Studies of hydrate nucleation with high pressure differential scanning calorimetry

Chemical Engineering Science 64 (2009) 370 -- 375

Contents lists available at ScienceDirect

Chemical Engineering Science journal homepage: w w w . e l s e v i e r . c o m / l o c a t e / c e s

Studies of hydrate nucleation with high pressure differential scanning calorimetry Simon R. Davies a , Keith C. Hester b , Jason W. Lachance a , Carolyn A. Koh a , E. Dendy Sloan a,∗ a b

Center for Hydrate Research, Department of Chemical Engineering, Colorado School of Mines, 1500 Illinois Street, Golden, CO 80401, USA Monterey Bay Aquarium Research Institute, 7700 Sandholdt Road, Moss Landing, CA 95039, USA

A R T I C L E

I N F O

Article history: Received 27 August 2008 Received in revised form 12 October 2008 Accepted 16 October 2008 Available online 1 November 2008 Keywords: Nucleation Gas hydrate Flow assurance Energy Gases Crystallization

A B S T R A C T

Current models for hydrate formation in subsea pipelines require an arbitrary assignment of a subcooling criterion for nucleation. In reality hydrate nucleation times depend on both the degree of subcooling and the amount of time the fluid has been subcooled. In this work, differential scanning calorimetry was applied to study hydrate nucleation for gas phase hydrate formers. Temperature ramping and isothermal approaches were combined to explore the probability of hydrate nucleation for both methane and xenon. A system-dependent subcooling of around 30 K was necessary for hydrate nucleation from both guest molecules. In both systems, hydrate nucleation occurred over a narrow temperature range (2–3 K). The system pressure had a large effect on the hydrate nucleation temperature but the ice nucleation temperature was not affected over the range of pressures investigated (3–20 MPa). Cooling rates in the range of (0.5–3 K/min) did not have any statistically significant effect on the nucleation temperature for each pressure investigated. In the isothermal experiments, the time required for nucleation decreased with increased subcooling. © 2008 Elsevier Ltd. All rights reserved.

1. Introduction Since Hammerschmidt (1934) discovered that hydrates were contributing to blockages in natural gas transmission lines, significant research efforts have concentrated on better understanding and avoiding hydrate plug formation. Early research focused on determining the thermodynamic conditions that favor hydrate formation, allowing process conditions to be selected which avoid hydrate plug formation. More recently, research has focused on managing the risk of forming a plug by studying time dependent or kinetic aspects, including hydrate nucleation, growth and agglomeration (Sloan and Koh, 2008). Nucleation is the focus of this paper. Classical nucleation theory was developed from the 1920s ¨ (Volmer and Weber, 1926; Becker and Doring, 1935). The theory describes the activation barrier to nucleation as the sum of the increase in free energy due to the creation of a new interface and the decrease from creating a more stable phase. The interfacial energy is proportional to the square of the crystal radius, and the free energy associated with the phase change is proportional to the cube of the crystal radius. This leads to a maximum in energy with respect to radius as the daughter phase emerges; once a nucleus of the daughter phase reaches this critical radius through a series of random

∗

Corresponding author. Tel.: +1 303 273 3723; fax: +1 303 273 3730. E-mail address: [email protected] (E. Dendy Sloan).

0009-2509/$ - see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2008.10.017

fluctuations, further growth is energetically favorable. Nucleation is of great importance in a diversity of disciplines from atmospheric science to industrial crystallization. A comprehensive review of nucleation theory and application is provided by Kashchiev (2000). Primary nucleation is divided into two broad categories: homogeneous and heterogeneous. Homogeneous nucleation occurs when a critical nucleus emerges directly from the parent phase. At low subcoolings this can have a very low probability since the critical radius can be appreciable. In the case of hydrate formation from air inclusions in ice cores, nucleation can take thousands of years (Ohno et al., 2004; Salamantin et al., 1998, 2001; Shimanda and Hondoh, 2004). At higher subcoolings, the difference in free energy between the parent and daughter phase increases, this shifts the critical nucleus to lower radii. At sufficiently high subcooling, homogeneous nucleation becomes deterministic; this point is known as the spinodal. In heterogeneous nucleation the cluster grows in contact with a third phase which lowers the interfacial energy cost of further growth, hence smaller clusters of the daughter phase are required for energetically favorable growth. The energy barrier associated with heterogeneous nucleation is therefore much smaller than for homogeneous nucleation, hence phase transitions can occur more rapidly in the presence of impurities. In the case of dispersed systems such as emulsions, water droplets can behave as independent reactors (Dalmazzone et al., 2006; Clausse et al., 2005; Lachance, 2008) and the nucleation of

Simon R. Davies et al. / Chemical Engineering Science 64 (2009) 370 -- 375

one droplet may not necessitate the nucleation of adjacent droplets. However, droplet collisions in sheared systems or in concentrated emulsions may cause nucleation propagation between droplets; this is known as secondary nucleation. Nucleation of a hydrate phase has been a source of interest and frustration in the hydrate community for a number of years. The stochastic nature of the nucleation event can often lead to large variations in the onset time for hydrate formation between experiments (Maini and Bishnoi, 1981; Englezos et al., 1987; Christiansen et al., 1994). Researchers have also focused on the molecular mechanisms for hydrate nucleation (Sloan and Fleyfel, 1991; Radhakrishnan and Trout, 2002), but a major drawback has been the difficulty in obtaining sufficient laboratory data to validate the proposed mechanisms. Perhaps the most important step towards a systematic laboratory study of the hydrate nucleation phenomenon has been the construction of the automated lag time apparatus or ALTA (Heneghan et al., 2001). The ALTA enables multiple repetitions of nucleation experiments under identical conditions, and can generate large quantities of statistical data on the nucleation tendency of a system. ALTA studies of heterogeneous hydrate nucleation from a model water-soluble hydrate former, tetrahydrofuran (THF) (Wilson et al., 2005) have shown that with constant cooling, a narrow temperature range of a few degrees can cause an increase in the probability of nucleation from almost zero to close to 100%. Before this temperature is reached, it is this very low probability of nucleation that leads to the large variations in nucleation times. While this has been shown for THF hydrate, it is not clear whether this narrow temperature range exists for gas phase hydrate formers, which are more hydrophobic and hence have a very low solubility in water. In subsequent work (Dalmazzone et al., 2006), isothermal methane hydrate nucleation in water in oil emulsions was studied by high pressure differential scanning calorimetry (DSC). It was shown that the hydrate nucleation peak becomes narrower and more symmetrical at higher subcoolings, indicating a shorter nucleation time. In this study, DSC has been applied to determine the hydrate nucleation point for gas phase hydrate formers. Constant cooling ramps were performed to study the effects of cooling rate and subcooling on the nucleation point. Complementary isothermal measurements were used to better understand the factors that affect the time required for hydrate nucleation under lower subcoolings. 2. Experimental methodology 2.1. Apparatus A high pressure micro-differential scanning calorimeter (-DSC) VIIa from Setaram Inc. was used in this study. Differential scanning calorimetry can be used to measure thermal properties at both atmospheric and pressurized conditions (Sorai, 1998). The pressure was controlled by a gas pressure panel in which a piston can be used to charge the sample with gas at pressures ranging from 0.1 to 40 MPa at temperatures between 228 and 393 K. 2.2. Procedure/Materials The main focus of this work was hydrate nucleation using the temperature ramping mode. All temperature ramping experiments were performed by loading 40 mg of HPLC grade water (SigmaAldrich) in a hastelloy pressure cell; this cell was then purged and pressurized to a given pressure with the desired gas: methane (Airgas, UHP Grade) or xenon (Spectra Gases, UHP Grade). After pressurization, the system was allowed to equilibrate for 3 h at 313 K. The system was then cooled from 313 to 228 K at various rates between 0.5 and 3 K/min. The temperature was then increased back to 313 K and held for one hour to ensure complete hydrate

371

Table 1 Chemical composition of the West African crude oil.

C1 C2 C3 iC4 nC4 iC5 nC5 C6 C7 C8 C9 C10 C15 C22 C32 C47 CO2

Component

Dead oil composition (mol%)

Specific gravity

Methane Ethane Propane i-butane n-butane i-pentane n-pentane Hexanes Heptanes Octanes Nonanes Decanes Pentadecanes Decosanes

0.46 0.26 0.69 0.36 1.09 0.93 1.26 4.13 6.52 5.04 5.52 7.5 17.19 20.49 17.87 10.68 0.01

0.3772 0.5093 0.5628 0.584 0.6244 0.6311 0.664 0.7465 0.7682 0.8008 0.8038 0.8578 0.8978

Carbon dioxide

dissociation. These ramping cycles were repeated multiple times to determine both the hydrate and ice nucleation temperatures. The hold time at 313 K was imposed to ensure the elimination of any residual structuring of the water molecules or “memory effect” (Wilson et al., 2008), (Buchanan et al., 2005). In order to ensure that the memory effect had been eliminated by this heating step, multiple experiments were performed at temperatures between 303 and 313 K with hold times varying from 30 min to 2 h. No differences were observed in the nucleation tendencies of the samples during the subsequent cooling step. The isothermal experiments were all performed with a methane atmosphere and with either 175 mg of pure water or with 30 mg of a 30 vol% water-in-oil emulsion (West African crude). Following initial pressurization and equilibration of the sample at 303 K, the temperature of the cells was decreased to either 263 or 268 K. The sample was held at the given temperature for approximately 6 h. Upon hydrate formation, the sample was heated back up to dissociate the hydrate. The pure water samples were then held at 303 K for 2 h to ensure complete hydrate dissociation and to eliminate the “memory effect” as in the ramped experiments. The DSC pure water runs were repeated multiple times to observe the time dependence of hydrate nucleation. In the West African crude (WAC) oil experiments, new samples were prepared for each run. WAC is an asphaltenic crude oil with a density of 0.915 g/cm3 , an interfacial tension of 32.14 mN/m, and a viscosity of 0.247 Pa s at 293 K. The oil contains 9.36 wt% resins and 7.12 wt% asphaltenes (Lachance, 2008). The chemical composition of WAC is provided in Table 1. Water-in-oil emulsions were prepared by first heating the crude to 333 K for one hour to dissolve the waxes into the crude oil while shaking the crude intermittently to ensure homogeneity. The crude was then homogenized using a Virtis Cyclone2 homogenizer at 8000 rpm for 2.5 min. During the homogenization, distilled water was added drop wise to the crude oil during the first minute. The emulsion was subsequently allowed to age for one day after the homogenization before experiments were performed. The droplet size in the emulsion was found from microscopy under ambient conditions and confirmed by DSC by cooling the sample from 313 to 228 K under ambient pressure and recording the onset temperature of ice nucleation. The ice nucleation temperature has been shown to decrease as the droplet size distribution becomes , and a quantitative correlation has been established between nucleation temperature and droplet size (Clausse et al., 2005; Lachance, 2008). The mean droplet size in the WAC oil emulsion prepared for these experiments was found to be less than 10 m (Lachance,

372

Simon R. Davies et al. / Chemical Engineering Science 64 (2009) 370 -- 375

50 40

Ice Nucleation

Heat Flow (mW)

30 20 10 0 -10 -20

Water: WAC

Run 1 Run 2

-30

70:30 vol.

Run 3

-40

Ice Melting

-50 200

220

240

260

280

300

Temperature (K) Fig. 1. A microscopic image of the WAC oil emulsion (left) and determining the droplet size distribution of the emulsion from the thermograms (right).

250 200 Heat Flow (mW)

150 100 50

Cooling Ih

sI

0 sI

-50 -100

Ih Heating

-150 -200 230

250

270 290 Temperature (K)

310

330

Fig. 2. Thermogram for CH4 +H2 O at 20 MPa with a scanning rate of 0.5 K/min. Formation exotherms are marked for hydrate (sI) and ice (Ih) formation as well as the corresponding melting endotherms when heated.

2008). The original thermograms and microscope images are shown in Fig. 1. 2.3. Distinguishing hydrate formation from ice formation DSC thermograms were used to determine the time or temperature at which hydrate nucleated for the isothermal and temperature ramping experiments, respectively. As an example, Fig. 2 shows a thermogram for methane+water at 20 MPa ramped at 0.5 K/min. Upon cooling, two exothermic responses were measured indicating nucleation and growth of both hydrate and ice phases. These thermal responses are directly proportional to the heat of formation for a given phase change (ice: 334 J/gm-water, sI CH4 hydrate: 503 J/gmwater) and the mass of the phase formed (Handa, 1986). However, because of the required subcooling, both exotherms occurred at temperatures below 273 K. Therefore, further analysis was needed to determine which of the exotherms corresponded to hydrate and ice nucleation. Differentiating hydrate exotherms from ice exotherms is relatively straightforward. Hydrate formation from an immiscible guest requires contact between the water and the guest phase, in this case the vapor phase. A thin hydrate film typically forms at the interface (Mori and Mochizuki, 2005). However, water can convert entirely

to ice. Hence the ice phase fraction should be much greater than that of the hydrate when formed from a gas phase guest. Due to the similar latent heats of formation, the integrated area of the hydrate exotherm was therefore expected to be much smaller than that for the ice exotherm. The validity of this hypothesis was verified upon heating. While the nucleation temperature cannot be used to directly distinguish between ice and hydrate below 273 K, endotherms upon heating occur at a given temperature based on phase equilibria. It was then verified that the area of the endotherm peak is similar in magnitude to that of the assigned exotherm. As shown in Fig. 2, the exotherm and endotherm for the ice phase are approximately equal in area; the same is true for the hydrate phase peaks. This gave added confidence to assigning an exotherm for a given phase. 3. Results and discussion 3.1. Temperature ramping experiments A methane/water system and a xenon/water system were cooled using temperature ramping to determine the effect of the subcooling (Section 3.1.1) and cooling rate (Section 3.1.2) on the hydrate nucleation tendency: the temperature at which nucleation occurred and its repeatability. Temperature ramping experiments were performed at different subcoolings using pressures of 3.2, 10, 15, and 20 MPa with cooling rates of 0.5, 1.5, and 3.0 K/min. In the temperature ramping experiments, the nucleation temperature was determined by the temperature at which the heat flux initially increased from the baseline (See Fig. 2). 3.1.1. Effect of subcooling For the methane/water system, a pressure increase from 3.2 to 20 MPa changes the equilibrium temperature (Teq ) from 275 to 292 K, which is a significant change in the driving force. In these experiments, it was observed that for each pressure, hydrate nucleation always occurred below 273 K. Therefore, ice formation was also possible but was distinguished from hydrate nucleation as discussed in Section 2.3. For each pressure, the hydrate nucleated within approximately a 2 K range. An example of this is shown in Fig. 3 for methane at 20 MPa where nucleation is indicated by an exothermic response. The average nucleation temperature was determined at each pressure and is shown in Fig. 4. The error bars show the temperature range in which nucleation occurred for all of the experiments. The nucleation temperature for the ice phase is also shown. For

Simon R. Davies et al. / Chemical Engineering Science 64 (2009) 370 -- 375

100% Fraction of Samples Nucleated

20

Heat Flow (mW)

18 16 14 12

Run 1

Run 2

Run 3

Run 4

Run 5

Run 6

Run 7

Run 8

90% 80% 70% 60% 50% Pressure = 1.95 MPa; Ramp = 0.5 K/min

40% 30%

Pressure = 3.1 MPa; Ramp = 0.5 K/min

20%

Pressure = 3.1 MPa; Ramp = 1.5 K/min

10% 0%

10 258

260

262 Temperature (K)

263

264

Fig. 3. Thermogram of multiple hydrate formation runs using the ramped mode in the DSC with methane+water at 20 MPa.

25 16

20 Pressure (MPa)

373

16

3

15 10

29

5 0 251

29

30

253

1

255

30

257 259 261 Temperature (K)

Ice Hydrate

263

265

Fig. 4. Pressure–temperature plot showing the temperature range for hydrate and ice nucleation at various pressures. Numbers of experimental runs for each point are shown above symbol.

the 3.2 MPa (Teq = 275 K) and 10 MPa (Teq = 286 K) runs, ice always formed before the hydrate. The onset of hydrate nucleation of 254 ± 0.85 and 253 ± 0.67 K were not statistically different between the 3.2 and 10 MPa runs even with a change of over 10 K in the driving force. However, the effect of the ice on the tendency for hydrate nucleation is not known. It should be noted that ice formation always occurred in a range from 257 to 259 K regardless of pressure or the presence of hydrate. At 15 MPa (Teq = 289 K), either ice or hydrate formed first depending on the individual run. From the dissociation endotherms it appeared that in many cases hydrate had nucleated at the same time as ice but the hydrate nucleation peak was obscured by the ice exotherm. The results from experiments where both phases nucleated at the same temperature were omitted from this paper due to the difficulties in deconvoluting the results. In one experimental run, hydrate nucleation clearly occurred before ice nucleation at around 261 K with a driving force of 28 K. At 20 MPa (Teq = 292 K), hydrate always formed before ice at 260 ± 0.5 K. Interestingly, the change in driving force between 15 and 20 MPa roughly coincided with the change in hydrate nucleation temperature. To further investigate the effect of subcooling on hydrate nucleation, a xenon/water system was measured. Xenon is only 0.1 Å larger than methane, but it is a much more stable hydrate guest, resulting in lower formation pressures at a given temperature. Experiments were performed in the same manner as the methane system

265

267 269 Temperature (K)

271

273

Fig. 5. Fraction of samples in which hydrate nucleated as a function of pressure and scanning rate for xenon.

at pressures of 1.95 MPa (Teq = 298 K) and 3.1 MPa (Teq = 303 K). Fig. 5 shows the results of the temperature ramping for the two different pressures. The plots show the fraction of experiments in which hydrate nucleation occurred before a given temperature was reached, each point in the figure represents an independent experiment. For example at 3.1 MPa and a cooling rate of 0.5 K/min, the first experiment to nucleate was at 272 K, all 14 experiments had nucleated before 270 K. At 1.95 MPa, hydrate nucleated at 268 ± 0.7 K which corresponded to a temperature driving force of 30 K, very similar to the subcooling required for the methane/water system. Hydrate nucleation occurred at 270 ± 0.5 K for the 3.1 MPa runs, corresponding to a subcooling of 32 K. These temperature ramping results show that similar driving forces are needed to induce nucleation, without the presence of ice, for two different hydrate guests. While the effect of ice on hydrate nucleation is not known, these results indicate that when ice is not present, the hydrate nucleation temperature was a function of subcooling for various pressures. When ice nucleated first, large changes in subcooling had little effect on the hydrate nucleation temperature. It should be noted that the absolute driving force needed for hydrate nucleation is expected to be very system-dependent; recently published preliminary results for methane hydrate nucleation in a high pressure ALTA with 100 mg samples in borosilicate cells (Wilson and Haymet, 2008) showed that methane hydrate nucleation occurred with only 14 K of subcooling. The results from the ramped experiments revealed that the hydrate nucleation tendency had a marked dependence on pressure. At pressures above 15 MPa, hydrate nucleated before ice but below this pressure ice nucleated first. Furthermore, the hydrate nucleation temperature also dropped dramatically between 15 and 10 MPa. One explanation for this change in the nucleation temperature could be an increased activation energy barrier between ice and hydrate compared to water and hydrate under these conditions. The change in free energy between ice and hydrate was less than that between water and hydrate and this might lead to the higher energy barrier. 3.1.2. Effect of cooling rate For both systems (methane+water and xenon+water), various cooling rates were employed to determine the effect on the hydrate nucleation temperature. For the methane and water system three cooling rates were investigated: 0.5, 1.5 and 3 K/min; for the xenon and water system two cooling rates were investigated: 0.5 and 1.5 K/min. The fraction of samples that nucleated for various cooling rates in a methane system where ice formed first (3.2 MPa) is shown in

374

Simon R. Davies et al. / Chemical Engineering Science 64 (2009) 370 -- 375

100% 0.5 K/min

80%

1.5 K/min

70%

3 K/min

60% 50% 40% 30% 20% 10% 0% 252

253

254

255

256

257

90%

3.2 Mpa 0.5 K/min

80%

3.2 MPa 1.5 K/min

70%

3.2 Mpa 3 K/min

60%

10 Mpa 0.5 K/min 10 Mpa 1.5 K/min

50%

10 Mpa 3 K/min

40%

20 Mpa 0.5 K/min

30%

20 Mpa 1.5 K/min

20% 10% 0% 256

258

257

258

Fig. 6. Fraction of samples in which hydrate nucleated as a function of scanning rate for methane–water at 3.2 MPa.

260

261

262

40

310

90%

305

80%

30 Temperature

300 Temperature (K)

70% 60% 50% 40% 30% 20%

0.5 K/min

10%

1.5 K/min

0% 258

259

260

261

263

Fig. 8. Fraction of samples in which ice nucleated a function of scanning rate for methane–water at pressures of 3.2, 10 and 20 MPa.

100% Fraction of Samples Nucleated

259

Temperature (K)

Temperature (K)

262

The temperature ramping runs have shown that hydrate nucleation is essentially deterministic at a given pressure, within a narrow range of subcooling temperatures for a given experimental system; in all cases nucleation occurred with approximately 30 K of subcooling. However, in the case of isothermal experiments performed with slightly lower subcoolings (20–25 K), nucleation often took several hours to occur. The nucleation time is defined as the time for which the sample had been held at the isothermal temperature (See

Nucleation Time (hrs)

280

-10

275

-20

270

-30 -40 5

10 15 Time (hrs)

20

25

Fig. 9. Determining the nucleation time for an isothermal experiment at 268 K.

Fraction of Experiments Without Nucleation

3.2. Isothermal experiments

0

285

0

Temperature (K)

Fig. 6. Fig. 7 shows the fraction that nucleated in the case where hydrate formed first (20 MPa). In both cases, a 2.5 K/min change in cooling rate did not have a significant effect on the temperature range in which nucleation occurred. Fig. 5 shows two cooling rates for the xenon+water system at 3.1 MPa. As with the methane system, the nucleation point did not change significantly as the cooling rate was increased from 0.5 to 1.5 K/min. In addition to hydrate nucleation, ice formed during each run with the methane–water system as shown in Fig. 4. The onset point of ice nucleation as a function of temperature was measured for various pressures and cooling rates. At 3.2 and 10 MPa, ice formed before hydrate, whereas hydrate formed first at 20 MPa. The pressure, cooling rate, and presence of hydrate all had little effect on the onset of ice nucleation which occurred between 257 and 259 K in all cases as shown in Fig. 8.

10

290

265

263

Fig. 7. Fraction of samples in which hydrate nucleated as a function of scanning rate for methane-water at 20 MPa.

20

Heat Flow

295

Heat Flow (mW)

90%

Fraction of Samples Nucleated

Fraction of Samples Nucleated

100%

100% 90%

268 K Isotherm

80%

266 K Isotherm 263 K Isotherm

70% 60% 50% 40% 30% 20% 10% 0% 0

100

200 300 Time (min)

400

500

Fig. 10. Fraction of samples without hydrate nucleation at a 263, 266 and 268 K isotherm for methane hydrate at 15 MPa.

Fig. 9). The time distribution for hydrate nucleation became narrower as subcooling increased. Fig. 10 shows hydrate nucleation results at 15 MPa with 25 K subcooling (263 K isotherm), 22 K subcooling (266 K isotherm) and 20 K subcooling (268 K isotherm).

Fraction of Experiments Without Nucleation

Simon R. Davies et al. / Chemical Engineering Science 64 (2009) 370 -- 375

375

Acknowledgments

100% 90%

Pure Water System at 263 K Isotherm

80%

West African Crude Emulsion at 263 K Isotherm

The authors wish to acknowledge the financial support received from the CSM Hydrate Consortium of energy companies: BP, Champion, Chevron, ConocoPhillips, ExxonMobil, Halliburton, Petrobras, Schlumberger, Shell, and StatoilHydro. Funding from ACS Petroleum Research Fund is also acknowledged.

70% 60% 50%

References

40% 30% 20% 10% 0% 0

100

200

300

Time (min) Fig. 11. Fraction of samples without hydrate nucleation in a water-in-WAC oil emulsion at 263 K isotherm with methane at 15 MPa.

Increased subcooling led to a decrease in the mean nucleation time in these isothermal experiments. The mean nucleation time was found from the numerical average of all of the experiments that were performed at a given subcooling. At 25 K subcooling (263 K isotherm), hydrate nucleation occurred in the narrowest time range, from 0 to 200 min with a mean nucleation time of 8 min; most of the runs nucleated within 30 min. At 22 K subcooling (266 K isotherm), hydrate nucleation occurred in the range from 0 to 760 min with a mean nucleation time of 85 min. At a subcooling of 20 K (268 K isotherm) the hydrate nucleation occurred over a wider time range, from 0 to 1200 min with a mean of 161 min. To test a more industrially realistic system, the 263 K isothermal experiment was also performed with an emulsified system of water-in-WAC with 30 wt% water cut. Fig. 11 shows that most of the experiments nucleated within 20 min. The overall time frame in the emulsified system increased slightly to 0–250 min compared to the pure water system (0–200 min) but was broadly similar. In the isothermal experiments, the time distribution of hydrate nucleation became narrower at higher subcoolings. This might correspond to the reduced height of the energy barrier and the reduced radius of the critical nucleus as the subcooling is increased and the difference in free energy between the parent and daughter phases increases. 4. Conclusions While hydrate nucleation is a stochastic process, the probability of nucleation increases from almost zero to close to 100% within a narrow band of subcooling of a few degrees. The subcooling associated with this increased nucleation tendency was approximately 30 K for both methane and xenon systems. Different cooling rates between 0.5 and 3 K/min did not have a significant effect on the onset of nucleation. Ice nucleation occurred within the same 2 K range, regardless of the pressure and cooling rate in the conditions investigated. The probability of nucleation determined in this study is likely affected by the walls of the DSC cell and by the presence of any impurities within the system. In industrial systems the concentration of impurities would be much higher than in these experiments so the probability of heterogeneous nucleation would be increased. In addition, the propagation of nucleation between emulsified droplets via secondary nucleation would be significantly enhanced by shear in a flowing system. Further experimental investigation is required in order to develop realistic probabilistic distributions for nucleation events in industrial systems.

¨ Becker, D., Doring, W., 1935. The kinetic treatment of nuclear formation in supersaturated vapors. Annalen der Physik 24, 719–752. Buchanan, P., Soper, A.K., Thompson, H., Westacott, R.E., Creek, J.L., Hobson, G., Koh, C.A., 2005. Search for memory effects in methane hydrate: structure of water before hydrate formation and after hydrate decomposition. Journal of Chemical Physics 123 (16), 164507. Christiansen, R.L., Bansal, V., Sloan, E.D., 1994. Avoiding hydrates in the petroleum industry: kinetics of formation. University of Tulsa Centennial Petroleum Engineering Symposium, 29–31 August 1994, SPE 27994, pp. 383–393. Clausse, D., Gomez, F., Dalmazzone, C., Noik, C., 2005. A method for the characterization of emulsions, thermogranulometry: application to water-incrude oil emulsion. Journal of Colloid and Interface Science 287, 694–703. Dalmazzone, D., Hamed, N., Dalmazzone, C., Rousseau, L., 2006. Application of high pressure DSC to the kinetics of formation of methane hydrate in water-in-oil emulsion. Journal of Thermal Analysis and Calorimetry 85 (2), 361–368. Englezos, P., Kalogerakis, N., Dholabhai, P.D., Bishnoi, P.R., 1987. Kinetics of formation of methane and ethane gas hydrates. Chemical Engineering Science 42 (11), 2647–2658. Hammerschmidt, E.G., 1934. Formation of gas hydrates in natural gas transmission lines. Industrial and Engineering Chemistry 26, 851. Handa, Y.P., 1986. Compositions, enthalpies of dissociation, and heat capacities in the range 85–270 K for clathrate hydrates of methane, ethane, propane, and enthalpy of dissociation of isobutane hydrate, as determined by a heat-flow calorimeter. Journal of Chemical Thermodynamics 18, 915–921. Heneghan, A.F., Wilson, P.W., Wang, G., Haymet, A.D.J., 2001. Liquid to crystal nucleation: automated lag time apparatus to study supercooled liquids. Journal of Chemical Physics 115 (16), 7599–7607. Kashchiev, D., 2000. Nucleation: Basic Theory with Applications. ButterworthHeinemann, Lachance, J., 2008. Investigation of gas hydrates using differential scanning calorimetry with water-in-oil emulsions. Masters Thesis, Colorado School of Mines. Maini, B.B., Bishnoi, P.R., 1981. Experimental investigation of hydrate formation behaviour of a natural gas bubble in a simulated deep sea environment. Chemical Engineering Science 36, 183–189. Mori, Y., Mochizuki, T., 2005. Clathrate-hydrate film growth along water/hydrateformer phase boundaries—a conductive heat transfer model. In: Proceedings of the Fifth International Conference on Gas Hydrates, vol. 1009, Trondheim, Norway, pp. 64–74. Ohno, H., Lipenkov, V.Y., Hondoh, T., 2004. Air bubble to clathrate hydrate transformation polar ice sheets: a reconsideration based on the new data from dome Fuji ice core. Geophysical Research Letters 31, L21401. Radhakrishnan, R., Trout, B.L., 2002. A new approach for studying nucleation phenomena using molecular simulations: application to CO2 hydrate clathrates. Journal of Chemical Physics 117 (4), 1786–1796. Salamantin, A.N., Hondoh, T., Uchida, T., Lipenkov, V.Y., 1998. Post-nucleation conversion of an air bubble to clathrate air-hydrate crystal in ice. Journal of Crystal Growth 193, 197–218. Salamantin, A.N., Lipenkov, V.Y., Ikeda-Fukazawa, T., Hondoh, T., 2001. Kinetics of air-hydrate nucleation in polar ice sheets. Journal of Crystal Growth 223, 285–305. Shimanda, W., Hondoh, T., 2004. In situ observation of the transformation from air bubbles to air clathrate hydrate crystals using a Mizuho ice core. Journal of Crystal Growth 265, 309–317. Sloan, E.D., Fleyfel, F., 1991. A molecular mechanism for gas hydrate nucleation from ice. A.I.Ch.E. Journal 37 (9), 1281–1291. Sloan, E.D., Koh, C.A., 2008. Clathrate hydrates of natural gasses. third ed. CRC Press, Taylor and Francis Group, Boca Raton. 712pp. Sorai, 1998. Comprehensive Handbook of Calorimetry and Thermal Analysis. Maruzen Company Limited, ¨ Volmer, M., Weber, A., 1926. Keimbildung in Ubers¨ attigten Gebilden. Zeitschrift Fur Physikalische Chemie—International Journal of Research in Physical Chemistry & Chemical Physics 119, 277–301. Wilson, P.W., Haymet, A.D.J., 2008. Heterogeneous nucleation of clathrates from supercooled THF/Water Mixtures and the Effect of an Added Catalyst. In: Proceedings of the Sixth International Conference on Gas Hydrates, July 6–10, Vancouver, Canada. Wilson, P.W., Lester, D., Haymet, A.D.J., 2005. Heterogeneous nucleation of clathrates from supercooled tetrahydrofuran (THF)/water mixtures and the effect of an added catalyst. Chemical Engineering Science 60, 2937–2941. Wilson, P.W., Haymet, A.D.J., Kozielski, K.A., Hartley, P., Becker, N.C., 2008. Nucleation of clathrates from supercooled THF/water mixtures shows that no memory effect exists. In: Proceedings of the Sixth International Conference on Gas Hydrates, July 6–10, Vancouver, Canada.