Induced Polarization of Unsaturated Sands Determinedthrough Time Domain Measurements K. Titov,* A. Kemna, A. Tarasov, and H. Vereecken Reproduced from Vadose Zone Journal. Published by Soil Science Society of America. All copyrights reserved. ABSTRACT Lesmes and Morgan, 2001; Slater and Lesmes, 2002b; Titov et al., 2002; Scott and Barker, 2003) were performed on saturated media, which restricts the applicability of the results to vadose zone studies. Moreover, the influence of vadose zone parameters and state variables on IP measurements is not clear because of the lack of corresponding petrophysical data. Studies on the variation of real (not complex) resistivity with water content were conducted by a number of authors in the context of hydrology and oil prospection (e.g., Keller, 1953; Knight, 1991; Taylor and Barker, 2002). The complex resistivity was investigated under different saturation degrees on sandstone cores in the frequency range of 100 to 107 Hz (Su et al., 2000); on sandstone, carbonate rocks, and synthetic porous media in the frequency range of 100 to 1010 Hz (Capaccioli et al., 2001); and on unconsolidated sediments in the frequency range of 0.1 to 1000 Hz (Ulrich and Slater, 2004). Time domain measurements on sands with different water content are reported in Komarov (1980) and Iliceto et al. (1982). In the low-frequency range typically used in electrical surveys, IP is related to ion diffusion produced by an electric current flowing through the porous medium. The electric current produces ion concentration gradients in areas where interfaces between solid and liquid phases are curved (Dukhin and Shilov, 1974; Fixman, 1980), for instance with pore constrictions. The ion concentration gradients in turn give rise to ion flows, which represent secondary electric currents within the pores (Marshall and Madden, 1959; Fridrikhsberg and Sidorova, 1961). These electric currents give rise to the secondary voltage, which is the manifestation of IP. Induced polarization can be measured by two different means. In the TD method the voltage decay after excitation by a current pulse is measured, while in the frequency domain method the phase shift between injection current and voltage response is measured. The latter gives rise to a complex resistance (i.e., impedance), or complex resistivity, which generally depends on the measurement frequency used. We present results of laboratory TD measurements conducted on sieved sands under different degrees of saturation. We discuss how the water content affects resistivity and polarization and propose a conceptual model to explain the experimental data. With regard to the application of the IP method in hydrocarbon contamination studies, we made additional measurements to investigate how the replacement of air by kerosene in unsatu- We studied the electrical induced polarization (IP) response of simple multiphase porous systems by conducting time-domain (TD) IP measurements on two different groups of sieved quartz samples: sands containing air in unsaturated pores and sands where the unsaturated pores were filled with kerosene. The analyzed chargeability vs. water content relationship showed an extreme behavior. The resistivity vs. water content relationship exhibited two distinct power law regions characterized by different values of the power-law exponents. Quartz–water–air and quartz–water–kerosene samples showed similar behavior. A conceptual model of polarizing cells is proposed to explain the observed IP phenomena. We consider a sequence of large and narrow passageways for electric current as the elementary polarizing cell. The polarization of the cell is related to the difference in effective radii of the passageways. In the saturated cell, the water-filling intergrain space is considered the large current passageway. Areas of grain contact are considered narrow passageways. In unsaturated cells, the thin water film on the grain surfaces is considered the narrow passageway. Areas of grain contact are viewed as large passageways. The polarization of unsaturated cells in this condition should be larger than that of saturated cells. With further drying, unsaturated cells start releasing water from the grain contact area, which leads to a convergence of the effective radii of large and narrow passageways and, consequently, to a decrease in cell polarization. The conceptual model is capable of explaining the observed dependence of polarization on water content. The chargeability maximum corresponds to the limit between the two distinct regions, each having a different resistivity vs. water content relationship, which we consider as the critical water content. Our model suggests that at the critical water content, pore water becomes predominantly adsorbed on the solid surface. I n the last decade, the IP method has proved to be of significant value for various environmental and hydrogeological investigations of the subsurface. It has been demonstrated in field applications that IP has the potential to distinguish between sediments of different lithological composition (e.g., Slater and Lesmes, 2002a; Kemna et al., 2004) and of different groundwater salinity (e.g., Seara and Granda, 1987), to detect inorganic and organic contaminants (e.g., Oldenburg, 1996; Kemna et al., 2004), and to predict hydraulic characteristics (e.g., Bo¨rner et al., 1996; Kemna et al., 2004). However, most of the underlying core-scale investigations (e.g., Bo¨rner and Scho¨n, 1991; Vanhala, 1997; Lesmes and Frye, 2001; K. Titov, Russian Institute of Exploration Geophysics, 20 Fayansovaya St., 193019, St. Petersburg, Russia; presently, St. Petersburg State University, Geophysical Department, 7/9 Universitetskaya nab., 199034, St. Petersburg, Russia; A. Kemna and H. Vereecken, Agrosphere Institute (ICG-IV), Forschungszentrum Ju¨lich GmbH, 52425 Ju¨lich, Germany; A. Tarasov, State Enterprise, Geologorazvedka, 17 Knipovich St., 193019, St. Petersburg, Russia. Received 31 Jan. 2004. Special Section: Hydrogeophysics. *Corresponding author (
[email protected]). Published in Vadose Zone Journal 3:1160–1168 (2004). © Soil Science Society of America 677 S. Segoe Rd., Madison, WI 53711 USA Abbreviations: EDL, electrical double layer; IP, induced polarization; QWA, quartz–water–air; QWK, quartz–water–kerosene; TD, time domain. 1160 (d) Excess and deficiency in ion concentration along a polarized throat. Fridrikhsberg and Sidorova. The concentration gradients give rise to ion flows. 2001) and the capillary model (e. The effective charge of the ion atmosphere compensates the present surface charge. the introduction of a nonwetting phase seems to be more difficult because a reasonable description would require numerical modeling. They found this geometrical representation useful to model water flow in pore corners and thin pores. and ␥ denote solid phase. The sequence of large and narrow pores can be considered as the polarizing cell. These secondary electric currents of diffusive nature are associated with a secondary out-of-phase voltage. 2002). (c) Excess and deficiency in ion concentration around a polarized charged spherical particle. 1. mostly represented by cations in the EDL. (e) Schematic distribution of the ion concentration around a polarized spherical particle or along a polarized pore throat. We propose distinguishing three types of cells on the basis of the degree of saturation: saturated cells (Fig. CONCEPTUAL MODELS In porous media. which produce a secondary out-of-phase voltage. Accordingly. For the granular model. respectively. 2e and 2f). The above two general concepts of the pore-scale mechanism of IP seem to be equivalent because both consider the same cause of IP and both account for similar characteristic lengths of diffusion. All copyrights reserved. Kormiltsev. For the capillary model of unsaturated sand we consider current passageways instead of pores. Titov et al. In the granular model. The ion transparency is the contribution of an individual ion type to the electric current along a pore. If the large pore is much longer than the narrow pore. and unsaturated cells with small water “rings” where water mostly represents a bound film adsorbed on the solid surface (Fig. solid arrow shows the electric field direction. Published by Soil Science Society of America. 1c). A grain surrounded by its own ion atmosphere can be considered as a polarizing cell. www. The concentration gradients give rise to ion flows. 1974. electric current also produces local ion concentration gradients in areas of variation of the pore radii (Fig. Helmholtz layer. are each surrounded by an oppositely charged ion atmosphere. Tuller et al. In the capillary model. dotted arrows indicate the local diffusion flows represented by both cations and anions. 1961. which are similar to the capillary models used to describe IP. 1e. 1d). in a study of water flow in partially saturated porous media. Induced polarization in ion-conductive media has been theoretically described on the basis of two representations of the media: the granular model (e. at least in a first approximation.Reproduced from Vadose Zone Journal.g.. According to these concepts. diffusion flows and electric field same as in Part c. water content and polarization vs. 1961. C* denotes the excess concentration produced by the polarizing electric field. and in equilibrium between diffusive and electrostatic forces the electrical double layer (EDL) is formed at the interface between solid and liquid phases (Fig. The relaxation time () characterizing the polarization of such a cell is related to the ion diffusion coefficient (D) and the characteristic length of diffusion (l). l is equal to the length of the narrow pore. Fridrikhsberg and Sidorova (1961) derived an expression for the . Figure 2 illustrates the concept of the equivalence of the granular and the capillary representations for sands. rated sand influences the resistivity vs. Dukhin and Derjaguin. dashed arrows show the local diffusion flows near the solid surface mostly represented by cations. ⫽ l 2/4D (Kormiltsev. a solid grain surrounded by its own ion atmosphere produces local ion concentration gradients under the influence of electric 1161 current (Fig.g. In contrast. The schematic distribution of ion concentration produced by electric current crossing such polarizing cells is shown in Fig. solid particles with an electrical surface charge. IP is related to the variations of ion transparencies along the current passageways. The relaxation time () characterizing polarization of this cell is related to the ion diffusion coefficient (D) and the grain radius (R). In the EDL. Schematic view of IP in ion-conductive rocks (according to Fridrikhsberg and Sidorova. 1962). however. (b) Schematic distribution of cation (Cc) and anion (Ca) concentrations in the EDL. C0 is the equilibrium ion concentration outside the EDL. 2a and 2b).org Fig. Dukhin and Shilov. 1963). . water content relationships. IP in fully saturated media is either sensitive to grain-size distribution or to pore-size distribution. unsaturated cells with large water “rings” in the grain contact area (Fig..vadosezonejournal. 1963. In the capillary model. For the investigation of unsaturated media we have to choose between the two concepts. ␣. (1999) proposed a capillary representation of the liquid phase configuration comprising large and narrow geometrical elements. Lesmes and Morgan. 2c and 2d). and diffuse layer. ⫽ R2/2D (Schwarz. 1974).. 1b). the average concentration of cations (in case of a negatively charged surface) is larger than that of anions (Fig. the capillary model offers an easy way to introduce a nonwetting phase that can be described analytically. mostly represented by cations in throats. (a) Scheme of electrical double layer at a negatively charged particle surface. usually negative. 1a). and we understand narrow passageways as narrow pores and large passageways as large pores. the narrower is the diffuse layer (see Eq. R ⫽ 8. the surface conductivity is expressed as (Dukhin and Derjaguin. Gray and white areas indicate water and particles. water-filling intergrain spaces can be considered large pores. Published by Soil Science Society of America. 3. d). T (K) is the absolute . f). where the water is in a closer bond on the grain surface. ␦ denotes the Debye length. For the saturated case (a) a1. a2 denotes the average thickness of the water film in a large pore. l2. Areas of grain contact. 1974) Ss ⫽ 4␦zFuC0(cosh⌫1 ⫺ 1) [2] where ␦⫽ 1 zF ε0εRT 冪 2C [3] 0 in which ␦ (m) is the Debye length. For a partially saturated cell (Fig. 2. ε ⫽ 80 is the relative permittivity of the solution. l1. To simplify the model. ␣⫺) in the EDL. respectively. The Debye length represents a characteristic thickness of the diffuse layer. respectively. VOL. for the unsaturated case (b) a2 denotes the characteristic thickness of the water film in a large slit. Fig. and ␣2 is the coefficient of efficiency of the narrow pore. e) Schematic view of polarizing cells based on the granular model and (b. Although this represents a two-dimensional approximation of a three-dimensional situation. respectively. In the partially saturated case (c.31 J mol⫺1 K⫺1 is the universal gas constant. (c–f) partial saturation. ε0 ⫽ 8. a2 denote the half-apertures of narrow and large slits. S1. NOVEMBER 2004 Fig. f) equivalent pore sketches for dense (right) and loose (left) packings of particles at different water content: (a. In the saturated case (a. Areas of grain contact. the Debye length (␦). and S2 are the lengths and cross-sectional areas of large and narrow pores.85 ⫻ 10⫺12 F m⫺1 is the dielectric constant. Symbolic graphs of ion concentrations illustrate excess of cations and deficiency of anions in the electrical double layer (EDL) relative to the equilibrium concentration C0. Figure 3a shows the main parameters for a saturated cell: slit half-apertures (a1. and the effective charges of cations and anions (␣⫹. The integrals of cation excess and anion deficiency over the slit aperture represent the effective charges of cations (␣ⴙ) and anions (␣⫺) in the EDL. F ⫽ 9. cells continuously loose water from the grain contact area and both thickness and diameter of the water rings decrease (e. can be viewed as large passageways (similar to large pores in the saturated case). we consider the large and narrow passageways as slits with different apertures.65 ⫻ 104 C mol⫺1 is the Faraday constant. magnitude of IP (m) produced by a sequence of large and narrow pores: m⫽ 2 冢 4(⌬t) l1 S1 S 2 l ⫹ 2 ⫹ S1 ␣2S2 l1 l2 冣冢 冣 [1] where ⌬t is the difference of cation transparencies in the large and narrow pores. With further desaturation. it provides insight into the general IP characteristics of a corresponding pore sequence. All copyrights reserved. can be considered throats. a2). b).. Schematic view of a “slit” sequence representing interconnected (a) saturated and (b) unsaturated pores. which depends on the surface conductivity and represents a ratio of the average capillary conductivity to the bulk solution conductivity. d. 3b). c. 1162 VADOSE ZONE J. (a. b) full saturation. 3. For a binary symmetric electrolyte (neglecting electroosmosis). [3]). z is the ion valence. which depends on the water salinity.Reproduced from Vadose Zone Journal. The higher the water salinity. where water is more abundant because of surface tension (water “rings”). the water film at the surface of moistened grains can be considered a narrow passageway for electric current (throats). or a sequence of current passageways with thicknesses a1 and a2. we obtain for the cation transparency: t⫹(a) ⫽ a ⫹ 2␣⫹ ␦ 1 2a ⫹ (␣⫹ ⫹ ␣⫺) ␦ [11] Considering now a sequence of slits with half-apertures a1 and a2 (Fig.1163 Reproduced from Vadose Zone Journal. u (m2 V⫺1 s⫺1) is the ion mobility and is assumed to be equal for cations and anions. Separating Eq. and 1 (V) is the potential at the outer side of the Helmholtz layer. All copyrights reserved. In contrast. (2002). from Eq.5 ms and tmax ⫽ 0. corresponding to a narrow slit with an aperture 1000 and 10 000 times larger than the Debye length. [2] into terms related to anions and cations and adding to each term the contribution of the volume conductivity. www. 1990): tmax 冮 U(t)dt 1000 tmin (mV/V) M⫽ tmax ⫺ tmin U0 [13] where U(t ) is the voltage between times tmin and tmax after the end of the current pulse (here we used a time window defined by tmin ⫽ 1. 2a and 2b). All graphs exhibit an asymptotic behavior. corresponding to a narrow slit with an aperture 10 and 100 times larger than the Debye length. 1c–1f). when the narrow slit has an aperture 10 and 100 times larger than the Debye length (two upper graphs). t⫺) as the partial cation and anion conductances: t⫹ ⫽ S⫹ S⫹ ⫹ S ⫺ [8] t⫺ ⫽ S⫺ S⫹ ⫹ S ⫺ [9] with t⫹ ⫹ t⫺ ⫽ 1 [10] Substituting Eq.org temperature. [12]).vadosezonejournal. The larger the ratio. and ␣⫹ and ␣⫺ are the effective charges of cations and anions. Calculated graphs of ⌬t vs. the more water is bound since a greater part of the slit volume is occupied by EDL. can be attributed to saturated cells (Fig. while the ratio of slit apertures a2/a1 strongly affects ⌬t values in the region 3 to 30.1 V. respectively. Upper graphs. respectively. The two lower graphs. Difference in cation transparency for a sequence of large and narrow slits with apertures a2 and a1. time is similar to that of the phase of complex electrical conductivity vs. for theoretical and experimental evaluation of the IP effect. Published by Soil Science Society of America. 3). C0 (mol m⫺3) is the equilibrium water salinity. The two upper graphs may characterize unsaturated cells with a narrow film of bound water on the grain surface (Fig. showing small values of ⌬t.92 s). Komarov (1980) proposed use of the derivative of the corresponding voltage transient with respect to the logarithm of time.g.. 1a and 1b). we obtain two partial conductances related to cations (S⫹) and anions (S⫺): S⫹ ⫽ zFuC0(a ⫹ 2␦␣⫹) [4] S⫺ ⫽ zFuC0(a ⫹ 2␦␣⫺) [5] with ␣⫹ ⫽ [exp(⌫1) ⫺ 1] [6] ␣⫺ ⫽ [exp(⫺⌫1) ⫺ 1] [7] where a (m) is the slit half-aperture. [4] and [5] into Eq. [12].. Now we can formulate the ion transparencies (t⫹. We consider these to be characteristic of saturated cells (Fig. . reciprocal of frequency. ⌬t becomes nearly constant when this ratio further increases. respectively (Eq. [11] we obtain after some algebra: ⌬t ⫽ t⫹(a2) ⫺ t⫹(a1) 冢 冣 冥冤 ␦ a 1 ⫺ 2 (a⫹ ⫺ a⫺) a1 a1 ⫽ ␦ ␦ a 2 1 ⫹ (a⫹ ⫹ a⫺) 2 ⫹ (a⫹ ⫹ a⫺) a1 a1 a1 冤 冥 [12] According to Eq. Lower graphs. MATERIALS AND METHODS Studied Parameters Wait (1982) defined the TD IP characteristic as the increase with time of the overvoltage caused by an infinite unit current step. played in Fig. For more details concerning d the reader is referred to Titov et al. We also determined the chargeability (M ). in the EDL (Fig. correspond to narrow slits with an aperture 103 and 104 times larger than the Debye length. which is the typically used measure of the IP effect in TD field surveys (e. 2c–2f). The graphs were calculated for different ratios of the Debye length to the aperture of the narrow slit (␦/a1) and for a value of 1 potential of 0. and U0 is the voltage averaged over the pulse duration. the difference in cation transparency is related to the ratios a2/a1 and ␦/a1. We find the differential polarizability convenient for analysis of IP because the behavior of d vs. the so-called differential polarizability (d). ⌫1 ⫽ zF1/(RT) is the dimensionless interface potential. 4. In our study we used the differential polarizability obtained at different times to evaluate the IP transient behavior. that is. The second ratio characterizes the bond of water in the narrow slit to the solid surface. can be attributed to unsaturated cells (Fig. Telford et al. 4 for different values of ␦/a1. 3a). [8]. ⌬t becomes considerably larger. The difference in cation transparency strongly increases when a2/a1 is in the region between 3 and 30. a2/a1 are dis- Fig. was used. As a result we obtained eight sand samples with volumetric water content in the range of 0.24 0. the chargeability of the QWA and QWK samples shows a similar behavior (Fig. 7. volumetric water content W. and the geometrical factor calculated for the employed holder configuration. the current crossing the sample. Because the chargeability represents a measure of polarization magnitude relative to conduction magnitude (Keller. We here used 50 to 200 different time windows.029 0. 1996). More details on the measurement setup and procedure were previously described in Titov et al. 5 on a double logarithmic plot. covered at both ends by cellophane porous membranes. in direct contact with the sample surface. The tube ends were squeezed between two copper electrodes used for current injection.02 to 0. This is relevant to the application of the IP method to environmental problems associated with subsurface hydrocarbon contamination. Table 1. 1984).021 0. The motivation for this additional series of measurements was to investigate the influence of a nonaqueous phase liquid within the pore space (here instead of air) on the IP response of the multiphase system. it tends to increase when the water content decreases.43 0.051 0. 8)..42 1. Sample Preparation Sieved commercial quartz sand of 0.1. and for unsaturated unconsolidated sediments (Ulrich and Slater.45 0. volumetric water content (W) on double logarithmic plots (Fig.021 0.15 0.093 0.89 1. the copper sulfate was actually prepared with gelatin. 6. 2002a) and thus is approximately linearly related to the bulk resistivity. 1974. Sample 11 1 10 9 3 4 8 7 Wm W n 0.15 0. Chargeability. a PVC tube (15 mm in external diameter. 3. 1999). As for the differential polarizability. a multifunctional measuring device developed at the Russian Institute of Exploration Geophysics (VIRG–Rudgeofizika). we refer to them hereafter as quartz–water–air (QWA) and quartz–water–kerosene (QWK) samples. in particular in the vadose zone.31 0.Reproduced from Vadose Zone Journal..44 0. the voltage decay.43 0. 1993.25-mm grain size was cleaned from clay and dust particles by repeated washing. to measure the voltage across the sample. The chargeability shows a maximum at W ⫽ 0. The employed transmitter is capable of switching off the current within several microseconds. and 100 mm long). was used in conjunction with a preamplifier with 90 M⍀ input resistance. Lesmes and Frye.to 0.62 g cm⫺3.3 mV V⫺1. As usual in the TD technique. For the measured time range the differential polarizability graphs show relatively weak time dependency.26 0. where pulses and pauses of the same duration were used (50% duty cycle).08. RESULTS Time Dependence of Differential Polarizability Examples of observed differential polarizability vs.51 Measurement Setup As the sample holder. The dynamic range of the instrument is 160 dB. The porosity was found to vary slightly with water saturation. We believe that these porosity variations are related to the repacking of samples and thus represent an experimental error. Rectangular current pulses of opposite polarity were injected into the sample using a laboratory transmitter. time are shown in Fig. U(t ). 2001. and porosity n. was sampled in a sequence of time windows during current offtime..47 0. Physical characteristics of investigated sand samples showing mass water content Wm.03 0..45 0.74 1. we also calculated the normalized chargeability (MN).49 0.53 1. we prepared samples with the same water content where the unsaturated (airfilled) part of the pores was filled with kerosene. Seven unsaturated samples were prepared on the basis of evaporative drying at 70⬚C. Slater and Lesmes. and Normalized Chargeability The results of the measurements on the QWA and QWK samples are displayed as plots of chargeability. 6). given as MN ⫽ M/. . The quartz mineral density was 2. In addition to the unsaturated samples. To distinguish the two groups of samples. Sharapanov et al. The first sample was fully saturated with 100 mg L⫺1 NaCl solution. Two Cu/CuSO4 nonpolarizing electrodes were symmetrically placed on the tube. These samples were initially saturated with water of different salinity to obtain the same value of 100 mg L⫺1 salinity in the residual water by the end of the drying. After the drying procedure the unsaturated samples were kept isolated from the atmosphere for a week to reach equilibrium between the liquid and solid phases. The differential polarizability slightly decreases with increasing time for all values of water content and for both QWA and QWK samples.016 g cm⫺3 1. 1164 VADOSE ZONE J. Receiver and transmitter were synchronized using a quartz timer. depending on the saturation level. For the voltage measurements. the STROB-M instrument (Shereshevsky et al.36 1.44 0. VOL.052 0. The mass water content and the bulk density were controlled on the basis of weighing and a volume measurement taken just before repacking the samples into the electrical measurement holder.078 0. To prevent leakage of electrolyte from the electrodes into the sample. Measurements are controlled by a built-in microprocessor.. frequency for saturated soils (Vinegar and Waxman. which divides the plot into two regions. Sand particles were of isometric form. 2004) were previously reported. Similar behavior of the phase of complex electrical conductivity vs. Bo¨rner et al.4 to 32.45. resistivity. Resistivity.081 0. and Ui is the average of the measured voltage during current on-time. to separate the effects of conduction and polarization.55 1.043 0. 1959. 12 mm in internal diameter. The chargeability was found to lie in the range of 2. Published by Soil Science Society of America. for soils contaminated by organic and inorganic substances (Bo¨rner et al. (2002). and normalized chargeability vs. The value recorded for time window i is given by 100 i ⫽ (tk⫹1 ⫺ tk)Ui tk⫹1 冮 U(t)dt (%) [14] tk where tk and tk⫹1 are the integration limits. The sample porosity range corresponds to a loose grain packing. NOVEMBER 2004 We calculated the bulk resistivity () of the sample from the measured voltage U0. All copyrights reserved.63 1. All measurements were made in a Faraday cage to reduce electromagnetic noise. bulk density . The volumetric water content and the porosity were calculated (Table 1). The power-law exponent was found to be 0. with slightly different exponents for the QWA (0. volumetric water content (W ) for quartz– water–air (open symbols) and quartz–water–kerosene (solid symbols) samples.08. Numbers on the graphs show the values of volumetric water content.53) and QWK (0. Chargeability vs.36) samples.08. the overall behavior can be roughly approximated by a power-law relationship. Resistivity vs. The resistivity of the QWA and QWK samples (Fig. 7) shows a similar behavior to that observed for chargeability and differential polarizability. Differential polarizability vs. (1982).08. volumetric water content (W ) for quartz–water– air (open symbols) and quartz–water–kerosene (solid symbols) samples.21 for W ⬍ 0. Fig. Fig. The maximum type behavior is in accordance with data reported in Komarov (1980) and Iliceto et al. www. Note the similarity of relationships for QWA and QWK samples. . and 1. Accordingly.08. Notice the maximum type behavior of the relationship. 5.org 1165 Fig.08 and 0. with a maximum occurring at W ⫽ 0. 6. each characterized by a power-law relationship. Published by Soil Science Society of America. time for (a) quartz–water–air (QWA) and (b) quartz–water–kerosene (QWK) samples for different volumetric water contents. Figure 8 shows the normalized chargeability of the QWA and QWK samples. 7.3 for W ⬎ 0. Note that the limit between the two regions (hereafter referred to as Region 1 and Region 2) determined from the resistivity measurements coincides with the water content value where maximum chargeability is observed. The plot can be also split into two regions. For both sample types the normalized chargeability shows a trend to increase with increasing water content. The powerlaw exponent calculated according to Archie’s Law (1942) was found to be 1.Reproduced from Vadose Zone Journal. Each curve is plotted on the basis of 59 data points evenly spaced on log scale. Solid lines show a power-law fit to the data for the two identified regions.21 for W ⬍ 0.vadosezonejournal. All copyrights reserved. The resistivity varies from 290 to 3600 ⍀ m depending on the saturation degree.3 for W ⬎ 0. 6 and 7). 1980). and similarly. the largest cells should drain first. In contrast to our data.1. To explain the chargeability behavior. 7). Therefore. Moreover. That is. The polarization of unsaturated cells should be higher than that of saturated cells because the variation in the effective pore radii becomes larger. Compared with the saturated cells. the narrow passageways). respectively. In the course of the drying procedure the number of unsaturated cells increases.g. 1166 VADOSE ZONE J. (W) shows a power-law relationship with a typical value of the power-law exponent (1. which produces high values of ⌬t. Because of surface tension the water also moves from cell centers into areas of grain contacts that produce unsaturated cells. The solid curve indicates the supposed behavior of normalized polarizability. Realistically. a decrease of the difference in ion transparency (Fig. NOVEMBER 2004 Fig.” can be considered as the large pores.21). chargeability of the entire sample decreases. Numbers show the corresponding power-law exponents. All copyrights reserved. that in Region 1 chargeability and resistivity decrease similarly with increasing water content (Fig. for the compact packing the section is of curvilinear triangle type. and thus forming “rings. these unsaturated cells should polarize differently. This in turn can result in a decrease of the variation of effective pore diameters and. the difference in ion transparency should be small (Fig. 8. Komarov. the polarization of the cells decreases. VOL. is limited by the total number of polarizing cells. 2e and 2f). 6). If sands are fully saturated (Fig. 2. The further decrease of the grain-contact water volume in the unsaturated cells in the course of drainage causes a reduction of both the diameter and thickness of the grain-contact water rings (Fig. in contrast to saturated cells. It may be noted though. the entire water in the pore space tends to transform into bond water. This increase of polarization. The bound water film on the grains corresponds to the narrow pore. Power-law fits to the data are shown by the dotted (QWA samples) and the dashed (QWK samples) lines.e. 2c and 2d. Moreover the effective diameter of the narrow pore seems to be much larger than the Debye length. It is only a rough approximation to assume that. and therefore also the variation in the ion transparency. upper graphs). The moderate saturation level corresponds to the transition between high and low saturations. let us assume that the samples are composed of spherical particles of the same size with a packing from loose to dense (Fig. 4). At high saturation levels (Region 1). there are two limiting cases for the form of polarizing cells. . 2a and 2b). a decrease of the power-law exponent with decreasing saturation is actually visible in the data (Fig. unsaturated cells cannot be electrically shunted by current flowing through the bulk solution. and correspondingly also the polarization of the whole sample (Fig. Most current density lines follow the way of minimum resistance in the bulk solution. however. for two samples in their study (corresponding to a drainage cycle).. 6). depending on the packing type. with further decrease of the saturation level (Fig. 2). Published by Soil Science Society of America. and the part of current flowing through the polarizable part of the cells near the grain contact becomes small. Normalized chargeability vs. We believe that the weak increase of resistivity with decreasing water content below the critical saturation is related to electrical conduction through water films surrounding the solid grains (i. As shown in Fig. consequently.. consequently.Reproduced from Vadose Zone Journal.25-mm sand samples. 2004). which corresponds to the region of critical saturation (Knight and Nur. We believe that the mechanism described above gives rise to the observed maximum of chargeability. This behavior is in agreement with data from Taylor and Barker (2002). considered as a capacitance/conductance ratio.to 0. and that the maximum will be reached when all saturated cells are transformed into unsaturated cells. DISCUSSION We measured IP on 0. in the course of evaporative drainage. 3. the power-law exponent becomes considerably smaller (0. Areas of grain contact filled with water. as shown in Fig. The further decrease of water content (Region 2) in the course of drying mainly affects the water rings. 6b and 6c in Ulrich and Slater.. Ulrich and Slater (2004) approximated the dependence of real conductivity on saturation by a single power-law relationship. The particle packing determines these forms: for the loose packing the section of inter-grain-filling water is of curvilinear rhomb type. lower graphs). these cells can be represented by a sequence of one large pore and three or four narrow pores. The bound water film should roughly correspond to narrow pores 10 to 100 times larger than the Debye length (Fig.3) according to Archie’s Law (1942) (Fig. However. volumetric water content (W ) for quartz–water–air (QWA) (open symbols) and quartz–water–kerosene (QWK) (solid symbols) samples. The polarization of these saturated cells is low because they are electrically shunted. At moderate saturation degrees (Region 2). The resistivity shows the typical dependence on water content (e. and they should release the intergrain-filling water first. may be explained in this region also by the variation of resistivity. 4. Therefore the variation of chargeability. 4. cells lose the water simultaneously and uniformly. except that we did not reach the third region of very low saturation where the resistivity increases at an increasing rate with decreasing saturation. 1987). Issledovanie sviazi yavlenia vyzvannoi polarizatsii s electrokineticheskimi svoistvami kapillarnyh sistem (A study of the relationship between the induced polarization phenomenon and the electrokinetic properties of capillary systems). 1987. F. The presented data do not show large differences in the electrical properties for QWA and QWK samples. Gruhne. Veronese. The electrical resistivity log as an aid in determining some reservoir characteristics. Therefore we believe that for such simple system as investigated here. New York. M. J. 92–111. we believe that the normalized chargeability actually increases with increasing water content up to the critical saturation and then becomes constant (solid curve in Fig. however. Therefore. and J. 51:62–65. We therefore believe that kerosene played an inert role and did not produce additional polarizing cells and charged interfaces.A. In J. 1980. 1959.J. two-dimensional) model to quantify the polarization of saturated and unsaturated sequences of narrow and large pores in terms of resulting differences in cation transparency (for negatively charged surfaces). Geophysics 52:644–654.A. Although the spreading of data points is large. application of the IP method in hydrocarbon contamination studies will probably always require some sort of site-specific calibration. for their constructive comments. F. is a prerequisite for exploiting the potential of the IP method proved for saturated environments. Lucchesi.. S. water content relationship (Fig. as well as an anonymous reviewer. G. and A. We also note that this supposed behavior of normalized chargeability seems to be confirmed by part of the data presented in Ulrich and Slater (2004. Electr. The replacement of air by kerosene did not produce significant changes in both resistivity and chargeability distributions. Moreover we acknowledge helpful discussions with Vladimir Komarov and Ivan Kharkhordin. 44:583–601. Casalini. Insul. and J.. M. Prospect. 146:54–62. Eng. saturation levels below the critical saturation do not frequently occur. R. A relation between the quadrature component of electrical conductivity and the specific surface area of sedimentary rocks. Bo¨rner. 41:83–98. www. New York. John Wiley and Sons. Min.) Vestnik Leningradskogo Universiteta. sedimentary and metamorphic rocks. which is expected to contribute to an improved understanding of IP signatures in vadose zone studies. Metall. Chem. Inst.H. and M. 6a). ACKNOWLEDGMENTS We thank Vladimir Tarasov and Vladimir Chernysh for their contribution to the laboratory IP measurements. However. Effect of wettability on the electrical resistivity of sand. this critical saturation corresponds to the change of the pore-water geometry from bulk water to an adsorbed water film. We presented a simple. Binley. analytical capillary “slit” (i. Finally. Bo¨rner.) Overvoltage research and geophysical applications.R. Geophys. Pet.V. however..S. The sphere. Geophysics 56:2139–2147. Knight. Schopper. Hysteresis in the electrical resistivity of partially saturated sandstones. 1974. and B.49 for QWK samples). Slater. An approach to the identification of fine sediments by induced polarization laboratory measurements.1167 Reproduced from Vadose Zone Journal. Electrorazvedka metodom vyzvannoi polarizat- . 1993. 2001. Dielectric phenomena and the double layer in disperse systems and polyelectrolytes. Contamination indications derived from electrical properties in the low frequency range.. Prospect. IEEE Trans. the influence of nonaqueous phase liquids on the IP response of partly water-saturated porous media will generally depend on the mineralogy of the solid matrix and the chemistry of the different phases filling the pore space. Nur. In the previous section we used power-law fits to describe the overall trend of the normalized chargeability vs. Bo¨rner. Knowing this relationship. Capaccioli. Keller. According to our conceptual model. and A. Knight.58 for QWA and 0. New York. p. Crosshole IP imaging for engineering and environmental applications. V.N. CONCLUSIONS As a result of our experiments we detected the point of critical water saturation from both resistivity and chargeability measurements.) Surface and Colloid Science.vadosezonejournal. Dielectr. However. Evaluation of transport and storage properties in the soil and groundwater zone from induced polarization measurements. 2004. Phys. Rolla. R. Komarov.V. Seria Chimia 4:222–226 Iliceto. Sidorova. Scho¨n. Vol. M. 8).R. S. REFERENCES Archie. and P. Fridrikhsberg. The Log Analyst 32:612–613. Oil Gas J. Pergamon Press. Trans. J. Shilov. Keller.e. A.. 1974. 1996. John Wiley and Sons. Analysis of some electrical transient measurements on igneous. which helped to improve the manuscript. In terms of electrical properties the critical saturation can be related to the disappearance of the linear relationship between chargeability and resistivity for higher saturation degrees. Derjaguin. Geophysics 69:97–107.S. and S. Am. Therefore. Geophys.D. see their Fig. for instance for improved lithological characterization or estimation of hydraulic permeability.. Fixman. 1953. the polarization of multiphase porous systems can be theoretically predicted with higher accuracy. 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