High Pressure Rheology of Hydrate Slurries Formed from Water-in

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High Pressure Rheology of Hydrate Slurries Formed from Water-inMineral Oil Emulsions Eric B. Webb, Carolyn A. Koh, and Matthew W. Liberatore* Center for Hydrate Research, Department of Chemical and Biological Engineering, Colorado School of Mines, Golden, Colorado 80401, United States S Supporting Information *

ABSTRACT: Structure I methane hydrates are formed in situ from water-in-mineral oil emulsions in a high pressure rheometer cell. Viscosity is measured as hydrates form, grow, change under flow, and dissociate. Experiments are performed at varying water volume fraction in the original emulsion (0−0.40), temperature (0−6 °C), and initial pressure of methane (750−1500 psig). Hydrate slurries exhibit a sharp increase in viscosity upon hydrate formation, followed by complex behavior dictated by factors including continued hydrate formation, shear alignment, methane depletion/dissolution, aggregate formation, and capillary bridging. Hydrate slurries possess a yield stress and are shear-thinning fluids, which are described by the Cross model. Hydrate slurry viscosity and yield stress increased with increasing water volume fraction. As driving force for hydrate formation decreases (increasing temperature, decreasing pressure), hydrate slurry viscosity increases, suggesting that slower hydrate formation leads to larger and more porous aggregates. In total, addition of water to a methane saturated oil can cause more than a fifty-fold increase in viscosity if hydrates form.

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flow rate. These correlations reduce the accuracy of the measurement and sometimes require significant assumptions. Other studies used rheometers; however, hydrates were formed from guest molecules that do not exist in oil pipelines, such as cyclopentane or tetra butylammonium bromide (a semiclathrate former), and thus, the measured rheological properties may not be fully representative of those found in oil pipelines.12,14−17,19−21 Most rheometers cannot operate at high pressure, and even when they do, rheometers are unable to generate enough mixing to dissolve gas, which may be necessary for significant hydrate formation. This work uses an apparatus that saturates emulsions with methane in an external mixing cell and then pumps the emulsion under pressure to a high pressure rheometer cell with concentric cylinders geometry, providing a method to study hydrate rheology in detail.22−24 Earlier work using this apparatus studied hydrate slurries and ice slurries formed from water-in-crude oil emulsions.23,25 Crude oil is difficult to study experimentally because it is extremely complex and difficult to use repeatably. However, crude oil is not a single chemical, but rather a class of chemicals, each of which contains thousands of components. The components are so numerous that they cannot all be determined.26 Also, the composition of oil can change over time, and as it is produced from a well, each batch of crude oil received from a well will be different. These concerns and others led us to study model emulsions rather than pipeline fluids. This study uses synthesized emulsions composed of water, mineral oil, and span 80 and AOT surfactants. Methane gas is

INTRODUCTION In subsea oil and gas production, a variety of events can occur which hinder or fully stop flow in the pipeline.1 Some of the problems that can occur in a subsea pipeline include wax precipitation, scale formation, asphaltene precipitation, sand deposition, and hydrate formation. The study of these phenomena is called flow assurance. Of all these phenomena, hydrate formation occurs much more rapidly than the others.1 Natural gas hydrates are solid crystal structures composed of water cages that form around small gas molecules (e.g., methane).2 The most common crystal structures formed are structure I (e.g., from methane, ethane, and carbon dioxide guests) and structure II (e.g., from propane, hydrogen, and mixed gas guests). Structure I methane hydrate only forms at high pressures and low temperatures. For example, hydrate thermodynamic phase equilibria software CSMGem3−7 predicts methane hydrate requires a pressure of 3.9 MPa at 4 °C. In an oil pipeline, hydrate slurries often form from a water-inoil emulsion under flow with a gas headspace. Oil pipeline operators need to know if hydrate formation will occur and to what extent flow in the pipeline will be impeded. The rheological properties (e.g., viscosity, yield stress) of hydrate slurries are important factors in determining the flowability of hydrate slurries. Due to the complexity of hydrate slurries in pipelines (e.g., emulsions which partially convert to aggregated suspensions), their rheological properties are not yet well understood. Prior work on the rheological properties of hydrate slurries are generally divided into two groups. First, studies performed using flowloops, pipes, or mixing cells8−18 have the advantage of nearly replicating hydrate slurry flow in subsea pipelines; however, as these devices are not rheometers, they can only determine viscosity through correlations, such as calculating shear stress and shear rate at the wall from pressure drop and © 2014 American Chemical Society

Received: Revised: Accepted: Published: 6998

March 1, 2014 April 2, 2014 April 3, 2014 April 3, 2014 dx.doi.org/10.1021/ie5008954 | Ind. Eng. Chem. Res. 2014, 53, 6998−7007

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syringe pump. The pump can hold a maximum pressure of 3750 psig and a maximum volume of 500 mL. During emulsion saturation, the mixing cell is connected to the syringe pump but isolated from the rheometer pressure cell. To begin saturation, a synthesized emulsion is placed in the mixing cell and then pressurized to the desired pressure with methane gas. Then, the syringe pump is set to hold at a constant set pressure by moving the piston (changing total system volume). After 5 min, the system is assumed to have reached thermal equilibrium, and the mixing cell motor is started. The system volume decreases until gas is fully dissolved into the liquid. The volume trace is used to calculate the amount of methane dissolved in the emulsion. Following saturation, 10 mL of emulsion is pumped from the mixing cell to the rheometer pressure cell. The rheometer is a TA Instruments DHR-2 rheometer. A pressure cell in a Peltier heating/cooling jacket (both from TA Instruments) is mounted on the rheometer. The Peltier jacket has a temperature range from −25 to 150 °C, maximum heating/cooling rate of 2 °C/ min, and ±0.1 °C temperature precision. A refrigerated/heated circulating bath (VWR) with a water and ethylene glycol mixture supplies the jacket with cooling fluid. A cooled circulating fluid allows for the low temperature (−5 °C) operation of the rheometer cell for the multiday duration of the hydrate experiments. The pressure cell consists of a steel outer cylinder and a titanium inner cylinder in a concentric cylinders (cup-and-bob) arrangement. The outer cylinder internal radius is 14.00 mm, while the inner cylinder radius is 13.00 mm, giving the cell a 1.00 mm gap size. The cell is rated for operation up to 2000 psi. The inner cylinder assembly contains a steel cap, which screws into the outer cylinder, and a rotor assembly, which screws into the steel cap. Rotation is achieved through a 4-pole magnet attached to the rheometer spindle which couples with another magnet on the inner rotor assembly. Further information for this apparatus is published elsewhere.22 Experimental Procedure. Once an emulsion is pumped into the rheometer pressure cell, a series of rheological tests are performed. Whenever hydrates are formed, the same experimental procedure is used except at varying temperature, pressure, and emulsion water volume fraction (Table 1). Every experiment is performed at constant volume, i.e., nothing is added or subtracted from the system.

dissolved into these emulsions in an external mixing cell, and then, emulsions are pumped into a high pressure rheometer. A series of tests are performed in the rheometer to measure viscosity evolution during hydrate formation, simulated shut-in (yield stress measurement), steady state flow at varying shear rates, and dissociation.

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EXPERIMENTAL METHOD AND SETUP Emulsion Synthesis and Characterization. Emulsions are composed of deionized water, Crystal Plus tech grade 70T mineral oil (STE Oil Company), span 80 surfactant (SigmaAldrich), and dioctyl sodium sulfosuccinate (AOT) surfactant (Fisher scientific) at water volume fractions of 0.10, 0.20, 0.30, and 0.40. Emulsion compositions and physical properties of the components are shown in Table S1 of the Supporting Information. Emulsions are prepared by dissolving surfactants (span 80 and AOT) in mineral oil at 35 °C on a magnetically stirred hot plate at 350 rpm. Then, water is added dropwise and mixed at 8000 rpm in a Virtis Cyclone I.Q.2 homogenizer for 3 min. The volume fraction of water in each emulsion is denoted ϕw. The average droplet size is 2−3 μm. No coalescence was visually observed in a bottle test after 1 week,27 and all experiments in this work are completed within 1 week of preparing each emulsion. Further details on the emulsions are discussed in the recent work by Delgado et al.27 High Pressure Rheometer Apparatus. In order to form hydrates in an emulsion, methane gas must be dissolved in the emulsion. Dissolving gas in the emulsion requires either high mixing or long time (tens of hours). The rheometer is unable to generate high mixing, and full saturation through diffusion takes too long; so, we dissolve gas in an external mixing cell and then pump the saturated emulsion through a syringe pump into the rheometer cell under pressure. On the basis of previous work in our laboratory,22−24 Figure 1 shows a schematic of the

Table 1. Rheology Procedure for Hydrate Slurries step

Figure 1. Schematic of the high pressure rheometer apparatus.

apparatus. The mixing cell (Autoclave Engineers) has a volume of 302 mL and operates at pressures up to 4750 psig. A belt connected to an electric motor drives the impeller of the mixing cell at 170 rpm. The mixing cell is placed in an ethylene glycol− water cooling bath set to 10 °C (temperatures lower than 10 °C could result in hydrate formation during saturation). The mixing cell is connected to a Teledyne ISCO 500D model 6999

duration

preparation

4−10 h

equilibration cooling

10 min 50 min

hydrate formation hardening stress ramp

24 h

conditioning flow curve

30 min ∼1 h

dissociation

50 min

8h 0−3 h

conditions emulsion saturated with CH4 at 1500 psig, 10 °C, and 170 rpm 25 °C ramp temperature from 25 to 0 °C at 0.5 °C/min, 100 s−1 0 °C, 100 s−1 0 °C, 2% oscillatory strain, 1 Hz frequency 0 °C, ramp shear stress from 0 to 3000 at 1000 Pa/h 0 °C, 500 s−1 0 °C, ramp shear rate from 500 to 1 to 500 s−1; steady state measurements: 3 s sample period, 3% tolerance, 3 consecutive within tolerance, 2 min maximum point time ramp temperature from 0 to 25 °C at 0.5 °C/min, 100 s−1

dx.doi.org/10.1021/ie5008954 | Ind. Eng. Chem. Res. 2014, 53, 6998−7007


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RESULTS AND DISCUSSION

This study seeks to understand the rheological properties of a hydrate slurry formed from a gas saturated emulsion. A hydrate slurry could contain water, continuous phase oil, surfactants, dissolved gas, and hydrate particles. In order to make informed observations on complex hydrate slurries, we first characterized simpler systems composed of one or more constituents of hydrate slurries, denoted control systems. Then, complex hydrate slurries are studied. The following systems were studied in this work: (1) 70T mineral oil; (2) 70T mineral oil + surfactants; (3) 70T mineral oil + methane gas (saturated oil); (4) 70T mineral oil + water + surfactants (emulsion); (5) 70T mineral oil + water + surfactants + methane gas (saturated emulsion); (6) 70T mineral oil + water + surfactants + methane gas + sI methane hydrate (hydrate slurry). The rheological properties of the first four systems are discussed in the Supporting Information. We list the key results here. Pure mineral oil is a Newtonian fluid (viscosity does not depend on shear rate) and an Arrhenius fluid with respect to temperature. The viscosity of mineral oil decreases as increasing amounts of methane are present; mineral oil with 1500 psig methane had a viscosity of 0.0087 Pa·s compared to 0.075 Pa·s at 0 psig methane. Emulsions were shear-thinning (viscosity decreased as shear rate increased) and followed Arrhenius behavior with respect to temperature. The degree of shearthinning in emulsions increased as water volume fraction increased. Hydrate Slurry Example Experiment. The last two systems to examine are saturated emulsions and hydrate suspensions. Since hydrate suspensions are formed from methane saturated emulsions, both of these systems were studied simultaneously. Experiments on these systems follow the procedure given in Table 1. Experiments were performed at varying water volume fraction (0, 0.05, 0.10, 0.20, 0.30, 0.40, and 0.50), temperature (0, 2, 4, and 6 °C), and pressure (750, 1000, 1250, and 1500 initial pressure methane). Many of the same qualitative features are observed in all or most of these experiments; so, the results of one experiment are presented first as an example. The conditions of the representative experiment are 0.30 water volume fraction, 0 °C, and 1500 initial pressure methane. During the cooling step, the pressure decreases and the viscosity increases in response to the temperature change (Figure 2). The pressure and viscosity shifts are only a reflection of the temperature change, not an indication of hydrate formation. After the cooling step, the system conditions are such that hydrate formation is thermodynamically favorable; however, hydrate formation does not occur for some time because nucleation of hydrate crystals in the emulsion is a random event.2 Hydrate formation is detected by a large increase in the viscosity coupled with a sharp decrease in pressure measured in the gas headspace (Figure 2). At least three factors can contribute to the initial viscosity increase during hydrate formation. First, liquid water drops are converted to solid hydrate particles. Viscosity of rigid particles is expected to be higher than deformable liquid droplets.9,28 Second, methane is removed from the external oil phase. Since methane is the lightest component in the oil phase, methane depletion will cause an increase in the continuous phase viscosity.22 Third, prior to hydrate formation, liquid droplets are stabilized by surfactant molecules. When water converts to hydrate, the surface chemistry of the suspended particle

Figure 2. Pressure, temperature, and viscosity evolution of a methane saturated water-in-mineral oil emulsion with 0.30 water volume fraction over time at γ̇ = 100 s−1.

changes, allowing particles to collide with one another, creating aggregates. Aggregated systems exhibit higher viscosity than nonaggregated systems.29−31 Changes in pressure can be explained by at least two phenomena. First, since the system is at a constant volume, any change to the liquid volume will also change the gas phase volume and, thus, the pressure. Second, methane molecules can diffuse from the gas phase to the liquid, decreasing the moles of methane in the gas phase and, thus, decreasing the pressure. During hydrate formation, the liquid volume decreases and, thus, pressure decreases. The initial hydrate formation event occurs over about 10 min. This time scale is too short to expect significant pressure change from the second mechanism, methane diffusion from gas to liquid.24 The initial viscosity spike ends when either all methane or all water is converted to hydrate in the liquid phase, whichever is limiting. In the example experiment, methane is the limiting reactant. So, at the end of the initial viscosity increase, the liquid phase contains continuous phase oil, hydrate, and unconverted water, but no methane. After the initial increase in viscosity, each experiment shows different behavior depending on the temperature, pressure, and water volume fraction of the emulsion. Many experiments show a rapid decrease in viscosity immediately following the initial increase in viscosity (Figure 2). This could be explained by the alignment of newly formed aggregates under flow.32 After this decrease, some experiments continue to show decreasing viscosity, while others show increasing viscosity. In Figure 2, methane from the gas phase slowly diffuses back into the liquid (at a rate of about 5 psi/h), causing pressure and viscosity to slowly decrease. However, once dissolved, methane is 7000



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enclathrated with the remaining water to form hydrate, which increases viscosity. Once all water has been converted to hydrate, viscosity will no longer increase. Rather, viscosity and pressure will decrease because gas continues to dissolve back into the liquid (Figure 2 from 7 to 25 h). Finally, one further phenomenon confuses the analysis even more. When both water and hydrate are present, water can form capillary bridges between hydrate particles. These capillary bridges hold aggregates together, which increases viscosity.33 So, when all of the water is eventually converted to hydrate, no more water exists for capillary bridging, and viscosity is actually expected to decrease. Recent work by Zylyftari et al.19 indicates maximum viscosity is expected to occur when between 60% and 80% of water is converted to hydrate. After transient hydrate formation (constant shear rate and temperature), the hydrate slurry is held under no shear conditions for 8 h at the experimental temperature (usually 0 °C). During this step, hydrate particles may harden. Previous work with water-in-crude oil emulsions showed no change in measured yield stress for slurries hardened for 8 h compared to longer than 8 h.23 Following the hardening step, hydrate slurry yield stress is measured by ramping shear stress from 0 to 3000 Pa on a log scale over 3 h. The yield stress is measured at the point the shear rate begins to increase. The yield stress for the example experiment is 19 Pa (Figure 3).

Figure 4. Steady state viscosity of methane hydrate slurry measured at varying shear rates. Symbols represent experimental data, line indicates Cross model fit to the 500 to 1 s−1 data. 0.30 water volume fraction water-in-mineral oil emulsion at 0 °C.

pattern; however, some experiments could only obtain steady state values in the shear-thinning regime. These data sets are fit to the two parameter power law model:

η = mγ ṅ − 1

(2)

where, η is viscosity, γ̇ is shear rate, m is the consistency, and n is the flow behavior index. Finally, the hydrate slurry is heated back to 25 °C at 0.5 °C/ min and 100 s−1 shear rate (Figure 5). As the slurry warms, the

Figure 3. Stress ramp used to determine hydrate slurry yield stress. 0.30 water volume fraction water-in-mineral oil emulsion at 0 °C after an 8 h hardening step.

Next, the hydrate slurry is sheared at 500 s−1 for 30 min to homogenize structures formed from the hardening step (Figure 4). Then, the shear rate is ramped from 500 to 1 to 500 s−1. In every experiment, hydrate slurries were found to be shearthinning, including the experiment shown in Figure 4. Most experiments show an s-shaped curve with a zero shear plateau (the viscosity approaches a constant value, η0, as shear rate approaches zero), a shear-thinning regime, and a high shear plateau (the viscosity approaches a constant value, η∞, as the shear rate approaches infinity). S-shaped curves are fit to the four-parameter Cross model:34 η − η∞ + η∞ η= 0 1 + (Cγ )̇ m (1)

Figure 5. Viscosity of methane hydrate slurry as temperature increases through hydrate dissociation. 0.30 water volume fraction water-inmineral oil emulsion at 0 °C and 100 s−1. Dotted red line indicates sI methane hydrate equilibrium temperature predicted by CSMGem.

viscosity decreases; however, there is a viscosity increase near 12 °C. The measured pressure at 12 °C was 1274 psig. The methane hydrate equilibrium temperature at 1274 psig is predicted to be 11.9 °C by CSMGem (Colorado School of Mines Gibbs Energy Minimization).3−7 Previous research shows that, as temperature increases, a water layer on the surface of hydrate particles grows thicker, allowing stronger cohesion forces between hydrate particles, thus increasing viscosity.35 Past the hydrate equilibrium temperature, the hydrate particles fully melt, and the viscosity returns to a lower value (Figure 5). In the remaining experiments, viscosity shows similar qualitative behavior, with viscosity shifting to higher values with increasing water volume fraction and the

where η0 is the viscosity at zero shear rate, η∞ is the viscosity at infinite shear rate, 1/C is the lower bound shear rate of the shear-thinning regime, and m is the slope of the shear-thinning regime. In all cases, the data is expected to follow an s-shaped 7001



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anomalous viscosity increase occurring at lower temperatures as driving force decreases. Rheology at Varying Water Volume Fraction, Temperature, and Pressure. Rheological behavior of hydrate slurries was studied over a range of water volume fractions (0.1−0.5), temperatures (0−6 °C), and pressures (750−1500 psig methane). Some experiments were repeated several times and found to be reproducible. Reproducibility of these experiments is discussed and shown in the Supporting Information. Experiments were performed at five different water-inmineral oil emulsion compositions: 0.1, 0.2, 0.3, 0.4, and 0.5 water volume fraction. The experiment at 0.5 water volume fraction could not be performed because the saturated emulsion could not be pumped from the mixing cell to the pressure cell. The viscosity increased as water volume fraction increased in every stage of the experiment (Figures 6 and 7). The fraction of Figure 7. Steady state viscosity of hydrate slurries formed from waterin-mineral oil emulsions at 0 °C and 1500 psig initial pressure of methane. Points are steady state viscosity measurements; lines are Cross model fits to the measurements.

for 0.40 water volume fraction). After the initial viscosity increase, methane begins to dissolve back into the liquid from the gas phase, where it becomes enclathrated with unconverted water. So, the 0.30 and 0.40 water volume fraction experiments show a second increase in viscosity as water continues to convert. The maximum in viscosity for each experiment occurred at less than χ = 1; that is, less than 100% conversion of water to hydrate (Figure 6). Capillary bridges formed by water between hydrate particles may help increase viscosity; so, at high χ, capillary bridges are depleted, causing viscosity to decrease. Yield stress increased as water volume fraction increased (Table 2). For comparison, the yield stress of ketchup is about Table 2. Hydrate Slurry Yield Stress

Figure 6. Pressure, fraction of water converted to hydrate (χ), and viscosity over time as hydrates form in water-in-mineral oil emulsions at 0 °C, 1500 psig initial pressure of methane, and 100 s−1.

water converted to hydrate is denoted χ and was calculated during transient hydrate formation (Figure 6). The calculations are based only on pressure measurements, not viscosity. The calculation details for χ is further explained in the Supporting Information. At both 0.10 and 0.20 water volume fraction, there is sufficient methane dissolved in the liquid at the beginning of the experiment to convert all water to hydrate. So, all water is converted during the initial increase in viscosity, or shortly thereafter (Figure 6). Note the smooth decrease in pressure observed at 0.10 and 0.20 water volume fraction compared to the pressure decreases for 0.30 and 0.40. At 0.30 and 0.40, there seems to be two distinct regions of pressure change; an initial region of fast pressure loss (∼20 psi/h) followed by a slower region (∼2 psi/h), similar to those observed at 0.10 and 0.20 water volume fraction. At 0.30 and 0.40 water volume fraction, the amount of methane initially dissolved in the liquid phase is not sufficient to convert all water to hydrate. So, partial conversion of water to hydrate occurs during the initial viscosity increase (χ = 0.68 for 0.30 water volume fraction and χ = 0.42

ϕw

T (°C)

Po (psig)

τo (Pa)

0.1 0.2 0.3 0.4 0.3 0.3 0.3 0.3 0.3 0.3

0 0 0 0 2 4 6 0 0 0

1500 1500 1500 1500 1500 1500 1500 750 1000 1250

3 11 18 21 43 110 30 380 75 65

15 Pa,36 and the yield stress of peanut butter is about 370 Pa.37 Interestingly, varying water volume fraction at constant pressure and temperature did not have a large effect on yield stress (first four rows of Table 1). Past studies on water-incrude oil emulsions observed similar low values of yield stress up to a critical water volume fraction at which the yield stress increased to a value above the instrument limit (3000 Pa).23 Intuition suggests that higher driving forces for hydrate formation (higher pressure, lower temperature) would cause more hydrates to form and, thus, higher yield stresses; however, experiments at lower driving forces tended to give higher yield stresses. In fact, experiments at varying temperature actually had about the same amount of hydrate at the time yield stress was measured (an explanation of the calculation details to 7002



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determine fraction of water converted to hydrate is provided in the Supporting Information). So, the difference between experiments at varying temperature seems to be related to the rate of hydrate formation rather than the amount of hydrate formation. The rate of hydrate formation increases with decreasing temperature.38−41 So, we observe that yield stress typically increases as rate of hydrate formation decreases. The experiment at 6 °C is an exception to this rule. As a general rule, the trend in yield stress for a set of experiments was the same as the trend in viscosity. Hydrate slurries were shear-thinning at each water volume fraction (Figure 7). Steady state hydrate slurry viscosity increased with increasing water volume fraction, the same trend as the transient viscosity. The steady state viscosity typically follows the same trend as the transient viscosity for varying water volume fraction, temperature, or pressure. The Cross model and power law parameters for each experiment are shown in Table 3. The zero-shear viscosity fitting parameter, η0, Table 3. Cross and Power Law Model Fit Parameters cross model parameters34

experimental conditions ϕw

P, psig

T, °C

0.10 0.20 0.30 0.40 0.30 0.30 0.30 0.30 0.30 0.30

1500 1500 1500 1500 1500 1500 1500 750 1000 1250

0 0 0 0 2 4 6 0 0 0

η0, Pa·s

η∞, Pa·s

0.99 0.11 1.6 0.090 0.96 0.22 29 0.24 1.6 0.35 5.5 0.33 0.81 0.18 m = 28 Pa·sn 4.6 0.33 no flow curve data

m 1.3 1.3 1.9 0.95 2.1 1.1 2.0 n = 0.32 1.4

C, s

Figure 8. Pressure, fraction of water converted to hydrate (χ), and viscosity over time as hydrates form in 0.30 water volume fraction water-in-mineral oil emulsions at 500 psig initial pressure of methane and 100 s−1.

0.056 0.12 0.026 1.7 0.032 0.12 0.0053 0.082

increased with increasing water volume fraction and increased with temperature (except at 6 °C), and the trend could not be determined with respect to pressure. The infinite-shear viscosity, η∞, followed the exact same trends as η0. No obvious trends were observed for m. Values of m across all experiments fell between 0.95 and 2.1, so the degree of shear-thinning was similar for all experiments. The C fitting parameter also did not show any obvious trends. Values of 1/C fell between about 1 and 200 s−1, which indicates the shear rate at which the sshaped curves begin to bend toward the zero-shear plateau. The experiment at 750 psig did not show s-shaped behavior and was better described by the power-law model. Steady state measurements at 1250 psig were not recorded due to a software error. Four experiments were performed on 0.30 water volume fraction emulsions at 1500 initial pressure of methane and 0, 2, 4, and 6 °C. At higher temperatures, the driving force for hydrate formation is lower. We expected higher temperatures would cause lower viscosity because the driving force for hydrate formation is lower; however, the results did not follow this intuition. Viscosity was observed to increase as temperature increased (Figures 8 and 9), i.e., as driving force decreased. Work on crystallization of supercooled liquids indicates crystal growth rate is inversely related to liquid viscosity.42 Also, other hydrate research shows that growth rate increases as driving force increases.38−41 Thus, it follows that viscosity increases as driving force for hydrate formation decreases. This result has strong implications for the oil industry, as it suggests that moving toward lower driving forces for hydrate formation

Figure 9. Steady state viscosity of hydrate slurries formed from 0.30 water volume fraction water-in-mineral oil emulsions at 1500 psig initial pressure of methane. Symbols represent data from 500 to 1 s−1; lines are model fits to the data.

(lower pressure, higher temperature) may actually cause hydrate slurries which are more difficult to flow. At 3 h after initial hydrate formation, viscosity shows an inverse trend with temperature; the 0 °C experiment shows the highest viscosity, followed by the 2, 4, and 6 °C experiments (Figure 8). Increasing temperature decreases hydrate formation rate; so, at short times after initial formation, experiments at low temperature may have more hydrate formed (and thus higher viscosity) than experiments at higher temperatures. Later, after all water has converted to hydrate, each experiment should have the same amount of hydrate; but, the morphology of the hydrate aggregates may differ significantly because they were formed at different rates.43 At 15 h after initial hydrate formation, the viscosity trend is opposite of that observed at 3 h 7003



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(Figure 8). The highest viscosity occurs at 6 °C and the lowest viscosity at 0 °C. At 17 h after formation, the experiment at 6 °C undergoes a strong decrease in pressure and viscosity (Figure 8). It is possible that hydrate may have initially only formed at the gas− liquid interface. The hydrate film that forms at the interface could block gas from diffusing to the liquid, hence the small pressure decrease before 17 h compared to the other three experiments. At 17 h, the film may have broken, causing a rapid decrease in viscosity and allowing gas to dissolve into the liquid. The flow curves show increasing viscosity with decreasing driving force (Figure 9); the same trend observed in the transient step after full conversion of water to hydrate. The 6 °C experiment is an exception to the trend. The data at 6 °C could be skewed because of the event that occurred at 17 h during the transient step. Four experiments were performed on 0.30 water volume fraction emulsions at 0 °C and 750, 1000, 1250, and 1500 psig initial pressure methane gas. Each emulsion was saturated at the same experimental pressure in the mixing cell prior to the start of each experiment. Much like the experiments at varying temperature, viscosity was typically found to increase with decreasing pressure, i.e., decreasing driving force (Figure 10).

times (before 100% conversion of water to hydrate), the driving force is directly proportional to viscosity because the higher driving force experiments contain more hydrate. At long times (after 100% conversion of water to hydrate), the viscosity is inversely related to driving force because each experiment contains the same amount of hydrate, but the lower driving force experiments have larger aggregates. The flow curves (Figure 11) show the same trend as the transient data at long times: viscosity increases with decreasing pressure (decreasing driving force).

Figure 11. Steady state viscosity of hydrate slurries formed from 0.30 water volume fraction water-in-mineral oil emulsions at 0 °C. Symbols are data from 500 to 1 s−1; lines are model fits to the data.

In this study, six types of systems were characterized: (1) pure 70T mineral oil, (2) mineral oil with AOT and span 80 surfactants, (3) mineral oil saturated with methane gas, (4) emulsions (water + mineral oil + surfactants) at varying water volume fraction, (5) emulsions saturated with methane gas, and (6) hydrate slurries (water, mineral oil, surfactants, methane, sI hydrate) (Figure 12). All six systems are shown in the leftmost part of Figure 12 for comparison. The difference in mineral oil viscosity with and without surfactants is very small compared to any of the other systems. Addition of methane to pure mineral oil can decrease the viscosity by more than an order of magnitude. Emulsion viscosity is always larger than pure mineral oil viscosity, and saturated emulsion viscosity is larger than saturated mineral oil; so, the addition of an internal phase to a pure liquid increases the viscosity. Hydrate viscosity is always larger than the one point for saturated emulsions, so hydrate aggregates always have larger viscosity than water droplets. Hydrate slurries sometimes but not always have higher viscosity than emulsions. The methane in hydrate slurries decreases viscosity below the emulsion value, but the hydrate particles increase viscosity above the emulsion value. Hydrate slurries are more strongly shear-thinning than emulsions, so usually hydrate slurries have a higher viscosity at low shear rates while emulsions have a higher viscosity at high shear rates. In an oil pipeline, flow begins with a saturated oil phase, analogous to system 3. During oil production, water is inevitably produced with oil with the amount of water increasing over the lifetime of the field, which leads to a saturated oil-in-water emulsion, system 5. Finally, hydrates may form (system 6). Viscosity of these systems increases in the order saturated mineral oil < saturated emulsion < hydrate slurry (Figure 12). At 0.40 water volume fraction, at 100 s−1,

Figure 10. Pressure, fraction of water converted to hydrate (χ), and viscosity over time as hydrates form in 0.30 water volume fraction water-in-mineral oil emulsions at 0 °C and 100 s−1.

Again, decreasing driving force causes decreasing hydrate formation rate,38−41 which causes higher viscosity.42 Shortly following initial hydrate formation, around 3 h, the measured viscosity decreased in the order 1500 > 1250 > 1000 > 750 psig for the four varying pressure experiments. At 15 h after initial hydrate formation, the viscosity decreased in the order 750 > 1000 > 1250 > 1500 psig, opposite the trend at 3 h. At short 7004



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Figure 12. Steady state viscosity at varying shear rate across six different systems and varying water volume fractions. All experiments are at 0 °C and 1500 psig methane initially. Filled circles, methane saturated emulsion; open diamonds, emulsion (no methane); filled upward pointing triangles, hydrate slurries.

Figure 13. Relative viscosity versus water or particle volume fraction from various hydrate rheology studies. References are listed in the legend by the first author and the year of publication. Solid lines show model predictions based only on particle volume fraction and maximum particle packing fraction.

the recent measurements by Zylyftari et al.19 which show multiple values of relative viscosity at the same water volume fraction, temperature, and pressure. The only difference between the values is the amount of hydrate formed. So, water volume fraction alone is not sufficient to predict hydrate slurry viscosity; the fraction of water converted to hydrate is also important. In work from our research group, hydrate slurries have been formed from three different water-in-oil emulsions. Water-inWest African crude oil emulsions (w/WAC) are found in actual pipelines, with oil viscosity of 0.51 Pa·s and about 2 μm droplet diameter.23 Water-in-dodecane emulsions with AOT surfactant (w/C12) are synthesized microemulsions with oil viscosity of 0.0026 Pa·s and about 50 nm droplet diameter.24 Finally, waterin-70T mineral oil with AOT and span 80 emulsions (w/70T) have already been discussed in the present work (0.075 Pa·s oil phase viscosity, 2−3 μm droplet diameter). The peak viscosity in each experiment occurs at less than 100% conversion of water to hydrate (Figure 14). The χ values at each viscosity are determined from pressure measurements during transient hydrate formation. Capillary bridging may have the strongest effect at less than χ = 1 (i.e., less than 100%

saturated mineral viscosity is 0.008 Pa·s, saturated emulsion viscosity is 0.091 Pa·s, and hydrate slurry viscosity is 0.479 Pa·s. So, introduction of water to saturated oil can increase viscosity by over an order of magnitude. Hydrate formation from a saturated emulsion causes another about 5-fold increase in viscosity. Hydrate Slurries Formed in Mineral Oil Compared to Other Hydrate Slurries. Since 2000, several other researchers have measured the viscosity of hydrate slurries in various systems.8,11−19,21,23,24,44−46 These various endeavors used many different starting fluids (some are not emulsions), different guest molecules (some are even semiclathrates12,15,17,21), different apparatuses, and different thermodynamic conditions (e.g., temperature, pressure, salt amount). A comparison of these various studies reveals some common trends (Figure 13). In every study, the relative visocosity (measured viscsoity normalized by continuous phase viscosity) increased with water volume fraction. For comparison, the Krieger-Dougherty47 and Mills48 models for viscosity as a function of particle volume fraction are shown with two different values of the maximum particle packing fraction, 0.63 and 0.74. In many cases, the models underpredict the measurements. Especially revealing are 7005



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viscosity was about 1 order of magnitude larger than saturated emulsion viscosity, which was about five times larger than saturated oil viscosity. So, the introduction of water to a pipeline can cause a fifty-fold increase in viscosity. Comparing with other hydrate slurries, viscosity was independent of continuous phase viscosity. The maximum viscosity observed in any experiment typically occurred when between 40% and 70% of water had converted to hydrate.

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ASSOCIATED CONTENT

S Supporting Information *

Tables of emulsion composition, component properties, and Arrhenius parameters, a discussion of the rheological properties of simple control systems, a discussion of experiment reproducibility, emulsion flow curves at each water volume fraction and 0−25 °C, and an explanation of the calculation scheme used to calculate the fraction of water converted to hydrate (χ). This material is available free of charge via the Internet at http://pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the support of the CSM Hydrate Consortium, which is presently sponsored by BP, Chevron, ConocoPhillips, ExxonMobil, Multichem, Nalco, Petrobras, Shell, SPT Group, Statoil, and Total.

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Figure 14. Hydrate slurry viscosity versus fraction of water volume converted to hydrate in (a) w/WAC, (b) w/C12, and (c) w/70T emulsions at varying water volume fraction. Hydrate slurry relative viscosity is shown on a secondary y-axis.

REFERENCES

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CONCLUSIONS Structure I methane hydrate was formed from methane saturated water-in-mineral oil emulsions with AOT and span 80 surfactants. At full conversion of water to hydrate, hydrate slurry viscosity and yield stress increased with increasing water volume fraction, increasing temperature, and decreasing pressure. The fraction of water converted to hydrate (χ) based on the pressure evolution with time was calculated. The evolution of viscosity with χ indicates a complex interplay of factors affecting viscosity, including hydrate formation, aggregation, methane depletion and dissolution, and capillary bridging. Steady state viscosity was found to increase with decreasing driving force because hydrate aggregates at lower driving forces likely are larger even though the amount of hydrate is comparable to higher driving forces. Hydrate slurry 7006



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High Pressure Rheology of Hydrate Slurries Formed from Water-in

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