A study on the Variation of Streaming Potential Coefficient with Physical Parameters of Rocks

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1 VNU Journal o Science: Mathematics Physics, Vol. 33, No. 1 (2017) A study on the Variation o Streaming Potential Coeicient with Physical Parameters o Rocks Luong Duy Thanh 1,*, Rudol Sprik 2 1 Thuy Loi University, 175 Tay Son, Dong Da, Hanoi, Vietnam 2 Van der Waals-Zeeman Institute, University o Amsterdam, The Netherlands Received 05 January 2017 Revised 16 February 2017; Accepted 20 March 2017 Abstract: Streaming potential is induced by the relative motion between a luid and a solid surace and is directly related to the existence o an electric double layer between the luid and the solid grain surace. Streaming potential depend not only on the luid and mineral composition o rocks but also on microstructure parameters o rocks. To investigate the variation o streaming potential with rock parameters including the eects o the variation o the zeta potential due to the dierence in mineral compositions between samples, we perorm streaming potential measurements on six samples o Berea sandstone saturated with our dierent NaCl solutions. The results show that the streaming potential coeicient strongly depends on permeability o rocks or low luid electric conductivity. However, when the luid conductivity is larger than a certain value, the streaming potential coeicient is completely independent o permeability. This observation is then explained by a theoretical model. Additionally, the results also show that there is no clear correlation between the streaming potential coeicient and porosity, grain density, tortuosity, ormation actor, bulk modulus and or shear modulus o rocks. Keywords: Streaming potential, microstructure parameters, porous media, rocks. 1. Introduction Streaming potential plays an important role in geophysical applications. For example, the streaming potential is used to map subsurace low and detect subsurace low patterns in oil reservoirs [1]. Streaming potential is also used to monitor subsurace low in geothermal areas and volcanoes [2, 3, 4]. Monitoring o streaming potential anomalies has been proposed as a means o predicting earthquakes [5, 6] and detecting o seepage through water retention structures such as dams, dikes, reservoir loors, and canals [7]. Permeability, porosity, grain density, tortuosity and ormation actor are important physical parameters to describe reservoir rocks. A link between streaming potential coeicient (SPC) and some o those parameters has been studied by a number o authors or dierent types o rocks. For example, permeability dependence o the SPC was studied in publications (e.g., [8, 9]) or sandstone and limestone. Jouniaux et al. also stated that there is no speciic correlation between Corresponding author. Tel.: luongduythanh2003@yahoo.com 60

2 L.D. Thanh, Rudol S. / VNU Journal o Science: Mathematics Physics, Vol. 33, No. 1 (2017) the SPC with porosity or ormation actor or volcanic rocks [10]. In the work [8-10], the authors presumed the zeta potential to be the same or the same amily o samples (or example, Fontainebleau sandstone). However, the mineral compositions are somehow dierent rom sample to sample even though they are taken rom the same block as shown in [11] and thereore, the zeta potential that depends on the mineral compositions would vary. Additionally, the variation o the SPC with elastic moduli o rocks has not yet reported in literature to the best o our knowledge. Thereore, we want to study the variation o the SPC with micro-structure parameters and elastic moduli o rocks when taking into account the eects o the dierence in the zeta potential between samples or a set o Berea sandstone that has not yet studied. To do so, the ratio o the SPC and zeta potential is used rather than the SPC only. The results have shown that the SPC strongly depends on the permeability and the porosity o the samples or low luid electrical conductivity. However, when the luid conductivity is larger than a certain value that is determined by the mineral compositions o the sample, the SPC is completely independent o permeability. The results also show that there is no clear correlation between the SPC and porosity, grain density, tortuosity, ormation actor, bulk modulus and or shear modulus o rocks. This paper includes ive sections. Section 2 describes the theoretical background o streaming potential. Section 3 presents the experimental measurement. Section 4 contains the experimental results and discussion. Conclusions are provided in the inal section. 2. Theoretical background o streaming potential The theoretical background o streaming potential in porous media has been already introduced [12]. Thereore, we just briely introduce the theory o streaming potential in porous media. Streaming potential is induced by the relative motion between the luid and the rock. Mineral grains orming the rock develop an electric double layer when in contact with an electrolyte. The electric double layer is made up o the Stern layer, where cations are adsorbed on the surace, and the diuse layer, where the number o counterions exceeds the number o anions (or a detailed description, see [13]). The streaming potential is due to the motion o the diuse layer induced by a luid pressure dierence along the interace. The zeta potential is deined at the slipping plane or shear plane (i.e., the potential within the double layer at the zero-velocity surace). In a porous medium the electric current density and the luid lux are coupled, so that the streaming potentials are generated by luids moving through porous media. The parameter that quantiies this coupling is the streaming potential coeicient (SPC) deined by V r o CS, (1) P e where V is the streaming potential, P is the luid pressure dierence, ε r is the relative permittivity o the luid, ε o is the dielectric permittivity in vacuum, η is the dynamic viscosity o the luid, σ e is the eective conductivity, and ζ is the zeta potential. The eective conductivity includes the luid conductivity and the surace conductivity. The zeta potential is a unction o many parameters including mineral composition o porous media, ionic species that are present in the luid, the ph o luid, luid composition, luid electrical conductivity and temperature etc. [14]. The SPC can also be written as [10] r o CS, (2) F r

3 62 L.D. Thanh, Rudol S. / VNU Journal o Science: Mathematics Physics, Vol. 33, No. 1 (2017) where σ r is the electrical conductivity o the sample saturated by a luid with a conductivity o σ and F is the ormation actor. The electrical conductivity o the sample can possibly include surace conductivity. I the luid conductivity is much higher than the surace conductivity, the eective conductivity is approximately equal to the luid conductivity, σ e = Fσ r = σ and the SPC becomes the well-known Helmholtz-Smoluchowski equation: C S r o. (3) 3. Experiment 3.1. Materials Streaming potential measurements have been perormed on a set o six Berea sandstone samples that were obtained rom Berea Sandstone Petroleum Cores Company in the US. Mineral composition o the sample is silica, alumina, erric Oxide, errous oxide ( Microstructure parameters (porosity, solid density, permeability and ormation actor) and elastic moduli o the samples have been reported in the previous article o VNU Journal o Science [15] and re-shown in Table 1. NaCl solutions are used with 4 dierent concentrations ( M, M, M, and M). All measurements are carried out at room temperature (22 ±1 o C). Table 1. Sample ID, parameters o the samples. Symbols k o (in md), ϕ (in %), F (no units), α (no units), ρ s (in kg/m 3 ), K (in GPa) and G (in GPa) stand or permeability, porosity, ormation actor, tortuosity, solid P S density, bulk modulus and shear modulus o the rocks, respectively. Sample ID k o ϕ F α ρ s K P [GPa] G S [GPa] 1 BereaUS BereaUS BereaUS BereaUS BereaUS BereaUS Experimental setup Figure 1. Experimental setup or streaming potential measurements. 1, Core holder; 2, Ag/AgCl electrodes; 3, Pump; 4, Pressure transducer; 5, NaCl solution container.

4 L.D. Thanh, Rudol S. / VNU Journal o Science: Mathematics Physics, Vol. 33, No. 1 (2017) The experimental setup or the streaming potential measurement is the same as reported in [12] and re-shown in Fig. 1. The core holder contains a cylindrical sample o 55 mm in length and 25 mm in diameter. Each sample is surrounded by a 4 mm thick silicone sleeve inside a conical stainless steel cell and inserted into a stainless steel holder to prevent low a long the interace o the sample. The solution is circulated through the samples until the electrical conductivity and ph o the solution reach a stable value measured by a multimeter (Consort C861). The ph values o equilibrium solutions are in the range 6.0 to 7.5. Electrical potential dierences across the samples are measured by a high input impedance multimeter (Keithley Model 2700). Pressure dierences across a sample are measured by a high-precision dierential pressure transducer (Endress and Hauser Deltabar S PMD75) Streaming potential measurement The way used to collect the SPC is similar to that described in [12] where Ag/AgCl electrodes are used to avoid polarization. In our measurements, Ag/AgCl wire electrodes are bought rom a manuacturer o A-M systems. Fig. 2 shows an example o streaming potential as a unction o pressure dierence at concentration o M. Thereore, the SPC is obtained as the slope o the straight line. Three measurements are perormed or all samples with each solution to ind the average value o the SPC. Figure 2. Streaming potential as a unction o pressure dierence or BereaUS5 at a concentration o M. 4. Results and discussion The SPC or all samples at dierent electrolyte concentrations is shown in Table 2 (that has been reported in [16]). The electrical conductivity o the sample saturated by the solution is obtained rom the resistance measured by an impedance analyzer (Hioki IM3570) with the knowledge o the geometry o the sample (the length, the diameter). Based on the measured SPC with the knowledge o electrical conductivity o the samples (σ r ), ormation actor, viscosity and dielectric constant, the zeta potential is deduced rom equation 2. The zeta potential at dierent electrolyte concentrations is also shown in Table 2. The result shows that or a given porous sample the zeta potential in magnitude increase with decreasing electrolyte concentration as expected [17]. Based on Table 1 and Table 2, the dependence o the SPC on permeability or a set o Berea samples at dierent concentrations is shown in Fig. 3. At irst sight, it seems that no speciic correlation between the SPC and permeability is observed, especially at low concentrations. This is because that the zeta potential is not the same or dierent samples.

5 64 L.D. Thanh, Rudol S. / VNU Journal o Science: Mathematics Physics, Vol. 33, No. 1 (2017) Table 2. The streaming potential coeicient (in mv/bar) and the zeta potential or dierent electrolyte concentrations. Sample ID M M M M C S ζ C S ζ C S ζ C S ζ 1 BereaUS BereaUS BereaUS BereaUS BereaUS BereaUS Figure 3. SPC versus permeability or Berea samples at dierent concentrations. The dash lines are the ones connecting the experimental points. To see how the permeability itsel aects the SPC without inluence o the zeta potential, the ratio o the SPC and the zeta potential is plotted against permeability at dierent electrolyte concentrations (Fig. 4). It is shown that the ratio o the SPC and zeta potential drastically increases with increasing permeability at low concentration solutions and does not depend on permeability at high concentration solutions starting rom a concentration o M. This permeability dependence may be a consequence o a change o the eective conductivity σ e with permeability [8, 9, 10] at low luid electric conductivity σ. The behavior observed in Fig. 4 (symbols) can be theoretically explained by the eect o surace conductivity. Eective conductivity σ e is given by 2 s e, (4) where Σ s is the surace conductance and is a characteristic length scale that describes the size o the pore network [18]. Figure 4. The ratio o SPC and zeta potential versus permeability or Berea samples at dierent electrolyte concentrations. The solid lines are rom the theoretical model. The points are experimental data.

6 L.D. Thanh, Rudol S. / VNU Journal o Science: Mathematics Physics, Vol. 33, No. 1 (2017) According to [19], the permeability o the porous medium k o is related to the characteristic length scale by 2 k0, (5) af where a is a parameter thought to be constant and equal to 8/3 or a wide range o porous media, including reservoir rock. Equation (4) can be rewritten as 2 s e, (6) afk And equation (1) can be rewritten as CS r o, 2 s afk 0 0 At salinity higher than 10-3 M, the speciic surace conductance almost does not vary with salinity [20]. Thereore, the surace conductance is assumed to be constant over the studied range o electrolyte concentration. As reported in [16], the surace conductance is ound to be S or Berea sandstone. From equations (6) and (7), it is seen that both permeability (k 0 ) and ormation actor (F) o rocks simultaneously inluence the SPC via the product Fk 0. For the Berea sandstone rocks, the ormation actor varies rom 14.4 to 21 (about 45%) but the permeability varies rom 22 md to 442 md (about 2000%). Thereore, the ormation actor can be approximately considered to be constant in the range o the permeability and taken as a constant averaged over all the samples (approximately 17.4). The value o r is normally taken to be 80 or an aqueous solution at 25 o C. In this work, the variation o the relative electric permittivity as a unction o luid electrolyte concentration and temperature is taken into account by using an empirical equation [21]:, (8) r ( T, C ) a0 a1t a2t a3t c1c c2c c3c where a 0 = , a 1 = K -1, a 2 = K -2, a 3 = K -3, c 1 = -13 Lmol -1, c 2 = (Lmol -1 ) 2, c 3 = (Lmol -1 ) 3, T is in Kelvin, the equation is valid in the range rom 273 K to 373 K, and C is the electrolyte concentration in mol/l. The variation o the viscosity o the luid against electrolyte concentration and temperature was mentioned in [22] ( T, C ) e1 e2 exp( 1T ) e3 exp( 2C ) e4 exp( 3T 4C ), (9) where e 1 = Pa.s, e 2 = Pa.s, e 3 = Pa.s, e 4 = Pa.s, α 1 = / o C, α 2 = /molar, α 3 = / o C, α 4 = /molar, T is in o C. By putting the surace conductance Σ s, the corresponding luid electric conductivities, the viscosity, and the relative electric permittivity at dierent electrolyte concentrations (at room temperature-22 o C) into equation (7), the ratio o the SPC and the zeta potential versus permeability or a set o Berea sandstone is theoretically plotted in Fig. 4 at dierent electrolyte concentrations (solid lines). It is shown that the SPC strongly depends on permeability o rocks or low luid electric (7)

7 66 L.D. Thanh, Rudol S. / VNU Journal o Science: Mathematics Physics, Vol. 33, No. 1 (2017) conductivity. When the luid electric conductivity is larger than 0.50 S/m, the SPC is completely independent o permeability. The value o electrical conductivity o 0.50 S/m above which the SPC becomes independent o permeability is generally not applicable thresholds or all rock types and brine composition. It is determined rom the condition or which the surace conductivity that partially depends on the permeability is much smaller than the luid electric conductivity. Figure 5. The ratio o SPC and zeta potential versus porosity at dierent electrolyte concentrations. Based on Table 1 and Table 2, the variation o the SPC with porosity, grain density, tortuosity, ormation actor, bulk modulus and shear modulus is shown in Figs. 5, 6, 7, 8, 9 and 10, respectively. The results in Fig. 5 and Fig. 6 show that there is no speciic correlation between the SPC and porosity or ormation actor. The observations are the same as what is stated or volcanic rocks [10]. It is also shown that no clear dependence o the SPC on grain density, tortuosity, bulk modulus or shear modulus is observed. The reason is that the SPC only depends on (1) the zeta potential that is determined by mineral composition o rocks, ionic species in the luid, the luid ph, luid electrical conductivity and temperature; (2) the relative permittivity o the luid, (3) the viscosity o the luid and (4) the eective conductivity that is partially determined by permeability. Thereore, the parameters o porosity, grain density, tortuosity, ormation actor, bulk modulus and shear modulus may inluence the mass, the length o the capillaries (due to tortuosity), the speed o acoustic waves propagating in rocks, etc. but they do not inluence the SPC. Figure 6. The ratio o SPC and zeta potential versus grain density at dierent electrolyte concentrations.

8 L.D. Thanh, Rudol S. / VNU Journal o Science: Mathematics Physics, Vol. 33, No. 1 (2017) Figure 7. The ratio o SPC and zeta potential versus tortuosity at dierent electrolyte concentrations. Figure 8. The ratio o SPC and zeta potential versus ormation actor at dierent electrolyte concentrations. Figure 9. The ratio o SPC and zeta potential versus bulk modulus at dierent electrolyte concentrations. Figure 10. The ratio o SPC and zeta potential versus shear modulus at dierent electrolyte concentrations.

9 68 L.D. Thanh, Rudol S. / VNU Journal o Science: Mathematics Physics, Vol. 33, No. 1 (2017) Conclusions Measurements o the SPC on a set o Berea sandstone o dierent permeability have clearly shown that the SPC strongly depends on permeability o porous media or low luid electric conductivity only i the variation o zeta potential between the samples is taken into account. We use a theoretical model to explain the relationship between the SPC and permeability. In the model, we take into account the variation o zeta potential rom sample to sample. Consequently, the modeled results are in good agreement with the experimental data. Additionally, the results show that there is no clear correlation between the SPC and porosity, grain density, tortuosity, ormation actor, bulk modulus and or modulus o rocks. The reason is that those parameters do not inluence the properties o the solidliquid interace o rocks as well as the surace conductivity o rocks. Thereore, they do not aect the streaming potential coeicient. Acknowledgments The irst author would like to thank the National Foundation or Science and Technology Development o Vietnam (NAFOSTED) or the inancial support o the Project with code number Reerences [1] B. Wurmstich, F. D. Morgan, Geophysics 59 (1994) [2] R. F. Corwin, D. B. Hoovert, Geophysics 44 (1979) [3] F. D. Morgan, E. R. Williams, T. R. Madden, Journal o Geophysical Research 94 (1989) [4] A. Revil, P. A. Pezard, Geophysical Research Letters 25 (1998) [5] H. Mizutani, T. Ishido, T. Yokokura, S. Ohnishi, Geophys. Res. Lett. 3 (1976). [6] M. Trique, P. Richon, F. Perrier, J. P. Avouac, J. C. Sabroux, Nature (1999) [7] A. A. Ogilvy, M. A. Ayed, V. A. Bogoslovsky, Geophysical Prospecting 17 (1969) [8] L. Jouniaux, J. Pozzi, Geophysical Research Letters 22 (1995), [9] Perrier F., T. Froideond, Earth and Planetary Science Letters 210 (2003), [10] L. Jouniaux, M. L. Bernard, M. Zamora, J. P. Pozzi, Journal o Geophysical Research, 105 (2000), [11] A. Pagoulatos, MS thesis, University o Oklahoma, USA (2004). [12] Luong Duy Thanh, Rudol Sprik, VNU Journal o Science: Mathematics Physics, Vol. 31, No. 4 (2015) [13] R. J. Hunter, Zeta Potential in Colloid Science, Academic, New York, [14] J. Davis, R. James, J. Leckie, Journal o Colloid and Interace Science 63 (1978). [15] Luong Duy Thanh, Rudol Sprik, VNU Journal o Science: Mathematics Physics, Vol. 32, No. 2 (2016) [16] Luong, D. T., Ph.D. thesis, University o Amsterdam, the Netherlands, 2014 [17] B. J. Kirby, E. J. Hasselbrink, Electrophoresis 25 (2004) [18] Ishido T. and H. Mizutani, Journal o Geophysical Research 86 (1981), [19] P.W.J. Glover, E. Walker, Geophysics 74 (2009), E17 E19 [20] A. Revil, P.W.J. Glover, Geophysical Research Letters 25 (1998), [21] Glover P.W.J., Walker E., M. Jackson, Geophysics 77 (2012), D17 D43 [22] Phillips S.L., Ozbek H., R. Otto, 6th International CODATA Conerence (1978).

The Zeta Potential Measurements in Sandpacks Saturated with Monovalent Electrolytes

VNU Journal o cience: Mathematics Physics, Vol. 34, No. 2 (218) 8-19 The Zeta Potential Measurements in andpacks aturated with Monovalent Electrolytes Luong Duy Thanh * Thuy Loi University, 175 Tay on,