# Modeling of Vapor-Liquid Equilibrium for Electrolyte Solutions Based on COSMO-RS Interaction

Authors: Weiping Liu; Chun Zhao; Yu Zhou; Xianzhen Xu
Journal: Journal of Chemistry
 (2022)

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## Abstract

The modeling of phase equilibrium for electrolyte solutions plays an important role in chemical thermodynamics. Modeling and calculation of the vapor-liquid equilibrium (VLE) for an electrolyte solution are studied in this paper. The influence mechanism for the microscopic interaction on the macroscopic VLE is further studied by COSMOtherm. Then, a developed model is proposed. The interaction parameters in the model are linked to the COSMO interaction energy (H_int). The interaction equations are remodeled using 1stopt software, and components are used to replace the “interaction parameters” used in a previous model. The developed model can be used to successfully predict VLE data for electrolyte solutions based on theα and hi parameters.


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## Body

## 1. Introduction

Simulation calculations of the phase equilibrium for electrolyte solutions play an important role in industrial and natural processes. Thermodynamic models are widely used in vapor-liquid equilibrium (VLE), solid-liquid equilibrium (SLE), and liquid-liquid equilibrium calculations. The most used thermodynamic model is the activity coefficient model. Therefore, the study of the activity coefficient model is traditional research, but it is more significant.Since the proposal of Debye–Hückel’s law [1] for a strong electrolyte solution, a number of models have been developed, including physical, chemical, and local composition models [2]. In the physical model, physical interactions have been used to describe the deviation from Debye–Hückel’s law, for example, the Pitzer model [3] and the modified Pitzer model [4, 5]. In the chemical model, chemical reactions have been used to describe the properties of electrolyte solutions: the Robinson and Stokes model [6] and the Lu–Maurer model [7]. The local composition models combine the short-range interactions (Wilson [8], NRTL [9], and UNIQUAC [10]) with the long-range interactions (Debye–Hückel’s law or modified Debye–Hückel’s law [1]. Some examples are the ElecNRTL model [11, 12], the OLI MSE model [13], and Thomsen’s model [14]. In addition, many models have been developed and evolved on the basis of the above models, such as the LIQUAC model [15], Xu’s model [16], the PSC model [17], the PC-SALT model [18], and so on. As the coefficient models have evolved, there has been great progress in the scope of application and calculation accuracy. Iwai et al. conducted research on simultaneous correlation of liquid-liquid equilibria of ternary systems and phase equilibria of constituent binary systems using an improved new activity coefficient model [19]. Noumir et al. conducted research on isobaric vapor-liquid equilibrium data modeling of ternary systems containing ionic liquids [20]. However, there are increased limitations in the interpretation of interactions, which represent the bottleneck problem for thermodynamic model research.In the study of thermodynamic models for electrolyte solutions, many scholars have realized the importance of microinteractions for thermodynamic research. Pitzer [3] recognized the correlation between the interaction between ions and ionic strength and established a more widely used activity coefficient model. Chen [11, 12] considered the contribution of ion electrostatic interactions and improved the local composition model. In addition, many activity coefficient models [21–23] have been established on the basis of the interaction hypothesis. Some scholars have studied the activity coefficient and interaction in thermodynamics using COSMO [24–26]. However, due to the limitation of the experimental conditions at the time, many microscopic interaction concepts are only used for the construction of electrolyte solution models, lacking quantification of the interaction and the structure-activity relationship with the phase balance properties. These are also the main research directions of this paper.


## 2. The Extended NRTL Model

In this part, the modified NRTL model proposed by Xu et al. [27, 28] was used. The model was applied to calculate the VLE data for mixed electrolyte solutions over wide ranges of temperature and molarity. Based on previous works [27, 28], the impact mechanism of microscopic interactions on macroscopic VLE was further investigated. The thermodynamic activity coefficient model is described as follows:(1)ntGNRTLeRT=mxmwτw,xGw,xmx+mwGw,x+τx,wGx,wmw+mxGx,w,(2)Gw,x=exp−ατw,x,(3)Gx,w=exp−ατx,w,where GNRTLe is the excess Gibbs energy equation of NRTL, nt is the total molar, mx is the total molality of solute, and α is the randomness parameter.(4)mw=1000Ms−∑i=1nhimi,where hi is the hydration parameter and Ms = 18.0152.(5)τw,x=∑i=1nτw,imi∑i=1nmi,(6)τx,w=∑i=1nτi,wmi∑i=1nmi,(7)τw,i=τw,i0+τw,i1T,(8)τi,w=τi,w0+τi,w1T,where τw, x, and τx, w are water-solute action terms and solute-water action terms. τw, i and τi, w are the temperature parameters.In the COSMO calculation process, equations (5) to (8) are very unsatisfactory for the description of the interaction. The new interaction equation is expressed as follows:(9)τw,x=∑i=1nτw,iaexpτw,ibmi+τw,icexpτw,idmi,(10)τx,w=∑i=1nτi,waexpτi,wbmi+τi,wcexpτi,wdmi,(11)τw,ix=τw,ix−0+τw,ix−1T+τw,ix−2lnT,(12)τi,wx=τi,wx−0+τi,wx−1T+τi,wx−2lnT,where τw,x and τx,w are water-solute action terms and solute-water action terms. τw,ia, τw,ib, τw,ic, τw,id, τi,wa, τi,wb, τi,wc, and τi,wd are the parameters at the same temperature and τw,i0, τw,i1, τw,i2, τi,w0, τi,w1, and τi,w2 are the temperature parameters.The final activity coefficient equation for VLE can be written as follows:(13)lnaw=∑i=1nτw,imiGw,x∑i=1nmi+mwGw,x+∑i=1nτi,wmiGx,wmw+∑i=1nmiGx,w+mw−∑i=1nτw,imiGw,x2∑i=1nmi+mwGw,x2−∑i=1nτi,wmiGx,wmw+∑i=1nmiGw,x2+ln1000/Ms1000/Ms+∑i=1nmi.In the original model, five parameters need to be correlated, and the interaction term has no physical meaning. In the new equation, two parameters (h and α) were fitted to the literature data. At the same time, the interaction parameters were given a physical meaning by the COSMO interaction. Therefore, the new model was called the NXC model.


### 2.1. Calculation and Treatment of Interactions

In this part, COSMOtherm 2021 and 1stOpt 9.0 as the main calculation tools were chosen. 1stOpt 9.0 was used to model the interaction data. COSMOtherm 2021 was chosen to calculate the intermolecular interactions in solutions. The model described above is strictly a semiempirical model. The hydration hypotheses and the model have been proposed in previous works. However, the law of microinteraction description is not clear, and the calculation result is not of physical significance. Therefore, the interaction term is remodeled based on COSMO calculation data. Therefore, the original model parameters were given the physical meaning of COSMO by calculation and modeling.


### 2.2. The Interaction in the COSMO Calculation

COSMOtherm 2021 (in short COSMO) is a program that computes thermophysical data for liquids. COSMO is based on the COSMO-RS theory of interacting molecular surface charges [29, 30]. For the calculation of intermolecular interactions, the COSMO-chemical potential-mixture module was used. Before the calculation, compound details need to be entered. There are two main ways to input the components: one is to select the compounds directly in the database, and the other is to establish the new compounds in COSMO-TmoleX. Because the ion pairs and hydration assumptions are involved in the new model, COSMO-TmoleX is selected.The calculation process is as follows:(1)
The necessary step needs to create a new ion pair “molecular” in TmoleX and optimize the structural formula, such as the sigma surface of NaCl, CaCl2, and H2O shown in Figure1.(2)
According to the optimization results, a preliminary study on the new ion pair “molecular” is conducted. Sigma profile/potentials are important interaction reference indicators, such as Figures2 and 3.(3)
The next step is as follows: open chemical potential-mixture in COSMOtherm 2021.(4)
When determining the compound, it is necessary to input the temperature and liquid phase composition and add a calculation table.(5)
Run the job to get the data.Figure 1
The sigma surface of NaCl, CaCl2, and H2O in COSMOtherm.
(a)(b)(c)Figure 2
The sigma profile and sigma potentials of the NaCl–H2O system (NaCl and H2O).Figure 3
The sigma profile and sigma potentials of the CaCl2–H2O system (NaCl and H2O).


### 2.3. The Results of COSMO Calculation

When the calculation is completed, the calculation results are analyzed. From the COSMO calculation results, it can be seen that some related data can be obtained, such as the chemical potential of the compound in the mixture, the total mean interaction energy in the mix (H_int), the misfit interaction energy in the mix (H_MF), the H-bond interaction energy in the mix (H_HB), and the vdW interaction energy in the mix (H_vdW).In the model section, equations (5)～(8) are the main interaction terms. They described the total interaction. So, the total mean interaction energy (H_int) in COSMOtherm is used as the main research object.


### 2.4. Modeling of the H_int Interaction by 1stOpt

When the H_int interaction calculation was completed, we modeled the data and established the equations. Then, the established equations were added to the NXC model. During the modeling process, Quick Fit in 1stopt 9.0 was used to model the H_int interaction equations. For this fitting, out of 100,000 equations, the best model was searched. The optimal equation forms are given as follows:(14)τx=∑i=1nτiaexpτibmi+τicexpτidmi,(15)τix=τi0+τi1T+τi2lnT.After the formulas were determined, the next important step was to fit the parameters for the above equations. These parameters are of physical significance in COSMO, and the interaction terms in the model also have a physical meaning. The parameter fitting was also performed by using 1stopt 9.0. The interaction parameters are listed in Tables1∼4.Table 1
Interaction parameters 1.
BaBr2CaBr2CaCl2CsBrCsClp1_1w−1.5769E +02−1.3593E +021.0610E +02−4.0859E +02−3.0218E +02p1_2w4.2414E +036.2605E +031.1310E +002.0634E +042.1218E +04p1_3w2.2515E +012.0118E +01−1.4046E +015.9403E +014.0615E +01p2_1w1.8751E +011.2875E +02−6.2080E− 01−1.7045E +007.2222E +01p2_2w−8.9121E +02−6.8412E +03−9.6625E +011.3260E +02−4.0655E +03p2_3w−2.7893E +00−1.8735E +011.2351E− 012.4239E− 01−1.0373E +01p3_1w1.2176E +02−6.6453E +01−2.6208E +01−2.5105E +02−1.2997E +03p3_2w−2.0657E +032.2229E +03−3.8316E +004.8514E +034.8162E +04p3_3w−2.0462E +019.3560E +00−4.5660E− 013.7830E +011.9558E +02p4_1w6.0187E +014.4694E +004.5781E− 02−7.6258E +006.6019E− 01p4_2w−6.8364E +02−2.0677E +02−5.0076E +013.7699E +02−5.7081E +01p4_3w−1.0406E +01−6.7164E− 01−1.6902E− 031.1046E +00−9.0556E− 02p1_w1−5.3010E +01−8.9423E +00−4.2979E +02−1.8027E +02−6.1446E +01p1_w2−9.4962E +014.9759E +02−8.0065E +006.5646E +033.2598E +03p1_w38.7205E +001.2512E +006.4195E +012.6804E +018.8857E +00p2_w1−4.6108E +00−1.3330E +013.5584E +007.7152E− 01−4.2985E +01p2_w2−4.3741E +003.8167E +022.4795E +01−3.1324E +011.1849E +03p2_w37.9556E− 011.9959E +00−7.0131E− 01−1.1968E− 016.7134E +00p3_w11.0934E +01−1.8255E +02−4.7059E +02−1.7505E +04−2.0388E +02p3_w22.0100E +026.6902E +03−8.6895E +001.3965E +057.4887E +03p3_w3−2.3611E +002.7161E +017.7010E +012.9901E +033.0391E +01p4_w18.0151E +001.0575E +00−3.4347E +012.0544E +04−2.2007E− 02p4_w2−1.6102E +01−3.2906E +013.3104E +014.3595E +01−9.6404E− 01p4_w3−1.3860E +00−1.6919E− 015.6556E +00−3.6060E +032.0855E− 03Table 2
Interaction parameters 2.
CsIK2SO4KBrKClKIp1_1w−1.5076E +02−1.1322E +03−5.2890E +01−5.4333E +02−1.8317E +02p1_2w2.6520E +034.2812E +043.0350E− 011.9740E +049.1426E +03p1_3w2.3379E +011.6695E +027.8620E +008.0107E +012.6456E +01p2_1w−5.8621E +002.6070E +001.1180E− 017.6838E− 013.4299E +00p2_2w2.4097E +02−9.6319E +011.0920E +01−3.7842E +01−3.4393E +02p2_3w8.9043E− 01−4.0825E− 01−4.7342E− 02−1.1964E− 01−4.6963E− 01p3_1w−2.6669E +021.9933E +04−4.3606E +021.9205E +01−2.6757E +02p3_2w1.2681E +04−4.5828E +051.8225E +04−6.4698E +028.5408E +03p3_3w3.7810E +01−3.1560E +036.4023E +01−3.0149E +003.9541E +01p4_1w7.0415E +001.0497E +02−2.4939E +008.7763E− 01−3.7790E− 02p4_2w−3.8769E +02−1.1148E +051.0771E +021.1484E +03−1.6918E +01p4_3w−1.0392E +002.6699E +013.7404E− 01−8.2115E− 011.2370E− 02p1_w1−1.8355E +02−1.5942E +02−1.7125E +02−4.9179E +031.0020E +00p1_w26.7704E +033.6753E +035.7061E +032.6542E +05−4.3740E +01p1_w32.7265E +012.6165E +012.5726E +017.1036E +02−2.0736E− 01p2_w18.0511E− 01−6.8439E +00−3.8125E− 011.8534E +011.1224E +00p2_w2−2.6358E +01−8.5162E +011.6559E +01−3.2290E +035.0608E +01p2_w3−1.2932E− 011.2096E +005.4912E− 02−3.6983E +00−2.5325E− 01p3_w10.0000E +00−3.6007E +01−1.7478E +01−1.8633E +02−1.8676E +02p3_w2−4.8000E +013.7047E +031.3177E +036.8740E +036.9394E +03p3_w32.1553E +012.8252E +002.2947E +002.7683E +012.7784E +01p4_w1−3.7960E +02−3.4604E +01−1.0760E +004.7385E− 01−1.9094E− 01p4_w23.7578E +061.5639E +036.7959E +01−1.6643E +011.4145E +01p4_w3−3.5545E +085.1440E +001.2830E− 01−7.4893E− 022.3459E− 02Table 3
Interaction parameters 3.
LiClMgCl2MgSO4Na2SO4NaBrp1_1w−1.9624E +020.0000E +004.6803E +011.5595E +044.7096E +01p1_2w8.3829E +037.0357E +02−5.9990E +04−7.1950E +05−2.8374E +03p1_3w2.9133E +010.0000E +005.0704E +01−2.3341E +03−7.0009E +00p2_1w5.6303E +00−5.4794E +024.6994E +00−1.9675E +02−1.2808E +01p2_2w−3.1557E +02−3.4876E− 02−2.7374E +029.3019E +035.0172E +02p2_3w−8.6033E− 01−6.2864E +01−6.8479E− 012.6397E +011.8845E +00p3_1w−2.4250E +023.1365E +00−6.1472E +02−7.3472E +02−4.8166E +02p3_2w9.0184E +031.4238E +018.2062E +042.8328E +041.9590E +04p3_3w3.5512E +019.9977E +033.4574E +011.0841E +027.0887E +01p4_1w1.7942E +00−1.6331E− 045.7804E +002.0889E +00−1.3560E +00p4_2w−8.3372E +01−5.5570E +01−3.3880E +02−8.3239E +015.7880E +01p4_3w−2.7306E− 01−1.5810E +02−8.4090E− 01−3.2257E− 011.9850E− 01p1_w1−1.6909E +02−3.4915E +01−1.8918E +02−1.9473E +02−1.2532E +02p1_w26.1039E +03−8.0377E +017.0911E +038.2187E +034.0464E +03p1_w32.5139E +01−1.5844E +012.8073E +012.8559E +011.8727E +01p2_w18.4758E− 01−2.3443E +002.8420E +00−1.9109E +001.3881E +00p2_w2−3.6891E +011.2393E +02−1.1058E +021.1746E +02−6.3787E +01p2_w3−1.2922E− 012.8080E− 01−4.4140E− 012.6448E− 01−2.0735E− 01p3_w1−2.2090E +012.4764E +01−7.5304E +014.2513E +00−5.8272E +01p3_w21.1497E +034.2759E +01−6.1590E +00−1.0872E +032.7566E +03p3_w33.1878E +001.5251E +01−2.2653E +01−2.9049E− 018.5269E +00p4_w1−1.8311E +013.1783E +012.5633E +01−9.4684E− 019.1862E− 01p4_w21.5655E +03−1.8591E +02−2.0188E +03−4.3411E +011.6165E +01p4_w32.2754E +00−5.4919E +00−6.6956E +001.9837E− 01−1.9654E− 01Table 4
Interaction parameters 4.
NaClNaIRbClSrCl2ZnCl2p1_1w−1.1661E +02−4.0262E +02−1.4861E +02−1.4894E +026.6039E +03p1_2w4.9274E +011.7533E +047.9653E +032.9476E +03−2.0810E +05p1_3w1.7656E +015.8586E +012.1317E +012.2622E +01−5.4124E +02p2_1w2.0329E +00−7.0058E− 01−2.0617E +004.9975E +00−3.4050E +02p2_2w−1.0981E +023.4959E +015.5783E +01−2.5181E +025.8513E +03p2_3w−2.9922E− 019.5589E− 023.4073E− 01−7.3430E− 013.6359E +01p3_1w−3.1042E +023.0597E +01−6.0264E +02−1.7136E +02−7.3847E +01p3_2w1.5486E +04−2.5349E +032.1380E +048.2118E +032.9548E +03p3_3w4.5170E +01−4.1664E +008.9281E +012.4363E +011.0794E +01p4_1w1.2298E +02−3.3004E +01−6.8398E− 011.6381E +014.6732E +00p4_2w−6.0785E +031.5906E +035.3327E +01−9.4137E +02−2.2010E +02p4_3w−1.8096E +014.7729E +008.1138E− 02−2.3786E +00−7.0826E− 01p1_w1−1.3776E +026.4223E +01−5.8723E +012.6023E +00−7.8527E +01p1_w24.4852E +03−3.9484E +033.2642E +039.2837E +003.0765E +03p1_w32.0579E +01−9.3726E +008.4339E +00−4.7917E− 011.1595E +01p2_w11.8386E +001.8314E− 015.6485E− 01−8.3981E +006.3595E +00p2_w2−8.8162E +01−1.5504E− 03−2.6417E +01−3.6593E +00−1.8121E +02p2_w3−2.7270E− 01−4.4962E− 02−6.2320E− 021.3420E +00−1.0067E +00p3_w1−9.6971E +01−2.5433E +02−1.2644E +02−1.9611E +02−9.3813E +01p3_w24.7896E +031.1051E +043.5827E +037.2753E +033.1889E +03p3_w31.4194E +013.7594E +011.9064E +012.9190E +011.4000E +01p4_w1−2.7864E +01−3.8597E +00−3.4679E− 01−2.2429E− 012.9848E +00p4_w21.1229E +031.9773E +023.6769E +011.8740E +01−1.9860E +02p4_w34.1234E +005.6372E− 013.9342E− 022.4635E− 02−4.1453E− 01Through the above derivation and processing, final model equations (9)～(14) were determined. Parameters τw,ix−0, τw,ix−1, τw,ix−2, τi,wx−0, τi,wx−1, and τi,wx−2 were fitted on the basis of the COSMO data. Therefore, it only needs to fit the parameters α and hi on the basis of the VLE data.


### 2.5. Determination of the Parametersα and hi

The determination of the model parameters is a critical step in this paper. The interaction parameters were determined based on the COSMO data. Parametersα and hi are further correlated by using phase equilibrium data. The data used for correlation are VLE data, and the references are listed in Table 5. The parameters α and hi are listed in Table 6.Table 5
Correlation of VLE data.
SystemT/KData pointsThis workReference and experimentdY/kPaadP/%bBaBr2298.15 to 343.15630.0580.81[31, 32]CaBr2298.15 to 343.15630.0531.13[31, 32]CaCl2273.15 to 415.152360.4571.19[9, 16, 31, 32]CsBr298.15 to 343.15510.0640.71[31, 32]CsCl298.15 to 343.15630.4571.19[31, 32]CsI298.15 to 343.15420.0320.54[31, 32]K2SO4298.15 to 373.651041.0672.72[9, 32]KBr298.15 to 343.15510.2513.28[31, 32]KCl273.15 to 343.15660.1942.50[9, 16, 31, 32]KI298.15 to 343.15600.1882.24[31, 32]LiCl298.15 to 394.4470.0110.42[32, 33]MgCl2298.15 to 377.851200.4901.86[9, 31, 32]MgSO4273.15 to 376.451200.8101.85[9, 31, 32]Na2SO4273.15 to 298.15300.0090.46[9, 32]NaBr298.15 to 343.15470.0110.21[31, 32]NaCl298.15 to 373.15890.0970.92[31, 32]NaI298.15 to 343.15580.4203.92[31, 32]RbCl298.15 to 343.15510.2933.12[31, 32]SrCl2298.15 to 343.15590.2303.13[31, 32]ZnCl2298.15 to 379.8230.0080.031[32, 33]Average0.261.611adY=1/N∑Pexp−Pcal, where N is the number of data points. bdP=1/N∑Pexp−Pcal/Pexp×100%, where N is the number of data points. Pexp represents the experimental pressure and Pcal represents the calculated pressure.Table 6
The parametersα and hi.
BaBr2CaBr2CaCl2CsBrCsClΑ7.9752E− 022.8767E– 011.6389E− 016.7821E− 154.5910E− 01hi4.6147E +005.6968E +002.3336E +00−8.4186E− 01−3.8792E− 01CsIK2SO4KBrKClKIΑ1.1545E− 145.9029E– 012.6438E− 029.8801E− 032.4789E− 02hi−4.6851E− 01−1.7788E +01−5.0900E +00−4.9304E +00−2.5134E +00LiClMgCl2MgSO4Na2SO4NaBrΑ8.1229E− 022.4432E– 033.2566E− 014.4404E− 013.4094E− 02hi1.6472E +006.2690E +009.8217E +00−2.4529E +001.4730E− 01NaClNaIRbClSrCl2ZnCl2Α−5.8248E− 01−4.9761E– 01−1.3570E− 038.2369E− 027.1066E− 01hi3.6925E +005.3929E +00−2.4792E +003.5726E +006.2096E +00


## 2.1. Calculation and Treatment of Interactions

In this part, COSMOtherm 2021 and 1stOpt 9.0 as the main calculation tools were chosen. 1stOpt 9.0 was used to model the interaction data. COSMOtherm 2021 was chosen to calculate the intermolecular interactions in solutions. The model described above is strictly a semiempirical model. The hydration hypotheses and the model have been proposed in previous works. However, the law of microinteraction description is not clear, and the calculation result is not of physical significance. Therefore, the interaction term is remodeled based on COSMO calculation data. Therefore, the original model parameters were given the physical meaning of COSMO by calculation and modeling.


## 2.2. The Interaction in the COSMO Calculation

COSMOtherm 2021 (in short COSMO) is a program that computes thermophysical data for liquids. COSMO is based on the COSMO-RS theory of interacting molecular surface charges [29, 30]. For the calculation of intermolecular interactions, the COSMO-chemical potential-mixture module was used. Before the calculation, compound details need to be entered. There are two main ways to input the components: one is to select the compounds directly in the database, and the other is to establish the new compounds in COSMO-TmoleX. Because the ion pairs and hydration assumptions are involved in the new model, COSMO-TmoleX is selected.The calculation process is as follows:(1)
The necessary step needs to create a new ion pair “molecular” in TmoleX and optimize the structural formula, such as the sigma surface of NaCl, CaCl2, and H2O shown in Figure1.(2)
According to the optimization results, a preliminary study on the new ion pair “molecular” is conducted. Sigma profile/potentials are important interaction reference indicators, such as Figures2 and 3.(3)
The next step is as follows: open chemical potential-mixture in COSMOtherm 2021.(4)
When determining the compound, it is necessary to input the temperature and liquid phase composition and add a calculation table.(5)
Run the job to get the data.Figure 1
The sigma surface of NaCl, CaCl2, and H2O in COSMOtherm.
(a)(b)(c)Figure 2
The sigma profile and sigma potentials of the NaCl–H2O system (NaCl and H2O).Figure 3
The sigma profile and sigma potentials of the CaCl2–H2O system (NaCl and H2O).


## 2.3. The Results of COSMO Calculation

When the calculation is completed, the calculation results are analyzed. From the COSMO calculation results, it can be seen that some related data can be obtained, such as the chemical potential of the compound in the mixture, the total mean interaction energy in the mix (H_int), the misfit interaction energy in the mix (H_MF), the H-bond interaction energy in the mix (H_HB), and the vdW interaction energy in the mix (H_vdW).In the model section, equations (5)～(8) are the main interaction terms. They described the total interaction. So, the total mean interaction energy (H_int) in COSMOtherm is used as the main research object.


## 2.4. Modeling of the H_int Interaction by 1stOpt

When the H_int interaction calculation was completed, we modeled the data and established the equations. Then, the established equations were added to the NXC model. During the modeling process, Quick Fit in 1stopt 9.0 was used to model the H_int interaction equations. For this fitting, out of 100,000 equations, the best model was searched. The optimal equation forms are given as follows:(14)τx=∑i=1nτiaexpτibmi+τicexpτidmi,(15)τix=τi0+τi1T+τi2lnT.After the formulas were determined, the next important step was to fit the parameters for the above equations. These parameters are of physical significance in COSMO, and the interaction terms in the model also have a physical meaning. The parameter fitting was also performed by using 1stopt 9.0. The interaction parameters are listed in Tables1∼4.Table 1
Interaction parameters 1.
BaBr2CaBr2CaCl2CsBrCsClp1_1w−1.5769E +02−1.3593E +021.0610E +02−4.0859E +02−3.0218E +02p1_2w4.2414E +036.2605E +031.1310E +002.0634E +042.1218E +04p1_3w2.2515E +012.0118E +01−1.4046E +015.9403E +014.0615E +01p2_1w1.8751E +011.2875E +02−6.2080E− 01−1.7045E +007.2222E +01p2_2w−8.9121E +02−6.8412E +03−9.6625E +011.3260E +02−4.0655E +03p2_3w−2.7893E +00−1.8735E +011.2351E− 012.4239E− 01−1.0373E +01p3_1w1.2176E +02−6.6453E +01−2.6208E +01−2.5105E +02−1.2997E +03p3_2w−2.0657E +032.2229E +03−3.8316E +004.8514E +034.8162E +04p3_3w−2.0462E +019.3560E +00−4.5660E− 013.7830E +011.9558E +02p4_1w6.0187E +014.4694E +004.5781E− 02−7.6258E +006.6019E− 01p4_2w−6.8364E +02−2.0677E +02−5.0076E +013.7699E +02−5.7081E +01p4_3w−1.0406E +01−6.7164E− 01−1.6902E− 031.1046E +00−9.0556E− 02p1_w1−5.3010E +01−8.9423E +00−4.2979E +02−1.8027E +02−6.1446E +01p1_w2−9.4962E +014.9759E +02−8.0065E +006.5646E +033.2598E +03p1_w38.7205E +001.2512E +006.4195E +012.6804E +018.8857E +00p2_w1−4.6108E +00−1.3330E +013.5584E +007.7152E− 01−4.2985E +01p2_w2−4.3741E +003.8167E +022.4795E +01−3.1324E +011.1849E +03p2_w37.9556E− 011.9959E +00−7.0131E− 01−1.1968E− 016.7134E +00p3_w11.0934E +01−1.8255E +02−4.7059E +02−1.7505E +04−2.0388E +02p3_w22.0100E +026.6902E +03−8.6895E +001.3965E +057.4887E +03p3_w3−2.3611E +002.7161E +017.7010E +012.9901E +033.0391E +01p4_w18.0151E +001.0575E +00−3.4347E +012.0544E +04−2.2007E− 02p4_w2−1.6102E +01−3.2906E +013.3104E +014.3595E +01−9.6404E− 01p4_w3−1.3860E +00−1.6919E− 015.6556E +00−3.6060E +032.0855E− 03Table 2
Interaction parameters 2.
CsIK2SO4KBrKClKIp1_1w−1.5076E +02−1.1322E +03−5.2890E +01−5.4333E +02−1.8317E +02p1_2w2.6520E +034.2812E +043.0350E− 011.9740E +049.1426E +03p1_3w2.3379E +011.6695E +027.8620E +008.0107E +012.6456E +01p2_1w−5.8621E +002.6070E +001.1180E− 017.6838E− 013.4299E +00p2_2w2.4097E +02−9.6319E +011.0920E +01−3.7842E +01−3.4393E +02p2_3w8.9043E− 01−4.0825E− 01−4.7342E− 02−1.1964E− 01−4.6963E− 01p3_1w−2.6669E +021.9933E +04−4.3606E +021.9205E +01−2.6757E +02p3_2w1.2681E +04−4.5828E +051.8225E +04−6.4698E +028.5408E +03p3_3w3.7810E +01−3.1560E +036.4023E +01−3.0149E +003.9541E +01p4_1w7.0415E +001.0497E +02−2.4939E +008.7763E− 01−3.7790E− 02p4_2w−3.8769E +02−1.1148E +051.0771E +021.1484E +03−1.6918E +01p4_3w−1.0392E +002.6699E +013.7404E− 01−8.2115E− 011.2370E− 02p1_w1−1.8355E +02−1.5942E +02−1.7125E +02−4.9179E +031.0020E +00p1_w26.7704E +033.6753E +035.7061E +032.6542E +05−4.3740E +01p1_w32.7265E +012.6165E +012.5726E +017.1036E +02−2.0736E− 01p2_w18.0511E− 01−6.8439E +00−3.8125E− 011.8534E +011.1224E +00p2_w2−2.6358E +01−8.5162E +011.6559E +01−3.2290E +035.0608E +01p2_w3−1.2932E− 011.2096E +005.4912E− 02−3.6983E +00−2.5325E− 01p3_w10.0000E +00−3.6007E +01−1.7478E +01−1.8633E +02−1.8676E +02p3_w2−4.8000E +013.7047E +031.3177E +036.8740E +036.9394E +03p3_w32.1553E +012.8252E +002.2947E +002.7683E +012.7784E +01p4_w1−3.7960E +02−3.4604E +01−1.0760E +004.7385E− 01−1.9094E− 01p4_w23.7578E +061.5639E +036.7959E +01−1.6643E +011.4145E +01p4_w3−3.5545E +085.1440E +001.2830E− 01−7.4893E− 022.3459E− 02Table 3
Interaction parameters 3.
LiClMgCl2MgSO4Na2SO4NaBrp1_1w−1.9624E +020.0000E +004.6803E +011.5595E +044.7096E +01p1_2w8.3829E +037.0357E +02−5.9990E +04−7.1950E +05−2.8374E +03p1_3w2.9133E +010.0000E +005.0704E +01−2.3341E +03−7.0009E +00p2_1w5.6303E +00−5.4794E +024.6994E +00−1.9675E +02−1.2808E +01p2_2w−3.1557E +02−3.4876E− 02−2.7374E +029.3019E +035.0172E +02p2_3w−8.6033E− 01−6.2864E +01−6.8479E− 012.6397E +011.8845E +00p3_1w−2.4250E +023.1365E +00−6.1472E +02−7.3472E +02−4.8166E +02p3_2w9.0184E +031.4238E +018.2062E +042.8328E +041.9590E +04p3_3w3.5512E +019.9977E +033.4574E +011.0841E +027.0887E +01p4_1w1.7942E +00−1.6331E− 045.7804E +002.0889E +00−1.3560E +00p4_2w−8.3372E +01−5.5570E +01−3.3880E +02−8.3239E +015.7880E +01p4_3w−2.7306E− 01−1.5810E +02−8.4090E− 01−3.2257E− 011.9850E− 01p1_w1−1.6909E +02−3.4915E +01−1.8918E +02−1.9473E +02−1.2532E +02p1_w26.1039E +03−8.0377E +017.0911E +038.2187E +034.0464E +03p1_w32.5139E +01−1.5844E +012.8073E +012.8559E +011.8727E +01p2_w18.4758E− 01−2.3443E +002.8420E +00−1.9109E +001.3881E +00p2_w2−3.6891E +011.2393E +02−1.1058E +021.1746E +02−6.3787E +01p2_w3−1.2922E− 012.8080E− 01−4.4140E− 012.6448E− 01−2.0735E− 01p3_w1−2.2090E +012.4764E +01−7.5304E +014.2513E +00−5.8272E +01p3_w21.1497E +034.2759E +01−6.1590E +00−1.0872E +032.7566E +03p3_w33.1878E +001.5251E +01−2.2653E +01−2.9049E− 018.5269E +00p4_w1−1.8311E +013.1783E +012.5633E +01−9.4684E− 019.1862E− 01p4_w21.5655E +03−1.8591E +02−2.0188E +03−4.3411E +011.6165E +01p4_w32.2754E +00−5.4919E +00−6.6956E +001.9837E− 01−1.9654E− 01Table 4
Interaction parameters 4.
NaClNaIRbClSrCl2ZnCl2p1_1w−1.1661E +02−4.0262E +02−1.4861E +02−1.4894E +026.6039E +03p1_2w4.9274E +011.7533E +047.9653E +032.9476E +03−2.0810E +05p1_3w1.7656E +015.8586E +012.1317E +012.2622E +01−5.4124E +02p2_1w2.0329E +00−7.0058E− 01−2.0617E +004.9975E +00−3.4050E +02p2_2w−1.0981E +023.4959E +015.5783E +01−2.5181E +025.8513E +03p2_3w−2.9922E− 019.5589E− 023.4073E− 01−7.3430E− 013.6359E +01p3_1w−3.1042E +023.0597E +01−6.0264E +02−1.7136E +02−7.3847E +01p3_2w1.5486E +04−2.5349E +032.1380E +048.2118E +032.9548E +03p3_3w4.5170E +01−4.1664E +008.9281E +012.4363E +011.0794E +01p4_1w1.2298E +02−3.3004E +01−6.8398E− 011.6381E +014.6732E +00p4_2w−6.0785E +031.5906E +035.3327E +01−9.4137E +02−2.2010E +02p4_3w−1.8096E +014.7729E +008.1138E− 02−2.3786E +00−7.0826E− 01p1_w1−1.3776E +026.4223E +01−5.8723E +012.6023E +00−7.8527E +01p1_w24.4852E +03−3.9484E +033.2642E +039.2837E +003.0765E +03p1_w32.0579E +01−9.3726E +008.4339E +00−4.7917E− 011.1595E +01p2_w11.8386E +001.8314E− 015.6485E− 01−8.3981E +006.3595E +00p2_w2−8.8162E +01−1.5504E− 03−2.6417E +01−3.6593E +00−1.8121E +02p2_w3−2.7270E− 01−4.4962E− 02−6.2320E− 021.3420E +00−1.0067E +00p3_w1−9.6971E +01−2.5433E +02−1.2644E +02−1.9611E +02−9.3813E +01p3_w24.7896E +031.1051E +043.5827E +037.2753E +033.1889E +03p3_w31.4194E +013.7594E +011.9064E +012.9190E +011.4000E +01p4_w1−2.7864E +01−3.8597E +00−3.4679E− 01−2.2429E− 012.9848E +00p4_w21.1229E +031.9773E +023.6769E +011.8740E +01−1.9860E +02p4_w34.1234E +005.6372E− 013.9342E− 022.4635E− 02−4.1453E− 01Through the above derivation and processing, final model equations (9)～(14) were determined. Parameters τw,ix−0, τw,ix−1, τw,ix−2, τi,wx−0, τi,wx−1, and τi,wx−2 were fitted on the basis of the COSMO data. Therefore, it only needs to fit the parameters α and hi on the basis of the VLE data.


## 2.5. Determination of the Parametersα and hi

The determination of the model parameters is a critical step in this paper. The interaction parameters were determined based on the COSMO data. Parametersα and hi are further correlated by using phase equilibrium data. The data used for correlation are VLE data, and the references are listed in Table 5. The parameters α and hi are listed in Table 6.Table 5
Correlation of VLE data.
SystemT/KData pointsThis workReference and experimentdY/kPaadP/%bBaBr2298.15 to 343.15630.0580.81[31, 32]CaBr2298.15 to 343.15630.0531.13[31, 32]CaCl2273.15 to 415.152360.4571.19[9, 16, 31, 32]CsBr298.15 to 343.15510.0640.71[31, 32]CsCl298.15 to 343.15630.4571.19[31, 32]CsI298.15 to 343.15420.0320.54[31, 32]K2SO4298.15 to 373.651041.0672.72[9, 32]KBr298.15 to 343.15510.2513.28[31, 32]KCl273.15 to 343.15660.1942.50[9, 16, 31, 32]KI298.15 to 343.15600.1882.24[31, 32]LiCl298.15 to 394.4470.0110.42[32, 33]MgCl2298.15 to 377.851200.4901.86[9, 31, 32]MgSO4273.15 to 376.451200.8101.85[9, 31, 32]Na2SO4273.15 to 298.15300.0090.46[9, 32]NaBr298.15 to 343.15470.0110.21[31, 32]NaCl298.15 to 373.15890.0970.92[31, 32]NaI298.15 to 343.15580.4203.92[31, 32]RbCl298.15 to 343.15510.2933.12[31, 32]SrCl2298.15 to 343.15590.2303.13[31, 32]ZnCl2298.15 to 379.8230.0080.031[32, 33]Average0.261.611adY=1/N∑Pexp−Pcal, where N is the number of data points. bdP=1/N∑Pexp−Pcal/Pexp×100%, where N is the number of data points. Pexp represents the experimental pressure and Pcal represents the calculated pressure.Table 6
The parametersα and hi.
BaBr2CaBr2CaCl2CsBrCsClΑ7.9752E− 022.8767E– 011.6389E− 016.7821E− 154.5910E− 01hi4.6147E +005.6968E +002.3336E +00−8.4186E− 01−3.8792E− 01CsIK2SO4KBrKClKIΑ1.1545E− 145.9029E– 012.6438E− 029.8801E− 032.4789E− 02hi−4.6851E− 01−1.7788E +01−5.0900E +00−4.9304E +00−2.5134E +00LiClMgCl2MgSO4Na2SO4NaBrΑ8.1229E− 022.4432E– 033.2566E− 014.4404E− 013.4094E− 02hi1.6472E +006.2690E +009.8217E +00−2.4529E +001.4730E− 01NaClNaIRbClSrCl2ZnCl2Α−5.8248E− 01−4.9761E– 01−1.3570E− 038.2369E− 027.1066E− 01hi3.6925E +005.3929E +00−2.4792E +003.5726E +006.2096E +00


## 3. Results and Discussion

### 3.1. The Results of Interaction and Parameters

In data processing, it can be found that H_int energy is related to concentration, temperature, etc. From Figures4∼7, it can be seen that the energy increases with temperature and concentration.Figure 4
Correlation of the interaction data for the BaBr2+H2O system. (a) The interaction of BaBr2 and (b) the interaction of H2O. Symbols (, T = 303.15 K; , T = 313.15 K; , T = 323.15 K; , T = 333.15 K; and , T = 343.15 K : ); COSMO data; lines: correlation.
(a)(b)Figure 5
Correlation of the interaction data for the CaBr2+H2O system. (a) The interaction of CaBr2 and (b) the interaction of H2O. Symbols (, T = 303.15 K; , T = 313.15 K; , T = 323.15 K; , T = 333.15 K; and , T = 343.15 K : ); COSMO data; lines: correlation.
(a)(b)Figure 6
Correlation of the interaction data for the CaCl2+H2O system. (a) The interaction of CaCl2 and (b) the interaction of H2O. Symbols (, T = 303.15 K; , T = 313.15 K; , T = 323.15 K; , T = 333.15 K; and , T = 343.15 K : ); COSMO data; lines: correlation.
(a)(b)Figure 7
Correlation of the interaction data for the LiCl + H2O system. (a) The interaction of LiCl and (b) the interaction of H2O. Symbols (, T = 303.15 K; , T = 313.15 K; , T = 323.15 K; , T = 333.15 K, and , T = 343.15 K : ); COSMO data; lines: correlation.
(a)(b)Equations (13) and (14) were used to correlate the H_int interaction. The calculation results are listed in Table 7. For all systems in this paper, the results show that dY ≤ 0.0408 kcal/mol and the average of dY = 0.0058 kcal/mol and dP≤2.71% and the average of dP=0.162%. So, the equations can be better used to describe the change of H_int energy.(16)dY=1N∑Pexp−Pcal,(17)dP=1/N∑Pexp−PcalPexp×100%.Table 7
Correlation of H int data.
SystemT/KSalt-water interactionWater-salt interactiondY/kcal.mol−1adP/%bdY/kcal.mol−1adP/%bBaBr2298.15 to 343.150.01050.09440.00240.0504CaBr2298.15 to 343.150.00010.01830.00030.0077CaCl2298.15 to 343.150.00130.02580.00040.0092CsBr298.15 to 343.150.00440.02610.00180.0385CsCl298.15 to 343.150.01440.07960.00150.0319CsI298.15 to 343.150.00050.00370.00070.6001K2SO4298.15 to 343.150.00720.02160.00090.0186KBr298.15 to 343.150.00310.02170.00150.0321KCl298.15 to 343.150.00730.04270.00210.0425KI298.15 to 343.150.00530.04230.00070.0172LiCl298.15 to 343.150.00670.11180.00290.0682MgCl2298.15 to 343.150.02540.86720.00290.0693MgSO4298.15 to 343.150.04082.70680.00210.0517Na2SO4298.15 to 343.150.01240.06880.00090.0187NaBr298.15 to 343.150.00340.03190.00240.0531NaCl298.15 to 343.150.00810.06140.00150.0335NaI298.15 to 343.150.00320.03690.00310.0699RbCl298.15 to 343.150.01830.09950.00310.0645SrCl2298.15 to 343.150.01760.15680.00070.0147ZnCl2298.15 to 343.150.00980.62540.00370.0812Average0.0100.2570.00180.0689adY=1/N∑Pexp−Pcal, where N is the number of data points. bdP=1/N∑Pexp−Pcal/Pexp×100%, where N is the number of data points. Pexp represents the experimental pressure and Pcal represents the calculated pressure.


### 3.2. Prediction of the VLE Data in Electrolyte Solutions

The modified model and parameters described above were used to calculate the VLE data for twenty electrolyte solutions at vapor pressures ranging between 6 kPa and 101.325 kPa. The results of the calculation are presented in Table5, and dY and dP are listed in Table x.For all systems in this paper, the results show that dY ≤ 1.067 kPa and the average of dY = 0.26 kPa and dP≤3.92% and the average of dP=3.92%. The calculation results for the VLE data are shown in Figure 8–11 for BaBr2, CaBr2, CaCl2, and LiCl systems, respectively.Figure 8
Calculation of the VLE for the BaBr2+H2O system. Symbols (, T = 303.15 K; , T = 313.15 K; , T = 323.15 K; , T = 333.15 K; and , T = 343.15 K : ); VLE data; lines: calculation.Figure 9
Calculation of the VLE for the CaBr2+H2O system. Symbols (, T = 303.15 K; , T = 313.15 K; , T = 323.15 K; , T = 333.15 K; and , T = 343.15 K : ); VLE data; lines: calculation.Figure 10
Calculation of the VLE for the CaCl2+H2O system. Symbols (, T = 303.15 K; , T = 313.15 K; , T = 323.15 K; , T = 333.15 K; and , T = 343.15 K : );VLE data; lines: calculation.Figure 11
Calculation of the interaction data for the LiCl + H2O system. Symbols (, T = 303.15 K; , T = 313.15 K; , T = 323.15 K; , T = 333.15 K, and , T = 343.15 K : ); VLE data; lines: calculation.


### 3.3. Comparison with the Results Obtained from the Previous Model

Some systems were selected to compare the results obtained in this paper and previous calculations. The results of the comparisons are shown in Table8. From the results, it can be concluded that the maximum dY of the developed model is 1.067 kPa and that the maximum dP is 3.92%. Similarly, the average dY is 0.26 kPa, and the average dP is 1.61%. In general, the results of the model calculations in this paper are not as good as those reported previously, but the parameters are given better physical meaning, and the number of parameters used is lower.Table 8
Calculations for VLE data.
SystemT/KactThis workPrevious workdY/kPaadP/%bdY/kPaadP/%bBaBr2298.15 to 343.150.0580.810.0790.78CaBr2298.15 to 343.150.0531.130.0491.1CaCl2273.15 to 415.150.4571.190.0811.82CsBr298.15 to 343.150.0640.710.0971.01CsCl298.15 to 343.150.4571.190.0910.97CsI298.15 to 343.150.0320.540.0390.42K2SO4298.15 to 373.651.0672.720.0511.15KBr298.15 to 343.150.2513.280.0770.87KCl273.15 to 343.150.1942.500.0440.67KI298.15 to 343.150.1882.240.0970.95LiCl298.15 to 394.40.0110.420.0181.25MgCl2298.15 to 377.850.4901.860.071MgSO4273.15 to 376.450.8101.850.0760.85Na2SO4273.15 to 298.150.0090.460.0120.53NaBr298.15 to 343.150.0110.210.0480.75NaCl298.15 to 373.150.0970.920.040.65NaI298.15 to 343.150.4203.920.090.929RbCl298.15 to 343.150.2933.120.0610.69SrCl2298.15 to 343.150.2303.130.0680.71ZnCl2298.15 to 379.80.0080.0310.031Average0.261.610.0610.905adY=1/N∑Pexp−Pcal, where N is the number of data points. bdP=1/N∑Pexp−Pcal/Pexp×100%, where N is the number of data points.


## 3.1. The Results of Interaction and Parameters

In data processing, it can be found that H_int energy is related to concentration, temperature, etc. From Figures4∼7, it can be seen that the energy increases with temperature and concentration.Figure 4
Correlation of the interaction data for the BaBr2+H2O system. (a) The interaction of BaBr2 and (b) the interaction of H2O. Symbols (, T = 303.15 K; , T = 313.15 K; , T = 323.15 K; , T = 333.15 K; and , T = 343.15 K : ); COSMO data; lines: correlation.
(a)(b)Figure 5
Correlation of the interaction data for the CaBr2+H2O system. (a) The interaction of CaBr2 and (b) the interaction of H2O. Symbols (, T = 303.15 K; , T = 313.15 K; , T = 323.15 K; , T = 333.15 K; and , T = 343.15 K : ); COSMO data; lines: correlation.
(a)(b)Figure 6
Correlation of the interaction data for the CaCl2+H2O system. (a) The interaction of CaCl2 and (b) the interaction of H2O. Symbols (, T = 303.15 K; , T = 313.15 K; , T = 323.15 K; , T = 333.15 K; and , T = 343.15 K : ); COSMO data; lines: correlation.
(a)(b)Figure 7
Correlation of the interaction data for the LiCl + H2O system. (a) The interaction of LiCl and (b) the interaction of H2O. Symbols (, T = 303.15 K; , T = 313.15 K; , T = 323.15 K; , T = 333.15 K, and , T = 343.15 K : ); COSMO data; lines: correlation.
(a)(b)Equations (13) and (14) were used to correlate the H_int interaction. The calculation results are listed in Table 7. For all systems in this paper, the results show that dY ≤ 0.0408 kcal/mol and the average of dY = 0.0058 kcal/mol and dP≤2.71% and the average of dP=0.162%. So, the equations can be better used to describe the change of H_int energy.(16)dY=1N∑Pexp−Pcal,(17)dP=1/N∑Pexp−PcalPexp×100%.Table 7
Correlation of H int data.
SystemT/KSalt-water interactionWater-salt interactiondY/kcal.mol−1adP/%bdY/kcal.mol−1adP/%bBaBr2298.15 to 343.150.01050.09440.00240.0504CaBr2298.15 to 343.150.00010.01830.00030.0077CaCl2298.15 to 343.150.00130.02580.00040.0092CsBr298.15 to 343.150.00440.02610.00180.0385CsCl298.15 to 343.150.01440.07960.00150.0319CsI298.15 to 343.150.00050.00370.00070.6001K2SO4298.15 to 343.150.00720.02160.00090.0186KBr298.15 to 343.150.00310.02170.00150.0321KCl298.15 to 343.150.00730.04270.00210.0425KI298.15 to 343.150.00530.04230.00070.0172LiCl298.15 to 343.150.00670.11180.00290.0682MgCl2298.15 to 343.150.02540.86720.00290.0693MgSO4298.15 to 343.150.04082.70680.00210.0517Na2SO4298.15 to 343.150.01240.06880.00090.0187NaBr298.15 to 343.150.00340.03190.00240.0531NaCl298.15 to 343.150.00810.06140.00150.0335NaI298.15 to 343.150.00320.03690.00310.0699RbCl298.15 to 343.150.01830.09950.00310.0645SrCl2298.15 to 343.150.01760.15680.00070.0147ZnCl2298.15 to 343.150.00980.62540.00370.0812Average0.0100.2570.00180.0689adY=1/N∑Pexp−Pcal, where N is the number of data points. bdP=1/N∑Pexp−Pcal/Pexp×100%, where N is the number of data points. Pexp represents the experimental pressure and Pcal represents the calculated pressure.


## 3.2. Prediction of the VLE Data in Electrolyte Solutions

The modified model and parameters described above were used to calculate the VLE data for twenty electrolyte solutions at vapor pressures ranging between 6 kPa and 101.325 kPa. The results of the calculation are presented in Table5, and dY and dP are listed in Table x.For all systems in this paper, the results show that dY ≤ 1.067 kPa and the average of dY = 0.26 kPa and dP≤3.92% and the average of dP=3.92%. The calculation results for the VLE data are shown in Figure 8–11 for BaBr2, CaBr2, CaCl2, and LiCl systems, respectively.Figure 8
Calculation of the VLE for the BaBr2+H2O system. Symbols (, T = 303.15 K; , T = 313.15 K; , T = 323.15 K; , T = 333.15 K; and , T = 343.15 K : ); VLE data; lines: calculation.Figure 9
Calculation of the VLE for the CaBr2+H2O system. Symbols (, T = 303.15 K; , T = 313.15 K; , T = 323.15 K; , T = 333.15 K; and , T = 343.15 K : ); VLE data; lines: calculation.Figure 10
Calculation of the VLE for the CaCl2+H2O system. Symbols (, T = 303.15 K; , T = 313.15 K; , T = 323.15 K; , T = 333.15 K; and , T = 343.15 K : );VLE data; lines: calculation.Figure 11
Calculation of the interaction data for the LiCl + H2O system. Symbols (, T = 303.15 K; , T = 313.15 K; , T = 323.15 K; , T = 333.15 K, and , T = 343.15 K : ); VLE data; lines: calculation.


## 3.3. Comparison with the Results Obtained from the Previous Model

Some systems were selected to compare the results obtained in this paper and previous calculations. The results of the comparisons are shown in Table8. From the results, it can be concluded that the maximum dY of the developed model is 1.067 kPa and that the maximum dP is 3.92%. Similarly, the average dY is 0.26 kPa, and the average dP is 1.61%. In general, the results of the model calculations in this paper are not as good as those reported previously, but the parameters are given better physical meaning, and the number of parameters used is lower.Table 8
Calculations for VLE data.
SystemT/KactThis workPrevious workdY/kPaadP/%bdY/kPaadP/%bBaBr2298.15 to 343.150.0580.810.0790.78CaBr2298.15 to 343.150.0531.130.0491.1CaCl2273.15 to 415.150.4571.190.0811.82CsBr298.15 to 343.150.0640.710.0971.01CsCl298.15 to 343.150.4571.190.0910.97CsI298.15 to 343.150.0320.540.0390.42K2SO4298.15 to 373.651.0672.720.0511.15KBr298.15 to 343.150.2513.280.0770.87KCl273.15 to 343.150.1942.500.0440.67KI298.15 to 343.150.1882.240.0970.95LiCl298.15 to 394.40.0110.420.0181.25MgCl2298.15 to 377.850.4901.860.071MgSO4273.15 to 376.450.8101.850.0760.85Na2SO4273.15 to 298.150.0090.460.0120.53NaBr298.15 to 343.150.0110.210.0480.75NaCl298.15 to 373.150.0970.920.040.65NaI298.15 to 343.150.4203.920.090.929RbCl298.15 to 343.150.2933.120.0610.69SrCl2298.15 to 343.150.2303.130.0680.71ZnCl2298.15 to 379.80.0080.0310.031Average0.261.610.0610.905adY=1/N∑Pexp−Pcal, where N is the number of data points. bdP=1/N∑Pexp−Pcal/Pexp×100%, where N is the number of data points.


## 4. Conclusions

Modeling and calculation of VLE for an electrolyte solution are studied in this paper. Based on previous works, a developed NRTL model is proposed. The influence mechanism for the microscopic interaction on macroscopic VLE is further studied by COSMOtherm. It can be obtained from the calculation result of COSMOtherm that the temperature and concentration of electrolyte solutions are higher, and the interaction energy (H_int) is larger. The interaction parameters in the model are successfully linked to the COSMO interaction energy (H_int) and given a new physical meaning. The model can be used to successfully predict the VLE data for electrolyte solutions at vapor pressures ranging between 6 kPa and 101.325 kPa. It is suitable for most electrolyte solutions. Although the calculation results are slightly inferior to those of previous works, there is an important significance for the establishment of the model framework in this work.



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*Source: 9070055-2022-09-29.xml*