Theoretic Calculation of Rocks Electrical Resistivity and Some Examples of Algorithm's Application

Abstract

At calculation of rocks resistivity some statistical formulas are frequently used, the best example is the Archie formula. In the present report calculations of rocks' resistivity are made on the basis of the exact physical-chemical theory. The merit of the exact theory application is that this approach allows understanding more directly the mechanism of rocks resistivity forming and the different factors' influence. The demerit is, that the algorithm requires a good knowledge of physics and chemistry and inputting additional information, which a practical geophysicist not always has. The main stages of rock' resistivity calculation are: electrical conductivity account for electroneutral solutions; calculation of electrical conductivity of a liquid in a double electric layer taking into account the electric properties of the solid phase, then calculation of rock's resistivity for definite lithology, porosity, humidity and grain size. On a series of examples the possibilities of such calculation and the influence of the different factors are shown. Most evidently the algorithm's opportunities are uncovered at resistivity calculation of sandy-clayish sediments. It is possible to use the algorithm at the inverse problem solution for resistivity method-for the estimation of rocks hydro-geological properties on their resistivity.

Determination of Soil Properties from Electrical Measurements in Agricultural Plots, Villa de Arriaga, San Luis Potosí, Mexico

“…Considering this model using equations ( 5) and ( 8), it is possible to generate theoretical curves of electrical resistivity from any soil consisting of sand and fines (clay and/or silt) versus pore water salinity (solution of the forward problem, Figure 3) from defined parameters: fines content, porosity, and CEC. Using the PetroWin program developed by Ryjov (Ryjov and Shevnin, 2002), an iterative inversion process of minimizing of the RMS error between the experimental (from electrical measurements in lab) and theoretical (theoretical model above described) curves is made. Different parameters can be modified during the iterative inversion process, such as pore-water salinity (including types of anions and cations with their valence, hydration number, sorption constant and mobility), porosity, capillary radii, moisture and cementation exponent for each fines and sand components of the soil, as well as the CEC for fines component and the temperature of the soil.…”

“…The forward petrophysical problem consists of the calculation of rock resistivity values on the base of properties of unconsolidated sediment (mixture of sand and clay). The inverse problem consists of the estimation of the properties' clay content, porosity and CEC on the base of soil resistivity and pore water salinity, taking into account the soil petrophysical model of the site (Ryjov and Shevnin, 2002). Subsequently, a new methodology applied to environmental impact studies of the oil industry in Mexico (Delgado-Rodríguez et al, 2018) was developed, including geoelectrical survey and electrical measurements in soil and groundwater samples (Shevnin et al, 2006a, b).…”

Oil pollution detection using resistivity sounding

“…Field studies of oil pollution are more difficult in the case of high groundwater salinity, as the resistivity contrast between soils with and without pollutants is minimal (Ryjov and Shevnin, 2002).…”

“…For this purpose we use a simulation of resistivity in non-contaminated formations based on water mineralization and rock lithology. The algorithm and software were developed by Ryjov (Ryjov and Sudoplatov, 1990;Ryjov and Shevnin, 2002). Program "Petrofiz" calculates rock resistivity on the base of physical -chemical theory, taking into account rock porosity, clay content, water salinity and types of salt in water, pore size and some other characteristics.…”

Using Electrical Profiling to Determine Soil Petrophysical Parameters in an Agricultural Field

“…Fifty-five EP measurements were distributed in five parallel profiles using a Schlumberger array for AB/2 = 2 m and 3 m ( The ρ a , soil moisture, and pore water salinity values were used to obtain the petrophysical parameters of the soil using Petrowin software developed by A. Ryjov [27][28]. The experimental relationship between electrical resistivity as a function of the mineralization of pore water and clay content was first published in Russia by Sharapanov et al [29].…”