CC BY
23
UDC 550.837
PETROPHYSICAL APPROACH TO ELECTRICAL PROPERTIES OF LOOSE SOILS
Vladimir A. SHEVNIN1, Dina A. KVON1, Albert A. RYZHOV2
1 Moscow State University, Moscow, Russia
2 VSEGINGEO, Moscow region, Noginsk district, settl. Zeleny, Russia
The paper focuses on the relation between geoelectrical characteristics of the soil: resistivity, polarizability and normalized polarizability (p, n, Mn) - and its superficial conductivity (SC or a") using methods of vertical electrical sounding with induced polarization (VES-IP), electric profiling with induced polarization (EP-IP) and frequency characteristic (FC-IP). The authors demonstrate that superficial conductivity can be determined not only from spectral IP data, but also from soil resistivity obtained through petrophysical measurements. In this case normalized polariza-bility (Mn) is equal to superficial conductivity (SC). Superficial conductivity, in its turn, is proportionate to clay content of the soil. Increasing clayiness reduces hydraulic conductivity. It has been demonstrated that interpretation of EP-IP results benefits from combined study of the plots of three abovementioned parameters (p, n, Mn). In the aeration zone, incomplete humidity has a significant effect on geoelectrical parameters of the soil. Petrophysical modelling helps to investigate the impact of humidity.
Key words: loose soil, electrical resistivity, polarizability, petrophysical soil properties, clay content, superficial conductivity, filtration coefficient
How to cite this article: V.A. Shevnin, D.A. Kvon, A.A. Ryzhov. Petrophysical Approach to Electrical Properties of Loose Soils. Zapiski Gornogo instituta. 2017. Vol. 226. P. 397-404. DOI: 10.25515/PMI.2017.4.397
Introduction. Current research has been inspired by the ideas of A.A.Ryzhov and A.Weller. A.A.Ryzhov revealed the opportunities of petrophysical approach by showing that soil resistivity could be theoretically described in the forward problem (calculation of resistivity from known petrophysical parameters) and the inverse one (estimation of petrophysical parameters basing on measured geophysical characteristics: resistivity of soil, water etc.). A.Weller demonstrated that a well known parameter of induced polarization (IP), also known as metal factor in mining geophysics and normalized polarizability in hydrogeophysics (Mn = ^k/pk, where - polarizability, pk -resistivity), is closely related to superficial conductivity. Metal factor was introduced by American geophysicists in late 1950s. In engineering geophysics N.N.Sharapanov proposed an IP parameter: A* [7], similar to the metal factor. V.A.Shevnin studied this parameter in 1970s during his work in Central Kazakhstan [3].
Petrophysical and electrical soil parameters
Parameter Known 1 Unknown 1 Known 2 Unknown 2 Depends on
1. Temperature + - + -
2. p_water + - + -
3. p_soil + - + -
4. Sand porosity + - - F
5. R_sand + - - F
6. Clay porosity - F + -
7. R_clay - F + -
8. IEC_clay - F + +
9. Humidity + + + +
10. Clay content - + - +
11. IEC - + - +
12. Soil porosity - + - + f (4, 6, 10)
13. Kf - + - + f (10)
14. RSC - + - + f (2, 8, 10)
Note. R - capillary radius, IEC - ion-exchange capacity, Kf - filtration coefficient, RSC - resistivity (reciprocal of superficial
conductivity); number 1 means prevailing sand, number 2 - prevailing clay; plus stands for a known value, minus - for an unknown or insignificant one, F - recommended value.
Methods. Relation between petrophysical soil properties and electrical resistivity was theoretically described by A.A.Ryzhov in [6] and later, in greater detail, in [2]. In these publications soil is regarded as a mix of coarse and fine fractions (e.g. sand and clay) and the pore liquid. Soil resistivity depends on the porosity and capillary radius of each fraction, their share in the overall composition, humidity and salinity (or resistivity) of the pore liquid, ion-exchange capacity and temperature. Knowing characteristics 1-2 and 4-10 (see Table), one can calculate soil resistivity, as well as parameters 11-14. If characteristics 1-9 are defined through experiment, solution of the inverse problem provides the values of parameters 10, 11 and 12-14.
A 2-D resistivity section was prepared, results of its conversion into the sections of clay content and filtration coefficient are presented in Fig.1. It was established that electrical resistivity of the rock can be expressed as a sum of electrolytic a' and surface o" conductivities: a = a' + a" [14]. In publication [10] authors proposed a dual-water model, where rock conductivity is a sum of electrolytic conductivity o' (water in wide pores) and superficial conductivity o" (water in narrow clay pores). Electrical conductivity is a complex value, its real part corresponds to electrolytic conductivity o' (water solution), and imaginary part - to superficial conductivity a" (associated with the double layer in narrow capillaries). F.Borner [9] discovered that a'' is related to Spor (relative pore surface - a ratio between pore surface and its volume) and hydraulic conductivity Kf (filtration coefficient). A possibility to assess hydraulic conductivity using spectral IP data was demonstrated in publications [12, 13].
There are two approaches to superficial conductivity estimation: by means of spectral induced polarization (SIP) [12, 13, 15] or using petrophysical approach to resistivity data, proposed by A.A.Ryzhov [11]. «Petro» software, developed by A.A.Ryzhov, calculates superficial conductivity using the following formula: &sc = Cciay&ciay /Kciay (where Cciay - clay content; aciay - clay conductivity, which depends on salinity of the pore liquid and ion-exchange capacity; KClay - clay porosity). These characteristics are determined using data on soil resistivity and pore liquid salinity and take into account the soil model [5]. Instead of superficial conductivity we often use its reciprocal -resistivity RSC [11].
In 2000-2007, investigations of oil contaminations in the soil led us to a discovery that superficial conductivity yielded the best results of separating clean soils from contaminated ones, as compared to resistivity and a number of other petrophysical parameters [11]. Resolution capacity was estimated using histogram separation index SI = dX / stnd (where dX - distance between maximum histogram values of clean and contaminated soils; stnd - standard deviation, measure of histogram width).
RSC parameter in Fig.2 was normalized in such a way that its positive values indicated that the soil was clean, whereas negative values meant it was contaminated. It corresponded to SI = 6 or, according to the three sigma rule, exhibited total histogram separation. For the case of electrical resistivity, the separation index was lower (SI = 2.5, Fig.2). Superficial conductivity of contaminated soils is closely related to oil biodegradation (its emulsification and development of biofilms - bacteria accumulations in the rock pores), which changes the structure of pore space and increases the role of electrical double layer (EDL) by raising the number of fine pores.
The authors of paper [15] established a high correlation (R2 = 0.907) between Mn and superficial conductivity (Fig.3). According to their calculations, Mn /o" ratio amounted to 0.2.
We checked the correlation between Mn and SC (a") using data from vertical electrical sounding with induced polarization (VES-IP) and electric profiling with induced polarization (EP-IP), obtained by the students of Moscow State University (MSU) during geophysical internship in the Kaluga Oblast. SC value was estimated in A.A. Ryzhov's software «Petrofizika» [2] basing on soil resistivity. We obtained a ratio of Mn/SC = 1, i.e. Mn was simply equal to superficial conductivity SC. Such difference can be explained by the fact that polarizability changes significantly depending on experiment conditions.
Fig.4 contains two groups of sampling points (two clouds), derived from a quantitative 1-D interpretation of VES-IP data. Greater values of Mn and SC correspond to loams, the second cloud -with smaller values - corresponds to sands.
Z,m 0 8 16 24 32 40 48 56 64 72 80 88 96 104 112 120 X, m
15 25 40 67 110 180 p,Ohm-m
b
-2 --4 --6 --8 -
Z, m ■ ■ ■ - X, m
K Clay, %
c
-2 -4
-6 -8
Z, m ¡; - ."m i-: m. 7: m -î-, nn m: i^i,m
(I.nis n.ii- r:.i il.;- | K, m/day
Fig.1. Example of a 2-D resistivity section (a), converted into the sections of clay content (b) and
filtration coefficient (c)
f, %
|..:i:i p, Ohmm
f, %
A
I.«
1-
2.4 Norm RSC
Fig.2. Histograms of electrical resistivity and RSC soil resistivity associated with superficial conductivity, and the separation index
for clean and contaminated soils
a
SC 0.1 —1
0.01
0,01
i i i 11 100 ct", mS/m
0.001
0.001
Fig.3. Correlation between Mn and superficial conductivity a" [15] Fig.4. Correlation between the values ofMn = n/p and superficial
, . ,, - , .. ,■ ,, „, ,, conductivity for the actual parameters (1-D interpretation)
1-4 - various soil collections; 5 - correlation line Mn = 0.2a" -T7T_,„, TTy , „ t , TT ,
of VES-IP profile layers (MSU facility «Maloye Ustye»,
July 2014)
0.1 0.2
0.5
r I 1 '1 "T-l rr
10 20 50 1
Frequency, Hz
Fig.5. Dependency between Mn = n/p and frequency for samples 1-4 [8]
1
2
5
Dependencies betweenMn and frequency (0.3-78 Hz) were plotted for four soil samples collected from EP-IP profiles (Fig.5) [8]. Advantages of usingMn parameter to separate the curves according to their clay content can clearly be seen (line 4 represents maximum clay content, line 1 - minimum one). Similar frequency characteristics (FC) were measured in the course of EP-IP explorations in 2014-2016. Basing on their Mn value, frequency characteristics could be divided into two clouds: an upper one for loams and a lower one for sands. The upper part of the territory section where EP-IP study has been performed was mostly composed of sands and loams, which resulted in clear separation of the curves. It should be noted that dependencies between frequency and nK could not be divided as easily as in the case of Mn.
Addition of normalized polarizability Mn to nk and pk plots in the profiling process (EP-IP) provides better understanding of the section structure (Fig.6). Geological section was obtained by means of electrical tomography on 23 June 2015. From top to bottom the section contains layers of sand, moraine loam, one more interlayer of sand, and bottom loam bed. The actual section differs from the ideal pattern as its slope is covered with a thin layer of scree debris, which conceals the actual outcrop of layer boundaries.
Vladimir A. Shevnin, Dina A. Kvon, Albert A. Ryzhov
Petrophysical Approach to Electrical Properties of Loose Soils
164 -
162 -
160 -
158 -
e 156 -
£ ig ei a 154 152 150 -
148 -
146 -
144
142
FC-66
Valley flat, profile start
I I|l III
0 5 10 15 20 25
30 35
111111111111 Mil INI Mil
40 45 50 55 60 65 X, m
5000 3000 2000 1000
e
§ 500 o 300 d 200
100
50 30
3 2
1
0.5
0.2 0.1
0 5 10 15 20 25
cN
0 5 10 15 20 25
30 35 40 45 50 55 60 65 X, m
=
30 35 40 45 50 55 60 65 X, m
I I |III l| I III |II I l|l I II |lI II | II I l|II I I | III l|I III | I II I|lI II |
0 5 10 15 20 25 30 35 40 45 50 55 60 65 X, m
Fig.6. EP-IP plots
Vladimir A. Shevnin, Dina A. Kvon, Albert A. Ryzhov
Petrophysical Approach to Electrical Properties of Loose Soils
n, %
0.1 0.07
2 O9, t ✓ © K • M »1 2
✓
22.' r 21
•o- i 3 /< 0 4
¥ ' 23 ■ •ic
7 « *1 2
/ / § •
✓ / s 9 1! 18 10
/ ✓ ✓ ✓ ✓ / ✓ * ✓ 7 19 9 11
M
/ IT
I I I 1 T I I
0.01
0.1 M,
0.001
Fig.7. Correlation between IP values of n andMn for samples 1-24
0.5
0.1
0.05
0.03
0.01
0.005
" N P
.—-------- _________________
= \ i
: 0 I
° \ d \i S i [ i i i i i i i i i : _0 O 0 OO 0 0 <9 oo ----------o------ \ o o \ o \ ° \ _____________v_
i-
........1 ...... 111
0.001
0.002
0.005
0.01
0.02
0.05 0.1 M,
Fig.8. Correlation between Kf and Mn
EP-IP study was carried out with Schlumberger array with AB = 5 m, MN = 1 m and a step of 1 m, using 2.44 Hz electrical equipment Astra-MARY. MARY measuring unit defined differential phase parameter (DFP) for the 1st and 3rd signal harmonics and registered their amplitudes. DFP value was used to determine polarizability = -2.5 DFP, whereas amplitudes of the 1st and 3rd harmonics allowed to calculate percent frequency effect (PFE) and logarithmic frequency effect (LFE). The amplitude of the 1st harmonic together with current intensity served to estimate pk. Five-point moving average smoothing was applied to EP-IP plots.
Comparison of EP-IP plots to the actual terrain and schematic geological section allows to observe the reaction of each parameter to the crossing of geological boundaries. Transition of the bottom sand layer to the slope corresponds to a drastic increase in resistivity, maximum polarizability and a decrease in Mn (at X = 27-33 m). An interlayer of loam between two sand layers (X = 33-40 m) corresponds to the minimums of polarizability and Mn. The upper layer of sand with its increased thickness is characterized by slowly growing resistivity and polarizability, as well as by a constant value of Mn.
During student internship a variety of soil samples (both from the surface and from the boreholes) were collected in order to measure their resistivity under different salinity, and to estimate polarizability and Mn under different frequencies. Resistivity-salinity plots have been quantitatively interpreted to evaluate clay content of the samples. Correlation between polarizability and Mn of the samples showed (Fig.7) that an increase in Mn coincided with the growth of polarizability. This relationship was slightly different for samples measured in the laboratory at full saturation and specimen measured in the field, where the rocks were partially located in the aeration zone and their saturation varied substantially - more for sands, less so for loams.
1
1
è Vladimir A. Shevnin, Dina A. Kvon, Albert A. Ryzhov
Petrophysical Approach to Electrical Properties of Loose Soils
Fig.8 demonstrates a correlation between hydraulic conductivity Kf and Mn for the same sample collection. It has been established that Kf visibly decreases with the growth of Mn.
The impact of soil humidity in the aeration zone can be examined using VES-IP method [4]. The final result for this study is presented in Fig.9 for Alexander plateau dominated by sands. Below the depth of 10 m in the zone of full water saturation bulk humidity equals sand porosity (23 %). The thickness of capillary fringe is 1 m (fine sand). Humidity in the upper part of capillary fringe (CF) amounts to around 20 % of that at the groundwater level (GWL) [1]. Above the capillary fringe humidity decreases and near the surface reaches the value of 1 % (at sand resistivity of (5-10)103 Ohmm). Top soil is dominated by light loams; within its limits an increase in humidity can be observed. In the areas with sand humidity of 2-5 %, VES-IP method detects a substantial growth of po-larizability (from 0.5 to 2.8 %) [5].
Conclusions
0 1 2
3
4
5
6
1 7 ■B
a u
Q 8
9
10 11 12
13
14
15
2500
p, Ohmm
0,8
n, %
1400
550 0,5 120
5
Humidity, %
10
20
1. Values of superficial conductivity calculated using IP data equal those obtained with resistivity method.
2. According to our estimations, normalized polarizability Mn equals superficial conductivity.
3. The plots ofMn against frequency display clay content of the soil.
4. Combined study of EP-IP plots of pk, nk and Mn values offers better understanding of the section structure and lithology.
Fig.9. Changes of humidity with depth according to VES-IP data
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Authors: Vladimir A. Shevnin, Doctor of Physics and Mathematics, Professor, [email protected] (Moscow State University, Moscow, Russia), Dina A. Kvon, Engineer, [email protected] (Moscow State University, Moscow, Russia), Al'bert A. Ryzhov, Candidate of Geological and Mineral Sciences, Leading Researcher, [email protected] (VSEGINGEO, Moscow region, Noginsk district, settl. Zeleny, Russia).
The paper was accepted for publication on 23 November, 2016.
