Hydrate Formation in Water-in-Crude Oil Emulsions Studied by Broad

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Hydrate formation in water-in-crude oil emulsions studied by broad-band permittivity measurements Kjetil Haukalid, Kjetil Folgerø, Tanja Barth, and Stian Landmark Fjermestad Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.6b03416 • Publication Date (Web): 06 Mar 2017 Downloaded from http://pubs.acs.org on March 6, 2017

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Hydrate formation in water-in-crude oil emulsions studied by broad-band permittivity measurements Kjetil Haukalid*†#, Kjetil Folgerø‡, Tanja Barth§ and Stian Landmark Fjermestad§ † Department of Physics and Technology, University of Bergen, Allégaten 55, NO-5007 Bergen, Norway, E-mail: [email protected], Fax: +47 55 58 94 40 ‡ Christian Michelsen Research AS, P.O. Box 6031, NO-5892 Bergen, Norway § Department of Chemistry, University of Bergen, Allégaten 41, NO-5007 Bergen, Norway

ABSTRACT

In order to develop more cost effective and environmentally friendly strategies to prevent formation of gas hydrate plugs in oil production pipelines, better understanding of the mechanisms of plug formation is needed. This paper presents broad-band permittivity measurements of hydrate formation in water-in-oil emulsions. The experiments were conducted at atmospheric pressure using dead crude oil and diesel fuel, with cyclopentane as hydrate former. However, the use of dielectric probes employed in this work can be extended to more realistic systems, as they are able to withstand high pressures and harsh chemical environments. The results show that broad-band permittivity measurements can be used to detect hydrate

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agglomeration and formation of hydrate deposits in oil-dominated systems. By applying existing dielectric mixing models, the fractions of oil, water and hydrates can be estimated.

INTRODUCTION Gas hydrates are ice-like clathrate compounds where gas molecules are trapped in a lattice of hydrogen bonded water molecules.1 Hydrates are stable at high pressures and low temperatures, and hydrate plugs may therefore form in pipelines transporting unprocessed or minimally processed well streams. Hydrate plugs may cause pipeline blockage, which must be prevented in order to avoid loss of production time and potential hazardous situations. The conservative approach to prevent hydrate plug formation is to keep the temperature and pressure conditions of the entire pipeline outside the hydrate stability region. This can be achieved e.g. by using isolated pipelines, direct electrical heating or by adding chemicals to the well stream to change the phase boundaries for hydrate formation. Such thermodynamic plug inhibition techniques are associated with considerable expenses and may prevent profitable exploitation of marginal fields.2 However, better understanding of hydrate formation kinetics and plug formation mechanisms has enabled use of more economical hydrate treatment strategies based on risk management.3,4 This development has been driven by a combination of field experiences and knowledge gained from lab-scale studies. Plug formation in oil-dominated systems is believed to be initiated by agglomeration of hydrate covered water droplets (see Figure 1).5 The agglomeration process may eventually lead to pipeline blockage. The tendency of hydrates to agglomerate and form plugs has been found to vary considerably from one crude oil and process water system to another.6-10 In systems showing strong anti-agglomerating properties, the hydrates can often be transported to the


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process platform as a slurry mixture. The tendency to form transportable slurries rather than plugs depends strongly on the water content and subcooling.4 Surface active chemicals that improve the anti-agglomerating properties of the system, so-called anti-agglomerants, can also be added to the well stream.11 Slurry transport of hydrates is considered to be fairly well understood and has led to considerable savings with regard to hydrate treatment in oil-dominated systems.4-12 While plug formation in oil-dominated systems is normally believed to be caused by agglomeration and subsequent jamming, plug formation in gas-dominated systems is believed to be caused by sloughing of hydrate deposits from the pipe wall and subsequent jamming.13 However, recent field trials have revealed that hydrate deposition on the pipe wall can be a key mechanism for plug formation also in oil-dominated systems.12 Such findings illustrate the need of further investigation of the mechanisms of hydrate plug formation in oil-dominated systems. This paper demonstrates how broad-band permittivity measurements obtained with open-ended coaxial probes can be used to monitor hydrate formation in oil-dominated systems. Open-ended coaxial probes have previously been found to be suitable to study hydrate formation in water-inoil (W/O) emulsions14-16 and formation of gas hydrate deposits.17 Haukalid et al.16 studied how formation of small amounts of gas hydrates in water-in-crude oil emulsions impacted important emulsion properties such as droplet size and stability. Live crude oils and associated process waters from North Sea oil fields were used in this study, which were performed in a highpressure sapphire cell. Jakobsen et al.14 and Jakobsen and Folgerø15 monitored hydrate formation in a W/O emulsion with relatively high water fraction (60 %). A mineral oil, the hydrate forming liquid trichlorofluormethane and surfactant were used as oil phase, and NaCl solutions were used as water phase. The experiments presented in this work resemble those of Jakobsen et al.14 and Jakobsen and Folgerø15 in being performed at atmospheric pressure, but here cyclopentane is


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used as hydrate former instead of trichlorofluormethane. Moreover, the emulsions studied in this work have lower water fractions (30 % and 50 %), and crude oil is used as the oil phase in some of the experiments. The permittivity is also measured in a broader frequency range, which provides significant additional information about the system. It is showed that by measuring such a broad frequency range, hydrate agglomeration and deposition may be detected from the permittivity spectra. Moreover, the broad measured permittivity spectra are used to evaluate dielectric mixing formulas that are applicable to model hydrate formation in W/O emulsions. The mixing formulas are also used to extract quantitative information (e.g. hydrate conversion) about the phases from the permittivity measurements. The aim of this paper is to show that dielectric spectroscopy is a promising instrumental technique to monitor hydrate formation in oildominated systems. The results demonstrate that the permittivity measurements can provide valuable additional information to the hydrate researcher apart from what would typically be available from visual observations, PVT analysis, indirect viscosity measurements, etc. The technique is considered especially suited for use in systems where visual observations are excluded or limited, as well as in opaque fluid systems. By applying dielectric mixing formulas, the permittivity measurements can be used to estimate the composition of hydrate slurries and deposits. The applied open-ended coaxial probes are able to withstand high pressures (the design pressure is 150 bar). DIELECTRIC SPECTROSCOPY Dielectric spectroscopy is measurement of the material property permittivity as function of frequency. The permittivity is in general a complex variable and is normally defined relative to the permittivity of vacuum


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∗ = − (1) where is the permittivity of vacuum, ∗ is the complex relative permittivity, and are the real and imaginary parts of the permittivity, respectively, and is the imaginary unit. In this work the term complex permittivity is used to refer to the complex relative permittivity ( ∗ ), while the term permittivity is used as a more general term. The terms dielectric constant and loss factor are used to refer to the real ( ) and imaginary ( ) part of the complex permittivity, respectively. If an electric field is applied to a material, the field will cause polar molecules to partly align with it. This leads to a net polarization of the material that opposes the applied electric field and thereby reduces the net electric field strength in the material. The dielectric constant can be thought of as a measure of how much a material opposes an applied electric field, as the net electric field in general will be reduced by a factor 1⁄√ . The loss factor is related to transformation of electromagnetic energy to heat, which may be observed for example in a microwave oven. The permittivity is in general dependent on the frequency of the electric field. Examples of typical complex permittivity spectra are shown for hydrates, water, oil and gas in Figure 2. Multiple spectra are plotted for hydrates, to illustrate that the complex permittivity of hydrates is dependent on type of hydrate former(s). The complex permittivity spectra of hydrates, oil and water differ significantly, making dielectric spectroscopy a suitable technique to study hydrate/water/oil systems. The rapid fall in the dielectric constants with frequency, accompanied by maximums in the loss factor, are referred to as dielectric dispersions in this work. The dielectric dispersions arise out of the inability of the polarization mechanisms to follow the oscillating electric field as the frequency increases. The frequency for which the loss factor reaches maximum is referred to as the dispersion frequency. The term dispersion strength


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is used to refer to the magnitude of the drop that the dielectric constant experiences during a dielectric dispersion. In heterogeneous materials, an additional polarization mechanism (apart from the polarization caused alignment of polar molecules) called interfacial polarization is often observed. Here, free charges can accumulate on interfaces between phases with different electrical conductivity and thereby increase the net polarization of the material even further. Interfacial polarization is typically observed in emulsions and other colloids,18 biological tissues19 and soils.20 The term effective permittivity is used in literature to refer to the resulting permittivity of heterogeneous materials, whose components in general have different permittivity. This work concerns permittivity measurements on W/O emulsions. Hence, interfacial polarization is likely to be observed. There are different dielectric mixing formulas in the literature for modelling the effective permittivity of heterogeneous systems (see e.g. Sihvola21). This work uses Hanai’s theory of interfacial polarization22 to model the permittivity of emulsions. Hanai’s theory is an extension of the more well-known Bruggeman’s theory23 to complex permittivity. According to Hanai,22 the complex effective permittivity of a dispersion of spherical particles is given by ∗

∗

∗ ∗

∗

∗

=1−

(2)

∗ where ∗ is the complex effective permittivity of the dispersion, is the complex permittivity

of the continuous phase, ∗ !"# is the complex permittivity of the dispersed phase, and is the volume fraction of the dispersed phase. Figure 3 shows the dielectric constant at 1 GHz for a W/O emulsion as function of water fraction, as given by equation (2). The permittivity of the water phase is given using empirical formulas for NaCl-solutions from Peyman et al.24 The NaCl


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concentration and the temperature is set to 0.1 mol/L and 20 °C, respectively. The dielectric ) and the loss factor ( ) of the oil phase is set to 2 and 0, respectively. The constant (

effective dielectric constant of a W/O emulsion increases with increasing water fraction, due to the higher dielectric constant of water. Figure 4 shows a complex permittivity spectrum for a W/O emulsion as given by equation (2). The water fraction is set to 50 %, and the permittivity of the water phase and oil phase is the same as for Figure 3. Two dielectric dispersions are observed. One dispersion around 15 MHz and one around 40 GHz. The high frequency dispersion is associated with the polarization of the water molecules. The low frequency dispersion is caused by interfacial polarization and is referred to as the Maxwell-Wagner25,26 dispersion in the following. Due to the dissolved ions, the water phase has a finite DC conductivity. When the electric field oscillates, positive and negative charged ions accumulate on opposite sides of the water droplet, and thereby give rise to interfacial polarization. Hanai’s theory has been extended to a model for dispersions of shelled spherical particles.27 This model is used in this work to model hydrate formation in W/O emulsions, assuming the hydrates to form shells around the water droplets. EXPERIMENTAL Fluids. Dead crude oil from a North Sea oil field and diesel fuel were used as the oil phase. Table 1 summarizes some key properties of the applied crude oil and diesel fuel. Cyclopentane (>99%) from Sigma Aldrich was added to the oil phase to serve as hydrate former.


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Cyclopentane (CP) hydrates are stable below 7 °C at atmospheric pressure. NaCl solutions were used as water phase in most experiments, with the exception of two experiments where process water from a North Sea oil field was used instead. The crude oil from the North Sea is moderately biodegraded, which implies an elevated content of surface active compounds compared to oils that are not biodegraded. NaCl solutions were prepared by weight, using distilled water and NaCl from Sigma Aldrich (≥99 %). The non-ionic surfactant Berol 26 (Akzo Nobel Surface Chemistry AB) was used as stabilizer in the experiments with diesel fuel and in some of the experiments with crude oil. The measuring cell. The measuring cell consists of a 3 inch brass pipe mounted on a plastic disk (see Figure 5). A copper pipe is wound around the pipe and connected to a refrigerated/heating circulator (Julabo F34) filled with ethylene glycol and water (approximately 50/50 by volume). The temperature of the emulsion is regulated by adjusting the temperature of the circulating bath fluid. A thermocouple was placed close to the inner pipe wall to monitor the temperature of the emulsion. Three open-ended coaxial probes (see Figure 6) were mounted in the cell. Two probes (Probe A and Probe C) were mounted through threaded holes in the pipe wall. The third probe (Probe B) was mounted through the plastic disk in the bottom of the cell. Preparation of emulsions. The crude oil sample was heated to 60 °C for about 20 min and rocked gently approximately every 5 minutes to melt precipitated wax particles. The required volume of crude oil or diesel fuel was added to a beaker. The surfactant (3% of oil phase by volume if used) was added to the crude oil/diesel fuel and mixed at 3000 rpm for about 3 min using a shear mixer (IKA T 18). Water was then added dropwise while mixing. After addition of water, the emulsion was mixed at 10000 rpm for about 3 min. The emulsion was then transferred from the beaker to the measuring cell. Finally, CP corresponding to 1 CP molecule


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per 15 water molecules was added to the emulsion under constant stirring, using a laboratory stirrer (IKA EUROSTAR 60) fitted with a metallic impeller. The molar ratio between CP and water (1:15) corresponds to a volumetric ratio about 35:100. The total volume of the added fluids was 500 ml. The emulsion was stirred continuously during the experiment. The stirring speed was typically set to 1000 rpm, dependent on the viscosity of the emulsion. Hydrate experiments. After preparation, the emulsion was cooled down in the measuring cell to approximately 0 °C. Hydrate formation was then initiated by adding a small amount of crushed ice to the emulsion. In some experiments, the hydrate formation showed a long induction time, and the bath fluid temperature was decreased (0.5 - 2 °C) to expedite hydrate formation. The motivation for this was to decrease evaporation of cyclopentane. However, decreasing the experimental temperature must be expected to cause increased hydrate formation rates and higher total hydrate conversion. Circulation of cooling fluid continued for 26 hours, until the measured permittivity indicated that hydrate formation had slowed down considerably (see Result section). The hydrates were then melted by stopping the circulation of cooling fluid. Table 2 summarizes selection of fluids and water fraction in the experiments reported in this work. Note that Experiment 9 was performed without addition of CP. This was done to compare hydrate formation with ice formation. Permittivity measurement. Three open-ended coaxial probes were used for permittivity measurement. An open-ended coaxial probe can be described as a coaxial transmission line that is cut off at one end. A signal transmitted to the probe will almost be totally reflected due to the severe impedance mismatch at the probe end. The amplitude and phase of the reflected signal


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depend on the dielectric properties of the material in front of the probe, making the probe suitable for permittivity measurements. The sensitivity to changes in the sample permittivity decreases roughly exponentially with distance from the probe’s inner conductor. The probe is therefore sensitive to changes in the permittivity in a small and roughly hemispherical shaped volume in front of the probe. The radius, or depth, of this volume is about the size of the outer conductor radius. The outer conductor radius of Probe A, Probe B and Probe C is 5.00 mm, 2.35 mm and 2.35 mm, respectively. Probe A and Probe C were connected to a vector network analyzer (Rohde & Schwarz, ZVL13) and Probe B to a vector reflectometer (Copper Mountain, Planar R54) through high quality coaxial cables. The frequency range of the vector network analyzer (VNA) and the vector reflectometer (VR) is 1 kHz-13.6 GHz and 85 MHz-14 GHz, respectively. The reflection coefficient was measured in the frequency range 1 MHz - 13.6 GHz with the VNA and 85 MHz 14 GHz with the VR. Prior to each experiment, both instruments were calibrated at the end of the coaxial cable using calibration standards (open circuit, short circuit and matched load). The permittivity was calculated from the measured reflection coefficient using the bilinear method described in Folgerø.28 RESULTS AND DISCUSSION This section is divided into four parts. First, one of the experiments will be discussed thoroughly. Then, the effect of varying water fraction and salinity (Experiment 1-4) is investigated. The section continues by showing how time variations in the measured dielectric constant at single frequency may reveal that hydrate agglomeration and deposition is taking place. In the last part of the section, it is shown that the permittivity spectra may also reveal hydrate agglomeration


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and/or deposition directly, hence without being dependent on following the single frequency time variations. Representative experiment. Before discussing differences between the individual experiments, the results from a representative experiment (Experiment 1) will be presented in some detail. In this experiment diesel was used as oil phase, the water fraction was 50 % and the NaCl concentration was 1 mol/L. Figure 7 shows the measured dielectric constant at 1 GHz and the measured temperature as function of time through Experiment 1. Blue, magenta, red and black data points correspond to Probe A, Probe B, Probe C and temperature, respectively. The solid vertical line corresponds to when the cooling was stopped (the circulation of cooling fluid switched off). The dashed vertical lines correspond to incremental changes in the set temperature of the cooling bath fluid. The magnitude of these changes is showed above the dashed lines. The grey shaded area indicates the time interval from onset of hydrate formation to the point where all hydrates have dissociated. The reason for plotting the dielectric constant at 1 GHz is that the measurement uncertainty is lowest in this range. For low frequencies, permittivity measurements obtained with open-ended coaxial probes are increasingly prone to noise and systematic errors with decreasing frequency. The increased sensitivity to noise can be observed from the measured permittivity spectra presented in Figure 8 and Figure 12. In Figure 12, minor systematic errors are also observed, as the measured loss factor crosses the horizontal axis. For high frequencies, open-ended coaxial probes start radiating, and the measurement uncertainty increases due to invalid assumptions in the model used to calculate the permittivity from the measured reflection coefficient. The measured dielectric constant follows the same trend for the three probes through the experiment, but there is an offset between the individual probes. Thus, the probes sense different


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water fractions (see Figure 3), which shows that water is unevenly distributed in the cell. The measured dielectric constant is generally higher after hydrate dissociation than before hydrate formation, especially for Probe A and Probe C. This shows that the hydrate formation and dissociation cycle have impacted the distribution of water in the cell. Lachance et al.29 has previously shown that hydrate formation and subsequent dissociation in W/O emulsions may increase the mean droplet size. In a stirred system such as the W/O emulsion under study, the mean droplet size may impact the distribution of water, since both gravitational and centrifugal sedimentation are dependent on the droplet size. Hydrate formation starts after approximately 0.2 hour and is followed by a decrease in the measured overall dielectric constant. The crystallization at this temperature is a hydrate phase, not ice, since the salinity depresses the freezing point of the aqueous solution to below - 3.7 °C (estimated with PVTsim (Calsep)). The dielectric constant of hydrates at this frequency (1 GHz) and temperature (≈ 0°C) is much lower than that of water (

%$&'("

≈ 3 vs. )'(& ≈ 87). During

hydrate formation, water is converted into hydrates. Thus, a component with high dielectric constant (water) is converted to a component with low dielectric constant (hydrates). Consequently, the measured dielectric constant drops upon hydrate formation. Correspondingly, the measured dielectric constant increases when cooling is switched off and the hydrates begin to melt. A small increase in the dielectric constant is also observed after approximately 3 hours, when the bath fluid temperature is increased by 1.5 °C. Here, a very clear correlation between measured dielectric constant and temperature is observed, as the shape of the curves is very similar. The observed variations in the measured dielectric constant is not due to variation in the dielectric constant of the pure phases (oil, water and hydrates) with temperature, which only shows minor variations within the experimental temperature range.


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The measured dielectric constant seems to almost level out before the last adjustment in bath fluid temperature. This indicates that hydrate formation has nearly stopped and suggests that equilibrium conditions have been reached. The salinity of the unconverted water increases during hydrate formation, since salt is not incorporated in the hydrate crystal structure. Higher salinity shifts the hydrate equilibrium temperature towards lower temperatures, which eventually causes hydrate formation to stop if the temperature is kept stable. Moreover, hydrate formation will decrease the concentration of CP in the oil phase, which will also contribute to lower the hydrate equilibrium temperature. In addition to the thermodynamic properties limiting hydrate formation, hydrate formation in water-in-oil emulsion can also be mass-transport limited.1 Hydrate formation takes place at the water/oil interface, where both water and hydrate forming gas molecules are present. The hydrates initially form a layer around the water droplets, while further hydrate formation necessitates transport of water and/or hydrate forming molecules through the hydrate layer. However, the clear correlation between measured dielectric constant and temperature following the increment in the cooling fluid temperature after approximately 3 hours suggests that it is the thermodynamic properties of the system that limit hydrate formation. As mentioned above, measuring the permittivity over a broad frequency range may reveal information not obtainable from single frequency permittivity measurements. Figure 8 shows two complex permittivity spectra obtained with Probe A in Experiment 1, and three model spectra calculated using Hanai’s theory. For lower frequencies, the sensitivity of an open-ended coaxial probe decreases with decreasing frequency.15 The measured permittivity spectra therefore become increasingly noisy with decreasing frequency. The blue spectrum was obtained before hydrate formation had started, and the red spectrum was obtained when the measured dielectric constant reached the minimum, approximately 3 hours after startup. The most striking


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difference between the two measured spectra is that both the dielectric constant and the loss factor have decreased significantly during hydrate formation. As discussed above, this is due to the loss of a component with high permittivity (water) when it is converted to a component with low permittivity (hydrates). Two slightly overlapping dielectric dispersions can be observed in both spectra: The Maxwell-Wagner dispersion, caused by interfacial polarization, has dispersion frequency around 550 MHz before hydrate formation and around 1100 MHz after hydrate formation. The dielectric dispersion associated with liquid water (water dispersion) can be observed in the upper frequency range. The dispersion frequency of the water dispersion is slightly above the frequency range under study, and the measured loss factor is therefore still increasing with frequency at 13.6 GHz, which is the upper frequency limit of the VNA. By fitting the solid model spectrum (before hydrate formation) and the dotted model spectrum (after hydrate formation) to the Cole-Cole model,30 it is found that the dispersion frequency of the water dispersion shifts from around 21 GHz to around 28 GHz during hydrate formation. Thus, both the Maxwell-Wagner dispersion and the water dispersion shifts to higher frequencies during hydrate formation. Lower liquid water fraction will cause both dispersions to shift to higher frequencies. However, the relative shift is approximately 3 times larger for the Maxwell-Wagner dispersion as compared to the water dispersion. The dissolved Na+ and Cl- ions are not incorporated in the hydrate crystal structure, and the salinity of the remaining liquid water therefore increases as result of the hydrate formation. Higher salinity causes the DC conductivity of the liquid water to increase, due to the higher concentration of (charged) ions. In W/O emulsions, the Maxwell-Wagner dispersion frequency increases with increasing water DC conductivity, since higher DC conductivity allows faster accumulation of charges on the water droplet interfaces.15,31


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Three model spectra are included in Figure 8. The solid spectrum is fitted to the measured permittivity before hydrate formation, while the dotted spectrum and the dashed spectrum are fitted to the measured permittivity after hydrate formation. Figure 9 illustrates the dielectric mixing models used to obtain the three model spectra. 1.

Solid spectrum: The solid model spectrum is obtained using equation 2. The permittivity

of the water phase is modelled using empirical formulas for NaCl solutions from Peyman et al.24 The dielectric constant of the oil phase (diesel + CP + surfactant) is approximately 2.1, while the loss factor of the oil phase is assumed to be negligible. The volume fraction of the dispersed phase ( in equation 2) was adjusted to 51.7 % to fit the measured spectrum. 2.

Dashed spectrum: In a W/O emulsion, hydrate formation takes place at the water

droplets’ interfaces, where both water and hydrate forming molecules are present. The dashed spectrum is obtained using Hanai’s model for emulsions of shelled spheres,27 assuming the hydrates to form a dense layer/shell around the water droplets. Hence, the porosity of the hydrate shell is assumed to be zero. The permittivity of the water phase changes during hydrate formation, since the salt is not incorporated in the hydrate crystal structure, causing increased NaCl concentration in the remaining liquid water. The dielectric constant of the CP-hydrates is assumed to be 3.15, while the loss factor is assumed to be negligible. Using this model, the hydrate conversion (amount of water by volume converted to hydrates) is adjusted to 15 % to fit the measured spectrum for low frequencies. 3.

Dotted spectrum: The dotted spectrum is also obtained using Hanai’s model for

emulsions of shelled spheres. However, here a shell with finite porosity is assumed, which should be considered to be more realistic than assuming a dense shell.32 The inner part of the


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shell is assumed to be water-continuous, while the outer part of the shell is assumed to be oilcontinuous (see Figure 9). The hydrate fraction in both the inner and the outer part of shell is assumed to be 80 %, while the remaining 20 % is assumed to be either water (inner shell) or oil (outer shell). Using this model, a total hydrate conversion of 27.5 % (27,5 % of the total amount of water converted to hydrates) gives a good fit to the measured spectrum if the volume ratio between the outer and the inner part of the shell is set to 50:50. Clearly, the dotted model spectrum gives the best fit to the measured spectrum obtained after hydrate formation. The dashed model spectrum overestimates the dielectric constant for high frequencies when the modelled hydrate conversion is adjusted to fit the measured spectrum for low frequencies. The dotted spectrum also fits the measured loss factor better than the dashed spectrum. The modelled hydrate conversion is much higher for the dotted spectrum (27.5 %) than the dashed spectrum (15 %). This should be kept in mind whenever using dielectric mixing formulas to quantify hydrate conversion in W/O emulsions. Hanai’s formula for emulsions of shelled spheres has previously been used to model hydrate formation in W/O emulsions,14,16 using the same model as for the dashed spectrum in Figure 8 (assuming dense hydrate shells). Based on the findings above, it seems that assuming dense hydrate shells causes the modelled permittivity for a given hydrate conversion to be too low (the forward problem). Correspondingly, the modelled/estimated hydrate conversion for a given measured spectrum will be too low if a dense layer is assumed (the inverse problem). A more thorough discussion of the models should be carried out elsewhere. But in short, the reason for the large difference in estimated hydrate fraction for the two models is that the hydrates in the water-continuous part of the shell (dashed spectrum) contribute to the effective volume fraction of the dispersed phase that


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has a finite DC conductivity. Thus, volume fraction of the dispersed phase with a finite DC conductivity “looks” larger than it actually is, due to the dispersed hydrate particles. Influence of water and salinity. In Experiment 1-4, the effects of varying the water fraction and the NaCl concentration are studied. Diesel fuel was used as oil phase in these experiments. Figure 10 shows the measured dielectric constant with Probe A (blue data points) and Probe C (red data points) in Experiment 1-4. The melting phase of the experiments is not shown. The initial water fraction (30 % or 50 %) and NaCl concentration (0.1 mol/L or 1.0 mol/L) is given in each plot. The dielectric constant before hydrate formation is higher for the two experiments with higher initial water fraction (Experiment 1 and 2). The reason for this is that the dielectric constant of W/O emulsions increases with increasing water fraction (see Figure 3). The total decrease in the dielectric constant during hydrate formation is also largest for the two experiments with higher initial water fraction. This is due to the non-linear variation of the dielectric constant of W/O emulsions with respect to the water fraction (see Figure 3). As evident in Figure 3, the dielectric constant changes more rapidly for higher water fractions. In addition to the water fraction, the salinity also affects the total decrease in the dielectric constant during hydrate formation. For a given water fraction, increasing the salinity causes a smaller drop in the dielectric constant during hydrate formation. The reason for this is believed to be the higher hydrate equilibrium temperature in the more saline systems. Hence, less hydrate conversion is needed for the system to reach thermodynamic equilibrium for a given experimental temperature. Table 3 presents fitting parameters to Equation 2 (water fraction without hydrates present in the emulsion) and fitting parameters to the porous shell model that was used to obtain the dotted spectrum in Figure 8, at 3 hours (2 hours for Experiment 4). The estimated water fraction deviates slightly from the average water fraction given in Table 2. These deviations are mainly


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due to the uneven distribution of water in the cell, causing the water fraction in front of the probes to deviate from the average water fraction in the cell. The fitting parameters to the porous shell model are hydrate conversion (volume fraction of water converted to hydrates), volume ratio between the outer and the inner part of the shell, and the volume fraction of hydrates in the shell. Higher hydrate conversion is observed for the two experiments with lowest initial salinity (0.1 mol/L in Experiments 2 and 4). This is expected, as the hydrate equilibrium temperature decreases with increasing salinity. However, the estimated hydrate conversion is much higher for Experiment 4 than Experiment 2. The reason for this is believed to be that the average experimental temperature was lower during hydrate formation in Experiment 4 as compared to Experiment 2. The estimated volume ratio between the outer and the inner part of the shell increases with increasing hydrate conversion. For Experiment 4, the estimated volume ratio is as high as 85/15. It could be questioned whether such a high volume ratio is realistic. Hydrate particles formed at the water/oil interface will not necessarily remain on the interface, but may detach from the droplets into the oil phase if the wetting conditions are favorable.33 From the dielectric modelling point of view, assuming an oil-continuous outer hydrate shell or assuming the hydrate particles to detach and disperse into the oil phase will result in similar dielectric model spectra Hydrate agglomeration and deposition. It will now be shown how permittivity measurements with open-ended coaxial probes can be used to monitor hydrate agglomeration and formation of hydrate deposits in W/O emulsions. First, the variations of the measured dielectric constant at single frequency as function of time is studied (Figure 11). Then, it is showed that hydrate agglomeration/deposition may also be detected from a single permittivity spectrum, due to the appearance of a characteristic dielectric dispersion in the measured


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permittivity spectra (Figure 12). To the best of our knowledge, similar findings have not been reported earlier. Figure 11 shows the measured dielectric constant at 1 GHz as function of time for Experiment 1, 4, 7 and 8. Blue, magenta and red data points correspond to Probe A, Probe B and Probe C, respectively. Solid vertical lines correspond to when the cooling was switched off. Dashed vertical lines correspond to small incremental adjustments in the bath fluid temperature. With exception of Experiment 4, the figure shows the measured dielectric constant from shortly before onset of hydrate formation to after the hydrates have melted. Experiment 4 was aborted before switching off the cooling, to investigate whether any hydrate deposits/agglomerates had formed in the cell. This was done by partially emptying the cell for fluid with a syringe to allow visual observations. These observations are discussed in more detail below. The measured dielectric constant generally varies quite smoothly until the cooling is switched off, or until the temperature of the bath fluid is increased. This part of the experiments is characterized by a more or less constant offset in the dielectric constant between the probes. Hence, the measured dielectric constant varies very similar for the three probes. This is referred to as the smooth trend below. In Experiment 1 the smooth trend is maintained through the entire experiment for all probes. A similar behavior was also seen in Experiment 2, 3 and 6 (Experiment 6 is not shown in Figure 11 or Figure 10, but is included as Supporting Information). Diesel fuel was used as oil phase in Experiment 1-3, while crude oil was used in Experiment 6. Common to the experiments where the smooth trend in measured dielectric constant is maintained through the entire experiment is the presence of added surfactant in the oil phase (added during preparation of the emulsions). In Experiment 4, 7 and 8 the measured dielectric constant obtained with Probe A and Probe C shows large deviations from the typical


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smooth trend. The largest and fastest variations are generally observed for Probe A, after cooling is switched off. For Probe C, the deviations from the smooth trend only emerge after cooling is switched off or after the temperature of the cooling bath fluid is adjusted. For Probe A, small but significant deviations from the typical smooth trend can be observed also before cooling is adjusted or switched off. This is most easily observed in Experiment 4, where the dielectric constant measured by Probe A deviates from the typical trend after about 1 hour. As mentioned above, Experiment 4 was aborted before cooling was switched off, and it was found that most hydrates had accumulated in a deposit around the pipe wall. The deposit was relatively soft, and it collapsed and loosened from the pipe wall upon removing the fluid. The deposit most likely consisted of hydrate covered water droplets and hydrate particles, with oil in between. Based on these observations we contend that the deviations in measured dielectric constant from the typical smooth trend observed for Experiment 4, 7 and 8 in Figure 11 are caused by formation of hydrate deposits in front of the probes. This assertion is supported by the fact that the deviations occur or are significantly amplified when the cooling is switched off and when the bath fluid temperature is increased. Hydrate agglomeration in oil-continuous systems is known to be more prominent during melting.29,34,35 Melting renders the surface of the hydrate particles wet, which makes them more sticky, due to easier formation of water/capillary bridges between the particles/droplets. With exception of Experiment 4, the deviations from the typical smooth trend only occur in the experiments where no surfactant was added to the emulsion. Though this crude oil is biodegraded and will contain surface active components, the content is lower than for the diesel experiments with 3 % added surfactant. It is well known that surfactants may prevent or reduce agglomeration of hydrate particles.36


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Whenever the deviations occur, the measured dielectric constant is always higher than the typical smooth trend. The dielectric constant of water, oil and gas hydrates at 1 GHz (the frequency for which the dielectric constant is plotted in Figure 11) is approximately 80, 2 and 3, respectively. Thus, higher measured dielectric constant indicates higher concentration of water, keeping in mind that the dielectric constant of hydrates and oil is very similar compared to the dielectric constant of water. The concentration of water in the deposits is expected to be higher than the average in the cell, due to relatively low concentration of oil in the agglomerates, and since most water probably exist as a core covered by hydrate shells. Thus, agglomeration of hydrates also implies agglomeration of water. The higher concentration of water in the deposits explains why the measured dielectric constant always is higher than the typical smooth trend whenever the deviations from the smooth trend is observed. These results demonstrate that open-ended coaxial probes are useful for monitoring the formation of hydrate deposits as well as hydrate formation in the bulk of oil-continuous emulsions. Above, the time variations of the measured dielectric constant for a single frequency were studied. Hydrate agglomeration and deposition may also be revealed by analyzing the permittivity spectrum form a single measurement without relying on studying variations in the permittivity versus time. Figure 12 shows four complex permittivity spectra obtained with Probe A in Experiment 7. In Figure 11, it is indicated when the spectra were obtained. The blue spectrum (no. 1) was obtained before hydrate formation started. The red spectrum (no. 2) was obtained during hydrate formation, but before the measured dielectric constant started to deviate from the smooth trend. Hence, no hydrate deposit is assumed present on the probe at this stage. The magenta spectrum (no. 3) was obtained shortly after the deviations from the smooth trend had started. For this spectrum, a hydrate deposit is assumed to have formed on the probe. The


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cyan spectrum (no. 4) was obtained early in the melting phase. Before hydrate formation (blue spectrum), the measured spectrum is relatively flat due to the low water fraction (30 %). The Maxwell-Wagner dispersion, occurring around 100 MHz, and the water dispersion, occurring around 20 GHz, are therefore partly masked by the measurement uncertainty. However, after the hydrates have started to form (red spectrum) an additional dielectric dispersion that partly overlaps the Maxwell-Wagner dispersion is easily observed at lower frequencies. This dispersion is referred to as the low-frequency dispersion (LF dispersion) in the following. The dispersion strength of the LF dispersion increases at the point when the hydrates are assumed to start to form deposit on the probe (cyan spectrum). During melting (magenta spectrum), the dispersion strength of the LF dispersion increases even further. Similar observations were made in all experiments with crude oil where no surfactant was added to the crude oil phase during preparation of the emulsions (Experiment 5, 7, 8 and 9). Permittivity spectra from Experiment 5, 8 and 9, where the LF dispersion can be observed, are available as Supporting Information. Please note that this includes the experiment where no CP was added to the crude oil (Experiment 9). This experiment was conducted to compare hydrate formation with ice formation. The LF dispersion was also observed in Experiment 4, where diesel fuel with added surfactant was used as oil phase. However, in this experiment the LF dispersion was only observed during the parts of the experiment where hydrates are believed to deposit on the probe. Thus, the LF dispersion is observed whenever deposits seem to be forming in front of the probes, but it is observed during hydrate formation in general in the experiments with crude oil where no surfactant was added to the oil phase. Thus, we contend that the LF dispersion is caused by hydrate agglomeration in the bulk of the emulsion and by formation of hydrate deposits on the probe.


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The emergence of an additional dielectric dispersion (the LF dispersion) in the measured spectra can only be explained by the emergence of an additional dielectric polarization mechanism. Since the LF dispersion is not observed in all hydrate experiments, and since it is observed in the ice experiment (Experiment 9), the LF dispersion cannot be related to the dielectric dispersion of pure CP hydrates (see black permittivity spectra in Figure 2). It is therefore likely that the LF dispersion is caused by some kind of interfacial polarization. As mentioned above, interfacial polarization is caused by accumulation of free ionic charges on interfaces between phases with different DC conductivity. Accumulation of ionic charges on the water droplet interfaces is responsible for the Maxwell-Wagner dispersion. A main mechanism for hydrate agglomeration in W/O emulsions is believed to be the formation of (water) capillary bridges between the particles/droplets.36 If capillary bridges are established, the capillary forces holding the particles/droplets together might exceed the shear forces drawing them apart. The degree of agglomeration therefore typically increases during melting, due to the wetter surface of the hydrate particles. In a cluster consisting of agglomerated hydrate particles and hydrate covered droplets that are bound together by capillary bridges, ionic charges may move not only within single water droplets (Maxwell-Wagner dispersion), but also between the particles/droplets through the capillary bridges. Thus, ionic charges may accumulate both on the interface of single water droplets inside the cluster, and they may accumulate on the interface of the clusters themselves. Agglomeration of hydrate particles and hydrate-covered droplets caused by formation of water bridges should therefore be expected to produce an additional dielectric polarization mechanism and hence cause an additional dielectric dispersion to appear in the measured spectra. We contend that the LF dispersion that is observed in the reported experiments is caused by this effect. The strength of a dielectric dispersion in mixed materials increases with


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increasing volume fraction of the phase of interest. Thus, the dispersion strength of the LF dispersion is expected to increase with increasing degree of agglomeration. This corresponds well with the fact that the LF dispersion first increases in strength when the hydrates seem to form a deposit on the probe, and then increases even further when the hydrates begin to melt. It is well known from colloid science that agglomeration of droplets in W/O microemulsions may lead to an additional dielectric dispersion caused by movement of ionic charges within the clusters.37 This phenomenon is referred to as cluster polarization and has been studied in particular by Feldman and co-workers.37-39 Although studying a different system, their results resemble those presented in this work in that agglomeration/cluster formation in a W/O emulsion/microemulsion causes the appearance of a new dielectric dispersion with lower dispersion frequency than the Maxwell-Wagner dispersion. CONCLUSION This paper has demonstrated how broad-band permittivity measurements can be used to monitor hydrate formation and hydrate agglomeration and deposition in oil-continuous emulsions. Valuable information can be obtained both by studying how the measured dielectric constant varies as function of time, and by analyzing single permittivity spectra. The permittivity sensors applied in this work, open-ended coaxial probes, can be installed non-intrusively in pipes, and they are able to withstand high pressures and harsh chemical environments. Thus, these sensors are suitable for realistic hydrate flow assurance studies. ACKNOWLEDGMENTS


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The Norwegian Deepwater Programme is acknowledged for financing the permittivity sensors used in the experiments. The Ph.D. position of Kjetil Haukalid was financed by Statoil through the Akademia agreement with the University of Bergen. SUPPORTING INFORMATION Measured dielectric constant at 1 GHz for Experiment 6. Permittivity spectra from Experiment 5, 8 and 9. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Present Addresses # Christian Michelsen Research AS, P.O. Box 6031, NO-5892 Bergen, Norway REFERENCES (1) Sloan, E. D.; Koh, C. A. Clathrate hydrates of natural gases, 3rd ed.; CRC Press (Taylor and Francis Group): Boca Raton, FL, 2007. (2) Borgund, A. E.; Høiland, S.; Barth, T.; Fotland, P.; Askvik, K. M. Appl. Geochem. 2009, 24, 777-786. (3) Sloan, E. D. Fluid Phase Equilib. 2005, 228-229, 67-74. (4) Kinnari, K.; Hundseid, J.; Li, X.; Askvik, K. M. J. Chem. Eng. Data. 2014, 60, 437-446. (5) Zerpa, L. E.; Sloan, E. D.; Sum, A. K.; Koh, C. A. J. Pet. Sci. Eng. 2012, 98-99, 122-129. (6) Fadnes, F. H. Fluid Phase Equilib. 1996, 117, 186-192.


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(7) Høiland, S.; Askvik, K. M.; Fotland, P.; Alagic, E.; Barth, T.; Fadnes, F. J. Colloid Interface Sci. 2005, 287, 217-225. (8) Hemmingsen, P. V.; Li, X.; Peytavy, J.; Sjöblom, J. J. Dispersion Sci. Technol. 2007, 28, 371-382. (9) Daraboina, N.; Pachitsas, S.; von Solms, N. Fuel. 2015, 148, 186-190. (10) Brown, E. P.; Koh, C. A. Energy Fuels 2016, 30, 8065-8071. (11) Kelland, M. A. Energy Fuels 2006, 20, 825-847. (12) Lachance, J. W.; Talley, L. D.; Shatto, D. P.; Turner, D. J.; Eaton, M. W. Energy Fuels 2012, 26, 4059-4066. (13) Lingelem, M. N.; Majeed, A. I.; Stange, E. Ann. N. Y. Acad. Sci. 1994, 715, 75-93. (14) Jakobsen, T.; Sjöblom, J.; Ruoff, P. Colloids Surf., A. 1996, 112, 73-84. (15) Jakobsen, T.; Folgerø, K. Meas. Sci. Technol. 1997, 8, 1006-1015. (16) Haukalid, K.; Askvik, K. M.; Folgerø, K.; Thomas, P. J. Energy Fuels 2015, 29, 43-51. (17) Haukalid, K.; Folgerø, K. Energy Fuels 2016, 30, 7196-7205. (18) Feldman, Y.; Skodvin, T.; Sjöblom, J. Dielectric Spectroscopy on Emulsion and Related Colloidal Systems - A Review. In Encyclopedic Handbook of Emulsion Technology. Sjöblom, J., Ed.; CRC Press: New York, NY, 2001; 109-168. (19) Gabriel, C.; Gabriel, S.; Corthout, E. Phys. Med. Biol. 1996, 41, 2231-2249.


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(20) Robinson, D. A.; Jones, S. B.; Wraith, J. M.; Or, D.; Friedman, S. P. Vadose Zone J. 2003, 2, 444-475. (21) Sihvola, A. Electromagnetic mixing formulas and applications, Electromagnetic Wave Series; The Institution of Engineering and Technology: London, United Kingdom, 1999; 47. (22) Hanai, T. Kolloid-Z. 1960, 171, 23-31. (23) Bruggeman, D. A. G. Ann. Phys. (Berlin, Ger.). 1935, 416, 636-664. (24) Peyman, A.; Gabriel, C.; Grant, E. H. Bioelectromagnetics (Hoboken, NJ, U. S.). 2007, 28, 264-274. (25) Maxwell, J. C. A Treatise on Electricity and Magnetism, Clarendon Press: Oxford, 1881. (26) Wagner, K. W. Electrical Engineering (Archiv fur Elektrotechnik). 1914, 2, 371-387. (27) Hanai, T.; Asami, K.; Koizumi, N. Bull. Inst. Chem. Res., Kyoto Univ. 1979, 57, 297-305. (28) Folgerø, K. Meas. Sci. Technol. 1996, 7, 1260-1269. (29) Lachance, J. W.; Sloan, E. D.; Koh, C. A. Chem. Eng. Sci. 2008, 63, 3942-3947. (30) Cole, K. S.; Cole, R. H. J. Chem. Phys. 1941, 9, 341-351. (31) Haukalid, K.; Folgerø, K. Measurements of water conductivity in oil continuous emulsions. In Proceedings of the 10th International Conference on Electromagnetic Wave Interaction with Water and Moist Substances, MFPA Weimar, Germany, Sept. 25−27, 2013; Kupfer, K., Wagner, N., Eds.; Weimar, Germany: 2013; pp 86−93.


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(32) Haber, A.; Akhfash, M.; Loh, C. K.; Aman, Z. M.; Fridjonsson, E. O.; May, E. F.; Johns, M. L. Langmuir. 2015, 31, 8786-8794. (33) Fotland, P.; Askvik, K. M. J. Colloid Interface Sci. 2008, 321, 130-141. (34) Boxall, J. A.; Greaves, D. P.; Mulligan, J.; Koh, C. A.; Sloan, E. D. Gas Hydrate Formation and Dissociation from Water-in-Oil Emulsions Studied Using PVM and FBRM Particle Size Aanalysis. Proceedings of the 6th International Conference on Gas Hydrates, Vancouver, Canada, July 6-20, 2008. (35) Maeda, N. Energies. 2015, 8, 5361-5369. (36) Zerpa, L. E.; Salager, J. L.; Koh, C. A.; Sloan, E. D.; Sum, A. K. Ind. Eng. Chem. Res. 2011, 50, 188-197. (37) Feldman, Y.; Kozlovich, N.; Nir, I.; Garti, N. Phys. Rev. E. 1995, 51, 478-491. (38) Feldman, Y.; Kozlovich, N.; Alexandrov, Y.; Nigmatullin, R.; Ryabov, Y. Phys. Rev. E. 1996, 54, 5420-5427. (39) Alexandrov, Y.; Kozlovich, N.; Feldman, Y.; Texter, J. J. Chem. Phys. 1999, 111, 70237028. (40) Sum, A. K.; Koh, C. A.; Sloan, E. D. Ind. Eng. Chem. Res. 2009, 48, 7457-7465.


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Figure 1. Conceptual picture of hydrate plug formation in oil-dominated systems. Redrawn from Sum et al.40

Figure 2. Complex permittivity spectra of hydrates, ice, water, oil and gas. The loss factor is not shown for oil and gas as it is negligible compared to the scale. The dispersion frequency of


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hydrates varies considerably with type of guest molecule. This is indicated by plotting several spectra for hydrates.

Figure 3. Dielectric constant of W/O emulsion at 1 GHz as function of water fraction as given by equation (2). The dielectric constant of the oil phase is set to 2, while the permittivity of the water phase is given using empirical formulas for NaCl-solutions from Peyman et al.24 The NaCl concentration and the temperature of the water phase are set to 0.1 mol/L and 20 °C, respectively.


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Figure 4. Model spectrum of W/O emulsion with water fraction 50 % as given by equation 2. The dielectric constant is plotted with a solid line, and the loss factor with a dashed line. Empirical formulas for NaCl solutions in Peyman et al.24 are used to model the complex permittivity of the water phase. The NaCl concentration and the temperature of the water phase are set to 0.1 mol/L and to 20 °C, respectively. The dielectric constant and the loss factor of the oil phase are set to 2 and 0, respectively.

Figure 5. Sketch of the measuring cell.

Figure 6. The three open-ended coaxial probes used in the experiments.


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Figure 7. Measured dielectric constant at 1 GHz and measured temperature through Experiment 1. Blue, magenta, red and black data points correspond to Probe A, Probe B, Probe C and temperature, respectively. The solid vertical line corresponds to when the cooling was switched off. The dashed vertical lines correspond to changes in bath fluid temperature, whose magnitudes are shown above the plot.


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Figure 8. Two complex permittivity spectra obtained with Probe A during Experiment 1. The blue spectrum was obtained before hydrate formation, while the red spectrum was obtained when the measured dielectric constant reached the minimum, approximately 3 hours after startup (with reference to Figure 7). Three model spectra (solid, dotted and dashed) are included in the figure. The solid spectrum is fitted to the measured permittivity before hydrate formation, while the dotted and the dashed spectra are fitted to the measured permittivity after hydrate formation.


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Figure 9. Illustration of the three dielectric mixing models used to obtain the three model spectra in Figure 8.


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Figure 10. Measured dielectric constant at 1 GHz in Experiment 1-4 (diesel as the oil phase) for Probe A (blue data points) and Probe C (red data points). The melting phase of the experiments is not shown. The water fraction (φ) and the NaCl concentration (c) for the respective experiments are showed in the text boxes. The discontinuity in Experiment 3 is due to a new calibration of the VNA, as it was discovered that the calibration prior to the experiment had been somewhat imprecise.


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Figure 11. Measured dielectric constant at 1 GHz for Experiment 1, 4, 7 and 8. Blue, red and magenta data points correspond to Probe A, Probe B and Probe C, respectively. Vertical solid lines correspond to when cooling was switched off. Vertical dashed lines correspond to small increments in bath fluid temperature. The four arrows in the lower left plot (Experiment 7) correspond to the four permittivity spectra that are plotted in Figure 12.


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Figure 12. Complex permittivity spectra obtained with Probe A in Experiment 7. The blue spectrum (no. 1) was obtained before hydrate formation started. The red spectrum (no. 2) was obtained during hydrate formation, but before the measured dielectric constant started to deviate from the smooth trend. The magenta spectrum (no. 3) was obtained shortly after the deviations from the smooth trend had started. The cyan spectrum (no. 4) was obtained during melting. Table 1. Key properties of diesel fuel and crude oil used in the experiments. Diesel Crude oil


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Density [g/cm3]

0.831

0.905

Viscosity [mPa*s]

3

36

Interfacial tension 63 [mN/m at pH = 6]

20.5

Table 2. Selection of fluids in the reported experiments. Oil phase

Water fraction

Surfactant Water phase

Experiment 1

Diesel fuel + CP

Yes

NaCl solution (c = 1.0 mol/L)

50 %

Experiment 2

Diesel fuel + CP

Yes


50 %

Experiment 3

Diesel fuel + CP

Yes


30 %

Experiment 4

Diesel fuel + CP

Yes


30 %

Experiment 5

Crude oil + CP

No


50 %

Experiment 6

Crude oil + CP

Yes

Process water

50 %

Experiment 7

Crude oil + CP

No

Process water

30 %

Experiment 8

Crude oil + CP

No


30 %

Experiment 9

Crude oil

No


30 %

Table 3. Fitted parameters to Equation 2 (water fraction without hydrates present in the emulsion) and fitting parameters to the porous shell model. Water fraction Hydrate Volume ratio outer Hydrate fraction without hydrates conversion shell vs. inner shell in shell Experiment 1

51.7 %

27.5 %

50/50

80 %

Experiment 2

50.5 %

47.0 %

70/30

80 %

Experiment 3

34.0 %

34.0 %

55/45

80 %


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Experiment 4

33.5 %

75.0 %

85/15

80 %


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Hydrate Formation in Water-in-Crude Oil Emulsions Studied by Broad

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