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Near Surface Geoscience 2012 – 18th European Meeting of Environmental and Engineering Geophysics
Paris, France, 3-5 September 2012


Electrical Resistivity of the Kotlin Clayey Formation: a Combined Interpretation of Physical Properties


K. Titov* (St Petersburg State University), G. Gurin (St Petersburg State University), D. Lantsova (St Petersburg State University), M. Kostin (St Petersburg State University) & A. Marenko (BGC Ltd.)

SUMMARY

In this paper, we present an application of the resistivity model based on a modified Archie’s law (Glower et al., 2000), and accounting for a conductivity of clay material, to the Kotlin clayey formation (Vendian age, St. Petersburg, Russia). We compare theoretical prediction of the model with experimental data based on the well logging and laboratory measurements of the core porosity and granulometric composition. We found that the experimental data are in agreement with the model prediction for the case of salty formation water (about 35 g/l). This fact is in accordance with sea conditions occurring in the region in Quaternary period.
Considering an abundance of sandy aquifers with fresh water in the formation, we believe that because of the salt diffusion, the formation water salinity in clayey sequences must be low in the vicinity of aquifers, and much larger in the middle of the sequences. Because the swelling pressure increases with decrease of the pore water salinity, clay with fresh water can be of high porosity. With this hypothesis we can explain an appearance of a seismic reflector at the depth of 60 m, which coincides with any lithological boundary, and which can be related to the high porosity zone.

Introduction

Physical properties of clayey material are of great interest because (1) clay formations prevent groundwater contamination; (2) they can serve as underground nuclear waste disposals; and (3) they frequently hold basements of engineering constructions. In St. Petersburg, Russia, the Kotlin clayey formation of Vendian age is the host for the underground railway, and it also will serve as the basement for a first in the city tower, actually planned for building. In this paper, we present data obtained in the framework of a large scale geotechnical investigation program carried out for a reconnaissance of area where the tower (400 m height) will be built. The area (400 x 400 m) is located on the Finland Gulf beach in the northwestern part of St. Petersburg city, 14 km far away from the city center. The reconnaissance campaign includes around 100 boreholes up to 150 m deep; 5 000 samples for laboratory analysis; pumping and geotechnical tests, as well as surface and borehole geophysics. Several formations from Proterozoic to Quaternary ages are presented in the site, situated geologically on the East European platform margin. The metamorphic basement is covered by the Kotlin sedimentary formation (PR2 v) including clay, sand and sandstone. The upper 25 meters represent Quaternary glacial and sea deposits. The tower basement will be based on the upper part of the Kotlin clayey formation. Clay mostly consists of kaolin, and also presents chlorite, mica and quartz. The overall goal of geophysical surveys was to build a 3D model of the site. However in this paper we restrict ourselves to the interpretation of the resistivity data obtained with the well logging in comparison with laboratory data concerning the core porosity and granulometric composition. We also consider surface seismic reflection data.

Methods


Because a fresh water mud was used in the drilling, the resistivity log was carried out with a standard pole-dipole downhole instrument (1.1 m length and 20 cm separation between the potential electrodes). For the electrical measurements a popular in Russia combination of receiver and transmitter ASTRA and MERY was applied. The current frequency was 4.88 Hz. The samples were taken in the holes each meter and were routinely analyzed for the porosity and granulometric composition. Reflection seismic data were obtained on the ground surface using a 24-channel commercial equipment ‘Laccolith24’. A high resolution acquisition system (at least 10 fold coverage) was used for further data processing on the basis of the common reflection point technique. Electrical resistivity log data were routinely corrected for the geometrical factor. Tacking into consideration that the drilling mud was made with fresh water (300 – 500 mg/l), and that the layers are relatively thick (a few meters to tenth of meters) comparing the downhole instrument size, we consider the apparent resistivity values to be close to the true formation resistivity. Because the sequences are well stratified, and their boundaries are almost horizontal, for six wells located along a circle with 40 m radius, we found average and standard deviation values of the resistivity vs. depth. Then we examined a correlation between the averaged resistivity and the depth for each sequence. Also for each sequence, we examined correlations between the porosity values and the depth; and the clay content values and the depth (Fig. 1). Reflection seismic data were filtered, routinely corrected for the offset, presented in the form of the two-way-time sections, migrated, and then presented as the depth sections on the basis of the velocity distribution previously obtained from the refraction seismic and vertical seismic profiling data.

Results and discussion

The overall resistivity level is small (10 – 16 Ohmm), however the values tend to increase with depth, which may reflect a decrease of the clay content, as well as a general decrease of the porosity with depth. For salty formation water, according to Archie’s law (Archie, 1942) with an additional term proposed by Johnson et al. (1986), the electrical conductivity, σ , depends on the formation factor, F , the water conductivity,  σwan the surface conductivity, σsurf

     

where ρ is the resistivity; F =φ−m is the formation factor; φ is the porosity; m is the Archie cementation exponent; 𝜎surf = 2Σ /ΛΣ is the surface conductance, related to a cation excess in a so-called electrical double layer surrounding the solid particles, and Λ is a characteristic pore size or the grain radius.



Figure 1. Plots of the porosity (black), clay volumetric content (blue), and electrical resistivity (red) vs. depth for the ‘Dislocated high porosity clay’ (a) and the ‘Low porosity sandy clay’ (b) sequences. Error bars on the resistivity distributions show the double standard deviation values. Solid lines are the best fits to data shown by points.

Figure 1 shows examples of relationships between the parameters, which may influence the clay resistivity for two selected sequences (the ‘Dislocated high porosity clay’, Layer 7; and the ‘Low porosity sandy clay’, Layer 9). For the dislocated clay sequence (Fig. 1a), φ decreases with depth, ρ increases with depth, and the correlation between the clay content, c, and the depth is poor. So the resistivity is mostly related to the porosity. In contrast, for the sandy clay sequence (Fig 1b) the variation of porosity is small and irregular, ρ increases and c χ decreases with increased depth. Therefore the resistivity is mostly determined by the clay content. In the sequence of sandy clay (the Layer 8) located between the Layer 7 and the Layer 9 the variations of ρ , φ and c are small (not shown). Taking into account different scales of sampling (the decimetric scale for φ and ᵡc; and the metric scale for the electrical logging), to obtain average relationships between ρ , φ and ᵡc, we found best fits to each parameter vs. depth (Fig. 1). To model the resistivity we applied a modified Archie’s law proposed by Glower et al. (2000) for a two phase system:



where 𝜎1 and 𝜎2 are the phases conductivities; 1 and 2  are their volumetric contents; and the exponents p, mp=log(1-ᵡ2m)[log(1-ᵡ2)]-1 ,depends on the phase connectivity. The model, Eq. (2), was applied twice: first for a mixture of clay particles and water, and then for a mixture of clay matrix and sand particles. At the first application, we calculated the water content in the clay matrix on the basis of the porosity values, and assuming that the water content in the matrix does not exceed the value of 0.3. For clay particles we calculated the surface conductivity assuming Σ = 2×10−9 S, Λ / 2 = 5×10−8 m, and m = 2.3 (e.g., Fridrikhsberg, 1974; Revil et al., 2002; Leroy and Revil, 2004). For the rest of the model parameters see Fig. 2. Results of the model application is shown as a family of relationships between (1) the resistivity and porosity at a fixed clay content value (Fig. 2a); and (2) the resistivity and clay content at a fixed porosity value (Fig. 2b). Different values of the water formation resistivity were used. The two experimental fits (the resistivity vs. porosity), and the one fit (the resistivity vs. clay content) for three above mentioned sequences are also shown (Fig. 2). The fit for the Layer 7 is in good agreement with the theoretical graph corresponding to the water resistivity value of 0.28 Ohmm (Fig. 2a). The center of fit for the Layer 8 is located directly on the same theoretical graph, but the fit is almost orthogonal to the graph. However recalling that the parameters variation for this sequence is very small, we consider that generally the experimental data agree with the theoretical model, and the fit for the Layer 8 can be viewed as an error bar, characterized overall error of our approach. The slope of fit for the Layer 9 (Fig. 2b), where the clay content decreased with depth (see Fig. 1b), is also in agreement with the slopes of the closest theoretical graphs. The fit is located between the graphs corresponding to the formation resistivity values of 0.28 Ohmm and 0.17 Ohmm. Therefore, according to the model, the formation water is salty, and its salinity is about 35 g/l. This value is not surprising because in the Quaternary period sea conditions occurred in the region.



Figure 2. Comparison of the experimental fits (Layer 7 – red line, Layer 8 – blue line, and Layer 9 –green line) with theoretical graphs calculated on the basis of the modified Archie’s law: a – resistivity vs. porosity at the clay content value of 0.37; b – resistivity vs. volumetric clay content at the porosity value of 0.16. Numerals show the formation water resistivity values.

  We performed an attempt to measure the water salinity directly on a sample. A cylindrical sample 34 mm in diameter and 45 mm height was put in a small reservoir (537 ml) filed with a KCl solution (325 μS/cm at 250C, or approximately 300 mg/l). We planned daily measuring of the solution conductivity and, then, calculating the formation water conductivity on the basis of (1) a steady-state value of the solution conductivity, (2) the sample volume, and (3) the porosity value. However the initially hard sample completely collapsed, and transformed to clay aggregates during the first hour of the experiment. Nevertheless we continued the conductivity measurements during one month and we obtained the formation salinity value of 28 g/l, which is very close to the value predicted by the model. In the Kotlin formation there is a number of sandy aquifers. The water formation salinity in a main aquifer is about 3 g/l because of the surface and atmospheric water infiltration within a recharge area. So, in the vicinity of aquifers, the formation water must be of smaller salinity, comparing to that in the middle of clayey sequences, because of the salt diffusion. With decrease of the water salinity, c , the Debye radius, δ , characterizing the thickness of the electrical double layer, increases as δ ~ c−1/ 2 (e.g., Fridrikhsberg, 1974). This phenomenon produces an increase of a so-called swelling pressure, known in clayey material. We believe that our sample collapsed because of the swelling pressure after being in contact with the fresh water. In the clay formation the swelling pressure may produce areas with increased porosity values, which must be considered in engineering applications. Reflection seismic data show reflectors, which correspond to all sequence boundaries known on the basis of drilling data (Fig. 3). However the second reflector (counting from the ground surface) coincides with any known sequence. Based on the above-mentioned data about soil physical properties, we believe this reflector was produced by an increased porosity due to increased swelling pressure. The laboratory data (Fig. 3b) also show increased porosity values at the reflector depth.


Figure 3. Seismic cross-sections showing a reflector at about 60 m depth (a), which was probably produced by a local increase of the formation porosity (b).

Conclusions

The double application of the modified Archie’s law correctly describes the resistivity of the clayey formation. The pore water in Kotlin formation is salty because of sea conditions occurred in the area in Quaternary period. We hypothesize that the swelling pressure can produce zones of increased porosity in clayey formations close to aquifers with fresh water.

Acknowledgments

We thanks JSC ‘SU-299’ who provided us with the laboratory data, JSC ‘Okhta center’ and St. Petersburg State University who partially supported this project. We are also grateful to Pavel Konosavsky and Alexander Potapov for important discussions about the water chemical composition.

References

Archie, G.E. [1942] The electrical resistivity log as an aid in determining some reservoir characteristics. Trans. AIME, 146, 54-62.
Johnson, D.L., Koplik, J. and Schwartz, L.M. [1986] New pore-size parameter characterizing transport in porous media. Physical Review Letters, 57, 2564-2567.
Leroy, P. and Revil, A. [2004] A triple-layer model of the surface electrochemical properties of clay minerals. Journal of Colloid and Interface Science, 270, 371-380, doi:10.1016/j.jcis.2003.08.007.
Fridrikhsberg, D.A. [1974] Kurs kolloidnoi khimii (Course of Colloidal Chemistry, In Russian), Leningrad, Chemistry-Press.
Revil, A., Hermitte, D., Spangenberg, E. and Cochemé, J.J. [2002] Electrical properties of zeolitized volcaniclastic materials. Journal of Geophysical Research, 107, doi: 10.1029/2001JB000599.

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