Effect of pressure on methane hydrate formation in graphite nanofluids in non-stirred system

Abstract Given the increasing demand for clean natural gas energy, solidified natural gas (SNG) is regarded as a potential natural gas storage technology owing to its numerous advantages. In this work, the effects of the concentration of graphite nanoparticles (GNs) on the rate of hydrate formation, gas consumption, induction time, and morphology of methane hydrates under different pressures were studied. The results showed that under lower pressure, the low concentration of GNs increased the gas consumption of hydrates, but the hydrate formation rate decreased by 50% and the induction time increased. The addition of high concentration GNs decreased the hydrate formation rate significantly, there was no obvious induction period, and the final gas consumption changed little. At the same time, only a small amount of hydrate was formed, accompanied by a considerable volume of foam. Under higher pressure, the addition of GNs promoted the formation of hydrates, increased the rate of hydrate formation. Among them, the 0.3 wt% concentration of GNs showed the best promotion effect, and the final gas consumption was higher than that of other metal and oxide nanofluids. Therefore, under the proper pressure, using cheap GNs as promoters can not only effectively promote hydrate formation, but also save costs. Graphical Abstract


Introduction
Natural gas is a clean, safe, and high-quality energy, which plays an important role in global energy consumption.Natural gas mainly contains methane and a small number of high hydrocarbons.It is estimated that by 2040, the consumption of natural gas will increase at a rate of 2% per year [1] .As a result, natural gas will become more and more necessary.
At present, natural gas is mainly stored by compressed natural gas (CNG) and liquefied natural gas (LNG).However, the traditional storage method requires higher energy costs.The use of hydrates for solidified natural gas storage (SNG) may be a more economical and flexible way.Natural gas hydrate is a non-stoichiometric compound formed by water and guest molecules at low temperature and high pressure [2,3] .The guest molecules are wrapped in a cage composed of water molecules under the action of van der Waals force.Hydrate crystals include three types of structures: type I, type II, and type H.Under standard conditions, 1 volume of hydrate can store 164-180 volumes of natural gas [4] .At the same time, based on the mild storage conditions, non-explosive and other attractive characteristics of hydrate, it is widely used in gas separation [5] , natural gas storage and transportation [6] , carbon dioxide capture [7] , seawater desalination [8] , and other fields.
However, due to the low solubility of methane in pure water, only a thin hydrate film will be formed at the gasliquid interface, which limited the mass transfer at the gaswater interface, resulting in a slow hydrate formation rate and low energy storage capacity [9] .Therefore, researchers used mechanical methods such as stirring [10] , spraying [11] , and bubbling [12] to increase the gas-liquid contact area and promote hydrate formation.In addition, from a chemical CONTACT Xiaoling Li zjq18642357316@sina.com Supplemental data for this article can be accessed online at https://doi.org/10.1080/01932691.2022.2122492.
point of view, adding promotors to water was considered to be an effective and economical method.Recently, some new promotors, such as natural derived surfactant [13] , amino acid [14,15] , protein [16] , etc., have also been used to improve the storage and transportation efficiency of natural gas.As a kinetic accelerator, surfactant was widely used, which greatly reduced the gas-liquid interfacial tension and improved the mass transfer [17] .Zhong and Rogers et al. [18] showed that when the concentration of surfactant sodium dodecyl sulfate (SDS) exceeded the critical micelle concentration (CMC), the hydrate formation rate increased by 700 times.Liu et al. [19] found that sodium laurate (SL), as a hydrate promoter, had the advantages of large methane reserves, shorten reaction time, and no foam during hydrate decomposition.Liu et al. [20] studied the micromorphology of hydrate in SDS solution by using a high-speed camera.They believed that the existence of SDS can reduce the critical size of hydrate core and energy barrier, and promote the formation of hydrate.Tajima et al. [21] and Qin et al. [22] both observed that the structure of hydrates in SDS solution was porous and heterogeneous.All these indicate that the addition of SDS was beneficial to the continuous process of mass transfer.However, there are also some concerns about adding SDS to the solution.For example, the large-scale use of SDS will cause environmental pollution, and the decomposition of hydrates will produce a large amount of foam, which had a negative impact on the practical application of natural gas hydrate.
Recently, based on the high thermal conductivity and mass transfer coefficient of nanoparticles, they have been used to improve the formation kinetics of natural gas hydrate.Many scholars have shown that carbon materials play a good role in promoting the storage of hydrate.Bai et al. [23] reported that the degree of heterogeneity provided by nano-graphite was much higher than that of microngraphite, which promoted the nucleation rate in the induction stage.When the graphite particle sizes decreased from 1 l to 20 nm, the gas-solid-liquid contact area increased, increasing the final gas consumption.Li et al. [24] used graphite to promote hydrate-based desalination.The results showed that the addition of graphite can shorten the induction time, promote the formation of hydrate and improve the desalination efficiency.Pasieka et al. [25] found that the low concentration of multi-walled carbon nanotubes (MWCNTs) promoted the growth rate of hydrate because it enhanced the mass transfer capacity.At high concentrations, this effectiveness decreased because the temperature rises in the system increased, which limited the mass transfer and heat transfer of hydrate formation.Zhou et al. [26] explored the influence of GNs on the formation of carbon dioxide hydrate.The results showed that the presence of GNs had a positive effect on the formation of hydrate, the induction time was shortened by 80.8%, and gas consumption increased by 12.8%.Then, they studied the effect of GNs on CO 2 hydrate in tetrabutylammonium bromide solution [27] .The results showed that the concentration of GNs had little effect on the phase equilibrium of CO 2 hydrate formation.In the 0.08% GNs þ 9.01% TBAB system, the hydrate formation rate was the highest, and the final water conversion rate reached 50.7%.Park et al. [28] found that the concentration of 0.004 wt% MWCNTs consumed 300% more gas than pure water.The duration of hydrate formation was shortened at lower undercooling.After further research, they found that the presence of oxidized carbon nanotubes could increase the gas consumption of methane by 4.5 times.At low undercooling (< 8 K), the formation rate of methane hydrate was accelerated [29] .Yan et al. [30] added a 0.5% mass fraction of GNs to the solution of tetrahydrofuran and SDS, the gas consumption increased significantly compared with no addition.However, the promotion effect of carbon nanotubes was weakened due to their tendency to aggregate.Therefore, scholars have prepared highly dispersed carbon nanotubes through some processes, which can not only promote the formation of hydrate but also do not produce foam in the dissociation process.Song et al. [31] prepared highly dispersed carbon nanotubes by coating styrene-co sodium styrene sulfonate (PSCS) on the surface of nanotubes, showing excellent performance during hydrate formation.After that, Song et al. [32] prepared water-soluble carbon nanotubes for the methane hydrate formation system, which improved the energy storage efficiency of hydrate.Finally, the gas storage capacity was increased from 40 v/v to 140 v/v and the induction time was shortened to 203 min.
The above research was carried out under stirring conditions, which will prevent the agglomeration and deposition of carbon nanoparticles.Therefore, the above carbon materials all meet the purpose of promoting hydrate formation, but the stirring process will increase additional energy consumption.The purpose of this study is to explore the gas consumption, hydrate formation rate, induction time and morphology of hydrate by adding graphite nanoparticles to SDS solution under different pressures, hoping to achieve better promotion effect and provide theoretical support for the application of graphite nanoparticles in the storage of methane hydrate in solidified natural gas.

Materials
Methane gas (purity > 99.99%) was purchased from Shenyang Kerui Special Gas Co., Ltd.Sodium dodecyl sulfate (SDS) (purity � 94%) was supplied by Guangdong Fine Chemical Engineering Research and Development Center.Graphite nanoparticles (purity > 99.9%) were provided by Qingdao new materials Co., Ltd.The basic information about GNs is shown in Table S1.Deionized water was prepared in the laboratory.Plastic containers with 5.3 � 10 cm were used to observe the side view of hydrate formation.

Experimental device
The KDSD-II type hydrate kinetics experimental set-up provided by Jiangsu Kedi Petroleum Instrument Co., Ltd.(China) is shown in Figure S1.The experimental set-up mainly consists of four parts, namely hydrate formation system, temperature-control system, pressure-control system, and data acquisition system.The hydrate formation system includes a stainless steel reactor with a glass window.The maximum volume of the reactor was 350 mL, the working temperature was À 10-90 � C, and the working pressure was not higher than 25 MPa.A 50 vol% alcohol solution was used as coolant in the cryogenic thermostat bath, which operating the temperature in the reactor.Two platinum resistance sensors were set inside the reactor with an uncertainty of 0.1 � C. Different electric quantities were generated by the temperature difference and converted into electrical signals, which were transmitted through the temperature sensor.The pressure in the reactor was controlled by the balance tank and transmitted through the pressure sensor with an uncertainty of 0.01 MPa.The experimental data were recorded by a data acquisition system every 20 s.

Experimental procedure
According to the research of Ganji et al. [33] , SDS with 0.03 wt% concentration can achieve a higher promoting effect.Therefore, 0.03 wt% concentration of SDS and different concentrations of graphite nanoparticles to conduct hydrate formation experiments.In order to prevent the electrical adsorption of GNs on the metal surface of the reaction vessel, and to better observe the hydrate formation, plastic containers with 5.3 � 10 cm were chosen as the hydrate reaction carrier.Before the experiment, the inner wall of the reactor and the plastic container was flushed with deionized water and dried to avoid the interference of residual magazines and residual water to the experiment.The plastic container was put into the reactor and then sealed the reactor.An air tightness test was carried out by injecting nitrogen into the reactor and pressurizing the reactor to 7 MPa.If the temperature and pressure were stable for at least 2 h, the container was considered to be air tight.Afterward, the nitrogen was released from the system and evacuated using a vacuum pump.After that, graphite nanofluid was prepared and then oscillated for 1 h at 40 W in an ultrasonic shaker.The obtained suspension was not disturbed within a certain period.100 mL of prepared compound solutions were injected into the reactor through the inlet.The reactor was placed in a 275.15K constant temperature water bath, and when the temperature dropped to the experimental temperature, and then methane gas was introduced into the reactor to 7 MPa at a rate of 0.1 MPa/s through the gas inlet.When the temperature and pressure reached the experimental conditions, the experiment was regarded as the beginning of the experiment.The data statistics system was used to record the data every 20 s.When the pressure in the container remained stable for 150 mins, the experiment was considered to be completed.Finally, the plastic container was taken out to observe the morphology of the hydrate.In order to ensure the repeatability and reliability of the experiments, three groups of experiments were carried out for each group.

Calculation formulas
According to the research of Abdi-Khanghah et al. [34] , the gas consumption of hydrate during hydrate formation is calculated by equation (1): Where Dn CH4 is the moles of CH 4 consumed during hydrate formation; P and T are the pressure and temperature in the reactor, respectively; V is the volume of methane gas; 0 and t are the initial time and t time, respectively.R is the general gas constant, taken as 8.314 J�mol À 1 K À 1 ; z t represents the compressibility factor and calculated by equation (2): For methane gas, T c is 190.6 K, P c is 4.599 MPa, x is 0.012.
According to Ren et al. [35] , the hydrate formation rate is calculated by the equation (2): where r is the rate of hydrate formation; Dn CH4,iþ1 and Dn CH4,i is moles of CH 4 consumed during hydrate formation at any given time t iþ1 and t i , respectively, and can be calculated using Eq.(1); t iþ1 À t i is the time interval for the data acquisition system to record experimental data; i is the number of experimental data records.
The gas storage capacity of solution S l is calculated by equation (3): where n w is the moles of water used in the experiment.

Results and discussion
The hydrate formation process can be divided into dissolution period, induction period, and growth period [36] .
During the dissolution period, methane gas is dissolved in the liquid through the gas-liquid interface, causing a small range of pressure drops.As reported in the literature [37] , induction time is defined as the time from the beginning of the experiments to the onset of hydrate nucleation.Hydrate nucleation during the induction period is random and related to parameters such as driving force, impurities, and saturation, so the induction time is usually discrete [38] .
During the induction period, hydrate nuclei grow into stable nuclei with critical size, and the pressure changes little at this stage.During the growth period, a large number of hydrate nuclei with critical size continue to accumulate and grow rapidly, which makes the pressure drop significantly at this stage.The experimental data of this study are shown in Table S2.

Low pressure conditions
The gas consumption in GNs and SDS solutions under the initial conditions of 4 MPa and 275.15K is shown in Figure 1.For the three groups of GNs concentration was 0.01, 0.05, and 0.1 wt% composite systems, the gas consumption curve showed similar jumps in different periods, the final gas consumption increases to about 0.15 mol, which exceeded the gas consumption in SDS system by 0.12 mol, which indicated that adding an appropriate amount of GNs at low pressure can improve the gas storage capacity of hydrates.This sudden jump is related to the increase of gas consumption and hydrate formation rate. Figure 2 shows the rate of hydrate formation.This may be due to the large specific surface area of GNs and the increase of the gas-liquid contact area.Therefore, CH 4 hydrate nucleated and grew faster in graphite nanofluids, resulting in a higher gas consumption rate during the growth of CH 4 hydrate in graphite nanofluids.However, when the GNs concentration was 0.15 wt%, the gas consumption was slightly lower than that of SDS system, and hydrates formed slowly.This may be due to the excessive aggregation of nanoparticles.Lu et al. [37] found that with the increase of GNs concentration, GNs will aggregate, thus increasing the particle size, which reduced the available area for hydrate nucleation and growth and limited the growth of hydrate.The above analysis shows that when the solution contains low or high GNs, the effect on the hydrate induction period or gas consumption of hydrate is not satisfactory.
It can be seen from Table 1 that the maximum hydrate formation rates of the three groups of compound systems with GNs concentrations of 0.01, 0.05, and 0.1 wt% were all around 1.5 mol/min, and the hydrate formation rate at 0.15 wt% was only 0.52 mol/min.It is worth noting that the addition of GNs reduces the hydrate formation rate.In addition, the duration of hydrate formation in SDS solutions was about 150 min.In the compound system, after the addition of 0.15 wt% GNs, the longest reaction time of hydrate was about 750 min, and the shortest reaction time of 0.05 wt% GNs was 250 min.Therefore, under low pressure conditions, the addition of GNs prolonged the duration of hydrate formation.
Figure 3 depicts the final morphology and growth pattern of gas hydrate in the reactor.It can be seen that the    [ 34 ] CH 4 6.114 274.65 0.068 0.000045M Ag [ 45 ] CH 4 7 273.65 0.037 0.0035 wt% SDS þ 0.05 wt% CuO [ 46 ] CH 4 6 274.15 0.089 4 mmol/L SDS þ 4 mmol/L Fe 3 O 4 [ 47 ] CH 4 6 275.15 0.023 0.00018M Cu þ 0.0022M CTAB [ 48 ] CH container contains a large amount of foam, there was a small amount of solution in the container, and only a small amount of hydrate was formed at the top, which reduced the gas storage capacity of the hydrate, which may be due to the insufficient driving force of the low pressure condition, the Brownian motion of the particles in the solution was weakened, and the nanoparticles will be deposited on the bottom of the container with the increase of time.Compared with other reaction systems, after the reaction of 0.05 wt% GNs, a small amount of hydrate and unreacted solution in the container were mixed with less foam.This suggests that adding an appropriate amount of GNs to the solution can reduce foam generation even under low driving force conditions.However, although low pressure conditions can save energy, they were not feasible in practical SNG technology applications.Therefore, we increased the initial pressure of the experiment to 7 MPa and continued to observe changes in hydrate growth.

High pressure conditions
Figure 4 shows the gas consumption in the presence of GNs and SDS at 7 MPa and 275.15 K.The gas consumption curves of the three groups of compound systems with GNs concentrations of 0.01, 0.03, and 0.1 wt% had similar upward trends, and the hydrate formation ended in the first 80 min.The maximum gas consumption was 0.537 mol at 0.03 wt% concentration.When the GNs concentration increased to 0.05 wt%, the trend of the curve changed, and the hydrate experienced a slow upward process in the first 80 min, and the final gas consumption did not decrease.
It can be seen from Figure 5 that the hydrate formation is completed in about 140 min after the addition of GNs, while the reaction of SDS alone system ends in 350 min.This showed that the addition of GNs shortened the duration of hydrate formation under high pressure.Moreover, the addition of GNs also improved the rate of hydrate formation.This may be because the presence of GNs enhanced heat transfer.During the formation of hydrate, as an exothermic reaction, the heat generated quickly flowed into the environment, which improved the formation rate of hydrate.In addition, in the practical application of SNG, the formation conditions of hydrate have an important influence on energy consumption.The driving force has a decisive influence on the hydrate growth kinetics in suspension.As shown in Table S2, compared with 4 MPa, the increase in gas consumption increased by 227%, 221%, and 244%, respectively.The hydrate formation rates increased by 702%, 844%, and 546%, respectively.The formation of hydrate under low pressure was generally 800 min, and the high pressure was generally 200 min.This suggested that the conversion of natural gas and water into hydrates was more complete at relatively higher pressures.
Different from low pressure, we observed that a large amount of hydrate was formed in the container at 7 MPa, and no obvious liquid phase and a lot of foam was observed in the container.The GNs did not settle at the bottom of the solution but were encapsulated by hydrates.This was due to the Brownian motion of GNs in the solution being intensified under high pressure, which enhanced the turbulence of the fluid and promoted the massive formation of hydrates.The hydrate formed under high driving force was loose and porous, and it is easy to burst in the air, which can also indicate that many GNs coalesced inside the hydrate.
Among them, there were obvious dense needlelike hydrates on the sidewall of the container in Figure 6(a) and (d), while the needlelike hydrate on the sidewall was not dense in Figure 6(b).Spherical and coarse needlelike hydrates were formed, and the hydrates move up some distance in Figure 6(c).The continued growth of needle hydrate may form thick needles.Previous studies have shown that needle hydrates can promote heat dissipation and maintain the low temperature environment required for hydrate formation [39] .Spherical hydrates may be formed by the collision and agglomeration of GNs covered by hydrate shells.
The study by Lu et al. proved that hydrate cores were first formed in the liquid phase and grow into hydrate crystals [37] .Afterward, the gas-liquid interface and the liquid phase were simultaneously generated, and dense hydrates were formed laterally and longitudinally along the reactor wall, which resulted in the phenomenon that the hydrate layer was hollow.The mode of hydrate growth along the wall was not only conducive to heat dissipation but also can increase the nucleation area.

Mechanism of hydrate formation
GNs suspended in solution have rough surfaces with a large number of nucleation sites.GNs have adsorptive properties, and more methane is adsorbed on the surface of GNs, forming locally aggregated regions with higher density, which enhances gas diffusion and promotes hydrate mass transfer through Brownian motion.Once the hydration conditions were satisfied, methane hydrate rapidly nucleated at the graphite-water interface.As the hydrate core continued to grow, a thin solid hydrate shell formed on the particle surface, which gradually thickened and wrapped around it (Figure 7).The hydrophobicity of GNs facilitated the rapid adsorption of CH 4 molecules on the surface and promoted hydrate nucleation [40] .Guo et al. [41] found that methane nanobubbles on the hydrophobic interface can act as nucleation centered for methane hydrate, thereby inducing rapid hydrate nucleation.
In addition, GNs have excellent heat transfer ability, as shown in Table S1, the heat transfer coefficient is 129 Wm À 1 K À 1 .It is well known that the hydrate formation reaction was exothermic.A large amount of hydrate was formed in our experiments at 7 MPa, thus releasing a large amount of heat.GNs can be used as a good heat carrier to remove the heat of hydrate formation and increase the reaction rate.Nanoparticle diameter, density, and ultrasonic vibration can affect the stability of nanofluids [42] .The attractive force was stronger than the repulsive force between GNs with a larger specific surface area in solution, so the nanoparticles were easily collided and aggregated.Initially, as the concentration of GNs increased from 0, the nucleation sites of hydrates increased, which promoted the heterogeneous nucleation of hydrates, thereby shortening the induction period.As the concentration of GNs in the solution continued to increase, the particles agglomerated and the particle size increased.Nashed et al. [43] reported that the kinetic size of the aggregated particles led to a reduction in the original specific surface area of GNs.Therefore, the total gas-liquid contact area was reduced, and this process hindered the mass transfer process.

Comparison of different nanofluid systems
GNs have stable chemical properties and are easy to separate, which is beneficial to the recycling of GNs and reduces secondary pollution.The lubricating properties of GNs reduce wear on mechanical equipment, so they can be widely used in hydrate generation technology.In addition, compared to other nanoparticles, GNs have higher heat transfer coefficients and are inexpensive, thereby reducing costs.The experimental results showed in Figure S2 that the gas consumption of the hydrates in the GNs system used in this experiment was improved compared with those reported in other literature, reaching the highest value.Therefore, CH 4 hydrate formation in the graphite nanofluids was significantly enhanced.

Conclusions
In this paper, hydrate formation experiments were performed using GNs and SDS at different pressures under non-stirred conditions.The kinetic effects of low or high pressure on the formation of methane hydrate were investigated.The formation mechanism of hydrate was discussed in detail with the combination of a data diagram and phenomenon diagram, and the excellent performance of carbon materials and other nanoparticles in gas consumption was compared.The following conclusions were drawn from this work: 1.Under low pressure conditions, due to the gradual aggregation and sedimentation of GNs, the formation rate of hydrate was reduced and the duration of hydrate formation was prolonged.Only a small amount of hydrate was formed in the container, but it was accompanied by a large amount of foam, which was not conducive to the application of hydrate technology.2. Under high pressure, the addition of GNs improved the hydrate formation rate and shortened the duration of hydrate formation.At the same time, compared with the low pressure environment, a large number of hydrates were generated, showing an excellent kinetic promotion effect.3. The gas consumption obtained in graphite nanofluids was greater than that of other metal or oxide nanofluids, so cheap GNs can be used as an effective method to solidify methane hydrate generation in natural gas storage.
This study provides a theoretical basis for the formation of hydrate in the composite system of GNs and surfactants.In addition, there are few studies on the formation kinetics and morphology of hydrates in graphite nanofluids under pressure.These results provide some bright light for future research.

Figure 2 .
Figure 2. Rate of hydrate formation in the systems of SDS and GN with different concentrations at 275.15 K and 4 MPa.

Figure 1 .
Figure 1.Gas consumption in the systems of SDS and GN with different concentrations at 275.15 K and 4 MPa.

Figure 3 .
Figure 3. Hydrate morphology in the complex systems of SDS and GN at 275.15 K and 4 MPa (a, b, c, d, and e correspond to GN concentrations of 0, 0.01, 0.05, 0.1, and 0.15 wt%).

Figure 4 .
Figure 4. Gas consumption in the systems of SDS and GN with different concentrations at 275.15 K and 7 MPa.

Figure 5 .
Figure 5. Maximum rate of hydrate formation and duration of hydrate formation in the systems of SDS and GN with different concentrations at 275.15 K and 7 MPa.

Figure 6 .
Figure 6.Hydrate morphology in the complex systems of SDS and GN at 275.15 K and 7 MPa (a, b, c, and d correspond to GN concentrations of 0.01, 0.03, 0.05, and 0.1.

Table 1 .
Comparison of the promotion efficiencies of GNs and other metal or oxide materials for hydrate formation.