Spontaneous Potentials in Hydrocarbon Reservoirs During ... - OnePetro

Spontaneous Potentials in Hydrocarbon Reservoirs During Waterflooding: Application to Water-Front Monitoring M.D. Jackson, SPE, M.Y. Gulamali, E. Leinov, J.H. Saunders, and J. Vinogradov, Imperial College London

Summary Spontaneous potential (SP) is routinely measured using wireline tools during reservoir characterization. However, SP signals are also generated during hydrocarbon production, in response to gradients in the water-phase pressure (relative to hydrostatic), chemical composition, and temperature. We use numerical modeling to investigate the likely magnitude of the SP in an oil reservoir during production, and suggest that measurements of SP, using electrodes permanently installed downhole, could be used to detect and monitor water encroaching on a well while it is several tens to hundreds of meters away. We simulate the SP generated during production from a single vertical well, with pressure support provided by water injection. We vary the production rate, and the temperature and salinity of the injected water, to vary the contribution of the different components of the SP signal. We also vary the values of the so-called “coupling coefficients,” which relate gradients in fluid potential, salinity, and temperature to gradients in electrical potential. The values of these coupling coefficients at reservoir conditions are poorly constrained. We find that the magnitude of the SP can be large (up to hundreds of mV) and peaks at the location of the moving water front, where there are steep gradients in water saturation and salinity. The signal decays with distance from the front, typically over several tens to hundreds of meters; consequently, the encroaching water can be detected and monitored before it arrives at the production well. Before water breakthrough, the SP at the well is dominated by the electrokinetic and electrochemical components arising from gradients in fluid potential and salinity; thermoelectric potentials only become significant after water breakthrough, because the temperature change associated with the injected water lags behind the water front. The shape of the SP signal measured along the well reflects the geometry of the encroaching waterfront. Our results suggest that SP monitoring during production, using permanently installed downhole electrodes, is a promising method to image moving water fronts. Larger signals will be obtained in low-permeability reservoirs produced at high rate, saturated with formation brine of low salinity, or with brine of a very different salinity from that injected. Introduction Measurements of SP, logged prior to production or injection using wireline tools, have long been used to characterize reservoir properties such as permeable-bed boundaries and formation-brine resistivity (Schlumberger et al. 1934; Mounce and Rust 1944; Doll 1948; Hallenburg 1971). The SP signal recorded during logging is primarily electrochemical (EC) in origin; contrasts in chemical composition between formation and drilling fluids give rise to so-called “junction” or “diffusion” potentials in permeable beds, while the exclusion of (typically negative) ions from the pore-space of fine-grained rocks such as mudstones and shales results in socalled “membrane” potentials. Together, these EC potentials typically dominate the SP log, although in some cases, electrokinetic (EK or streaming) potentials, which arise from gradients in fluid Copyright © 2012 Society of Petroleum Engineers This paper (SPE 135146) was accepted for presentation at the SPE Annual Technical Conference and Exhibition, Florence, Italy, 20–22 September 2010, and revised for publication. Original manuscript received for review 21 October 2010. Revised manuscript received for review 27 January 2011. Paper peer approved 22 March 2011.

March 2012 SPE Journal

pressure (relative to hydrostatic), may also contribute (Mounce and Rust 1944; Doll 1948; Wyllie 1949, 1951; Wyllie et al. 1953). However, gradients in fluid pressure, chemical composition, and temperature will also be present during hydrocarbon production, particularly during water- or steamflooding, when colder or hotter water of a chemical composition different from that of the formation brine is injected into the reservoir. Consequently, SP signals will be observed during production. The aim of this paper is to characterize the likely magnitude of these SP signals, and to determine whether their measurement, using electrodes permanently installed downhole, may be of use in monitoring fluid flow during production and, in particular, whether water fronts may be tracked while they are still some distance away from a production well equipped with monitoring electrodes. Such model-based studies provide motivation for implementing field trials. The measurement of EK and thermoelectric (TE) potentials to characterize flow during hydrocarbon production was suggested as early as 1972. Traugott (1972) measured the EK potential in openhole water-injection wells, and injection wells cased with fiberglass, to identify injective reservoir intervals. The measurements were obtained using a standard SP logging tool. Dorfman et al. (1977) measured the TE potential in laboratory and field experiments to monitor heat flow in an oil field undergoing steam- and fireflooding. The field measurements were obtained at the surface above the oil field, using standard geophysical surveying equipment. However, there was little further interest in monitoring flow during production using measurements of SP until Wurmstich and Morgan (1994) pointed out that EK potentials will be generated during production, and used numerical modeling to determine their likely value at an openhole monitoring well and at the surface. Their results suggested that the signals would be too small to measure. However, the experimental and numerical results of Jackson and coworkers (Jackson et al. 2005; Jackson et al. 2011; Jackson 2008, 2010; Jaafar et al. 2009; Saunders et al. 2006, 2008; Vinogradov et al. 2010; Vinogradov and Jackson 2011) are more promising. These suggest that EK potential at a production well should be measurable above background noise in a wide range of reservoir and production scenarios, and could be used to detect and characterize an approaching water front while the front is still several tens to hundreds of meters away. This contrasts with most downhole-monitoring methods, which sample only the region within, or immediately adjacent to, the wellbore. The numerical models of Jackson and coworkers assume that SP measurements may be acquired downhole at the production well, using permanently installed electrodes, and that any casing is either nonmetallic or is electrically insulated from the formation. The acquisition of SP measurements, using permanently installed downhole electrodes in both openhole wells and casedhole wells with insulated steel casing, has been demonstrated by Chen et al. (2006). The previously mentioned papers mostly focus on production monitoring using measurements of the EK component of the SP. None has yet considered the contribution of the EC potential, and only one has investigated the TE potential. Yet all these components of the SP will be present during waterflooding, and their likely magnitudes are poorly understood. The objectives of this paper are therefore three-fold. The first is to quantify the likely magnitude of these hitherto-neglected components of the SP during production by water injection. The second is to determine whether, and under what reservoir and production conditions, the resulting SP will be large 53

(a) Solid surface Pore fluid Electrical double layer

(b) Solid surface Pore fluid

(c)

Temperature

Solid surface Pore fluid

Voltage Fig. 1—Schematic showing the separation of charge at the mineral/water interface and the origin of the (a) EK potential, (b) EC potential, and (c) TE potential. The electrical double layer is shown in a highly simplified form.

enough to be detected at a production well. The third is to investigate whether measurements of the SP at the well provide useful information to monitor water fronts moving in the vicinity of the well. We begin by reviewing the origin of the SP signal in a hydrocarbon reservoir during production before describing the numerical model we use to investigate the likely magnitude of the signal. We simulate the SP generated during production from a single vertical well, with pressure support provided by water injection. We vary the production rate, and the temperature and salinity of the injected water, to vary the contribution of the different components of the SP signal. We demonstrate that the SP signal peaks at the location of the moving water front, where there are steep gradients in water saturation and salinity. The signal decays with distance from the front, typically over several tens to hundreds of meters; hence, the encroaching water front can be detected before it arrives at the well. Before water breakthrough, the SP signal at the well is dominated by the components arising from gradients in water-phase pressure (relative to hydrostatic) and salinity. Origin of the Spontaneous Potential The SP acts to maintain overall electroneutrality when a separation of electrical charge occurs in response to gradients in pressure, chemical composition, or temperature (Marshall and Madden 1959; Corwin and Hoover 1979; Revil 1999). In a water-wet reservoir rock, charge separation occurs at the mineral/water interface, because the water reacts with the mineral surfaces to leave an excess of (typically) negative charge on the mineral surface, and 54

an excess of positive charge in the water adjacent to the mineral surface (Wyllie 1951; Lynch 1962). This arrangement of charge at the mineral/water interface is known as the electrical double layer and is shown schematically in Fig. 1 (Hunter 1981). The negative charge on the mineral surface is immobile, but some of the excess positive charge in the adjacent water is mobile and will move with the fluid. If the water is subjected to a pressure gradient that causes it to flow relative to the mineral surfaces, then some of this positive charge is transported with the flow (Fig. 1a). The net excess of positive charge moving with the flow (denoted in Fig. 1a by the length of the arrows) gives rise to a so-called streaming current. To balance this streaming current, a conduction current is established and the electrical potential required to maintain this conduction current is the EK or, more specifically, the streaming potential. We will use the term EK throughout this paper, for consistency with the terminology used to describe the EC and TE potentials. Variations in water composition result in concentration gradients down which the ionic species migrate (Fig. 1b). However, the ions have differing mobility, and do not migrate at the same rate. For example, the mobility of sodium ions at 25°C is around 70% that of chloride ions (e.g. Braun and Weingartner 1985). This results in charge separation, which is countered by the EC potential to maintain electroneutrality (Revil 1999). If the solid surfaces are not electrically charged, the EC potential is solely attributable to the liquid junction or diffusion potential, which arises from the mobility contrasts between ionic species (Ortiz et al. 1973). However, the presence of an electrical double layer at the mineral/water interface means that some of the (typically) negative ions in the brine are excluded from the pore space, so a net excess of positive charge migrates down the concentration gradient (denoted in Fig. 1b by the length of the arrows). This gives rise to a membrane potential. The relative contribution of the membrane and liquid-junction potentials to the overall EC potential depends upon the mobility contrast between ionic species, and the thickness of the electrical double layer relative to the radius of the water-occupied pores (Ortiz et al. 1973). The TE potential has a similar origin to that of the EC potential. Variations in water temperature result in temperature gradients down which the ionic species migrate (Fig. 1c). The differing mobility of the ions again results in charge separation (denoted in Fig. 1c by the length of the arrows), which is countered by the TE potential to maintain electroneutrality (Tasaka et al. 1965; Revil 1999). If we assume that only the water phase in the reservoir gives rise to SP (which is equivalent to assuming that the hydrocarbon phases are nonpolar), and neglect interactions between fluxes other than those that result from separation of charge, then the constitutive equations describing the transport of charge, mass, heat, and species can be described with ⎛ j⎞ ⎜q ⎟ ⎜ w⎟ = ⎜ h⎟ ⎜ ⎟ ⎝ ⎠ ⎛ s ( Sw ) LEK ( Sw ) ⎜L S kk ( ) EK w rw ( S w ) w −⎜ ⎜ LTE ( Sw ) 0 ⎜ 0 ⎝ LEC ( Sw )

∇V LTE ( Sw ) LEC ( Sw )⎞ ⎛ ⎞ 0 0 ⎟ ⎜ ∇ ( Pw − w g z )⎟ ⎟⎜ ⎟ ∇T ⎟ ( Sw ) 0 ⎟⎜ ⎟⎜ ⎟ ∇C f 0 D ( Sw ) ⎠ ⎝ ⎠ . . . . . . . . . . . . . . . . . . . . . . . . (1)

The on-diagonal terms in the matrix yield the well-known constitutive equations of Ohm’s law, Darcy’s law, Fourier’s law, and Fick’s law, respectively. The nonzero off-diagonal terms describe the cross couplings between these constitutive equations that arise as a result of charge separation. The matrix is symmetric in linear thermodynamics (DeGroot and Mazur 1962). A key problem in predicting and interpreting SP signals during hydrocarbon production is to identify appropriate values for the nonzero off-diagonal terms, which we term the coupling terms. We return to this issue later in the paper. March 2012 SPE Journal

well

Reservoir Inlet boundary

Sandstone

(a) Shale

100 m

1200 m

600 m 800 m

(b) Earth’s surface 0 100

Weathered layer

Well

φ=1% (c) 200 m

400 500 600

Depth [m]

700

Confining layer

φ=30%

Reservoir layer Confining layer

50 m φ=30%

1000

1500

2000 m 800 m

2000 m

1200 m 600 m

2000

Fig. 2—The numerical reservoir model, which is based on that used by Wurmstich and Morgan (1994) and Saunders et al. (2006, 2008). (a) Perspective view of the 100-m-thick sandstone reservoir layer and surrounding shale and sandstone. Water enters the reservoir over the inlet boundary and flows toward the production well; this water is sourced from injection wells that are not explicitly described in the model. The sandstone and shale layers around the reservoir allow us to treat the model boundaries as infinitely far away in the electrical problem. (b) Section through the entire model. The reservoir layer, between 500 and 600 m in depth, lies between two electrically conductive but impermeable shale layers. Further sandstone layers lie above and below the shales, with a thin weathered layer at the Earth’s surface. (c) Grid used for modeling. The location of the well and reservoir layer are indicated by refinement of the grid.

Numerical Modeling Reservoir Model. The 3D reservoir model is based on that used by Wurmstich and Morgan (1994), Saunders et al. (2006, 2008), and Jackson et al. (2011). The horizontal sandstone reservoir layer contains a single vertical production well (Fig. 2). This is March 2012 SPE Journal

completed over the central 80 m of the 100-m-thick layer, which lies between 500 and 600 m in depth. The reservoir layer measures 1150 × 500 m in plan view and is bounded above and below by 100-m-thick shales, and laterally by 50-m-wide shales around three of the four vertical sides. The shales are water saturated and 55

TABLE 1—ROCK AND FLUID PROPERTIES Property (unit)

Rock

Viscosity (cp ) –3

Density (kgm ) –1

Compressibility (bar ) Specific heat capacity (J kg

–1

°K )

Water

–

1

1

2100

1000

1000

1 10 –1

Oil

–5

1 10

900

–4

2200

5 10

–5

4200

Formation (initial) salinity (M)

–

–

0.5–5

Injection salinity (M)

–

–

0.5 (approx. seawater)

30–130

30–130

30–130

–

–

30

Formation (initial) temperature (°C) Injection temperature (°C) Porosity Permeability (md )

0.25

–

–

75–1500

–

–

Irreducible water saturation

0.2

–

–

Residual oil saturation

0.2

–

–

Endpoint water relative permeability

0.3

–

–

Endpoint oil relative permeability

0.8

–

–

Note: Where ranges are shown, the value is varied in a simple sensitivity analysis.

thus are electrically conductive, but the water is immobile. The fourth side is bounded by a sandstone layer that measures 800 × 500 m in plan view (Fig. 2a). These additional parts of the model allow us to use the potential at the outer boundary as a reference; numerical tests show that increasing the size of the model domain beyond that used does not affect the results. In reality, the reference would be one or more distant electrodes, which could be located at the surface, or at the well in a shallower rock formation. During oil production, water moves into the reservoir layer over the left (“inlet”) face, which is bounded by the sandstone layer; this water is sourced from injection wells which are not explicitly described in the model. The refinement of the grid around the well allows a high degree of resolution in calculating fluid flow while reducing the computational burden of modeling in a large domain. Rock and Fluid Properties. The porosity of the rock layers surrounding the reservoir is given in Fig. 2; the permeability of these layers is assumed to be zero, so there is no flow. The rock and fluid properties of the reservoir layer are summarized in Table 1. Initially, we assume the reservoir layer is homogeneous; later, we investigate the effect of varying the permeability to introduce some simple reservoir heterogeneity. We assume that flow is dominated by viscous forces, and we neglect gravity and capillary pressure. This is a reasonable assumption in the vicinity of a production well where fluid pressure gradients are large (Dake 1978; Shook et al. 1992). We also assume that water is the wetting phase, oil is the nonwetting phase, and that there is no free gas present in the reservoir. The relative permeabilities kr are given by simple Corey-type functions of saturation: 2 krw = krwe Swn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)

kro = kroe (1 − Swn ) , 2

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (3)

in which Swn is the normalized water saturation, Swn =

Sw − Swirr , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (4) 1 − Swc − Sor

and Swirr and Sor are the irreducible water and residual oil saturations. The chosen fluid viscosities yield a shock-front-dominated displacement of oil by water, which is typical of many reservoirs. The conductivity s of a rock with porosity saturated with water and oil is calculated using Archie’s law, neglecting the conductivity of the rock grains and the oil phase (Telford et al. 1990): 56

s = 1.8 w Sw2 , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (5) where Sw is the water saturation and w is the electrical conductivity of the brine, which is related to the brine salinity by (Worthington et al. 1990) log10C f = −1.03024 + 1.06627 ( log10 w ) + 2.41239 × 10 −2 ( log10 w )

2

+ 3.68102 × 10 −3 ( log10 w )

3

+ 1.46369 × 10 −4 ( log10 w )

. . . . . . . . . . . . . . . (6)

4

where salinity Cf is in M and brine conductivity is in Sm–1. SP Coupling Coefficients. The relatively sparse data available must be used to estimate values of the cross-coupling terms in Eq. 1 that apply to a hydrocarbon reservoir during production. We wish to model the injection of water of varying temperature and salinity into a reservoir that initially contains oil and irreducible water, so we must be able to describe the impact of varying water saturation, temperature, and salinity on the values used. The cross-coupling terms can be expressed in terms of the rock electrical conductivity and a coupling coefficient C by L x = sC x ,

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (7)

where x represents the subscripts EK, EC, or TE (Ishido and Mizutani 1981; Revil 1999). The coupling coefficients (CEK, CEC, and CTE) are key petrophysical properties that relate the magnitude of a given SP signal to the associated gradient in fluid pressure, concentration, or temperature, and have units of VPa–1, VM–1, and VK–1, respectively. We begin by identifying the salinity and temperature dependence of these coupling coefficients at the saturation endpoints (Sw = 1–Sor and Sw = Swirr), before considering their behavior at intermediate values of saturation. We consider first the value of the electrokinetic coupling coefficient (CEK). Experimental data suggest that, at the end of drainage with oil displacing brine (i.e., when Sw = Swirr), CEK is zero in waterwet sandstones, while at the end of imbibition with brine displacing oil (i.e., when Sw = 1–Sor), CEK is similar to the value when the rock is fully water-saturated [Sw = 1; Vinogradov and Jackson (2011)]. We use experimental data to relate CEK in brine-saturated sandstones (Sw = 1) to the salinity of the saturating brine [see Vinogradov et al. (2010) for a summary], noting that these data were obtained using simple NaCl brine, but that laboratory measurements suggest that March 2012 SPE Journal

100000

(b)

(a) EC ccoupling coefficient (mV V·M–1)

EK coupling coefficient (mV·MPa –1)

1000

100

10

Sw =(1–Sor)

1

0.1 0.001

0.01

0.1 Salinity (M) Salinity (M)

1

10000

100

Sw =Swirr

10

1 0.001

10

Sw =(1–Sor)

1000

0.01

0.1

1

10

Salinity (M) 1.2

TE coupling g coefficient (mV·K–1)

(c) 1 Sw =(1–Sor)

0.8

0.6

04 0.4 Sw =Swirr

0.2

0 0.001

0.01

0.1

1

10

Salinity (M) Fig. 3—Dependence of the SP coupling coefficients at Sw = Swirr and Sw = (1–Sor) on salinity and temperature. (a) CEK vs. salinity, calculated using Eq. 8. We assume no temperature dependence; note also that CEK (Sw = Swirr) is not shown as zero and cannot be plotted on a log scale. (b) CEC vs. salinity, calculated over the temperature range 293 K (approximately 20°C, solid line) to 393 K (approximately 120°C, dashed line) using Eq. 9 (identical results are obtained using Eq. 12). (c) CTE vs. salinity, calculated over the temperature range 293 K (solid line) to 393 K (dashed line) using Eq. 10. The temperature dependence is small, so the modeling results presented later in the paper were obtained using the bold line, calculated using Eq. 14.

the EK coupling is not affected by the presence of other salt species in natural seawater and formation brine (Jackson et al. 2011). We neglect the effect of temperature because the available data suggest that temperature variations over the range of 20–120°C have little effect on the EK coupling (Reppert and Morgan 2003a, b). Combining this earlier work, we model the salinity and temperature dependence of CEK at the saturation endpoints as CEK ( Swirr ) = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (8a) CEK (1 − Sor ) ≈ CEK (Sw = 1) = −1.36C −f 0.9123mV·MPa −1

. . . . (8b)

where the brine salinity Cf is expressed in M (Fig. 3). We consider next the values of the EC and TE coupling coefficients (CEC and CTE) at the saturation endpoints. We follow the approach of Ortiz et al. (1973), who suggested that when the water saturation is high, most of the pores are occupied by water and, if the thickness of the electrical double layer is small compared to the pore March 2012 SPE Journal

radius, the transport of electrical charge is predominantly through the water outside the double layer, in which the concentration of positive and negative charge is equal. Consequently, the rock tends to behave like an uncharged porous medium. Conversely, when the water saturation is low, most of the pores are occupied by oil, so the transport of electrical charge is predominantly in the wetting-water layers, which are sandwiched between the oil and the mineral surfaces. The (typically) negative ions are largely excluded from these wetting-water layers, so the rock tends to behave like a membrane. On the basis of this conclusion, we model the saturation and temperature dependence of CEC and CTE at the saturation endpoints, assuming that the rock behaves as an uncharged porous medium at Sw = 1–Sor and as a membrane at Sw = Swirr, and use the appropriate expressions for the EC and TE coupling coefficients (Revil 1999; Leinov et al. 2010) CEC ( Sw = Swirr ) =

k BT 1 , . . . . . . . . . . . . . . . . . . . . . . . . . (9a) e Cf 57

Relative coupling coefficient (CrEC )

Relative coupling coefficient (CrEK)

(a)

1

0.8

0.6

0.4

0.2 Model of Jackson (2010) Data from Revil and Cerepi (2004)

0

1

(b)

Data from Ortiz et al. (1973) SC SF1 SF2 H W F LP3

0.8

0.6

0.4

0.2

0 0

0.2 0.4 0.6 0.8 Normalised water saturation (S ) wn (Swn) Normalized water saturation

1

0

0.2 0.4 0.6 0.8 Normalised water saturation (Swn(S ) wn) Normalized water saturation

1

Fig. 4—Relative coupling coefficient as a function of water saturation. (a) The relative EK coupling coefficient (CrEK) is chosen to match the model of Jackson (2010), in which it is assumed that bulk electrical conductivity dominates. This assumption is reasonable in clean reservoir sandstones saturated with typical formation brine. Also shown are experimental data obtained by measuring the EK potential across a water-wet dolomite plug during drainage by nitrogen injection (Revil and Cerepi 2004). (b) The relative EC coupling coefficient (CrEK) is chosen to match the experimental data of McCall (1970; reported in Ortiz et al. 1973) obtained by partially draining sandstone coreplugs by paraffin injection and then imposing a salinity gradient across the plugs while measuring the EC potential. The symbol labels refer to the sample descriptions reported by Ortiz et al. (1973).

CEC ( Sw = 1 − Sor ) =

CTE ( Sw = Swirr ) =

k BT ( 2t Na − 1) , e Cf

. . . . . . . . . . . . . . . . . . (9b)

* ⎞ kB 1 ⎛ 0 QNa , . . . . . . . . . . (10a) ln C f + ⎜ SNa − e e⎝ T ⎟⎠

CTE ( Sw = 1 − Sor ) =

( )

( 2tNa − 1) kB ln e

+

(C ) + t e

Na

f

tCl ⎛ 0 QCl* ⎞ SCl − e ⎜⎝ T ⎟⎠

⎛ 0 QN* a ⎞ ⎜⎝ SNa − T ⎟⎠

. . . . . . . . . . . . . . . .(10b)

Substituting appropriate values of Q* and S0 for Na and Cl in Eqs. 9 and 10 (Agar et al. 1989) yields the curves shown in Fig. 3, with tNa given by (Braun and Weingartner 1985):

(

CTE ( Sw = 1 − Sor ) = −1.984 × 10 −1 ( 2t Na − 1) log10C f

)

, + 1.059t Na − 5.673 × 10 −1 mV K −1 . . . . . . . . . . . . . . . . . . . . . . (13b)

where the brine salinity Cf is expressed in M. We now consider the behavior of the coupling coefficient at intermediate values of water saturation by defining a saturationdependent relative coupling coefficient (Jackson 2010): Crx =

C x ( Sw ) − C x ( Sw = Swirr ) . . . . . . . . . . . . . . . . . (14) C x ( Sw = 1 − Sor ) − C x ( Sw = Swirr )

We describe CrEK in terms of the normalized water saturation as 0.6 CrEK = Swn , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (15)

0.39, C f < 0.09 M ⎪⎧ t Na = ⎨ −1 −2 C ⎪⎩3.66 × 10 − 2.12 × 10 log10C f , f > 0.09 M . . . . . . . . . . . . . . . . . . . . . . . (11)

which provides a reasonable match to the model of Jackson (2010) (Fig. 4), and CrEC as

and tCl = 1–tNa. It is clear that the values of both CEC and CET are strongly salinity-dependent, but only weakly temperature-dependent; indeed, CET varies by 103). The crosscoupling terms have negligible impact on the transport of mass, heat, and chemical species and therefore are neglected (Ishido and Mizutani 1981; Wurmstich and Morgan 1994; Revil 1999; March 2012 SPE Journal

(a)

(b)

(c)

( d)

Time Until Breakthrough [days]

Relative Contribution [%]

Distance From Well [m]



Fig. 5—Numerical results from a homogeneous reservoir model. (a) Panels show (from top to bottom) brine saturation, fluid potential, temperature, salinity, and EK, TE, and EC potential, as a function of distance from the production well (marked by the vertical dotted line) along a 1D horizontal profile through the center of the model at four different timesteps (annotated here as time until water breakthrough). (b) Panels show (from top to bottom) brine saturation, fluid potential, temperature, salinity, and EK, TE, and EC potential, as a function of time until water breakthrough, recorded at the center of the borehole. (c) Magnitude of the change in the total electrical potential relative to the potential 1,000 days before breakthrough, as a function of time until water breakthrough, recorded at the center of the well. The likely downhole noise of 0.1 mV is indicated by the dashed line. (d) Relative contribution of the EK, TE, and EC potentials to the overall SP signal, as a function of time until water breakthrough, recorded at the center of the well. The small fluctuations observed in (b) and (d) are numerical artifacts and are not included in the analysis of results.

Saunders et al. 2008). However, we solve Ohm’s law, including the cross-coupling terms, using the values of water phase potential, concentration, and temperature obtained from Eclipse 100 and an in-house finite-element code that has been carefully benchmarked (Saunders et al. 2006, 2008). We assume that there are no external current sources or sinks, and the net current flow through the boundaries of the model is zero, so ∇.j = 0.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (18)

Furthermore, we set V = 0 at all the boundaries, except on the left-side face (Fig. 2a), where we set ∇V = 0, and at the Earth’s surface we set j.n = 0, where n is the unit vector that is normal to the Earth’s surface. March 2012 SPE Journal

Results EK, EC, and TE Potentials Within the Reservoir. We begin by simulating a case where oil is produced at a rate of 10,000 B/D and brine flows into the reservoir at the same rate, with a salinity of 0.5 M and a temperature of 30°C. The reservoir permeability is uniformly 150 md, and the initial temperature and formation-brine salinity are 80°C and 1 M, respectively. The chosen parameters represent the injection of seawater into a reservoir containing a typical saline-formation brine. We investigate the impact of varying the permeability, production rate, and salinity contrast between formation and injected brine in a later section. Fig. 5a shows data from the simulation obtained along a 1D profile at the center of the reservoir layer, oriented parallel to the long axis of the model and passing through the well, for four 59

different timesteps. A water-saturation front moves toward the well. Ahead of the front, oil flows in the presence of irreducible water; behind the front, water flows in the presence of residual oil. At the front, water saturation varies rapidly over a limited spatial interval. Temperature and salinity fronts also move toward the well; however, these both lag behind the saturation front because of mixing of the injected and formation brines, and because sensible heat is required to change the temperature of the reservoir rock and fluids. The pressure gradient in the water phase gives rise to an EK potential, which has a peak at the location of the water front and decays toward zero (measured with respect to a distant reference electrode) ahead of and behind the front, as observed in previous studies (Saunders et al. 2008; Jackson et al., 2011). The EK potential falls to zero ahead of the front because there is no streaming current associated with the flow of oil, and falls to zero behind the front because the streaming current is constant where the water saturation is constant. The peak EK potential follows the water front as it moves through the reservoir, and is associated with the front because the divergence of the streaming current becomes nonzero where the saturation changes, so the water front acts as a current source. Note that the nonzero value of the EK potential at the inlet boundary arises because the boundary is also a current source; the potential falls to zero at the left-side far-field boundary of the model (1800 m from the well; not shown). The salinity and temperature gradients in the water phase also give rise to EC and TE potentials. The TE potential is zero ahead of the temperature front and negative behind the leading edge of the front (measured with respect to a distant reference electrode), reaching a maximum value (in magnitude) at the trailing edge of the temperature front. The TE potential is significantly larger in magnitude than the EK potential, which reflects the large magnitude of the TE coupling coefficient (Fig. 3). The EC potential is also zero ahead of the salinity front, but becomes positive behind the leading edge of the front, reaching a maximum value some distance behind the trailing edge of the front. The difference in the shape of the TE and EC potentials along the profile reflects the difference in the salinity and temperature dependence of the respective coupling coefficients (Fig. 3). The magnitude of the EC potential is intermediate between the EK and TE potentials, which reflects the magnitude of the coupling coefficient and the salinity contrast between injected and formation brine. Fig. 5b shows data from the simulation at the center of the production well as a function of time, while Fig. 5c shows the total potential and Fig. 5d shows the relative contribution of the EK, EC, and TE potentials at the center of the well as a function of time. The water saturation at the well remains constant (at Swirr) until water breakthrough occurs; the pressure initially decreases (reflecting the decreasing total mobility as water is injected into the reservoir) before rising at water breakthrough. The temperature and salinity at the well both remain approximately constant; there is a small decrease in salinity after breakthrough. This is because the temperature and salinity fronts both lag behind the water front (as discussed previously and as shown in Fig. 5a). If the simulations are run for longer post-breakthrough, both salinity and temperature are observed to change at the well as the respective fronts arrive. The EK potential increases as water approaches the production well, rising above the estimated noise level of 0.1 mV (which we discuss in more detail later in the paper) around 600 days before water reaches the well, while the approaching water front is still 180 m away. Similar results have been obtained in previous studies and suggest that EK potentials can be resolved in the subsurface and may be useful for detecting water encroaching on a well some time (and distance) before breakthrough occurs (Saunders et al. 2008; Jackson et al., 2011). However, despite their much larger magnitude at the salinity and temperature fronts, the TE and EC potentials recorded at the well are smaller than the EK potential, because the salinity and temperature fronts lag behind the saturation front. The EC potential increases as water approaches the well, but comprises only 20% of the total SP signal at breakthrough; the TE potential remains approximately constant (the fluctuations observed in Fig. 5b are small numerical artifacts). The EK 60

potential comprises approximately 80% of the total SP signal at water breakthrough (Fig. 5d). Fig. 6 shows the potentials recorded along the production well within the reservoir interval. The increase in the EK and EC potentials as water approaches the well can be clearly observed, although the EC signal is much smaller in magnitude. The TE potential is negligible (at least an order of magnitude smaller) in comparison with the EK and EC potentials. The individual EK, EC, and TE contributions combine to yield a total SP signal that reaches approximately 1.5 mV at water breakthrough (0 days) and exceeds the estimated noise level of 0.1 mV approximately 1,000 days before breakthrough. At this time, the water front is still approximately 250 m away from the production well (see the upper panel of Fig. 5a). Effect of Production Rate, Reservoir Permeability, Reservoir Temperature, and Formation-Brine Salinity. The results presented in the previous section suggest that, although EC and TE potentials in the reservoir are large, the TE potential makes a negligible contribution to the SP signal, that would be recorded at a production well prior to water breakthrough, and the EC potential makes a much smaller contribution than the EK potential. However, the magnitude of the EK, EC, and TE potentials is affected by the pressure, concentration, and temperature gradients in the reservoir. In this section, we vary the pressure gradient by varying the production rate over the range of 1,000–20,000 B/D and reservoir permeability over the range of 75–1,500 md. We also change the salinity and temperature gradients by varying the formation-brine salinity over the range of 0.5 to 5 M while keeping the injected-brine salinity constant at 0.5 M, and varying the formation temperature over the range of 30 to 130°C while keeping the injected-brine temperature constant at 30°C. The EK potential increases as the pressure gradient increases; consequently, the EK potential increases as the production rate increases and, for a given production rate, as the reservoir permeability decreases (Fig. 7a). Consequently, the largest EK signals will be recorded in low-permeability reservoirs produced at high rate, which have large drawdown-pressure gradients into the production wells. For the temperature and concentration gradients investigated in Fig. 7a, the EK potential is larger in magnitude than the EC potential except at low production rates (700 md at a production rate of 10,000 B/D). The SP signal reaches a maximum of 2 mV at the highest production rate (20,000 B/D in a 150-md reservoir) and lowest reservoir permeability investigated (75 md at a production rate of 10,000 B/D) and exceeds 0.3 mV even for the lowest value of production rate (1,000 B/D in a 150-md reservoir) and highest value of reservoir permeability investigated (1,500 md at a production rate of 10,000 B/D); the signal therefore comfortably exceeds the estimated noise level of 0.1 mV over the range of reservoir production rate and permeability investigated. However, note that the signal continues to decrease with decreasing production rate or increasing permeability. The TE potential is significantly smaller in magnitude than either the EK or EC potential (typically over an order of magnitude) and lies below the estimated noise level. The estimated noise level is analyzed in more detail in the Discussion section. The EK potential decreases with increasing formation-brine salinity because of the strong salinity dependence of the EK coupling coefficient [Fig. 3; see Jaafar et al. (2009) and Vinogradov et al. (2010)]. However, the EC potential increases with increasing formation-brine salinity, even though the EC coupling coefficient decreases with increasing salinity (Fig. 3). This is because the contrast in salinity between injected and formation brine increases, so the salinity gradients in the reservoir are larger. For the pressure and temperature gradients investigated in Fig. 7b, the EC potential is larger in magnitude than the EK potential at high salinity (>3 M). The lowest formation salinity investigated is 0.5 M; this is the same salinity as the injected brine, and represents the case when either natural formation brine encroaches on the well or the formation and injected brines are very similar. Under these conditions, the EC potential is zero because there is no concentration gradient; hence, March 2012 SPE Journal

(b)

(c)

(d)

Depth [m]

Depth [m]

(a)

1,500 days 1,000 days 500 days 0 days

Fig. 6—Numerical results from a homogeneous reservoir model, showing the (a) EK, (b) TE, (c) EC, and (d) total SP potentials as a function of depth along the production well, at four different times before water breakthrough at the well. Line styles and simulation times shown are consistent with Fig. 5a.

Permeability [mD]

Potential at breakthrough [V]

(a)

Production rate [bbl/day] Fig. 7—EK, EC, TE, and total SP signal at the center of the production well at water breakthrough. The production rate is 10,000 B/D; the reservoir permeability is 150 md; the formation-brine salinity and temperature are 1 M and 80°C, respectively; and the injection-brine salinity and temperature are 0.5 M and 30°C, respectively, except when they are varied to investigate the effect of (a) production rate and reservoir permeability, (b) formation brine salinity, and (c) formation temperature. The estimated downhole noise level of 0.1 mV is shown by the dashed line; see the Discussion section for the origin of this estimated noise level. March 2012 SPE Journal

61


(b)

Formation brine salinity [M]


(c)

Formation brine temperature [°C] Fig. 7 (continued)—EK, EC, TE, and total SP signal at the center of the production well at water breakthrough. The production rate is 10,000 B/D; the reservoir permeability is 150 md; the formation-brine salinity and temperature are 1 M and 80°C, respectively; and the injection-brine salinity and temperature are 0.5 M and 30°C, respectively, except when they are varied to investigate the effect of (a) production rate and reservoir permeability, (b) formation brine salinity, and (c) formation temperature. The estimated downhole noise level of 0.1 mV is shown by the dashed line; see the Discussion section for the origin of this estimated noise level.

there is no EC datapoint at this salinity in Fig. 7b. However, the total SP is a maximum at this salinity (just under 2 mV) because the relatively fresh formation brine gives rise to a large EK signal. The minimum SP signal is observed at the highest formation-brine salinity investigated (a highly saline 5 M, 10 times seawater salinity), but the signal is still >1 mV because the large salinity contrast between injected and formation brine generates a large EC potential; the EK potential is also significant. Consequently, the total SP signal comfortably exceeds the estimated noise level regardless of salinity, because the EK potential is large when the formation-brine salinity is low, while the EC potential is large (and the EK potential still significant) when the formation-brine salinity is high. The TE potential is again significantly smaller than either the EK or EC potential, and it lies below the estimated noise level. This is the case regardless of the temperature contrast (Fig. 7c). 62

Effect of Reservoir Heterogeneity. The results presented in the previous sections were all acquired using a homogeneous reservoir model in which the encroaching water front is a flat interface. In reality, reservoirs are heterogeneous, which results in fingering of the encroaching water front as the water exploits high-permeability layers and is held up by low-permeability layers. Pressure drawdown along the well may also lead to cusping or coning of the water front. We investigate the impact of reservoir heterogeneity on the SP signal at the production well using three simple cases, in which high-permeability layers of 1,500 md are embedded in a reservoir of 150 md (Fig. 8). The layers are not intersected by the production well, so their presence would likely not be captured in reservoir models, leading to incorrect predictions of water movement during production. Our aim is to determine whether the presence of these layers, and their impact on water movement, could March 2012 SPE Journal

(a )

(b )

(c)

Fig. 8—Cross section through the reservoir layer showing the permeability distribution in the three heterogeneous-reservoir models investigated. The dashed line shows the location of the production well.

be identified prior to water breakthrough at the well. In a well equipped with inflow-control valves, this information would allow proactive control of inflow to delay or prevent water breakthrough (Jackson et al. 2005). Fig. 9 shows a cross section through the model showing water saturation at three different times, and the corresponding potentials observed along the production well. The maximum potentials are observed at the center of the well, even though the water front is flat; this reflects the electrically conductive shales above and below the reservoir (Saunders et al. 2008). The TE potential at the well is negligible; the total SP signal is dominated by the EK and EC potentials. The corresponding data for each of the three heterogeneous-reservoir models are shown in Figs. 10 through 12. The encroaching water exploits the high-permeability layers, moving more rapidly through these toward the production well. The resulting SP signals at the well reflect fingering of the water front. In Fig. 10, the maximum SP has shifted upward and reflects the movement of water through the high-permeability layer near the top of the reservoir. The EK potential is generally smaller in

magnitude than in the homogeneous model because the presence of the high-permeability layer increases the overall permeability of the reservoir. Consequently, the EC signal makes a larger contribution to the overall SP signal (compare Figs. 9d and 10d). However, the SP signal is above the estimated downhole noise level, even when the closest location of the water is over 50 m away. In Fig. 11, the maximum potential has again shifted upward toward the top of the reservoir, reflecting the movement of water through the highpermeability layer. Moreover, the EK potential is again smaller in magnitude than in the homogeneous model, so the EC potential makes a larger contribution to the overall SP signal (compare Figs. 9d and 11d). However, the breadth of the SP anomaly associated with the encroaching water is larger than in Fig. 10, which reflects the increased thickness of the high-permeability layer. The total SP signal is again above the estimated noise level, even when the closest location of the water is over 50 m away. In Fig. 12, the maximum potential has shifted back to the center of the reservoir, reflecting the movement of water through two high-permeability layers in the upper and lower parts of the reservoir.

Depth [m]

Depth [m]

Depth [m]

Saturation

Distance [m] Fig. 9—Numerical results from a homogeneous reservoir model. The cross section through the reservoir layer shows water saturation when the water front is (a) 50 m away from the production well, (b) 25 m away from the well, and (c) at breakthrough. The well is shown by the vertical dashed line. (d) through (f) present the corresponding potentials recorded along the well. The model used to produce these results is the same as the model used to produce the results shown in Figs. 5 through 7. March 2012 SPE Journal

63

Depth [m]

Depth [m]

Depth [m]

Saturation

Distance [m] Fig. 10—Numerical results from a heterogeneous-reservoir model with a single high-permeability layer of thickness of 15 m and permeability of 1,500 md embedded in a reservoir with permeability of 150 md. The cross section through the reservoir layer shows water saturation when the water front is (a) 50 m away from the production well, (b) 25 m away from the well, and (c) at breakthrough. The well is shown by the vertical dashed line. (d) through (f) present the corresponding potentials recorded along the well.

The symmetric nature of the SP anomaly in Fig. 12 makes this heterogeneous case more difficult to distinguish from the homogeneous case with the naked eye (compare Figs. 12d through 12f with Figs. 9d through 9f). However, careful inspection reveals that the SP curve in the heterogeneous model with two high-permeability layers has a broader, shallower shape, and is smaller in magnitude, when compared with the SP curve in the homogeneous model. This is more clearly visible in Fig. 13, which shows the difference in SP signal along the well between each of the heterogeneous-reservoir models and the homogeneous model [i.e., shows the difference between Figs. 10, 11, and 12 (e,f) and Fig. 9 (e,f)]. It is clear that the varying shape of the water front in the different heterogeneous models yields an SP signal at the well that can clearly be distinguished from that of a homogeneous reservoir. The magnitude of the difference in behavior between the reservoir models is significantly larger than the estimated background noise (Fig. 13). Moreover, the different heterogeneous models could be distinguished on the basis of the SP signals recorded at the well. Discussion Our numerical-modeling results suggest that waterflooding of an oil reservoir leads to the generation of significant SP signals that may be tens to hundreds of mV in magnitude. The signals are caused by the separation of electrical charge resulting from gradients in water pressure (relative to hydrostatic), salinity (or concentration), and temperature. All three of these effects may be significant at or close to the saturation front, where water saturation, salinity, and temperature vary rapidly, and may give rise to SP signals at a production well that could be monitored using permanently installed downhole electrodes. Moreover, these measurements at the well could be used to detect and monitor an encroaching water front while it is still several tens to hundreds of meters away from the well. Our results confirm the earlier findings of Jackson and coworkers (Jackson et al. 2005, 2011; in press; Saunders et al. 2006, 2008) concerning 64

the nature of the EK potential that might be recorded at a well. However, our results also show that temperature and concentration gradients, induced by injecting water with temperature and salinity that differ from those of the formation brine, may result in the generation of significant TE and EC potentials. The TE potentials recorded at the well are likely to be small until long after water breakthrough, not because TE potentials are small (they may reach hundreds of mV in the reservoir), but because the temperature front associated with the injected water lags far behind the saturation front. In contrast, the EC potential recorded at the well may be significant before breakthrough occurs, and may add to the EK signal generated by the flowing water. Moreover, in high-permeability reservoirs saturated with brine of high salinity, or in reservoirs produced at low rate, the magnitude of the EC potential exceeds the magnitude of the EK potential. However, regardless of whether the EK or EC potential dominates the SP signal at the well, the measured SP can be used to detect and monitor water encroaching on the well. If reservoir heterogeneity results in an uneven water front, with water fingering along highpermeability layers or being held up by low-permeability layers, the shape of the SP anomaly along the production well reflects the geometry of the water front. Higher SP signals are generally aligned with sections of the water front that are closer to the well, while lower SP signals are associated with sections of the water front that are farther away. These results are promising because they suggest that water fronts can be tracked and imaged using downhole measurements of SP at one or more production wells. In wells equipped with inflow-control valves, this information would allow proactive control of inflow to delay or prevent water breakthrough (Jackson et al. 2005). We have obtained results so far for only a single production scenario. Further work is required to test other applications of SP monitoring during production. For example, the injection of low-salinity brine has been proposed to increase oil production March 2012 SPE Journal

Depth [m]

Depth [m]

Depth [m]

Saturation

Distance [m] Fig. 11—Numerical results from a heterogeneous reservoir model with a single high-permeability layer with thickness of 30 m and permeability of 1,500 md embedded in a reservoir with permeability of 150 md. The cross section through the reservoir layer shows water saturation when the water front is (a) 50 m away from the production well, (b) 25 m away from the well, and (c) at breakthrough. The well is shown by the vertical dashed line. (d) through (f) present the corresponding potentials recorded along the well.

(Tang and Morrow 1997). The salinity contrast between such lowsalinity brine and the formation brine may be large, in which case EC potentials may be generated that could be used to specifically monitor the low-salinity part of the water front. Steam- and fireflooding induce large thermal gradients, which could be monitored using downhole measurements of TE potential rather than the surface measurements proposed previously (Dorfman et al. 1977). Moreover, the water that condenses from a steamflood has low salinity, which may give rise to significant EC potentials. The use of inflow-control valves to modify flow into the well will change the pressure gradient in the reservoir and therefore the EK signal; this raises the prospect of probing the reservoir using transient SP measurements. In all these production scenarios, the downhole electrodes could also be used to measure resistivity, which may yield additional information to aid in characterizing flow (Bryant et al. 2002, 2004). Despite these promising results, significant uncertainties remain in characterizing SP measurements for oilfield monitoring. One key issue relates to the noise level associated with the downhole electrodes used to acquire the data. As yet, only Chen et al. (2006) have reported SP measurements in an oil reservoir during production. They installed an array of 16 electrodes in a vertical water-injection well in a Mansfield sandstone reservoir in Indiana. Reservoir depth, pressure and temperature and rock and fluid properties were not reported. The lowermost eight joints of casing were electrically insulated, and the electrodes were mounted on the outside of the insulated casing before being cemented in place. Chen et al. (2006) observed stable electrode signals to 10 μV, with occasional transient spikes on the order of 0.1 mV (e.g., Fig. 14). Those authors suggested that these spikes originated in the downhole-to-surface connections or in the surface electronics and could be reduced by improved wiring or electronics, or removed using a simple frequency filter. Consequently, they argued that March 2012 SPE Journal

electrode stability was on the order of 10 μV, and that signal levels on the order of 0.1 mV were adequate for monitoring. Our simulated SP signals comfortably exceed this value by at least a factor of three. Chen et al. (2006) provide no details of electrode type or reference electrode location, but their electrode array was originally designed for resistivity measurements, so it is unlikely to be optimal for SP measurements. Jackson et al. (in press) report data from an array of nine electrodes installed in an openhole monitoring well within a chalk aquifer in the UK. They used nonpolarizing electrodes and shielded coaxial cables of ideal design for SP-data acquisition, and found that the electrode stability (with respect to the other electrodes in the array) was on the order of 10 μV, similar to the results of Chen et al. (2006) (Fig. 14). Consequently, we suggest that our assumed noise level of 0.1 mV is reasonable. However, further field trials are required to confirm this. Another key uncertainty is the value of the cross-coupling coefficients that relate gradients in fluid-phase pressure (relative to hydrostatic), concentration, and temperature to gradients in electrical potential. Despite significant recent progress in characterizing these at conditions relevant to hydrocarbon reservoirs [see, for example, Jaafar et al. (2009), Vinogradov et al. (2010), Leinov et al. (2010), and Jackson et al. (2011)] and the use of data acquired in earlier, unrelated studies (Ortiz et al. 1973), additional experimental data are required to reduce these uncertainties. For example, understanding the nature of the coupling coefficients in oil-wet and mixed-wet reservoirs requires knowledge of the nature of the electrical double layer at oil/mineral interfaces and at the oil/water interface. As yet, both of these are poorly understood. Moreover, ambient reservoir temperature is higher than the temperature in experiments used to measure SP signals to date (i.e., room temperature). In such conditions, the values of the crosscoupling terms might be different. 65

Depth [m]

Depth [m]

Depth [m]

Saturation

Distance [m] Fig. 12—Numerical results from a heterogeneous-reservoir model with two high-permeability layers of thickness of 20 m and permeability 1,500 md embedded in a reservoir with permeability 150 md. The cross section through the reservoir layer shows water saturation when the water front is (a) 50 m away from the production well, (b) 25 m away from the well, and (c) at breakthrough. The well is shown by the vertical dashed line. (d) through (f) present the corresponding potentials recorded along the well.

Conclusions Our numerical-modeling results suggest that the magnitude of the SP generated within a hydrocarbon reservoir during waterflooding can be large (up to hundreds of mV) and peaks at the location of the moving water front, where there are steep gradients in water saturation, temperature, and salinity. The signal decays with distance from the front, typically over several tens to hundreds of meters; consequently, the encroaching water can be detected before it arrives at the production well. Before water breakthrough, the SP at the well is dominated by the EK and EC components arising from gradients in fluid potential and salinity; thermoelectric potentials only become significant after water breakthrough because the temperature change associated with the injected water lags behind the water front. The shape of the SP signal measured along the well reflects the geometry of the encroaching water front. These results are promising, because they suggest that water fronts can be tracked and imaged using downhole measurements of SP at one or more production wells. In wells equipped with inflowcontrol valves, this information would allow proactive control of inflow to delay or prevent water breakthrough. However, the magnitude of the signal recorded at a well will depend upon a number of reservoir and production parameters, including production rate, reservoir permeability and permeability heterogeneity, formationbrine salinity and temperature, and the cross-coupling terms that relate gradients in fluid-phase pressure (relative to hydrostatic), concentration, and temperature to gradients in electrical potential. Consequently, the SP signal will be specific to a given reservoir and production scenario. Moreover, the values of the cross-coupling terms are still poorly understood. Future work will need to address three key issues. The first of these concerns the downhole hardware required to acquire SP data during production and transmission of data to surface. Only one study has reported SP measurements from a permanently installed downhole electrode array, and, although the results were encouraging, 66

such installations are not routine. The second issue concerns interpretation of the measured signals for reservoir properties of interest. Our forward models demonstrate that SP signals at a well are sensitive to the location and geometry of an encroaching water front; the next step is to develop methods to determine the water front location and geometry from the measured signals in conjunction with other reservoir data. The third issue concerns the nature of the SP crosscoupling terms; further laboratory work is required to characterize these at oilfield-relevant conditions. Finally, a field trial is required to confirm the numerical-modeling results. Such a trial needs to be conducted in a well-characterized reservoir, so that the predictions of the SP measurements can be independently confirmed. The likely SP signals for the given test reservoir and production properties will need to be identified prior to the trial using forward modeling. Such modeling may be facilitated using the ECLIPSE SP post-processor software developed in this study. Nomenclature CEC = electrochemical coupling coefficient, VM–1 CEK = electrokinetic coupling coefficient, VPa–1 Cf = brine concentration (salinity), M Cr = relative coupling coefficient, dimensionless CTE = thermoelectric coupling coefficient, VK–1 D = diffusion coefficient, m2s–1 e = charge on an electron, = 1.602×10–19 C g = gravitational acceleration, ms–2 h = heat flux, Wm–2 j = charge flux, Am–2 k = permeability, md kB = Boltzmann’s constant, = 1.38×10–23 JK–1) kro = oil relative permeability, dimensionless kroe = oil endpoint relative permeability, dimensionless March 2012 SPE Journal

Depth [m] Depth [m] Fig. 13—Difference in magnitude of the total SP signal between the heterogeneous and homogeneous models, recorded along the well, (a–c) when the water front is 25 m away from the well and (d–f) at water breakthrough. Plots (a) and (d) show the difference between the heterogeneous, single, thin, high-permeability layer model and the homogeneous model (i.e., data in Fig. 10e minus data in Fig. 9e and data in Fig. 10f minus data in Fig. 9f); Plots (b) and (e) show the difference between the single, thick, high-permeability layer model and the homogeneous model (i.e., data in Fig. 11e minus data in Fig. 9e and data in Fig. 11f minus data in Fig. 9f); Plots (c) and (f) show the difference between the dual, thin, high-permeability layers model and the homogeneous model (i.e., data in Fig. 12e minus data in Fig. 9e and data in Fig. 12f minus data in Fig. 9f).

(a)

mV) Measured voltage (m

Dimensionless (scaled) pressure Voltage

0

Estimated noise level of ±0.1mV (this study)

-0.2 Start of water injection

ΔV(electrode voltage–average voltage) (mv)

0.2

-0.4

0.5

(b)

9

0.4 0.3

3 Estimated noise level of ±0.1mV (this study)

0.2 0.1

6 4 7

0 -0.1

1 8

-0.2

5

-0.3

2

-0.4 115

116 Time (days)

117

0

2000

4000 Time (s)

6000

Fig. 14—Stability of a downhole electrode array for SP-data acquisition. (a) Data from a vertical production well in an oil reservoir in Indiana, USA. Voltages from three of the 16 electrodes in the array are reported, along with dimensionless (scaled) bottomhole pressure, before and during water injection. The noise level indicated is that assumed in this study. Modified from Chen et al. (2006). (b) Data from a vertical observation well in a shallow chalk aquifer in Berkshire, UK. Voltages from each of the nine electrodes in the array are reported, relative to the average reported for the whole array. The noise level indicated is that assumed in this study. Modified from Jackson et al. (in press). March 2012 SPE Journal

67

krw krwe LEC LEK LTE Pw qw QCl* * QNa sCl0 0 sNa Sor Sw Swirr Swn tCl tNa T V w ν s w

= = = = = = = = = = = = = = = = = = = = = = = = =

water relative permeability, dimensionless water endpoint relative permeability, dimensionless electrochemical coupling term, AM–1m–1 electrokinetic coupling term, APa–1m–1 thermoelectric coupling term, AK–1m–1 water pressure, Pa flow of water, ms–1 heat of transport of chloride ions, JM–1 heat of transport of sodium ions, JM–1 partial molal entropy of chloride ions, JM–1K–1 partial molal entropy of sodium ions, JM–1K–1 residual-oil saturation, dimensionless water saturation, dimensionless irreducible water saturation, dimensionless normalized water saturation, dimensionless Hittorf transport number for chloride ions, dimensionless Hittorf transport number for sodium ions, dimensionless temperature, K electrical potential, V thermal conductivity, Wm–1K–1 water viscosity diffusion flux, Mm–2s–1 conductivity of the saturated rock, Sm–1 conductivity of the brine, Sm–1 porosity

Acknowledgments This work was funded by Shell International Exploration and Production B.V. who are gratefully acknowledged. Schlumberger is also thanked for providing the Eclipse 100 simulator. Reviewer Tianhua Zhang is thanked for constructive comments, as are two other anonymous reviewers and the Associate Editor. References Agar, J.N., Mou, C.Y., and Lin, J.L. 1989. Single-ion heat of transport in electrolyte solutions: a hydrodynamic theory. J. Phys. Chem. 93 (5): 2079–2082. http://dx.doi.org/10.1021/j100342a073. Braun, B.M. and Weingartner, H. 1985. Transference numbers of aqueous NaCl and Na2SO4 at 25°C from EMF measurements with sodium-selective glass electrodes. Journal of Solution Chemistry 14 (9): 675–686. http://dx.doi.org/10.1007/BF00646059. Bryant, I.D., Chen, M.-Y., Raghuraman, B., Raw, I., Delhomme, J.-P., Chouzenoux, C., Pohl, D., et al. 2002. An Application of Cemented Resistivity Arrays to Monitor Waterflooding of the Mansfield Sandstone, Indiana, USA. SPE Res Eng 5 (6): 447–454. SPE-81752-PA. http://dx.doi.org/10.2118/81752-PA. Bryant, I.D., Chen, M.-Y., Raghuraman, B., Schroeder, R., Supp, M., Navarro, J., Raw, I., Smith, J., and Scaggs, M. 2004. Real-Time Monitoring and Control of Water Influx to a Horizontal Well Using Advanced Completion Equipped With Permanent Sensors. SPE Drill & Compl 19 (4): 253-264. SPE-77522-PA. http://dx.doi.org/10.2118/77522-PA. Chen, M.-Y., Raghuraman, B., and Bryant, I.D. 2006. Streaming Potential Applications in Oil Fields. Paper SPE 102106 presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 24–27 September. http://dx.doi.org/10.2118/102106-MS. Corwin, R.F. and Hoover, B.H. 1979. The self-potential method in geothermal exploration. Geophysics 44 (2): 226–245. http://dx.doi.org/ 10.1190/1.1440964. Dake, L.P. 1978. Fundamentals of Reservoir Engineering, No. 8. Amsterdam: Developments in Petroleum Science, Elsevier Science BV. DeGroot, S.R. and Mazur, P. 1962. Non-Equilibrium Thermodynamics. Amsterdam, The Netherlands: North-Holland Publishing Company. Doll, H.G. 1948. The SP Log: Theoretical Analysis and Principles of Interpretation. SPE-949146-G. Trans., AIME, 179: 146–185. Dorfman, M.H., Oskay, M.M., and Gaddis, M.P. 1977. Self-Potential Profiling—A New Technique for Determination of Heat Movement in a Thermal Oil Recovery Flood. Paper SPE 6790 presented at the SPE Annual Technical Conference and Exhibition, Denver, 9–12 October. http://dx.doi.org/10.2118/6790-MS. 68

Hallenburg, J.K. 1971. A Resume of Spontaneous Potential Measurements. Paper 1971-H presented at the SPWLA 12th Annual Logging Symposium, The Woodlands, Texas, USA, 2–5 May. Hunter, R.J. 1981. Zeta Potential in Colloid Science. New York: Academic Press. Ishido, T. and Mizutani, H. 1981. Experimental and Theoretical Basis of Electrokinetic Phenomena in Rock-Water Systems and Its Applications to Geophysics. J. Geophys. Res. 86 (B3): 1763–1775. http://dx.doi. org/10.1029/JB086iB03p01763. Jaafar, M.Z., Vinogradov, J., and Jackson, M.D. 2009. Measurement of streaming potential coupling coefficient in sandstones saturated with high salinity NaCl brine. Geophys. Res. Lett. 36 (21): L21306. http:// dx.doi.org/10.1029/2009gl040549. Jackson, M.D. 2008. Characterization of multiphase electrokinetic coupling using a bundle of capillary tubes model. J. Geophys. Res. 113 (B4): B04201. http://dx.doi.org/10.1029/2007jb005490. Jackson, M.D. 2010. Multiphase electrokinetic coupling: Insights into the impact of fluid and charge distribution at the pore scale from a bundle of capillary tubes model. J. Geophys. Res. 115 (B7): B07206. http:// dx.doi.org/10.1029/2009jb007092. Jackson, M.D., Butler, A.P., Vinogradov, J., and Saunders, J.H. In press. Measurements of spontaneous potential in chalk with application to aquifer characterisation in the southern UK. Q. J. Eng. Geol. Hydrogeol. Jackson, M.D., Saunders, J.H., and Addiego-Guevara, E.A. 2005. Development and Application of New Downhole Technology To Detect Water Encroachment Toward Intelligent Wells. Paper SPE 97063 presented at the SPE Annual Technical Conference and Exhibition, Dallas, 9–12 October. http://dx.doi.org/10.2118/97063-MS. Jackson, M.D., Vinogradov, J., Saunders, J.H. and Jaafar, M.Z. 2011. Laboratory Measurements and numerical Modeling of Streaming Potential for Downhole Monitoring in Intelligent Wells. SPE J. 16 (3): 625–636. http://dx.doi.org/10.2118/120460-PA. Leinov, E., Vinogradov, J., and Jackson, M.D. 2010. Salinity dependence of the thermoelectric coupling coefficient in brine-saturated sandstones. Geophys. Res. Lett. 37 (23): L23308. http://dx.doi.org/10.1029/ 2010gl045379. Lynch, E.J. 1962. Formation Evaluation. New York: Harper and Row. Marshall, D.J. and Madden, T.R. 1959. Induced Polarization, A Study of its Causes. Geophysics 24 (4): 790-816. http://dx.doi.org/10.1190/ 1.1438659. McCall, C.M. 1970. The Effect of Hydrocarbons on the Electrochemical Potential Across Porous Media. PhD thesis, Texas A&M University, College Station, Texas. Mounce, W.D. and Rust, W.M. Jr. 1944. Natural potentials in well logging. SPE- 944049-G. Trans., AIME, 155: 49–55. Ortiz Jr., I., Osoba, J.S., and von Gonten, W.D. 1973. Relationship of the Electrochemical Potential of Porous Media with Hydrocarbon Saturation. The Log Analyst 14 (2): 25–32. SPWLA 1973-vXIVn2a3. Reppert, P.M. and Morgan, F.D. 2003a. Temperature-dependent streaming potentials: 1. Theory. J. Geophys. Res. 108 (B11): 2546. http://dx.doi. org/10.1029/2002jb001754. Reppert, P.M. and Morgan, F.D. 2003b. Temperature-dependent streaming potentials: 2. Laboratory. J. Geophys. Res. 108 (B11): 2547. http:// dx.doi.org/10.1029/2002jb001755. Revil, A. 1999. Ionic Diffusivity, Electrical Conductivity, Membrane and Thermoelectric Potentials in Colloids and Granular Porous Media: A Unified Model. J. Colloid Interface Sci. 212 (2): 503-522. http://dx.doi. org/10.1006/jcis.1998.6077. Revil, A. and Cerepi, A. 2004. Streaming potentials in two-phase flow conditions. Geophys. Res. Lett. 31 (11): L11605. http://dx.doi.org/10.1029/ 2004gl020140. Saunders, J.H., Jackson, M.D., and Pain, C.C. 2006. A new numerical model of electrokinetic potential response during hydrocarbon recovery. Geophys. Res. Lett. 33 (15): L15316. http://dx.doi.org/10.1029/ 2006gl026835. Saunders, J.H., Jackson, M.D., and Pain, C.C. 2008. Fluid flow monitoring in oil fields using downhole measurements of electrokinetic potential. Geophysics 73 (5): E165–E180. Schlumberger, C., Schlumberger, M., and Leonardon, E.G. 1934. Some Observations Concerning Electrical Measurements in Anisotropic Media and Their Interpretations. Trans., AIME, 110: 159–182. March 2012 SPE Journal

Shook, M., Li, D., and Lake, L.W. 1992. Scaling immiscible flow through permeable media by inspectional analysis. In Situ 16 (4): 311–349. http://dx.doi.org/10.1016/0148-9062(93)91860-L. Tang, G.Q. and Morrow, N.R. 1997. Salinity, Temperature, Oil Composition, and Oil Recovery by Waterflooding. SPE Res Eng 12 (4): 269–276. SPE-36680-PA. http://dx.doi.org/10.2118/36680-PA. Tasaka, M., Morita, S., and Nagasawa, M. 1965. Membrane Potential in Nonisothermal Systems. The Journal of Physical Chemistry 69 (12): 4191-4197. http://dx.doi.org/10.1021/j100782a021. Telford, W.M., Geldart, L.P., and Sheriff, R.E. 1990. Applied Geophysics, second edition. Cambridge, UK: Cambridge University Press. Traugott, M.O. 1972. Use of the SP Log in Waterflood Surveillance. J Pet Technol 24 (2): 151–153. SPE-3570-PA. http://dx.doi.org/10.2118/3570-PA. Vinogradov, J. and Jackson, M.D. 2011. Multiphase streaming potential in sandstones saturated with gas/brine and oil/brine during drainage and imbibition. Geophys. Res. Lett. 38 (1): L01301. http://dx.doi. org/10.1029/2010gl045726. Vinogradov, J., Jaafar, M.Z., and Jackson, M.D. 2010. Measurement of streaming potential coupling coefficient in sandstones saturated with natural and artificial brines at high salinity. J. Geophys. Res. 115 (B12): B12204. http://dx.doi.org/10.1029/2010jb007593. Worthington, A.E., Hedges, J.H., and Pallat N. 1990. SCA guidelines for sample preparation and porosity measurement of electrical resistivity samples: Part I—Guidelines for preparation of brine and determination of brine resistivity for use in electrical resistivity measurements. The Log Analyst 31 (1): 20–28. SPWLA 1990-v31n1a3. Wurmstich, B. and Morgan, F.D. 1994. Modeling of streaming potential responses caused by oil well pumping. Geophysics 59 (1): 46-56. http://dx.doi.org/10.1190/1.1443533. Wyllie, M.R.J. 1949. A Quantitative Analysis of the Electrochemical Component of the S.P. Curve. SPE-949017-G. Trans., AIME, 186: 17–26. Wyllie, M.R.J. 1951. An Investigation of the Electrokinetic Component of the Self-Potential Curve. In Transactions of the American Institute of Mining, Metallurgical, & Petroleum Engineers, Vol. 192, 1–18. Dallas, Texas: Society of Petroleum Engineers. Wyllie, M.R.J., de Witte, A.J., and Warren, J.E. 1953. On the Streaming Potential Problem in Well Logging. SPE-1045-G. Trans., AIME, 213: 409–416. Matthew D. Jackson is professor of geological fluid mechanics in the Department of Earth Science and Engineering, Imperial College London. email [email protected].

March 2012 SPE Journal

His research interests include the impact of geological heterogeneity on flow during hydrocarbon recovery, application of new reservoir-modeling techniques, and development of novel well technology for monitoring and control. He leads the Smart Wells Group and coleads the Reservoir Modeling Group at Imperial College London. Jackson holds a BS degree in physics from Imperial College London and a PhD degree in geological fluid mechanics from the University of Liverpool. He is an Associate Editor of the SPE Journal and a board member of the London Section of the SPE. Jackson received the SPE Regional Distinguished Achievement Award in 2011. At press time, no biographical information was available for M.Y. Gulamali. Eli Leinov is a postdoctoral research associate in the Smart Wells Group in the Department of Earth Science and Engineering, Imperial College London. email: [email protected]. His research interests include spontaneous electrical potentials arising from coupled flows (thermoelectric, electrochemical, and electrokinetic couplings) in saturated porous media as a method for monitoring subsurface fluid flow. Leinov holds BSc and MSc degrees in mechanical engineering and a PhD degree in hydrodynamic instability from Ben-Gurion University of the Negev, Israel. Jonathan H. Saunders is a postdoctoral research associate in the Applied Modelling and Computation Group in the Department of Earth Science and Engineering, Imperial College London. email: [email protected]. His research interests include modeling of multiphase fluid flow in porous media and electrical techniques for characterizing and investigating Earth systems, with particular focus on the use of self-potentials for detecting and monitoring underground fluid flow. He holds a BA degree in astrophysics from Cambridge University and a PhD degree in electrical methods in geophysics from Imperial College London. Jan Vinogradov is a research associate in petroleum reservoir engineering in the Department of Earth Science and Engineering, Imperial College London. email: j.vinogradov@ imperial.ac.uk. His research interests include the experimental and theoretical study of single-and multiphase flows in porous media, the investigation of spontaneous potentials, and the development of novel smart-well technology. He is a member of the Smart Wells Group at Imperial College London. Vinogradov holds BSc, MSc, and PhD degrees in mechanical engineering from Ben-Gurion University of the Negev, Israel.

69