Axiomatic characterization of the general mixture rule

Korvin, Gábor

doi:10.1016/0016-7142(82)90031-x

Cited by 54 publications

(22 citation statements)

References 14 publications

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“…The p-order power average (Korvin, 1982;Ababou and Wood, 1990;Gomez-Hernandez and Gorelick, 1989;Green et al, 1996) or p-normxðpÞ for a set of N parameter values x iŝ…”

Section: Optimized P-order Power and Effective Scaling Factormentioning

confidence: 99%

Effective scaling factor for transient infiltration in heterogeneous soils

Zhu

Mohanty

2006

Journal of Hydrology

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“…The p-order power average (Korvin, 1982;Ababou and Wood, 1990;Gomez-Hernandez and Gorelick, 1989;Green et al, 1996) or p-normxðpÞ for a set of N parameter values x iŝ…”

Section: Optimized P-order Power and Effective Scaling Factormentioning

confidence: 99%

Effective scaling factor for transient infiltration in heterogeneous soils

Zhu

Mohanty

2006

Journal of Hydrology

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“…Recall that the general upscaling trends exhibited by the tuff data are consistent with volume averaging, although not according to a linear volume average. Because of this non-linearity we employ a volume poweraverage model [e.g., Korvin, 1981;Deutsch, 1989;Desbarats, 1992bDesbarats, , 1994 …”

Section: Local Upscalingmentioning

confidence: 99%

Upscaling experiments conducted on a block of volcanic tuff: Results for a bimodal permeability distribution

Tidwell¹,

Wilson²

1999

Water Resources Research

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Abstract. Permeability upscaling is physically investigated by making over 31,000 permeability measurements on a meter-scale block of volcanic tuff. The experiments are made possible by a specially adapted minipermeameter test system. Here we present and analyze 5185 permeability values, corresponding to five different sample supports (i.e., sample volumes) collected from one of the six block faces. The results show that the measured spatial permeability patterns, bimodal permeability distribution, and semivariogram structure/length scales are closely related to the strong textural contrast characterizing the tuff sample (i.e., highly porous pumice fragments embedded in a tight rock matrix). Each of the summary statistics shows distinct and consistent trends with increasing sample support (i.e., upscaling). As the sample support increases, the mean and variance decrease according to a power law relation, and the semivariogram range increases linearly, while the general structure of the semivariogram (isotropic, spherical model) remains unchanged. Interpretation of these results is pursued from two very different points of view; one addresses upscaling of the ensemble statistics, while the second examines upscaling from a local or pointwise perspective. We find the general upscaling trends exhibited by the ensemble statistics (given above) to be consistent with the basic concepts of volume averaging, albeit nonlinear volume averaging. The bimodal characteristics of the tuff sample and the nonuniform flow conditions imparted by the minipermeameter contribute to the nonlinearity. The local analysis reveals strong variability in permeability upscaling from point to point throughout the sampling domain. Specifically, the permeability upscaling exhibited by zones rich in pumice is very different from zones dominated by matrix, unless the averaging volume is significantly larger than the spatial correlation scale.

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“…Another method that is based on the mixing of conductivities of two components, and that is derivable analytically, is that of Korvin (1982) and Tenchov (1998). We later compare the Bussian equation with the modified Archie's law and the Korvin and Tenchov approach.…”

Section: Introductionmentioning

confidence: 99%

A simple method for solving the Bussian equation for electrical conduction in rocks

Glover¹,

Ransford²,

Auger³

2010

Solid Earth

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Abstract.One of the most general and effective models for calculating the complex electrical conductivity and relative dielectric permittivity of rocks saturated with pore fluids is that of Bussian. Unlike most models, it is non-linear and cannot be solved algebraically. Consequently, researchers use reiterating numerical routines to obtain a solution of the equation, and then only for the real part of the solution. Here we present a different approach to the solution that uses conformal mapping in the complex plane, and implements it within Maple TM . The method is simple and elegant in that it requires, for example, only 3 lines of code in Maple TM 11 and little programming experience. The approach has been shown to be as precise as using the classical reiterating bisection method for real data implemented in C++ on an ordinary desktop computer to within a probability over 1 in 10 9 . However, the conformal mapping approach is 52 times as fast. We show once more that the Bussian equation breaks down for low fluid conductivities, but recommend it (with the modified Archie's law) for use with rocks saturated with high salinity fluids when the matrix is conductive.

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Axiomatic characterization of the general mixture rule

Cited by 54 publications

References 14 publications

Effective scaling factor for transient infiltration in heterogeneous soils

Effective scaling factor for transient infiltration in heterogeneous soils

Upscaling experiments conducted on a block of volcanic tuff: Results for a bimodal permeability distribution

A simple method for solving the Bussian equation for electrical conduction in rocks

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