Promoting Effect of Ultra-Fine Bubbles on CO2 Hydrate Formation

When gas hydrates dissociate into gas and liquid water, many gas bubbles form in the water. The large bubbles disappear after several minutes due to their buoyancy, while a large number of small bubbles (particularly sub-micron-order bubbles known as ultra-fine bubbles (UFBs)) remain in the water for a long time. In our previous studies, we demonstrated that the existence of UFBs is a major factor promoting gas hydrate formation. We then extended our research on this issue to carbon dioxide (CO2) as it forms structure-I hydrates, similar to methane and ethane hydrates explored in previous studies; however, CO2 saturated solutions present severe conditions for the survival of UFBs. The distribution measurements of CO2 UFBs revealed that their average size was larger and number density was smaller than those of other hydrocarbon UFBs. Despite these conditions, the CO2 hydrate formation tests confirmed that CO2 UFBs played important roles in the expression of the promoting effect. The analysis showed that different UFB preparation processes resulted in different promoting effects. These findings can aid in better understanding the mechanism of the promoting (or memory) effect of gas hydrate formation.


Introduction
Methane hydrates existing below the deep seafloor are attracting significant attention as an unconventional natural gas resource, and many studies and developments have been conducted on this topic [1][2][3][4]. In the field of oil and gas development, gas hydrate research has focused on suppressing the formation and growth of gas hydrates, and this problem remains one of the main topics in gas hydrate research.
However, gas hydrates have unique properties, such as a large gas storage capacity; therefore, they are a promising medium for transporting and storing gases [5][6][7]. Additionally, gas hydrates, or more generally clathrate hydrates, have attracted attention as refrigerants owing to their melting points that are higher than that of ice [8][9][10][11], as they have a large latent heat similar to ice. Research on gas hydrate utilization has increased in recent years, and such research has focused on efficient gas hydrates formation.
Gas hydrates form from water and guest gases, which are stable under low-temperature and high-pressure conditions. Gas hydrate crystal formation requires relatively high supersaturation (or supercooling) conditions, similar to ice formation. Therefore, it is difficult to use gas hydrates in industry as the formation process is difficult to control and requires excess energy. Currently, the most promising approach to promoting the formation process is applying the "memory effect" phenomenon.
Under the memory effect, gas hydrate crystallization occurs under milder conditions than the initial formation conditions when its dissociated water is used. The mechanism of the memory effect remains unknown, and there are several hypotheses to explain it. One such hypothesis is the "water structuring hypothesis", which states that the fragments of the crystal lattice remain in the dissociated water, even after several hours, and act as the nuclei of hydrate reformation [2,[12][13][14][15][16]. This hypothesis is based on the concept that water has a hydrogen-bonding network. However, it has not yet been successful in experimentally verifying such structures or been proven. The other is the "gas dissolution hypothesis", which states that a sufficient number of guest molecules remain in the dissociated water and will shorten the dissolution of guest molecules during the reformation process [17]. As guest molecules are typically hydrophobic and have relatively low solubility in pure water, a large amount of gas must be dissolved into the liquid after it is consumed in the liquid. This process is a major barrier to crystallization. Although this hypothesis was proposed in a simulation study [17], Uchida et al. [18][19][20] demonstrated the existence of a large amount of ultra-fine bubbles (UFBs) in dissociated water, along with the memory effect expression of UFB-containing water without hydrate dissociation, which supported the "gas dissolution hypothesis".
UFBs are small gas bubbles with diameters of less than 1 µm [21] and unique properties, such as high internal pressure, low buoyancy, and the suppression of coalescence growth due to the presence of negative surface charges (ζ-potential). Based on these properties, UFBs are considered to have a long lifespan in liquids [22][23][24]. Our previous studies [18][19][20] confirmed that a large amount of UFB is formed in water when gas hydrate is dissociated. This process has also been supported by molecular dynamic simulations [25][26][27].
In our previous studies, we explored the expression of the memory effect (or promoting the phenomenon of gas hydrate formation) using hydrocarbon gases, such as methane (CH 4 ) [18], ethane (C 2 H 6 ) [19], and propane (C 3 H 8 ) [20], and demonstrated the promotion of gas hydrate formation, not only with hydrate-dissociated water, but also with the UFBcontaining water prepared by an UFB generator without any hydrate dissociation processes. Based on these studies, UFBs are considered to play important roles in the hydrate memory effect. Carbon dioxide (CO 2 ) is a hydrate-forming greenhouse gas and can be separated and stored under deep-sea conditions to prevent its release into the atmosphere [28], or be injected into national gas hydrate layers for effective natural gas development [29]. CO 2 hydrate formation must be controlled if it is to be used in these industrial applications. Therefore, this study aims to experimentally verify the promoting effect of CO 2 UFBs on the hydrate formation process, which produces structure I-type hydrates, such as CH 4 and C 2 H 6 . However, the solubility of CO 2 in water is approximately two orders of magnitude higher than those of CH 4 and C 2 H 6 [30]. Kondori et al. [27] demonstrated the size difference between CH 4 and CO 2 UFBs formed after hydrate dissociation. Additionally, solutions containing dissolved CO 2 have high acidity (low pH). As the high solubility and low pH are considered to significantly reduce the lifetime of UFBs, whether CO 2 UFBs contribute to the memory effect of CO 2 hydrates must be confirmed. The memory effect of CO 2 hydrate was previously demonstrated using ice-melted water [31]. As this supports the water structuring hypothesis, comparison with this study allows us to discuss the role of UFBs for expressing the memory effect.

Materials and UFB Measurements
We used three types of liquid samples to evaluate the effect of UFBs on the promotion of CO 2 hydrate formation, as used in our previous studies [18][19][20], including deionized pure water, hydrate-dissociated water prepared by dissolving CO 2 hydrate, and CO 2 -UFB-containing water. Pure water was prepared by ion exchange (Essential Elix, Merck KGaA, Darmstadt, Germany), with a resistivity of approximately 15 MΩ cm. CO 2 -hydratedissociated water was prepared by dissolving CO 2 hydrates (approximately 10 wt%) in pure water at room temperature (approximately 293 K). CO 2 -UFB-containing water was generated using a micro-bubble generator (Aura tec, OM4-MDG-045) at 293 K by supplying CO 2 gas (99% in purity, Sankemi Co., Ltd., Hokkaido, Japan) for over 1 h. When using liquid samples for the CO 2 hydrate formation test, every liquid was verified to be transparent, indicating the complete disappearance of micro-or macroscopic bubbles. We used both the light scattering technique and freeze-fractured replica observation using a transmission electron microscope (FFT) to characterize the CO 2 UFBs. The former includes two methods depending on the size of the UFBs. The number density (N) of UFBs with diameters larger than approximately 300 nm was measured by the laser-light scattering (LS) method. An argon-ion laser (λ = 514.5 nm) was introduced to the liquid sample in the glass cell (approximately 1 cm 3 ), and the bright spots (more than 20 UFBs in each sample, corresponding to N > 10 6 mL −1 ) were measured using a CCD camera (Watec Co., Ltd., Yamagata, Japan, type WAT-232S) from the 90 • direction. The particle-tracking analysis (PTA) method (MicrotracBEL, Co., Osaka, Japan, Zeta View) was used to measure smaller UFBs, which can measure both the particle size distributions (estimating N and average diameter D) and the ζ-potentials of UFBs with sizes of approximately 100 nm by tracking over 100 UFBs. The pH of the solution was measured using a pH sensor (Sato Keiryoki Mfg. Co., Ltd., Tokyo, Japan, type SK-620PHII). We followed the FFT method in our previous studies [18][19][20]; therefore, we have only briefly described it here. A small amount (less than 10 µL) of the liquid sample was quenched in liquid nitrogen, and set in the replication system (JEOL Ltd., Tokyo, Japan, type JFD-9010). The roughness of the freshly fractured surface (formed under approximately 150 K and 10 −5 Pa conditions) was replicated by depositing platinum and carbon. The replica film was transferred onto a Cu-grid with a 43 × 43 µm opening and observed using a high-resolution transmission electron microscope (TEM: JEOL Ltd., Tokyo, Japan, type JEM-2010, accelerating voltage of 200 kV). Based on the image resolution of the imaging plate (Fujifilm Co., Tokyo, Japan, type FDL-UR-V) and noise from the surface roughness, we could identify UFBs with diameters ranging from several tens of nanometers to several microns. The existence of a UFB was verified by a hemispherical dent, while impurity appeared as convex protrusion. Therefore, this method allowed us to separately observe UFBs and other impurities. Over 200 UFBs were observed to obtain the size distribution and N in each liquid sample following the FFT method.

Promoting Effect of CO 2 Hydrate Formation Evaluation
We used the same system used in our previous study [19] for the CO 2 hydrate formation tests. A liquid sample (approximately 50 cm 3 ) was placed in a reaction vessel (232.2 cm 3 ), whose temperature was controlled by a cooling bath (274.2 ± 0.2 K). After purging the headspace with CO 2 gas, a test gas was introduced to the vessel at approximately 2.5 MPa. This experimental protocol was verified to remove the effect of gas contamination (such as air in the headspace of the vessel) on the hydrate formation results [19]. The gas hydrate formation test began with gentle agitation (approximately 300 rpm).
We measured the induction time to indicate the ease of CO 2 hydrate formation, which was defined as the time taken to reach the time of gas hydrate formation after reaching the equilibrium condition, as indicated by a sudden temperature increase or pressure drop. As the gas hydrate nucleation process is stochastic, we evaluated the nucleation probability distribution for ten repeated experiments. Significance was estimated using the Dunnett test (MS Excel 2010 and BellCurve) with at least 99% confidence (p < 0.01).

Characteristics of UFBs in Liquid Samples
Some of the liquid sample used for the hydrate formation experiment was used to analyze the characteristics of the UFBs contained within by three methods. The typical TEM images of the CO 2 UFBs in the CO 2 -hydrate-dissociated water obtained following the FFT method are shown in Figure 1. Most of the UFBs were spherical or oval, and relatively larger than those observed in other gas UFBs [18][19][20]. We also observed a thin layer at the bubble surface (Figure 1b) or surrounding the bubble in the liquid phase (Figure 1c). the FFT method are shown in Figure 1. Most of the UFBs were spherical or oval, and relatively larger than those observed in other gas UFBs [18][19][20]. We also observed a thin layer at the bubble surface (Figure 1b) or surrounding the bubble in the liquid phase ( Figure 1c).   Table 1 shows the average diameter D and number density N of the CO2 UFBs in each tested liquid sample. These figures and tables show that the CO2 UFB in CO2-hydrate-dissociated water exhibited a similar N value to other gas hydrate-dissociated water [18][19][20]. This is consistent with the finding that the D of CO2 UFBs obtained by FFT was relatively larger than those observed in other gas hydrate systems. Although the N values measured by FFT and LS were similar, the values measured by the PTA method were two orders smaller than the others. This discrepancy could be because most of the UFBs were larger than several hundred nanometers ( Figure 2), exceeding the measurable size of the PTA method. Therefore, we will conduct a quantitative comparison in the future.   Table 1 shows the average diameter D and number density N of the CO 2 UFBs in each tested liquid sample. These figures and tables show that the CO 2 UFB in CO 2 -hydrate-dissociated water exhibited a similar N value to other gas hydrate-dissociated water [18][19][20]. This is consistent with the finding that the D of CO 2 UFBs obtained by FFT was relatively larger than those observed in other gas hydrate systems. Although the N values measured by FFT and LS were similar, the values measured by the PTA method were two orders smaller than the others. This discrepancy could be because most of the UFBs were larger than several hundred nanometers (Figure 2), exceeding the measurable size of the PTA method. Therefore, we will conduct a quantitative comparison in the future.   These results have important implications for the stability of CO2 UFBs. The low pH value of 4.0 indicated that CO2 was sufficiently dissolved in water. Therefore, the effect of contamination of gases other than CO2 was considered negligible in this study. The ζ-potential of CO2 UFBs exhibited a small absolute value of −10 mV, which was smaller than that of O2 UFBs (-40 mV) under a pH of approximately 6.2 [32]. The relationship between the pH and ζ-potential is consistent with previous results reported by Takahashi [24]. Therefore, the smaller UFBs may tend to disappear by dissolving CO2 molecules due to their higher internal pressure, and CO2 UFBs are more likely to coalesce with one another due to their lower ζ-potential. Both effects would result in a larger average diameter. This is consistent with the finding that the CO2 generator was required to operate for a longer time than those of other gases to form a sufficient number density of CO2 UFBs. Figure 3 shows the typical temperature profiles of CO2 hydrate formation in the three types of liquid samples. After the vessel containing pressurized CO2 was immersed in the cooling bath, the temperature decreased from room temperature to the set temperature of approximately 274.2 K. When the temperature reached equilibrium under the set pressure (approximately 279 K), the induction time began (shown as t = 0 in Figure 3). These results have important implications for the stability of CO 2 UFBs. The low pH value of 4.0 indicated that CO 2 was sufficiently dissolved in water. Therefore, the effect of contamination of gases other than CO 2 was considered negligible in this study. The ζpotential of CO 2 UFBs exhibited a small absolute value of −10 mV, which was smaller than that of O 2 UFBs (-40 mV) under a pH of approximately 6.2 [32]. The relationship between the pH and ζ-potential is consistent with previous results reported by Takahashi [24]. Therefore, the smaller UFBs may tend to disappear by dissolving CO 2 molecules due to their higher internal pressure, and CO 2 UFBs are more likely to coalesce with one another due to their lower ζ-potential. Both effects would result in a larger average diameter. This is consistent with the finding that the CO 2 generator was required to operate for a longer time than those of other gases to form a sufficient number density of CO 2 UFBs. Figure 3 shows the typical temperature profiles of CO 2 hydrate formation in the three types of liquid samples. After the vessel containing pressurized CO 2 was immersed in the cooling bath, the temperature decreased from room temperature to the set temperature of approximately 274.2 K. When the temperature reached equilibrium under the set pressure (approximately 279 K), the induction time began (shown as t = 0 in Figure 3). The duration until the sudden temperature increased due to CO 2 hydrate formation (indicated by the arrows in Figure 3) was taken as the induction time.

CO 2 Hydrate Formation with Various Liquid Samples
As shown in Figure 3, the formation of CO 2 hydrates began before the temperature reached the set temperature in CO 2 -hydrate-dissociated (red solid line) and CO 2 UFBcontaining water (green dotted line). However, in the formation experiment using pure water (blue dashed line), CO 2 hydrates formed after the temperature reached the set temperature. Therefore, it was confirmed that the induction time was shortened when using a liquid sample containing CO 2 UFBs, and the promoting effect was expressed.
The duration until the sudden temperature increased due to CO2 hydrate formation (indicated by the arrows in Figure 3) was taken as the induction time. As shown in Figure 3, the formation of CO2 hydrates began before the temperature reached the set temperature in CO2-hydrate-dissociated (red solid line) and CO2 UFB-containing water (green dotted line). However, in the formation experiment using pure water (blue dashed line), CO2 hydrates formed after the temperature reached the set temperature. Therefore, it was confirmed that the induction time was shortened when using a liquid sample containing CO2 UFBs, and the promoting effect was expressed.
Another characteristic of CO2 hydrate formation is that the reaction occurs in a cascade, rather than the two-step formation of C2H6 hydrate [19]. This would be due to the high solubility of CO2 in water; therefore, even if dissolved CO2 is consumed by hydrate formation, the amount of dissolved CO2 did not sufficiently decrease to interrupt hydrate formation, and/or the dissolution rate from the gas phase was sufficiently fast.

Comparison of Memory Effects and Roles of UFBs
To explore the relationship between the probability nucleation rate and the induction time, formation experiments were repeatedly conducted to measure the induction time. Figure 4 shows the relationship between the probability nucleation rate of CO2 hydrates P(τ) and the induction time τ obtained in this study.
This figure shows that both the nucleation probability curves of the CO2-hydrate-dissociated (▲) and CO2-UFB-containing water (■) were observed at a shorter induction time than that of pure water (◆). Again, it was confirmed that both types of liquid samples, including CO2 UFBs, exhibited a memory effect. As CO2-UFB-containing water did not contain any hydrate structures, the guest dissolution hypothesis would be more appropriate for this CO2 hydrate system than the water structuring hypothesis. This is the same conclusion as those drawn in our previous studies [18][19][20]. Another characteristic of CO 2 hydrate formation is that the reaction occurs in a cascade, rather than the two-step formation of C 2 H 6 hydrate [19]. This would be due to the high solubility of CO 2 in water; therefore, even if dissolved CO 2 is consumed by hydrate formation, the amount of dissolved CO 2 did not sufficiently decrease to interrupt hydrate formation, and/or the dissolution rate from the gas phase was sufficiently fast.

Comparison of Memory Effects and Roles of UFBs
To explore the relationship between the probability nucleation rate and the induction time, formation experiments were repeatedly conducted to measure the induction time. Figure 4 shows the relationship between the probability nucleation rate of CO 2 hydrates P(τ) and the induction time τ obtained in this study.   Table A1) and each line shows the fitting curve of Equation (1).
We then conducted a quantitative analysis of the promoting effect of CO2 hydrate following a previous work [31]. Equation (1) was fitted to the probability of nucleation rate (P(τ)) curves presented in Figure 4, and the fitting parameters of the nucleation frequency J and offset time τ0 were examined.
As shown in Table 2, CO2-hydrate-dissociated water had a promoting effect, such  Table A1) and each line shows the fitting curve of Equation (1).
This figure shows that both the nucleation probability curves of the CO 2 -hydratedissociated ( ) and CO 2 -UFB-containing water ( ) were observed at a shorter induction time than that of pure water ( ). Again, it was confirmed that both types of liquid samples, including CO 2 UFBs, exhibited a memory effect. As CO 2 -UFB-containing water did not Energies 2021, 14, 3386 7 of 10 contain any hydrate structures, the guest dissolution hypothesis would be more appropriate for this CO 2 hydrate system than the water structuring hypothesis. This is the same conclusion as those drawn in our previous studies [18][19][20].
We then conducted a quantitative analysis of the promoting effect of CO 2 hydrate following a previous work [31]. Equation (1) was fitted to the probability of nucleation rate (P(τ)) curves presented in Figure 4, and the fitting parameters of the nucleation frequency J and offset time τ 0 were examined.
As shown in Table 2, CO 2 -hydrate-dissociated water had a promoting effect, such that τ 0 was lower than that of pure water, while J changed little. However, for CO 2 -UFBcontaining water, the promoting effect caused J to increase, although τ 0 remained almost the same. For the C 2 H 6 hydrate, both the hydrate-dissociation and UFB-containing water exhibited a promoting effect by increasing J and decreasing τ 0 to the same extent. Therefore, the expression of the promoting effect of the CO 2 hydrate may differ slightly to that of hydrocarbon hydrates; that is, CO 2 UFBs promoted CO 2 hydrate formation; however, the mechanism differed between the preparation processes. Here, we discussed the nucleation probability with ten replicate experiments; however, more experiments are required for a detailed investigation [33]. Additionally, we only focused on the surface properties of the experimental materials (such as hydrophobic or hydrophilic) to consider the effect of fine surface bubbles on hydrate formation [34].  [31] 7.9 0.295 meltwater [31] 58. 8 2.29 Compared to the parameters obtained to evaluate the freezing-memory effect [31], the value of J was much larger in this study, which could be due to the differences in hydrate formation, such as differences in the reaction systems with or without agitation. The expression pattern of the promoting effect with CO 2 -UFB-containing water was qualitatively similar to that observed with meltwater, but differed to that observed with CO 2 -saturated meltwater (similar to nitrogen-saturated meltwater) [31]. The reason for this discrepancy is unclear, but an additional number of experiments would provide a better understanding.
As in the previous study [19], we then compared the expected induction time <∆t ind > of the promoting effect with the difference in the area of the nucleation probability diagram (Figure 4). The magnitude of the promoting effect slightly differed between the CO 2hydrate-dissociated and CO 2 -UFB-containing water. The <∆t ind > value of CO 2 -hydratedissociated water was approximately 1.4 times that of CO 2 -UFB-containing water, as shown in the final column of Table 2. Compared to the case of C 2 H 6 hydrate, in which the two <∆t ind > values were almost identical [19], this difference may be due to N, as CO 2 hydrates tend to nucleate at the gas-liquid interface [35]. However, Tables 1 and 2 show that the relationship between J and N was opposite. This novel insight into the promoting effect on CO 2 hydrate formation is discussed in the following paragraph.
As shown in Section 3.1, CO 2 UFBs have a relatively larger diameter and smaller number density than hydrocarbon gas UFBs [18][19][20], which is consistent with the low pH (approximately 4) of the solution containing CO 2 UFBs, as the low-pH condition could not prevent coalescence between the UFBs [24]. However, the CO 2 hydrate formation promoting effect were confirmed to be expressed in both CO 2 -UFB-containing solutions. Therefore, we considered that CO 2 UFBs play important roles in the promoting effect of Energies 2021, 14, 3386 8 of 10 CO 2 hydrate formation, despite their larger size and lower number density. The promoting mechanisms between the hydrate-dissociated water and UFB-containing water derived from the analysis of the nuclear probability curves differed, which is inconsistent with the results of previous works [18][19][20]. A possible cause of this difference is the difference in CO 2 saturation in water. Based on the preparation protocols, the UFB-containing water would be saturated with CO 2 even though CO 2 has high solubility. In contrast, the amount of CO 2 hydrate may be insufficient under the saturated conditions of hydrate-dissociated water.
As mentioned above, these parameters also differ to the memory effect observed with ice-melting water [31]. Therefore, we should also consider the terminology of 'memory' effect, which has been used as a general term for the formation-promoting phenomena. The mechanism of the promoting effect should also be considered when discussing the 'memory effect' of gas hydrate formation.

Conclusions
In this study, we investigated the relationship between the expression of the promoting effect and existence of UFBs using CO 2 -hydrate-dissociated and CO 2 -UFB-containing water. As CO 2 UFBs are generated under low-pH and high-solubility conditions, they tend to have smaller numbers (lower number density) and larger sizes (large average diameter) than other hydrocarbon UFBs. Nevertheless, the CO 2 hydrate formation induction time shortened for both liquid samples; thus, the promoting effect was confirmed to be expressed in the CO 2 -UFB-containing system. These results support the gas dissolution hypothesis for memory effect mechanisms, rather than the water structuring hypothesis. Therefore, CO 2 UFBs would act as guest-molecule resources in the liquid phase. However, the analysis of the probability of nucleation rate curves suggested that CO 2 UFBs may exhibit different patterns for the promoting effect of CO 2 hydrates. This property is unique for CO 2 UFBs and is due to the high solubility of CO 2 in pure water.