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An investigation of the validity of first‐order stochastic dispersion theories in isotropie porous media
Author(s) -
Chin David A.,
Wang Tiezheng
Publication year - 1992
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/92wr00666
Subject(s) - monte carlo method , isotropy , porous medium , statistical physics , mathematics , constant (computer programming) , mathematical analysis , physics , porosity , statistics , geotechnical engineering , quantum mechanics , geology , computer science , programming language
Monte Carlo simulations are used to (1) investigate the accuracy of approximations that are implicit in first‐order stochastic dispersion theories and (2) identify the accuracy limits of first‐order dispersion theories in isotropic porous media. The Fickian theory of Gelhar and Axness (1983), as well as the Fickian and non‐Fickian theories of Dagan (1984) and Neuman and Zhang (1990) are investigated. All Monte Carlo simulations are in three dimensions. Confidence limits of ensemble‐averaged Monte Carlo results in isotropic porous media are established for 0.1 ≤ σ Y ≤ 1.5. These results showed that first‐order theoretical estimates of the Eulerian velocity covariance function are quite accurate for σ Y < 1; theoretical estimates of the non‐Fickian longitudinal dispersivity do not deviate significantly from theory for at least σ Y ≤ 1.5; theoretical estimation of the transverse dispersivity is limited to σ Y < 1; and, the Fickian longitudinal dispersivity is overestimated by the theory of Gelhar and Axness (1983). Of all first‐order dispersion theories, the theory of Dagan (1984) is most robust in estimating the dispersivity tensor.