Shear and Electrical Property Measurements of Water-in-Oil

3308

Energy & Fuels 2008, 22, 3308–3316

Shear and Electrical Property Measurements of Water-in-Oil Emulsions and Implications for Multiphase Flow Meters Eric F. May,*,† Brendan F. Graham,† Aman S. Chauhan,† and Robert D. Trengove‡ Centre for Petroleum, Fuels and Energy, School of Mechanical Engineering, The UniVersity of Western Australia, Crawley, Western Australia 6009, Australia, and Separation Science Laboratory, Murdoch UniVersity, Murdoch, Western Australia 6150, Australia ReceiVed June 12, 2008. ReVised Manuscript ReceiVed June 26, 2008

We prepared water-in-oil emulsions by blending a synthetic brine representative of the formation water from a production well with dead oil samples from the same well. The composition of the oil was thoroughly characterized using an extended saturates-aromatics-resins-asphaltenes analysis, high-temperature gas chromatography, and two-dimensional gas chromatography with time-of-flight mass spectrometry. The relative dielectric permittivities of the emulsions (10-50% water volume fraction) were measured at 1 kHz using a coaxial capacitor and between 0.2 and 13.5 GHz using dielectric relaxation spectroscopy. The dielectric permittivity is one of the properties used by some multiphase flow meters to determine water volume fractions in production systems. The water volume fractions calculated from the measured oil, water, and emulsion permittivities using the Bruggeman equation were systematically above the measured water fraction by an average of 10% and a maximum of 20%. In contrast, one of Hanai’s equations systematically underpredicts the water fraction by an average of 6%, with a maximum of 12%. Importantly, the permittivities measured using a capacitor changed by 14% over 15 min before reaching its steady-state value. This result has significant implications on the required residence time of fluids in capacitance-based multiphase flow meters. The emulsion permittivities exhibited significant dispersion at frequencies between 0.2 and 1 GHz, a result of importance to multiphase flow meters operating at microwave frequencies. We also measured the shear properties of the emulsion samples and compared them to standard models for estimating emulsion viscosities. The results of the shear experiments have implications for total mass flow rates estimated from multiphase flow meters using differential pressure measurements.

1. Introduction Multiphase flows, such as oil-gas, oil-water, gas-water, and oil-water-gas, are commonly encountered in the hydrocarbon industry. Conventional single-phase metering systems require the phases of the well streams to be fully separated upstream of the point of measurement. Multiphase flow measurement technology is an attractive alternative because it enables, in principle, continuous measurement of unprocessed well streams very close to the well with no disruption to the production. The installation of multiphase flow meters (MPFMs) at the wellhead is claimed to have a number of benefits in comparison to well testing. In general, these benefits are expected to lead to increased production, increased recovery, and lower investment costs.1 Continuous monitoring of well performance and real time data enable changes in the gas/oil ratio or water cut or problems with gas lifting to be identified immediately. In principle, this would allow operators to react faster to well performance changes and perform more effective reservoir management.2,3 Other claimed benefits of MPFMs include aiding production optimization by varying operating conditions, such as choke * To whom correspondence should be addressed. E-mail: eric.may@ uwa.edu.au. † The University of Western Australia. ‡ Murdoch University. (1) Thorn, R.; Johansen, G. A.; Hammer, E. A. Three-phase flow measurement in the offshore oil industry: Is there a place for process tomography. In 1st World Conference on Industry Process Tomography, Buxton, Greater Manchester, U.K., 1999.

position, gas lift rates, and gas lift injection pressures and evaluating, in real time, the effect of such changes on the flow rates of oil, water, and gas without deferring production. Changes with a negative impact could be identified rapidly and reversed.4-6 In addition, the use of MPFMs can allow for the removal of test separators from topside facilities. The facilities required for separator-based well test systems are expensive to install and have large maintenance and operating costs. Test separators are also large and occupy a significant portion of the deck of a topside facility.7 The need for well test flow lines can also be eliminated with the installation of MPFMs, reducing costs, especially for unmanned, deepwater, and satellite developments. By eliminating equipment associated with conventional (2) Falcone, G.; Hewitt, G. F.; Alimonti, C.; Harrison, B. Multiphase flow metering: Current trends and future developments. J. Pet. Technol. 2002, 54, 77. (3) Caetano, E. A review of multiphase applications in the Campos Basin. In Multiphase Metering, IBC U.K. Conferences Limited, 1997. (4) Poulisse, H.; van Overschee, P.; Briers, J.; Mincur, C.; Goh, K. C. Continuous well production flow monitoring and surveillance. In Intelligent Energy Conference and Exhibition, Society of Petroleum Engineers, Amsterdam, The Netherlands, 2006. (5) Retnanto, A.; Azim, A. Monitoring well performance using multiphase flow meter. In SPE Asia Pacific Oil and Gas Conference and Exhibition, Society of Petroleum Engineers, Jakarta, Indonesia, 2001. (6) Retnanto, A.; Weimer, B.; Kontha, I. N. H.; Triongko, H.; Azim, A.; Kyaw, H. A. Production optimization using multiphase well testing: A case study from East Kalimantan, Indonesia. In SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers, New Orleans, LA, 2001. (7) Millington, B. Multiphase flow metering: A review. In Multiphase Metering, IBC U.K. Conferences Limited, 1997.

10.1021/ef800453a CCC: $40.75  2008 American Chemical Society Published on Web 08/22/2008

Implications for Multiphase Flow Meters

well testing, safety is also improved. Furthermore, the use of MPFMs can remove the requirement to defer production that is normally associated with well tests.1,2 However, the installation of a MPFM still represents a large capital and operating expenditure, particularly in subsea applications, where their reliability is arguably unproven. In deepwater applications, installation and the retrieval or replacement of a malfunctioning MPFM is extremely costly. The nonzero operating costs associated with MPFMs also need to be considered.2 There are several different types of multiphase flow meters, but the different types commonly employ the same basic strategy to estimate the mass flow rates of each phase: (a) determine the velocity of the multiphase flow, (b) determine the volume fractions occupied by each phase, and (c) use information about the phase densities to convert volume flow rates to mass flow rates. The slip of phases relative to each other and the difficulty in estimating effective viscosities for multiphase flows are the principal impediments to determining the velocity of the flow. To address these impediments, mixing systems to homogenize the flow are often used prior to the flow velocity determination system, which is usually based on differential pressure measurements and/or the cross-correlation of time series signals.8 Phase densities are sometimes calculated from pressure and temperature readings and an equation of state. Some MPFMs use γ-ray densitometers to determine the effective density of the multiphase mixture; such a measurement enables use of an equation between the apparent multiphase mixture density, the (unknown) component phase densities, and the (unknown) phase fractions.8 These unknowns can be determined if this equation is combined with others arising from independent measurements of the phase fractions. A number of techniques have been developed to determine the phase fractions, including γ densitometry at two different energies, electrical impedance measurements, and microwave techniques.2,8 Other emerging technologies include pulsed neutron activation and nuclear magnetic resonance. Most relevant to the results presented in this paper, however, are MPFM systems based on electrical impedance or microwave techniques, which essentially aim to determine the dielectric permittivity, ε, and/or electrical conductivity, σ, of the multiphase mixture. Equations relating the permittivity of the mixture (or conductivity) to the permittivities of the component phases and the phase volume fractions are then solved simultaneously with other relevant equations (such as that for the density of the multiphase mixture plus the normalization equations) to determine the phase fractions. The accuracy of the models that relate the electrical properties of the multiphase mixture to those of the component phases is, therefore, central to the viability of MPFMs based on electrical impedance or microwave measurement systems. Almost as important is the reliability of models used to predict the effective viscosity of the multiphase mixtures, which is required in the conversion of measured differential pressures to mass flow rates. In this work, we report permittivity and viscosity data for highly stable water-in-oil (w/o) emulsions formed with a dead oil from a production well and a synthetic brine. Our data deviate significantly from several literature models often used to estimate the shear and electrical properties of w/o emulsions. Furthermore, we observed a significant time dependence in the apparent dielectric permittivity of w/o emulsions measured at low (8) Hammer, E. A.; Johansen, G. A.; Dyakowski, T.; Roberts, E. P. L.; Cullivan, J. C.; Williams, R. A.; Hassan, Y. A.; Claiborn, C. S. Advanced experimental techniques. In Multiphase Flow Handbook; Crowe, C. T., Ed.; Taylor and Francis CRC Press: Oxford, U.K., 2005; Chapter 14, p 125.

Energy & Fuels, Vol. 22, No. 5, 2008 3309

frequencies, which could have significant implications for the required residence time of multiphase mixtures in MPFMs using electrical impedance sensors. In section 2, we discuss the theoretical basis of models used to estimate the dielectric permittivity of w/o emulsions. In section 3, we discuss the methods and techniques used to thoroughly characterize the composition of the oil, and in section 4, we describe the preparation of the w/o emulsions, the measurements of their shear properties, and the comparisons of the viscosity data with models from the literature. The results of the dielectric permittivity measurements and comparisons of them with various models are presented in section 5. In section 6, the implications of the measurement results for MPFMs are summarized, and a new technique is proposed to measure quantitatively the energy required to produce an emulsion. This proposal is important because without such information, it can be unclear whether the injection of (costly) de-emulsification chemicals into a production system is actually necessary. 2. Theory An emulsion may be defined as a colloidal mixture of two immiscible fluids, one being dispersed in the other in the form of droplets. For a w/o emulsion, the oil is the continuous phase and, consequently, the electrical conductivity of the emulsion is negligible. For an oil-in-water (o/w) emulsion, water is the continuous phase and, because the water is usually a brine, the bulk electrical conductivity of the o/w emulsion is large (∼10 S/m). In this work, the only stable emulsions formed were of the w/o type, as determined by electrical conductivity measurements. The dielectric permittivity of a sample is a measure of the polarization field induced in that sample resulting from the application of an external electric field. The external field is generally time-dependent; in the limit of zero frequency, the material property ε is often called the dielectric constant. However, in both homogeneous (single phase) and heterogeneous samples (e.g., emulsions), there is a characteristic minimum amount of time, τ, required for the induced polarization field to align itself with the external field. If the frequency of the applied field is comparable to or greater than 1/τ, the polarization field can no longer stay completely in phase with the external field and the dielectric permittivity of the sample becomes a complex quantity, ε* ) ε′ + jε′′, where j ) -1. The real part of the permittivity, ε′, decreases below its static value as frequency increases; this phenomenon is known as dispersion, and it represents a reduction in the ability of the sample to store electric-field energy. If the electrical conductivity of the sample is negligible, then the imaginary part of the permittivity, ε′′, increases initially with frequency as electricfield energy is absorbed and dissipated by the sample. At frequencies near 1/τ, ε′′ reaches a maximum and then decreases at higher frequencies. Two general approaches have been applied to predict the dielectric properties of emulsions: the macroscopic, classical electrodynamics approach and the statistical mechanics, charge density approach. The former approach leads to useful working equations from which εmix may be estimated from the dielectric permittivities of the single phases. However, the classical approach assumes that droplet sizes are much larger than the Debye screening lengths and that the conductivities of each phase are uniform and constant. However, for the aqueous phase in an emulsion, the non-uniform distribution of counter-ions near the charged droplet surface makes a substantial contribution to the dielectric response of the emulsion. This level of

3310 Energy & Fuels, Vol. 22, No. 5, 2008

May et al.

complexity can only be treated using the charge density approach, which requires the solution of Poisson’s equation. Thus, the models derived via the classical approach will always be approximate in nature. Maxwell9 and Wagner10 were among the first to apply the classical approach to dilute dispersions of spherical particles.11 They developed the following expression for the dielectric constant of the dispersion, εmix, in terms of the dielectric constants of the dispersed phase εw and the continuous phase εo and the volume fraction of the dispersed phase, φw: εmix ) εo

2εo + εw-2φw(εo - εw) , (φw , 1) 2εo + εw + φw(εo - εw)

(1)

Bruggeman12 extended the Maxwell-Wagner result to include more concentrated systems by considering the effect on εmix of an infinitesimal increase in φw. Replacing εmix and φw with dεmix and dφw, respectively, in eq 1 and then integrating, Bruggeman obtained

( )

εo εmix - εw × εo - εw εmix

1⁄3

) 1 - φw

(2)

Hanai13-15 conducted comprehensive experimental and theoretical studies of the dielectric properties of w/o and o/w emulsions. Allowing for the fact that dielectric properties of an emulsion are frequency-dependent and, therefore, complex, he derived the following complex analogue of Bruggeman’s equation ε∗mix - εw∗ ε∗o - εw∗

×

( ) ε∗o

1⁄3

) 1 - φw

ε∗mix

(3)

Surprisingly, eq 3 reduces to the (purely real) Bruggeman equation only for frequencies much greater than 1/τ; strictly, Hanai14 showed that eq 2 was not directly applicable for determining the dielectric constant of an emulsion. However, for oil-in-water emulsions, the effects of dispersion are small, and thus, Bruggeman’s equation adequately predicts εmix at most frequencies of practical importance to MPFM technology. Hanai13 demonstrated experimentally that Bruggeman’s equation could predict the dielectric constant of o/w emulsions for the complete range of oil volume fractions. For water-in-oil emulsions, the dispersion effect is significant and there is a large difference between the dielectric constant predicted by eq 3 at low frequencies and the dielectric permittivity predicted at high frequencies. For the dielectric constant of water-in-oil emulsions, Hanai14 showed that eq 3 reduces to εmix ) εo

1

(1 - φw)3

(4)

Hanai15 also demonstrated experimentally that Bruggeman’s / equation was only accurate for the real part of εmix of w/o emulsions at high frequencies and that eq 4 was a better predictor of their dielectric constants; while eq 4 does not represent Hanai’s low frequency data for w/o emulsions well, it is an order of magnitude better than eq 2. (9) Maxwell, J. C. A Treatise on Electricity and Magnetism, 2nd ed.; Clarendon: Oxford, U.K., 1881. (10) Wagner, K. W. Arch. Electrotechnol. 1914, 2, 371. (11) Becher, P. In Emulsions: Theory and Practice, 3rd ed.; Oxford University Press: New York, 2001; pp 76-112. (12) Bruggeman, D. A. G. Ann. Phys. Lpz. 1935, 24, 636. (13) Hanai, T.; Koizumi, N.; Rempei, G. Kolloid-Z 1959, 167, 41. (14) Hanai, T. Kolloid-Z 1960, 171, 23. (15) Hanai, T. Kolloid-Z 1961, 177, 57.

The reproducibility of the dielectric constants of the w/o emulsions measured by Hanai15 at frequencies from 20 Hz was significantly worse than it was for the permittivities measured at frequencies approaching 5 MHz. This indicates that some of the discrepancy between Hanai’s low-frequency permittivity measurements of w/o emulsions15 and eq 4 may be attributable to the measurements. Several other authors have since confirmed various aspects of Hanai’s work; for example, Deschamps and Haine16 measured w/o emulsion permittivities at 10 GHz and found that eq 2 did represent their data reasonably. We conclude this section by noting that Hanai15 also demonstrated another effect very relevant to the multiphase metering of w/o emulsions using measurements of the dielectric constant: the strong dependence on shear rate. Hanai made dielectric permittivity measurements of w/o emulsions within a rotational viscometer at shear rates of 0, 100, 200, and 300 rpm. The effect of increasing shear was to decrease the dielectric permittivity at all frequencies. The effect of shear was most pronounced at low frequencies for w/o emulsions; Hanai found that for φw > 0.2, dielectric constants measured at 200 rpm were on average 56% of the zero-shear measurements. The effects of shear could therefore lead to pronounced errors in water-cuts determined by multiphase flow meters measuring the dielectric constant of w/o emulsions. The effect of shear on the electrical properties of w/o emultions has been studied by other workers, usually with a focus on the induced change in droplet shape. Boned and Peyrelasse17 developed equations for the electrical properties of a dispersion of randomly oriented spheroids. Boyle18 argued that, as the concentration of the dispersed phase increases and as the droplets deviate further from a spherical shape, coherent orientation of the droplets with the electric field becomes increasingly probable. Boyle18 generalized eq 3 to describe emulsions containing oriented spheroidal droplets by replacing the exponent 1/3 with a parameter Aa called the depolarization factor: for oblate spheroids, 0 < Aa < 1/3; and for prolate spheroids, 1/3 < Aa < 1/2. Modern multiphase flow meters that convert dielectric permittivity to phase volume fractions typically do so by measuring εmix with a capacitor operating at 75 kHz.19 At this frequency, the capacitor is measuring the dielectric constant of the mixture. On the basis of Hanai’s results,15 the use of the Bruggeman equation (eq 2) may be adequate for metering oilin-water emulsions but it is unlikely to be adequate for waterin-oil emulsions because of the significant effects of dispersion. For w/o emulsions, eq 3 (or Boyle’s modification) should be used; its agreement with experimental values of the dielectric constant is poor but better than any competing model. At increased shear rates, the agreement between eq 4 and experimental dielectric constants is improved, and this may improve the results obtained with multiphase flow meters. In situ adjustment of the depolarization factor Aa may also improve that agreement. 3. Compositional Characterization A sample of the dead oil from Western Australia’s North West Shelf was provided by the production company together with compositional analyses of the recombined hydrocarbon fluid and formation water of the production well. The reported compositions were measured by a commercial laboratory. We (16) (17) (18) (19)

Deschamps, A.; Haine, N. J. Chim. Phys. 1989, 86, 2225. Boned, C.; Peyrelasse, J. Colloid Polym. Sci. 1983, 261, 600. Boyle, M. H. Colloid Polym. Sci. 1985, 263, 51. Kolsrud, T. R. In May, E. F., Ed.; 2006.



Table 1. Compositional Analysis of the Reservoir Hydrocarbon Phases from Gas Chromatography component

oil (mol %)

gas (mol %)

CO2 N2 CH4 C2H6 C3H8 i-C4H10 n-C4H10 i-C5H12 n-C5H12 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C31 C32 C33 C34 C35 C36+

0.00 0.00 0.16 0.03 0.01 0.01 0.01 0.01 0.00 0.08 0.13 0.12 0.57 2.22 2.57 3.88 3.66 5.73 6.41 6.75 5.25 5.78 5.58 4.80 4.58 4.38 3.72 3.06 3.15 2.73 2.47 2.39 2.38 2.10 1.78 1.66 1.34 1.18 0.99 8.33

3.47 4.18 90.17 1.77 0.10 0.08 0.06 0.01 0.00 0.08 0.04 0.02 0.01 0.01

Figure 1. (a) Chromatogram of the oil used in the emulsion studies. (b) Two-dimensional GC-MS chromatogram of the oil. The two regions circled show the distributions of the solubility classes “saturates” and “aromatic and resins”, which are measured quantitatively in SARA analyses (Table 2). The distributions of compounds in homologous series are indicated by lines.

Table 2. Extended SARA Analysis of the Dead Oil Samplea extended SARA analysis of dead oil weight %

Vol

Sa

Ar

nbR

6.09

84.88

5.03

3.32

As ppt 0.68 BR 0.22

RA 0.34

a Vol, volatiles; Sa, saturates; Ar, aromatics; nbR, nonbinding resins; As ppt, asphaltene precipitate; BR, binding resins; RA, refined asphaltene. The solubility classes BR and RA are separated from the asphaltene precipitate using the method described in Graham et al.;20 some additional mass loss occurs during this secondary separation.

characterized the dead oil further with an extended saturatesaromatics-resins-asphaltenes (SARA) fractionation, hightemperature gas chromatography (GC), and two-dimensional GC with time-of-flight mass spectrometry (2D GC-MS). The results of the compositional characterisations for the produced hydrocarbon fluid are presented in Tables 1 and 2; for a detailed description of the extended SARA and 2D GC-MS methodologies, the reader is referred to Graham et al.20 Our high-temperature GC analysis of the dead oil indicated that it was heavily biodegraded; the chromatogram, shown in Figure 1a, displays a “hump” characteristic of an unresolved complex mixture with almost no straight chained hydrocarbons (SCHCs) discernible. The lack of indicative alkane peaks in the chromatogram makes identification of single carbon number (20) Graham, B. F.; May, E. F.; Trengove, R. D. Emulsion inhibiting components in crude oils. Energy Fuels 2008, 22, 1093–1099.

fractions difficult. The problem was addressed by (1) using highmolecular-weight polywax standards as well as another wellcharacterized oil with large amounts of SCHCs to provide reference retention times and (2) conducting a 2D GC-MS analysis, which provided a far greater resolution of the components of the oil. The two-dimensional chromatogram produced by this measurement is shown in Figure 1b. The mole fraction compositions of the single carbon number fractions that we determined with the high-temperature GC analysis were consistent with those reported by the production company. Extracted ion analysis of the 2D GC-MS data showed the aromatic and polar compounds to be spread evenly throughout the low-, middle-, and high-molecular-weight range. This indicates that the response of the high-temperature GC detector was evenly distributed across the single carbon number fractions and not distorted toward any particular mass range. The results of the extended SARA fractionation are listed in Table 2, with the resin content of the oil being 3.3% and its asphaltene content being just 0.7%. The SARA fractionation served two primary purposes. First, as demonstrated and discussed in ref 20, the ratio of binding resins to refined asphaltenes (both subclasses of the asphaltene precipitate) was 0.7, which indicated that it was likely to form a stable emulsion. Second, the SARA analysis provides a defacto quantitative calibration for the results of the 2D GC-MS characterization, which has tremendous resolution but is virtually impossible to calibrate on a quantitative basis. While the 2D GC-MS chromatogram allows for identification of over 6000 compounds, the distributions of those compounds also allows for particular


May et al.

Table 3. Types and Masses of Salts Used To Prepare the Synthetic Brine Salt

Grams per Kilogram of H2O

CaCl2 KHCO3 KCl NaCl

0.98 1.63 9.60 22.80

groupings to be identified, for example, as solubility classes. In Figure 1b, the distributions corresponding to the saturate class are highlighted, together with a combined distribution for the aromatic and resin classes. The SARA fractionation indicates that the large region designated as aromatics and resins in the 2D chromatogram represents just 8.3% by mass of the total amount of sample. The gas and oil compositions were used to estimate the dielectric permittivities of the hydrocarbon phases. At the reservoir saturation condition of the fluid (63 °C and 1603 psia), by treating the C9 and C10 as C8, we calculated εgas ) 1.095 using the gas composition listed in Table 1, the GERG-2004 equation of state,21 and the dielectric constant correlation of Harvey and Lemmon,22 as implemented by the computer package REFPROP 8.0.23 At the same conditions, pure methane has a dielectric permittivity of 1.088. The default gas permittivity value used by electrical-impedance MPFMs is 1, although there is the capacity to tune this value to the particular fluid. An untuned gas permittivity used by such a MPFM could in this case contribute an error as large as 10% to the determination of the phase fractions. The calculation of the permittivity of the oil from its composition is discussed in section 5. A synthetic brine was prepared gravimetrically using the formation water analysis provided by the production company. The types and masses of the salts dissolved in 800 mL of deionized water are listed in Table 3. The stability of w/o emulsions is significantly enhanced by the presence of divalent cations, such as Ca2+; therefore, its inclusion was essential.24 However, upon the addition of these salts, a small amount of CaCO3 precipitate was observed. To force the Ca2+ ions back into solution, hydrochloric acid was added to the synthetic formation water, which resulted in a pH of approximately 2.0. This is significantly lower than the reported 6.9 pH of the natural brine; however, the low pH of the formation water is not likely to significantly affect the results reported here, particularly in terms of testing the accuracy of models, such as eq 2 or 4. The effect of the increased concentration of H+ ions is to increase electrical conductivity of the formation water, decrease its permittivity, and increase the stability of the w/o emulsions.25 The impact on the shear and electrical properties of the emulsions should only be through the change in the pure phase properties; there should be no impact on the observed mixture properties. 4. Emulsion Preparation and Shear Property Measurements A blender with a variable speed drive was used to prepare 50 mL of emulsion at 22 °C from measured volumes of the (21) Kunz, O.; Klimeck, R.; Wagner, W.; Jaeschke, M. The GERG2004 Wide-Range Equation of State for Natural Gases and Other Mixtures, VDI Verlag GmbH: Dusseldorf, Germany, 2007. (22) Harvey, A. H.; Lemmon, E. W. Method for estimating the dielectric constant of natural gas mixtures. Int. J. Thermophys. 2005, 20 (1), 31–46. (23) Lemmon, E. W.; Huber, M. L.; McLinden, M. O. REFPROP, 8.0; National Institute of Standards and Technology (NIST): Gaithersburg, MD, 2007. (24) Kokal, S. SPE Production and Facilities (SPE 77497). In Feb 2005; p 5. (25) Mooney, M. J. Colloid Sci. 1951, 6, 162.

Figure 2. (a) Unmixed oil on top of synthetic brine and (b) w/o emulsions of various water cuts after shear were applied using a blender at 15 000 rpm. The 70 and 90% emulsions were not stable and separated rapidly. The properties of the emulsions with 70 and 90% water volume fractions were not measured.

formation water and the oil. The uncertainty in the values of φw was estimated to be 2%. The emulsions were prepared under two different shear regimes. In both cases, the oil and water were mixed for a total of 5 min. The difference between the shear regimes was the mixer speed, which was controlled using one of two different drive voltages and measured with a tachometer to be 15 000 or 7500 rpm. However, this speed was observed to decrease when emulsions with significant watercuts were formed because of the increase in the emulsion viscosity. The color of the mixture was also observed to change as the emulsion formed, from the dark black of the oil to a light brown color as shown in Figure 2. The average diameter of the water droplets in the emulsion prepared by blending at 15 000 rpm for 5 min was 14 µm. Unfortunately, we did not have an opportunity to measure the droplet size distribution for the emulsions prepared at 7500 rpm. Presumably, the average diameter of the water droplets in this case was greater than 14 µm; the differences in dielectric permittivities measured for the two cases provide evidence of this. To form an emulsion, a turbulent shear field is required. The geometry of the mixer blade of the blender provides the necessary turbulence but prevents any quantitative connection between the speed of the mixer and the shear rate applied to the liquids. However, it was possible to establish the minimum speed required to form a stable emulsion that did not separate for several hours, well after all of the shear and electrical property measurements were complete. The minimum mixer speed necessary to form an emulsion was observed to be 7500 rpm for the 30 and 50% water-cut samples. The 10 and 20% water-cut samples required a minimum preparation speed of 15 000 rpm to create a stable emulsion. For the 30 and 50% samples, a sudden drop in mixer speed clearly indicated the time at which the emulsion formed; this coincided with a change in sample color. Approximately 80 s of mixing at 15 000 rpm was required to form a stable 50% water-cut emulsion and, at 7500 rpm, about 220 s were required. A summary of these results is presented in Table 4. It may be possible to extend this method and estimate the amount of energy needed to form the emulsion. This would require a measurement of the torque applied by the mixing motor in addition to its speed. A proposal for doing so is briefly outlined in section 6. Such a measurement of the energy required to form an emulsion in the laboratory may provide a means of linking the laboratory results to field conditions. A Haake VT-550 rotating cylinder viscometer was used to measure the viscosity of the emulsion samples. Approximately 9 mL of the prepared emulsion was placed into the region between the cup and rotor of the viscometer. The viscometer measures the torque required to move the rotor at a given speed because of the viscous drag of the sample; the well-defined geometry of the rotor and cup allows for the measured torque and rotational speed to be converted to a shear stress and shear rate, from which the viscosity of the sample is calculated. The



Table 4. Preparation Details, Measured Viscosity, η, and Measured Permittivities in the Limit of Zero Frequency, ε(0), and at 13.5 GHz, of the w/o Emulsionsa emulsion water-cut φw (vol %) 0 10 20 30 50

preparation blender speed (rpm) 15 000 15 000 7500 15 000 7500 15 000

viscosity

permittivity

formation time (s)

η (194 Hz) (Pa s)

η (387 Hz) (Pa s)

ε(0)

ε(13 GHz)

not measurable not measurable 50 30 200 80

0.22 0.29 0.39 0.60 0.63 1.57 1.66 0.001

0.22 0.29 0.38 0.58 0.62 1.35 1.50 0.001

2.4 ( 0.1 3.3 ( 0.1 4.5 ( 0.1 6.4 ( 0.3 6.0 ( 0.2 17.1 ( 0.5 14.3 ( 0.4 66.3

2.4 2.9 3.9 5.3 5.1 10.8 10.2 47.6

100 a

The relative uncertainties of φw, η, and ε(13 GHz) were 2, 6, and 5%, respectively. The uncertainty of each ε(0) is indicated in the table. The value of ε(0) for the formation water was taken from the DRS measurements.

ηr )

ηmix 1 ) ηo 1 - kφw

(5)

Here, ηmix is the emulsion viscosity; ηo is the viscosity of the oil; and k is an adjustable parameter, which Oliver and Ward26 varied from 2.34 to 2.77 to describe a variety of suspension viscosity data. For the 10, 20, and 30% water-cut emulsion viscosities listed in Table 4, the average relative deviation of the ηmix predicted using eq 5 is 1%, if k ) 2.2. However, the model cannot be used reliably for higher water cuts because it diverges at φw ) 1/k ) 0.46. Mooney’s model25

( )

ln

Figure 3. Viscosity of the emulsions relative to the oil viscosity at a shear rate of 194 Hz as a function of the water volume fraction, φw. Data for both preparation shear rates are shown, together with predictions from three literature models: Oliver,26 Mooney,25 and Sibree.27,28

rotor used was designed to measure viscosities in the 1 Pa s range. Shear rates of 193.5 and 387 Hz (corresponding to 150 and 300 rpm) were applied for 5 min periods, every 15 min for an hour after the emulsion was prepared. A water bath was used to control and maintain the temperature of the sample in the viscometer between 20 and 21 °C. The results of the rheological measurements are listed in Table 4. The uncertainty of the emulsion viscosity measurements was dominated by the repeatability observed between different samples prepared with the same φw and the same method. The oil was found to be a Newtonian fluid, with a viscosity of 0.22 Pa s at 20 °C for all shear rates accessible to the viscometer (up to 1032 Hz). The emulsions, however, behaved in a nonNewtonian fashion and did so increasingly as φw increased. The viscosity of the emulsions could only be measured at two relatively low shear rates, 194 and 387 Hz, because it was found that higher rotational speeds sometimes caused the emulsions to separate. Figure 3 shows the viscosity of the w/o emulsions measured at 194 Hz relative to the viscosity of the oil as a function of water cut and compares the measurements with the predictions of various models from the literature. Oliver and Ward26 found that eq 5 described the relative viscosity, ηr, of stable suspensions of spherical particles with volume concentrations up to 20%. (26) Oliver, D. R.; Ward, S. G. Nature 1953, 171, 162. (27) Sibree, J. O. Trans. Faraday Soc. 1930, 26, 26. (28) Sibree, J. O. Trans. Faraday Soc. 1931, 27, 161.

ηmix 2.5 ) ηo 1 - zφw

(6)

describes our measured ηmix for φw e 0.3 with an average deviation of 2% with no adjustment of the self-crowding factor z ) 1.11 For higher water cuts, it is also known to be deficient,11 and for φw ) 0.5, eq 6 predicts a value of ηmix 61% larger than the measured value. In contrast, for φw ) 0.5, the model of Sibree,27,28 shown in eq 7, gives ηmix within 1% of the measured value, without any adjustment of the “volume factor” h from its standard value of 1.3. ηmix 1 ) ηo 1 - (hφw)1⁄3

(7)

However, this model leads to significant overestimates of ηmix for φw e 0.3, with an average deviation of 46%. Thus, none of these three models would be suitable for describing w/o emulsion viscosities over the range of water cuts that could be encountered during the production life of a well. Given the general sensitivity of emulsion viscosity to water cut, any small deficiency in the predictive capability of any model is likely to have a significant impact on the mass flow rate calculated by a MPFM from differential pressure measurements. The emulsion viscosity models shown in eqs 5-7 are based on observations and considerations of the rheological properties of suspensions of hard spheres at moderate concentrations.11 As such, they predict emulsion properties that only depend upon the oil viscosity and the water cut. In principle, however, there should also be a dependence on droplet size; emulsion viscosity should increase with decreasing droplet size. Our data are consistent with this concept: the viscosity of the 50% watercut emulsion for a preparation shear of 7500 rpm is 5% lower than that of the 15 000 rpm sample. However, this difference is approximately the same as the experimental uncertainty of the viscosity measurements. In contrast, the dielectric permit-


May et al.

tivity data for the emulsions (also listed in Table 4) show a more significant dependence on droplet size. 5. Dielectric Permittivity Measurements A coaxial capacitor was used to measure the dielectric permittivity of the oil and the emulsions in the limit of zero frequency. The capacitor electrodes consisted of a solid aluminum cylinder, 2 cm in diameter and 7.5 cm long, located centrally within a 3 cm internal diameter and 7.5 cm long aluminum tube. The 0.5 cm gap between the electrodes was large enough that air was not trapped when the emulsion was poured into it. The capacitance was measured with a LCR impedance meter, which operated at 1 kHz. When the 0.5 cm gap was filled with air, the electrodes had a capacitance of 11.5 ( 0.1 pF. The capacitor was calibrated using liquid hexane, which has ε ) 1.88 at 22 °C,29 to determine the fringing field capacitance. The static permittivity results are listed in Table 4. Measurements of the oil with the capacitor gave εoil ) 2.44 ( 0.06. This value was compared to a calculation based on the composition of the oil and estimates of the molar polarizabilities of the single carbon number fractions, PSCN, for the oil phase listed in Table 1. PSCN cm3 mol-1

) 0.3341MSCN + 0.4208

(8)

Here, MSCN is the molar mass of the single carbon number fraction, which was calculated using the correlation of Katz and Firoozabadi.30 Equation 8 was derived from liquid refractive index and density data for alkanes and aromatics taken from the literature.31-35 The molar polarizability of the oil was then estimated from a mole fraction average of the PSCN. The density of the oil at standard conditions, which was estimated using the correlation of Katz and Firoozabadi,30 was combined with the molar polarizability of the oil in the Claussius-Mossotti equation to determine the dielectric permittivity of the oil. Further detail is provided in May et al.36 The calculated value of εoil was 2.1. The calculation excludes the contribution of the polar resin and asphaltene fractions in the oil; the impact of these polar fractions would be to increase the value of εoil. The default oil permittivity value used by electrical impedance MPFMs is 2, although there is the capacity to tune this value to the particular fluid. Use of the default or even the calculated value of εoil by such a MPFM could, in this case, contribute an error of 12-20% in the determination of the phase fractions. (29) Hermiz, N. A.; Hasted, J. A. J. Chem. Soc. 1981, 8, 147. (30) Katz, D. L. Predicting phase behavior of condensate-crude-oil systems using methane interaction coefficients. J. Pet. Technol. 1978, 1649– 1655. (31) Rubio, J. E. F.; Arsuaga, J. M.; Taravillo, M.; Baonza, V. G.; Caceres, M. Refractive index of benzene and methyl derivatives: Temperature and wavelength dependencies. Exp. Therm. Fluid Sci. 2004, 28, 887– 891. (32) Scaife, W. G. S.; Lyons, C. G. R. Dielectric permittivity and pvT data of some n-alkanes. Proc. R. Soc. London, Ser. A 1980, 370 (1741), 193–211. (33) American Petroleum Institute (API). Technical Data BooksPetroleum Refining, 3rd ed.; American Petroleum Institute: Washington, D.C., 1976. (34) Hales, J. L.; Townsend, R. Liquid densities from 293 to 490 K of nine aromatic hydrocarbons. J. Chem. Thermodyn. 1972, 4, 763–772. (35) Ben’kovskii, B. G.; Bogoslovskaya, T. M.; Nauruzov, M. K. Density, surface tension and refractive index of aromatic hydrocarbons at low temperatures. Chem. Technol. Fuels Oils 1966, 2 (1), 23–26. (36) May, E. F.; Miller, R. C.; Goodwin, A. R. H. Dielectric constants and molar polarizabilities for vapor mixtures of methane + propane and methane + propane + hexane obtained with a radio frequency reentrant cavity. J. Chem. Eng. Data 2002, 47, 102–105.

Figure 4. Observed time dependence of the relative permittivity derived from a capacitor measurement for a 50% water-cut emulsion prepared with a mixer speed of 15 000 rpm.

Significant transients were observed during the emulsion permittivity measurements using the capacitor, a typical example of which is shown in Figure 4. The initial permittivity reading immediately after the capacitor was filled with the sample was always significantly higher (∼15%) than the final steady-state value. Approximately 20 min was required before the permittivity value was within 1% of its steady-state value. We attempted to eliminate electrode polarization as a cause of the transient by switching off the electric field in between spot measurements; this action had no impact on the nature of the transient. It is possible that a thermal transient caused the variation in the measured capacitance, resulting from a difference in temperature between the sample and the aluminum electrodes. However, the effect did not appear to depend upon the amount of time that the sample was allowed to cool following its preparation. Clearly, residence times of 1 h are not feasible for MPFMs in operating production systems; however, without them, such transients could result in significant errors in estimated phase fractions. The uncertainties for the dielectric permittivities of the emulsions measured with the capacitor are listed in Table 4. The uncertainty of the capacitance measurements (fringing fields and empty and filled capacitances) amounted to 2.5% of ε(0). The other contribution to the uncertainty of ε(0) was the repeatability achieved with different emulsions of the same φw prepared in the same way. This uncertainty ranged in magnitude between 1 and 4% of ε(0). The combined uncertainties range from 2.5% of ε(0) for the emulsions with φw ) 0.5 to 4.5% of ε(0) for the emulsions with φw ) 0.1. Dielectric relaxation spectroscopy (DRS) was used to measure the complex permittivities, ε* ) ε′ + jε′′, of the oil, brine, and emulsion samples at frequencies between 0.2 and 13.5 GHz. The DRS system consisted of a vector network analyzer connected to a 2.2 mm coaxial probe, which was inserted into the sample to a depth of at least 5 mm. It was necessary to calibrate the DRS system by measuring the reflection coefficient when the probe was terminated by an infinite impedance (air), a zero impedance (electrical short), and a reference liquid of known permittivity. We used both deionized water and hexane as the reference liquid for DRS calibrations. The difference between emulsion permittivity measurements with the two calibrants was within the specified uncertainty of the DRS system (5% of ε′). We report here only the results obtained with the hexane calibration. The DRS measurements of the oil showed no dispersion in εoil and were consistent with the capacitor measurements. The permittivity of the brine at audio frequencies (listed in Table 4) was taken from the DRS values



Figure 6. High-frequency complex permittivities for 50% water-cut emulsions measured with the DRS system. The real and imaginary values of ε* ) ε′ + jε′′ for the emulsion prepared at 15 000 rpm indicate that the water-droplet dipoles are slightly smaller than those for the preparation speed of 7500 rpm.

Figure 5. (Top) Dielectric permittivities for the w/o emulsions εmix measured with the capacitor as a function of the volume fraction, φw. Also shown are emulsion permittivities predicted using the single-phase properties and the models of Bruggeman12 (eq 2) and Hanai15 (eq 4). (Bottom) Water fractions inferred from the measured εmix, εo, and εw and eqs 2 and 4, compared to the measured water fraction values.

of ε′ measured between 0.2 and 0.8 GHz, which had an average value of 66 ( 1. The steady-state relative permittivities of the emulsions measured with the capacitor are shown as a function of water cut in Figure 5a. The effect of preparation shear on the measured capacitance was significant; the dielectric permittivity of the 50% water-cut emulsion prepared at 7500 rpm was 20% larger than the same emulsion prepared at 15 000 rpm. Also shown in Figure 5a are predictions of the emulsion permittivity based on the water-cut and single-phase static permittivities using eqs 2 and 4. The Bruggeman12 equation (eq 2) is optimized for oil-inwater emulsions, where dielectric dispersion is not pronounced.11 For w/o emulsions, its predictive performance is best for permittivities measured in the high-frequency limit, which, for these samples, is above 3.5 GHz. For the permittivity values likely to be measured by a MPFM operating at audio frequencies, eq 2 predicts εmix ) 11.9 for a 50% water-cut emulsion, which is significantly below the observed values of 14.3 ( 0.4 (15 000 rpm) and 17.1 ( 0.5 (7500 rpm). The low-frequency model of Hanai,14 eq 4, which is specific to the static permittivities of w/o emulsions, provides more reliable predic-

tions particularly for the low preparation shear samples. The Hanai model predicts εmix ) 19.2 for a 50% water-cut emulsion (independent of the static permittivity of the formation water). It should be noted that the MPFMs of interest actually handle the inverse problem of determining φw from a measurement of εmix. The propagation of errors in this case is damped by the exponent 1/3 in both eqs 2 and 4. In Figure 5b, the true water cuts of the sample emulsions are plotted as a function of their static permittivity, together with the predicted φw calculated from eqs 2 and 4. The Bruggeman equation systematically overpredicts the true water volume fraction, with an average deviation of +10.2% and a maximum deviation of +20% for the 50% water cut prepared at 7500 rpm. In contrast, the Hanai equation systematically underpredicts the true water cut, with an average deviation of -6.4% and a maximum deviation of -12.3% for the 30% water-cut emulsion prepared at 15 000 rpm. Some MPFM systems determine phase fractions by measuring the permittivity of the multiphase mixture at microwave frequencies; such systems are constrained to operate at frequencies greater than the cutoff frequency of the formation water, which is about 1.3 GHz for the wells in the North Sea.8 The results of our DRS permittivity measurements between 0.2 and 13.5 GHz for the w/o emulsions are relevant to such MPFM systems. The dielectric relaxation spectrum of the 50% watercut emulsion is shown in Figure 6. There is significant dispersion between 0.2 and 1 GHz, and it is not until the frequency is above 3.5 GHz that the high-frequency limit for the emulsion permittivity is reached. The DRS permittivities at 0.2 GHz are similar to the values measured with the capacitor, which establishes that there is no significant dispersion at frequencies below 0.2 GHz. The dielectric loss spectra are unremarkable;


May et al.

the expected absorption peak is obscured by the low-frequency limit of the instrumentation. Emulsions made with a preparation shear of 7500 rpm exhibit larger static and high-frequency permittivities than those produced with a preparation shear of 15 000 rpm but have similar relaxation frequencies. Hanai14,15 showed that eq 2 was able to determine reliably the water volume fraction of w/o emulsions in the limit of high frequency. The high-frequency DRS data confirmed this. The root-mean-square (rms) deviation between the φw listed in Table 4 and those calculated using eq 2 with the εo, εw, and εmix measured at 13 GHz is just 0.02, with a maximum absolute deviation of 0.03. However, MPFMs that infer phase fractions from dielectric permittivities measured at microwave frequencies are becoming less common than those that use electrical impedance measurements at audio frequencies because of the potential problems associated with dispersion.19 The results of this work suggest that this trend be re-examined, at least in the case of w/o emulsions. Dispersion can be avoided by simply using sufficiently high frequencies (e.g., J10 GHz), and at these conditions, eq 2 is clearly much more reliable for determining φw. 6. Conclusions Water-in-oil emulsions are clearly problematic for MPFMs that determine phase fractions from audio frequency measurements of dielectric permittivity. In the field, such a MPFM is likely to be configured to determine φw from a measured εmix by solving eq 2 and taking εo ) 2. Doing so with the 50% water-cut emulsion prepared in this work at 7500 rpm would lead to an error of +25%. Use of the more theoretically robust eq 4 with a measured value of εo for the equivalent emulsion prepared at 15 000 rpm would lead to an error in φw of -10%. The errors could be even larger if the residence time of the emulsion in the MPFM is too short. The error of the phase fraction determination could be compounded further in the estimation of phase mass flow rates by inadequate emulsion viscosity predictions if the MPFM system uses differential pressure measurements to obtain total mass flow rates. Cross-correlation (time-of-flight) measurement systems are sometimes used by MPFMs to avoid this problem. However, because of the potential for slip between phases, these correlation techniques must usually satisfy so-called quality requirements to be regarded as valid, including a satisfactory comparison to simultaneous differential pressure velocity determinations.37 One alternative for use under “emulsion conditions” is the use of two cross-correlation systems, which aim to measure directly and account for phase slip. This requires, however, an a priori knowledge of whether a stable emulsion is likely to form in a given production system. Our observations during the emulsion preparation phase of this work lead us to suggest the possibility of measuring the energy required to produce a stable emulsion from a given volume of water and oil. We found that, using the blender at a given rotational speed, the amount of time required to form the emulsion was a measurable quantity with good repeatability. A simultaneous measurement of the rotor torque of the blender could be combined with the rotational speed and emulsion (37) ROXAR. Capability of emulsion measurement by ROXAR subsea and topside MPFM. RFM-TD-01676-191, 2006.

Figure 7. Schematic of a proposed “emulsion dynamometer” designed to measure the torque applied by the rotor of the blender to the oil and water during the preparation of an emulsion. Such a system may allow measurement of the energy required to form an emulsion of a given volume.

formation time to give the total mechanical energy imparted by the blender on the known volume of liquid. In situ determination of the rotor torque could be achieved by placing the beaker containing the oil and water on a frictionless air bearing and using a load cell, at a known distance from the rotation axis, to measure the reaction force required to prevent the beaker from rotating. A schematic diagram of a possible “emulsion dynamometer” is shown in Figure 7. Laboratory measurements of the energy per unit volume required to form a stable emulsion may be useful if they could be compared to shear fields in production systems predicted using computational fluid dynamic simulations. If so, the technique may shed light on the important question of whether problematic emulsions will actually form in a given production system. Such information would enable important cost-benefit analyses to be conducted, for example, on the continuous injection of expensive de-emulsification chemicals into the production system. Acknowledgment. We thank Holly Rose for assistance with the measurements, and we thank Mark Jackson for his support of the project. We also thank the Australian Research Council for the LIEF grant to acquire the 2D GC-MS, and B.F.G. thanks the Western Australian Energy Research Alliance for funding his position. EF800453A

Shear and Electrical Property Measurements of Water-in-Oil

Recommend Documents