The Thermodynamic and Kinetic Effects of Sodium Lignin Sulfonate on Ethylene Hydrate Formation

: Hydrate-based technologies (HBTs) have high potential in many ﬁelds. The industrial application of HBTs is limited by the low conversion rate of the water into hydrate ( R WH ), and sodium lignin sulfonate (SLS) has the potential to solve the above problem. In order to make the HBTs in the presence of SLS applied in industry and promote the advances of commercial HBTs, the effect of SLS on the thermodynamic equilibrium hydrate formation pressure ( P eq ) was investigated for the ﬁrst time, and a new model (which can predict the P eq ) was proposed to quantitatively describe the thermodynamic effect of SLS on the hydrate formation. Then, the effects of pressure and initial SLS concentration on the hydrate formation rate ( r R ) at different stages in the process of hydrate formation were investigated for the ﬁrst time to reveal the kinetic effect of SLS on hydrate formation. The experimental results show that SLS caused little negative thermodynamic effect on hydrate formation. The P eq of the ethylene-SLS solution system predicted by the model proposed in this work matches the experimental data well, with an average relative deviation of 1.6% and a maximum relative deviation of 4.7%. SLS increased R WH : the ﬁnal R WH increased from 57.6 ± 1.6% to higher than 70.0% by using SLS, and the highest ﬁnal R WH (77.0 ± 2.1%) was achieved when the initial SLS concentration was 0.1 mass%. The r R did not signiﬁcantly change as R WH increased from 35% to 65% in the formation process in the presence of SLS. The effect of increasing pressure on increasing r R decreased with the increase in R WH when R WH was lower than 30%, and the difference in pressure led to little difference in the r R when R WH was higher than 30%. studies on the interfacial tensions between FCC dry gas and PSS solution [15], as well as air and n-octyl- β -D-glucopyranoside solution [54]. Taking the foaming ability, resource utilization, environmental protection and the performance of SLS on decreasing gas–liquid interfacial tension into consideration, SLS is a surfactant with good potential in hydrate formation. Author Contributions: Conceptualization, Y.W.; methodology, Y.W.; software, Q.S.; validation, L.Y., L.W., Z.H. and Y.L.; formal analysis, Y.W.; investigation, L.W., Z.H. and Y.L.; resources, J.G., A.L. and X.G.; data curation, Y.W. and X.G.; writing—original draft preparation, Y.W.; writing—review and editing, Y.W., A.L. and X.G.; visualization, L.Y.; supervision, J.G. and X.G.; project administration, Y.W. and X.G.; funding acquisition, Y.W. and X.G. All authors have read and agreed to the published version of the manuscript.


Introduction
Clathrate hydrates are crystal inclusion compounds which are made up of water molecules and guest molecules (such as CH 4 , C 2 H 4 , CO 2 , etc.) [1]. The guest gas molecules are captured into hydrate cages by van der Waal interaction forces [2], and the water molecules in clathrate hydrates are connected by hydrogen bonds [3]. The three common hydrate structures are cubical structure I (sI), cubical structure II (sII) and hexagonal structure H (sH) [4]. Due to the properties of clathrate hydrate shown in the literature (such as environmental friendliness [5], high gas storage capacity [6], different selectivity on gas species [7], moderate operating condition [7], high energy content [8] and non-explosive nature [9]), hydrate-based technologies have been proved to have high potential in many fields, such as carbon dioxide capture [10], gas separation [11], gas storage/transportation [12], water desalination [13] and cold storage [8]. However, few conditions, etc.) [29], so that the gas-to-water ratio of molecular numbers in the hydrate is variable, which is why R WH cannot be accurately calculated. It needs to be pointed out that the relationship between the r R and the R WH is different from the relationship between the r R and the amount of the gas in the hydrate formed by the gases that can occupy both the small cavities and the large cavities. Because the θ is variable, the amount of the gas in the hydrate in experiment A can be higher than the amount of gas in the hydrate in experiment B when the R WH in experiment A is lower than the R WH in experiment B.
Surfactants do not form hydrate [15] and the concentration of the SLS in the liquid phase (w p ) increases as R WH increases, so that the thermodynamic effect of SLS on hydrate formation increases as R WH increases. Since SLS is a kind of salt, it might have a considerable negative thermodynamic effect on hydrate formation when R WH is high [30]. In addition, the effect of SLS on the hydrate formation in Section 4.3 is the combination of the thermodynamic and kinetic effects of SLS on hydrate formation, so that the kinetic effects would be easy to investigate when the thermodynamic effect is known. For the above reasons, the thermodynamic effect of SLS on hydrate formation was investigated in Section 4.1 before the investigation in Section 4.3 was carried out. Since the gas-liquid interfacial tension is necessary for the discussion on the kinetic effect of SLS on hydrate formation, the interfacial tension between ethylene gas and SLS solution was investigated in Section 4.2. Since the difference between the final state of the hydrate formation and the state of thermodynamic phase equilibrium needs to be quantitatively described in the discussion in Section 4.3, the thermodynamic phase equilibrium pressure under the condition at the end of the hydrate formation (P eq,end ) needs to be calculated, so that a prediction model of the ethylene-SLS solution system is necessary.
The two most used mechanism models in hydrate formation are the van der Waals-Platteeuw (vdW-P) model [31] and Chen-Guo model [32], which are the foundation of most hydrate formation models. Both the vdW-P model and Chen-Guo model assume that: (a) one hydrate cavity contains at most one guest molecule, (b) the guest molecule-guest molecule interaction can be neglected and (c) the effects of the encaged guest molecules on the hydrate host lattice can be neglected [31,32]. Those assumptions make model calculations simple but at the same time limits the application range and the prediction accuracy of hydrate formation models. In the hydrates formed by small gas molecules, such as hydrogen, oxygen and nitrogen, one cavity can capture two or more than two gas molecules under specific conditions [33]. For example, in the hydrogen hydrate (structure II) formed at 260 K under 20 MPa, more than 80% of the large cavities are occupied by more than one hydrogen molecules [34]. The literature also shows that the guest molecule-host molecule interaction [35], guest molecule-guest molecule interaction [33] and the host relaxation [33] can significantly affect the structure of the hydrate and properties of the corresponding systems.
Many investigations have been done to overcome the limitations caused by the above assumptions. For the models based on the vdW-P theory, the most effective method to overcome the limitations caused by the above assumptions is introducing the host lattice relaxation, guest-guest interactions, guest-host interactions, the quantum nature of guest behavior and the possibility of occupation of single cage by several guests into the method for calculating the chemical potential of water in hydrate [34,[36][37][38], and the models using that method work very well on predicting the phase equilibrium conditions of methane/xenon -hydrate-ice Ih system [36], argon/krypton -hydrate-ice Ih system [38], hydrogen/(hydrogen+propane)-hydrate-ice Ih system [34], helium-ice based hydrateice systems [37] and so on. For the models based on the Chen-Guo theory, the host lattice relaxation, guest-host interactions and the quantum nature of guest behavior are introduced into the models by introducing an Antoine-type equation into the calculation of the fugacity of the components in hydrate, and the Antoine parameters are fitted using the pure gas hydrate formation data for a particular structure only [39]. The guestguest interaction between the guest molecules in small cavities and in large cavities are introduced into models by introducing a correction term into the calculation of the fugacity of the components in hydrate, and the parameters in the correction term are fitted using experimental data [39]. The possibility of the occupation of a single cage by several guests into the calculation has not been introduced into the models based on the Chen-Guo theory so far.
The number of the parameters required in the Chen-Guo model is less than that of the parameters required in the vdW-P model, which makes the calculations of new systems in the Chen-Guo model simple [31,39]. Since SLS is a new prompter for the hydrate formation model and the occupation of a single cage by several ethylene molecules does happen in the formation of ethylene hydrate (multiple occupancies by carbon dioxide and methane are not supported by experimental data, and the size of ethylene molecule is larger than those of carbon dioxide and methane) [27,33], the Chen-Guo model was chosen to describe the hydrate formation process in the new model in this work, which is described in Section 3 and validated in Section 4.1. It needs to be pointed out that, in the assumptions of the Chen-Guo model, the first step is always the formation of large cavities, which is not in the assumptions of the vdW-P model [31,39]. Though that assumption makes the calculation process of the Chen-Guo model simple, it may limit the application range of the model.
The experimental apparatus used in Sections 2.2 and 2.4 is shown in Figure 1. The maximum volume of the variable cell is 665.0 mL. The uncertainty of the measured temperature inside the crystallizer is ±0.05 K. The uncertainty of the measured pressure inside the crystallizer is ±0.005 MPa.
data [39]. The possibility of the occupation of a single cage by several guests into the calculation has not been introduced into the models based on the Chen-Guo theory so far.
The number of the parameters required in the Chen-Guo model is less than that of the parameters required in the vdW-P model, which makes the calculations of new systems in the Chen-Guo model simple [31,39]. Since SLS is a new prompter for the hydrate formation model and the occupation of a single cage by several ethylene molecules does happen in the formation of ethylene hydrate (multiple occupancies by carbon dioxide and methane are not supported by experimental data, and the size of ethylene molecule is larger than those of carbon dioxide and methane) [27,33], the Chen-Guo model was chosen to describe the hydrate formation process in the new model in this work, which is described in Section 3 and validated in Section 4.1. It needs to be pointed out that, in the assumptions of the Chen-Guo model, the first step is always the formation of large cavities, which is not in the assumptions of the vdW-P model [31,39]. Though that assumption makes the calculation process of the Chen-Guo model simple, it may limit the application range of the model.
The experimental apparatus used in Sections 2.2 and 2.4 is shown in Figure 1. The maximum volume of the variable cell is 665.0 mL. The uncertainty of the measured temperature inside the crystallizer is ±0.05 K. The uncertainty of the measured pressure inside the crystallizer is ±0.005 MPa.
When the crystallizer is isolated from the outside, the pressure inside the crystallizer can be increased/decreased by decreasing/increasing the volume of the crystallizer. The volume of the crystallizer is adjusted by adjusting the position of the piston inside the crystallizer, and the position of the piston is adjusted by using the manual pump with scale division lines (±0.05 mL uncertainty).

The Measurement of Peq
The method for measuring the Peq of the ethylene gas + SLS solution/pure water system in this work is reported in detail in the literature [15], and the reliability of the method has been ensured in the literature published by this laboratory [40,41]. The When the crystallizer is isolated from the outside, the pressure inside the crystallizer can be increased/decreased by decreasing/increasing the volume of the crystallizer. The volume of the crystallizer is adjusted by adjusting the position of the piston inside the crystallizer, and the position of the piston is adjusted by using the manual pump with scale division lines (±0.05 mL uncertainty).

The Measurement of P eq
The method for measuring the P eq of the ethylene gas + SLS solution/pure water system in this work is reported in detail in the literature [15], and the reliability of the method has been ensured in the literature published by this laboratory [40,41]. The experiment under each operating condition was repeated three times to ensure the repeatability of the experimental data.

Interfacial Tension Measurement
The experimental apparatus and procedures in this section are the same as those reported in the literature published by this laboratory [42,43]. In order to ensure the repeatability of the experimental data, the experiment was repeated at least four times under each experimental condition.

Ethylene Hydrate Formation in the Presence of SLS
The experimental procedure is briefly described as follows: 1.
The crystallizer was washed and dried before each experiment.

2.
The temperature inside the crystallizer was kept at the experimental temperature.

3.
A total of 40 mL SLS solution/pure water was injected from the liquid inlet into the crystallizer. 4.
The air inside the crystallizer was completely replaced by ethylene gas. 5.
The temperature inside the crystallizer was kept at the experimental temperature. 6.
Ethylene gas was injected into the crystallizer to increase the pressure. 7.
Once the pressure inside the crystallizer reached the experimental value, the valves of the crystallizer were closed to isolate the crystallizer from the outside. The stirrer was set at a constant speed of 500 rpm. This moment was noted as the start of a hydrate formation experiment. 8.
Along with the consumption of the ethylene gas by hydrate formation, the pressure inside the crystallizer was kept constant by decreasing the volume of the crystallizer. The data of time vs. the volume of the crystallizer was recorded. 9.
When the volume of the crystallizer remained constant for at least 2 h, the hydrate formation was considered to have ended. 10. The experiment under each operating condition was repeated three times.

Ethylene Hydrate Formation in the Presence of SLS
The amount of the ethylene in the hydrate slurry at time t (N d,t , mol) can be calculated by Equation (1): where V cr,0 is the volume of the crystallizer at the beginning of the hydrate formation, V cr,t is the volume of the crystallizer at the time t in the hydrate formation, P f and T f are the experimental pressure and temperature, respectively, and they are kept constant in each individual experiment, R is 8.3145 J·mol −1 ·K −1 and Z is the compressibility factor of the gas inside the crystallizer under the experimental condition, which is calculated by Patel-Teja EOS [44]. The gas storage capacity of the hydrate slurry (GSCHS, NL/L) is calculated by Equation (2): where V sol is the volume of the SLS solution/pure water at the beginning of an experiment, P st is 101,325 Pa, T st is 273.15 K, N d,end is the amount of the ethylene in the hydrate slurry at the end of the hydrate formation and Z st is the compressibility factor of the ethylene gas under 273.15 K, 101325 Pa. The hydrate formation rate (r R=X ,%/min) when R WH is X (%) is calculated as the average formation rate during the period that R WH increases from X − 1.0% to X + 1.0%: where t (X+1.0%) is the time when R WH is X + 1.0% and t (X−1.0%) is the time when R WH is X − 1.0%. The average data (Data) and the uncertainty for the repeated experiments (Data u ) are calculated as follows: The experiment, under each operating condition, was repeated jj times to ensure repeatability. jj is 4 for the experiments in Sections 3 and 4.2 for the experiments in Sections 4.1 and 4.3. jjj is the sequence number. Data max and Data min are the maximum value and minimum value of a data in jj times repeated experiments, respectively.

Modeling
The model in this work uses "the difference in chemical potentials is zero when pressure is P eq " [15] as the convergence condition of the iterative algorithm and uses Modified PT EOS [45] to introduce the thermodynamic effect of SLS on the hydrate formation into the model, which distinguishes the model in this work from the other models based on the Chen-Guo two-step hydrate formation mechanism [32,39].
The first step in the Chen-Guo two-step hydrate formation mechanism is the formation of basic hydrate (the small cavities are all empty): each ethylene molecule in liquid phase forms an unstable molecular cluster with the water molecules nearby, and this molecular cluster is the structure of the large cavity. As discussed in the Introduction, one large cavity is occupied by one ethylene molecule. Then, the clusters connect with each other to form stable basic hydrate, and the connection among the clusters in this step leads to the formation of the linked cavities, which are also called the small cavities [32]. It should be pointed out that basic hydrate is stoichiometric, and for the hydrate with a specific structure (structure I, etc.), the ethylene-to-water ratio of molecular numbers in basic hydrate (λ 2 ) is a fixed constant (3/23 for structure I hydrate) [39]. This step can be illustrated as [32]: The second step is that the molecules (S), which are smaller than the small cavities, are adsorbed into the empty small cavities of basic hydrate [32]. In this step, hydrate converts from basic hydrate to final hydrate: where λ 1 is the ratio of the small cavity-to-water molecule numbers in basic hydrate (1/23 for structure I hydrate) and θ is the occupation fraction (%) of the small cavities filled by small gas molecules. It should be pointed out that, since ethylene molecules are larger than the small cavities of hydrate, the second step does not occur in the formation of ethylene hydrate, which is different from the prediction models mentioned in Section 4.1 [15,[46][47][48][49]. When the basic hydrate formation shown in Equation (6) reaches equilibrium [15]: where µ 0 B is the chemical potential of the basic hydrate, µ C 2 H 4 and µ w are the chemical potentials of C 2 H 4 and water, respectively, µ 0 C 2 H 4 is the chemical potential of the C 2 H 4 at ideal gas state, f C 2 H 4 is the fugacity of the C 2 H 4 under the experimental condition and is calculated by Patel-Teja EOS [44] and f 0 C 2 H 4 is the fugacity of the C 2 H 4 in the basic hydrate under the experimental condition. Since the second step does not occur in the formation of ethylene hydrate, the basic hydrate is the final hydrate, so that the chemical potential of the final hydrate (µ B ) can be calculated as follows [39]: The change of the chemical potential during the hydrate formation (∆µ) is the difference between the final chemical potential and the initial chemical potential (µ B − µ initial ) [15]: Combining Equations (8)- (11): f 0 C 2 H 4 is calculated as follows [39]: where β is a structure parameter (0.4242 K/bar for structure I hydrate) and α w is the activity of the water in the liquid phase. The host lattice relaxation, guest-host interactions and the quantum nature of guest behavior are introduced into the models by introducing an Antoine-type equation f 0 T (T) into the calculation of f 0 C 2 H 4 , and the Antoine parameters are fitted using the pure gas hydrate formation data for a particular structure only [39]: where A is 4.8418 × 10 11 bar, B is −5597.59 K and C is 51.8 K [39]. SLS does not form hydrate, and its thermodynamic effect on hydrate formation in the model calculation mainly manifests as its effects on α w . The SLS solution is an electrolyte solution, the α w is calculated by the Modified PT EOS [44,50] and the calculation process is shown in the Supplementary Materials. Since the ionic diameter and polarizability of the anion of SLS used for the calculation of α w have not been reported, they (23.87 Å and 35.92 Å 3 ) were fitted using the experimental data in Section 4.1; the fitting process is shown in the Supplementary Materials. The parameters used for the calcuation of f 0 C 2 H 4 is shown in Table S4 in the Supplementary Materials. P eq,Cal is the P eq in the model calculation. Whether hydrate can be formed can be determined directly according to ∆µ. Because ∆µ is negative when the pressure is higher than the P eq,Cal , ∆µ is positive when the pressure is lower than P eq,Cal , and ∆µ equals to zero when the pressure equals to P eq,Cal [15]. It should be pointed out that P eq,Cal is unique when temperature and phase compositions are all determined [15]. Since P eq,Cal could be an irrational number, it is not certain whether P eq,Cal can be determined directly by a trial-and-error method. However, the range of P eq,Cal can be easily determined, because ∆µ increases monotonously with the decrease of pressure [15]. The flow chart of the calculation of P eq,Cal is shown in Figure 2. The iterative computation was edited by Visual basic 6.0 and can also be edited by the software which can be used in iterative computation.
In Figure 2, w p is the concentration of the promoter (SLS) in the liquid phase and P u is the uncertainly of P eq,Cal and is set at 0.001 MPa in this work, because P u should be smaller than the uncertainty of the experimental P eq (0.01 MPa in Section 4.1).
When ∆µ is positive under P − 0.5P u and negative under P + 0.5P u , which means that P − 0.5P u is lower than P eq,Cal and P + 0.5P u is higher than P eq,Cal , the difference between P and P eq,Cal is smaller than P u , which means that P can be regarded as P eq,Cal and the accuracy meets the requirement of the model calculation. When ∆µ is positive under P − 0.5P u as well as P + 0.5P u , P is lower than P eq,Cal and the difference between P and P eq,Cal can be larger than P u . When ∆µ is negative under P − 0.5P u as well as P + 0.5P u , P is higher than P eq,Cal and the difference between P and P eq,Cal can be larger than P u . It should be pointed out that if ∆µ is negative under P − 0.5P u but positive under P + 0.5P u (which never happened in this work), which means that P eq,Cal is smaller than P − 0.5P u but is higher than P + 0.5P u , which is contrary to reality, then the calculation would end and the model would be rechecked. Start Calculate Δμ(P+0.5P u ) and Δμ(P-0.5P u ) by Equation (12) Enter w P , T, P u End P eq,Cal =P, Export P eq,Cal In Figure 2, wp is the concentration of the promoter (SLS) in the liquid phase and Pu is the uncertainly of Peq,Cal and is set at 0.001 MPa in this work, because Pu should be smaller than the uncertainty of the experimental Peq (0.01 MPa in Section 4.1).
When ∆μ is positive under P − 0.5Pu and negative under P + 0.5Pu, which means that P − 0.5Pu is lower than Peq,Cal and P + 0.5Pu is higher than Peq,Cal, the difference between P and Peq,Cal is smaller than Pu, which means that P can be regarded as Peq,Cal and the accuracy meets the requirement of the model calculation. When ∆μ is positive under P − 0.5Pu as well as P + 0.5Pu, P is lower than Peq,Cal and the difference between P and Peq,Cal can be larger than Pu. When ∆μ is negative under P − 0.5Pu as well as P + 0.5Pu, P is higher than Peq,Cal and the difference between P and Peq,Cal can be larger than Pu. It should be pointed out that if ∆μ is negative under P − 0.5Pu but positive under P + 0.5Pu (which never happened in this work), which means that Peq,Cal is smaller than P − 0.5Pu but is higher than P + 0.5Pu, which is contrary to reality, then the calculation would end and the model would be rechecked. The relative deviation (RD), maximum relative deviation (MRD), average relative deviation (ARD) and goodness of fit (GF) are used to describe the deviation between P eq,Cal and P eq,Exp : where n is the number of the experiments in Section 4.1, nn denotes the number of the experimental temperatures in Section 4.1 and ii denotes the serial number. Smaller RD, MRD and ARD indicate a better prediction accuracy of the model. A value of GF close to 1 means that the model can predict the effect of temperature on P eq accurately. The initial related deviation (DRS 0 ) is used to quantitatively described the initial THFDF and the difference between the initial state of the hydrate formation and the state of thermodynamic phase equilibrium. The final related deviation (DRS end ) is used to quantitatively described the THFDF at the end of the hydrate formation and the difference between the final state of the hydrate formation and the state of thermodynamic phase equilibrium: DRS end = (P f − P eq,end )/P eq,end × 100% (20) where P eq,0 and P eq,end are the thermodynamic phase equilibrium pressures under the initial condition of the hydrate formation and the condition the end of the hydrate formation, respectively, which are calculated using the method shown in Figure 2. Since the gas composition (pure ethylene), pressure and temperature were all kept constant in each individual hydrate formation process, the difference between P eq,0 and P eq,end is caused by the change in the SLS concentration in liquid phase. The SLS concentration in the liquid phase at the end of the hydrate formation (w p,end ) is calculated using the amount of the water in the hydrate phase (N w,h ), and N d comes from experimental data. Ethylene molecules only occupy the large cavities of hydrate, so that no ethylene molecule is in the small cavities. The N w,h , w p,end and R WH can be calculated as: where m SLS is the mass of the SLS in the solution and m 0 is the mass of the SLS solution injected into the crystallizer. SLS does not form hydrate and rarely goes into gas phase, so that m SLS is assumed constant during the hydrate formation process.

The Thermodynamic Effect of SLS on Ethylene Hydrate Formation
The thermodynamic effect of SLS on hydrate formation manifests as the effect of SLS on the P eq . As discussed previously, the w p increases with the increase in R WH , and SLS might have a significant thermodynamic effect on hydrate formation when R WH is high [30]. The surfactants used in hydrate formation should not have a significant negative thermodynamic effect on hydrate formation. The thermodynamic effect of SLS on hydrate formation was investigated in this section to ensure that SLS meets the thermodynamic requirement of the surfactants, as well as to lay a foundation for the investigation in Section 4.3.
In the previous research [7], the maximum R WH in hydrate formation in the presence of SDS can be as high as 90%. The w p is about 10 times as high as w p,0 when R WH is 90% and about twice the w p,0 when R WH is 50%. Since the w p,0 in Section 4.3 is not higher than 0.5 mass%, the SLS concentrations in the liquid phase were set at 1.0 mass% (=0.5 mass% × 2) and 5.0 mass% (=0.5 mass% × 10). The P eq of ethylene gas with different liquids at different temperatures are shown in Table 1. The uncertainties of the experimental data and calculated data are ±0.01 MPa and ±0.001 MPa, respectively. The experimental data in Table 1 shows that P eq,Exp increases with the increase in w p , which confirms the hypotheses that SLS has a negative thermodynamic effect on hydrate formation and the negative thermodynamic effect increases with the increase in the w p . However, the increase in P eq,Exp caused by SLS are very small in Table 1, and the difference between the P eq,Exp of the pure water system and the P eq,Exp of the 1.0 mass% SLS system at the same temperature is smaller than 0.03 MPa, while the difference between the P eq,Exp of the pure water system and the P eq,Exp of the 5.0 mass% SLS system at the same temperature is smaller than 0.08 MPa. The increases in P eq,Exp caused by SLS are smaller than those caused by other salts (sodium chloride etc. [51]) and hydrate inhibitors (methanol etc. [27]) with the same mass fraction. Since the w p,0 is not higher than 0.5 mass% when SLS is used as a surfactant, the SLS concentration in liquid phase is normally not higher than 5.0 mass% during the hydrate formation process. For this reason, the hypotheses that the negative thermodynamic effect of SLS on hydrate formation is significant when R WH is very high is not true.
The prediction data (P eq,Cal ) are provided in Table 1 for verification. The model predicts well the effects of temperature and the SLS concentration in the liquid phase on the P eq , the ARD of all the data in Table 1 is 1.6%, the MRD of all the data in Table 1 is 4.7% and the GF for the three curves of the P eq vs. temperature of the pure water system, 1.0 mass% SLS system and 5.0 mass% SLS system are all higher than 0.994. The performance of this model is as good as the performances of the models in the literature on predicting the P eq under the experimental conditions in their own works (ARD is 2.6% for the fluid catalytic cracking (FCC) dry gas + Poly (sodium 4-styrenesulfonate) (PSS) solution/pure water system [15], 2.56% for the N 2 +CO 2 +water system [46], 0.66% for the CH 4 +CO 2 +H 2 S+N 2 +methanol solution system [47], 5.8% for the H 2 S(liquid)+water system [48], 1.1% for the H 2 S(gas)+water system [48] and 1.43% for the CH 4 +water system [49]. GF is 0.994 for the N 2 +CO 2 +water system [46] and is higher than 0.978 for the FCC dry gas + PSS solution/pure water system [15]).
According to the results of Section 4.1, SLS meets the thermodynamic requirement of the surfactants used in hydrate formation, and the model proposed in this paper can accurately describe the thermodynamic effect of SLS on hydrate formation.

The Interfacial Tension between the Ethylene Gas and SLS Solution
Since the gas-liquid interfacial tension is necessary for the discussion on the kinetic effect of SLS on hydrate formation in Section 4.3, the interfacial tension of the ethylene-SLS solution was measured and is shown in Figure 3. The average values of the data are shown as symbols, and the uncertainties of data caused by repeated experiments are shown as error bars. Since the uncertainties of the data are too small compared with the average data, the error bars are not distinct in Figure 3. The data of each individual experiment are shown in Tables S1 and S2 in Supplementary Materials.
As is shown in Figure 3, the interfacial tension is effectively decreased by using SLS. The gas-liquid interfacial tensions of water system are all higher 73 mN·m −1 , whereas those of the SLS solution systems are all lower than 65 mN·m −1 .

The Interfacial Tension between the Ethylene Gas and SLS Solution
Since the gas-liquid interfacial tension is necessary for the discussion on the kinetic effect of SLS on hydrate formation in Section 4.3, the interfacial tension of the ethylene-SLS solution was measured and is shown in Figure 3. The average values of the data are shown as symbols, and the uncertainties of data caused by repeated experiments are shown as error bars. Since the uncertainties of the data are too small compared with the average data, the error bars are not distinct in Figure 3. The data of each individual experiment are shown in Table S1 and Table S2  As is shown in Figure 3, the interfacial tension is effectively decreased by using SLS. The gas-liquid interfacial tensions of water system are all higher 73 mN·m −1 , whereas those of the SLS solution systems are all lower than 65 mN·m −1 .
In Figure 3, an increase in either temperature or pressure leads to a decrease in the interfacial tension, and this phenomenon is also found in the studies on the interfacial tensions between coal seam gas and TBAB solution [52], as well as ethylene gas and SDS solution [53].
In Figure 3b, as the SLS concentration increases, the interfacial tension between ethylene gas and liquid phase decreases at first then slightly increases. The inflection point in the above relationship between SLS concentration and the interfacial tension is at 0.1 mass% SLS, which indicates that the critical micelle concentration (CMC) of SLS is about 0.1 mass%. The relationship between the concentration of the surfactant in liquid phase and the gas-liquid interfacial tension, which is the same as that between the SLS concentration and the interfacial tension in this work, can also be found in the studies on the interfacial tensions between FCC dry gas and PSS solution [15], as well as air and noctyl-β-D-glucopyranoside solution [54].
Taking the foaming ability, resource utilization, environmental protection and the performance of SLS on decreasing gas-liquid interfacial tension into consideration, SLS is a surfactant with good potential in hydrate formation.  In Figure 3, an increase in either temperature or pressure leads to a decrease in the interfacial tension, and this phenomenon is also found in the studies on the interfacial tensions between coal seam gas and TBAB solution [52], as well as ethylene gas and SDS solution [53].
In Figure 3b, as the SLS concentration increases, the interfacial tension between ethylene gas and liquid phase decreases at first then slightly increases. The inflection point in the above relationship between SLS concentration and the interfacial tension is at 0.1 mass% SLS, which indicates that the critical micelle concentration (CMC) of SLS is about 0.1 mass%. The relationship between the concentration of the surfactant in liquid phase and the gas-liquid interfacial tension, which is the same as that between the SLS concentration and the interfacial tension in this work, can also be found in the studies on the interfacial tensions between FCC dry gas and PSS solution [15], as well as air and n-octyl-β-D-glucopyranoside solution [54].
Taking the foaming ability, resource utilization, environmental protection and the performance of SLS on decreasing gas-liquid interfacial tension into consideration, SLS is a surfactant with good potential in hydrate formation.

The Kinetic Effect of SLS on Ethylene Hydrate Formation
The kinetic effect of SLS on hydrate formation, which mainly manifests as the effects of SLS on the hydrate formation rate (r R ) and the conversion rate of the water into hydrate at the end of the hydrate formation (R WH,end ) in the hydrate formation controlled by mass transfer, was investigated by investigating the effects of w p,0 and pressure on the final state of ethylene formation, as well as on the r R at different stages in the process of hydrate formation in this section.
The changes of temperature, pressure and gas composition can lead to significant changes in the THFDF, and the effect of the change in THFDF can override the thermodynamic and kinetic effects of SLS on hydrate formation [15]. For the above reasons, pure ethylene gas was used as the experimental gas so that the gas composition did not change along with hydrate formation, and the temperature as well as the pressure was kept constant in each individual experiment in this work.  [53] and Poly (sodium 4-styrenesulfonate) [15]). Since the gas-liquid interfacial tension is affected by the SLS concentration in liquid, the effect of the w p,0 on the ethylene hydrate formation was investigated in this section. The P f and T f were set at 278.15 K under 1.24 MPa to ensure a strong THFDF. The average data and the uncertainties of the average data are presented in Table 2. The data of each individual hydrate formation experiment are shown in Table  S3 in Supplementary Materials. The difference between P eq,0 and P eq,end represents the change in THFDF during hydrate formation. DRS 0 and DRS end represent the THFDF at the initial stage and final stage of hydrate formation, respectively. In each experiment in Table 2, DRS 0 and DRS end have no significant difference, which means that the decrease in THFDF during hydrate formation was very small. This is because the difference between P eq,0 and P eq,end was very small in each experiment. Since pressure, temperature and gas composition kept constant in each individual experiment, the difference between P eq,0 and P eq,end was determined by the change in the liquid composition during hydrate formation. Since the increase in the w p during hydrate formation was not significant (smaller than 1.50 mass% SLS) and the thermodynamic effect of SLS on hydrate formation is small, the difference between P eq,0 and P eq,end was small.
Based on the data in Table 2, it was the hydrate shell effect (ethylene gas and water were separated by hydrate, so that they could not contact with each other) [55] rather than the thermodynamic phase equilibrium that stopped the hydrate formations in this section. DRS end is far higher than 0%, which indicates that THFDF was still strong at the end of the hydrate formation. R WH,end is far less than 100%, since ethylene was oversupplied in each experiment, and the end of the hydrate formation was not caused by the lack of water nor by the lack of ethylene.
In Table 2, the presence of SLS makes little difference in DRS 0 , whereas it significantly increases R WH,end : R WH,end is 57.6 ± 1.6% in the hydrate formation using pure water, whereas it is higher than 70.0% in the hydrate formations using SLS solutions, which indicates the increased R WH,end is from the kinetic effect of SLS on ethylene hydrate formation. As discussed previously, the hydrate shell effect ends hydrate formation before the THFDF decreases to zero, and the hydrate shell effect is caused by the low mass transfer rate (which makes the r R in liquid phase much lower than the r R in the areas that are near the gas-liquid interface, so that the gas-liquid interface is covered by hydrate before all the water converts into hydrate) and the aggregation of hydrate particles (which makes water wrapped by hydrate) [56]. SLS increases the mass transfer rate [16], which effectively reduces the difference in the r R in different areas [55]. SLS adsorbs on the surface of hydrate and decreases the liquid force between adjacent hydrate particles [17], which effectively prevents the aggregation of hydrate particles [55]. For the above reasons, SLS can effectively reduce the hydrate shell effect.
In Table 2, as w p,0 increases, R WH,end increases at first then slightly decreases, and the inflection point in the above relationship between w p,0 and R WH,end is at 0.10 mass%. This may be caused by the change in the gas-liquid interfacial tension, which is caused by the change in w p,0 . SLS increases R WH,end by reducing the hydrate shell effect, which is reduced by increasing the mass transfer rate and preventing the aggregation of hydrate particles. Since the SLS increases the mass transfer rate and decreases the liquid force between adjacent hydrate particles by decreasing the gas-liquid interfacial tension [55], the increase of R WH,end is affected by the gas-liquid interfacial tension. Since the w p increases with the increase in the R WH in hydrate formation process and the lowest gas-liquid interfacial tension is achieved at 0.1 mass% SLS, the gas-liquid interfacial tensions of the 0.2 mass% SLS system and the 0.5 mass% SLS system were higher than the gas-liquid interfacial tension 0.1 mass% SLS system during the whole hydrate formation process. In most stages of hydrate formation, the gas-liquid interfacial tension of the 0.05 mass% SLS system was lower than those of the other SLS solutions. Though the increases in R WH led to the decrease in the gas-liquid interfacial tension of the 0.05 mass% SLS system, which caused the increase of R WH , the increase in R WH led to the increase in the mass transfer resistance and the decrease in the fluidity of the hydrate slurry at the same time, which overrides the effect of the decrease in the gas-liquid interfacial tension. Compared with the difference between the R WH,end of the water system and the R WH,end of the SLS solution system, the differences among the R WH,end of the different SLS solution systems are not significant, which may be because the gas-liquid interfacial tensions of the SLS solutions in Table 2 are close, which can be seen from either Figure 3 or the data of the gas-liquid interfacial tensions in the Supplementary Materials. In Table 2, GSCHS is proportional to R WH,end , because ethylene is stored by forming hydrate. Figure 4 represents the average kinetic data of the hydrate formation with different w p,0 at 278.15 K under 1.24 MPa (calculated by Equation (4)). The uncertainties of the kinetic data for the three repeated experiments are shown as error bars (calculated by Equation (5)). The effect of w p,0 on the relationship between R WH and time is shown in Figure 4a. Since the introduction periods of hydrate formations were not obvious under the operating conditions in this work, the time zero in Figure 4a is set at the time the experiment begins. The effect of w p,0 on the r R at different stages in the process of hydrate formation is shown in Figure 4b and the data are from the R WH of 5%. The temperature inside the crystallizer normally slightly fluctuated when hydrate started forming, and it returned to the experimental temperature and was kept constant before R WH increased to 5%.  In Figure 4a, the hydrate formation in the presence of SLS is slower than the hydrate formation using pure water at first, but the hydrate in the presence of SLS still forms after the hydrate formation using pure water ends. This may be caused by the adsorption of the anion of SLS (LS -) on the hydrate surface [57,58] and the decrease in the liquid force between adjacent hydrate particles caused by SLS [17,55]. The adsorption of LSon the In Figure 4a, the hydrate formation in the presence of SLS is slower than the hydrate formation using pure water at first, but the hydrate in the presence of SLS still forms after the hydrate formation using pure water ends. This may be caused by the adsorption of the anion of SLS (LS − ) on the hydrate surface [57,58] and the decrease in the liquid force between adjacent hydrate particles caused by SLS [17,55]. The adsorption of LS − on the hydrate surface decelerates the growth of hydrate, which causes a negative effect on hydrate formation [57,58]. However, the adsorption of LS − on the hydrate surface prevents the agglomeration of hydrate particles, which causes a positive effect on hydrate formation at the same time [17,55]. The adsorption of LS − on the hydrate surface and the decrease in the liquid force between adjacent hydrate particles effectively reduces the hydrate shell effect [17,55], which ensures the hydrate in the presence of SLS still forms after the hydrate formation using pure water ends [17].
In Figure 4a,b, the r R in the hydrate formation using SLS solution does not decreases with the increase in w p,0 , which indicates that the negative effect of SLS on r R does not increases with the increase of w p,0 in the experimental range. The r R in the hydrate formation using the 0.2 mass% SLS solution is slightly faster than those of the hydrate formations using the other SLS solutions, whereas the formation rates of the hydrate formation using the 0.1 mass% SLS solution and 0.5 mass% SLS solution show little difference. That indicates that, in a specific SLS concentration range, increasing w p,0 can increase the positive effect of SLS on the r R , and this trend is also found in the hydrate formations of the CH 4 + lithium dodecyl sulfate solution system [59] and CH 4 + dodecylbenzene sulfonic acid solution system [59].
In Figure 4b, the r R in the hydrate formation using pure water is faster than the r R in the hydrate formation using the SLS solution when R WH is lower than 30%, whereas it is slower than the r R in the hydrate formation using the SLS solution when R WH is higher than 55%.
The r R in the hydrate formation using pure water decreases with the increase in R WH whereas the r R in the hydrate formations in the presence of SLS rarely changes as R WH increases from 25% to 65%, which indicates that the r R is determined by mass transfer resistance and the mass transfer resistance in the hydrate formation using SLS solution rarely increases as R WH increases from 25% to 65%, whereas the mass transfer resistance in the hydrate formation using pure water significantly increases continuously with the increase of R WH .
The r R in the hydrate formation using 0.05 mass% SLS solution significantly decreases with the increase in R WH when R WH is higher than 65%, whereas the r R in the hydrate formations using the other SLS solutions significantly decrease with the increase in R WH when R WH is higher than 70%. That means that the effect of SLS on reducing the hydrate shell effect is not unlimited; when R WH reaches a specific value, SLS cannot promote the hydrate formation any longer. In this paper, the specific value of R WH is about 65% for the hydrate using the 0.05 mass% SLS solution and is about 70% for the hydrate using the other SLS solutions.

The Effect of Pressure on Ethylene Hydrate Formation
The effect of the THFDF (which is proportional to pressure) on the hydrate formation in the presence of SLS was investigated by investigating the effect of pressure on ethylene hydrate formation in the presence of SLS, and the corresponding experimental data are presented in Table 3. The data of each individual hydrate formation experiment are shown in Table S3 in the Supplementary Materials. The w p,0 was set at 0.10 mass%, and the temperature was set at 278.15 K to ensure a strong THFDF.
In Table 3, the difference between DRS 0 and DRS end as well as the difference between P eq,0 and P eq,end is small under each pressure, which indicates that the decrease in THFDF during the hydrate formation is very small regardless of whether the pressure is high. The reasons for those little differences are the little thermodynamic effect of SLS on hydrate formation and the difference between w p,0 and w p,end , which has been discussed in Section 4.3.1. Since DRS end values are all far higher than 0% and R WH,end values are all far less than 100% in this section, the hydrate formations were stopped by mass transfer resistance, which are the same as those in Section 4.3.1. In Table 3, the R WH,end in the hydrate formation under 1.12 MPa (64.8 ± 1.5%) is lower than those in the hydrate formations under the other pressures, whereas the R WH,end values in the hydrate formations under the other three pressure have no significant difference. The R WH,end in the hydrate formation under 2.00 MPa is slightly lower than R WH,end in the hydrate formation under 1.49 MPa. The above indicates that the increase in the pressure leads to an increase in the R WH,end when the pressure is lower than 1.49 MPa, whereas the increase in pressure leads to a slight decrease in the R WH,end when the pressure is higher than 1.49 MPa. The above relationship between the R WH,end and pressure may be caused by the effects of THFDF and the mass transfer. The increase in pressure leads to the the increase of THFDF and the mass transfer force, and that leads to the increase of the r R and R WH,end ; however, when pressure is higher than a specific value, as pressure increases, the increase in the mass transfer rate cannot keep up with the increase of the r R , which leads to the increase in the hydrate shell effect and leads to the decrease of the R WH,end [60].
In Table 3, GSCHS and w p,end increase with the increase in pressure and then decreases, and their highest values are achieved under 1.49 MPa. This is because ethylene is stored by forming hydrate and w p,end is inversely proportional to the amount of residual water, which makes GSCHS and w p,end proportional to R WH,end . Figure 5 represents the kinetic data of the hydrate formation under different pressures at 278.15 K with the w p,0 of 0.10 mass%. In Figure 5a,b, a higher pressure leads to a higher r R , which is because a higher pressure leads to a higher THFDF. However, when the r R is very high, the mass transfer rate cannot keep up with the r R , which increases the hydrate shell effect, and that leads to a low R WH,end [60]. For the above reason, the r R in the hydrate formation under 2.00 MPa is faster than the r R in the hydrate formations under the other pressures, but the R WH,end in the hydrate formation under 2.00 MPa is smaller than R WH,end in the hydrate formation under 1.49 MPa.
Though the THFDF values are proportional to pressure and do not significantly change along with the hydrate formation in each individual experiment, in Figure 5b, the differences among the r R under different pressures grow smaller as R WH increases from 5% to 30%, which indicates that the mass transfer resistance increases as R WH increases from 5% to 30%. The r R under different pressures have no significant difference when R WH is between 30% and 65%, which indicates that the hydrate formations are controlled by mass transfer and the mass transfer resistance does not significant increases as R WH increases from 30% to 65%. The steady r R makes the hydrate process easier to control, which indicates that SLS has a good potential in the application of hydrate-based technologies.
The r R in the hydrate formation under 1.12 MPa significantly decreases with the increase in R WH when R WH is higher than 65%, whereas the r R in the hydrate formations under the other pressures significantly decrease with the increase in R WH when R WH is higher than 70%. The above indicates that when the pressure is higher than a specific value, r R can no longer be kept by increasing the pressure.
sures at 278.15 K with the wp,0 of 0.10 mass%. In Figure 5a,b, a higher pressure leads to a higher rR, which is because a higher pressure leads to a higher THFDF. However, when the rR is very high, the mass transfer rate cannot keep up with the rR, which increases the hydrate shell effect, and that leads to a low RWH,end [60]. For the above reason, the rR in the hydrate formation under 2.00 MPa is faster than the rR in the hydrate formations under the other pressures, but the RWH,end in the hydrate formation under 2.00 MPa is smaller than RWH,end in the hydrate formation under 1. Though the THFDF values are proportional to pressure and do not significantly change along with the hydrate formation in each individual experiment, in Figure 5b, the differences among the rR under different pressures grow smaller as RWH increases from 5% to 30%, which indicates that the mass transfer resistance increases as RWH increases from 5% to 30%. The rR under different pressures have no significant difference when RWH is between 30% and 65%, which indicates that the hydrate formations are controlled by mass transfer and the mass transfer resistance does not significant increases as RWH increases from 30% to 65%. The steady rR makes the hydrate process easier to control, which indicates that SLS has a good potential in the application of hydrate-based technologies.
The rR in the hydrate formation under 1.12 MPa significantly decreases with the increase in RWH when RWH is higher than 65%, whereas the rR in the hydrate formations under the other pressures significantly decrease with the increase in RWH when RWH is higher than 70%. The above indicates that when the pressure is higher than a specific value, rR can no longer be kept by increasing the pressure.

Conclusions
How to increase RWH through a cheap method is the key concern in the advances in gas hydrate technologies, and SLS shows good potential to increase RWH. The thermodynamic effect of SLS on hydrate formation was experimentally investigated and

Conclusions
How to increase R WH through a cheap method is the key concern in the advances in gas hydrate technologies, and SLS shows good potential to increase R WH . The thermodynamic effect of SLS on hydrate formation was experimentally investigated and quantitatively described for the first time in this paper. The effects of the initial SLS concentration and pressure on the hydrate formation at different stages of the hydrate formation process was experimentally investigated for the first time.
A new model was proposed to predict the P eq . Based on the model, the thermodynamic effect of SLS on the hydrate formation, the THFDF and the difference between the state of hydrate formation and thermodynamic phase equilibrium can be quantitatively described. The P eq,Cal matches the P eq,Exp well, the ARD is 1.6% and the MRD is 4.7%. The GF of the P eq vs. temperature of the pure water system, 1.0 mass% SLS system and 5.0 mass% SLS system are all higher than 0.994.
The gas-liquid interfacial tension was effectively decreased by using SLS. SLS had no significant negative thermodynamic effect on hydrate formation. SLS increased the R WH,end : R WH,end was increased from 57.6 ± 1.6% to higher than 70.0% by using SLS, and the highest R WH,end (77.0 ± 2.1%) was achieved when w p,0 was 0.1 mass%.
The formation rate of the hydrate in the presence of SLS did not significantly change as R WH increased from 35% to 65%. The effect of increasing pressure on an increasing hydrate formation rate decreased with the increase in R WH . When R WH was higher than 30%, the hydrate formation was controlled by mass transfer and increasing pressure could not significantly increase the hydrate formation rate.
Since SLS increases R WH,end and steadies the hydrate formation rate in a large R WH range, it has good potential in the application of hydrate-based technologies.