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Power‐law velocity distributions in fracture networks: Numerical evidence and implications for tracer transport
Author(s) -
Painter Scott,
Cvetkovic Vladimir,
Selroos JanOlof
Publication year - 2002
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/2002gl014960
Subject(s) - power law , advection , range (aeronautics) , pareto distribution , mechanics , statistical physics , fracture (geology) , dispersion (optics) , residence time (fluid dynamics) , law , distribution (mathematics) , physics , mathematics , geology , mathematical analysis , thermodynamics , materials science , statistics , geotechnical engineering , political science , optics , composite material
Velocity distributions in two‐ and three‐dimensional networks of discrete fractures are studied through numerical simulations. The distribution of 1/v , where v is the velocity along particle trajectories, is closely approximated by a power law (Pareto) distribution over a wide range of velocities. For the conditions studied, the power law exponents are in the range 1.1–1.8, and generally increase with increasing fracture density. The same is true for the quantity 1/bv , which is related to retention properties of the rock; b is the fracture half‐aperture. Using a stochastic Lagrangian methodology and statistical limit theorems applicable to power‐law variables, it is shown that the distributions of residence times for conservative and reacting tracers are related to one‐sided stable distributions. These results are incompatible with the classical advection dispersion equation and underscore the need for alternative modeling approaches.