We have measured the streaming potential in water-wet sandstones during both drainage and imbibition, and demonstrate that it behaves differently in oil/brine and gas/brine displacements. During drainage, the streaming potential remains significantly greater than zero at the irreducible water saturation in oil/brine displacements, but falls to zero in gas/brine displacements. During imbibition, the streaming potential at partial saturation in oil/brine displacements exceeds that measured at saturation, but not in gas/brine experiments. Our results have application to streaming potential measurements in the vadose zone, hydrocarbon reservoirs, contaminated aquifers and during CO2 sequestration.
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 Measurements of the streaming potential may be used to monitor subsurface fluid flow in regions where two or more mobile fluid phases occupy the pore-space, such as the vadose zone, hydrocarbon reservoirs, contaminated aquifers and CO2 sequestration [Darnet and Marquis, 2004; Moore et al., 2004; Saunders et al., 2006, 2008]. However, to interpret the measurements requires knowledge of the streaming potential coupling coefficient during multiphase flow. The coupling coefficient (C) relates the fluid (∇P) and streaming (∇V) potential gradients when the total current density (j) is zero [Sill, 1983]
When there is more than one fluid phase present in the pore space, the coupling coefficient is a function of phase saturation, and can be described in terms of a saturation-dependent relative coupling coefficient (Cr) and the value of the coupling coefficient when the pore-space is fully saturated by the wetting phase [Revil and Cerepi, 2004; Jackson, 2008]
where Sw denotes the wetting phase saturation and it is assumed that there are only two mobile fluid phases.
 The functional relationship between coupling coefficient and phase saturation during drainage and (in particular) imbibition remains uncertain, with little published experimental data and at least seven different published expressions (see Jackson  for a review). Revil and Cerepi  and Revil et al.  conducted capillary desaturation experiments in which a non-wetting gas (argon, air or nitrogen) invaded initially brine-saturated dolomite core-plugs, while Moore et al.  conducted unsteady-state displacement experiments in which a non-wetting liquid (carbon dioxide) was injected into initially brine-saturated sandstone core-plugs. Guichet et al.  allowed brine to drain from an initially brine-saturated sandpack with an invading, non-wetting gas (nitrogen or argon). None of these studies investigated imbibition.
 The aim of this paper is to present the first comparison of multiphase streaming potential in initially brine-saturated sandstone cores, during drainage with either a gas (nitrogen) or a liquid (undecane) non-wetting, non-polar phase, and then during the subsequent imbibition of brine. We present results which are not captured by any current models of multiphase streaming potential, and have application to the interpretation of streaming potential measurements in hydrocarbon reservoirs, contaminated aquifers, the vadose zone and CO2 sequestration.
2. Materials and Methods
 The experimental apparatus used in this study is modified from that described by Jaafar et al. . The core sample is held in a pressure vessel, and to measure the streaming potential, a syringe pump is used to induce a pressure difference across the sample, causing fluid to flow through the sample from reservoirs connected to each side of the pressure vessel (Figure 1a). The voltage across the sample is measured using a pair of non-polarizing Ag/AgCl electrodes located on each face of the sample (Figure 1b). The noise level of the voltage measurements is dictated by the stability of the electrodes (c. 100μV). Measurements of the pressure difference across the sample, the brine electrical conductivity and pH, and the electrical conductivity of the saturated sample (σm), are obtained using the equipment and methodology described by Vinogradov et al. . The relative electrical conductivity (σr) is calculated using
where σ(Sw = 1) is the value of conductivity when the sample is fully saturated with brine. The average brine saturation in the plug (Sw) during drainage is calculated using measurements of the initial (Vwi) and produced (Vwp) volumes of the wetting phase, and during imbibition using measurements of the produced volume of the non-wetting phase (Vnwp) and the total produced volume of the wetting phase at the end of drainage (Vwd)
The brine used is a simple 0.01M solution of NaCl in de-ionized water (pH 7–8 in all experiments), and the non-wetting, non-polar second phase is either liquid undecane or gaseous nitrogen. A barbotage is used to increase the humidity of the nitrogen before it enters the core holder, to reduce brine evaporation within the pore space. The dimensions and properties of the samples are given in Table 1. Prior to starting a series of experiments, the samples are saturated with 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 the same brine flowed repeatedly through the sample from one reservoir to the other and back again, until the electrical conductivity of the brine in each reservoir remains constant and equal within a 10% tolerance.
Table 1. Mineralogy and Properties of Rock Samples Used in This Studya
 We begin by measuring the streaming potential coupling coefficient at saturation (Sw = 1) for each sample using two different approaches. The first is termed the ‘paired-stabilized’ (PS) method, described by Vinogradov et al. . The second approach is termed the ‘pressure-ramping’ (PR) method. The pressure difference across the sample is increased linearly with time, from zero to a maximum value of c. 0.4 MPa, over a period of one minute. The pressure difference and voltage across the sample are monitored and, if the pressure is not ramped too quickly, steady-state is achieved at which the streaming and conduction currents balance, yielding a linear regression between the measured data. From equation (1), the gradient of the regression yields the coupling coefficient. The disadvantage of the PR method is that flow occurs in only one direction so electrode polarization effects cannot be identified; the disadvantage of the PS method is that it cannot be used at partial saturation. The coupling coefficient obtained when it is possible to use both approaches differs by <5%, which suggests electrode effects are small (Figure 2).
 We then begin drainage by injecting the non-wetting phase in an unsteady-state displacement, initially at 0.2 PVhr−1 (pore volumes per hour) but increasing to 3 PVhr−1 when the downstream flow rate of the displaced brine becomes small (<5 × 10−4 PVhr−1). The coupling coefficient is measured at regular intervals using the PR method, initially every 30 minutes but progressively increasing to 10 hours as the saturation decreases. The electrical conductivity of the saturated sample is also measured. The drainage experiments continue until the downstream flow rate of the displaced brine has fallen to zero within experimental error (no brine droplets are observed in the outlet reservoir after >50 PV of undecane injected) so the irreducible brine saturation (Swirr) has been reached. We then conduct a final PR experiment, and validate this using a PS experiment. Finally, we begin imbibition by injecting brine, following a very similar experimental approach to drainage. The imbibition experiments continue until the residual non-wetting phase saturation (Snwr) is reached. We conduct a final PR experiment, and validate this using a PS experiment. Note that the coupling coefficient we report at the saturation end-points (Sw = 1, Sw = Swirr and Sw = 1-Snwr) corresponds to the true value for the plug, but the value we report at intermediate water saturation is an apparent value, because the water saturation varies during the unsteady-state displacement. The true value for the plug at intermediate water saturation must be obtained by modelling [Linde et al., 2007].
Figure 2 shows typical experimental results. Figure 2a shows voltage against pressure difference across the Stainton sample at the oil/brine saturation endpoints (Sw = 1, Sw = Swirr and Sw = 1-Snwr). The corresponding results for the St. Bees sample at the nitrogen/brine saturation endpoints are shown in Figure 2d. The values of the coupling coefficient at saturation (Sw = 1) obtained from these data are within 10% of previous measurements at the same brine salinity [Vinogradov et al., 2010]. Note that the measured coupling coefficient is always negative (Table 2).
Table 2. Values of the Streaming Potential Coupling Coefficient Obtained From the Curves Shown in Figure 2a
Coupling Coefficient (mV/MPa)
Note that the coupling coefficient we report at the saturation end-points (Sw = 1, Sw = Swirr and Sw = 1-Snwr) corresponds to the true value for the plug, but the value we report at intermediate water saturation is an apparent value, because the water saturation varies during the unsteady-state displacement.
Figure 2b shows voltage against pressure difference across the Stainton sample at different values of average brine saturation during drainage. At high brine saturation, a linear response between voltage and pressure difference is always obtained. However, at lower brine saturation, a threshold pressure is observed which must be exceeded before a change in voltage is recorded. Above this threshold pressure, a linear response between voltage and pressure difference is again obtained. We observe no threshold pressure during imbibition (Figures 2c and 2e) or during drainage when nitrogen invades (Figure 2e). The threshold pressure increases with decreasing brine saturation during drainage in both samples (Figure 2f).
Figure 3 shows the relative streaming potential coupling coefficient (Cr) and electrical conductivity (σr) as a function of brine saturation (Sw), for both Stainton (Figures 3a and 3b) and St. Bees (Figures 3c–3f) samples saturated with brine/undecane (Figures 3a–3d) and brine/nitrogen (Figures 3e and 3f). The uncertainty in the reported values of Cr and σr is estimated from the reproducibility of results. The uncertainty in Sw arises from the relatively low (±0.1mL) precision in measuring the volume of produced liquid, which cumulatively increases the uncertainty during drainage and imbibition.
 During drainage, Cr and σr generally decrease with decreasing Sw. However, when oil is the invading phase, Cr remains significantly above zero at Swirr, decreasing slowly over >100 hrs of flow, during which time negligibly small volumes of brine are produced and Sw and σr remain constant within experimental error. When nitrogen is the invading phase, Cr falls to zero at Swirr within experimental error. During imbibition, Cr and σr both increase with increasing at Sw. However, when oil is the displaced phase, Cr exceeds unity (i.e., the coupling coefficient is greater than that recorded at saturation Sw = 1) close to the residual non-wetting phase saturation (1-Snwr). Cr remains below unity when nitrogen is the displaced phase.
 During drainage, we observe a non-zero streaming potential at the irreducible brine saturation when oil displaces brine, which is consistent with that observed by Moore et al.  when liquid carbon-dioxide displaced brine. This arises from the flow of brine within wetting layers, which is important at low values of the wetting (brine) phase saturation and is caused by the hydraulic coupling between wetting and non-wetting phases [Dullien, 1992]. The small volumes of flowing brine are difficult to measure, and the saturation and electrical conductivity appear to remain constant. However, the brine contains a very high density of excess positive charge, because it lies within the diffuse part of the electrical double layer arising at the mineral-brine and oil-brine interfaces [Revil et al., 1999; Beattie and Djerdjev, 2004]. Consequently, the streaming current is significant, giving rise to a non-zero streaming potential.
 We record zero streaming potential at the irreducible saturation when gas displaces brine, because of the smaller hydraulic coupling between brine and low-viscosity gas. The threshold pressure required to generate a streaming potential during drainage reflects the minimum pressure difference required to mobilize the wetting layers. It is likely that the threshold pressure increases with decreasing non-wetting phase viscosity, because of the reduced hydraulic coupling. Consequently, we may have observed a non-zero streaming potential in our gas-brine drainage experiments if we had been able to impose a larger pressure difference. Note that zero streaming potential at the irreducible saturation will always be observed in capillary desaturation experiments, because there is no flow of either the wetting or non-wetting phases [Guichet et al., 2003; Revil and Cerepi, 2004; Revil et al., 2007].
 During imbibition, we observe a streaming potential coupling coefficient at the residual oil saturation, which is greater than the value obtained at Sw = 1. However, such behaviour is not observed at the residual gas saturation. In the St Bees plug, where direct comparison between gas-brine and oil-brine displacements is possible, the residual oil saturation is higher than the residual gas saturation, and the electrical conductivity and permeability to water of the saturated plug are both lower. However, the excess charge density transported by the flow (calculated using equation 41 of Jackson ) is higher, so the reduction in the streaming current is proportionately less than the reduction in electrical conductivity, relative to the value at saturation. We hypothesize that the reduction in the streaming current is less in the oil-water displacement, because of the excess charge in the electrical double layer at the oil-brine interface [e.g., Samec et al., 1985]. A double layer is also present at the gas-brine interface, but we suggest that this contributes less to the excess charge transported by the flow. In the gas-brine drainage experiment, the behaviour of the coupling coefficient is similar to that predicted by models [Revil et al., 2007; Jackson, 2010], in that it decreases with decreasing brine saturation and falls to zero at the irreducible water saturation. However, in the oil-brine drainage experiment, and during imbibition, the behaviour of the coupling coefficient differs from model predictions.
 The streaming potential in water-wet sandstones during both drainage and imbibition behaves differently in oil/brine and gas/brine displacements. During drainage, the streaming potential remains greater than zero at the irreducible water saturation in oil/brine displacements, but falls to zero (within experimental error) in gas/brine displacements for applied pressure differences up to 0.4MPa. The non-zero streaming potential arises from the hydraulic coupling between wetting and non-wetting phases. During imbibition, the streaming potential coupling coefficient in oil/brine displacements exceeds the value measured at saturation, but remains below the value measured at saturation in gas/brine displacements. Our results suggest that significant streaming potentials may be observed in the subsurface even when the wetting brine saturation is very small, if the non-wetting phase has a similar viscosity to brine (e.g., oil or liquid CO2) but not if the non-wetting phase has a significantly lower viscosity (e.g., air or gaseous CO2). Moreover, the streaming potential during imbibition may be enhanced at partial saturation relative to the value at saturation.