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Macrodispersivity Tensor for Nonreactive Solute Transport in Isotropic and Anisotropic Fractal Porous Media: Analytical Solutions
Author(s) -
Zhan Hongbin,
Wheatcraft Stephen W.
Publication year - 1996
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 - 10.1029/95wr02282
Subject(s) - isotropy , tortuosity , anisotropy , fractal dimension , fractal , porous medium , bounded function , tensor (intrinsic definition) , transverse plane , geometry , statistical physics , mathematical analysis , mixing (physics) , mathematics , physics , mechanics , porosity , geology , geotechnical engineering , optics , quantum mechanics , structural engineering , engineering
Using spectral stochastic theory, macrodispersivity tensors are developed for one‐, two‐, and three‐dimensional isotropic and anisotropic fractal porous media. Since natural geologic aquifers are always bounded, we introduce the concept of a maximum length scale (( L max ). In the one‐dimensional case, the asymptotic (long‐time) longitudinal macrodispersivity ( A ∞ ) is proportional to L max 2 , and in the multidimensional cases, A ∞ ∝ L max . In the multidimensional cases, as the fractal dimension increases, A ∞ decreases, because a larger fractal dimension means the tortuosity of solute particles is larger, leading to more mixing in the transverse direction, which in turn reduces longitudinal spreading. The transverse macrodispersivities are shown to be analogous to traditional spectral stochastic results. In the multidimensional cases, L max is shown to be controlled by the aquifer thickness. As a result, ergodic conditions may be reached in relatively thin aquifers, allowing the use of the asymptotic macrodispersivity expressions obtained here for single realizations.