Calorimetric and Rheological Studies on Cyclopentane Hydrate

Oct 20, 2014 - ... City College of City University of New York, New York, New York 10031, United States ... Microdifferential scanning calorimetry dat...
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Calorimetric and Rheological Studies on Cyclopentane HydrateForming Water-in-Kerosene Emulsions Amit Ahuja, Genti Zylyftari, and Jeffrey F. Morris* Benjamin Levich Institute and Department of Chemical Engineering, City College of City University of New York, New York, New York 10031, United States ABSTRACT: The effect of salt, a thermodynamic inhibitor of hydrate, on a density-matched cyclopentane hydrate-forming waterin-kerosene emulsion with a fixed aqueous phase mass fraction of 0.4 is presented, based on studies by microdifferential scanning calorimetry (μDSC) and rheometry. Kerosene is a candidate material for flow loop studies. Microdifferential scanning calorimetry data are presented on the equilibrium temperature (liquidus line); water-to-hydrate conversions are computed using the liquidus line. Mechanical properties obtained using a stress controlled rheometer are correlated to thermodynamic properties. Effects of subcooling, salt concentration, and shear rate dependence are studied and presented along with oscillatory rheometric and yield stress measurements. Critical time is defined as the onset of a viscosity jump, and the viscosity evolution time is the time from the initial jump to 90 % attainment of the final viscosity; both times are shortened by higher subcooling. The final viscosity, storage modulus and yield stress achieve a peak between 0.85 to 0.95 (mass fraction) water-to-hydrate conversion indicating a mechanical influence of capillary bridge formation. The hydrate slurry exhibits a shear thinning behavior when cycled up and down in shear rate, showing negligible hysteresis in the rate dependence.

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INTRODUCTION The undesirable formation of gas hydrates in gas and oil subsea pipelines results in blockage, emergency shutdown, and economic losses. Hydrate formation and evolution is a rapid process, and the onset is stochastic. To achieve maximum throughput in pipelines, or flow assurance, avoidance of hydrate formation or mitigation of its undesirable effects is a critical issue in petroleum production. Gas hydrates are crystalline compounds formed by the hydrogen-bonded water molecules in cages that are stabilized by encapsulating a small guest molecule, such as methane, ethane, or propane.1 Hydrates form in the presence of appropriate quantities of gas and water molecules, typically under the conditions of high pressures and low temperatures. It is useful to have a reliable method for the prevention and handling of hydrate slurries in pipelines, and particularly for the prediction of start-up flow following pipeline shutdown. To develop such methodology necessitates a thorough understanding of the rheological behavior of water-in-oil emulsions under hydrate-forming conditions. Owing to the practical difficulties involved in obtaining the flow properties of highpressure systems, results of only limited work have been published on the rheology of hydrate slurry. We note some studies on flow characterization of hydrate slurries in dedicated, custom-made flow loop setups. Peng et al.2 studied the flow characteristics of hydrate slurries formed from natural gas, diesel oil, and water in the presence of an antiagglomerant. They found that hydrate slurries obtained © XXXX American Chemical Society

with a water fraction as high as 30 % by volume can safely and successfully flow without plugging. The hydrate slurries were found to be shear-thinning and pseudoplastic in nature. Using a flow loop reactor working on a gas-lift principle, Fidel-Dufour et al.3 studied the rheology of methane hydrate slurries obtained from a water-in-dodecane emulsion with an antiagglomerant. They assumed the agglomeration between hydrate particles and water drops to be irreversible, modeled it using the population balance approach, and reported that hydrate aggregates are porous in nature with a fractal dimension of 1.8. Andersson and Gudmundsson4 performed flow loop tests along with a tube viscometer to characterize hydrate-inwater slurry. The hydrate slurries flowed through straight pipe sections in laminar and turbulent conditions, and flow rate and pressure drops were recorded. The apparent viscosities of the slurries were found to be increasing with increasing hydrate concentrations. Delahaye et al.5 studied the rheology of CO2 hydrate slurry; this study was not directed toward flow assurance but instead toward the application of hydrate slurries in refrigeration. Joshi et al.6 used a flow loop set up to study the methane hydrate slurries in a high water fraction system. The Special Issue: In Honor of E. Dendy Sloan on the Occasion of His 70th Birthday Received: July 2, 2014 Accepted: October 7, 2014

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properties of oil-field emulsions. There are only a few reports on the rheological properties of hydrate slurries formed in a liquid hydrocarbon phase. Owing to its excellent cold flow properties and low viscosity, here we chose to work with kerosene, a clear liquid obtained from a fractional distillation of crude oil, as our organic carrier phase. Kerosene is immiscible with water but is miscible with cyclopentane. As a distillate product which is clear, it is a candidate for large-scale flow loop studies, and thus studying hydrate formation in kerosene continuous phase emulsions is of value to provide a foundation for such studies. The presence of salt in the aqueous phase during hydrate formation is another important factor which will be studied to determine the influence of the variable conversion level of water-to-hydrate upon the mechanical properties. To understand the role of the conversion of water-to-hydrate on the rheological properties, we have studied neutrally buoyant emulsions of water in an organic continuous phase containing kerosene and cyclopentane. By developing a hydrate−brine phase diagram based on calorimetry, the thermodynamic conversion of water-to-hydrate (going from emulsion drops to suspended solids) and equilibrium temperature data were related to the rheological response. In particular, effects of varying subcooling, salt concentration, and shear rate on the viscosity were examined, along with oscillatory rheometric and yield stress measurements on a density-matched emulsion with aqueous phase mass fraction of 0.4.

pressure drop across the pump was found to increase abruptly, which serves as an indication for onset of hydrate formation, when a certain amount of gas hydrate (ϕtransition) forms in the line. ϕtransition was found to be an increasing function of mixture velocity and was found to be independent of liquid loading and the presence of salt in the aqueous phase. A correlation relating ϕtransition and mixture velocity is proposed along with a mechanism which discusses a transition from an initial homogeneous suspension of dispersed hydrate particles to a heterogeneous suspension due to increased particle−particle interactions and subsequent agglomeration and finally resulting in a hydrate bed and deposition on the pipe wall. We also briefly note certain studies which used standard rheometers on hydrate slurries. Webb et al.7 studied the rheological properties of methane gas hydrate slurries obtained from water-in-crude oil emulsions. Methane gas hydrate slurries were obtained from these emulsions at 0 °C and 13.9 MPa initial pressure. Rensing et al.8 studied the rheology of ice slurries formed from water-in-oil emulsions with average droplet size of 1.5 μm, claiming this to be a model equivalent system for hydrate slurries. Viscosity and yield stress of ice slurries were measured at different mass fractions of pure water and brine by quenching the emulsion to −10 °C. Recently, Webb et al.9 investigated the rheological properties of methane hydrate slurries obtained from water-in-oil microemulsions of water, dodecane, and dioctyl sodium sulfosuccinate (AOT) surfactant with droplet size varying from (22 to 48) nm for water mass fractions ranging from (0.066 to 0.36). Hydrate slurry final viscosity and yield stress were found to be increasing functions of initial water fraction and initial pressure while they were decreasing functions of temperature and slurry formation shear rate. Webb et al.10 used water-in-mineral oil emulsions with typical droplet size of 2 μm using span 80 and AOT surfactants and methane gas as a hydrate former in a highpressure rheometer to study the rheological properties of methane hydrate slurries obtained from water mass fractions ranging from (0 to 0.44) at temperatures from (0 to 6) °C and initial pressures from (5.3 to 10.4) MPa. Camargo et al.11 characterized a gas hydrate suspension obtained in asphaltenic crude oils using a high-pressure cell. Cyclopentane hydrate provides an option for the study of hydrates at atmospheric pressure, and Zylyftari et al.12 studied the effect of salinity on cyclopentane hydrate forming emulsion with aqueous phase mass fraction of 0.4 using microdifferential scanning calorimetry and rheometry. One of the important highlights of this study was that the maximum viscosity is observed at an intermediate water-to-hydrate conversion (Xw) while the maximum yield stress is obtained at Xw = 0.8 rather than at Xw = 1, where Xw is the mass fraction of theoretical water-to-hydrate conversion based on the total initial mass of water. This trend was suggested to be due to the presence of capillary bridges formed by unconverted water between the hydrate particles. Here, we investigate cyclopentane hydrate, which as noted forms at atmospheric pressure at sufficiently low temperature, providing greater convenience in the experiments.13 As a model system, cyclopentane offers the advantageous features of forming a structure II hydrate which is frequently observed in petroleum fields, and it is immiscible with water. The immiscibility introduces the mass transfer limitations commonly observed in gas hydrate emulsion systems (where the gas forming the hydrate is dissolved in crude oil), making cyclopentane an appropriate model material for investigating

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MATERIALS AND METHODS The dispersed aqueous phase consisted of deionized water from a Millipore QTM system, with dissolved sodium chloride (purity of 0.99 mass fraction, Fisher Scientific). The continuous oil phase was formed by mixing kerosene (from University of Tulsa, OK), Halocarbon 27 (polychlorotrifluoroethylene polymer, Halocarbon Products Corporation), and cyclopentane (purity of 0.99 mass fraction, Fisher Scientific). Kerosene is a complex mixture of branched and straight-chain compounds and consists of paraffins, naphthenes, and aromatics in the mass fractions of 0.55, 0.41, and 0.04, respectively. Halocarbon 27, of density approximately 1900 kg·m−3 at 25 °C, is used as a fraction of the organic phase to densify it and allow matching of the density of the aqueous phase, thereby minimizing separation of the phases by settling of the water drops. A nonionic and oil soluble surfactant, [2-(3,4-dihydroxyoxolan-2yl)-2-hydroxyethyl]octadec-9-enoate (Span 80; Sigma-Aldrich) was used. All the materials were used as obtained without further purification (Table 1). Physical properties of the materials used here are given in Table 2. To determine the equilibrium temperature and dissociation heat of cyclopentane hydrate, a microdifferential scanning calorimeter (μDSC VII; Setaram) was used. The μDSC records Table 1. Specifications of Chemical Samples Used in This Study chemical name

source

sodium chloride cyclopentane kerosene Halocarbon 27

Fisher Scientific Fisher Scientific University of Tulsa, OK Halocarbon Products Corporation Sigma-Aldrich

Span 80 B

initial mass fraction purity

purification method

0.99 0.99 not available not available

none none none none

not available

none

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experimental temperature. To avoid long and unpredictable induction time involved in hydrate nucleation,13 the emulsion is seeded with a few externally prepared cyclopentane hydrate seed crystals of roughly 1 mm diameter as soon as shearing is started.15

Table 2. Density (ρ), Viscosity (η), and Molecular Weight (MW) of the Emulsion Components Used in This Study materials

ρ/kg·m−3

η/Pa·s

MW

kerosene Halocarbon 27 cyclopentane Span 80

800 1900 750 986

0.00164 (27 °C) 0.1 (25 °C) 0.000419 (25 °C) 1.2−2.0 (20 °C)

70.1 428.6

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RESULTS AND DISCUSSION Calorimetric Data. The methods used to determine the equilibrium temperatures and percentage water converted are adopted from Zylyftari et al.12 A typical temperature protocol in μDSC experiments involves quenching segregated aqueous and oil phases without any surfactant to −40 °C to form ice and then raising the temperature above the equilibrium temperature of ice. At this point where the ice is melted, the temperature is held constant for 1 h, which allows hydrate formation to proceed. To determine the hydrate dissociation temperature, the temperature is then slowly increased at a rate of 0.2 °C/ min. Table 3 shows the equilibrium temperature (Teq) data

the heat flux required to heat the sample compared to the reference at the same scan rate. The heat flux resolution is 0.02 μW. A more detailed setup of the apparatus is described by Zylyftari et al. and Karanjkar et al.12,14 In μDSC experiments, oil phases containing Xcp = 0.277 and 0.375 (mass fractions) cyclopentane, with the remaining fractions being a mix of kerosene and halocarbon 27, were investigated. Rheometric data obtained using a stress-controlled rheometer (AR 2000ex, TA Instruments) equipped with concentric cylindrical Couette geometry are reported. The outer cylinder of the Couette fixture has a 15 mm radius, the inner rotor has a 14 mm radius, and thus the geometry has a 1 mm gap. The rotor has a height of 42 mm and has a conical bottom. For yield stress measurements, we used a vane geometry, which includes a four equally spaced blade rotor of the same dimensions as the cylindrical rotor of Couette geometry and the same outer cylindrical cup with its inner walls roughened. To eliminate the possibility of wall slip effects, a piece of waterproof sandpaper with the rms value of the roughness O(100) μm and adhesive backing is glued on the inner wall of the cylindrical cup. This reduces the radius of the cup to 14.8 mm so that the effective Couette gap is slightly less than the original 1 mm. The measured data are gap-corrected. As the roughness of sandpaper is O(100) μm while the droplet size is O(10) μm, this roughness level is found to eliminate wall slip. The ratio of Couette gap to droplet/particle size is approximately 80, which is well above the recommended gap-to-particle size ratio of 10. The Couette geometry seats in a Peltier jacket, which is mounted to the rheometer. The Peltier jacket has a temperature range from (−20 to 150) °C, and ± 0.1 °C of temperature uncertainty. In the rheometric experiments, the oil phase of emulsion contains a 0.375 mass fraction of cyclopentane and the remainder is kerosene and halocarbon 27. The oil mixture with 4.95 × 10−3 (mass fraction, based on oil) of Span 80 was prepared first. We found that, unlike emulsions in mineral oil where 4.95 × 10−4 to 9.9 × 10−4 mass fractions of Span 80 yielded a stable emulsion,12−15 this higher surfactant loading was needed for a stable emulsion with kerosene. A 50 mL sample was prepared each time by mixing water and oil using the IKA T25 Digital Ultra-Turrax at an intensity of 7000 rpm for a duration of 5 min. Emulsions were found to be stable against coalescence for 24 h under quiescent conditions. The droplet size was estimated based on optical micrographs. A freshly prepared sample, with 80 % dilution of 0.4 mass fraction w/o emulsion into continuous phase, is transferred into a rectangular capillary (0.1 mm × 1 mm) placed over a glass slide for microscopy. The mean droplet size at t = 0 and t = 24 h was (5 ± 2.5) μm and (5.4 ± 1.2) μm, respectively. To estimate the mean droplet size, 800 droplets were counted for each condition. The sample volume used in an experiment was 19.6 mL for Couette geometry and 28 mL for vane geometry. The emulsion prepared at room temperature was gently transferred to the cylindrical cup where the temperature was previously set to the desired lower

Table 3. Hydrate Liquidus Data for the Density-Matched Kerosene Emulsion Oil Phase (Kerosene, Cyclopentane and Halocarbon 27 (KRS+CP+HLC))a Xcp

Xs−in

Teq/°C

XW

0.375

0.0 0.035 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.23 0.0 0.035 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.23

5.1 3.8 3.0 1.0 −0.7 −2.6 −4.9 −7.7 −9.9 −11.9 4.1 3.0 1.4 −0.2 −2.0 −3.6 −5.6 −8.4 −11.0 −13.2

0.026 0.017 0.014 0.012 0.009 0.016 0.006 0.004 0.008 0.001 0.014 0.004 0.013 0.005 0.01 0.005 0.009 0.004 0.003 0.001

0.277

a

Xcp is the cyclopentane concentration (mass fraction) in the oil phase, Xs−in is the initial salt concentration (mass fraction) in the aqueous phase, Teq is the equilibrium temperature, and Xw is the water-tohydrate conversion.

representing an experimental determination of liquidus line for the hydrate−brine system. In Figure 1, the experimental liquidus temperatures for varying salt concentrations are plotted. As conversion of water-to-hydrate is minimal in these segregated bulk phases because of the availability of only a small interfacial area between the aqueous and oil phases, it allows us to determine thermodynamic properties accurately. The μDSC experiments are designed such that we avoid reaching a condition where hydrate formation will be limited by water or cyclopentane due to large or full conversion. When the interface is covered with hydrate, the reaction shuts down with little further hydrate formation (due to slow mass transfer through solid) and thus a low water-to-hydrate conversion. As shown in Table 3, the maximum water-to-hydrate conversion C

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cyclopentane concentration in the oil phase is then obtained using Xw =

⎛ X w − 37 + X w − 50 ⎞ ⎛ + X w − 50 ⎞ X ⎜ ⎟X ⎟X + ⎜1 − w − 37 ⎝ ⎠ w − 37 ⎝ ⎠ w − 50 2 2 (2)

where Xw−37 and Xw−50 are the conversions of water estimated at cyclopentane mass fractions of Xcp = 0.277 and 0.375 (equivalent to 37 % and 50 % by volume) in the oil phase, respectively. Rheometric Measurements. Figure 2 shows time evolution of viscosity for a w/o emulsion with 0.4 mass

Figure 1. Cyclopentane hydrate liquidus curves for Xcp = 0.277 and 0.375 (mass fractions) cyclopentane concentrations for the densitymatched kerosene emulsion oil phase (kerosene, cyclopentane, and Halocarbon 27 (KRS + CP + HLC)): ■, Xcp = 0.277; ●, Xcp = 0.375.

obtained is only Xw = 0.026: for this small conversion level, the composition changes in salt and cyclopentane concentrations are assumed to be negligible. With an increase in salt concentration from 0 to 0.23 mass fraction for Xcp = 0.375 mass fraction of cyclopentane in the oil phase, the hydrate equilibrium temperature shifts from (5.1 to −11.9) °C, while the ice equilibrium temperature shifts from (0 to −21.1) °C.16 As the concentration of cyclopentane in the oil phase is lowered to 0.277 mass fraction, the hydrate equilibrium temperature shifts to lower values. The theoretical water-to-hydrate conversion levels for the specific conditions studied in the rheology section are shown in Table 4. These conversions are computed using the data in

Figure 2. Evolution of viscosity (η) for w/o cyclopentane hydrateforming emulsions with 0.4 mass fraction of aqueous phase and with Xs−in = 0.035 at γ̇ = 100 s−1 and at three different temperatures: ■, T = −5 °C; red ●, T = −7 °C; blue ▲, T = −10 °C.

fraction of an aqueous phase with a fixed initial salt concentration Xs−in = 0.035 at γ̇ = 100 s−1 and varying temperatures. The final viscosity (ηf) of hydrate slurry formed at γ̇ = 100 s−1 is plotted as a function of the theoretical waterto-hydrate conversion at T = −7 °C in Figure 3. The points in Figure 3 from left to right correspond, respectively, to initial salt concentration (mass fraction) of Xs−in = 0.1, 0.07, 0.05, 0.035, 0.015, 0.0075, 0. As the conversion level (Xw) increases, the final slurry viscosity (ηf) attains a maximum among the sampled conditions at Xw = 0.92. The final viscosity at Xw = 1.0 is

Table 4. Thermodynamic Conversion of Water-to-Hydrate in Emulsion T/°C

Xs−in

Xw

−7

0.0 0.0075 0.015 0.027 0.035 0.05 0.07 0.1 0.125 0.035 0.035 0.035

1.0 0.96 0.92 0.85 0.81 0.72 0.605 0.42 0.26 0.77 0.81 0.84

−5 −7 −10

Table 3 and equations derived in Zylyftari et al.12 and rewritten below. The theoretical water-to-hydrate conversion at a given temperature (T) is computed using X w (T ) =

Xs ‐ brine(T ) − Xs ‐ in Xs ‐ brine(T )(1 − Xs ‐ in)

(1) Figure 3. Final viscosity (ηf) of cyclopentane hydrate-forming densitymatched kerosene-based emulsion at T = −7 °C and γ̇ = 100 s−1 plotted as a function of theoretical water-to-hydrate conversion (Xw, mass fractions). The points from left to right correspond to initial salt concentration (mass fractions) of Xs−in = 0.1, 0.07, 0.05, 0.035, 0.015, 0.0075, 0.

where Xs‑brine is the fraction of salt in the remaining brine at equilibrium which is obtained from the liquidus line and Xs‑in is the initial salt concentration (mass fraction, based on total aqueous phase). The fraction of water-to-hydrate conversion weighted between the absolute upper and lower limits of D

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Figure 5 shows the effect of subjecting the final hydrate slurry, obtained for a w/o emulsion with 0.4 mass fraction of aqueous

considerably lower than that at Xw = 0.92. In our previous study, Zylyftari et al.12 studied the behavior of rheological properties as a function of thermodynamic water-to-hydrate conversion. The authors observed that the maximum viscosity is obtained at 0.61−0.85 water-to-hydrate conversion; based on their experimental data, they found it reasonable to neglect the role of contact-induced and shear-induced agglomeration, and advocated the presence and impact of capillary bridging in their system. The results presented here, with a viscosity maximum at the intermediate conversion level, are in line with Zylyftari et al.12 It is useful to consider the role of capillary bridging seen in other works. McCulfor et al.17 studied a suspension of glass particles in mineral oil as a model system for hydrate suspension and reported that the addition of small amounts of water leads to large increases in viscosity due to formation of water bridges between glass particles that give rise to capillary forces between them. Koos and Wilenbacher18 also reported the importance of capillary bridging, which form on adding a small amount of immiscible liquid to the continuous phase of a solid particle suspension, in the transition of the suspension from fluid-like behavior to formation of particle network resulting in gelation and paste-like behavior. This transition can lead to a dramatic increase in the yield stress by more than 1 order of magnitude. Our results indicate that a similar mechanism is responsible for the viscosity maximum at intermediate conversion levels. Figure 4 shows the effect of shear rate on the viscosity evolution of a w/o emulsion with 0.4 mass fraction of aqueous

Figure 5. Shear rate ramps on the hydrate slurry obtained for a w/o cyclopentane hydrate-forming emulsion with 0.4 mass fraction of aqueous phase and with Xs−in = 0.07 at γ̇ = 100 s−1 and T = −7 °C: ●, γ̇ = (100 to 1) s−1; blue ■, γ̇ = (1 to 100) s−1.

phase for Xs−in = 0.07 at γ̇ = 100 s−1 and T = −7 °C, to shear rate ramps from (1 to 100) s−1 in 15 min in increasing and decreasing directions. The hydrate slurry exhibits a shear thinning behavior. The decreasing shear rate curve follows the increasing shear rate curve very closely not showing significant rate-dependent hysteresis. A vane rotor with roughened cylindrical cup is used for the oscillatory tests. This geometry allows us to prevent wall slip effects and gives a reliable measure of yield stress (τy). The emulsion prepared at room temperature is transferred into the cup where temperature is set at −7 °C. The oscillatory strain is fixed at 10 % and frequency is 1 Hz. Figure 6 shows the

Figure 4. Effects of shear rate on the final viscosity of the densitymatched kerosene-based cyclopentane hydrate-forming emulsion at T = −7 °C and at Xs−in = 0.035 and 0.07: ○, Xs−in = 0.035, γ̇ = 10 s−1; red □, Xs−in = 0.035, γ̇ = 100 s−1; blue ×, Xs−in = 0.07, γ̇ = 10 s−1; green ◆, Xs−in = 0.07, γ̇ = 100 s−1.

phase and with Xs−in = 0.035 and 0.07. An initial slow rise in viscosity followed by a rapid upturn is observed for each shear rate. For a fixed salt concentration, lower shear rate generally leads to a longer critical time (although this behavior has some stochasticity) and higher final viscosity. Higher shear rates and high droplet population (0.4 mass fraction of aqueous phase) leads to faster nucleation and hydrate growth because of enhanced droplet interactions. A droplet on which hydrate has formed at the interface would act as a nucleating agent for the neighboring droplets. For a fixed shear rate, the critical time is found to be longer while the final slurry viscosity is found to be lowered at higher salt concentration. For example, the critical time for Xs−in = 0.035 at a shear rate of 100 s−1 is shorter than for Xs−in = 0.07 because of the difference in the degree of subcooling and different water-to-hydrate conversion levels.

Figure 6. Evolution of G′ for a w/o cyclopentane hydrate-forming emulsion with 0.4 mass fraction of aqueous phase and with no salt at T = −7 °C, strain = 10 %, and frequency = 1 Hz.

evolution of storage modulus (G′) for a w/o emulsion with 0.4 mass fraction of aqueous phase and with no salt. Similar to the rapid viscosity increase observed in the shear rheology experiments, G′ for the w/o emulsion with 0.4 mass fraction of aqueous phase suddenly increases by several orders of magnitude as a result of hydrate formation, as shown in Figure 6. As the water-to-hydrate conversion approaches completion, G′ attains a statistically constant and steady-state value. Figure 7 shows the final storage modulus obtained for hydrate slurry prepared at T = −7 °C, strain = 10 % and frequency = 1 Hz E

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Figure 7. Final G′ obtained at T = −7 °C, strain = 10 % and frequency = 1 Hz plotted as a function of theoretical water-to-hydrate conversion (Xw). The points from left to right correspond to initial salt concentration (mass fractions) of Xs−in = 0.1, 0.07, 0.05, 0.035, 0.027, 0.015, 0. Figure 8. Elastic stress (G′·γ) for hydrate slurries obtained from w/o emulsions with 0.4 mass fraction of aqueous phase at T = −7 °C for varying initial salt concentration. The maximum in elastic stress is interpreted here as the yield stress of the sample: ○, Xs−in = 0.0; green □, Xs−in = 0.035; +, Xs−in = 0.05; ∗, Xs−in = 0.07; red ×, Xs−in = 0.1.

plotted as a function of theoretical water-to-hydrate conversion. For complete water-to-hydrate conversion (Xw = 1), the final G′ value was found to be lower than that obtained for Xw = 0.85 and 0.92. At low water-to-hydrate conversions (0.606 and 0.422), the storage modulus is significantly smaller. The behavior of the storage modulus as a function of conversion follows a similar trend as the viscosity and the yield stress (the latter shown in Figure 9). The hydrate slurry as prepared in the rheometer (with evolution shown in Figure 6) is used further for yield stress measurements. The hydrate slurry is subjected to a continuous oscillatory stress ramp in which the amplitude of oscillatory stress (σo) is increased logarithmically from (0.1 to 1000) Pa at a frequency of 1 Hz and the material response is recorded in terms of G′ and G″. The yield stress values can be estimated by plotting the product of elastic modulus and strain, G′·γ, as a function of amplitude of applied oscillatory stress as shown in Figure 8. Below the yield stress, the elastic stress increases linearly with the applied oscillatory stress and above the yield stress, the elastic stress deviates from linear dependence; in fact, the elastic stress drops catastrophically. Figure 9 shows the yield stress obtained from Figure 8 plotted as a function of theoretical water-to-hydrate conversion. We note some studies related to the yield stress measurements on hydrate and ice slurries obtained at different conditions for comparison purpose. Webb et al.7 measured the yield stress of methane hydrate slurries obtained from a water-in-crude oil emulsion at 0 °C and 13.9 MPa initial pressure. On the basis of the initial water mass fractions, three regimes of yield stresses were observed. Below the water mass fraction of 0.32, the slurries were found to be flowable, and there was no significant yield stress. From (0.32 to 0.52) water mass fractions, the yield stresses were found to be less than 25 Pa while above 0.52, the yield stress was above the instrument limit of 3000 Pa. Rensing et al.8 measured the yield stress of ice slurries at different mass fractions of pure water and brine in the emulsions at −10 °C. There was no significant yield stress for the 0.27 mass faction of pure water and 0.32 mass fraction of brine solution. A yield stress of 300 Pa was measured for water mass fractions in the range of (0.27 to 0.57). For water fractions above 0.57, the yield stress was found to be greater than the instrument limit of 3000 Pa. For water mass fractions ranging from (0.066 to 0.36) in

Figure 9. Yield stress (τy) plotted as a function of theoretical water-tohydrate conversion (Xw) at T = −7 °C. The points from left to right correspond to initial salt concentration (mass fractions) of Xs−in = 0.1, 0.07, 0.05, 0.035, 0.027, 0.015, 0.

Webb et al.,9 the yield stress at 0 °C and initial pressure of 10.4 MPa was found to vary from 1 Pa to 20 Pa. Webb et al.10 measured the yield stress of methane hydrate slurries for water mass fractions ranging from (0 to 0.44) at temperatures from (0 to 6) °C and initial pressures from (5.2 to 10.4) MPa. At a fixed temperature of 0 °C and an initial pressure of 10.4 MPa, the yield stresses were found to vary from 3 Pa to 21 Pa for water mass fractions ranging from (0.12 to 0.44). For 0.335 water mass fraction at 0 °C, the yield stress was found to vary from 380 Pa to 65 Pa for initial pressures varying from (5.2 to 8.7) MPa. In our study, the yield stress for a w/o emulsion with 0.4 mass fraction of aqueous phase at Xw = 1.0 (no salt) and at −7 °C is found to be 31 Pa while for Xw = 0.81 (Xs−in = 0.035), the yield stress is found to be 145 Pa. The minimum and maximum yield stresses measured in our work are 4 Pa and 1105 Pa for Xw = 0.42 (Xs−in = 0.1) and Xw = 0.92 (Xs−in = 0.015), respectively. We find the yield stress to be a strong function of the surfactant loading, and the yield stresses here at 4.95 × 10−3 mass fraction of Span 80 (based on oil) are lower F

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than we find at 9.9 × 10−4 mass fraction of Span 80 in a mineral oil emulsion.19,20

(10) Webb, E. B.; Koh, C. A.; Liberatore, M. W. High pressure rheology of hydrate slurries formed from water-in-mineral oil emulsions. Ind. Eng. Chem. Res. 2014, 53, 6998−7007. (11) Camargo, R.; Palermo, T. Rheological properties of hydrate suspensions in an asphaltenic crude oil. Proceedings of the 4th International Conference on Gas Hydrates (ICGH), Yokohama, Japan, May 19−23, 2002. (12) Zylyftari, G.; Lee, J. W.; Morris, J. F. Salt effects on thermodynamic and rheological properties of hydrate forming emulsions. Chem. Eng. Sci. 2013, 95, 148−160. (13) Peixinho, J.; Karanjkar, P. U.; Lee, J. W.; Morris, J. F. Rheology of hydrate forming emulsions. Langmuir 2010, 26, 11699−11704. (14) Karanjkar, P. U.; Lee, J. W.; Morris, J. F. Calorimetric investigation of cyclopentane hydrate formation in an emulsion. Chem. Eng. Sci. 2012, 68, 481−491. (15) Zylyftari, G.; Ahuja, A.; Morris, J. F. Nucleation of cyclopentane hydrate by ice studied by morphology and rheology. Chem. Eng. Sci. 2014, 116, 497−507. (16) Stephen, H.; Stephen, T. Solubilities of Inorganic and Organic Compounds; Macmillan: New York, 1963; Vol. I. (17) McCulfor, J.; Himes, P.; Anklam, M. R. The effects of capillary forces on the flow properties of glass particle suspensions in mineral oil. AIChE J. 2011, 57, 2334−2340. (18) Koos, E.; Willenbacher, N. Capillary forces in suspension rheology. Science 2011, 311, 897. (19) Karanjkar, P. U. Evolving morphology and rheological properties of an emulsion undergoing clathrate hydrate formation. Ph.D. Thesis, City University of New York, New York, 2012. (20) Ahuja, A.; Zylyftari, G.; Morris, J. F. Yield stress measurements of cyclopentane hydrate slurry. J. Non-Newt. Fluid Mech.: Special IssueVPF:2013 (under review).

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CONCLUSION We have studied the thermodynamic and rheological properties of hydrate-forming water-in-kerosene emulsions in the presence of salt. Kerosene is chosen as a clear organic liquid which can be obtained in large volumes as a distillate of crude oil, and thus is a candidate for a large-scale flow loop study. Using calorimetric techniques, we have measured equilibrium temperature and fractional water-to-hydrate conversion by varying the salt concentration in the aqueous phase. The mechanical properties obtained are correlated to thermodynamic properties. At higher subcooling, the critical and evolution times are found to be shorter. In simple shear flow, the final viscosity data for hydrate slurries are obtained by varying the salt concentration in the aqueous phase and are plotted as a function of theoretical water-to-hydrate conversion. A peak in the final viscosity data is observed in the range of 0.85 to 0.95 (mass fractions) theoretical conversion, strongly suggesting the presence of capillary bridges between the hydrate particles. In oscillatory shear flow, a similar maximum was observed in the final storage modulus and yield stress data at the same conversion level.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +1 212 650 6844. Fax: +1 212 650 6835. Funding

We acknowledge support from Chevron and discussions with the Chevron Flow Assurance Core Team. Notes

The authors declare no competing financial interest.

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REFERENCES

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dx.doi.org/10.1021/je500609q | J. Chem. Eng. Data XXXX, XXX, XXX−XXX