Catastrophic Growth of Gas Hydrates in the Presence of Kinetic

Article pubs.acs.org/JPCA

Catastrophic Growth of Gas Hydrates in the Presence of Kinetic Hydrate Inhibitors Minjun Cha Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Republic of Korea

Kyuchul Shin and Yutaek Seo* Ocean Systems Engineering Division, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Republic of Korea

Ju-Young Shin Department of Chemical Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 133-791, Republic of Korea

Seong-Pil Kang Climate Change Research Division, Korea Institute of Energy Research, 152 Gajeong-ro, Yuseong-gu, Daejeon 305-343, Republic of Korea ABSTRACT: The effect of the concentration of kinetic hydrate inhibitors, polyvinylpyrrolidone (PVP), and polyvinylcaprolactam (PVCap) on the onset and growth of synthetic natural gas hydrates is investigated by measuring the hydrate onset time and gas consumption rate. Although the hydrate onset time is extended by increasing the concentration from 0.5 to 3.0 wt % for both PVP and PVCap, the growth rate of hydrates shows that the different tendency depends on the type of kinetic hydrate inhibitor and its concentration. For PVCap solution, the hydrate growth was slow for more than 1000 min after the onset at the concentration of 0.5 and 1.5 wt %. However, the growth rate becames almost 8 times faster at the concentration of 3.0 wt %, representing the catastrophic growth of hydrate just after the hydrate onset. 13C NMR spectra of hydrates formed at 3.0 wt % of PVP and PVCap indicate the existence of both structures I and II. Cage occupancy of methane in large cages of structure II decreases significantly when compared to that for pure water. These results suggest that increasing the concentration of KHI up to 3.0 wt % may induce the earlier appearance of catastrophic hydrate growth and the existence of metastable structure I; thus, there needs to be an upper limit for using KHI to manage the formation of gas hydrates.

1. INTRODUCTION Gas hydrates are nonstoichiometric crystalline compounds that are classified into three structural families of cubic structure I (sI), cubic structure II (sII), and hexagonal structure H (sH).1 The studies of gas hydrates have attracted attention because of their great potential as a source for methane gas deposited in the marine sediment and the permafrost region.1−4 Other studies have been focusing on the efficient way for gas storage5−7 or separation8,9 using the selective enclathration of gas molecules under specific conditions. Gas hydrates have been a particular concern of the oil and gas industry as the operating conditions of offshore flowlines may be favorable for the formation of gas hydrate that results in the blockage of offshore flowlines.10−13 Therefore, offshore flowlines trans© 2013 American Chemical Society

porting hydrocarbons have to be operated very carefully to avoid the formation of gas hydrates. One issue that has been discussed within the hydrate research community is the best way to prevent hydrate formation in the offshore flowlines. Understanding hydrate equilibrium thermodynamics of natural gases in the presence of alcohol or glycol solutions has been central to the complete avoidance of hydrate formation in offshore flowlines.14,15 Although extensive efforts have been carried out to develop a thermodynamic model1,16,17 and to analyze structural characterReceived: August 20, 2013 Revised: November 28, 2013 Published: December 2, 2013 13988

dx.doi.org/10.1021/jp408346z | J. Phys. Chem. A 2013, 117, 13988−13995

The Journal of Physical Chemistry A

Article

istics of gas hydrates,18−20 there have been fewer advances in understanding the kinetics of hydrate formation due to the stochastic nature of hydrate kinetics.10 Hydrate prevention strategies are now moving toward hydrate risk management, which allows hydrates to form but delays the formation significantly or prevent the complete hydrate blockage. Understanding of time-dependent variation of hydrate formation, structures, and compositions is essential for the successful development of hydrate management, which will be also transferred to the technologies of gas storage and separation using gas hydrates.21,22 In the last 2 decades, many researchers developed watersoluble polymers that are able to delay the formation of hydrate crystals. These polymers are termed kinetic hydrate inhibitors (KHIs)23 and include homo- and copolymers of the N-vinyl pyrrolidone (PVP) and N-vinyl caprolactam (PVCap). To date, many chemical compounds such as anti freeze protein (AFP)based polymers24,25 and polyaspartamides26 have been tested for their ability to delay hydrate onset by measuring the hydrate induction time in autoclave cells and flow loops.27 Spectroscopic studies using 13C NMR and in situ Raman reported complicated interactions between KHI, water, and gases as KHI could impact the kinetics of cavity formation and hydrate metastability.19,20 It is also considered in the industry that KHIs may have difficulty in preventing sI hydrate.28,29 Therefore, structure dependency of KHI performance has to be evaluated when applying the KHI to gas fields if the temperature and pressure conditions fall into the stability region of sI hydrate. Recent studies suggest that hydrate formation in the presence of KHI can be divided into two stages, slow growth and catastrophic growth.30,31 This is an important finding as the slow growth can be beneficial to manage the hydrate formation kinetics. However, most of these studies conducted experiments at the concentration of 0.5 wt %. The evaluation of KHIs in the laboratory using high-pressure cells is normally performed at the concentration range between 0.5 and 2.0 wt %.32 Adding more KHI up to 3.2 wt % based on water decreases the probability of hydrate nucleation,33 which suggests that a longer hydrate onset time might be achievable at the concentration higher than 3.0 wt %. Moreover, there have been industry practices to increase the concentration to take into account the mechanical uncertainties. However, most research on KHIs has focused on the development of new molecular structures and the evaluation of their performance at low concentration. Therefore, the effect of the concentration on hydrate onset and growth needs to be explored more thoroughly at the extended concentration up to 3.0 wt % to set an upper limit of using KHIs. In an effort to understand hydrate onset and growth at various concentrations of KHIs, we carried out experiments to measure the hydrate onset time, subcooling, and gas consumption rate while varying the concentration of PVP and PVCap from 0.5 to 3.0 wt %. The other objective of this work is to investigate the appearance of catastrophic hydrate growth in the presence of KHI at different concentrations. 13C NMR spectroscopic analysis is also carried out to analyze the hydrate samples formed in the presence of a high concentration of PVP or PVCap and to identify the structure type and cage occupancies. These studies will lead to a better understanding of hydrate formation characteristics at a high concentration of KHI.

2. EXPERIMENTAL SECTION Hydrate Onset and Growth Measurements. A synthetic gas mixture consisting of methane (0.89), ethane (0.07), and propane (0.04) by mole fraction basis was used in all experiments. Two KHIs, polyvinylpyrrolidone (PVP, MW ≈ 15 000, purity 99.0%) and poly(N-vinylcaprolactam) (PVCap, MW ≈ 5,000, purity 98.0 wt %) were used without further purification. Deionized water with a purity of 99.99 mol % was used to make aqueous solutions containing hydrate inhibitors. The experimental apparatus is designed to measure the volumetric consumption rate of the gas mixture while monitoring the change of pressure and temperature. An autoclave cell made of 316 stainless steel is equipped with an impeller to mix the liquid phase well. The liquid volume is usually 50 mL with a total volume of 200 mL, and the system can be operated up to 150 bar in the temperature range of −20−50 °C. The autoclave is immersed in a temperaturecontrolled liquid bath, connected to an external refrigerated heater (Jeiotech). The liquid bath temperature can be maintained within 0.05 °C. A platinum resistance thermocouple monitors the temperature of the fluids inside of the autoclave with an uncertainty of 0.1 °C. The pressure is measured by a pressure transducer with an uncertainty of 0.01 bar in a range of 0−120 bar. To maintain a constant system pressure (100 bar), a high-pressure syringe pump (Teledyne ISCO 260D) is connected to the autoclave head and provides data for the consumed volume of gas. A data acquisition system was used to record the temperature, pressure, and pump volume throughout the experiment. The pure water was considered as a baseline for comparison. PVP and PVCap were dissolved in water, and the concentration was varied from 0.5 to 3.0 wt %. The autoclave was filled with the aqueous solution containing dissolved KHI. The impeller housing was then mounted on top of the autoclave body, and the autoclave was placed into the liquid bath. The temperature of the bath was monitored at 23 °C, where no hydrate formation is expected at the pressure conditions to be studied. After purging the autoclave three times, the autoclave was pressurized to the desired pressure (100 bar) while stirring at 600 rpm. The constant-pressure operation mode commenced with the high-pressure syringe pump. The internal pump volume decreased until the liquid phase was saturated with gas. Once the pressure and pump volume reached steady state, the preprogrammed cooling procedures were commenced. The constant cooling was carried out by cooling the autoclave from 23 to 4 °C within 1 h. The internal pump volume decreased continuously as the temperature decreased, and then, there was a precipitous volume decrease and temperature peak upon hydrate formation. The hydrate onset time was identified on the basis of a sudden pump volume change, and the initial growth rate of hydrate was calculated during the linear gas consumption stage that was below a 1 h range for pure water and the PVP solution but was several hours for the PVCap solution. Figure 1 shows the repeated experiments to observe the hydrate onset and growth for 3.0 wt % PVCap solution. Four to five experiments were carried out to obtain the average value of the hydrate onset time and the initial growth rate at the corresponding KHI concentration. 13 C NMR Spectroscopic Analysis. Hydrate samples for 13 C solid-state NMR analysis were obtained when the previously described experiments were completed. We analyzed the structure of formed hydrates and the cage occupancies of 13989



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spectra were recorded at −90 °C by placing the hydrate samples in a 4.0 mm diameter ZrO2 rotor that was loaded into the variable-temperature (VT) probe of a Varian 600 MHz solid-state NMR spectrometer. All spectra were recorded at a Larmor frequency of 100.6 MHz under high-power proton decoupling (HPDEC) and at a spinning rate of 10 kHz. A pulse length of 4 μs and pulse repetition delay of 15 s were used with a radio frequency field strength of 50 kHz corresponding to a 90° pulse of 5 μs duration. The downfield carbon resonance peak of adamantine, assigned a chemical shift of 38.3 ppm at 27 °C, was used as an external chemical shift reference.

3. RESULTS AND DISCUSSION The initial experiment was carried out with pure water. The obtained hydrate onset temperature (Tonset), subcooling temperature (ΔTsub), hydrate onset time (tonset), and initial growth rate (rini) are tabulated in Table 1. The time for the hydrate onset was defined as the time difference between the hydrate onset and the time when the temperature becomes lower than the hydrate equilibrium temperature, which indicates how long hydrate onset is delayed. In this work, conventional continuous cooling and heating at a rate of 0.1 °C/h were employed to measure the hydrate equilibrium temperature (Teq), and then, thermodynamic simulation was carried out to confirm the measured data. The equilibrium temperature was measured at 20.8 °C while maintaining the pressure constant at 100.0 bar using the ISCO syringe pump, which was in good agreement with the calculated value. Therefore, the hydrate equilibrium temperature of 20.8 °C was used to calculate the hydrate onset temperature. The hydrate onset temperature Tonset was usually measured below the hydrate equilibrium temperature, and the subcooling temperature is defined by the difference between Teq and Tonset to define the subcooled temperature before the aqueous phase experiencing hydrate formation. For pure water, the hydrate onset time was 27.4 min, and subcooling was 10.8 °C. Once nucleated, hydrates grow rapidly while consuming both water and gas molecules surrounding hydrate crystals. The amount of gas consumed during the hydrate formation was monitored to investigate the hydrate growth rate. The gas consumption curve when forming hydrate with pure water is shown in Figure 2 along with those of PVP solutions. Among four gas consumption profiles of pure water, the one representative profile was chosen to be displayed in the figure. As seen in Figure 2, the linear gas consumption is observed during the initial growth stage as the hydrate formation is mainly controlled by mass transfer. Previous study on the reaction rate constant of propane hydrate suggested that hydrate growth is mostly affected by the

Figure 1. (a) Consumed gas profiles and (b) temperature change during the cooling of a 3.0 wt % PVCap solution from 23.0 to 4.0 °C at 100 bar (four repetition).

guest molecules in order to elucidate the kinetic process in conjunction with the structural characteristics. We presumed that the hydrate formation was complete when the pump volume was stabilized and the temperature was maintained for at least 24 h. Then, the hydrate samples were collected from the autoclave cell, finely ground, and transported to the ZrO2 rotor that was inserted into the precooled NMR probe under liquid nitrogen conditions. The 13C NMR analysis for the hydrate sample of 3.0 wt % PVP and PVCap solutions was repeated three times to confirm the hydrate structure and cage occupancies. For determining the hydrate structure and guest distribution over hydrate cages, 13C magic angle spinning (MAS) NMR

Table 1. Hydrate Onset Time, Subcooling, and Growth Rate for PVP and PVCap Solutions system pure water PVP solution

PVCap solution

xa (wt %)

Tonset (°C)

ΔTsub (°C)

sb (°C)

tonset (min)

sb (min)

rini (mmol/min)

sb (mmol/min)

0.5 1.5 3.0 0.5 1.5 3.0

10.0 5.4 4.5 3.7 4.0 3.8 3.4

10.8 15.4 16.3 17.1 16.8 17.0 17.4

0.8 0.8 0.7 0.2 0.1 0.4 0.1

27.4 39.6 44.7 48.7 105.6 217.0 332.3

2.7 10.3 6.8 4.5 32.2 22.6 77.0

15.25 0.97 1.49 3.14 0.17 0.08 9.33

5.70 0.03 0.03 0.08 0.003 0.008 1.41

a

x indicates the concentration of KHI in aqueous solution. bs indicates the standard deviation of the subcooling temperature (ΔTsub), hydrate onset time (tonset), and initial growth rate (rini). 13990



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concentration of PVP retards hydrate onset; however, it allows fast hydrate growth rather than suppressing the growth of hydrate crystals. The initial growth rate in the presence of PVP is lower than that of pure water at all concentrations studied in this work. It is noted that mass-transfer limitation would be similar for the PVP-added system to that of pure water as the mixing conditions such as the volume of gas and liquid, temperature cooling rate, experimental pressure, and agitation speed were the same as those in experiments with pure water. We presumed that the addition of PVP in the aqueous phase may affect the intrinsic kinetics for hydrate growth. As seen in Figure 3, PVCap shows a lot better performance than PVP. When adding 0.5 wt % PVCap, the hydrate onset

Figure 2. Gas consumption profiles during hydrate formation at various concentrations of PVP. Time zero in the graph corresponds to the hydrate onset condition.

mass transfer limitation in the initial stage and can be described with linear consumption of gas molecules.34 Other literature also indicated that hydrate nucleation and initial growth depend on the mass-transfer characteristics and the thermodynamic properties such as temperature, pressure, and gas composition.35,36 Since the onsets of hydrate nucleation, they would grow into particles while consuming water and dissolved gas molecules in the aqueous phase. As indicated by Zepra et al.,35 heat- and mass-transfer limitation needs to be considered for modeling of hydrate growth in the initial stage rather than using the intrinsic kinetics alone. Then, the agglomeration of hydrate particles could be modeled based on a steady-state balance between the interparticle adhesion force and the shear forces. Therefore, the agglomeration of hydrate particles depends on physical and mechanical properties such as the fluid dynamics of the system, particle size, and interparticle adhesion force. In this study, we decided to focus on the initial growth stage of hydrate particles with or without KHIs as the effect of KHI on this stage can be discussed without considering the complex agglomeration process of hydrate particles. During the initial growth stage of hydrate particles for pure water, the gas consumption rate was observed as a linear curve with a slope of 15.25 mmol/min. We postulate that the linear gas consumption is due to mass transfer of gas molecules from the vapor to aqueous phase, while the intrinsic kinetics would not be the limitation step. Heat-transfer limitation is also not considered in this work as the temperature is well-maintained at the desired value even during the initial growth stages where the heat of hydrate formation would be highest. The initial growth rate was considered to be 15.25 mmol/min from the gas consumption rate during the linear growth stage for pure water and was used to compare this gas consumption rate to those of KHI solutions. Figure 2 shows also the gas consumption profiles in the presence of PVP at concentrations of 0.5, 1.5, and 3.0 wt %. Time zero in the graph corresponds to the hydrate onset condition. By increasing the concentration to 3.0 wt %, the hydrate onset time increases slightly from 39.6 to 48.7 min. The initial growth rate becomes increased slightly from 0.970 to 1.49 mmol/min when increasing the concentration from 0.5 to 1.5 wt %, and it increases almost 3 times, 3.14 mmol/min, when adding 3.0 wt %. This result indicates that increasing the

Figure 3. Gas consumption profiles during hydrate formation at various concentrations of PVCap. Time zero in the graph corresponds to the hydrate onset condition.

time increases to 105.6 min, which is about 2.5 times than that of 0.5 wt % PVP. Increasing the concentration to 3.0 wt % shows the hydrate onset time of 332.3 min, which confirms that PVCap performs better than PVP as a KHI. The percent variation in hydrate onset time was about 18−34% for all experiments, which was close to those in the literature.13,30 However, Figure 3 shows gas consumption profiles of PVCap solutions and suggests that more careful approach would be required when judging the performance of PVCap as a KHI. For an increasing concentration of PVCap from 0.5 to 1.5 wt %, the initial growth rate decreases from 0.17 to 0.08 mmol/min, which is the slowest hydrate growth rate ever observed in this work. However, when time reaches 1045 min, rapid growth of the hydrate is observed, which can be considered as two-stage hydrate growth reported by other researchers.30,31 Once again, it is observed that the hydrate growth becomes slow in the presence of PVCap even under the same mixing conditions as those in pure water. This result indicates that the addition of PVCap would slow down the intrinsic kinetics of hydrate growth; thus, the overall growth rate of hydrate became slower than that in pure water. However, for 3.0 wt % PVCap solution, the slow hydrate growth of 1.11 mmol/min was observed only for 50 min after hydrate onset, and then, the growth rate became 9.33 mmol/min, which is the highest growth rate among PVP and PVCap solutions studied in this work. The standard deviation for measured growth rates at each concentration is tabulated in Table 1. The maximum percent variation in growth rate for 3.0 wt % was 28% when the average value was 9.33 mmol/min with a standard deviation of 1.41. 13991



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Raman analysis on methane−ethane metastability suggested that PVCap retards the structural transition from metastable sI to thermodynamically stable sII, representing the coexistence of sI and sII in the hydrate phase. In order to find out the outcomes of catastrophic hydrate growth such as hydrate structure and cage occupancies, we carried out an analysis of hydrate samples formed at 3.0 wt % PVCap and 3.0 wt % PVP solutions and compared the results with that of pure water. Figure 4 shows 13C NMR spectra of gas hydrate samples retrieved after hydrate growth is completed in previous kinetics

However, for 1.5 wt %, the maximum percent variation in growth rate was 13% when the average growth rate was 0.08 mmol/min with a standard deviation of 0.008. It is noted that the deviation of growth rates becomes large when PVCap concentrations increase from 1.5 to 3.0 wt %, which indicates that the hydrate growth shows scattering when catastrophic growth happens. As the initial growth rate at 3.0 wt % of PVCap is the closest value to that of pure water, we consider this high growth rate as the catastrophic growth of hydrate crystals in the presence of KHI molecules. The slow growth was followed by catastrophic growth at 0.5 wt % in the literature;30,31 however, in this work for 3.0 wt % PVCap solution, the catastrophic growth appears after a long hydrate onset time. This result provides important insight for the role of PVP and PVCap molecules during the hydrate growth. Both PVP and PVCap molecules are able to suppress the nucleation and growth of hydrate crystals efficiently until 1.5 wt %; however, more addition to 3.0 wt % induces faster hydrate growth, as seen for PVP or catastrophic hydrate growth as for PVCap, rather than suppressing the growth of hydrate crystals. It is postulated that hydrate growth was controlled by both intrinsic and mass-transfer limitation when the concentration of PVCap was less than 1.5 wt %; however, the limitation on the intrinsic kinetics became less when the concentration of PVCap was 3.0 wt %, which resulted in the catastrophic hydrate growth soon after the hydrate onset. Previous studies suggest that KHIs delay or slow down the process of hydrate nucleation by surface adsorption on nuclei, forcing an increased induction or hold time. Moreover, recent studies using the crystal growth inhibition technique suggest that hydrate inhibition by inhibitors can be distinguished from complete inhibition through severely to moderately reduced growth rates, ultimately to final rapid growth as subcooling increases due to its adsorption on hydrate faces favored for crystal development. Although it is not yet clear what mechanisms dictate the hydrate growth rate in the presence of KHIs, previous molecular dynamic studies suggest that hydrate inhibition in the presence of a KHI occurs via a twostep mechanism, (i) raising the barrier to nucleation and nuclei propagation and (ii) the inhibitor binding to the surface of the hydrate crystal and retarding further growth once nucleation occurs.37,38,40 In this work, we observed that the addition of PVP and PVCap induces a longer hydrate onset time; thus, the concept of raising the barrier to nucleation and nuclei propagation is confirmed. As seen in the slow growth up to 1.5 wt % of PVP and PVCap, it is also confirmed that the growth is retarded in the presence of PVP and PVCap. It is presumed that the intrinsic kinetics becomes slow as the inhibitor molecules bind to the surface of the hydrate crystal. However, for a 3.0 wt % PVCap solution, the nucleation is well suppressed, as witnessed by the longest hydrate onset time, 332.3 min in Table 1, which is about 12 times higher than that in pure water. However, during this period, the aqueous phase becomes a highly subcooled condition just like supercooled water below the freezing point. Once the hydrate nucleates from this highly subcooled condition, it seems that the catastrophic growth of hydrates happens, and PVCap molecules are no longer effective in biding to the surface of growing hydrate particles. Recent studies19,20 with 13C NMR and in situ Raman spectroscopy suggested that KHI affects the hydrate growth by promoting the early formation of metastable sI hydrate. In situ

Figure 4. 13C MAS NMR spectra of gas hydrates in the presence of 3.0 wt % PVP and PVCap. (a) Pure water, (b) PVP, and (c) PVCap.

experiments. NMR spectroscopy has proved useful for identifying hydrate structures and quantifying cage occupancies of gas molecules. As seen in NMR spectra of hydrates from pure water, Figure 4a, methane molecules show two resonances at −4.3 and −8.3 ppm, indicating that they are occupying both small and large cages of sII. Single resonance for ethane is at 5.9 ppm; two resonance lines for propane are shown at 16.5 and 17.3 ppm, clearly representing the formation of sII only. However, in NMR spectra of hydrates from 3.0 wt % PVP and 3.0 wt % PVCap solutions, an additional resonance is shown at −6.8 ppm, which is for methane molecules occupying large cages of sI. Ethane and propane molecules occupy the large cages of sII and do not participate in the formation of sI. In our previous work,8 the structure of hydrate formed with pure water and natural gas was sII; however, the coexistence of sI and sII was observed when the formation occurred when ethane and propane were depleted during the formation process. In this work, we continuously provide fresh natural gas to the autoclave using an ICSO syringe pump in order to maintain the pressure constant at 100 bar and measure the gas-phase composition continuously. As the composition variation is almost negligible, the depletion of ethane and propane during the formation process is unlikely in this work. Therefore, it is 13992



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and PVCap. However, cage occupancies of ethane and propane increase significantly, especially 5 times for propane when comparing the composition of hydrate for pure water with that of the 3.0 wt % PVCap solution. This fractionation might be due to the preferential occupation of ethane and propane molecules in large cages of sII; however, the low cage occupancy of methane in small and large cages of sII needs to be considered carefully with the existing metastable sI. Table 2 shows the ratio of hydrocarbons in sI to those in sII. For both PVP and PVCap, the ratio is 0.35 and 0.31, respectively, and indicates that the amount of sI is about 25% of the hydrate phase. These spectroscopic results confirm the existence of metastable sI for both 3.0 wt % PVP and PVCap. It is likely that during the catastrophic growth period, methane forms thermodynamically stable sII together with ethane and propane; however, it forms metastable sI as well if PVCap molecules disrupt the local organization of water and gas molecules to form sII by increasing the energy barrier. Once overcoming the energy barrier, the suppressed energy to form hydrate may induce catastrophic hydrate growth of both sI and sII. Therefore, structural characteristics of the hydrate phase become complex as its composition, dissociation conditions, and the heat required to decompose would be affected by the ratio of sI and sII. These properties are important for the energy industry dealing with hydrate formation risks in offshore flowlines transporting hydrocarbon fluids. The slow conversion of metastable sI to thermodynamically stable sII might explain the coexistence of sI and sII;19,20 however, more precise studies are required to understand when metastable sI forms and how it interacts with thermodynamically stable sII, possibly using in situ spectroscopic methods. The obtained results in this study provide important insights for hydrate growth and structural characteristics in the presence of 3.0 wt % PVP and PVCap. Our works on hydrate kinetics and subsequent 13 C NMR analysis suggest that the concentration of KHIs might be an important parameter to model the hydrate growth in the kinetics model as catastrophic growth may happen at a high concentration of KHI. This catastrophic hydrate growth needs further studies including in situ spectroscopic measurements and the effect of the molecular structure of KHI polymer. Understanding the effect of concentration in hydrate growth will provide more scientific background for the efficient design of the KHI structure.

evident that metastable sI is formed and exists together with thermodynamically stable sII when hydrates form in the presence of PVP or PVCap. However, there still remain questions such as when metastable sI is formed and how much. In order to find out the effect of PVP and PVCap on the structural characteristics of hydrates when the catastrophic growth happens, more experiments with autoclave and in situ spectroscopy will be carried out in the near future. The ratio of integrated intensities, calculated from Gaussian− Lorentzian fitting of spectra with standard errors within 5%, gives different guest distributions over cages of hydrate structures. The cage occupancies of methane, ethane, and propane molecules over hydrate cages can be calculated from the ratio of the integrated intensity of NMR signals with the statistical thermodynamic equations for the hydrate phase. Structure I: μw (h) − μw (h°) =

RT [3 ln(1 − θL,CH4) 23 + ln(1 − θS,CH4)]

Structure II: μw (h) − μw (h°) =

RT [ln(1 − θL,C3H8 − θL,C2H6 − θL,CH4) 17 + 2 ln(1 − θS,CH4)]

where μw (h°) is the chemical potential of water molecules of a hypothetical empty lattice and θS and θL are the fractional occupancy of small and large cages, respectively. When the hydrate is in equilibrium with ice, the left side of the above equations becomes μw(ice) − μw(h°) = −Δμw° , where Δμw° is the chemical potential of the empty lattice relative to ice. The value of Δμ°w(h°) used for sII was 883.8 J/mol, while it was 1297.0 J/mol for sI. It is assumed that the large cages of sII are completely filled with hydrocarbon molecules to maintain hydrate stability from the single-crystal X-ray analysis results. As small cages of sI and sII have same five12 cage structures, the methane in small cages of both structures shows single resonance at −4.3 ppm, as seen in Figure 4b and c. We adopt a deconvolution process of the resonance to obtain each peak for methane in small cages of sI and sII from the assumption of the relative cage occupancy ratio, θS,CH4/θL,CH4, which would be 0.8160, which was observed frequently in our previous works.39 Table 2 represents the calculated cage occupancies of methane, ethane, and propane molecules in each hydrate cages along with the molar ratios of the hydrocarbons occupying each hydrate structure. The cage occupancy of methane in large cages of sII is 0.69 for pure water; however, it decreases in the presence of PVP

4. CONCLUSIONS The studies of hydrate onset and growth are carried out by measuring the hydrate onset time, subcooling, and gas consumption rate while varying the concentration of PVP and PVCap from 0.5 to 3.0 wt %. 13C NMR spectroscopic analysis is also carried out to analyze the hydrate samples formed in the presence of a high concentration of PVP or PVCap and to identify the structure type and cage occupancies. For pure water, the hydrate onset time is 27.4 min, and subcooling is 10.8 °C. Once nucleated, hydrates grow rapidly while consuming both water and gas molecules surrounding hydrate crystals with an initial growth rate of 15.25 mmol/min. When adding 0.5 wt % PVCap, the hydrate onset time increases to 105.6 min, and a further increase of the concentration to 3.0 wt % shows the delay of the hydrate onset time to 332.3 min. By increasing the PVCap concentration from 0.5 to 1.5 wt %, the initial growth rate decreases from 0.17 to 0.08 mmol/min, which is the slowest hydrate growth rate in this work of 0.08

Table 2. Cage Occupancies of Gas Molecules in Hydrate Cages in the Presence of 3.0 wt % PVP and PVCap CH4 in sI

CH4 in sII

C2H6 in sII

C3H8 in sII

system

θS,C1

θM,C1

θS,C1

θL,C1

θL,C2

θL,C3

sI/sII ratio

pure water 3 wt % PVP 3 wt % PVCap

0.78 0.76

0.93 0.93

0.84 0.79 0.76

0.69 0.55 0.35

0.17 0.23 0.33

0.06 0.21 0.29

0.35 0.31

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mmol/min. However, a further increase to 3.0 wt % induces the catastrophic hydrate growth, as seen in the initiral growth rate of 9.33 mmol/min. It is presumed that at 3.0 wt % PVCap, the hydrate onset is well suppressed by increasing the barrier for hydrate nucleation substantially; however, in return, once the hydrate nucleates, the barrier is overwhelmed by the energy to form the hydrate, which results in catastrophic growth. 13C NMR spectroscopic results confirm the existence of metastable sI for 3.0 wt % PVCap and 3.0 wt % PVP solutions, while cage occupancies of ethane and propane increase significantly, almost 5 times for propane when comparing the NMR spectra of pure water and the 3.0 wt % PVCap solution. These results suggest that the suppressed energy to form the hydrate may induce catastrophic hydrate growth of both sI and sII, and the metastable sI will coexist together with sII in the presence of a high concentration of PVP and PVCap.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +82 42 350 1521. Fax: +82 42 350 1510. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Technology Innovation Program (10045068) funded by the Ministry of Trade Industry and Energy (MI, Korea). This work was partially supported by the Energy Efficient & Resources Program of Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Trade, Industry and Energy (No. 2013251010005C).

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Catastrophic Growth of Gas Hydrates in the Presence of Kinetic

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