Relations between formation resistivity and specific conductance

An example of inversion solution transferred from geophysical data to physical parameters has been done by Fitterman. [7,8] for a study area in Florida and on the base model development and laboratory measurements sand probes from the study area in Marina Di Ragusa, Sicily, 2002. Archie’s law relates the electrical resistivity of water saturated rocks (ρ_f) to the resistivity of the contained pore water (ρ_o) through the formation factor F = ρ_f /ρ_o. The formation factor accounts for the influence of porosity on the electrical resistivity. If the formation factor can be estimated from borehole measurements, then formation resistivity values obtained from interpretation of surface and laboratory geophysical measurements of the sample soils can be used to estimate the specific conductance (SC) of the pore fluid and mineral geological formation. If, in addition, the relationship between specific conductance and chloride concentration is known, then the chloride concentration of the formation can be estimated from the geophysical data. Laboratory measurement of water samples provides a means of determining this latter relationship (Fig.9).

To estimate the formation factor, induction logs were measured in a total of 23 existing and specially drilled boreholes in the study area. This provided very detailed resistivity–depth information. The formation resistivity was averaged over the screened interval of the wells (typically 10 ft). The wells were then pumped and a water sample collected after sufficient time for the well bore to be purged.

The specific conductance of the sample was measured. For shallow wells the conductivity was directly measured in the well.

FIG.9. Relationship between formation resistivity, pore water conductivity and chloride content based on induction logs and water sample measurements. Relationship valid for the surficial aquifer in the study [6].

The data for all of the measured wells is shown in Fig.9. Both the formation resistivity and SC span over two sets of measurements gives a good range of values for developing a correlation. Due to the inherent scatter in the data, the pore water conductivity is estimated from the formation resistivity with an uncertainty of a factor of 2–3. While this uncertainty is much larger than expected for conductivity probe or laboratory measured values, it is adequate for use in regional scale aquifer studies where the value of SC would be interpolated between wells that are 10 or more km apart. Some of this uncertainty stems from the fact that the wells are from a wide range of depths with some of the deeper wells being below the study aquifer. Thus there are some differences in the geologic units, though all wells were screened in porous zones, which were good water producers.

From induction logs, which measure formation resistivity and measurements of water conductivity, both in the borehole and from samples pumped from the wells, the following relationship was established:

SC = 81200ρ_f ^–1.062 (4)

where SC is the specific conductance in µS/cm and ρ_f is the formation resistivity in Ω·m. This relationship (Fig.9) can be used to convert interpreted layer resistivity to SC of the saturating pore fluid.

Often chloride ion concentration is of interest to hydrogeologic modelers. To convert specific conductance to chloride ion concentration we use a relationship established for surface waters shown in Fig.9. The specific conductivity increases nonlinearly with chloride concentration for chloride levels below 650 ppm. At higher chloride concentrations, the relationship becomes linear. Using the local data for SC–Cl relation and equation (1.4), the ρ_f – Cl graph in Fig.10 was generated.

The chloride ion concentrations of fresh and saline groundwaters are usually quite different resulting in large differences in formation resistivity for fresh and saline saturated geologic materials. The graph shown in Fig.10 provides a way of estimating chloride levels from inverted TEM data, however, it must be stressed that this relationship is based upon an assumption that ground water in the area has the same SC–Cl relationship as surface water. This is a reasonable assumption as the source of Cl is most likely from seawater for both ground and surface water. Because of its statistical nature there is

some uncertainty in eq.(4), and consequently in the formation–resistivity–chloride relationship.

Nonetheless, this relationship is useful provided its limitations are understood.

FIG.10. Empirical relationship between formation resistivity and

chloride concentration of pore water on the basis of [7, 8] interpretation results.

Using the above results for the comparative analysis of the data and techniques on the basis of modeling development and laboratory measurements of soil probes the following dependencies which enable connection of the data on geophysical sounding directly with salinity and porosity subsurface horizons were received in a model relationship (Figs. 11, 12).

FIG.11. Model relationship between formation resistivity [Ω·m], pore water conductivity [μS/cm], and sodium chloride content [mg/L] in pore water for fractionary (0.25 < d < 0.5 mm), full water saturated sands based on laboratory resistivity measurements sand probes from study area (Marina Di Ragusa study area) in frequency range 0.3 – 10 MHz for different pore coefficient K: 1 - КП = 30%; 2 - КП = 35%; 3 - КП = 42.5%; 4 - КП = 50%.

More detailed description and comparative analysis of the given model development and laboratory measurements for interpretation results of geophysical sounding will be submitted in the second part of the given work.

FIG.12. Relationship between pore water resistivity (Ω·m) and chloride content (mg/L) on the base model performance and laboratory measurements of sand probe from study area in Marina Di Ragusa.