Measurement of streaming potential coupling coefficient in sandstones saturated with high salinity NaCl brine

Transcription

1 GEOPHYSICAL RESEARCH LETTERS, VOL. 36, L21306, doi: /2009gl040549, 2009 Measurement of streaming potential coupling coefficient in sandstones saturated with high salinity NaCl brine M. Z. Jaafar, 1,2 J. Vinogradov, 1 and M. D. Jackson 1 Received 20 August 2009; revised 2 October 2009; accepted 7 October 2009; published 10 November [1] We present measurements of the streaming potential coupling coefficient in intact sandstone samples saturated with NaCl brines at concentrations up to 5.5 moll 1. The values we record at low salinity are consistent with those reported previously. As brine salinity increases, the coupling coefficient decreases in magnitude, but is still measureable up to the saturated concentration limit. The magnitude of the zeta potential also decreases with increasing salinity, but approaches a constant value at high salinity. This behaviour is not captured by current models of the electrical double layer. Our results suggest that streaming potential measurements may be used to monitor flow in saline subsurface environments such as deep saline aquifers and hydrocarbon reservoirs. However, they were obtained at laboratory temperature. Future work will focus on the effect of elevated temperatures at high salinity. Citation: Jaafar, M. Z., J. Vinogradov, and M. D. Jackson (2009), Measurement of streaming potential coupling coefficient in sandstones saturated with high salinity NaCl brine, Geophys. Res. Lett., 36, L21306, doi: /2009gl Introduction [2] Measurements of streaming potential have been used to characterize subsurface flow in numerous earth science applications, where the brine under investigation has been of relatively low salinity (less than seawater; see Corwin and Hoover [1979] for geothermal examples, and Ishido [2004] for examples of volcano monitoring, amongst numerous publications). Measurements of streaming potential 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 these measurements requires knowledge of the streaming potential coupling coefficient at high salinity. The coupling coefficient (C) is a key petrophysical property which relates the fluid (rp) and streaming (rv) potential gradients when the total current density (j) is zero [Sill, 1983] C ¼ rv ð1þ rp j¼0 1 Department of Earth Science and Engineering, Imperial College London, London, UK. 2 Now at Petroleum Engineering Department, Universiti Teknologi Malaysia, Johor Bahru, Malaysia. Copyright 2009 by the American Geophysical Union /09/2009GL The magnitude and sign of the coupling coefficient depends upon the electrical conductivity of the brine (s w ) and brinesaturated rock (s rw ), the permittivity (e w ) and viscosity (m w ) of the brine, and the zeta potential (z), which is the electrical potential associated with the counter charge in the electrical double layer at the mineral-fluid interface [e.g., Jouniaux and Pozzi, 1995] C ¼ e wz m w s rw F where F is the formation factor ( = s w /s rw ) measured when surface electrical conductivity is negligible (typically with a very saline brine) and s rw includes the contribution of surface conductivity. When surface conductivity is negligible, equation (2) simplifies to the well known Helmholtz- Smoluchowski equation, which is valid in homogenous granular porous media so long as the thickness of the electrical double layer is less than the characteristic radius of curvature of the pores and electro-osmosis induced by the streaming potential can be neglected [e.g., Hunter, 1981] C ¼ e wz m w s w [3] Values of the streaming potential coupling coefficient have been measured experimentally in samples of sandstone and sand saturated with relatively low salinity NaCl or KCl brines (less than 1 mol L 1 )[Sprunt et al., 1994; Jouniaux and Pozzi, 1995, 1997; Li et al., 1995; Jiang et al., 1998; Pengra et al., 1999; Alkafeef and Alajmi, 2006; Block and Harris, 2006]. These data show that the coupling coefficient decreases with increasing brine salinity. However, it is not possible to extrapolate measurements of the streaming potential coupling coefficient obtained at low salinity into the high salinity domain using a simple regression, because the variation in zeta potential with salinity must also be accounted for. To extrapolate requires an understanding of either the magnitude and sign of the zeta potential, or the charge density in the diffuse part of the electrical double layer, at high salinity. However, there are no published measurements of zeta potential on quartz or glass in NaCl or KCl brine above 0.1 mol L 1, or on clays above 1 mol L 1. Moreover, published models of the charge density in the diffuse layer rely either on the Boltzmann transport equation [e.g., Revil et al., 1999] or Donnan equilibria [e.g., Revil and Leroy, 2004]. The assumptions underlying both of these approaches break down in sandstones saturated with high salinity brine, when the counter-charge is confined to the Stern layer and a very thin diffuse layer adjacent to the mineral surface. [4] The lack of measured data at high salinity, and of a model which can be used to extrapolate data measured at low salinity into the high salinity domain, means that the ð2þ ð3þ L of6

2 Figure 1. Experimental apparatus for measuring the streaming potential coupling coefficient. (a) Brine is pumped through the saturated core sample, which is confined in a pressurized core holder located between two reservoirs. The syringe pump maintains constant flow rate to high accuracy. Synthetic oil is used as a hydraulic fluid to drive the brine from the inlet to the outlet reservoir, because this allows air bubbles in the brine to be captured at the top of the oil layer in each reservoir, eliminates the flow of electrical current through the brine along a path parallel to the core sample and reduces corrosion of the pump. Brine can be pumped in either direction through the sample by adjusting the valves (V1 V6) on the flowlines (shown as solid lines; dashed lines denote electrical connections), so each reservoir can act as the inlet or outlet depending upon the chosen flow direction. (b) The external electrodes are located out of the flow path in an NaCl solution which is more saline than the flowing brine. The electrodes are in electrical contact with the flowing brine via a low permeability porous disc. (c) Cross-section through the core holder. The internal electrodes are located on each face of the sample and can be used to measure streaming potential or resistivity. They are permeable meshes with the same diameter as the samples. interpretation of subsurface measurements of streaming potential obtained at high salinity is uncertain. The aim of this paper is to present the first measured values of streaming potential coupling coefficient in intact sandstone cores saturated with NaCl brine at salinities higher than 1 mol L 1. 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. 2. Materials and Methods [5] We have two different sets of experimental apparatus which can be run simultaneously. The first holds the brinesaturated core sample in a stainless steel pressure vessel with oil as the confining fluid (Figure 1). The steel vessel is electrically isolated from the sample by a rubber sleeve and plastic caps at both ends, and provides an earthed Faraday enclosure to eliminate spurious external currents. The second holds the sample in an acrylic pressure vessel with nitrogen as the confining fluid. The vessel is wrapped in earthed foil to provide a Faraday enclosure. [6] To measure the streaming potential coupling coefficient, a syringe pump is used to induce a fluid pressure difference across the sample, causing brine to flow through the sample from reservoirs connected to each side of the pressure vessel (Figure 1a). The 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) and the voltage across the sample is measured using two pairs of non-polarizing 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 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 low permeability plug (Figure 1b) and provide voltage measurements which are stable to c. 10 mv. The other pair of electrodes are located on each face of the core sample and comprise a permeable mesh with the same diameter as the core sample (Figure 1c). These internal electrodes, which are in the path of the flow, are less stable than the external electrodes and record flow-rate dependent voltages at high salinity which are independent of flow direction. However, they can be used to measure the conductivity of the saturated core. [7] The brine used in the experiments is a simple solution of NaCl in de-ionized water. Brine salinity varies from mol L 1 to 5.5 mol L 1, which is a saturated solution at laboratory temperature. The core samples are Triassic 2of6

3 Table 1. Rock Samples Used in the Experiments Sample Name St. Bees #1 St. Bees #2 Origin Sandstone Outcrop at St. Bees, Cumbria, U.K. Sandstone Outcrop at St. Bees, Cumbria, U.K. Age Triassic Triassic Depositional environment Aeolian Aeolian Porosity 19% 19% Liquid permeability 70 md 30 md Mineralogy Quartz 90% 90% Feldspar 5% 5% Other rock fragments 5% 5% Cement Calcite Calcite Formation factor Grain size mm mm Dimensions 7.7 cm length and 3.7cm diameter 7.7 cm length and 3.7cm diameter aeolian sandstones from the St. Bees Formation near Durham, UK, measuring 7.7 cm in length and 3.7 cm in diameter. Sample St. Bees #1 was cut parallel to bedding and St. Bees #2 perpendicular to bedding; the properties of the samples are very similar (Table 1). Prior to starting a series of experiments at a given salinity, the sample is saturated with the brine in a vacuum and then left for several days to allow the brine to equilibrate with the mineral surfaces. The sample is then loaded into the pressure vessel, and brine of the same salinity flowed repeatedly through the sample from one reservoir to the other and back again, until the conductivity of the brine remains constant and equal within a 10% tolerance. Measurements of streaming potential then begin. [8] For each value of brine salinity, brine is flowed through the core sample at constant rate until stabilized pressure and voltage differences are recorded (e.g., Figure 2a). 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 pressure difference (DP) and streaming potential (DV) measured across the sample. To eliminate the effect of slow temporal variations in static voltage recorded across the sample, paired experiments are conducted for each flow rate, in which brine is pumped through the sample in first one direction, and then the opposite direction, over a short time interval (c. 1 hr.), during which the variation in static voltage is small (<5 mv) compared to the measured streaming potential (>30 mv) (e.g., Figure 2a). The streaming potential for a given pressure difference is then obtained from the difference in stabilized voltage and pressure recorded in the paired pumping experiments. A linear regression through these data, obtained for a number of constant flow rates, yields the streaming potential coupling coefficient (e.g., Figure 2b). [9] During the experiments, the conductivity of the brine in each reservoir is measured at regular intervals to ensure it remains constant and equal using a Metrohm 712 conductometer. The resistance of the saturated sample is also measured at regular intervals, over the frequency range 10 Hz 2 MHz, using a QuadTech7600 Precision LCR meter and the two internal electrodes. The conductivity of the saturated sample is calculated using the resistance measured at the frequency which yields the minimum value of reactance; this frequency is typically c. 2 khz but varies between 1 and 5 khz. The ph of the brine is measured before and after each experiment using a Hanna H8519 ph meter and, in the measurements reported here, varied between 6 and 8 ph units. 3. Results [10] Figure 2 shows a typical example of data recorded from the experiments. Figure 2a shows a plot of voltage and pressure difference against time for St. Bees #2, flowing 5.5 mol L 1 brine at ml s 1. Pumping in opposite directions, but at the same flow rate, causes the pressure and voltage to respond in the opposite sense but with the same magnitude, which gives us confidence that electrode polarization effects are small. Figure 2b shows a plot of streaming potential (DV) against the corresponding pressure difference (DP) for St. Bees #2, Figure 2. Typical experimental results. (a) Measured voltage and pressure difference against time for St. Bees #2, saturated with 5.5 mol L 1 NaCl flowing at ml s 1. (b) Streaming potential against pressure difference at different flowrates, for St. Bees #2 saturated with 5.5 mol L 1 NaCl. The regression gives a value of C = VPa 1 with R 2 = of6

4 flowing 5.5 mol L 1 brine. A linear regression through these data yields a value of the streaming potential coupling coefficient C = VPa 1 with R 2 = [11] Figure 3 shows the measured value of coupling coefficient as a function of brine salinity, for both St. Bees samples, along with data from previous studies on consolidated sandstones and unconsolidated sand. Also shown are values of the coupling coefficient predicted using a relationship between zeta potential and brine salinity given by z ¼ a þ b log C f and equation (3). Equation (4) was originally obtained from an empirical fit to measured zeta potential data in the low salinity range [Pride and Morgan, 1991], but can also be derived from a model of the electrical double layer which captures the partitioning of counter-charge between the Stern and diffuse layers and invokes the Boltzmann transport equation to describe the charge density in the diffuse layer [Revil et al., 1999]. Fitting this equation to published zeta potential data for quartz, silica and glass in NaCl brine (Figure 3c) yields values of a = 6.43 mv and b = mv. Our new data are not included in the fit. [12] The magnitude of the measured coupling coefficient for both St. Bees samples decreases with increasing salinity. At low salinity, the values are consistent with those obtained in previous studies. At high salinity, the coupling coefficient does not fall to zero as rapidly as predicted by equations (3) and (4), but remains non-zero until the NaCl saturation limit is approached. The coupling coefficient is always negative, so the zeta potential is also negative. The uncertainties in coupling coefficient shown in Figure 3b were estimated from the voltage noise level, which gives the uncertainty in each individual measurement of stabilized voltage, and the repeatability of results, which gives the uncertainty in multiple measurements of stabilized voltage for a given salinity and flow rate. Each data point was obtained from three repeat experiments. [13] We calculate the effective zeta potential from the streaming potential coupling coefficient using equation (2) in conjunction with measurements of the electrical conductivity of the saturated rock, to account for the effect of ð4þ 4of6 Figure 3. (a) Streaming potential coupling coefficient as a function of brine salinity measured for St. Bees #1 and St. Bees #2, compared with published data. All values are negative; only the magnitude of the coupling coefficient is shown. The curve is the predicted coupling coefficient using equation (4) fitted to published data for zeta potential in the low salinity range and equation (3). Data from [1] sandstone with NaCl electrolyte [Sprunt et al., 1994; Jouniaux and Pozzi, 1995, 1997; Li et al., 1995; Jiang et al., 1998; Pengra et al., 1999]; [2] sandstone with KCl electrolyte [Alkafeef and Alajmi, 2006]; [3] sand with NaCl electrolyte [Guichet et al., 2003; Block and Harris, 2006]. (b) Close-up of the measured coupling coefficient in the high salinity region showing the estimated errors on the St. Bees#1 measurements. The errors are similar for St. Bees#2. (c) Zeta potential as a function of brine salinity for St. Bees #1 and St. Bees #2, compared with published data. The line represents equation (4) fitted to the data for quartz, silica and glass in NaCl brine with values of a = 6.43 mv and b = mv with R 2 = Our new data are not included in the fit. Data from [4] quartz [Pride and Morgan, 1991]; [5] silica [Gaudin and Ferstenau, 1955; Li and de Bruyn, 1966; Kirby and Hasselbrink, 2004]; [6] glass beads [Bolève et al., 2007].

5 surface conductivity (Figure 3c). At low salinity, the magnitude of the zeta potential for both St. Bees samples 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., 1999]. However, at salinities higher than approximately 0.4 mol L 1, the zeta potential reaches a constant value of approximately 20 mv within experimental error. Given the scatter in the data, there is considerable uncertainty in both the value of the constant zeta potential and the salinity at which it is reached. 4. Discussion [14] The magnitude of the measured streaming potential coupling coefficient decreases with increasing brine salinity but is non-zero up to the saturated brine concentration at laboratory temperature. At low salinity, the magnitude of the zeta potential also decreases with increasing brine salinity, as observed in previous studies, but reaches a constant value at high salinity. This behaviour has not been observed previously in sandstones, although non-zero values of zeta potential have been measured on clay minerals in high salinity brines of varying composition [Kosmulski and Dahlsten, 2006]. [15] At high brine salinity, models based on the Boltzmann equation predict that the diffuse layer thickness collapses to zero, in which case the counter-charge resides entirely within the Stern layer. The zeta potential also falls to zero, as predicted by equation (4) when extrapolated into the high salinity domain (Figure 3c). We hypothesize 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 counter-charge 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 counter-charge remains mobile within the diffuse layer, at a maximum charge density which is limited by the size of the hydrated counter-ions. We note that the zeta potential reaches a constant value at a salinity of approximately 0.4 mol L 1 and that 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]. This suggests that the constant zeta potential we observe at salinities higher than 0.4 mol L 1 reflects the maximum charge density in the diffuse layer, which is reached when the diffuse layer thickness approaches the diameter of the counter-ions. Further work is required to test this hypothesis. 5. Conclusions [16] The magnitude of the streaming potential coupling coefficient in sandstones saturated with NaCl brine decreases with increasing brine salinity, but is non-zero up to the saturated brine concentration at laboratory temperature. These results suggest that streaming potential measurements may be used to monitor flow in saline subsurface environments such as deep saline aquifers and hydrocarbon reservoirs. However, the data were obtained at laboratory temperature; future work will focus on the elevated temperatures typical of subsurface environments. At low salinity, the magnitude of the zeta potential also decreases with increasing brine salinity, but approaches a constant value at high salinity. This behaviour is not captured by current models of the electrical double layer. References Alkafeef, S. F., and A. F. 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6 Sill, W. R. (1983), Self-potential modeling from primary flows, Geophysics, 48, 76 86, doi: / Sprunt, E. S., T. B. Mercer, and N. F. Djabbarah (1994), Streaming potential from multiphase flow, Geophysics, 59, , doi: / Yang, K.-L., S. Yiacoumi, and C. Tsouris (2004), Electrical Double-Layer Formation, Dekker Encyclopaedia Nanosci. Nanotechnol., vol. 2, edited by J. A. Schwarz, C. I. Contescu, and K. Putyera, Taylor and Francis, London. M. Z. Jaafar, Petroleum Engineering Department, Universiti Teknologi Malaysia, UTM Skudai, Johor Bahru, Malaysia. M. D. Jackson and J. Vinogradov, Department of Earth Science and Engineering, Imperial College London, Exhibition Rd., London SW7 6AS, UK. 6of6