The Zeta Potential Measurements in Sandpacks Saturated with Monovalent Electrolytes

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1 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, Dong Da, Hanoi, Vietnam Received 16 October 217 Revised 15 November 217; Accepted 16 January 218 Abstract: Measurements o the zeta potential in sandpacks saturated with monovalent electrolytes at six dierent electrolyte concentrations have been reported. The values we record are classiied into two groups based on the magnitude o the zeta potential: group 1 (samples 1 and 2) and group 2 (samples 3 and 4). The measured zeta potential in magnitude in group 1 is much smaller than that in group 2 and in literature at the same electrolyte concentration. The reason or a big variation o the zeta potential between group 1 and group 2 may be due to the dierence in technique o making sand particles o dierent size leading to change o particle surace properties. Consequently, the zeta potential that depends on the surace properties would vary. The results show that there is a gradual decrease in the zeta potential with increase in monovalent electrolyte concentration (rom 1 4 M to 1 2 M). Additionally, the empirical expressions between the zeta potential and electrolyte concentration are obtained in this work or both group 1 and group 2. The obtained expression or group 2 is in good agreement with those available in literature. From the experimental data in combination with a theoretical model, the binding constants or Na + and K + cations are obtained or the samples o group 2 and they are in the same range reported in literature or silica-based samples. Keywords: treaming potential, zeta potential, porous media, sands, electrolytes 1. Introduction The streaming potential is induced by the relative motion between the luid and the solid surace. In porous media such as rocks, sands or soils, the electric current density, linked to the ions within the luid, is coupled to the luid low. treaming 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 [e.g., 1]. treaming potential is also used to monitor Tel.: luongduythanh23@yahoo.com https//doi.org/ / /vnumap

2 L.D. Thanh / VNU Journal o cience: Mathematics Physics, Vol. 34, No. 2 (218) subsurace low in geothermal areas and volcanoes [e.g., 2, 3]. Monitoring o streaming potential anomalies has been proposed as a means o predicting earthquakes [e.g., 4, 5] and detecting o seepage through water retention structures such as dams, dikes, reservoir loors, and canals [6]. The zeta potential is one o the key parameters in streaming potential. The zeta potential o liquidrock systems depends on many parameters such as mineral composition o rocks, luid properties, temperature etc [7]. At a given porous media, the most inluencing parameter is the luid conductivity. Thereore, it is useul to have an empirical relation between the zeta potential and luid conductivity or electrolyte concentration. For example, by itting experimental data or quartz and NaCI or KCI at ph = 7 and temperature o 25 C, Pride and Morgan [8] obtain an empirical relation between the zeta potential and electrolyte concentration. imilarly, Vinogradov et al. [9] obtain another relation between the zeta potential and electrolyte concentration based on published zeta potential data or quartz, silica, glass beads, sandstone, tainton and Fontainebleau in NaCl at ph = 6-8. However, experimental data sets they used or itting are rom dierent sources with dissimilar luid conductivity, luid ph, temperature, mineral composition o porous media. All those dissimilarities may cause the empirical expressions less accurate. To critically seek empirical expressions to estimate the zeta potential rom electrolyte concentration, we have carried out zeta potential measurements or a set o our sandpacks (denoted as 1, 2, 3 and 4) saturated by our monovalent electrolytes (NaCl, NaI, KCl and KI) at six dierent electrolyte concentrations (1 4 M, M, 1 3 M, M, M, and 1 2 M). The measured values o the zeta potential are classiied into two groups based on the magnitude: group 1 (samples 1 and 2) and group 2 (samples 3 and 4). The magnitude o the zeta potential in group 1 is much smaller than that in group 2 and in literature at the same electrolyte concentration. The reason or a big variation o the zeta potential between samples may be due to the dierence in technique o making sand particles o dierent size leading to change o particle surace properties. Consequently, the zeta potential that depends on the surace properties would vary. The results also show that there is a decrease in the zeta potential with increase in monovalent electrolyte concentration. Additionally, the empirical expressions between the zeta potential and electrolyte concentration are obtained in this work or both group 1 and group 2. The obtained expression or group 2 is in good agreement with those available in literature. From the experimental data in combination with the theoretical model, the binding constants or Na + and K + cations are obtained or the samples o group 2 and they are in the same range reported in literature or silica-based samples. 2. Theoretical background o streaming potential 2.1. Physical chemistry o the electric double layer treaming potential is the result o a coupling between luid low and electric current low in a porous medium which is ormed by mineral solid grains such as silicates, oxides, carbonates. It is directly related to the existence o an electric double layer (EDL) that exists at the solid-liquid interace. Most substances acquire a surace electric charge when brought into contact with aqueous systems. To understand the origin o surace charge, the physical chemistry at a silica surace in the presence o the aqueous luids is presented. The discussion o the reactions at a silica surace in contact with aqueous luids has been introduced [7, 1]. It is stated that there are two types o neutral surace group or silica: doubly coordinated siloxal >i 2 O and singly coordinated silanol >ioh (where > reer to the mineral lattice and the superscript means no charge). The siloxal group (>i 2 O ) can be considered inert. However, the surace silanol group (>ioh ) can react readily to

3 1 L.D. Thanh / VNU Journal o cience: Mathematics Physics, Vol. 34, No. 2 (218) 8-19 produce positive surace sites (>ioh 2 + ) at very acid ph < ph pzc = 2-3 and negative surace sites (>io ) at ph > ph pzc where ph pzc is the ph at the point o zero charge (at which concentration o >ioh 2 + is equal to that o >io ). The surace mineral reactions at the silanol suraces in contact with 1:1 electrolyte solutions with the luid ph limited to a range o 6-8 are: To simpliy the problem, silica grains in contact with 1:1 electrolyte solutions (i.e., monovalent electrolytes with one cation and one anion) such as NaCl is considered with the luid ph limited to a range o 6-8. The surace mineral reactions at the silanol surace sites are: or deprotonation o silanol groups >ioh >io + H +, (1) or cation adsorption on silica suraces >ioh + Me + >iome + H +, (2) where Me + stands or monovalent cations in the solutions such as Na + or K +. Note that the positive surace site (>ioh 2 + ) does not exist at the silica-electrolyte interace or ph > 6. Thereore, three types o sites are present at the silica suraces, one negative (>io ) and two neutral ones (>ioh and >iome ). The law o mass action at equilibrium is used to calculate the equilibrium constants or those reactions in the ollowing manner K and ( ) K Me. io H ioh iome ioh.. H Me, (3), (4) where K ( ) is the disassociation constant or deprotonation o silanol surace sites, K Me is the binding constant or cation adsorption on the silica suraces, is the surace site density o surace species i (sites/m 2 ) and i is the activity o an ionic species i at the closest approach o the mineral surace (no units). The total surace site density ( ) is ioh io iome (5) Eq. (5) is a conservation equation or mineral surace groups. From Eq. (3), Eq. (4) and Eq. (5), the surace site density o sites and are obtained. The mineral surace charge density Q in io iome C/m 2 can be ound by summing the surace densities o charged surace groups (only one charged surace group o in this problem) as. io io Q e (6) where e is the elementary charge. The mineral surace charge repels ions in the electrolyte whose charges have the same sign as the surace charge (called the coions ) and attracts ions whose charges have the opposite sign (called the counterions and normally cations) in the vicinity o the electrolyte-silica interace. This leads to the i

4 L.D. Thanh / VNU Journal o cience: Mathematics Physics, Vol. 34, No. 2 (218) charge distribution known as the electric double layer (EDL) (see Fig. 1). The EDL is made up o the tern layer, where cations are adsorbed on the surace and are immobile due to the strong electrostatic attraction, and the diuse layer, where the ions are mobile. The distribution o ions and the electric potential within the diuse layer is governed by the Poisson-Boltzman (PB) equation which accounts or the balance between electrostatic and thermal diusional orces [11]. The solution to the linear PB equation in one dimension perpendicular to a broad planar interace is well-known and produces an electric potential proile that decays approximately exponentially with distance as shown in Fig. 1. In the bulk liquid, the number o cations and anions is equal so that it is electrically neutral. The closest plane to the solid surace in the diuse layer at which low occurs is termed the shear plane or the slipping plane, and the electrical potential at this plane is called the zeta potential (ζ) as shown in Fig. 1. Figure 1. tern model or the charge and electric potential distribution in the EDL at a solid-liquid interace [12, 13] Zeta potential According to a theoretical model or the zeta potential that has been well described by [7, 1], the electrical potential distribution φ in the EDL has, approximately, an exponential distribution as ollows: d exp( ), (7) d where φ d is the tern potential (V) given by 3 ph ph ph pkw 2k bt 8.1 o r kbtn (1 K MeC ) C 1 1 d ln (8) 3e 2e K ( ) C and χ d is the Debye length (m) given by k T o r b d, (9) 2 2Ne C and χ is the distance rom the mineral surace (m). The zeta potential (V) can then be calculated as

5 12 L.D. Thanh / VNU Journal o cience: Mathematics Physics, Vol. 34, No. 2 (218) 8-19 d exp( ), (1) d where is the shear plane distance - the distance rom the mineral surace to the shear plane (m). There is currently no method to evaluate the shear plane distance. In the work reported by [7], the shear plane distance was taken as m to compare the theoretical model with experimental datasets o 17 dierent solid-luid combinations. It was shown that the theoretical model its the experimental data well. Thereore, the shear plane distance ( ) is taken as m in this work or modeling. In Eq. (8) and Eq. (9), k b is the Boltzmann s constant ( J/K [14]), ε is the dielectric permittivity in vacuum ( F/m [14]), ε r is the relative permittivity (no units), T is temperature (in K), e is the elementary charge ( C [14]), N is the Avogadro s number ( /mol [14]), C is the electrolyte concentration (mol/l), ph is the luid ph, K Me is the binding constant or cation adsorption (no units), K ( ) is the disassociation constant or dehydrogenization o silanol surace sites (no units), is the surace site density (sites/m 2 ) and K w is the disassociation constant o water (no units) treaming potential In a porous medium the electric current density and the luid lux are coupled, so that the streaming potential is generated by luids moving through porous media. The parameter that quantiies this coupling is the streaming potential coeicient (PC) and is deined as V r o C, (11) P e where V is the measured streaming potential (V), P is the applied pressure dierence (Pa), η is the dynamic viscosity o the luid (Pa.s), σ e is the eective conductivity (/m), and ζ is the zeta potential (V). The eective conductivity includes the luid conductivity and the surace conductivity. The PC can also be written as ([15] and reerence therein) C r o, (12) F r where σ r (/m) is the electrical conductivity o the sample saturated by a luid with a conductivity o σ (/m) and F is the ormation actor (no units). 3. Experiment amples and electrolytes used in this work are the same as ones that have been already reported in [15]. The samples are our unconsolidated samples o sand particles with dierent diameters denoted as 1, 2, 3 and 4 (ee Table 1). The samples are made up o blasting sand particles obtained rom Unicorn IC BV Company. Four monovalent electrolytes (NaCl, NaI, KCl and KI) are used with 6 dierent concentrations (1 4 M, M, 1 3 M, M, M, and 1 2 M). All measurements are carried out at room temperature (22 ±1 o C).

6 L.D. Thanh / VNU Journal o cience: Mathematics Physics, Vol. 34, No. 2 (218) Figure 2. Experimental setup or streaming potential measurements. The experimental setup and the way used to collect the PC is similar to that described in [15] and re-shown in Fig. 2. The values o the PC or all samples at dierent electrolyte concentrations are already reported in [15] and re-shown in Table 1 except or two samples 1 and 2 at electrolyte concentration o 1-2 M. Because these samples are very permeable, they need a very large low rate to generate measurable electric potentials at high electrolyte concentration. It is ound that the PC is negative or all samples and all electrolytes. The electrical conductivity o the samples saturated by electrolytes (σ r ) is obtained rom the resistance measured by an impedance analyzer (Hioki IM357) with the knowledge o the geometry o the sample (the length, the diameter). In order to measure the resistance o saturated samples, two silver meshes acting as two electrodes are used. The electrodes are placed on both sides against the sample. Based on the measured PC, the measured electrical conductivity o the samples (σ r ), ormation actors that are measured and re-shown in Table 1, the viscosity and dielectric constant o water, the zeta potential is deduced rom equation 2. The zeta potential at dierent electrolyte concentrations is reported in Table 2. The maximum error o measured zeta potential is 12%. The result shows that or a given sample the zeta potential in magnitude increase with decreasing electrolyte concentration or all electrolytes. The observation is in good agreement literature [e.g., 7, 16]. Table 1. The streaming potential coeicient (mv/bar) or dierent electrolyte concentrations and the ormation actor o the samples F already reported in [15] ample ize (μm) F Electrolyte 1 4 M M 1 3 M M M 1 2 M NaCl NaI KCl KI NaCl NaI KCl KI

7 14 L.D. Thanh / VNU Journal o cience: Mathematics Physics, Vol. 34, No. 2 (218) NaCl NaI KCl KI NaCl NaI KCl KI Results and discussion From Table 2, the dependence o the zeta potential on types o electrolyte is shown in Fig. 3 or a representative sample (or example, sample 3). Fig. 3 shows that the magnitude o the zeta potential decreases with increasing electrolyte concentration or all electrolytes as reported in literature [e.g., 7, 16]. This behavior is similar to other samples. As stated in [15], it is seen that that the zeta potential mostly depend on types o cation in electrolytes. This can be qualitatively explained by the dierence in the binding constant o cations. For example, the binding constant o K + is larger than Na + [7]. Thereore, at the same ionic strength more cations o K + are absorbed on the negative solid surace than cations o Na +. This makes the electric potential on the shear plane (the zeta potential) smaller in the electrolyte containing cations o K + than that in the electrolyte containing cations o Na +. Table 2. Zeta potential or our monovalent electrolytes at dierent concentrations ample Electrolyte 1 4 M M 1 3 M M M 1 2 M NaCl NaI KCl KI NaCl NaI KCl KI NaCl NaI KCl KI NaCl NaI KCl KI

8 L.D. Thanh / VNU Journal o cience: Mathematics Physics, Vol. 34, No. 2 (218) Figure 3. The variation o the zeta potential in magnitude with electrolyte concentration or dierent electrolytes and or the sample 3. Fig. 4 shows the variation o the zeta potential with samples or electrolyte NaI, or example. It is seen that at a given electrolyte concentration, the samples can be classiied into two groups based on the magnitude o the zeta potential: group 1 (larger sand particle group) includes samples 1 and 2 and group 2 (smaller sand particle group) includes samples 3 and 4. This can be explained by the dierence in technique used to produce sand particles leading to the change o particle surace properties. Figure 4. The magnitude o the zeta potential as a unction o electrolyte concentration or dierent samples saturated by electrolyte NaI. The variation o the zeta potential o group 1 and group 2 with monovalent electrolyte concentration is shown by a lower part and upper part in Fig. 5, respectively. By itting the

9 16 L.D. Thanh / VNU Journal o cience: Mathematics Physics, Vol. 34, No. 2 (218) 8-19 experimental data o the group 1 (the red solid line in Fig.5), the empirical relation between the zeta potential and electrolyte concentration or the group 1 is obtained as log1( C ), (13) and the empirical relation the group 2 (the black solid line in Fig. 5) is obtained as 27 12log1( C ), (14) where is in mv and C is the electrolyte concentration (in mole/lit). Expressions in Eq. (13) and Eq. (14) are similar to ones available in literature. For example, by itting experimental data or quartz and NaCI and KCI at ph = 7 and temperature o 25 C, Pride and Morgan [8] obtain the empirical relation between the zeta potential and electrolyte concentration as 26log1( C ). (15) 8 Figure 5. Zeta potential in magnitude as a unction o electrolyte concentration or group 1 (lower part) and group 2 (upper part) and dierent electrolytes (NaCl, NaI, KCl and KI). ymbols are experimental data. The solid lines are the itting ones. The dashed lines are predicted rom [8, 9]. Vinogradov et al. [9] obtain the another relation between the zeta potential and electrolyte concentration based on published zeta potential data or quartz, silica, glass beads, sandstone, tainton and Fontainebleau in NaCl at ph = 6-8 as log1( C ). (16) 9 The prediction o zeta potential as a unction o electrolyte concentration rom the empirical expressions o [8, 9] is also shown in Fig. 5 (see the upper dashed lines). It is seen that the empirical expressions obtained [8, 9] can predict the variation o the measured zeta potential with electrolyte concentration or group 1. The reason or the deviation between the empirical expressions may be due to dissimilarities o luid conductivity, luid ph, mineral composition o porous media, temperature etc. To quantitatively explain the experimental data measured in this work by the theoretical model introduced in section 2, the input parameters given in [7] or silica-based samples are used. The value o the disassociation constant, K ( ) or dehydrogenization o silanol surace sites is taken as The

10 L.D. Thanh / VNU Journal o cience: Mathematics Physics, Vol. 34, No. 2 (218) shear plane distance, is taken as m. The surace site density is taken as site/m 2. The disassociation constant o water, K w, at 22 o C is The luid ph is taken as 6.5. The binding constant or cation adsorption on silica varies according to which are the dominant cations in the electrolyte and it is not well known. For example, K Me (Na + ) = and K Me (K + ) = given by [7]; K Me (Li + ) = and K Me (Na + ) = or silica given by [17]; K Me (Li + ) = 1 7.7, K Me (Na + ) = and K Me (Cs + ) = given by [18]. Figure 6. Zeta potential in magnitude as a unction o electrolyte concentration or group 2 (samples 3 and 4) or electrolytes containing Na + cations (NaCl, NaI). ymbols are experimental data. The solid line is the itting one predicted rom the theoretical model in [7]. Figure 7. Zeta potential in magnitude as a unction o electrolyte concentration or group 2 (samples 3 and 4) or electrolytes containing K + cations (KCl, KI). ymbols are experimental data. The solid line is the itting one predicted rom the theoretical model in [7].

11 18 L.D. Thanh / VNU Journal o cience: Mathematics Physics, Vol. 34, No. 2 (218) 8-19 By itting the experimental data o the measured zeta potential (see Fig. 6 or electrolytes containing Na + cations and Fig. 7 or electrolytes containing K + cations), the binding constants or cations are obtained as K Me (Na + ) = 1 4., K Me (K + ) = or the samples o group 2 and they are in the same range reported in literature or silica-based samples. It should be noted that we only use the experimental data o group 2 or itting because the measured zeta potential o group 1 is ar rom those available in literature as shown in Fig Conclusions Measurements o the zeta potential in unconsolidated samples saturated with monovalent electrolytes (NaCl, NaI, KCl and KI) at six dierent electrolyte concentrations have been reported. The values we recorded are classiied into two groups based on the magnitude: group 1 (samples 1 and 2) and group 2 (samples 3 and 4). The measured zeta potential in magnitude in group 1 is much smaller than that in group 2 and in literature at the same electrolyte concentration (about three times smaller). The reason or a big variation o the zeta potential between samples may be due to the dierence in technique o making sand particles o dierent size leading to change o particle surace properties. Consequently, the zeta potential that depends on the surace properties would vary. The results show that there is a gradual decrease in the zeta potential with increase in monovalent electrolyte concentration (rom 1 4 M to 1 2 M). For any sample, the zeta potential in magnitude is larger in the electrolyte containing cations o Na + than that in the electrolyte containing cations o K +. This is qualitatively explained by the dierence in the binding constant or cation adsorption on the silica suraces. Additionally, the empirical expressions between the zeta potential and electrolyte concentration are obtained in this work or both group 1 and group 2. The obtained expression or group 2 is quite suitable with those available in literature. From the experimental data in combination with the theoretical model, the binding constants or Na + and K + cations are also obtained or the samples o group 2 and they are in the range reported in literature or silica-based samples. Acknowledgments This research is unded by Vietnam National Foundation or cience and Technology Development (NAFOTED) under grant number Additionally, the author would like to thank Dr. Rudol prik or granting a three month visit at University o Amsterdam and or his helpul comments and suggestions. 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] H. Mizutani, T. Ishido, T. Yokokura,. Ohnishi, Geophys. Res. Lett. 3 (1976). [5] M. Trique, P. Richon, F. Perrier, J. P. Avouac, J. C. abroux, Nature (1999) [6] A. A. Ogilvy, M. A. Ayed, V. A. Bogoslovsky, Geophysical Prospecting 17 (1969) [7] P. W. J. Glover, E. Walker, and M. D. Jackson, Geophysics 77 (212) D17 D43. [8]. R. Pride and F. D. Morgan, Geophysics 56 (1991)

12 L.D. Thanh / VNU Journal o cience: Mathematics Physics, Vol. 34, No. 2 (218) [9] Vinogradov, J., M. Z. Jaaar, and M. D. Jackson, Journal o Geophysical Research Atmospheres 115 (21) B1224. [1] O. tern, Z. Elektrochem 3 (1924) [11] T. Ishido, H. Mizutani, Journal o Geophysical Research 86 (1981) [12] H. M. Jacob, B. ubirm, Electrokinetic and Colloid Transport Phenomena, Wiley-Interscience, 26. [13] Revil A. and P. W. J. Glover, Physical Review B 55 (1997) [14] Lide, D.R., 29, Handbook o chemistry and physics, 9 th ed., CRC Press. [15] Luong Duy Thanh, Rudol prik, VNU Journal o cience: Mathematics Physics, (217) streaming potential coeicient in unconsolidated samples saturated with monovalent electrolytes (accepted). [16] B. J. Kirby, E. J. Hasselbrink, Electrophoresis 25 (24) [17] Dove, P. M., and J. D. Rimstidt, Reviews in Mineralogy and Geochemistry 29 (1994) [18] Kosmulski, M., and D. Dahlsten, Colloids and uraces, A: Physicocemical and Engineering Aspects 291 (26)