Power-law velocity distributions in fracture networks: Numerical evidence and implications for tracer transport

Details Power-law velocity distributions in fracture networks: Numerical evidence and implications for tracer transport Power-law velocity distributions in fracture networks: Numerical evidence and implications for tracer transport

Jul 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002georl..29n..21p&link_type=abstract

Geophysical Research Letters, Volume 29, Issue 14, pp. 21-1, CiteID 1676, DOI 10.1029/2002GL014960

Physics

Geophysics

8

Hydrology: Groundwater Transport, Hydrology: Stochastic Processes, Mathematical Geophysics: Fractals And Multifractals, Physical Properties Of Rocks: Fracture And Flow

Scientific paper

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.

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