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Study of the properties of non-gas dielectric capacitors in porous media

Study of the properties of non-gas dielectric capacitors in porous media Pet. Sci. (2015) 12:104–113 DOI 10.1007/s12182-015-0015-z OR IGINAL PAPER Study of the properties of non-gas dielectric capacitors in porous media • • Hong-Qi Liu Yan Jun You-Ming Deng Received: 2 April 2014 / Published online: 1 February 2015 The Author(s) 2015. This article is published with open access at Springerlink.com Abstract The size of pores and throats is at the nano- calculated, and its polarization and relaxation mechanisms meter scale in tight oil and shale gas zones, and the are analyzed. resistivity of these reservoirs is very high, so the reservoirs show more dielectric properties than conductivity proper- Keywords NaCl solution  Debye model  Single micro ties. The conductive and dielectric characteristics of a ion capacitor  Dielectrics  Micro capacitivity parallel plate capacitor full of fresh water, NaCl solutions, and solid dielectrics, for example, sands are investigated in this paper, and the capacitance data of the non-gas capac- 1 Introduction itor are measured at different salinities and frequencies by a spectrum analyzer. The experimental results illustrate that As we know, rocks have both conductive and dielectric the capacitance of this kind of capacitor is directly pro- properties. The conductivity is completely determined by ? 2? 2? ? portional to the salinity of the solutions and inversely various anions and cations, such as Na ,Mg ,Ca ,K , - - - 2- 2- proportional to the measuring frequency, the same as a Cl ,OH , HCO ,SO , and CO in water solution in 3 4 3 vacuum parallel plate capacitor. The remarkable phenom- the intergranular pores of rocks. Which property of the enon, however, is that the capacitance is inversely pro- rocks will play a predominant role depends on the salinity, portional to the square of the distance between two plates. porosity, permeability, and the geometric structure of the The specific characteristic of this capacitor is different pores. In fact, almost all substances in nature are dielec- from the conventional parallel plate capacitor. In order to trics, and only a few have conductivity (r) (Havriliak and explain this phenomenon, the paper proposed a new con- Negami 1966). The conductive paths of these charges are cept, named ‘‘single micro ion capacitor’’, and established usually continuous in relatively high porosity and high a novel model to describe the characteristics of this par- permeability reservoirs, but in most occasions, they are ticular capacitor. Based on this new model, the theoretical discontinuous in tight oil and shale gas zones, or in the low capacitance value of the single micro ion capacitor is porosity and low permeability reservoirs (Gasparrini et al. 2014; Ghanizadeh et al. 2014). Therefore, the electric properties of rocks include two major aspects: one is the conductive capability of free positive and negative charges H.-Q. Liu (&)  Y.-M. Deng in the water solution through the paths formed by pores and State Key Laboratory of Oil and Gas Reservoir Geology and throats which connected with each other; the other is the Exploitation, Southwest Petroleum University, dielectric capability of the bound charges of the non-con- Chengdu 610500, Sichuan, China ductive substances and particles, including rock matrix e-mail: lhqjp1@126.com particles, oil or gas molecules, and pure water molecules Y. Jun (Freedman and Vogiatzis 1979; Jonscher 1983; Endres and Centrica Energy (E&P) Upstream Kings Close, 62 Huntly Street, Bertrand 2006). Nevertheless, whether conductive or Aberdeen AB 101 RS, UK dielectric, the current paths in the formation are influenced by the geometric pore structure of rocks. The relationship Edited by Jie Hao 123 Pet. Sci. (2015) 12:104–113 105 between the conductive and dielectric properties of rocks negative ions dissolved in water solution. Generally, these ? - and the pore structure has been widely discussed in detail different ions can be equivalent to Na and Cl in view of in the literature (Toumelin and Torres-Verdin 2009), so it their conductive property. Therefore, it is crucial to study is not described here. Prior to 1940, studies on the electrical the conductive and dielectric properties of NaCl solutions properties of rocks mainly focused on conductivity. In (Jonscher 1999; Lesmes and Morgan 2001). The pure water 1941, K. S. Cole and R. H. Cole established the Cole–Cole and hydrocarbon molecules cannot conduct current, and the model for dielectric constants (Cole and Cole 1941); later, conductive ions are separated from each other by water and many scholars studied ionic conduction and rock polari- hydrocarbon molecules, as shown in Fig. 1. So the solution zation processes, analyzing the dielectric constant property in the pores can be regarded as a mixture of non-conductive of non-homogeneous multi-pore materials (Hilfer et al. molecules and conductive free ions (Fig. 2). Considering 1995, 1999; Nover et al. 2000; Ruffett et al. 1991; the water and hydrocarbon molecules as non-conductive ? - Davidson and Cole 1950, 1951). land, the Na and Cl ions are an isolated conductive river With regard to the electrical logging technology in the separated by this land, and the ion river moves through this petroleum industry, almost all research has focused on the land in a tortuous path. Then a model with ‘‘ion flux’’ and detection and interpretation of formation resistivity. How- ‘‘molecule land’’ can be established to explain the con- ever, more and more complex and unconventional reser- ductive and dielectric mechanisms. In Fig. 1, the yellow or voirs have been discovered, and the traditional, simple gray blocks denote rock particles of different minerals, the geophysical conductive model cannot solve the problems of blue parts represent the formation water, the red belts strongly heterogeneous reservoirs, such as low porosity and denote hydrocarbons dispersed in the water, which are non- low permeability oil reservoirs, tight oil zones, and shale conductive parts; and the green solid ball denotes free Cl , gas zones. Although scholars have proposed various solu- the red solid ball denotes free Na , which are conductive tions and models for some important questions to describe parts. Of course, the rock matrix is also non-conductive. the electrical conductivity mechanism in rocks (Chelidze Figure 2 illustrates the distribution of the non-conductive and Gueguen 1999; Chelidze et al. 1999; Asami 2002), it is molecules of water and hydrocarbon, and the conductive ? - increasingly difficult to accurately determine fluid types and ions of Na and Cl in an external electromagnetic field calculate the saturation of hydrocarbon. In 1988, Clark et al. (EMF). If an alternating EMF, such as I ¼ I sinðxt þ h Þ, 0 0 proposed an electromagnetic propagation tool (EPT) to is applied on both sides of rocks, the free ions will be measure the dielectric constant of the formation at fre- rearranged quickly according to the external EMF, resulting quencies of 2 MHz–1.1 GHz (Glover et al. 1994a, b, 1996; in a regular arrangement of ions. The rearranged ions move Clark et al. 1990). This method can identify fluid types and directionally under the effect of the external EMF as shown calculate the fluid saturation in high porosity and high in Fig. 3. These ions gradually move to the ends of mineral permeability reservoirs. Dong and Wang (2009) studied the grains through pores. Generally the Cl ions gather at the dielectric constant of several common minerals, including anode, and Na ions gather at the cathode. An internal quartz, calcite, and dolomite, within a frequency range from electric field is created in the rock, whose field direction is Hz to GHz level, and they identified pore structures and the opposite to the external field. The time of this process distribution of formation water using the dielectric constant. depends on the conductive properties of rocks. But after the In 1985, Lockner and Byerlee (1985) studied the complex established relatively stable EMF within a remarkably short resistivity of rocks; later, other scholars also studied the complex resistivity of rocks. However, due to the extraor- dinarily complex heterogeneity of porous rocks, there are still many disputes over the conductive and dielectric mechanisms in rocks (Clavier et al. 1984; Zemanek 1989; Hamada and Al-Awad 1998). Scholars have proposed many conductive models for rocks, of which the most represen- tative is the dual-water argillaceous sandstone conductive model proposed by Waxman and Smits in 1968 (Waxman and Smits 1968; Knight and Nur 1987; Hassoun et al. 1997). 2 Micro ion capacitor model Fig. 1 Schematic diagram of a rock with pure water (blue), ? - Obviously, the conductive and dielectric capabilities of hydrocarbon (red belt), and Na (small red ball) and Cl (large rocks depend on the amount of different positive and green ball) in the rock 123 106 Pet. Sci. (2015) 12:104–113 Fig. 2 Distribution of the non- conductive water and hydrocarbon molecules and ion flux without external EMF with poor connectivity, the occurring phenomenon is shown in Fig. 5. In tight oil and shale gas zones, several anions and cations respectively gather at the opposite ends of the particle as polar plates like a usual parallel plate capacitor, whereas the non-conductive molecules in the middle are dielectrics, thus a microscopic capacitor, called a ‘‘micro ion capacitor’’, is established. Numerous such micro ion capacitors can be created almost at the same time in the formation, and they may be connected in series or parallel. 3 Theoretical value of single ion capacitor ? - ? The radii of Na ,Cl , and H ions are 0.95, 1.81, and 2.08 A, respectively. The size of the pore throats in rocks Fig. 3 Schematic diagram of a rock with pure water (blue), ranges from several to more than 10 microns, and the hydrocarbon (red belt), and ions traversing through the rock under thickness of the water membrane is less than 1 micron. The the influence of an external electromagnetic field (EMF) space for ion transportation is tens of thousands of times time, the amount of free ions in rock pores becomes less and larger than the ion diameter. As shown in Fig. 5, there may less, and the ions and molecules form a new distribution, as be at least tens of thousands of positive and negative ions shown in Fig. 4. gathering at the ends of rock particles in the water-wet The movements of the positive and negative ions result phase, and a microscopic capacitor is formed with Na and in the establishment of a capacitor. The positive pole is Cl ions as two polar plates, with the rock particles ? 2? 2? ? composed of cations, such as Na ,Ca ,Mg , and K , wrapped by water membrane with a certain thickness as a - - the negative pole is composed of anions, such as Cl ,OH , dielectric. Although the capacitance of this micro ion 2- and SO , and the dielectric is water or hydrocarbon capacitor cannot be accurately calculated at present, a molecules. From this moment on, the rocks will show theoretical value can be estimated. dielectric properties rather than conductivity at the macro If the pores are very small and are not connected, ions level. are likely to form isolated capacitors with water molecules The polarization process above, perhaps will not exist in as dielectric. In case of extreme conditions, a single ion and high porosity and especially high permeability reservoirs. a single water molecule constitute a micro ion capacitor, as As for tight formations, the pore throats are very narrow. shown in Fig. 6. According to the definition of a capacitor, For example, when the pores are at the nanometer scale assuming the voltage of an external EMF is 1 V, the 123 Pet. Sci. (2015) 12:104–113 107 Fig. 4 The non-conductive water and hydrocarbon molecules and ions form a micro ion capacitor with an external EMF (–) (+) (–) Fig. 5 A single water-wet mineral particle with ions at two sides H forming a micro ion capacitor (+) ? -19 Fig. 6 A single ion capacitor, one sodium ion and one chloride ion quantity of the charge for example Na is 1.6 9 10 C, respectively as positive and negative plates with a non-conductive then the capacitance of a single ion capacitor is: H O molecule as media Q 1:6  10 C C ¼ ¼ ¼ 1:6  10 F ð1Þ V 1V 4.2 Experimental process 4 Experiments First, fresh water with different volumes was injected into the PVC pipe, and the upper plate was put at different 4.1 Experimental instrument distances corresponding to the fluid volume. Then the resistance (R ) and capacitance (C ) were tested with a p p Figure 7 illustrates a measuring device using a PVC pipe frequency spectrum analyzer. In this experiment, 12 groups with a diameter of 2.5 cm and a length of 150 cm. Two of data were recorded at 12 different distances. At each test plates were placed, one was fixed on the bottom, the other point, R and C were tested at frequencies of 100 Hz and p p was movable on the top, and the pipe was full of NaCl 1 kHz, where the subscript ‘‘p’’ means parallel connection. solution. So the resistivity and capacitance of NaCl solu- Second, NaCl solution was injected into the same pipe. tion can be detected at different distances, salinities, and Then, we repeat the experimental process like that of fresh frequencies. One important aspect must be noted that the water, 12 groups of data of R and C of NaCl solution with p p material of plates should be gold, rather than iron, alumi- salinities of 0.2 and 1.2 g/L were recorded. The capacitance num, copper, and others, to avoid corrosion by the NaCl data are listed in Table 1 and resistance data in Table 2. solution. 123 108 Pet. Sci. (2015) 12:104–113 Table 2 Resistance (R , X) at different salinities (S), frequencies (f), and distances (d) in the PVC pipe d (m) S (g/L) Water 0.2 1.2 0.2 1.2 f (Hz) 100 1 k 0.1 23.1 3.19 0.56 3.08 0.51 0.2 45.1 6.24 1.01 6.14 0.96 0.3 67.45 9.35 1.47 9.25 1.43 0.4 90.44 12.42 1.92 12.32 1.88 0.5 113 15.56 2.38 15.46 2.34 0.6 136 18.61 2.85 18.5 2.81 0.7 159 21.77 3.3 21.67 3.26 0.8 183 24.9 3.78 24.79 3.74 Fig. 7 A PVC pipe with copper wireline and full of NaCl solution, 0.9 205 27.92 4.22 27.82 4.18 the dimension is length 9 diameter = 150 cm 9 2.5 cm 1.0 228 31.1 4.69 30.96 4.65 1.1 253 34.21 5.15 34.1 5.12 Figure 8 illustrates a plastic container, with a dimension 1.2 277 37.3 5.61 37.2 5.57 of 17 cm 9 5.0 cm 9 4.7 cm, filled with sand which is saturated with NaCl solution. The sand was collected from a river, and was washed many times. Moreover, the sand was The measurement results of C are listed in Table 3 and filtered by a sorting sieve in order to keep sand almost at the R in Table 4, the distance and frequency changed with a same size. Its mineral composition is mainly quartz. During fixed salinity of 1.5 g/L. the experiments, the conditions were changed as follows: Table 5 lists the capacitance data of sand saturated with NaCl solution with different salinities and a fixed distance (1) The distance between the polar plates varied from 2 of 17 cm, and Table 6 lists the resistance data of sand to 17 cm, with eight test points; saturated with NaCl solution with different salinities and a (2) The frequency changed from 4 Hz to 5 MHz, with fixed distance of 17 cm. 100 test points, only seven points listed in the tables; (3) The salinity varied from 1.5 to 200 g/L, with eight test points. 5 Analysis of experimental results 5.1 Relationship between conductive and dielectric Table 1 Capacitance (C , lF) at different salinities (S), frequencies (f), and distances (d) in the PVC pipe properties and the distance between plates d (m) S (g/L) Based on the experimental results in the PVC pipe, and the Water 0.2 1.2 0.2 1.2 data in Table 1, Fig. 9 demonstrates the characteristics of f (Hz) this capacitor with fresh water and 0.2 and 1.2 g/L NaCl 100 1 k solutions at 100 Hz and 1 kHz. The capacitance changes with different salinities of the solution and different dis- 0.1 970 23,500 286,000 642.0 11,200 tances between the two plates. Generally, we can conclude 0.2 252 6,170 83,800 160.0 3,010 as follows: 0.3 112 2,730 39,900 71.0 1,340 0.4 61 1,550 22,500 39.0 763 (1) Under the same conditions, the higher the salinity, 0.5 41 976 15,100 24.0 491 the larger the capacitance; 0.6 25 694 10,300 18.1 345 (2) Under the same conditions, the higher the frequency, 0.7 21 510 7,730 13.0 248 the lower the capacitance; 0.8 15 371 5,760 10.0 192 (3) Under the same conditions, the capacitance is 0.9 12 303 4,820 8.0 153 approximately inversely proportional to the square 1.0 9 241 3,740 6.0 121 of the distance. 1.1 7 201 3,150 5.0 98 As shown in Fig. 9, there are five different curves, 1.2 6 165 2,550 4.5 82 corresponding to 1.2 g/L salinity at 100 Hz, 0.2 g/L 123 Pet. Sci. (2015) 12:104–113 109 4 Hz to 5 MHz and with different salinities, and all of the results prove the same rule, that is, the capacitance is approximately inversely proportional to the square of the distance. Why does this phenomenon occur? It is well known that the capacitance of a parallel plate capacitor is proportional to the area of the plate (A), and is inversely proportional to the distance between the plates (d), denoted by Eq. (2) C ¼ e ð2Þ But for the PVC pipe capacitor, according to the defi- nition of capacitance and the rule mentioned above, the equation of C can be expressed by C ¼  ; ð3Þ Fig. 8 A plastic container with copper plate and sand saturated with p NaCl solution, the dimension is length 9 width 9 height = 17 cm 9 5.0 cm 9 4.7 cm where  is a coefficient. The key point should be noted that is not the dielectric constant e because the units of these two parameters are different, and then the physical defi- salinity at 100 Hz, 1.2 g/L salinity at 1 kHz, fresh water at nition is also different. Based on SI unit, the dimension of 100 Hz, 0.2 g/L salinity at 1 kHz, respectively. It can be is F, which is the same as capacitance. Here, we call  as seen that with either the fresh water or the NaCl solution, micro capacitivity. either at 100 Hz or 1 kHz, the capacitance is a function of According to Eq. (3),  can be expressed as follows: the square of the distance. By the least square method, we know that the distance’s exponent of each curve is very ¼ C ð4Þ close to two. We test it at many different frequencies from Table 3 Capacitance (C , lF) of sands saturated with NaCl solution at different frequencies and distances in a plastic container f,Hz d,cm 17 15 13 10 8 5 3 2 4 1.40E?02 1.79E?02 2.39E?02 4.22E?02 6.37E?02 1.60E?03 4.41E?03 9.88E?03 10.2 7.06E?01 8.93E?01 1.19E?02 2.11E?02 3.14E?02 8.02E?02 2.23E?03 5.01E?03 70.1 6.95E?00 8.92E?00 1.29E?01 2.01E?01 3.13E?01 8.02E?01 2.29E?02 5.00E?02 286.8 1.40E?00 1.79E?00 2.38E?00 4.01E?00 6.04E?00 1.58E?01 4.36E?01 9.74E?01 1019.1 1.87E-01 2.42E-01 3.15E-01 5.38E-01 8.31E-01 2.14E?00 5.41E?00 1.32E?01 5029.1 1.40E-02 1.70E-02 2.30E-02 3.80E-02 6.10E-02 1.57E-01 4.34E-01 9.81E-01 10,171 3.00E-03 4.00E-03 6.00E-03 1.00E-02 1.60E-02 4.00E-02 1.20E-01 2.23E-01 Table 4 Resistance (R , X) of sands saturated with NaCl solution at different frequencies and distances in a plastic container f,Hz d,cm 17 15 13 10 8 5 3 2 4 1.67E?02 1.64E?02 1.60E?02 1.54E?02 1.51E?02 1.47E?02 1.42E?02 1.35E?02 10.2 1.17E?02 1.13E?02 1.08E?02 1.01E?02 9.65E?01 9.17E?01 8.86E?01 8.66E?01 70.1 7.42E?01 6.86E?01 6.24E?01 5.38E?01 4.81E?01 4.07E?01 3.66E?01 3.48E?01 286.8 6.19E?01 5.60E?01 4.94E?01 4.01E?01 3.37E?01 2.49E?01 1.98E?01 1.75E?01 1019.1 5.77E?01 5.17E?01 4.50E?01 3.54E?01 2.88E?01 1.92E?01 1.33E?01 1.03E?01 5029.1 5.60E?01 4.99E?01 4.32E?01 3.35E?01 2.68E?01 1.70E?01 1.07E?01 7.43E?00 10,171 5.57E?01 4.96E?01 4.28E?01 3.32E?01 2.65E?01 1.67E?01 1.03E?01 6.99E?00 123 110 Pet. Sci. (2015) 12:104–113 Table 5 Capacitance (C , pF) varies with frequency (f) and salinity (S) f,Hz S, g/L 1.5625 3.125 6.25 12.5 25 50 100 200 4 8.31E?03 1.95E?04 4.32E?04 8.23E?04 1.36E?05 2.13E?05 3.03E?05 3.43E?05 6.1 4.75E?03 1.16E?04 2.70E?04 5.52E?04 9.69E?04 1.57E?05 2.28E?05 2.60E?05 9.8 2.43E?03 6.24E?03 1.53E?04 3.35E?04 6.39E?04 1.08E?05 1.65E?05 1.87E?05 15.6 1.20E?03 3.21E?03 8.28E?03 1.93E?04 3.98E?04 7.30E?04 1.17E?05 1.34E?05 25 5.73E?02 1.60E?03 4.29E?03 1.05E?04 2.35E?04 4.62E?04 8.07E?04 9.23E?04 39.9 2.68E?02 7.66E?02 2.12E?03 5.42E?03 1.28E?04 2.75E?04 5.27E?04 6.14E?04 63.9 1.23E?02 3.61E?02 1.03E?03 2.67E?03 6.66E?03 1.53E?04 3.18E?04 3.83E?04 102.1 5.53E?01 1.66E?02 4.86E?02 1.29E?03 3.30E?03 7.97E?03 1.78E?04 2.25E?04 163.3 2.46E?01 7.53E?01 2.26E?02 6.12E?02 1.60E?03 3.96E?03 9.35E?03 1.25E?04 261.1 1.08E?01 3.36E?01 1.03E?02 2.85E?02 7.58E?02 1.92E?03 4.68E?03 6.86E?03 417.6 4.80E?00 1.48E?01 4.64E?01 1.31E?02 3.55E?02 9.08E?02 2.28E?03 3.80E?03 1,708 4.50E-01 1.26E?00 3.99E?00 1.17E?01 3.35E?01 8.97E?01 2.34E?02 7.68E?02 4368.4 1.20E-01 2.70E-01 7.80E-01 2.26E?00 6.57E?00 1.81E?01 4.83E?01 2.72E?02 17,867 4.00E-02 5.00E-02 8.00E-02 1.70E-01 4.50E-01 1.16E?00 3.11E?00 4.99E?01 32,895 4.00E-02 4.00E-02 4.00E-02 4.00E-02 7.00E-02 8.00E-02 1.20E-01 2.05E?01 45,695 3.00E-02 3.00E-02 3.00E-02 1.00E-02 -2.00E-02 -1.60E-01 -5.80E-01 1.16E?01 186,900 3.00E-02 2.00E-02 1.00E-02 -3.00E-02 -1.20E-01 -4.40E-01 -1.35E?00 -1.81E?00 764,420 3.00E-02 2.00E-02 1.00E-02 -3.00E-02 -1.20E-01 -4.30E-01 -1.25E?00 -2.94E?00 1,955,000 2.00E-02 2.00E-02 1.00E-02 -3.00E-02 -1.20E-01 -4.00E-01 -1.09E?00 -2.44E?00 3,126,500 2.00E-02 2.00E-02 1.00E-02 -3.00E-02 -1.20E-01 -3.90E-01 -9.40E-01 -1.92E?00 5,000,000 2.00E-02 2.00E-02 0.00E?00 -3.00E-02 -1.30E-01 -3.70E-01 -7.40E-01 -1.32E?00 Cole and R. H. Cole found that the relaxation of most solid The experiments with the capacitor filled with sand dielectrics does not satisfy the Debye model. They cor- saturated with NaCl solution in a plastic container also rected the Debye model by taking into account the elec- show the same rule. From Fig. 10, it can be seen that the trical conductance, and they proposed the so-called Cole– capacitance is also approximately inversely proportional to Cole model, as shown in Eq. (6) the square of the distance between plates. The six curves in Fig. 10 were tested at six different e  e s 1 e ðxÞ¼ e þ ð5Þ frequencies. In fact, from 4 Hz to 5 MHz, we recorded 100 1 þ ixs groups of capacitance data, and each group shows the e  e s 1 e ðxÞ¼ e þ ; ð6Þ inversely proportional relationship between the capacitance 1a 1 þðixsÞ and the square of the distance. In the above experiments, the dielectrics are fresh water, where, e is the optical frequency dielectric constant, e is ? s pffiffiffiffiffiffiffi saline solution, or sand mixed with saline solution, which the static dielectric constant, i ¼ 1, s is the time con- have different salinities and different saturations. We can stant, and a is the empirical coefficient, 0 \ a \ 1. see that whether the measurement was carried out in a PVC The above two and other models, such as Lorentz– pipe or in a plastic container, and whether the measured Lorenz, Maxwell–Wagner, and Onsager models, describe dielectric is liquid or solid, all of the results indicate that the dielectric constant of isolated material. In our experi- the capacitance is approximately inversely proportional to ment, the medium is a mixture of conductive materials, ? - the square of the distance between plates. Such phenome- such as Na ,Cl , and other cations or anions, and insu- non may be related to the polarization and relaxation lating matter, such as water and hydrocarbon molecules. In processes. As early as 1929, Debye assumed that the dipole the pores of rocks, the conductive and non-conductive relaxation of a dielectric is a purely viscous process with- materials coexist, and in most cases, they can form out elastic forces, and established an equation to describe numerous micro capacitors, that is the micro ion capacitor the relationship of the dielectric constant and the angular mentioned before. Obviously, the inversely proportional frequency as shown in Eq. (5) (Debye 1929). In 1941, K. S. relationship between ionic capacitance and the square of 123 Pet. Sci. (2015) 12:104–113 111 Table 6 Resistance (R , X) varies with frequency (f) and salinity (S) f,Hz S, g/L 1.5625 3.125 6.25 12.5 25 50 100 200 4 7.94E?02 4.66E?02 2.83E?02 1.88E?02 1.27E?02 8.73E?01 6.52E?01 6.10E?01 6.1 7.64E?02 4.42E?02 2.62E?02 1.70E?02 1.14E?02 7.87E?01 5.86E?01 5.46E?01 9.8 7.40E?02 4.20E?02 2.44E?02 1.54E?02 1.01E?02 6.93E?01 5.15E?01 4.78E?01 15.6 7.21E?02 4.03E?02 2.30E?02 1.40E?02 8.98E?01 6.05E?01 4.46E?01 4.12E?01 25 7.09E?02 3.92E?02 2.19E?02 1.30E?02 8.05E?01 5.29E?01 3.81E?01 3.54E?01 39.9 7.00E?02 3.83E?02 2.12E?02 1.23E?02 7.38E?01 4.68E?01 3.25E?01 3.02E?01 63.9 6.94E?02 3.78E?02 2.07E?02 1.18E?02 6.92E?01 4.24E?01 2.83E?01 2.60E?01 102.1 6.91E?02 3.74E?02 2.03E?02 1.15E?02 6.61E?01 3.94E?01 2.53E?01 2.31E?01 163.3 6.88E?02 3.71E?02 2.01E?02 1.13E?02 6.40E?01 3.75E?01 2.33E?01 2.10E?01 261.1 6.86E?02 3.70E?02 1.99E?02 1.11E?02 6.27E?01 3.63E?01 2.20E?01 1.96E?01 417.6 6.85E?02 3.69E?02 1.98E?02 1.10E?02 6.17E?01 3.54E?01 2.12E?01 1.86E?01 1,708 6.84E?02 3.67E?02 1.97E?02 1.09E?02 6.03E?01 3.42E?01 2.00E?01 1.64E?01 4368.4 6.83E?02 3.67E?02 1.96E?02 1.08E?02 6.00E?01 3.39E?01 1.97E?01 1.52E?01 17,867 6.83E?02 3.67E?02 1.96E?02 1.08E?02 5.98E?01 3.37E?01 1.95E?01 1.38E?01 32,895 6.82E?02 3.67E?02 1.96E?02 1.08E?02 5.98E?01 3.37E?01 1.95E?01 1.34E?01 45,695 6.82E?02 3.66E?02 1.96E?02 1.08E?02 5.98E?01 3.36E?01 1.95E?01 1.32E?01 186,900 6.80E?02 3.66E?02 1.96E?02 1.08E?02 5.98E?01 3.37E?01 1.95E?01 1.29E?01 764,420 6.74E?02 3.64E?02 1.95E?02 1.08E?02 5.99E?01 3.39E?01 1.99E?01 1.33E?01 1,955,000 6.56E?02 3.57E?02 1.93E?02 1.07E?02 5.98E?01 3.46E?01 2.15E?01 1.58E?01 3,126,500 6.31E?02 3.47E?02 1.89E?02 1.05E?02 5.96E?01 3.55E?01 2.38E?01 1.98E?01 5,000,000 5.74E?02 3.22E?02 1.78E?02 1.01E?02 5.86E?01 3.75E?01 2.85E?01 2.92E?01 5.2 Preliminary explanation Water (100 Hz) 0.2 g/L (100 Hz) 1.2 g/L (100 Hz) The main reason of this remarkable phenomenon is that in 0.2 g/L (1 kHz) the pores and fractures, especially in tight oil and shale gas 1.2 g/L (1 kHz) zones, various ions, water molecules, and hydrocarbon 3 molecules can form numerous micro ion capacitors, which will parallel or series connect with each other. Compared with conventional capacitors, the outstanding characteristic 100 of this micro capacitor is that the length of the plates nearly equals the distance between the plates. The parameter A is the surface area of the ion, and the distance d is the diameter of water or hydrocarbon molecules. For the micro ion capacitor mentioned above, if one or ? - 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 several water molecules are dielectric, and Na and Cl or other cations and anions are plates, the distance between d, cm plates almost equals the size of ionic plates. Then the Fig. 9 The relationship of NaCl solution’s capacitance and the distance capacitance of micro ion capacitor also accords with the between plates at different salinities and frequencies. The capacitance rule as shown in Eq. (3). The diameter of a water molecular increases with increasing salinity and decreasing frequency, and is about 4 A, and we can estimate the capacitance of such a decreases with the increase of the square of the distance. 1. C = -2.0048 2 -1.9980 2 9.2428d , R = 0.9987; 2. C = 243.92d , R = 0.9998; 3. micro ion capacitor as follows: -1.9038 2 -2.009 2 C = 3841.50d , R = 0.9992; 4. C = 6.2724d , R = p p -1.981 2 A pr pð1:81=2Þ 0.9996; 5. C = 122.11d , R = 0.9997 C þ ¼  ¼  ¼ Na 2 2 2 d d ð4 þ 0:95=2 þ 1:81=2Þ the distance cannot be explained by either the Debye model ¼ 0:088851 ð7Þ or the Cole–Cole model. We should create a novel model to explain this rule. C, pF 112 Pet. Sci. (2015) 12:104–113 Fig. 10 The relationship 1.E+05 4 Hz 1019.1 Hz between capacitance and the 10.2 Hz 5029.1 Hz distance between two plates at 1.E+04 −1.9854 70.1 Hz 1017.1 Hz 1. C=39225d different frequencies. The figure 286.8 Hz R =0.999 illustrates the increase of the 1.E+03 −1.992 2. C=19912d capacitance with decreasing 1 R =0.9999 frequency, and the increase with 1.E+02 −1.9933 3. C=2005.4d a decrease in the square of the R =0.9997 distance, which is different from 1.E+01 −1.9828 4. C=383.61d conventional capacitors 4 2 R =0.9999 1.E+00 −1.973 5. C=50.194d R =0.9997 1.E−01 −2.0011 6. C=3.9099d 1.E−02 R =0.9999 −2.025 7 7. C=1.0189d 1.E−03 R =0.9977 0 1 2 3 4 5 6 7 8 9 1011 12131415161718 d, cm 2 novel concept and a model, single micro ion capacitor, are A pr pð0:95=2Þ C ¼  ¼  ¼ Cl first proposed in this paper. Based on the experimental 2 2 d d ð4 þ 0:95=2 þ 1:81=2Þ results, we found that: ¼ 0:024477 ð8Þ (1) The ionic capacitance is inversely proportional to the According to the theoretical value estimated in Eq. (1), square of the distance, which remarkably differs from the value of micro capacitivity  can be calculated: that of parallel plate capacitors with air dielectric; þ ¼ 1:80  10 pF; ð9Þ (2) Compared with conventional capacitors, the out- Na standing characteristic of a micro ion capacitor is ¼ 6:54  10 pF; ð10Þ Cl that the length of the plate nearly equals the distance ? - Because the different diameters of Na and Cl , the between the plates; -6 micro capacitivity  varies from 1.8 9 10 to 6.54 9 (3) Based on the micro ion capacitor model, the micro -6 -6 10 pF. capacitivity  varies from 1.8 9 10 to 6.54 9 -6 For capacitors with liquid and solid dielectrics, many 10 pF. aspects remain unclear, especially the mechanisms of Such phenomenon may be also related to the relatively polarization and relaxation. The reasons may be related to complex polarization and relaxation mechanisms of the the single ionic capacitors formed between free Na and numerous single micro ion capacitors, and another impor- Cl ions in the non-conductive liquid or solid molecules, tant reason may be the tortuosity of the ion conductive path and the single ionic capacitors are connected in series or in porous solid media, which will be discussed later. parallel. However, the distance between molecules in a gas dielectric or vacuum dielectric capacitor is too long to form Acknowledgments The authors are grateful for the financial sup- a microscopic capacitor. This may be the important reason port from Basic Science Program of Advanced Well Logging Tech- nology of CNPC (2014A-2319) and support from the Science and for the remarkable difference between these two types of Technology Program (G12-3) of State Key Laboratory of Oil and Gas capacitors. Another reason may be the complexity of Reservoir Geology and Exploitation of SWPU (Southwest Petroleum channels for ion transportation (Ma et al. 2014). University). Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, dis- 6 Conclusions tribution, and reproduction in any medium, provided the original author(s) and the source are credited. We measured the capacitance and resistance of non-gas dielectrics in a PVC pipe and a plastic container, and the References experimental results illustrated an unusual rule in the ionic capacitance of fluid or solid dielectrics. Although many Asami K. Characterization of heterogeneous systems by dielectric models have been established, there are still many prob- spectroscopy. Prog Polym Sci. 2002;27(8):1617–59. lems about the polarization and relaxation of the ions or Chelidze TL, Gueguen Y. Electrical spectroscopy of porous rocks: a review—I. Theoretical model. Geophys J Int. 1999;137(1):1–15. molecules under the external EMF that are not solved. A C, pF Pet. Sci. (2015) 12:104–113 113 Chelidze TL, Gueguen Y, Ruffet C. Electrical spectroscopy of porous Hamada GM, Al-Awad MNJ. Petrophysical evaluation of low rocks: a review—II. Experimental results and interpretation. resistivity sandstone reservoirs. International Symposium of Geophys J Int. 1999;137(1):16–34. Core Analysts. The Hague. 14–16 Sept 1998. Clark B, Allen DF, Best DL, et al. Electromagnetic propagation Hassoun TH, Zainalabedin K, Minh CC. Hydrocarbon detection in logging while drilling: theory and experiment. 1990. SPE low contrast resistivity pay zones, capillary pressure and ROS 18117-PA. determination with NMR logging in Saudi Arabia. SPE Paper Clavier C, Coates G, Dumanoir J. Theoretical and experimental bases 37770. 10th MEOS, Bahrain. 15–18 March 1997. for the dual-water model for interpretation of shaly sands. Soc Havriliak S, Negami S. A complex plane analysis of a-dispersions in Petrol Eng J. 1984;24:153–68. some polymer systems. J Polym Sci Part C. 1966;14(1):99–117. Cole KS, Cole RH. Dispersion and absorption in dielectrics. J Chem Hilfer R, Prigogine I, Rice SA. Transport and relaxation phenomena Phys. 1941;9(4):341–51. in porous media. Adv Chem Phys. 1995;92:299. Davidson DW, Cole RH. Dielectric relaxation in glycerine. J Chem Hilfer R, Widjajakusuma J, Biswal B. Macroscopic dielectric constant Phys. 1950;18(10):1417. for microstructures of sedimentary rocks. Granular Matter 2. Davidson DW, Cole RH. Dielectric relaxation in glycerol, propylene Berlin: Springer-Verlag; 1999. pp. 137–41. glycol and n-propanol. J Chem Phys. 1951;19(12):1484–90. Jonscher AK. Dielectric relaxation in solids. London: Chelsea Press; Debye PW. Polar molecules. New York: Chemical Catalog Co.; 1929. 1983. pp. 219–26. Dong XB, Wang YH. A broadband dielectric measurement technique: Jonscher AK. Dielectric relaxation in solids. J Phys D. theory, experimental verification, and application. J Environ Eng 1999;32:57–70. Geophys. 2009;14(1):25–38. Knight RJ, Nur A. The dielectric constant of sandstones, 60 kHz to Endres AL, Bertrand EA. A pore-size scale model for the dielectric 4MHz. Geophysics. 1987;52(5):644–54. properties of water-saturated clean rocks and soils. Geophysics. Lesmes DP, Morgan FD. Dielectric spectroscopy of sedimentary 2006;71:F185–93. rocks. J Geophys Res. 2001;106(B7):13329–46. Freedman R, Vogiatzis JP. Theory of microwave dielectric constant Lockner DA, Byerlee JD. Complex resistivity measurements of logging using the electromagnetic wave propagation method. confined rock. J Geophys Res. 1985;90:7837–47. Geophysics. 1979;44(5):969–86. Ma JS, Sanchez JP, Wu KJ, et al. A pore network model for Gasparrini M, Sassi W, Gale JFW. Natural sealed fractures in simulating non-ideal gas flow in micro- and nano-porous mate- mudrocks: a case study tied to burial history from the Barnett rials. Fuel. 2014;116(15):498–508. Shale, Fort Worth Basin, Texas, USA. Mar Petrol Geol. Nover G, Heikamp S, Freund D. Electrical impedance spectroscopy 2014;55:122–41. used as a tool for the detection of fractures in rock samples Ghanizadeh A, Gasparik M, Amann-Hildenbrand A, et al. Experi- exposed to either hydrostatic or triaxial pressure conditions. Nat mental study of fluid transport processes in the matrix system of Hazards. 2000;21(2–3):317–30. the European organic-rich shales: I. Scandinavian Alum Shale. Ruffett C, Gueguen Y, Darot M. Complex conductivity measurements Mar Pet Geol. 2014;51:79–99. and fractal nature of porosity. Geophysics. 1991;56(6):758–68. Glover PWJ, Gomez JB, Meredith PG, et al. Modelling the stress– Toumelin E, Torres-Verdin C. Pore-scale simulation of kHz-GHz strain behavior of saturated rocks undergoing triaxial deforma- electromagnetic dispersion of rocks: effects of rock morphology, tion using complex electrical conductivity measurements. Surv pore connectivity, and electrical double layers. In: SPLWA 50th Geophys. 1996;17(3):307–30. Annual Logging Symposium. 21–24 Jun 2009. Glover PWJ, Meredith PG, Sammonds PR, et al. Ionic surface Waxman MH, Smits LJM. Electrical conductivities in oil-bearing electrical conductivity in sandstone. J Geophys Res. shaly sands. Soc Petrol Eng J. 1968;8(2):107–22. 1994;99(B11):21635–50. Zemanek J. Low-resistivity hydrocarbon-bearing sand reservoirs. SPE Glover PWJ, Meredith PG, Sammonds PR, et al. Measurements of Form Eval. SPE-15713-PA. 1989;4(4):515–21. complex electrical conductivity and fluid permeabilities in porous rocks at raised confining pressures. Rock Mechanics in Petroleum Engineering. Delft, Netherlands. 29–31 August 1994b. pp. 29–36. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Petroleum Science Springer Journals

Study of the properties of non-gas dielectric capacitors in porous media

Liu, Hong-Qi; Jun, Yan; Deng, You-Ming
Petroleum Science , Volume 12 (1) – Feb 1, 2015
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Earth Sciences; Mineral Resources; Industrial Chemistry/Chemical Engineering; Industrial and Production Engineering; Energy Economics
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Pet. Sci. (2015) 12:104–113 DOI 10.1007/s12182-015-0015-z OR IGINAL PAPER Study of the properties of non-gas dielectric capacitors in porous media • • Hong-Qi Liu Yan Jun You-Ming Deng Received: 2 April 2014 / Published online: 1 February 2015 The Author(s) 2015. This article is published with open access at Springerlink.com Abstract The size of pores and throats is at the nano- calculated, and its polarization and relaxation mechanisms meter scale in tight oil and shale gas zones, and the are analyzed. resistivity of these reservoirs is very high, so the reservoirs show more dielectric properties than conductivity proper- Keywords NaCl solution  Debye model  Single micro ties. The conductive and dielectric characteristics of a ion capacitor  Dielectrics  Micro capacitivity parallel plate capacitor full of fresh water, NaCl solutions, and solid dielectrics, for example, sands are investigated in this paper, and the capacitance data of the non-gas capac- 1 Introduction itor are measured at different salinities and frequencies by a spectrum analyzer. The experimental results illustrate that As we know, rocks have both conductive and dielectric the capacitance of this kind of capacitor is directly pro- properties. The conductivity is completely determined by ? 2? 2? ? portional to the salinity of the solutions and inversely various anions and cations, such as Na ,Mg ,Ca ,K , - - - 2- 2- proportional to the measuring frequency, the same as a Cl ,OH , HCO ,SO , and CO in water solution in 3 4 3 vacuum parallel plate capacitor. The remarkable phenom- the intergranular pores of rocks. Which property of the enon, however, is that the capacitance is inversely pro- rocks will play a predominant role depends on the salinity, portional to the square of the distance between two plates. porosity, permeability, and the geometric structure of the The specific characteristic of this capacitor is different pores. In fact, almost all substances in nature are dielec- from the conventional parallel plate capacitor. In order to trics, and only a few have conductivity (r) (Havriliak and explain this phenomenon, the paper proposed a new con- Negami 1966). The conductive paths of these charges are cept, named ‘‘single micro ion capacitor’’, and established usually continuous in relatively high porosity and high a novel model to describe the characteristics of this par- permeability reservoirs, but in most occasions, they are ticular capacitor. Based on this new model, the theoretical discontinuous in tight oil and shale gas zones, or in the low capacitance value of the single micro ion capacitor is porosity and low permeability reservoirs (Gasparrini et al. 2014; Ghanizadeh et al. 2014). Therefore, the electric properties of rocks include two major aspects: one is the conductive capability of free positive and negative charges H.-Q. Liu (&)  Y.-M. Deng in the water solution through the paths formed by pores and State Key Laboratory of Oil and Gas Reservoir Geology and throats which connected with each other; the other is the Exploitation, Southwest Petroleum University, dielectric capability of the bound charges of the non-con- Chengdu 610500, Sichuan, China ductive substances and particles, including rock matrix e-mail: lhqjp1@126.com particles, oil or gas molecules, and pure water molecules Y. Jun (Freedman and Vogiatzis 1979; Jonscher 1983; Endres and Centrica Energy (E&P) Upstream Kings Close, 62 Huntly Street, Bertrand 2006). Nevertheless, whether conductive or Aberdeen AB 101 RS, UK dielectric, the current paths in the formation are influenced by the geometric pore structure of rocks. The relationship Edited by Jie Hao 123 Pet. Sci. (2015) 12:104–113 105 between the conductive and dielectric properties of rocks negative ions dissolved in water solution. Generally, these ? - and the pore structure has been widely discussed in detail different ions can be equivalent to Na and Cl in view of in the literature (Toumelin and Torres-Verdin 2009), so it their conductive property. Therefore, it is crucial to study is not described here. Prior to 1940, studies on the electrical the conductive and dielectric properties of NaCl solutions properties of rocks mainly focused on conductivity. In (Jonscher 1999; Lesmes and Morgan 2001). The pure water 1941, K. S. Cole and R. H. Cole established the Cole–Cole and hydrocarbon molecules cannot conduct current, and the model for dielectric constants (Cole and Cole 1941); later, conductive ions are separated from each other by water and many scholars studied ionic conduction and rock polari- hydrocarbon molecules, as shown in Fig. 1. So the solution zation processes, analyzing the dielectric constant property in the pores can be regarded as a mixture of non-conductive of non-homogeneous multi-pore materials (Hilfer et al. molecules and conductive free ions (Fig. 2). Considering 1995, 1999; Nover et al. 2000; Ruffett et al. 1991; the water and hydrocarbon molecules as non-conductive ? - Davidson and Cole 1950, 1951). land, the Na and Cl ions are an isolated conductive river With regard to the electrical logging technology in the separated by this land, and the ion river moves through this petroleum industry, almost all research has focused on the land in a tortuous path. Then a model with ‘‘ion flux’’ and detection and interpretation of formation resistivity. How- ‘‘molecule land’’ can be established to explain the con- ever, more and more complex and unconventional reser- ductive and dielectric mechanisms. In Fig. 1, the yellow or voirs have been discovered, and the traditional, simple gray blocks denote rock particles of different minerals, the geophysical conductive model cannot solve the problems of blue parts represent the formation water, the red belts strongly heterogeneous reservoirs, such as low porosity and denote hydrocarbons dispersed in the water, which are non- low permeability oil reservoirs, tight oil zones, and shale conductive parts; and the green solid ball denotes free Cl , gas zones. Although scholars have proposed various solu- the red solid ball denotes free Na , which are conductive tions and models for some important questions to describe parts. Of course, the rock matrix is also non-conductive. the electrical conductivity mechanism in rocks (Chelidze Figure 2 illustrates the distribution of the non-conductive and Gueguen 1999; Chelidze et al. 1999; Asami 2002), it is molecules of water and hydrocarbon, and the conductive ? - increasingly difficult to accurately determine fluid types and ions of Na and Cl in an external electromagnetic field calculate the saturation of hydrocarbon. In 1988, Clark et al. (EMF). If an alternating EMF, such as I ¼ I sinðxt þ h Þ, 0 0 proposed an electromagnetic propagation tool (EPT) to is applied on both sides of rocks, the free ions will be measure the dielectric constant of the formation at fre- rearranged quickly according to the external EMF, resulting quencies of 2 MHz–1.1 GHz (Glover et al. 1994a, b, 1996; in a regular arrangement of ions. The rearranged ions move Clark et al. 1990). This method can identify fluid types and directionally under the effect of the external EMF as shown calculate the fluid saturation in high porosity and high in Fig. 3. These ions gradually move to the ends of mineral permeability reservoirs. Dong and Wang (2009) studied the grains through pores. Generally the Cl ions gather at the dielectric constant of several common minerals, including anode, and Na ions gather at the cathode. An internal quartz, calcite, and dolomite, within a frequency range from electric field is created in the rock, whose field direction is Hz to GHz level, and they identified pore structures and the opposite to the external field. The time of this process distribution of formation water using the dielectric constant. depends on the conductive properties of rocks. But after the In 1985, Lockner and Byerlee (1985) studied the complex established relatively stable EMF within a remarkably short resistivity of rocks; later, other scholars also studied the complex resistivity of rocks. However, due to the extraor- dinarily complex heterogeneity of porous rocks, there are still many disputes over the conductive and dielectric mechanisms in rocks (Clavier et al. 1984; Zemanek 1989; Hamada and Al-Awad 1998). Scholars have proposed many conductive models for rocks, of which the most represen- tative is the dual-water argillaceous sandstone conductive model proposed by Waxman and Smits in 1968 (Waxman and Smits 1968; Knight and Nur 1987; Hassoun et al. 1997). 2 Micro ion capacitor model Fig. 1 Schematic diagram of a rock with pure water (blue), ? - Obviously, the conductive and dielectric capabilities of hydrocarbon (red belt), and Na (small red ball) and Cl (large rocks depend on the amount of different positive and green ball) in the rock 123 106 Pet. Sci. (2015) 12:104–113 Fig. 2 Distribution of the non- conductive water and hydrocarbon molecules and ion flux without external EMF with poor connectivity, the occurring phenomenon is shown in Fig. 5. In tight oil and shale gas zones, several anions and cations respectively gather at the opposite ends of the particle as polar plates like a usual parallel plate capacitor, whereas the non-conductive molecules in the middle are dielectrics, thus a microscopic capacitor, called a ‘‘micro ion capacitor’’, is established. Numerous such micro ion capacitors can be created almost at the same time in the formation, and they may be connected in series or parallel. 3 Theoretical value of single ion capacitor ? - ? The radii of Na ,Cl , and H ions are 0.95, 1.81, and 2.08 A, respectively. The size of the pore throats in rocks Fig. 3 Schematic diagram of a rock with pure water (blue), ranges from several to more than 10 microns, and the hydrocarbon (red belt), and ions traversing through the rock under thickness of the water membrane is less than 1 micron. The the influence of an external electromagnetic field (EMF) space for ion transportation is tens of thousands of times time, the amount of free ions in rock pores becomes less and larger than the ion diameter. As shown in Fig. 5, there may less, and the ions and molecules form a new distribution, as be at least tens of thousands of positive and negative ions shown in Fig. 4. gathering at the ends of rock particles in the water-wet The movements of the positive and negative ions result phase, and a microscopic capacitor is formed with Na and in the establishment of a capacitor. The positive pole is Cl ions as two polar plates, with the rock particles ? 2? 2? ? composed of cations, such as Na ,Ca ,Mg , and K , wrapped by water membrane with a certain thickness as a - - the negative pole is composed of anions, such as Cl ,OH , dielectric. Although the capacitance of this micro ion 2- and SO , and the dielectric is water or hydrocarbon capacitor cannot be accurately calculated at present, a molecules. From this moment on, the rocks will show theoretical value can be estimated. dielectric properties rather than conductivity at the macro If the pores are very small and are not connected, ions level. are likely to form isolated capacitors with water molecules The polarization process above, perhaps will not exist in as dielectric. In case of extreme conditions, a single ion and high porosity and especially high permeability reservoirs. a single water molecule constitute a micro ion capacitor, as As for tight formations, the pore throats are very narrow. shown in Fig. 6. According to the definition of a capacitor, For example, when the pores are at the nanometer scale assuming the voltage of an external EMF is 1 V, the 123 Pet. Sci. (2015) 12:104–113 107 Fig. 4 The non-conductive water and hydrocarbon molecules and ions form a micro ion capacitor with an external EMF (–) (+) (–) Fig. 5 A single water-wet mineral particle with ions at two sides H forming a micro ion capacitor (+) ? -19 Fig. 6 A single ion capacitor, one sodium ion and one chloride ion quantity of the charge for example Na is 1.6 9 10 C, respectively as positive and negative plates with a non-conductive then the capacitance of a single ion capacitor is: H O molecule as media Q 1:6  10 C C ¼ ¼ ¼ 1:6  10 F ð1Þ V 1V 4.2 Experimental process 4 Experiments First, fresh water with different volumes was injected into the PVC pipe, and the upper plate was put at different 4.1 Experimental instrument distances corresponding to the fluid volume. Then the resistance (R ) and capacitance (C ) were tested with a p p Figure 7 illustrates a measuring device using a PVC pipe frequency spectrum analyzer. In this experiment, 12 groups with a diameter of 2.5 cm and a length of 150 cm. Two of data were recorded at 12 different distances. At each test plates were placed, one was fixed on the bottom, the other point, R and C were tested at frequencies of 100 Hz and p p was movable on the top, and the pipe was full of NaCl 1 kHz, where the subscript ‘‘p’’ means parallel connection. solution. So the resistivity and capacitance of NaCl solu- Second, NaCl solution was injected into the same pipe. tion can be detected at different distances, salinities, and Then, we repeat the experimental process like that of fresh frequencies. One important aspect must be noted that the water, 12 groups of data of R and C of NaCl solution with p p material of plates should be gold, rather than iron, alumi- salinities of 0.2 and 1.2 g/L were recorded. The capacitance num, copper, and others, to avoid corrosion by the NaCl data are listed in Table 1 and resistance data in Table 2. solution. 123 108 Pet. Sci. (2015) 12:104–113 Table 2 Resistance (R , X) at different salinities (S), frequencies (f), and distances (d) in the PVC pipe d (m) S (g/L) Water 0.2 1.2 0.2 1.2 f (Hz) 100 1 k 0.1 23.1 3.19 0.56 3.08 0.51 0.2 45.1 6.24 1.01 6.14 0.96 0.3 67.45 9.35 1.47 9.25 1.43 0.4 90.44 12.42 1.92 12.32 1.88 0.5 113 15.56 2.38 15.46 2.34 0.6 136 18.61 2.85 18.5 2.81 0.7 159 21.77 3.3 21.67 3.26 0.8 183 24.9 3.78 24.79 3.74 Fig. 7 A PVC pipe with copper wireline and full of NaCl solution, 0.9 205 27.92 4.22 27.82 4.18 the dimension is length 9 diameter = 150 cm 9 2.5 cm 1.0 228 31.1 4.69 30.96 4.65 1.1 253 34.21 5.15 34.1 5.12 Figure 8 illustrates a plastic container, with a dimension 1.2 277 37.3 5.61 37.2 5.57 of 17 cm 9 5.0 cm 9 4.7 cm, filled with sand which is saturated with NaCl solution. The sand was collected from a river, and was washed many times. Moreover, the sand was The measurement results of C are listed in Table 3 and filtered by a sorting sieve in order to keep sand almost at the R in Table 4, the distance and frequency changed with a same size. Its mineral composition is mainly quartz. During fixed salinity of 1.5 g/L. the experiments, the conditions were changed as follows: Table 5 lists the capacitance data of sand saturated with NaCl solution with different salinities and a fixed distance (1) The distance between the polar plates varied from 2 of 17 cm, and Table 6 lists the resistance data of sand to 17 cm, with eight test points; saturated with NaCl solution with different salinities and a (2) The frequency changed from 4 Hz to 5 MHz, with fixed distance of 17 cm. 100 test points, only seven points listed in the tables; (3) The salinity varied from 1.5 to 200 g/L, with eight test points. 5 Analysis of experimental results 5.1 Relationship between conductive and dielectric Table 1 Capacitance (C , lF) at different salinities (S), frequencies (f), and distances (d) in the PVC pipe properties and the distance between plates d (m) S (g/L) Based on the experimental results in the PVC pipe, and the Water 0.2 1.2 0.2 1.2 data in Table 1, Fig. 9 demonstrates the characteristics of f (Hz) this capacitor with fresh water and 0.2 and 1.2 g/L NaCl 100 1 k solutions at 100 Hz and 1 kHz. The capacitance changes with different salinities of the solution and different dis- 0.1 970 23,500 286,000 642.0 11,200 tances between the two plates. Generally, we can conclude 0.2 252 6,170 83,800 160.0 3,010 as follows: 0.3 112 2,730 39,900 71.0 1,340 0.4 61 1,550 22,500 39.0 763 (1) Under the same conditions, the higher the salinity, 0.5 41 976 15,100 24.0 491 the larger the capacitance; 0.6 25 694 10,300 18.1 345 (2) Under the same conditions, the higher the frequency, 0.7 21 510 7,730 13.0 248 the lower the capacitance; 0.8 15 371 5,760 10.0 192 (3) Under the same conditions, the capacitance is 0.9 12 303 4,820 8.0 153 approximately inversely proportional to the square 1.0 9 241 3,740 6.0 121 of the distance. 1.1 7 201 3,150 5.0 98 As shown in Fig. 9, there are five different curves, 1.2 6 165 2,550 4.5 82 corresponding to 1.2 g/L salinity at 100 Hz, 0.2 g/L 123 Pet. Sci. (2015) 12:104–113 109 4 Hz to 5 MHz and with different salinities, and all of the results prove the same rule, that is, the capacitance is approximately inversely proportional to the square of the distance. Why does this phenomenon occur? It is well known that the capacitance of a parallel plate capacitor is proportional to the area of the plate (A), and is inversely proportional to the distance between the plates (d), denoted by Eq. (2) C ¼ e ð2Þ But for the PVC pipe capacitor, according to the defi- nition of capacitance and the rule mentioned above, the equation of C can be expressed by C ¼  ; ð3Þ Fig. 8 A plastic container with copper plate and sand saturated with p NaCl solution, the dimension is length 9 width 9 height = 17 cm 9 5.0 cm 9 4.7 cm where  is a coefficient. The key point should be noted that is not the dielectric constant e because the units of these two parameters are different, and then the physical defi- salinity at 100 Hz, 1.2 g/L salinity at 1 kHz, fresh water at nition is also different. Based on SI unit, the dimension of 100 Hz, 0.2 g/L salinity at 1 kHz, respectively. It can be is F, which is the same as capacitance. Here, we call  as seen that with either the fresh water or the NaCl solution, micro capacitivity. either at 100 Hz or 1 kHz, the capacitance is a function of According to Eq. (3),  can be expressed as follows: the square of the distance. By the least square method, we know that the distance’s exponent of each curve is very ¼ C ð4Þ close to two. We test it at many different frequencies from Table 3 Capacitance (C , lF) of sands saturated with NaCl solution at different frequencies and distances in a plastic container f,Hz d,cm 17 15 13 10 8 5 3 2 4 1.40E?02 1.79E?02 2.39E?02 4.22E?02 6.37E?02 1.60E?03 4.41E?03 9.88E?03 10.2 7.06E?01 8.93E?01 1.19E?02 2.11E?02 3.14E?02 8.02E?02 2.23E?03 5.01E?03 70.1 6.95E?00 8.92E?00 1.29E?01 2.01E?01 3.13E?01 8.02E?01 2.29E?02 5.00E?02 286.8 1.40E?00 1.79E?00 2.38E?00 4.01E?00 6.04E?00 1.58E?01 4.36E?01 9.74E?01 1019.1 1.87E-01 2.42E-01 3.15E-01 5.38E-01 8.31E-01 2.14E?00 5.41E?00 1.32E?01 5029.1 1.40E-02 1.70E-02 2.30E-02 3.80E-02 6.10E-02 1.57E-01 4.34E-01 9.81E-01 10,171 3.00E-03 4.00E-03 6.00E-03 1.00E-02 1.60E-02 4.00E-02 1.20E-01 2.23E-01 Table 4 Resistance (R , X) of sands saturated with NaCl solution at different frequencies and distances in a plastic container f,Hz d,cm 17 15 13 10 8 5 3 2 4 1.67E?02 1.64E?02 1.60E?02 1.54E?02 1.51E?02 1.47E?02 1.42E?02 1.35E?02 10.2 1.17E?02 1.13E?02 1.08E?02 1.01E?02 9.65E?01 9.17E?01 8.86E?01 8.66E?01 70.1 7.42E?01 6.86E?01 6.24E?01 5.38E?01 4.81E?01 4.07E?01 3.66E?01 3.48E?01 286.8 6.19E?01 5.60E?01 4.94E?01 4.01E?01 3.37E?01 2.49E?01 1.98E?01 1.75E?01 1019.1 5.77E?01 5.17E?01 4.50E?01 3.54E?01 2.88E?01 1.92E?01 1.33E?01 1.03E?01 5029.1 5.60E?01 4.99E?01 4.32E?01 3.35E?01 2.68E?01 1.70E?01 1.07E?01 7.43E?00 10,171 5.57E?01 4.96E?01 4.28E?01 3.32E?01 2.65E?01 1.67E?01 1.03E?01 6.99E?00 123 110 Pet. Sci. (2015) 12:104–113 Table 5 Capacitance (C , pF) varies with frequency (f) and salinity (S) f,Hz S, g/L 1.5625 3.125 6.25 12.5 25 50 100 200 4 8.31E?03 1.95E?04 4.32E?04 8.23E?04 1.36E?05 2.13E?05 3.03E?05 3.43E?05 6.1 4.75E?03 1.16E?04 2.70E?04 5.52E?04 9.69E?04 1.57E?05 2.28E?05 2.60E?05 9.8 2.43E?03 6.24E?03 1.53E?04 3.35E?04 6.39E?04 1.08E?05 1.65E?05 1.87E?05 15.6 1.20E?03 3.21E?03 8.28E?03 1.93E?04 3.98E?04 7.30E?04 1.17E?05 1.34E?05 25 5.73E?02 1.60E?03 4.29E?03 1.05E?04 2.35E?04 4.62E?04 8.07E?04 9.23E?04 39.9 2.68E?02 7.66E?02 2.12E?03 5.42E?03 1.28E?04 2.75E?04 5.27E?04 6.14E?04 63.9 1.23E?02 3.61E?02 1.03E?03 2.67E?03 6.66E?03 1.53E?04 3.18E?04 3.83E?04 102.1 5.53E?01 1.66E?02 4.86E?02 1.29E?03 3.30E?03 7.97E?03 1.78E?04 2.25E?04 163.3 2.46E?01 7.53E?01 2.26E?02 6.12E?02 1.60E?03 3.96E?03 9.35E?03 1.25E?04 261.1 1.08E?01 3.36E?01 1.03E?02 2.85E?02 7.58E?02 1.92E?03 4.68E?03 6.86E?03 417.6 4.80E?00 1.48E?01 4.64E?01 1.31E?02 3.55E?02 9.08E?02 2.28E?03 3.80E?03 1,708 4.50E-01 1.26E?00 3.99E?00 1.17E?01 3.35E?01 8.97E?01 2.34E?02 7.68E?02 4368.4 1.20E-01 2.70E-01 7.80E-01 2.26E?00 6.57E?00 1.81E?01 4.83E?01 2.72E?02 17,867 4.00E-02 5.00E-02 8.00E-02 1.70E-01 4.50E-01 1.16E?00 3.11E?00 4.99E?01 32,895 4.00E-02 4.00E-02 4.00E-02 4.00E-02 7.00E-02 8.00E-02 1.20E-01 2.05E?01 45,695 3.00E-02 3.00E-02 3.00E-02 1.00E-02 -2.00E-02 -1.60E-01 -5.80E-01 1.16E?01 186,900 3.00E-02 2.00E-02 1.00E-02 -3.00E-02 -1.20E-01 -4.40E-01 -1.35E?00 -1.81E?00 764,420 3.00E-02 2.00E-02 1.00E-02 -3.00E-02 -1.20E-01 -4.30E-01 -1.25E?00 -2.94E?00 1,955,000 2.00E-02 2.00E-02 1.00E-02 -3.00E-02 -1.20E-01 -4.00E-01 -1.09E?00 -2.44E?00 3,126,500 2.00E-02 2.00E-02 1.00E-02 -3.00E-02 -1.20E-01 -3.90E-01 -9.40E-01 -1.92E?00 5,000,000 2.00E-02 2.00E-02 0.00E?00 -3.00E-02 -1.30E-01 -3.70E-01 -7.40E-01 -1.32E?00 Cole and R. H. Cole found that the relaxation of most solid The experiments with the capacitor filled with sand dielectrics does not satisfy the Debye model. They cor- saturated with NaCl solution in a plastic container also rected the Debye model by taking into account the elec- show the same rule. From Fig. 10, it can be seen that the trical conductance, and they proposed the so-called Cole– capacitance is also approximately inversely proportional to Cole model, as shown in Eq. (6) the square of the distance between plates. The six curves in Fig. 10 were tested at six different e  e s 1 e ðxÞ¼ e þ ð5Þ frequencies. In fact, from 4 Hz to 5 MHz, we recorded 100 1 þ ixs groups of capacitance data, and each group shows the e  e s 1 e ðxÞ¼ e þ ; ð6Þ inversely proportional relationship between the capacitance 1a 1 þðixsÞ and the square of the distance. In the above experiments, the dielectrics are fresh water, where, e is the optical frequency dielectric constant, e is ? s pffiffiffiffiffiffiffi saline solution, or sand mixed with saline solution, which the static dielectric constant, i ¼ 1, s is the time con- have different salinities and different saturations. We can stant, and a is the empirical coefficient, 0 \ a \ 1. see that whether the measurement was carried out in a PVC The above two and other models, such as Lorentz– pipe or in a plastic container, and whether the measured Lorenz, Maxwell–Wagner, and Onsager models, describe dielectric is liquid or solid, all of the results indicate that the dielectric constant of isolated material. In our experi- the capacitance is approximately inversely proportional to ment, the medium is a mixture of conductive materials, ? - the square of the distance between plates. Such phenome- such as Na ,Cl , and other cations or anions, and insu- non may be related to the polarization and relaxation lating matter, such as water and hydrocarbon molecules. In processes. As early as 1929, Debye assumed that the dipole the pores of rocks, the conductive and non-conductive relaxation of a dielectric is a purely viscous process with- materials coexist, and in most cases, they can form out elastic forces, and established an equation to describe numerous micro capacitors, that is the micro ion capacitor the relationship of the dielectric constant and the angular mentioned before. Obviously, the inversely proportional frequency as shown in Eq. (5) (Debye 1929). In 1941, K. S. relationship between ionic capacitance and the square of 123 Pet. Sci. (2015) 12:104–113 111 Table 6 Resistance (R , X) varies with frequency (f) and salinity (S) f,Hz S, g/L 1.5625 3.125 6.25 12.5 25 50 100 200 4 7.94E?02 4.66E?02 2.83E?02 1.88E?02 1.27E?02 8.73E?01 6.52E?01 6.10E?01 6.1 7.64E?02 4.42E?02 2.62E?02 1.70E?02 1.14E?02 7.87E?01 5.86E?01 5.46E?01 9.8 7.40E?02 4.20E?02 2.44E?02 1.54E?02 1.01E?02 6.93E?01 5.15E?01 4.78E?01 15.6 7.21E?02 4.03E?02 2.30E?02 1.40E?02 8.98E?01 6.05E?01 4.46E?01 4.12E?01 25 7.09E?02 3.92E?02 2.19E?02 1.30E?02 8.05E?01 5.29E?01 3.81E?01 3.54E?01 39.9 7.00E?02 3.83E?02 2.12E?02 1.23E?02 7.38E?01 4.68E?01 3.25E?01 3.02E?01 63.9 6.94E?02 3.78E?02 2.07E?02 1.18E?02 6.92E?01 4.24E?01 2.83E?01 2.60E?01 102.1 6.91E?02 3.74E?02 2.03E?02 1.15E?02 6.61E?01 3.94E?01 2.53E?01 2.31E?01 163.3 6.88E?02 3.71E?02 2.01E?02 1.13E?02 6.40E?01 3.75E?01 2.33E?01 2.10E?01 261.1 6.86E?02 3.70E?02 1.99E?02 1.11E?02 6.27E?01 3.63E?01 2.20E?01 1.96E?01 417.6 6.85E?02 3.69E?02 1.98E?02 1.10E?02 6.17E?01 3.54E?01 2.12E?01 1.86E?01 1,708 6.84E?02 3.67E?02 1.97E?02 1.09E?02 6.03E?01 3.42E?01 2.00E?01 1.64E?01 4368.4 6.83E?02 3.67E?02 1.96E?02 1.08E?02 6.00E?01 3.39E?01 1.97E?01 1.52E?01 17,867 6.83E?02 3.67E?02 1.96E?02 1.08E?02 5.98E?01 3.37E?01 1.95E?01 1.38E?01 32,895 6.82E?02 3.67E?02 1.96E?02 1.08E?02 5.98E?01 3.37E?01 1.95E?01 1.34E?01 45,695 6.82E?02 3.66E?02 1.96E?02 1.08E?02 5.98E?01 3.36E?01 1.95E?01 1.32E?01 186,900 6.80E?02 3.66E?02 1.96E?02 1.08E?02 5.98E?01 3.37E?01 1.95E?01 1.29E?01 764,420 6.74E?02 3.64E?02 1.95E?02 1.08E?02 5.99E?01 3.39E?01 1.99E?01 1.33E?01 1,955,000 6.56E?02 3.57E?02 1.93E?02 1.07E?02 5.98E?01 3.46E?01 2.15E?01 1.58E?01 3,126,500 6.31E?02 3.47E?02 1.89E?02 1.05E?02 5.96E?01 3.55E?01 2.38E?01 1.98E?01 5,000,000 5.74E?02 3.22E?02 1.78E?02 1.01E?02 5.86E?01 3.75E?01 2.85E?01 2.92E?01 5.2 Preliminary explanation Water (100 Hz) 0.2 g/L (100 Hz) 1.2 g/L (100 Hz) The main reason of this remarkable phenomenon is that in 0.2 g/L (1 kHz) the pores and fractures, especially in tight oil and shale gas 1.2 g/L (1 kHz) zones, various ions, water molecules, and hydrocarbon 3 molecules can form numerous micro ion capacitors, which will parallel or series connect with each other. Compared with conventional capacitors, the outstanding characteristic 100 of this micro capacitor is that the length of the plates nearly equals the distance between the plates. The parameter A is the surface area of the ion, and the distance d is the diameter of water or hydrocarbon molecules. For the micro ion capacitor mentioned above, if one or ? - 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 several water molecules are dielectric, and Na and Cl or other cations and anions are plates, the distance between d, cm plates almost equals the size of ionic plates. Then the Fig. 9 The relationship of NaCl solution’s capacitance and the distance capacitance of micro ion capacitor also accords with the between plates at different salinities and frequencies. The capacitance rule as shown in Eq. (3). The diameter of a water molecular increases with increasing salinity and decreasing frequency, and is about 4 A, and we can estimate the capacitance of such a decreases with the increase of the square of the distance. 1. C = -2.0048 2 -1.9980 2 9.2428d , R = 0.9987; 2. C = 243.92d , R = 0.9998; 3. micro ion capacitor as follows: -1.9038 2 -2.009 2 C = 3841.50d , R = 0.9992; 4. C = 6.2724d , R = p p -1.981 2 A pr pð1:81=2Þ 0.9996; 5. C = 122.11d , R = 0.9997 C þ ¼  ¼  ¼ Na 2 2 2 d d ð4 þ 0:95=2 þ 1:81=2Þ the distance cannot be explained by either the Debye model ¼ 0:088851 ð7Þ or the Cole–Cole model. We should create a novel model to explain this rule. C, pF 112 Pet. Sci. (2015) 12:104–113 Fig. 10 The relationship 1.E+05 4 Hz 1019.1 Hz between capacitance and the 10.2 Hz 5029.1 Hz distance between two plates at 1.E+04 −1.9854 70.1 Hz 1017.1 Hz 1. C=39225d different frequencies. The figure 286.8 Hz R =0.999 illustrates the increase of the 1.E+03 −1.992 2. C=19912d capacitance with decreasing 1 R =0.9999 frequency, and the increase with 1.E+02 −1.9933 3. C=2005.4d a decrease in the square of the R =0.9997 distance, which is different from 1.E+01 −1.9828 4. C=383.61d conventional capacitors 4 2 R =0.9999 1.E+00 −1.973 5. C=50.194d R =0.9997 1.E−01 −2.0011 6. C=3.9099d 1.E−02 R =0.9999 −2.025 7 7. C=1.0189d 1.E−03 R =0.9977 0 1 2 3 4 5 6 7 8 9 1011 12131415161718 d, cm 2 novel concept and a model, single micro ion capacitor, are A pr pð0:95=2Þ C ¼  ¼  ¼ Cl first proposed in this paper. Based on the experimental 2 2 d d ð4 þ 0:95=2 þ 1:81=2Þ results, we found that: ¼ 0:024477 ð8Þ (1) The ionic capacitance is inversely proportional to the According to the theoretical value estimated in Eq. (1), square of the distance, which remarkably differs from the value of micro capacitivity  can be calculated: that of parallel plate capacitors with air dielectric; þ ¼ 1:80  10 pF; ð9Þ (2) Compared with conventional capacitors, the out- Na standing characteristic of a micro ion capacitor is ¼ 6:54  10 pF; ð10Þ Cl that the length of the plate nearly equals the distance ? - Because the different diameters of Na and Cl , the between the plates; -6 micro capacitivity  varies from 1.8 9 10 to 6.54 9 (3) Based on the micro ion capacitor model, the micro -6 -6 10 pF. capacitivity  varies from 1.8 9 10 to 6.54 9 -6 For capacitors with liquid and solid dielectrics, many 10 pF. aspects remain unclear, especially the mechanisms of Such phenomenon may be also related to the relatively polarization and relaxation. The reasons may be related to complex polarization and relaxation mechanisms of the the single ionic capacitors formed between free Na and numerous single micro ion capacitors, and another impor- Cl ions in the non-conductive liquid or solid molecules, tant reason may be the tortuosity of the ion conductive path and the single ionic capacitors are connected in series or in porous solid media, which will be discussed later. parallel. However, the distance between molecules in a gas dielectric or vacuum dielectric capacitor is too long to form Acknowledgments The authors are grateful for the financial sup- a microscopic capacitor. This may be the important reason port from Basic Science Program of Advanced Well Logging Tech- nology of CNPC (2014A-2319) and support from the Science and for the remarkable difference between these two types of Technology Program (G12-3) of State Key Laboratory of Oil and Gas capacitors. Another reason may be the complexity of Reservoir Geology and Exploitation of SWPU (Southwest Petroleum channels for ion transportation (Ma et al. 2014). University). Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, dis- 6 Conclusions tribution, and reproduction in any medium, provided the original author(s) and the source are credited. We measured the capacitance and resistance of non-gas dielectrics in a PVC pipe and a plastic container, and the References experimental results illustrated an unusual rule in the ionic capacitance of fluid or solid dielectrics. Although many Asami K. Characterization of heterogeneous systems by dielectric models have been established, there are still many prob- spectroscopy. Prog Polym Sci. 2002;27(8):1617–59. lems about the polarization and relaxation of the ions or Chelidze TL, Gueguen Y. Electrical spectroscopy of porous rocks: a review—I. Theoretical model. Geophys J Int. 1999;137(1):1–15. molecules under the external EMF that are not solved. A C, pF Pet. Sci. (2015) 12:104–113 113 Chelidze TL, Gueguen Y, Ruffet C. Electrical spectroscopy of porous Hamada GM, Al-Awad MNJ. Petrophysical evaluation of low rocks: a review—II. Experimental results and interpretation. resistivity sandstone reservoirs. International Symposium of Geophys J Int. 1999;137(1):16–34. Core Analysts. The Hague. 14–16 Sept 1998. Clark B, Allen DF, Best DL, et al. Electromagnetic propagation Hassoun TH, Zainalabedin K, Minh CC. Hydrocarbon detection in logging while drilling: theory and experiment. 1990. SPE low contrast resistivity pay zones, capillary pressure and ROS 18117-PA. determination with NMR logging in Saudi Arabia. SPE Paper Clavier C, Coates G, Dumanoir J. Theoretical and experimental bases 37770. 10th MEOS, Bahrain. 15–18 March 1997. for the dual-water model for interpretation of shaly sands. Soc Havriliak S, Negami S. A complex plane analysis of a-dispersions in Petrol Eng J. 1984;24:153–68. some polymer systems. J Polym Sci Part C. 1966;14(1):99–117. Cole KS, Cole RH. Dispersion and absorption in dielectrics. J Chem Hilfer R, Prigogine I, Rice SA. Transport and relaxation phenomena Phys. 1941;9(4):341–51. in porous media. Adv Chem Phys. 1995;92:299. Davidson DW, Cole RH. Dielectric relaxation in glycerine. J Chem Hilfer R, Widjajakusuma J, Biswal B. Macroscopic dielectric constant Phys. 1950;18(10):1417. for microstructures of sedimentary rocks. Granular Matter 2. Davidson DW, Cole RH. Dielectric relaxation in glycerol, propylene Berlin: Springer-Verlag; 1999. pp. 137–41. glycol and n-propanol. J Chem Phys. 1951;19(12):1484–90. Jonscher AK. Dielectric relaxation in solids. London: Chelsea Press; Debye PW. Polar molecules. New York: Chemical Catalog Co.; 1929. 1983. pp. 219–26. Dong XB, Wang YH. A broadband dielectric measurement technique: Jonscher AK. Dielectric relaxation in solids. J Phys D. theory, experimental verification, and application. J Environ Eng 1999;32:57–70. Geophys. 2009;14(1):25–38. Knight RJ, Nur A. The dielectric constant of sandstones, 60 kHz to Endres AL, Bertrand EA. A pore-size scale model for the dielectric 4MHz. Geophysics. 1987;52(5):644–54. properties of water-saturated clean rocks and soils. Geophysics. Lesmes DP, Morgan FD. Dielectric spectroscopy of sedimentary 2006;71:F185–93. rocks. J Geophys Res. 2001;106(B7):13329–46. Freedman R, Vogiatzis JP. Theory of microwave dielectric constant Lockner DA, Byerlee JD. Complex resistivity measurements of logging using the electromagnetic wave propagation method. confined rock. J Geophys Res. 1985;90:7837–47. Geophysics. 1979;44(5):969–86. Ma JS, Sanchez JP, Wu KJ, et al. A pore network model for Gasparrini M, Sassi W, Gale JFW. Natural sealed fractures in simulating non-ideal gas flow in micro- and nano-porous mate- mudrocks: a case study tied to burial history from the Barnett rials. Fuel. 2014;116(15):498–508. Shale, Fort Worth Basin, Texas, USA. Mar Petrol Geol. Nover G, Heikamp S, Freund D. Electrical impedance spectroscopy 2014;55:122–41. used as a tool for the detection of fractures in rock samples Ghanizadeh A, Gasparik M, Amann-Hildenbrand A, et al. Experi- exposed to either hydrostatic or triaxial pressure conditions. Nat mental study of fluid transport processes in the matrix system of Hazards. 2000;21(2–3):317–30. the European organic-rich shales: I. Scandinavian Alum Shale. Ruffett C, Gueguen Y, Darot M. Complex conductivity measurements Mar Pet Geol. 2014;51:79–99. and fractal nature of porosity. Geophysics. 1991;56(6):758–68. Glover PWJ, Gomez JB, Meredith PG, et al. Modelling the stress– Toumelin E, Torres-Verdin C. Pore-scale simulation of kHz-GHz strain behavior of saturated rocks undergoing triaxial deforma- electromagnetic dispersion of rocks: effects of rock morphology, tion using complex electrical conductivity measurements. Surv pore connectivity, and electrical double layers. In: SPLWA 50th Geophys. 1996;17(3):307–30. Annual Logging Symposium. 21–24 Jun 2009. Glover PWJ, Meredith PG, Sammonds PR, et al. Ionic surface Waxman MH, Smits LJM. Electrical conductivities in oil-bearing electrical conductivity in sandstone. J Geophys Res. shaly sands. Soc Petrol Eng J. 1968;8(2):107–22. 1994;99(B11):21635–50. Zemanek J. Low-resistivity hydrocarbon-bearing sand reservoirs. SPE Glover PWJ, Meredith PG, Sammonds PR, et al. Measurements of Form Eval. SPE-15713-PA. 1989;4(4):515–21. complex electrical conductivity and fluid permeabilities in porous rocks at raised confining pressures. Rock Mechanics in Petroleum Engineering. Delft, Netherlands. 29–31 August 1994b. pp. 29–36.

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