Influence of Degree of Saturation in the Electric Resistivity–Hydraulic Conductivity Relationship |
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Authors: | Mohamed Ahmed Khalil Fernando A Monterio Santos |
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Institution: | 1.Centro de Geofísica da Universidade de Lisboa-IDL,Universidade de Lisboa,Lisbon,Portugal;2.National Research Institute of Astronomy and Geophysics,Cairo,Egypt |
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Abstract: | The relationship between aquifer hydraulic conductivity and aquifer resistivity, either measured on the ground surface by
vertical electrical sounding (VES) or from resistivity logs, or measured in core samples have been published for different
types of aquifers in different locations. Generally, these relationships are empirical and semi-empirical, and confined in
few locations. This relation has a positive correlation in some studies and negative in others. So far, there is no potentially
physical law controlling this relation, which is not completely understood. Electric current follows the path of least resistance,
as does water. Within and around pores, the model of conduction of electricity is ionic and thus the resistivity of the medium
is controlled more by porosity and water conductivity than by the resistivity of the rock matrix. Thus, at the pore level,
the electrical path is similar to the hydraulic path and the resistivity should reflect hydraulic conductivity. We tried in
this paper to study the effect of degree of groundwater saturation in the relation between hydraulic conductivity and bulk
resistivity via a simple numerical analysis of Archie’s second law and a simplified Kozeny-Carmen equation. The study reached
three characteristic non-linear relations between hydraulic conductivity and resistivity depending on the degree of saturation.
These relations are: (1) An inverse power relation in fully saturated aquifers and when porosity equals water saturation,
(2) An inverse polynomial relation in unsaturated aquifers, when water saturation is higher than 50%, higher than porosity,
and (3) A direct polynomial relation in poorly saturated aquifers, when water saturation is lower than 50%, lower than porosity.
These results are supported by some field scale relationships. |
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Keywords: | |
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