Measurement and correlation of the solubility of sodium acetate in eight pure and binary solvents

Xi Wu,Shuaishuai Yang,Shiming Xu,Xinjie Zhang,Yujie Ren

Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education,School of Energy and Power Engineering,Dalian University of Technology,Dalian 116024,China

Keywords:Solubility Sodium acetate Solution Water Solvent

ABSTRACT The knowledge of solubility of a salt in either the pure solvent or blend solvent is of great importance for studying or operating the crystallization,extraction,and distillation processes.The solubility of sodium acetate(NaAc)in four pure solvents(water,ethanol,acetic acid and 2,2,2-trifluoroethanol)and four binary solvents (water–ethanol,water-acetic acid,acetic acid–ethanol,and acetic acid-ethyl acetate) were measured by using the laser dynamic method at temperatures from 288.15 K to 338.15 K at 0.1 MPa.The results showed that the solubility of NaAc was influenced by either the solution temperature or solvent composition.The aqueous sodium acetate solution possessed the maximal solubility under the experimental conditions.The solubility of NaAc in 2,2,2-trifluoroethanol was found to be decreased with the increase of the solution temperature.While,the solubilities of NaAc in other seven solvents increased as the solution temperature was elevated.Besides,five correlation models,including the van’t Hoff model,modified Apelblat model,Yaws model,λh model,and modified Apelblat-Jouyban-Acree model were used to correlate the solubility data of those sodium acetate solutions with acceptable deviation,respectively.Finally,van’t Hoff analysis method was selected to analyze the change law of thermodynamic properties of a salt during the dissolution process.

1.Introduction

Solubility is defined in quantitative terms as the concentration of a solute in its saturated solution at a certain temperature,and also defined as the spontaneous interaction of two or more substances to form a homogeneous molecular dispersion.The knowledge of solubility of the solid salts in the liquid solvents(either the pure or blend solvents)is of great importance for studying or operating the solubilization,crystallization,extraction,distillation,and separation processes [1].It is also known that the solid–liquid phase equilibrium is useful to the brine resources exploitation,energy conversion and utilization,chemical industry production and biomedicine development [2,3].Recently,solubility of the working solution has been found to be a key thermodynamic property that affects the harvestability of the salinity gradient energy(SGE)existing between the concentrated and diluted feeding solutions for a closed-loop type reverse electrodialysis (RED) power and/or hydrogen generation system driven by the thermal energy[3–7].The closed-loop type RED system can be regarded as an integrated system where a RED process (converting SGE to electricity and/or hydrogen) is coupled with a thermal regeneration process(restoring the working solutions to the initial concentrations).The working principles of which have been detailedly introduced in references [5–10].

Working solution is the medium for heat and mass transfer in energy conversion system,which influences the performance and efficiency of the whole system strongly.A methodology has been developed to assess the suitable working solutions for the closed-loop type RED system [11],and both the thermodynamic and electrochemical properties are concerned and analyzed to ensure the large Gibbs free energy of mixing and low energy consumption of the solution regeneration,concurrently.The available working solutions should meet the requirements in terms of four major characteristics:to be in high solubility,high conductivity,low normal boiling point (NBP),and low heat of vaporization(HOV).Among which,the solubility,closely related to the dissolution,maximal concentration and ionic strength of the solution,will affect the performance in electromotive force,power density,or energy density significantly [4,12].

Tamburiniet al.investigated the performance differences of a closed-loop type RED system working with 16 kinds of monovalent salt aqueous solutions respectively,and they found the conventional aqueous sodium chloride (NaCl) solution did not exhibit the best performance in terms of power density and open circuit voltage [13].While,some unconventional solutions that took lithium chloride (LiCl) or potassium acetate (KAc) as the solutes could improve the performance [13,14].Giacaloneet al.studied the properties of aqueous KAc,cesium acetate (CsAc),and sodium acetate(NaAc)solutions,and they resulted the use of the aqueous acetate salt solutions for the RED system improved the energy efficiency compared with the conventional aqueous NaCl solution,due to the higher solubility and Gibbs free energy of mixing[10].Water is an excellent and safe inorganic solvent,which is the favorable choices for open-type RED process.However,water is not a perfect single component solvent for the thermal regeneration process,owing to its huge HOV and high operating temperature [14,15].Some researchers have transferred attention to the organic solvents with low NBPs,and the water-organic solvent mixtures with good comprehensive performances.

Several binary and ternary solutions consists of the acetate salts and appropriate solvents have been expected to be new potential working fluids for the closed-loop type RED energy conversion system recently.Ethanol and methanol are two easily obtained solvents,and their HOVs and NBPs are lower than water.Acetic acid is considerable since it has the same functional group and anion as NaAc when dissolved.2,2,2-trifluoroethanl has the bigger dielectric constant and dipole moment than either the ethanol or acetic acid.Water-organic solvent mixtures are attached great importance.Water is a strong polarity solvent,and which is conducive to improve the dissolution and ionization processes of the electrolyte-water-organic solvent solution system.The Gibbs free energy of mixing and electrical conductivity of NaAc in methanol and 2,2,2-trifluoroethanl solvents were tested in previous work[16].The existing research results of the solubility of NaAc in water,methanol and their mixtures at 298.2 K are valuable[17,18],but insufficient to satisfy the practical development requirements.Therefore,the solubility of NaAc in four pure solvents (water,ethanol,acetic acid and 2,2,2-trifluoroethanol) and four binary solvents (water–ethanol,water-acetic acid,acetic acid–ethanol,and acetic acid-ethyl acetate)were measured in this study,after comprehensively assessing the NBP,heat consumption of separation,safety,electrical conductivity,and electrical convertibility.The experiments were done by using the laser dynamic method at temperatures from 288.15 to 338.15 K at 0.1 MPa,

In the past decades,many models have been established to predict the phase equilibrium,thermodynamic properties and solubility of various electrolytes in different solvents,such as the Pitzer’s model,e-Wilson model,e-NRTL model,and UNIQUAC model[2,19].However,these models are often complex,consequently,leading to the time-consuming and difficult in calculation and regression.In this study,the van’t Hoff model,modified Apelblat model,Yaws model,λhmodel and modified Apelblat-Jouyban-Acree model were developed to correlate the solubility of NaAc solutions,which provided the accurate mathematical descriptions in relatively simple styles.

2.Experimental

2.1.Materials and XRPD measurement

The materials used in this test are described in Table 1.The chemical structure of NaAc is illustrated in Fig.1.To determine the crystal form of the tested NaAc,the X-ray powder diffraction spectrum of the sample was performed by using a XRD equipment(D8 Advance from AXS,Bruker,Germany),with Cu Kα radiation(0.071073 nm) in the 2θ range of 5°–70°.The scanning rate was set as 5(°)?min-1at 298.15 K and 0.1 MPa.The measured XRPD pattern was presented in Fig.1.Further,compared with the standard pattern provided by MDI Jade 6.0 software,it is determined that the NaAc used in this experiment is anhydrous sodium acetate,the crystal form of which is orthorhombic and the space group type is Pmnm.

Table 1 Detailed information of materials used in this work

2.2.Solubility measurements

The laser monitoring observation technique is used to determine the disappearance of the last crystal in solid–liquid system dynamically [20,21],classed as a kind of the synthetic solubility measurement method,which is much faster and more effective than the analytical method[22,23].The schematic of the solubility measurement system can be seen in Fig.2.The experimental device consists of the laser detection system (LMS),jacketed glass vessel (300 ml) reaction system,intelligent thermostatic system,data acquisition and monitoring system,and the material pretreatment system.The experimental procedure is similar to those described in literatures[3,20,21],and introduced briefly as follows.

Fig.1.Chemical structure and X-ray powder diffraction pattern of NaAc.

Fig.2.Experimental apparatus of solubility measurement of the solid–liquid system.1-stirrer;2-laser generator;3-light intensity indicator;4-thermometer;5-reaction vessel;6-rotor;7-photoelectric transformer;8-thermostatic bath.

Step (1),the solute was dried in an electrical oven (Senxin Instrument)for about 3 h;Step(2),either a certain mass of solvent or solute was weighed by an analytical balance(Ohaus,±0.1 mg in distinguishability) and then was transferred into the glass vessel;Step (3),the reaction vessel was placed on the upper platform of a stirrer(Honour Instrument)to accelerate the dissolution process and facilitate the homogeneity of the temperature and concentration of the solution;Step(4),the temperature of solution was measured by a standard mercury thermometer (Zhongxing Glass Instrument,±0.05 K),inserted into the solution from the top of the reaction vessel.The stability of solution temperature during the dissolution process was maintained with the circulating water provided by an intelligent thermostatic bath (Julabo,uncertainty ± 0.05 K);Step (5) the LMS,mainly consisted of the laser generator(Yuanda Laser,650±10 nm),light intensity indicator and photoelectric transformer (TES Electrical Electronic,± 0.01 lux)was applied to determine whether the solution was saturated by detecting the change of light intensity when the laser beam penetrated the solution in real time during the test.When the last part of solid solute disappeared,the solution became clear and at this point the maximal light intensity was obtained;Step(6),then,a very small amount of additional solute was carefully added into the solution,and the process was repeated until the laser intensity of penetration could not be restored to the maximum value.The total amount of solute was consumed and recorded to calculate the mole fraction solubilityx1as per Eq.(1).Each point was tested three times at least under the same condition to reduce the experimental error.

where,mandMare the mass and molar mass,and subscripts 1 represents the solute,2 and 3 represent two solvents,respectively.With regard to the pure solvent system,m1andm2represent the masses of solute and solvent,M1andM2are the molar masses of solute and solvent,andm3=0.

2.3.Reliability test and uncertainty

The comparative experiments were carried out before the formal measurement to verify the reliability of the experimental method and accuracy of the experimental instrument.The solubility data of NaAc in water and acetic acid reported by other researchers previously were cited and compared with the results obtained by this work [18,24–28],as shown in Fig.3.The relative deviation (RD%)and relative standard deviation (RSD%) were used to indicate the consistency and accuracy,as the Eq.(2) and Eq.(3)describe.The RSD%of all comparison points was 3.46%,which indicates that the experimental method and equipment of this study are reliable and workable.

Fig.3.Comparison of the measured data to published literature values for aqueous NaAc solution and NaAc-acetic acid solution.

wherexi,expis the experimental solubility,xi,refis the referenced solubility,xi,calis calculated solubility based on correlation models,andNis number of testing points.

2.4.Thermodynamic correlation models

van’t Hoff model.It describes the linear relationship between the logarithm of the mole fraction solubility of solution and reciprocal of absolute temperature [29].

wherea1andb1are the equation constants.

Modified Apelblat model.This semi-empirical model descibes a relationship of solubility as a function of temperature derived from Clausius-Clapeyron equation [20,30,31].

wherea2andb2represent the change of activity coefficient and the solubility of solute in non-ideal solution;c2represents the effect of temperature on melting enthalpy.

Yaws model.It is a widely used solubility correlation equation under the varying temperature conditions [32],written as follows

where thea3,b3andc3are empirical coefficients under the testing temperature ranges.

λh model.It.This semi-empirical correlation equation describe the solution system of association [33,34],and also reflects the effect of temperature on the solubility.

whereTmis the melting point of solute;λ value reflects the nonideality of the solution system;andhis the excess enthalpy factor.The characteristics of many solid–liquid equilibrium systems can be realized with only two adjustable parameters,λ andh.

Modified Apelblat-Jouyban-Acree model.It provides a relatively accurate mathematical description of phase equilibrium,and reflects the variation of solubility with the changes of the solution temperature and solvent composition [35–37].

wherew1andw2are the mass fraction of cosolvent and organic solvent in the absence of solute,respectively;A1,B1,C1,A2,B2,C2andJiare the constants of the model.

3.Results and Discussion

The measured solubilities of NaAc in four pure solvents(water,ethanol,acetic acid and 2,2,2-trifluoroethanol) and in four binary solvents (water–ethanol,water-acetic acid,acetic acid–ethanol,and acetic acid-ethyl acetate) are listed in Tables 2-5,and Table 6 respectively.

3.1.Solubility data correlation

The important purpose of solubility measurement and correlation is to enrich the existing solubility data and provide reference for practical application.The correlation model should provide a relatively accurate mathematical description in simple style and fast calculation in practical application.In this study,the van’t Hoff model,modified Apelblat model,Yaws model and λhmodel and modified Apelblat-Jouyban-Acree model were used to correlate the solubility of NaAc solutions.The correlation equation coefficients and RSD are obtained and shown in Tables 7 and 8.The fitting curves can be found in Figs.4-11.The results show the modified Apelblat model and Yaws model can provide more accurate mathematical description than the other two models for the solubility of NaAc in pure water,ethanol,acetic acid and 2,2,2-trifluoroethanol.It is also found that the λhmodel is not available for correlating the solubility of NaAc in 2,2,2-trifluoroethanol.As for NaAc in the binary solvents,the modified Apelblat-Jouyban-Acree model is workable(seen Figs.8-11),which is well correlated with the dissolution processes of these NaAc ternary solutions.

3.2.Solubility of NaAc in pure solvents

The mole fraction solubilities of NaAc in water,ethanol,2,2,2-trifluoroethanol and acetic acid are influenced by the solution temperature and selected solvents,as shown in Figs.3-5.The solubility of NaAc in 2,2,2-trifluoroethanol is found to be decreased with the increase of the solution temperature.While,the measured solubility data of NaAc in other three pure solvents (water,ethanol,and acetic acid) increase as the solution temperature is elevated,as described in Tables 2-4.The solubility variation by reason of the solution temperature is explainable from the aspect of the dissolution process:an endothermic or exothermic process.For the heat absorption dissolution process,the solution enthalpy change(ΔH) should be larger than zero as described in the Le Chatelier’s principle[38],at this situation,the solution temperature elevation promotes the dissolution of the solute in solution.Conversely,if it is an exothermic dissolution process,the increase of the solution temperature will inhibit the salt from being dissolved in solution,such as the dissolution behavior of NaAc-2,2,2-trifluoroethanol solution.

The aqueous NaAc solution possesses the maximal mole fraction solubility under this testing condition,which is larger than NaAc in acetic acid at the same temperature,then followed by NaAc in 2,2,2-trifluoroethanol,and relatively smallest of NaAc in ethanol.The dielectric constant (one of the parameters indicates polarity)of the solvent is a significant impact factor on the solubility by following a‘‘like dissolves like”relationship[29].The dielectric constant decreases in the order:water (80.1) >2,2,2-trifluoroethanol (27.7) >ethanol (25.3) >acetic acid (6.25) [24],as Table 9 shows.However,the solubility of NaAc is not strictly consistent with the order of dielectric constants of these solvents.

Actually,solubility also depends on the intermolecular association and other physical–chemical properties of the solute and solvent [39],such as the hydrogen bond acceptor and donor propensity.The solvent proton-donor ability and existing steric hindrances for hydrogen bonding plays an important role in the solvation of solute [46].Each NaAc molecule has two hydrogen bond acceptor groups,which means that the solute and solvent can form hydrogen bonds and have a considerable hydrogen interaction.As Table 9 shows,the hydrogen bond donor propensities of solvents decrease in the order:water(1.17)>acetic acid(0.61)>2,2,2-trifluoroethanol (0.57) >ethanol (0.37).It is consistent with the order of measured solubility of NaAc in these four solvents(water,acetic acid,2,2,2-trifluoroethanol and ethanol).The steric hindrance effect for NaAc-acetic acid solution is smaller than either the NaAc-2,2,2-trifluoroethanol or NaAc-ethanol solutions.One of the possible reasons is the ionized acetic acid solvent can supply H+and CH3COO-,and the ionized solute NaAc supplies the sameanion.The smaller the steric hindrance,the stronger the ability of hydrogen bond formation and solvation of the solute in solution,and consequently the better dissolution.

Table 2 Experimental mole fraction solubility (x1,exp) and calculated solubility (x1,Eq) of NaAc in water at P=0.1 MPa

Table 3 Experimental mole fraction solubility (x1,exp) and calculated solubility (x1,Eq) of NaAc in ethanol at P=0.1 MPa

Table 4 Experimental mole fraction solubility (x1,exp) and calculated solubility (x1,Eq) of NaAc in acetic acid at P=0.1 MPa

Table 5 Experimental mole fraction solubility (x1,exp) and calculated solubility (x1,Eq) of NaAc in 2,2,2-trifluoroethanol at P=0.1 MPa

3.3.Solubility of NaAc in binary blending solvents

It is concluded from the experimental results listed in Table 6 that NaAc-water–ethanol,NaAc-water-acetic acid,NaAc-acetic acid–ethanol,and NaAc-acetic acid-ethyl acetate are all endothermic during the dissolution processes,because of the solubility enlargement with the increase of solution temperature,at the same solvent composition condition.Table 6 also shows that the solubility of NaAc in water,ethanol and their binary solvent are increased with the increase of the mass fraction of water(regarded as a cosolvent)at the same solution temperture.Similarly,the solubilities of NaAc in binary solvents acetic acid–ethanol and acetic acid-ethyl acetate are increased with the increase of the mass fraction of acetic acid(another cosolvent).It is worth mentioning that NaAc is substantially insoluble in pure ethyl acetate(it is not completely dissolved even only 0.077 g of NaAc is added into 100 g of ethyl acetate at 288.15–333.15 K),however,the solubility is found to be increased sharply when adding the acetic acid into NaAcethyl acetate solution.

Table 6 Experimental mole fraction solubility (x1,exp) and calculated solubility (x1,Eq) of NaAc in binary solvents with different mass fraction (w2) at P=0.1 MPa

Table 7 The regression parameters for NaAc in four pure solvents (P=0.1 MPa)

Table 8 The regression parameters for NaAc in four binary solvents (P=0.1 MPa)

Some scholars attribute that phenomenon to the preferential dissolution of a solute in two different solvents,that is,for the binary solvent,the polar solute may preferentially dissolve in the highly polar solvent composition,rather than in the weak or non-polar solvent composition.Seedher and Bhatia believed thatthe solubility improvement by adding the cosolvent may result from the specific physical and chemical properties of the selected solvents [47],including the polarity,intermolecular interaction and ability of solvents of forming hydrogen bonds with solute molecules.The solubilization process involves the breaking of intermolecular or interionic bonds of the solute,the separation ofthe solvent molecules to provide the indispensable space,and the interaction between the molecules or ionized solute and solvents[39].The addition of a certain amount of cosolvent can help to increase the dipole moment and enhance the polarity of the solvent [48].The greater the polarity of the solvent,the easier of breaking the attractions of the molecules or ions in solution,consequently,the dissolution process is improved and solubility is elevated.

Fig.4.Solubility correlation by van’t Hoff model.

Fig.5.Solubility correlation by modified Apelblat model.

As Tables 2,4 and 6 show,the solubility of NaAc in water-acetic acid binary solvent is increased by increasing the mass fraction of water;and the solubility of NaAc-water-acetic acid solution increases to a peak value and then gradually decreases on a further increase of the ratio of water to acetic acid,within the experimental temperature range of 293.15–323.15 K.Thus,a maximum solubility exists.It can be explained according to the synergistic effect theory and Hildebrand-Scatchard solubility parameter model[49,50].The solubility of solid solute in liquid solvent will reach the maximum value when the solubility parameters of the solvent and solute are close to each other [51].When the solute is dissolved in a binary solvent that consists of two carefully selected pure solvents,the solubility of which is adjustable by setting the suitable composition ratio of these two solvents.As Domanska’s suggestion [52],the solution systems with synergistic effects can be divided into two categories:the first group comprises solutes with stable intramolecular hydrogen bonds and non-polar compounds as well as solutes forming stable aggregates in solutions;and the second group includes compounds form intermolecular hydrogen bonds with solvents [52].NaAc does not contain any hydrogen bond donor,but it contains hydrogen bond acceptors.The affinity of hydrogen bond donors of water,acetic acid and ethanol are high enough,which can form the strong hydrogen bonds with NaAc in good association.Besides,from the view of the molecular structure,NaAc contains two oxygen atoms,which may form hydroxyl group in solution.NaAc is a kind of polarcompounds,which has inherent dipole and strong polarity.The polarity force and hydrogen bonding force are the main forces in the NaAc solutions.With the increase of proportion of the strong polar solvent in solution,the polarity force and hydrogen bond adhesion force are increased,and the solvation effect of the anions by means of the hydrogen bond is also strengthened.Moreover,the possibility of the cation attracts oxygen atom is increased.As a result,the interaction between solute and solvent is promoted and the solubility is improved.

Table 9 The main physical–chemical properties of the selected solvents [39–45]

Table 10 Values of apparent thermodynamic properties of solutions ξH and ξTS) of NaAc in four binary solvents (P=0.1 MPa)

Table 10 Values of apparent thermodynamic properties of solutions ξH and ξTS) of NaAc in four binary solvents (P=0.1 MPa)

Note: u(P)=5 kPa; w2 is mass fraction of cosolvent in the blend solvents and ur(w2)=0.002.

Fig.6.Solubility correlation by Yaws model.

Fig.7.Solubility correlation by λh model.

Fig.8.Solubility correlation of the NaAc (1)-water (2)-ethanol (3).

Fig.9.Solubility correlation of the NaAc (1)-water (2)-acetic acid (3).

Fig.10.Solubility correlation of the NaAc (1)-acetic acid (2)-ethanol (3).

Fig.11.Solubility correlation of the NaAc (1)-acetic acid (2)-ethyl acetate (3).

3.4.Apparent thermodynamic analysis

The dissolution process of a salt in the solvent is related to changes in thermodynamic properties.The standard dissolution enthalpycan be obtained from the well-known van’t Hoff analysis [53].

whereRis 8.314 J?K-1?mol-1;Thmis the mean harmonic temperature that can be calculated as follows:

wherenis the number of temperature points.can be obtained from the slope of the solubility curves of lnx1vs(1/T-1/Thm).The change in apparent standard Gibbs energy of the dissolution processcan be derived by means of

Then,the contribution of the solute to the entropy and enthalpy in the dissolution process with mixed solvents can be judged through the Eq.(13) and Eq.(14)

The detailed calculation results related to the apparent standard thermodynamic function are listed Table 10.For all the solution systems in this study,a linear model with a good coefficient of certainty (R2) has been obtained.As Table 10 shows,are always larger than zero (positive value) in this study,accordingly [54],the dissolution behaviors of NaAc in these solvents are spontaneous [55].With the increase of cosolvent composition ratio in the mixed solvents,thedecreases.It indicates that the addition of cosolvent is helpful for promoting the possibility of the spontaneous dissolution process.In addition,is also always positive in this study,which indicates that the dissolution process of NaAc in the four binary solutions is endothermic.

4.Conclusions

The solubility data and correlation model coefficients of NaAc in eight solvents (water,ethanol,acetic acid and 2,2,2-trifluoroethanol,water–ethanol,water-acetic acid,acetic acid–ethanol,and acetic acid-ethyl acetate) were measured and correlated at 288.15–338.15 K at 0.1 MPa.The following main conclusions are obtained:

(1) The measured mole fraction solubility is influenced by the solution temperature.The solubility of NaAc in 2,2,2-trifluoroethanol is decreased with the increase of the solution temperature.While,the experimental solubilities of NaAc in other three pure solvents and four binary blend solvents increase as the solution temperature is elevated.

(2) The mole fraction solubility is influenced by the selected pure solvent.The aqueous NaAc solution possesses the maximal mole fraction solubility under this testing condition,which is larger than NaAc in acetic acid at the same temperature,then followed by NaAc in 2,2,2-trifluoroethanol,and relatively smallest of NaAc in ethanol.

(3) The measured mole fraction solubility is influenced by the composition of the mixed solvents.For NaAc-acetic acidethyl acetate,NaAc-acetic acid–ethanol and NaAc-water–ethanol solutions,the solubilities are increased with the increase of the mass fraction of the cosolvent.While the solubility of NaAc in water-acetic acid binary solvent are increased by increasing the mass fraction of water at the very beginning;however,the solubility of NaAc-wateracetic acid solution will increase to a peak value and then gradually decreases on a further increase of the ratio of water to acetic acid at 293.15–323.15 K.

(4) The van’t Hoff model,modified Apelblat model,Yaws model and λhmodel are selected to correlate the experimental solubility data of NaAc in four pure solvents.The modified Apelblat model and Yaws model provide more accurate mathematical description than the other two models,and λhmodel is not available for correlating the solubility of NaAc in 2,2,2-trifluoroethanol.The modified Apelblat-Jouyban-Acree model is selected to correlate the solubility of NaAc in four binary solvents successfully.

(5) NaAc-water-acetic acid system is recommended as the potential working medium for RED energy conversion system,based on comprehensive considerations of the electrochemical and thermodynamic properties.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

Supported by the National Natural Science Foundation of China(52076026,51606024,51776029),the Project of the Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education,China (LOEC-201904).