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Analytical Solutions for Macrodispersion in a 3D Heterogeneous Porous Medium with Random Hydraulic Conductivity and Dispersivity

机译:具有随机水力传导性和分散性的3D非均质多孔介质中宏观分散的解析解

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摘要

A stochastic analysis of macrodispersion for conservative solute transport in three-dimension (3D) heterogeneous statistically isotropic and anisotropic porous media when both hydraulic conductivity and local dispersivity are random is presented. Analytical expressions of macrodispersivity are derived using Laplace and Fourier transforms. The effects of various parameters such as ratio of transverse to longitudinal local dispersivity, correlation length ratio, correlation coefficient and direction of flow on asymptotic macrodispersion are studied. The behaviour of growth of macrodispersivity in preasymptotic stage is also shown in this paper. The variation in local dispersion coefficient causes change in transverse macrodispersivity. The consideration of random dispersivity along with random hydraulic conductivity indicates that the total dispersion is affected and important in the case when the hydraulic conductivity and dispersivity are correlated. It is observed that the pre-asymptotic behavior of the macrodispersivity is not sensitive to the choice of spectral density functions.
机译:提出了当水力传导率和局部分散性都是随机的时,在三维(3D)非均质统计各向同性和各向异性多孔介质中用于保守溶质传输的宏观分散的随机分析。宏观分散性的解析表达式是使用拉普拉斯和傅里叶变换得出的。研究了横向和纵向局部分散率之比,相关长度比,相关系数和流动方向等参数对渐近宏观分散的影响。本文还显示了渐近期宏观分散性的增长行为。局部色散系数的变化会引起横向大分散度的变化。将随机分散性与随机水力传导率一起考虑,表明总分散度会受到影响,并且在水力传导率和分散度相互关联的情况下很重要。观察到,大分散度的渐近行为对光谱密度函数的选择不敏感。

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