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Dec 11, 2014 - ABSTRACT: We systematically studied the formation probability distributions of methane−propane (C1/C3) mixed gas hydrates on a quasi-...
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Fuel Gas Hydrate Formation Probability Distributions on Quasi-free Water Droplets Nobuo Maeda* Materials Science & Engineering, Commonwealth Scientific and Industrial Research Organisation (CSIRO), Ian Wark Laboratory, Bayview Avenue, Clayton, Victoria 3168, Australia ABSTRACT: We systematically studied the formation probability distributions of methane−propane (C1/C3) mixed gas hydrates on a quasi-free water droplet as a function of the mixed gas pressure of up to 14 MPa. It was found that the maximum achievable subcooling temperature (ΔT) distributions of C1/C3 mixed gas hydrates on a quasi-free water droplet were significantly greater than those on a water sample contained in a glass sample cell, for all of the mixed gas pressures studied. The most probable subcooling was on average around 31 K on quasi-free water droplets, which was significantly greater than that on the water sample in a glass sample cell of around 14 K. The minimum subcooling was around 18 K on a quasi-free water droplet, which was significantly greater than that on a water sample in a glass sample cell of 4 K. The width of the Tf distribution showed a wide variation, from 6 to 22 K. This range of variation was similar to that of a water sample contained in a glass sample cell. We also carried out a series of control experiments using nitrogen gas at elevated gas pressures to decouple the C1/C3 mixed gas hydrate formation events from the ice formation events. Finally, the effect of ethanol vapor, a thermodynamic hydrate inhibitor (THI), which had been reported to enhance the rate of methane hydrate growth when seeded with ice, was also studied. The results showed that ethanol vapor reliably inhibited nucleation of C1/C3 mixed gas hydrate at all gas pressures studied.

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linearly increases with increasing subcoolings.12 The use of linear cooling ramps thus effectively compresses the induction time distributions at constant subcoolings to more compact maximum achievable subcooling temperature distributions. In an earlier version of the HP-ALTA (which we refer to as MkI hereafter), sample water is contained in a glass sample cell (also known as a “boat”). 10 As a consequence, the experimentally measured hydrate formation temperature (Tf) distributions are functions of not only the usual physical parameters, such as gas pressures, but also the heterogeneous nucleation properties of the walls that contain the sample. In the second-generation HP-ALTA (which we refer to as MkII hereafter), a sample water droplet sits on a hydrophobic fluorocarbon liquid.13 In MkII, the formation of ice or gas hydrates still occurs via heterogeneous nucleation. The probability of heterogeneous nucleation is proportional to the interfacial area. This is in contrast to the probability of homogeneous nucleation which is proportional to the volume. Then the experimentally measured Tf distributions should still depend upon the interfacial area of the water droplet. The difference in the Tf distributions measured by the two versions of HP-ALTA is thus attributable to the heterogeneous nucleation properties of glass and hydrophobic fluorocarbon liquid. HP-ALTA MkI has been applied for the study of the effect of guest gas pressures, cooling rate, and gas compositions.14 The instrument has also been used for the relative efficacy ranking of thermodynamic hydrate inhibitors (THIs)15 and kinetic

INTRODUCTION Gas hydrates are clathrate compounds in which a hydrogenbonded network of water molecules encloses guest molecules, such as methane and carbon dioxide.1 The formation of gas hydrates is desirable for some applications, such as gas storage2 and desalination of water,3 while it is undesirable in other applications, such as multiphase pipeline transport of hydrocarbons in natural gas pipelines.1,2 In either case, a formation probability distribution of gas hydrates is a central quantity that characterizes the likelihood of such events. From a physical point of view, formation probability distributions should take the form of distributions of nucleation rates.4 The inverse of the nucleation rate or induction time at a constant subcooling (driving force) can be experimentally measured.5,6 However, measurements of induction times are time-consuming, and distributions of induction times from repeated measurements are usually highly stochastic. Zeng et al. studied the formation of propane and methane hydrates with the use of high-pressure nuclear magnetic resonance (NMR).7 In this study, the number of the samples was not reported but, from their figure, appears to be about 10. Davies et al.8 and Ohno et al.9 used high-pressure differential scanning calorimetry (HP-DSC) for the study of statistical hydrate formation data with cooling ramps. In either case, the number of repeat runs or samples was limited to about 30, presumably because of the time-consuming nature of the measurements. A high-pressure automated lag time apparatus (HP-ALTA) is an instrument that is designed to measure gas hydrate formation probability distributions at elevated gas pressures.10 Because measurements of induction times are experimentally time-consuming and challenging, we typically use HP-ALTA to measure the maximum achievable subcooling temperature (ΔT) distributions in lieu of induction time distributions or nucleation rate distributions.11 The driving force for nucleation © 2014 American Chemical Society

Received: October 20, 2014 Revised: November 26, 2014 Published: December 11, 2014 137

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hydrate inhibitors (KHIs),16 and quantification of the so-called memory effect.16 The more recently developed MkII, on the other hand, is yet to be applied to any of such investigations. The use of MkII provides an estimate on the importance of the glass walls in the heterogeneous nucleation of natural gas hydrates. In this paper, we report measurements of gas hydrate formation probability distributions in the form of maximum achievable subcooling temperature (ΔT) distributions as a function of a model natural gas pressure. In addition, we measured the effect of saturated ethanol vapor on the system, which was reported to enhance the rate of methane hydrate formation when seeded with ice.17 We also measured Tf distributions of ice formation in a nitrogen atmosphere at comparable pressures for control purposes.

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the path of a light beam. The support block had a through hole of 5 mm diameter at the center, which allowed light to pass. A photodiode detector positioned above the top window measured the intensity of the transmittance beam. The MkII chamber was connected to a high-pressure gas line via a Swagelok connection and pressurized using a pneumatically driven gas booster pump (Haskel Australasia Pty Ltd, Queensland, Australia, model number AG-62). The maximum experimental pressure was limited to 15 MPa by the pressure rating of the sodalime glass windows (NAR Engineering, Leeming, Western Australia, Australia). The actual gas pressure was measured and monitored using a capacitance-diaphragm-type pressure transducer (model A-10, WIKA). The heating and cooling of the sample were achieved using two Peltier devices (Peltier-CP1.4-127-06L-RTV, Melcor). A pair of heat sinks absorbed excess heat generated by the Peltier devices, which is then dissipated by a refrigerated bath (model WCR-P12, All-Lab Scientific). The system temperature, which was measured using a resistance thermometer (PT100 HEL705, Honeywell) at a reference point located about 5 mm away from the sample in the MkII chamber, was recorded by a personal computer (PC). The measured temperature was then related to the sample temperature using a precalibrated table. The calibration table, which relates the thermometer reading to the actual sample temperature inside the MkII chamber, was derived from control experiments using a thermometer immersed in ethanol in the sample cell within the MkII sample chamber (but not under pressure). A window heater (K005020C5-0009B, Watlow Australia, Victoria, Australia) was placed around each high-pressure window to prevent condensation of sample water, especially during the dissociation cycle. The cooling rate used in HP-ALTA MkII was 0.01 K/s for all of the results shown below. We note at this stage that we had previously used HP-ALTA MkI to study the effect of the cooling rate on Tf between 0.01 and 0.075 K/s and found that the results were very insensitive to the cooling rate in the range accessible to the instrument.14 Solid formation in the sample caused scattering of the light beam and resulted in a sudden drop in transmittance (similar to that shown in Figure 2 of ref19). The time and temperature at which this event occurred were recorded by a PC and marked the end of an experimental run. At the end of each run, the sample was heated to a pre-specified temperature (310 K for the experiments in methane− propane mixed gas and 280 K for the experiments in nitrogen gas) for a pre-specified time (200 s in this study) before the next cooling cycle commenced. The superheating temperature was chosen to avoid the so-called memory effect.1 The temperature at which solid formation was detected in each run is denoted as Tf, and the thermodynamic hydrate equilibrium dissociation temperature is denoted as Teq, which was calculated using CSMGem.1 The relationship between ΔT, Teq and Tf are ΔT ≡ Teq − Tf. The methane−propane (C1/C3) mixed gas had the composition of 90 mol % methane and 10 mol % propane and forms structure II (sII) gas hydrates. The gas was obtained from BOC Limited. For the experiments with ethanol vapor, a small amount (about 1 mL) of ethanol was introduced onto the bottom window before the sample cell was put in place. The system was sealed; therefore, ethanol vapor gradually saturated the space above it. We allowed 30 min for ethanol evaporation prior to the commencement of the first cooling ramp experiment.

MATERIALS AND METHODS

The details of the HP-ALTA MkII is described in our earlier publication.10 Figure 1 shows the schematic illustration of HP-ALTA

Figure 1. Schematic illustration of HP-ALTA MkII. MkII. Briefly, the HP-ALTA MkII chamber is made of stainless steel, and its dimensions are 40 × 30 × 45 mm. In comparison to MkI (50 × 50 × 20 mm), the heat capacity is similar but the thickness of the thinnest dimension is greater, to accommodate for the flat-bottom glass sample cell that is used in MkII. This factor restricts the maximum cooling rate achievable within the cooling power of the Peltier devices to a smaller value compared to MkI. The glass flatbottom sample cell has dimensions of 9 mm outer diameter, about 6.8 mm inner diameter, and about 15 mm height. The cell can contain up to 500 μL of liquid, in contrast to a glass “boat” used in MkI, which can only contain up to 150 μL. The cell wall was coated with 1H,1H,2H,2H-perfluorodecyltriethoxysilane (PFDTES; 97%, Sigma-Aldrich). The details are documented in our earlier publication,10 which basically followed the protocol described by Choi et al.18 Perfluorooctane (98%, Sigma-Aldrich) was placed at the bottom of the PFDTES-coated container. Because perfluorodecalin wets PFDTES, a meniscus formed around the inner wall of the container, rendering the surface of the perfluorodecalin at the center of the cell the lowest point (gravity wise). A water droplet (deionized water from a Milli-Q unit with 18.2 MΩ resistivity) was placed on top of perfluorodecalin at the center of the cell. We note that the contact angle of water on PFDTES was about 100°, whereas the contact angle of perfluorodecalin on PFTDES was very small, with cos θ close to 1. It is likely that a thin film of perfluorocarbon oil separates the water droplet and PFTDES. However, we cannot rule out the possibility that the PFDTES coating had some defects, and consequently, the water droplet may come into contact with the solid wall. For operation, the sample cell was placed in the MkII chamber above the bottom window on a support block made of Teflon and in

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RESULTS AND DISCUSSION Figure 2 shows typical chronological histograms (“Manhattan plots”) and the corresponding survival curves (“S curves”) of C1/C3 mixed gas hydrate or ice formation. This particular data example was collected under 8.2 MPa of C1/C3 mixed gas. The subcooling here was calculated from Teq of C1/C3 mixed gas hydrate at 8.2 MPa. Because Tf below 273 K could result from the formation of C1/C3 mixed gas hydrate or ice, we carried out a series of control experiments using nitrogen gas. Nitrogen gas hydrate 138

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shows typical chronological histograms and the corresponding survival curves of ice formation under 8.0 MPa of nitrogen gas. It is important to note that the subcooling here was measured from Teq of ice. Figure 4 shows typical chronological histograms and the corresponding survival curves of C1/C3 mixed gas hydrate or

Figure 2. Typical (a) chronological histograms (“Manhattans”) and (b) survival curves (“S curves”) of C1/C3 mixed gas hydrate or ice formation under 8.2 MPa of C1/C3 mixed gas. The subcooling here is measured from Teq of C1/C3 mixed gas hydrate.

cannot form above 253 K at 9 MPa;20 therefore, any Tf above that temperature must be a result of ice formation. Figure 3

Figure 4. Typical (a) chronological histograms (“Manhattans”) and (b) survival curves (“S curves”) of C1/C3 mixed gas hydrate or ice formation in saturated ethanol vapor under 7.5 MPa of C1/C3 mixed gas. The subcooling here is measured from Teq of C1/C3 mixed gas hydrate.

ice formation in saturated ethanol vapor under 7.5 MPa of C1/ C3 mixed gas. The subcooling here was measured from Teq of C1/C3 mixed gas hydrate. We note that the survival curves for ice in a nitrogen atmosphere were sharp. In contrast, the survival curves for C1/ C3 mixed gas hydrate formation were significantly broader. In particular, the higher end of a Tf distribution (where the subcooling was shallow) often had a scarcely populated “tail” (see Figure 2), whereas the lower end (where the subcooling was deep) was usually sharper. This apparent asymmetry is presumably due to the onset of the ice cutoff. A bimodal stepwise distribution, which we reported earlier,14 with one mode most likely corresponding to C1/C3 mixed gas hydrate formation and the other corresponding to ice formation, was also occasionally observed. In Figure 5, we show all of the data measured over a range of gas pressures. The gas pressure refers to C1/C3 mixed gas pressure (black and red) or nitrogen gas pressure (blue). Instead of presenting the results in terms of subcooling for which ice and C1/C3 mixed gas hydrate have different reference points, here, we show the results in terms of absolute Tf. The thermodynamic phase boundary (Teq) for pure water−C1/C3 mixed gas hydrate is also shown as a solid curve. The results are shown in the form of the most probable Tf16 and the stochasticity (i.e., the whole range of Tf distribution).14

Figure 3. Typical (a) chronological histograms (“Manhattans”) and (b) survival curves (“S curves”) of ice formation under 8.0 MPa of nitrogen gas. The subcooling here is measured from Teq of ice. 139

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The Tf probability distribution in C1/C3 mixed gas at elevated pressures extended to below 273 K; however, the distribution width of ice in nitrogen gas was narrow, and Tf for ice was lower than the vast majority of the measured Tf distributions in C1/C3 mixed gas. Therefore, the vast majority of the measured Tf distribution in C1/C3 mixed gas at elevated pressures must be that of C1/C3 mixed gas hydrates. We note, at this stage, that a slight negative bias was observed in Tf for ice with increasing gas pressures, as expected, reflecting the negative slope of the ice phase boundary with pressure. We note that the Tf distribution for methane gas hydrate was much lower than that for C1/C3 mixed gas hydrates. It could not be measured on quasi-free water droplets within the experimentally accessible pressure range, because of the limited cooling ability of the Peltier modules and the ice cutoff. Figure 5 also shows that the width of the Tf distribution (the length of the stochasticity bar) varied significantly. It can be seen that the distribution width ranged from around 6 to 22 K. In our recent study,15 we observed that the width of the Tf distribution of water in the presence of glass walls varied substantially (from about 10 to 30 K but typically around 25− 30 K) and that the width of the Tf distribution of water in the presence of glass walls and silver iodide (AgI; a well-known nucleation agent for ice that is used for cloud seeding) varied from around 10 to 20 K. For that particular study, we concluded that the presence of AgI rendered the heterogeneous nucleation properties of C1/C3 mixed gas hydrates more deterministic. Now, in light of the present results, it might appear that perfluorodecalin had also made the heterogeneous nucleation of C1/C3 mixed gas hydrates more deterministic. However, this is not the case. The greatly increased maximum achievable subcoolings on perfluorodecalin shifted the Tf distribution much closer to the ice cutoff and truncated the distribution width. Likewise, the apparently narrow distribution of Tf values with ethanol vapor is most likely due to ice formation or the 6000 s cutoff that we used for the cooling ramps and does not necessarily reflect the reduced stochasticity of the system. The interesting result is that, unlike the heterogeneous nucleation properties of C1/C3 mixed gas hydrate, the heterogeneous nucleation properties of ice hardly depended upon the presence of glass walls or perfluorodecalin. We previously measured the Tf distribution in nitrogen gas in HPALTA MkI (i.e., in a glass sample cell) and found it in the range of 263.9−267.3 K at 7.3 MPa.16 This value is only 5−7 K higher than the Tf distribution on quasi-free water droplets in HP-ALTA MkII (the blue data points in Figure 5) or about one-third of the difference observed for C1/C3 mixed gas hydrate formation. It is almost inconceivable that the observed ice formation here resulted from homogeneous nucleation. We note that the spinodal for supercooled water below which homogeneous nucleation of ice becomes labile is around −42 °C or 231 K.15 Then, our result raises the question as to why the glass walls, which were apparently effective in promoting the heterogeneous nucleation of C1/C3 mixed gas hydrates, failed to do the same to the heterogeneous nucleation of ice. It is possible that the observed difference is due to the difference in the nature of the two-phase transitions, in which ice formation is a bulk phase transition but gas hydrate formation is an interfacial phenomenon. Figure 5 further shows the Tf distribution of C1/C3 mixed gas hydrates in saturated ethanol vapor. Ethanol is fully miscible

Figure 5. Experimentally measured Tf probability distributions of C1/ C3 mixed gas hydrate formation (black), ice formation in nitrogen gas (blue), and C1/C3 mixed gas hydrate or ice formation in saturated ethanol vapor in C1/C3 mixed gas (red). The gas pressure refers to C1/C3 mixed gas pressure for the black and the blue symbols and nitrogen gas pressure for the red symbols. The thermodynamic phase boundary (Teq) for pure water−C1/C3 mixed gas hydrate is also shown as a solid curve.

The most probable Tf was calculated by integrating the area enclosed by a cumulative probability distribution function (CPDF) or a S curve and the three axis boundaries of a graph, such as Figures 2b, 3b, 4b.16 We note that the number of data points on either side of a median is the same, and hence, the length of a stochasticity bar is inversely proportional to the number density of the data points.14 The same cannot be said for the most probable Tf; however, the most probable Tf and the median were close to each other for each Tf distribution. Importantly, the “stochasticity bars” shown in Figure 5 must not be confused with the traditional error bars that show the middle 68% of the range of ubiquitous random errors. The stochasticity bars contain both the random errors as well as genuine “stochasticity” that is inherent in the heterogeneous nucleation of gas hydrates. There is no a priori method to decouple the genuine stochasticity from the ubiquitous random error with certainty. However, our past studies offer a reasonable hypothesis that the random errors in a gas hydrate formation probability distribution are 2−3 K, whereas any scatter that exceeds this 2−3 K range is attributable to genuine stochasticity, which is system-dependent.14,15 We note that we had to set the maximum run time for each cooling ramp to 6000 s. The cooling power of our Peltier device was limited and struggled to reach below 250 K. Many of the cooling ramps in the presence of ethanol vapor reached this limit without the formation of ice or gas hydrates. For these runs, we show the temperature at the time of 6000 s in Figure 5. These data points in effect represent upper bounds for the real Tf values in these runs. Figure 5 shows that the Tf probability distributions of C1/C3 mixed gas hydrates on quasi-free water droplets were significantly lower than those on water in a glass boat,14 for all gas pressures studied. The median subcooling was on average around 31 K for quasi-free water droplets, which was significantly greater than that for the water sample in a glass sample cell (“boat”) of on average about 14 K.14 Likewise, the minimum subcooling was on average around 18 K for quasi-free water droplets, which was significantly greater than that for the water sample in a glass sample cell of on average about 4 K.14 We hypothesize that glass walls offer significantly more potent heterogeneous nucleation sites than perfluorodecalin. 140

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points). We may thus conclude that ethanol vapor reliably (without exception in >100 trials at each model natural gas pressure) inhibits nucleation of both natural gas hydrate and ice.

with water; therefore, ethanol vapor will condense onto water with time. The reduced chemical potential of ethanol solution compared to pure ethanol (because of the entropy of mixing) will eventually transport all of the (initially introduced) pure ethanol to the sample and form ethanol−aqueous solution. Then, the composition of the sample will keep changing during the course of the experiment, with the ethanol concentration increasing all the time. Consequently, the saturated vapor pressure of ethanol will also shift from that above pure ethanol to that above the ethanol−aqueous solution. Unfortunately, we could not confirm the presence of excess pure ethanol at the bottom of the HP-ALTA MkII chamber at the end of each experiment because the depressurization process prior to the opening of the chamber caused mixing of the fluids inside the chamber. Ethanol is a thermodynamic hydrate inhibitor (THI), which inhibits gas hydrate formation by lowering the activity of water in the surrounding liquid phase. Figure 5 shows a significant inhibition effect of ethanol vapor, and no hint of enhanced hydrate formation could be observed. This result may appear in contrast to an earlier report by Chen et al., who reported enhanced methane hydrate formation when seeded with ice.17 There are a few clear possibilities that can account for the observed difference. First and foremost, Chen et al. seeded the methane hydrate growth with ice (an excellent nucleation site for gas hydrates); thus, there was no nucleation barrier.17 In contrast, HP-ALTA measured combined effects of nucleation and growth. In fact, it has been hypothesized that the typically deep subcoolings that are required for nucleation of gas hydrates would lead to rapid growth of gas hydrate films once the nucleation barrier is surmounted, because of the large driving forces at deep subcoolings.10,14 This is not necessarily the case in the presence of a kinetic hydrate inhibitor (KHI), which is known to slow the growth rate. However, in the absence of a KHI, we established that the systematic error in Tf that could arise from this effect is at most 1 K for MkI.10,14 For MkII, which uses even slower cooling rates than MkI, the growth rate of gas hydrate films and the size of the sample cell in a HP-ALTA are such that any lag between the nucleation and detection because of the finite growth rates of gas hydrate films would be negligible. This small difference means that any accelerated growth rates of gas hydrates because of ethanol vapor reported by Chen et al. would not be visible in the HP-ALTA data. These results underscore the point that the Tf distributions measured by HP-ALTA must be close to nucleation probability distributions, as opposed to growth rate distributions. Another possibility is that methane hydrate studied by Chen et al. forms structure I (sI) hydrate, whereas C1/C3 mixed gas hydrate forms sII hydrate.1 A number of important differences exist between the sI and sII hydrates in the kinetics of formation and dissociation. Probably the most notable difference is that the self-preservation has been observed for sI hydrates but not for sII hydrates.1,21−24 We note that our results using methane and our earlier results on methane hydrate formation using HP-ALTA MkI both showed that the highly symmetrical sI-forming methane hydrate required much greater subcoolings than the less symmetrical sII-forming C1/ C3 mixed gas hydrate. Figure 5 also shows that the Tf distribution of ice in the absence of ethanol vapor (the blue data points) appears at a substantially higher temperature than the Tf distribution of ice or C1/C3 mixed gas hydrate in ethanol vapor (the red data

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CONCLUSION AND FUTURE WORK We systematically studied the formation probability distributions of methane−propane (C1/C3) mixed gas hydrates on a quasi-free water droplet as a function of the mixed gas pressure of up to 14 MPa. It was found that the maximum achievable hydrate formation temperature (Tf) distributions of C1/C3 mixed gas hydrates on a quasi-free water droplet were significantly lower than those on a water sample contained in a glass sample cell, for all of the mixed gas pressures studied. The most probable subcooling was on average around 31 K on quasi-free water droplets, which was significantly greater than that on the water sample in a glass sample cell of around 14 K. The minimum subcooling was around 18 K on a quasifree water droplet, which was significantly greater than that on a water sample in a glass sample cell of 4 K. The width of the Tf distribution showed a wide variation, from 6 to 22 K. HP-ALTA is a laboratory-scale test instrument. It remains to be seen as to how the results obtained using a HP-ALTA can be transferred to real industrial scales. Homogeneous nucleation probability is proportional to volume, while heterogeneous nucleation probability is proportional to the interfacial area. The heterogeneous nucleation probability distributions measured by HP-ALTA may offer a basis for scale up. The size of the water droplet in HP-ALTA MkII is of the order of 10 μL. If we ignore gravity and assume a spherical shape of the droplet, the radius of such a droplet is of the order of 1.5 mm and its surface area is of the order of 30 mm2. The sample will slowly evaporate during the course of the measurements; therefore, this estimate provides an upper bound. We may be able to convert the maximum achievable subcooling distributions to induction time distributions at constant subcoolings and then invert the induction time distributions to nucleation rate distributions, to calculate the nucleation rate per unit surface area. We had previously derived an empirical equation that enables such conversion for water in a glass sample cell using HP-ALTA MkI.11 We still need to derive a similar empirical equation for a quasi-free water droplet using MkII. We will leave this for future study.

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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 This work was supported by the Australian Research Council Future Fellowship (FT0991892) and CSIRO’s Energy Flagship.

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REFERENCES

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