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Stochastic analysis of paths of high hydraulic conductivity in porous media
Author(s) -
Silliman S. E.,
Wright A. L.
Publication year - 1988
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/wr024i011p01901
Subject(s) - hydraulic conductivity , conductivity , discretization , monte carlo method , grid , porous medium , mathematics , porosity , physics , geology , geotechnical engineering , soil science , mathematical analysis , geometry , statistics , quantum mechanics , soil water
Recent investigations of heterogeneity within subsurface media have shown the importance of understanding the structure of hydraulic conductivity fields when considering either flow or transport within porous media. In the present study, a Monte Carlo approach is utilized to investigate the existance and structure of continuous paths of high hydraulic conductivity within low conductivity media. The rock mass is modeled as a discretized grid of elements, each element characterized by a single value for the hydraulic conductivity. By transforming the hydraulic conductivity utilizing the cumulative distribution function of the conductivity, a new random variable is obtained which is uniformly distributed in the range (0, 1). Utilizing this parameter, we can locate the path (termed the extreme path) which (1) connects two specified faces of the simulation grid and (2) contains the maximum value for the minimum conductivity along all such paths. The transform of this maximized minimum is termed the extreme path value. Grids are analyzed which are characterized either by (1) independence between grid elements, (2) correlation between grid elements, or (3) conditioning on field values obtained from a site in southern Arizona. It is shown that for all grids analyzed, there will exist, on average, at least one path crossing the grid along which the hydraulic conductivity is everywhere greater than the effective conductivity of the medium. Further, when the minimum conductivity along such extreme paths is analyzed, it is observed that the expected value of this minimum conductivity increases with correlation. Finally, conditioning simulations on field values resulted in a decrease in the estimation variance of the minimum conductivity.