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| Titel |
A simple method for solving the Bussian equation for electrical conduction in rocks |
| VerfasserIn |
P. W. J. Glover, T. J. Ransford, G. Auger |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1869-9510
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| Digitales Dokument |
URL |
| Erschienen |
In: Solid Earth ; 1, no. 1 ; Nr. 1, no. 1 (2010-09-28), S.85-91 |
| Datensatznummer |
250000120
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| Publikation (Nr.) |
 copernicus.org/se-1-85-2010.pdf |
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| Zusammenfassung |
| 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 MapleTM. The method is simple and elegant in
that it requires, for example, only 3 lines of code in MapleTM 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 109. 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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