂缝进行建模,相比整个区域而言裂缝的宽度很小并且把裂缝视为一个一维的界面,流体通过裂缝会和周围多孔介质发生耦合现象.在裂缝和周围多孔介质中,流体流动均遵循达西定律和守恒定律.采用差分方法来求解降维模型中推导的流体流动方程.通过数值实验验证了该方法的有效性,并证明了裂缝是快速通道还是地质屏障取决于裂缝处渗透率张量的大小.
        In this paper, finite different methods has been used to simulate the single phase Darcy flow in two-dimensional fractured porous media. The reduced model has been used to model the fracture in the two-dimensional region. The fractures have a small width and are treated as interfaces between subdomain media. In fracture and surrounding porous media, the fluid flow obeys Darcy's law and conservation law. The difference method has also been used to solve the fluid flow equations derived from the dimensionality reduction model. The validity of the method is verified by numerical experiments. It is demonstrated whether the fracture acts as a fast pathway or geological barrier is totally determined by the value of its permeability tensor.

引文

[1] JéR?ME J,MARTIN V,ROBERTS J.Modeling Fractures and Barriers as Interfaces for Flow in Porous Media [J].SIAM Journal on Scientific Computing,Society for Industrial and Applied Mathematics,2005,26(5):1667-1691.
    [2] ALBOIN C,JAFFRé J,ROBERTS J E,et al.Domain Decomposition for Some Transmission Problems in Flow in Porous Media [J].Lecture Notes in Physics,2000,552:22-34.
    [3] CHEN Z,YOU J.The Behavior of Naturally Fractured Reservoirs Including Fluid Flow in Matrix Blocks [J].Transport in Porous Media,1987,2(2):145-163.
    [4] FRIH N,ROBERTS J E,SAADA A.Modeling Fractures as Interfaces:a Model for Forchheimer Fractures [J].Computational Geosciences,2008,12(1):91-104.
    [5] DAWSON C,SUN S,WHEELER M F.Compatible Algorithms for Coupled Flow and Transport [J].Computer Methods in Applied Mechanics and Engineering,2015,193(23):2565-2580.
    [6] SONG P,SUN S.Contaminant Flow and Transport Simulation in Cracked Porous Media Using Locally Conservative Schemes [J].Advances in Applied Mathematics and Mechanics,2012,4(4):389-421.
    [7] HOTEIT H,FIROOZABADI A.An Efficient Numerical Model for Incompressible Two-Phase Flow in Fractured Media [J].Advances in Water Resources,2008,31(6):891-905.
    [8] CHEN H,SUN S.A Residual-Based a Posteriori Error Estimator for Single-Phase Darcy Flow in Fractured Porous Media [J].Numerische Mathematik,2016,136(3):1-35.
    [9] REICHENBERGER V,JAKOBS H,BASTIAN P,et al.A Mixed-Dimensional Finite Volume Method for Two-Phase Flow in Fractured Porous Media [J].Advances in Water Resources,2006,29(7):1020-1036.
    [10] ZIDANE A,FIROOZABADI A.An Efficient Numerical Model for Multicomponent Compressible Flow in Fractured Porous Media [J].Advances in Water Resources,2014,74:127-147.
    [11] 刘建康,秦煜哲,张晓晶,等.Robin型边界阻尼波动方程的有限差分格式 [J].贵州师范大学学报(自然版),2016,34(3):48-55.
    [12] 唐之韵,欧增奇.一类非局部问题解的存在性与多重性 [J].西南大学学报(自然科学版),2018,40(4):48-52.
    [13] LI X,RUI H.Characteristic Block-Centered Finite Difference Method for Simulating Incompressible Wormhole Propagation [J].Computers and Mathematics with Applications,2017,73(10):2171-2190.
    [14] WEISER A,WHEELER M F.On Convergence of Block-Centered Finite Differences for Elliptic Problems [J].SIAM Journal on Numerical Analysis,1988,25(2):351-375.
    [15] ZHAO D,PAN H,RUI H.Block-Centered Finite Difference Methods for Darcy-Forchheimer Model with Variable Forchheimer Number [J].Numerical Methods for Partial Differential Equations,2015,31(5):1603-1622.