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Hydraulic conductivity, velocity, and the order of the fractional dispersion derivative in a highly heterogeneous system
Author(s) -
Herrick Matt G.,
Benson David A.,
Meerschaert Mark M.,
McCall Katherine R.
Publication year - 2002
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 - 10.1029/2001wr000914
Subject(s) - monte carlo method , dispersion (optics) , power law , hydraulic conductivity , exponent , plume , advection , statistical physics , anomalous diffusion , fractional calculus , field (mathematics) , physics , vector field , mathematics , mechanics , mathematical analysis , meteorology , thermodynamics , statistics , geology , soil science , optics , soil water , linguistics , philosophy , innovation diffusion , knowledge management , computer science , pure mathematics
A one‐dimensional, fractional order, advection‐dispersion equation accurately models the movement of the core of the tritium plume at the highly heterogeneous MADE site. An a priori estimate of the parameters in that equation, including the order of the fractional dispersion derivative, was based on the assumption that the observed power law (heavy) tail of the hydraulic conductivity ( K ) field would create a similarly distributed velocity field. Monte Carlo simulations were performed to test this hypothesis. Results from the Monte Carlo analysis show that heavy tailed K fields do give rise to heavy tailed velocity fields; however, the exponent of the power law (the tail parameter) describing these two distributions is not necessarily the same. The tail parameter that characterizes a velocity distribution is not solely dependent on the tail parameter that characterizes the K distribution. The K field must also have long‐range dependence so that water may flow through relatively continuous high‐ K channels.