Measurement of streaming potential coupling coefficient in sandstones saturated with natural and artificial brines at high salinity

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi: /2010jb007593, 2010 Measurement of streaming potential coupling coefficient in sandstones saturated with natural and artificial brines at high salinity J. Vinogradov, 1 M. Z. Jaafar, 1,2 and M. D. Jackson 1 Received 26 March 2010; revised 14 July 2010; accepted 3 August 2010; published 3 December [1] We report experimental measurements of the streaming potential coupling coefficient in sandstones saturated with NaCl dominated artificial and natural brines up to 5.5 M (321.4 g L 1 of NaCl; electrical conductivity of 23 S m 1 ). We find that the magnitude of the coupling coefficient decreases with increasing brine salinity, as observed in previous experimental studies and predicted by models of the electrical double layer. However, the magnitude of the coupling coefficient remains greater than zero up to the saturated brine salinity. The magnitude of the zeta potential we interpret from our measurements also decreases with increasing brine salinity in the low salinity domain (<0.4 M; 23.4 g L 1 of NaCl and 3.4 S m 1 ) but reaches a constant value at higher salinity (>0.4 M). We hypothesize that the constant value of zeta potential observed at high salinity reflects the maximum packing of counterions in the diffuse part of the electrical double layer. Our hypothesis predicts that the zeta potential becomes independent of brine salinity when the diffuse layer thickness is similar to the diameter of the hydrated counterion. This prediction is confirmed by our experimental data and also by published measurements on alumina in KCl brine. At high salinity (>0.4 M), values of the streaming potential coupling coefficient and the corresponding zeta potential are the same within experimental error regardless of sample mineralogy and texture and the composition of the brine. Citation: Vinogradov, J., M. Z. Jaafar, and M. D. Jackson (2010), Measurement of streaming potential coupling coefficient in sandstones saturated with natural and artificial brines at high salinity, J. Geophys. Res., 115,, doi: /2010jb Introduction [2] Streaming potentials in fluid saturated rocks arise from the electrical double layer, which forms at solid fluid interfaces [e.g., Hunter, 1981]. In the fluid immediately adjacent to the charged mineral surface, there is a layer of adsorbed countercharge termed the Stern layer. This excess of countercharge is immobile. However, there is an excess of countercharge in the fluid adjacent to the Stern layer, which is mobile; this is termed the diffuse or Gouy Chapman layer. Within the diffuse layer, the concentration of excess countercharge decreases away from the mineral surface until the fluid becomes electrically neutral; this is termed the free electrolyte. Overall, the electrical double layer remains neutral, as the excess countercharge in the fluid balances the surface charge on the mineral. However, if the fluid is induced to flow by an external potential (pressure) gradient, then some of the excess charge within the diffuse layers is transported with the flow, giving rise to a streaming current. Divergence 1 Department of Earth Science and Engineering, Imperial College London, London, UK. 2 Now at the Petroleum Engineering Department, Universiti Teknologi Malaysia, Johor Bahru, Malaysia. Copyright 2010 by the American Geophysical Union /10/2010JB of the streaming current density establishes an electrical potential, termed the streaming potential. The closest plane to the mineral surface at which flow occurs in the diffuse layer is termed the shear plane; the electrical potential at this plane is termed the zeta potential. [3] Measurements of streaming potential have been used to characterize the subsurface flow of relatively low salinity brine in numerous Earth science applications (see Corwin and Hoovert [1979] for geothermal examples and Ishido [2004] for examples of volcano monitoring amongst numerous publications). They have also been proposed to characterize flow in subsurface environments, such as hydrocarbon reservoirs and deep saline aquifers, which are fully or partially saturated with brine of considerably higher salinity [e.g., Saunders et al., 2006, 2008]. However, to interpret measurements of streaming potential in these more saline environments requires knowledge of the behavior of the streaming potential coupling coefficient at high salinity. The coupling coefficient (C) is a key petrophysical property that relates the fluid (rp) and streaming (rv) potential gradients when the total current density ( j) is zero[sill, 1983], rv ¼ CrPj j¼0 : The magnitude and sign of the coupling coefficient depends upon the formation factor (F; measured when surface elec- ð1þ 1of18

2 trical conductivity is negligible) and electrical conductivity of the brine saturated rock (s rw ), the dielectric permittivity (" w ) and dynamic viscosity (m w ) of the brine, and the zeta potential (z) [e.g., Jouniaux and Pozzi, 1995], C ¼ " w w rw F : When surface conductivity is negligible, equation (2) simplifies to the well known Helmholtz Smoluchowski equation [e.g., Hunter, 1981], C ¼ " w w w ; where s w is the electrical conductivity of the brine saturating the rock. [4] Most experimental measurements of the streaming potential coupling coefficient in Earth materials have been obtained using samples saturated with relatively low salinity NaCl or KCl brines (less than 1 M, which corresponds to a concentration of 58.4 g L 1 and electrical conductivity of 8.5 S m 1 for NaCl brine) [e.g., Morgan et al., 1989; Sprunt et al., 1994; Jouniaux and Pozzi, 1995, 1997; Li et al., 1995; Jiang et al., 1998; Pengra et al., 1999; Reppert et al., 2001; Reppert and Morgan, 2003; Revil et al., 2003; Alkafeef and Alajmi, 2006; Block and Harris, 2006]. Only Jaafar et al. [2009] have presented data obtained at higher salinity. They measured the streaming potential coupling coefficient in intact sandstone samples saturated with artificial NaCl brine and found that the magnitude of the coupling coefficient decreased with increasing brine salinity but was nonzero up to the saturated brine concentration at laboratory temperature (5.5 M or g L 1 of NaCl; electrical conductivity of 23 S m 1 ). The measured coupling coefficient was always negative, so the zeta potential interpreted from the measurements using equation (2) was also negative. At low salinity, their results were consistent with those obtained previously. [5] Jaafar et al. [2009] also found that, at low salinity, the magnitude of the zeta potential decreased with increasing brine salinity, as observed in previous studies [Gaudin and Fuerstenau, 1955; Li and de Bruyn, 1966; Kirby and Hasselbrink, 2004; Bolève et al., 2007; Kosmulski and Dahlsten, 2006; see also the compilation in Pride and Morgan, 1991] and predicted by models of the electrical double layer based on the Boltzmann equation [e.g., Hunter, 1981; Revil et al., 1999a]. However, at salinities higher than approximately 0.4 M (23.4 g L 1 of NaCl; electrical conductivity of 3.4 S m 1 ), they found that the zeta potential reached a constant value within experimental error. At high salinity, models based on the Boltzmann equation predict that the diffuse layer thickness collapses to zero, in which case the countercharge resides entirely within the Stern layer. Consequently, the zeta potential is also predicted to fall to zero [Hunter, 1981]. Jaafar et al. [2009] suggested that ion interactions cause the reduction in thickness of the diffuse layer at high salinity to be less than predicted by the Boltzmann equation, in which it is assumed that the ions are point charges. Moreover, the countercharge required to balance the mineral surface charge is not accommodated entirely within the Stern layer, so the diffuse layer does not collapse to zero. Some of the countercharge remains mobile within ð2þ ð3þ the diffuse layer, at a maximum charge density which is limited by the size of the hydrated counterions. They noted that the Debye length, calculated for the salinity at which the zeta potential reaches a constant value, is comparable with the diameter of a hydrated sodium ion, which suggests that the constant zeta potential they observed at high salinity reflects the maximum charge density in the diffuse layer. This behavior is not captured by current models of the electrical double layer. [6] Jaafar et al. [2009] measured the coupling coefficient in only two samples of the same sandstone, saturated with artificial NaCl brine. Consequently, it is not clear whether the same results would be obtained in samples with differing mineralogy or texture, saturated with brines containing a wider range of ionic species. Moreover, Jaafar et al. [2009] did not report in detail how they were able to obtain reliable measurements at high salinity, when the magnitude of the streaming potential is very small. The aims of this paper are therefore twofold. The first is to present measured values of streaming potential coupling coefficient in intact sandstone cores of varying mineralogy and texture, saturated with both natural and artificial brines, at salinities up to 5.5 M. The results have application to the interpretation of streaming potential measurements to characterize fluid flow in deep saline aquifers, hydrocarbon reservoirs, and other saline subsurface environments; they also have implications for our understanding of the charge distribution within the electrical double layer in natural porous media saturated with highsalinity brine. The second is to clearly explain the experimental methodology required to acquire streaming potentials of very small magnitude in natural porous media. This same methodology was followed by Jaafar et al. [2009]. We place particular emphasis on reporting our quality control procedures. 2. Experimental Methodology 2.1. Apparatus [7] The experimental setup is shown schematically in Figure 1a and is the same as that used by Jaafar et al. [2009]. The experiments are carried out on cylindrical (1.5 and 1 inch diameter) sandstone core samples, which are tightly confined within a core holder. A cross sectional view of the core holder containing a sample is shown in Figure 1b. To prevent brine flowing along the external surface of the sample, the latter is held within a rubber sleeve embedded in the core holder. Three different core holders of similar design are used in the experiments, two of stainless steel which can hold 1.5 and 1 inch diameter cores and one of acrylic which can hold 1.5 inch diameter cores. The samples are held in place by nonmetallic end caps in the stainless steel core holders which, in conjunction with the rubber sleeve, ensure that steel does not come into contact with the sample or brine. The stainless steel body of the core holders was connected to Earth and served as a Faraday enclosure, while the acrylic core holder is wrapped in an earthed, conductive mesh. The cores are held within the holders by a confining pressure applied via a hydraulic fluid (oil in the stainless steel 1.5 inch cell; nitrogen in the other two) pumped through the purge opening into the space between the outer hull and the inner sleeve. The confining pressure is kept several hundreds of kpa higher than the maximum pressure used in experiments. 2of18

3 Figure 1. Experimental apparatus for measuring the streaming potential coupling coefficient. (a) Pressure vessel, brine reservoirs, pump, flow lines (solid lines), and electrical connections (dashed lines). (b) Cross section through the external electrodes. (c) Cross section through the coreholder. For details, see Jaafar et al. [2009]. 3of18

4 Table 1. Mineralogy and Properties of Rock Samples Used in This Study a Fontainebleau Stainton St. Bees 1 Sandpack Porosity 7.2% 17% 19% 43% Grain size 250 mm mm mm mm Permeability 25 md 38 md 70 md 3 D Mineralogy >99% quartz 90% quartz 5% clay and feldspar 90% quartz 5% white >99% quartz <5% white mica <5% calcite mica 5% clay Formation factor N/A Dimensions 47.8 cm length 2.54 cm diameter 6.92 cm length 3.73 cm diameter 7.76 cm length cm diameter 7.2 cm length 3.9 cm diameter a Sample St. Bees 1 was also used by Jaafar et al. [2009]. [8] A syringe pump (either a GDS Standard Pressure/ Volume Controller or a GDS Advanced Pressure/Volume Controller) is used to flow brine through the sample from reservoirs connected to each side of the pressure vessel, and the resulting pressure difference across the sample is measured using a pair of calibrated Druck PDCR 810 pressure transducers (accuracy 0.1% of measured value, resolution 70 Pa) (Figure 1a). Synthetic oil is used to translate the pressure from the pump to the brine in the inlet reservoir, which allows air bubbles in the brine to be captured at the top of the oil layer in each reservoir, prevents exposure of the brine to air which may cause a change in ph, eliminates the flow of electrical current through the brine along a path parallel to the core sample, ensures that the stainless steel pump cylinder does not come into contact with the brine, and reduces corrosion of the pump. Each syringe pump maintains constant rate to high accuracy, and flow can be directed in either direction through the samples by adjusting the flow valves (denoted V1 V6 in Figure 1a). [9] The streaming potential induced across the sample is measured using two pairs of nonpolarizing Ag/AgCl electrodes and either an HP3490A voltmeter (internal impedance 10 GW, accuracy 0.15%, resolution 10 nv) or an NI9219 voltmeter (internal impedance >1 GW, accuracy 0.18%, resolution 50 nv). The electrodes are connected to the voltmeter using copper coaxial cables, with the outer stainless steel cable earthed to shield the inner cable which carries the signal. One electrode in each pair is earthed. The noise level of the measurements is dictated by the stability of the electrodes rather than the performance of the voltmeters. One pair of electrodes is positioned out of the flow path to eliminate electrode flow effects [e.g., Korpi and debruyn, 1972]. These external electrodes are located in a brine reservoir which is in electrical contact with the flowing brine via a lowpermeability ceramic disc (Figure 1c) and provide voltage measurements which are stable to approximately 10 mv. The other pair of electrodes is located on each face of the core sample and comprises a permeable AgCl membrane of the same diameter as the core sample, connected via Ag rods through the nonmetallic end caps and through both the fine and the coarse meshes placed on the core faces (Figure 1b). These nylon meshes of the same diameter as the core sample are used as flow dispersers. The internal electrodes, which are in the path of the flow, are less stable than the external electrodes and, as discussed in section 3.1, record flow ratedependent voltages at high salinity which are independent of flow direction. However, they can be used to measure the conductivity of the saturated core. To confirm these measurements, the saturated samples are occasionally removed from the core holder, and the conductivity across them is measured using two Ag membranes of 1.5 inch diameter which are clamped to each end of the sample using an adjustable jig. The conductivity of the brine is measured using a Metrohm 712 conductometer, and the ph of the brine is measured using a Hanna H8519 ph meter. Both of these meters are regularly calibrated Samples and Sample Preparation [10] We used three different sandstones samples and one unconsolidated sandpack (Table 1). The St. Bees 1 sample is the same as that used by Jaafar et al. [2009]. The brines used in our experiments were simple NaCl solutions in deionized water, two natural brines (seawater sampled from the Dorset coast, UK, and Dead Sea water) and tap water from Rijswijk, Netherlands. The chemical composition of the natural brines is given in Table 2. [11] Prior to conducting any experiments, each sample is cleaned using a 50:50 toluene/methanol solution for 24 h and then flushed with a methanol solution for 24 h. This is a standard method for cleaning core samples [e.g., Byrne and Patey, 2004]. The cleaned sample is then dried at 80 C for 48 h. Finally, the sample is saturated with the brine to be used in the streaming potential measurements for 24 h in a vacuum chamber. The sample is then loaded into the pressure vessel, and the same brine flowed repeatedly through the sample from one reservoir to the other and back again, until the conductivity and ph of the brine in each reservoir remain constant and equal within a 10% tolerance. Measurements of streaming potential then begin Measurements of Streaming Potential [12] The experiments for each core sample and brine composition begin with a measurement of the initial voltage across the sample. We term this voltage, when there is no Table 2. Composition of the Natural Brines Used in This Study a Composition (M) Species UK Seawater Dead Sea Water Cl SO Na Mg Ca K HCO Br Sr Li Mn a The data for seawater are taken from Adams and Bachu [2002], and the data for the Dead Sea water are taken from Nissenbaum [1977]. 4of18

5 fluid flow, the static voltage. The syringe pump is then used to induce brine flow through the sample at constant rate, resulting in a change in pressure and voltage across the sample, which is recorded at a frequency of 1 Hz (e.g., Figure 2), along with the volume of fluid in the pump cylinder, from which we can calculate the flow rate and confirm the target setting on the pump controller. Flow is terminated once stable voltage and pressure are recorded across the sample, defined as a variation of <10 mv and <2 kpa over 1200 s (20 min). The system is then allowed to relax, and the conductivity of the saturated sample and the conductivity and ph of the brine in each reservoir are measured. [13] We then adjust the valves V1 V6 and set the syringe pump so that flow through the sample occurs in the opposite direction, but at the same flow rate, until stable voltage and pressure are again recorded across the sample (e.g., Figure 2). The conductivity of the saturated sample and the conductivity and ph of the brine in each reservoir are then measured. As discussed later, these paired experiments (which we term the paired stabilization method), in which flow is induced through the sample at the same rate but in opposing directions, ensure that electrode polarization effects are negligible [e.g., Ball and Fuerstenau, 1973] and eliminate the effect of temporal variations in the static voltage. The paired experiments are conducted using at least four different flow rates for each sample and brine composition and repeated 3 times for each flow rate to evaluate experimental uncertainty (e.g., Figure 2). [14] To validate the voltage measurements obtained using the paired stabilization method, we also use a second approach termed the pressure ramping method. The pressure difference across the sample is increased linearly with time, from zero to a maximum value of approximately 0.5 MPa over a period of 120 s, and the pressure difference and voltage across the sample are recorded at a frequency of 1 Hz (e.g., Figure 3). The advantage of the pressure ramping method is that it is much quicker to implement than the paired stabilization method; the disadvantage is that poor results can be obtained if the pressure is ramped too quickly, because an equilibrium state is not achieved at which the streaming and conduction currents balance and equation (1) is valid. [15] To ensure that electrochemical and thermoelectric potentials are eliminated during measurements of the streaming potential, uniform and constant brine conductivity and ph (6 8) in each reservoir, and uniform and constant temperature (23 C), are maintained within a 5% tolerance. Redox potentials are minimized by ensuring that the Ag/AgCl electrodes are the only metal in contact with the samples and brine Measurements of Saturated Rock Conductivity [16] The conductivity of the saturated sample is measured using a two electrode configuration (either the internal Ag/AgCl electrodes shown in Figure 1b or similar external Ag electrodes with the sample removed from the pressure vessel) over the frequency range 10 Hz to 2 MHz. The measured parameters are frequency ( f), impedance (Z), and resistance (R). The resulting reactance (X) is then calculated, p X ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðz 2 R 2 Þ: ð4þ The value of measured resistance that corresponds to the minimum reactance is taken to be the resistance of the sample to direct current (e.g., Figure 4). Values of frequency that correspond to the minimum reactance are normally 1 5 khz. The conductivity of the saturated sample (s rw ) is calculated using rw ¼ L Rr 2 ; where r is the radius of the cylindrical core sample and L is the length. There is typically a small difference (<5%) in conductivity values obtained using the internal and external electrodes; the mean of the two measurements is taken as the final value Interpretation of the Streaming Potential Coupling Coefficient [17] Interpretation of the results from the paired stabilization experiments follows from the observation that at steady state, the streaming current induced by the flow is balanced by a conduction current to maintain overall electrical neutrality. It is reasonable to assume that the currents follow approximately the same 1 D path along the samples, so equation (1) can be used to determine the coupling coefficient with rp and rv replaced by the stabilized pressure difference (DP m ) and voltage (V m ) measured across the sample. Typically, the streaming potential coupling coefficient is given by the slope of a linear regression through a plot of stabilized voltage against pressure difference obtained for a number of different flow rates [e.g., Jouniaux and Pozzi, 1995, 1997; Lorne et al., 1999] (see Figures 5a and 5b). This approach works well in samples saturated with brine of relatively low salinity (<0.1 M) when the streaming potential is large compared to the static potential, and the absence of electrode polarization effects is confirmed if the calculated coupling coefficient is independent of flow direction (e.g., Figures 5a and 5b). However, in samples saturated with brine of higher salinity, the streaming potential is much smaller in magnitude and it is necessary to account for temporal variations in the static potential (V static ; e.g., Figures 5c and 5d). We eliminate this by conducting paired experiments over short time intervals (ca. 1 h) during which the variation in static voltage is small (<5 mv) compared to the measured streaming potential (>30 mv). The stabilized voltage measured in each experiment within a pair (denoted 1 and 2) is given by V m1 ¼ V s þ V static1 ; V m2 ¼ V s þ V static2 ; ð5þ ð6aþ ð6bþ where V s is the streaming potential. Assuming V static1 V static2 and subtracting the stabilized voltage and pressure difference measured in experiment 1 of a pair from those measured in experiment 2 yields V m1 V m2 ¼ 2V s ; DP m1 DP m2 ¼ 2DP: ð7aþ ð7bþ The streaming potential coupling coefficient is given by the slope of a linear regression through a plot of (V m1 V m2 )/2 against (DP m1 DP m2 )/2 (e.g., Figures 5e and 5f). The 5of18

6 Figure 2. Typical results for measured pressure difference and voltage against time obtained using the paired stabilization method for different rock samples and brines. (a) Stainton, 0.57 M NaCl, 3 ml/min; (b) Stainton, 0.1 M NaCl, 3 ml/min; (c) Stainton, M NaCl, 4.3 ml/min; (d) Stainton, 3.98 M NaCl, 3 ml/min; (e) Fontainebleau, M NaCl, 3 ml/min; (f) Fontainebleau, 0.23 M NaCl, 4.3 ml/min. 6of18

7 Figure 3. Measured voltage against pressure difference obtained using the pressure ramping method. The slope of the regression yields the coupling coefficient. (a) Stainton, 3.98 M NaCl, C = mv MPa 1, R 2 = ; (b) Stainton, 0.5 M NaCl, C = mv MPa 1, R 2 = ; (c) Stainton, Dead Sea water, C = mv MPa 1, R 2 = ; (d) St. Bees 1, 0.9 M NaCl, C = 1.35 mv MPa 1, R 2 = advantage of this approach is that we do not need to monitor or identify a value for the static voltage in order to interpret the measured data; moreover, we can still interpret the data for a given sample and brine salinity even if considerable time (e.g., 48 h over a weekend) has elapsed between measurements at different flow rates, so long as paired experiments for a given rate are conducted over a short time interval. A good fit of the data to a linear regression confirms that electrode polarization effects and variations in the static voltage are both small. Data for three repeat experiments are shown in Figures 5e and 5f Interpretation of the Zeta Potential [18] We calculate zeta potential from the measured streaming potential coupling coefficient using equation (2). We calculate the formation factor F by plotting the measured values of saturated sample conductivity against brine conductivity (Figure 6). During the establishment of thermodynamic equilibrium between the brine and the samples, a change in brine conductivity is recorded, which corresponds to a change in salinity. We relate conductivity and salinity using an empirical correlation [Worthington et al., 1990] and published data [CRC Handbook of Chemistry and Physics, 1989; Sen and Goode, 1992] at 23 C (Figures 7a and 7b). A comparison between these sources shows good agreement at low brine conductivity but significant differences for conductivity >1 S m 1. We therefore combined the sources, using the expression of Worthington et al. [1990] for brine conductivity <1 S m 1, and at higher conductivity, a new polynomial function of the same order as that suggested by Worthington et al. [1990] fitted to published data in the CRC Handbook of Chemistry and Physics [1989] and Sen and Goode [1992], C f ¼ 5: : þ 7: : þ 4: þ 3: þ 3: ; ð8þ 7of18

8 Figure 4. Measurements of saturated sample conductivity. (a) Impedance and resistance against frequency for the Fontainebleau sample saturated with 0.01 M NaCl brine. (b) Reactance against resistance for the same sample and brine as Figure 4a. The sample conductivity of S m 1 is obtained at the minimum reactance which corresponds to a frequency of 5.5 khz. (c) Impedance and resistance against frequency for the Stainton sample saturated with 1.92 M NaCl brine. (d) Reactance against resistance for the same sample and brine as Figure 4c. The sample conductivity of S m 1 is obtained at the minimum reactance which corresponds to a frequency of 1.4 khz. where the brine salinity (C f ) is expressed in M and conductivity (s f )isinsm 1. To relate the brine viscosity to salinity, we linearly interpolated the measured data at 25 C reported by Zhang and Han [1996] and that at 20 C reported in the CRC Handbook of Chemistry and Physics [1989] to yield values at 23 C (Figure 7c). The electrical permittivity as a function of brine salinity is calculated using the correlation suggested by Malmberg and Maryott [1956], which is similar to that used by Revil et al. [1999b]. 3. Results 3.1. Measurements of Streaming Potential [19] Figure 2 shows typical measurements of voltage and pressure difference across each sample against time for the paired stabilization experiments at different flow rates and brine salinity. Each plot shows a single paired experiment at a given flow rate for a given sample and brine composition. Our data set comprises approximately 200 of these paired experiments, so only a small subset is shown here. Brine is flowed through the sample in first one direction, until stable voltage and pressure differences are observed, at which time the pump is stopped and the voltage across the sample returns to approximately its initial (static) value. The brine is then flowed through the sample in the opposite direction but at the same rate, which causes the pressure and voltage to respond in the opposite sense but with the same magnitude. This gives us confidence that electrode polarization effects are small. [20] Figures 5a 5d shows typical plots of stabilized voltage against pressure difference. Each datapoint is obtained from a single flow experiment of the type described above. In samples saturated with low salinity brine (<0.1 M), the 8of18

9 stabilized voltage varies linearly with pressure difference and the streaming potential coupling coefficient is given by the slope of a linear regression through the data (Figures 5a and 5b). However, in samples saturated with higher salinity brine, the measured voltages are much smaller and a linear relationship is no longer observed because of temporal variations in the static potential across the sample (Figures 5c and 5d). However, as described in section 2.5, we can eliminate Figure 5 9of18

10 Figure 6. Saturated sample conductivity versus brine conductivity. The slope of the linear regression at brine conductivities greater than 1 S m 1 yields the formation factor (Table 1). the effect of the static potential by plotting the difference in stabilized pressure and voltage obtained between a pair of flow experiments (equation (7)). Figures 5e and 5f show the same data as Figures 5c and 5d, but each datapoint represents a pair of flow experiments, as described above. The voltage varies linearly with pressure difference, and the coupling coefficient is given by the slope of a linear regression through the data. [21] Figure 3 shows measured voltage against pressure difference from pressure ramping experiments on a range of different samples saturated with brines of different salinity and composition. The voltage varies linearly with pressure difference and the streaming potential coupling coefficient is given by the slope of a linear regression through the data. Figure 3a shows pressure ramping data from the same sample, saturated with brine of the same salinity (Stainton, 3.98 M NaCl brine), as the paired stabilization data shown in Figures 5c and 5e. The pressure ramping method yields a value of mv MPa 1 for the coupling coefficient (Figure 3a), while the paired stabilization method yields a value of mv MPa 1 (Figure 5e). In general, the results of the paired stabilized and pressure ramping experiments differ by less than 10%. [22] Figure 8 compares the stabilized voltage versus the pressure difference obtained using the internal and external electrodes. At low salinities, the electrodes yield similar values of the streaming potential coupling coefficient ( and mv MPa 1 for the internal and external electrodes, respectively; Figure 8a). However, at higher salinities (>0.1 M), the internal electrodes record flow rate dependent voltages, which are independent of flow direction (Figure 8b) Measurements of Saturated Rock Conductivity [23] Figure 4 shows typical measurements of saturated sample resistance and impedance against frequency and reactance against resistance. At low frequency, electrode polarization effects become significant, while at high frequency, capacitance effects become significant. The conductivity of the saturated sample is obtained using the approach outlined in section 2.4. Figure 6 shows the relationship between saturated sample conductivity and the conductivity of the saturating brine for three of the four samples investigated; the saturated sample conductivity was not measured over the range of brine salinities for the sandpack. The data follow a linear trend at brine conductivities >1 S m 1 when bulk conductivity dominates, but the behavior at lower salinity reflects the increasing contribution of surface conductivity [e.g., Lorne et al., 1999]. Including only data at brine conductivities >1 S m 1, we calculate the formation factor F as the reciprocal of the slope of a linear regression through the data. Values are reported in Table Relationship Between Flow Rate and Pressure Drop [24] At high salinities, the change in voltage which results from an applied pressure difference is small, so a large pressure difference is required to record a measurable voltage. However, a large pressure difference may result in nonlaminar flow, in which case Darcy s law is no longer obeyed and equation (2) is not valid [e.g., Lorne et al., 1999]. To verify that the flow is laminar, we plot flow rate Q as a function of applied pressure difference DP (e.g., Figure 9) and confirm that a linear relationship is observed with slope k/m w, where k is the sample permeability (reported in Table 1) and m w is the brine viscosity (Figure 7c). In all experiments, we find that a linear regression fits the measured data with R 2 >0.99, and the value of permeability calculated from the slope varies by <5%. Note also that the Reynolds number for these experiments, calculated using equations (22) and (23) of Bolève et al. [2007], is always less than 10 5, suggesting that inertial forces are negligible Salinity Dependence of the Streaming Potential Coupling Coefficient [25] Figure 10 shows the streaming potential coupling coefficient as a function of brine salinity along with data from previous studies on consolidated sandstones and unconsolidated sand. Also shown are values of the coupling coefficient Figure 5. Stabilized voltage (V m ) against stabilized pressure difference (DP m ) for different rock samples and brines. (a) V m against DP m for the Stainton sample saturated with M NaCl brine. The temporal variation of static voltage is negligible compared to the measured voltage. A linear regression through data yields C = mv MPa 1 with R 2 = (b) V m against DP m for the Fontainebleau sample saturated with M NaCl brine. A linear regression through data yields C = mv MPa 1 with R 2 = (c) V m against DP m for the Stainton sample saturated with 3.98 M NaCl brine. The temporal variation of static voltage is comparable to the measured voltage, so the data are scattered. (d) V m against DP m for the Fountainbleau sample saturated with 3.08 M NaCl brine. The temporal variation of static voltage is comparable to the measured voltage, so the data are scattered. (e) (V m1 V m2 )/2 against (DP 1 DP 2 )/2 for the same data as shown in Figure 5c. A linear regression through these data yields C = mv MPa 1 with R 2 = (f) (V m1 V m2 )/2 against (DP 1 DP 2 )/2 for the same data as shown in Figure 5d. A linear regression through these data yields C = mv MPa 1 with R 2 = of 18

11 Figure 7. Brine salinity versus brine conductivity plotted (a) log log scale and (b) linear scale, showing our expression to relate the two (equation (8)) compared against that of Worthington et al. [1990] and published data in the CRC Handbook of Chemistry and Physics [1989] and Sen and Goode [1992]. (c) Brine viscosity versus brine salinity showing our expression to relate the two. predicted in two ways. The first uses equation (3) and a relationship between zeta potential and brine salinity, which we discuss in section 3.5. The second uses an empirical relation between the coupling coefficient and brine salinity obtained directly from a regression through the available data, C ¼ 1:36C 0:9123 f ; ð9þ where the coupling coefficient is expressed in mv MPa 1 and the brine salinity is expressed in M. This regression matches the available data with R 2 = [26] The magnitude of the measured coupling coefficient decreases with increasing salinity. At low salinity, the values we record are consistent with those obtained in previous studies. At high salinity, the coupling coefficient does not fall to zero, but remains nonzero until the NaCl saturation limit is approached, in agreement with the data obtained by Jaafar et al. [2009]. The value of the measured coupling coefficient for a given brine salinity, particular at high salinity (>0.5 M), is similar regardless of the composition of the brine or the mineralogy and texture of the sample. The coupling coefficient is always negative, so the zeta potential is also negative Salinity Dependence of the Zeta Potential [27] Figure 11a shows the zeta potential as a function of brine salinity along with data from previous studies on quartz, silica, and glass. At low salinity, the magnitude of the zeta potential decreases with increasing salinity, as observed in previous studies and predicted by models of the electrical double layer based on the Boltzmann transport equation [e.g., Hunter, 1981; Revil et al., 1999a]. However, at salinities above approximately 0.4 M, the zeta potential reaches a constant value within experimental error, which is consistent with the findings of Jaafar et al. [2009]. [28] Also shown in Figure 11a are values of the zeta potential predicted using a relationship between zeta potential and brine salinity given by ¼ a þ b log C f ; C f < 0:4M ¼ c; C f 0:4M; ð10aþ ð10bþ 11 of 18

12 Figure 8. Comparison between stabilized voltages measured using the external and internal electrodes. (a) Stabilized voltage versus pressure difference for the Stainton sample saturated with 0.04 M NaCl brine yields C = mv MPa 1 and R 2 = using the external electrodes and C = mv MPa 1 and R 2 = using the internal electrodes. (b) Stabilized voltage versus pressure difference for the Stainton sample saturated with 0.31 M NaCl brine yields C = 3.77 mv MPa 1 and R 2 = using the external electrodes and C = 4.06 mv MPa 1 and R 2 = using the internal electrodes. where z is expressed in mv and C f is expressed in M. A relationship of the form of equation (10a) between zeta potential and salinity was originally proposed based on measured zeta potential data in the low salinity range (<0.1 M) [Pride and Morgan, 1991] and can also be derived from a model of the electrical double layer which captures the partitioning of countercharge between the Stern and diffuse layers and invokes the Boltzmann equation to describe the charge density in the diffuse layer [Revil et al., 1999a]. Jaafar et al. [2009] suggested that the zeta potential is constant at high salinity (>0.4 M; equation (10b)). We find the best fit to the data shown in Figure 11 is obtained with a = 9.67 mv, b = mv, and c = 17 mv. The quality of the fit is given by R 2 = Pride and Morgan [1991] reported a = 8 mv and b = 26 mv, Boléve et al. [2007] suggested a = 14.6 mv and b = 29.1, while Revil et al. [1999a] estimate a 10 mv and b 20 mv. All of these studies implicitly assumed c =0.Jaafar et al. [2009] suggest a = 6.43 mv, b = mv and c = 20 mv, which are similar to the values proposed here Time Dependence of the Streaming Potential Coupling Coefficient [29] Reppert and Morgan [2003] found that measured values of the streaming potential coupling coefficient decreased significantly with time. For example, in a Fontainebleau sample saturated with approximately M NaCl brine (i.e., much lower salinity than the brines considered in this Figure 9. Flow rate against applied pressure difference. (a) Stainton saturated with 0.1 M NaCl brine, linear regression through the origin fits with R 2 = (b) Fountainbleau saturated with 0.56 M NaCl brine, linear regression through the origin fits with R 2 = of 18

13 Figure 10. Streaming potential coupling coefficient as a function of brine salinity, plotted with published data. Also shown are curves calculated using equation (10) in conjunction with equation (3) and equation (9). All values of the coupling coefficient are negative; only the magnitude of the coupling coefficient is presented. (a) Data from (1) sandstone and NaCl brine [Jiang et al., 1998; Spruntetal., 1994; Jouniaux and Pozzi, 1995; Jouniaux and Pozzi, 1997; Li et al., 1995; Pengra et al., 1999], (2) sandstone and KCl brine [Alkafeef and Alajmi, 2006], (3) sand and NaCl brine [Ahmad, 1964; Block and Harris, 2006; Guichet et al., 2003; Ogilvy et al., 1969; Schriever and Bleil, 1957], (4) silica nanochannels and KCl brine, (5) glass beads and NaCl brine [Block and Harris, 2006; Li et al., 1995; Pengra et al., 1999], (6) St. Bees 1 and NaCl brine [Jaafar et al., 2009], (7) St. Bees 2 and NaCl brine [Jaafar et al., 2009], (8) Stainton and NaCl brine, (9) Fountainbleau and NaCl brine, (10) Fountainbleau and seawater, (11) Stainton and Dead Sea water (plotted at the NaCl salinity which yields the same electrical conductivity), (12) sandpack and tap water, (13) St. Bees 2 and seawater. (b) The inset focusing on the high salinity domain. The axis labels and data legend are the same as in Figure 10a. paper), they found that the coupling coefficient decreased in magnitude from approximately 360 mv MPa 1 to approximately 250 mv MPa 1 over a period of approximately 46 days (their Figure 6). In general, the values of coupling coefficient and zeta potential they report for their sandstone samples are smaller than those reported previously, and they ascribed this to the increased equilibration time in their study. To confirm that our reported values of the streaming potential coupling coefficient and zeta potential reflect equilibrium conditions, we ran an extended experiment for one sample in which the coupling coefficient, and brine conductivity and ph in each column were measured twice a week over a period of 77 days (Figure 12). We recorded no change in the measured streaming potential, brine conductivity, or ph within experimental error and conclude that our preparation of the samples prior to conducting streaming potential measurements (see section 2.2) ensures equilibrium between samples and saturating brines Uncertainties in the Reported Values of Streaming Potential Coupling Coefficient and Zeta Potential [30] The error bars shown in Figures 10 and 11a are representative of all samples and brines investigated. Uncertainty in the measured value of the coupling coefficient is assessed from the reproducibility of experiments. The uncertainty in measured voltage increases with increasing salinity, since the magnitude of the voltage decreases. Consequently, the reproducibility of results deteriorates with increasing brine salinity, resulting in an increased scatter of data and reducing the quality of fit of a linear regression through the voltage and pressure data from R 2 = at 1 M to R 2 = at 5 M (e.g., Figure 5). The resulting uncertainties in 13 of 18

14 Figure 11. (a) Zeta potential as a function of brine salinity, compared with published data. The curve represents equation (10) fitted to the data for silica, quartz, and glass in NaCl brine (including the data from this study) with values a = 9.67 mv, b = mv, and c = 17 mv; R 2 = The transition from equation (10a) to equation (10b) occurs at a salinity of 0.4 M. Data from (1) silica [Gaudin and Fuerstenau, 1955; Li and de Bruyn, 1966; Kirby and Hasselbrink, 2004], (2) quartz [Pride and Morgan, 1991; Kosmulski et al., 2003], (3) glass beads [Bolève et al., 2007],(4)St.Bees1[Jaafar et al., 2009], (5) St. Bees 2 [Jaafar et al., 2009], (6) Stainton, (7) Fountainbleau, (8) Fountainbleau and UK seawater, (9) Stainton and Dead Sea water (plotted at the NaCl salinity which yields the same electrical conductivity), and (10) St. Bees 2 and UK seawater. (b) Zeta potential as a function of brine salinity measured on alumina particles in KCl [Dukhin et al., 2005]. Note that the zeta potential is positive, reflecting the positively charged alumina surfaces. The curve represents equation (10) fitted to their data with a = 9 mv, b = 27 mv and c = 9 mv; R 2 = The transition from equation (10a) to equation (10b) occurs at a salinity of 1 M. the coupling coefficient are carried through into the interpreted values of zeta potentials using equation (2). 4. Discussion 4.1. Dependence of the Zeta Potential on Brine Salinity [31] The values of zeta potential we interpret from our streaming potential measurements on different sandstone samples are consistent with those reported by Jaafar et al. [2009]. The magnitude of the zeta potential decreases with increasing brine salinity, up to a threshold value above which the zeta potential remains constant. The threshold salinity and the constant value of zeta potential above this threshold are both uncertain given the scatter in the data. [32] At high brine salinity, models of the double layer based on the Boltzmann equation predict that the diffuse layer thickness collapses to zero, in which case the countercharge must reside entirely within the Stern layer and the zeta potential falls to zero, as predicted by equation (10a) when extrapolated into the high salinity domain. Jaafar et al. [2009] suggested that ion interactions cause the reduction in thickness of the diffuse layer at high salinity to be less than predicted by the Boltzmann equation, in which it is assumed that the ions are point charges. Moreover, the countercharge required to balance the mineral surface charge is not accommodated entirely within the Stern layer, so the diffuse layer does not collapse to zero. Rather, some of the countercharge remains mobile within the diffuse layer, at a maximum charge density which is limited by the size of the hydrated counterions. Jaafar et al. [2009] noted that the zeta potential reaches a constant value at a salinity of approximately 0.4 M, while the Debye length, which is a measure of the thickness of the diffuse layer derived from the Boltzmann model [e.g., Hunter, 1981], is approximately 0.47 nm at this salinity, which is comparable with the diameter of a hydrated sodium ion [e.g., Yang et al., 2004; Figure 13]. This suggests that the constant zeta potential observed at salinities higher than 0.4 M Figure 12. Coupling coefficient and brine conductivity measured over 77 days for the Stainton sample saturated with 1 M NaCl brine. 14 of 18

15 Figure 13. Debye length versus salinity of 1 1 brine. Also shown are the estimated diameters of hydrated Na + and K + ions. reflects the maximum charge density in the diffuse layer, which is reached when the diffuse layer thickness approaches the diameter of the counterions. At high brine concentration, the double layer therefore resembles the Helmholtz model, in which the excess charge distribution approximates that of a parallel capacitor, with a single layer of hydrated, immobile ions accommodated within the Stern layer, and a single layer of hydrated, mobile ions accommodated within the diffuse layer, and the so called shear plane located at the boundary between the Stern and diffuse layers (a boundary sometimes termed the Outer Helmholtz Plane) [Bard and Faulkner, 2001]. [33] This hypothesis is supported by our new data and also by data obtained by Dukhin et al. [2005] in the high salinity domain. They measured the zeta potential of alumina particles in KCl solutions up to 2 M using the electroacoustic method, in which the application of ultrasound waves causes relative motion between the suspended particles and the solution, resulting in the generation of an alternating current and an associated electrical potential. They also found that the zeta potential decreased with increasing salinity but reached a constant value of approximately 10 mv at salinities higher than approximately 1 M (Figure 11b). Our hypothesis predicts that the Debye length at this salinity should be similar to the radius of a hydrated potassium ion, which is indeed thecase(figure13).themeasurementsofdukhin et al. [2005] are supported by those of Johnson et al. [1999a, 1999b] on the same materials, which yielded zeta potentials of approximately mv at 1 M Dependence of the Streaming Potential Coupling Coefficient on Brine Salinity [34] We have presented a new regression to the measured values of streaming potential coupling coefficient as a function of salinity (equation (9)). However, we can also use our new regression for zeta potential (equation (10)) in conjunction with equation (3) to predict the value of the coupling coefficient as a function of salinity (Figure 10a). Equation (3) neglects the effect of surface conductivity, which depends upon the texture of the porous medium and becomes more significant at lower salinity (<0.1 M). Consequently, predicted values of the coupling coefficient obtained using a regression to zeta potential data are larger in magnitude than those obtained experimentally at low salinity, so our two approaches to predicting the salinity dependence of the coupling coefficient yield different values (Figure 10). However, they agree to within 5% at high salinity, when surface conductivity is less important Effect of Rock Texture and Mineralogy [35] The samples investigated in this paper and by Jaafar et al. [2009] vary in texture and mineralogy. However, the values of coupling coefficient obtained at salinities above approximately 0.1 M, where the surface electrical conductivity is negligible (Figure 6; a salinity of 0.1 M corresponds to a brine conductivity of approximately 1 S m 1 ) are the same within experimental error, regardless of rock texture and mineralogy (Figure 14). Zeta potentials for salinities above 0.4 M are also found to be independent of rock texture and mineralogy, which agrees with equation (10). Figure 14 shows data from one consolidated sample with low porosity and high formation factor which is entirely composed of quartz and two consolidated samples which have higher porosity and lower formation factor, but which also contain mica and clay minerals (Table 1). The surface charge of clay minerals is known to differ from that of quartz, because the crystalline structure of clay minerals promotes the exchange of cations with the brine [e.g., van Olphen, 1963]. However, we do not need to invoke the high surface charge on clay minerals to explain the zeta potentials we record at high salinity. We record the same zeta potential, within experimental error, in samples which do not contain clay Effect of Brine Composition [36] The presence of multivalent ions in high enough concentration can lead to charge inversion, which occurs when the accumulation of multivalent ions within the Stern layer causes the apparent surface electrical charge to change sign, and is characterized by a change in sign of the measured streaming potential coupling coefficient (and hence zeta potential) [Hunter, 1981]. We have investigated simple NaCl brines which contain no multivalent ions and natural brines (seawater and Dead Sea water) which contain multivalent ions in concentrations up to 1.62 M (Table 2). However, we record the same coupling coefficient and zeta potential for a given sample and brine salinity regardless of brine composition, and observe no evidence of charge inversion (Figure 15). The zeta potentials we obtain from samples saturated with seawater are consistent in both sign and magnitude with those obtained by Kim [2000] for quartz sand powders in seawater, but are rather larger in magnitude than those reported by Kosmulski et al. [2003] for amorphous quartz (Figure 11). Multivalent ions in natural brines do not appear to be present in high enough concentration to cause charge inversion in quartz rich sandstones. This is consistent with the observations of van der Heyden et al. [2005], who found that charge inversion in quartz nanochannels was suppressed at high ionic strength (ca M, which spans the value of 0.6 M typical of seawater) in KCl dominated 15 of 18