Calculated tie line data, distribution coefficient, and separation factor for the ternary system of water (1) + phosphoric acid (2) + DCM (3), according to the GMDH* results .
Various ternary and quaternary liquid‐liquid phase equilibrium data for water + phosphoric acid + solvent(s) have been reported. Salting‐out, solvent, and temperature effects on the binodal curve and the tie lines have been highlighted and the capability of solvents with different functional groups to extract phosphoric acid from water has been compared. Studying of influence of magnetic, electromagnetic, and ultrasonic fields on the separation factors and distribution coefficients of aqueous phosphoric acid mixtures has been proposed. Moreover, a summary of the optimized binary interaction values, which resulted from non‐random two‐liquid (NRTL) and universal quasi‐chemical (UNIQUAC) thermodynamic models using genetic algorithm (GA), bee algorithm (BA), and simulated annealing (SA), has been presented. Group method of data handling (GMDH) and linear solvation energy relationship (LSER) methods for the correlation of experimental liquid‐liquid equilibrium (LLE) data have been used.
- phosphoric acid
- optimization algorithms
The phosphoric acid due to its potential applications in various industries attracted a great deal of attention in the area of petrochemical operations, pharmaceutical productions, food industry, detergents, insecticides, and agricultural fertilizers. Generally, there are two basic methods in commercial use for the production of phosphoric acid—thermal and wet processes. The thermal process produces a pure acid with huge energy consumption, whereas the wet process is economic and practiced everywhere in the world . Nevertheless, phosphoric acid produced from both methods contains a variety of impurities, which could affect quantity and the quality of the product. Therefore, for efficient removal and decreasing the impurities to below acceptable regulatory levels
Liquid‐liquid extraction or solvent extraction is now one of the most important and widely employed separation techniques in the modern process industries. It is well known due to various practical characteristics, including simplicity, rapid method development, and reasonable selectivity. Moreover, it can be used for several purposes, for instance, to separate the systems with similar boiling points, high boiling points, and temperature‐sensitive components .
Success of liquid‐liquid extraction and accurate understanding of the performance of that is measured through the liquid‐liquid equilibrium (LLE) data. LLE is described with the separation of components of a feed solution, containing the carrier and extract components, using an additional liquid solvent, as the mixture of feed and solvent—if enough solvent is added—forms two immiscible liquid phases. LLE is based on the differences in solubility and equilibrium distribution of these components between the two produced immiscible—or partially miscible—phases. In other words, it depends on the mass transfer of the component to be extracted from the carrier to the solvent. For having an effective extraction, the extract component should more preferably dissolve in the solvent. After settling the two phases, the raffinate and the extract phases are formed. The raffinate phase contains mostly the carrier, as well as a residue of the extracted component and solved solvent, whereas the extract phase consists of the main the solvent, a part of the extracted component, and solved carrier. Solvent extraction is a separation process aiming to purify the feed or to recover one or more components from it . Nowadays, enormous amounts of acid, specifically high‐purity phosphoric acid, can be commercially produced through liquid‐liquid equilibrium process.
2. Phase diagram of multicomponent liquid mixtures: measurement and visualization
Only systems with at least three components and a miscibility gap can be used for extractions. Phase behavior of such systems at a constant temperature and pressure is conveniently represented on an equilateral triangular diagram, which its corners indicate the pure components, binary compositions are along the edges, and ternary mixtures are located inside the triangle. A common phase diagram is type I system and shown in Figure 1, where a pair of components propylene carbonate and water are partially miscible, and liquid phosphoric acid dissolves completely in propylene carbonate or water . In this figure, the boundaries that each one of them separates the single‐phase region from the two‐phase region are named binodal (solubility) curves. The two‐phase region is included inside below the curved envelope. The binodal curve results are determined by cloud‐point titration method . According to this method, a binary mixture of known composition was titrated with the third component at each mixture using non‐sealed glass vessels. The transition point is taken as the appearance/disappearance of turbidity in the sample and it is defined as a cloud point. The mixture temperature is regulated by a thermostatic thermometer with an accuracy of ±0.1 K. Every point on the binodal curve also has another corresponding point on the binodal curve, as these two points represent the phase equilibrium. The lines between these two equilibrium points are called tie lines. The tie lines are usually not parallel and their slopes can increase and decrease drastically. Tie line experiments were carried out in a jacketed 150 ml glass cell. The biphasic mixture with known compositions was placed in the extraction cell and was vigorously agitated by a magnetic stirrer for 4 h, and then left to settle for minimum 4 h for phase separation. After separation, samples of both phases were transparent and were carefully weighed and analyzed to determine their compositions. Then, the concentrations of the acid in both the phases were obtained by potentiometric NaOH titration . Besides, the water content of the organic phase was measured by the Karl‐Fisher method  and the water contained in the aqueous layer was determined using refractive index measurement method . The obtained tie line data for (water + phosphoric acid + methyl isoamyl ketone (MIAK))  and (water + phosphoric acid + dichloromethane (DCM))  ternary systems are presented in Figure 2 and Table 1, respectively. As either the temperature or pressure is varied, the location of the binodal curve and slopes of the tie lines may change (see Figures 1 and 2).
|Aqueous phase (raffinate) mass percent||Organic phase (extract) mass percent|
3. Separation factor and distribution coefficients
In order to evaluate the extracting capability of the solvent for the separation of components from feed solutions with liquid‐liquid extraction, the separation factor,
In recent years, significant investigations on LLE measurements and the extraction of phosphoric acid from aqueous solutions have been carried out, while many solvents have mainly been tested, in order to understand and provide further information for accurate interpretation of phase equilibria of the different multicomponent mixtures with phosphoric acid [12–27]. As a detailed evaluation of extraction abilities of the different solvents reported in the literature, including alcohols, esters, ethers, ketones, and hydrocarbons to extract phosphoric acid from aqueous solutions, a comparative study is listed in Table 2. Figure 3 also highlights the definitive effects of different chemical structures present in solvents on recovering of the acid. As it is drawn, results show the following order of effectiveness of solvent for systems containing phosphoric acid: methylcyclohexane > ethyl benzene > isoamyl acetate > n‐pentane > 1‐octanol > bis(2‐methylpropyl) ether. From the obtained experimental results, it can be concluded that methylcyclohexane is the most appropriate solvent for the separation of a mixture of water and phosphoric acid. It is also apparent from Figure 4 that bis(2‐methylpropyl) ether is a less favorable solvating agent for phosphoric acid.
|Water + phosphoric acid + 1‐butanol||Alcohol||308.2||1.65|||
|Water + phosphoric acid + 2‐methyl‐2‐butanol||Alcohol||298.2||1.82|||
|Water + phosphoric acid + isoamy1 alcohol||Alcohol||308.2||1.82|||
|Water + phosphoric acid + 2‐ethyl‐1‐hexanol||Alcohol||298.2||1.46|||
|Water + phosphoric acid + 1‐octanol||Alcohol||298.2||6.35|||
|Water + phosphoric acid + 1‐nanonol||Alcohol||298.2||3.54|||
|Water + phosphoric acid + 1‐decanol||Alcohol||303.2||3.80|||
|Water + phosphoric acid + 1‐dodecanol||Alcohol||303.2||4.30|||
|Water + phosphoric acid + cyclohexanol||Alcohol, cyclic alcohol||308.2||1.57|||
|Water + phosphoric acid + 1‐dodecanethiol||Thiol, aliphatic thiol||303.2||18.20|||
|Water + phosphoric acid + butyl acetate||Ester||308.2||5.78|||
|Water + phosphoric acid + isobutyl acetate||Ester||298.2||7.46|||
|Water + phosphoric acid + isoamyl acetate||Ester||298.2||19.70|||
|Water + phosphoric acid + hexyl acetate||Ester||298.2||7.00|||
|Water + phosphoric acid + cyclohexyl acetate||Ester||298.2||6.20|||
|Water + phosphoric acid + propylene carbonate||Ester||298.2||2.82|||
|Water + phosphoric acid + tributyl phosphate||Ester||298.2||3.40|||
|Water + phosphoric acid + diisopropyl ether||Ether||293.2||1.89|||
|Water + phosphoric acid + bis(2‐methylpropyl) ether||Ether||298.2||3.76|||
|Water + phosphoric acid + n‐pentane||Hydrocarbon||308.2||15.08|||
|Water + phosphoric acid + 2‐methylpentane||Hydrocarbon||308.2||3.36|||
|Water + phosphoric acid + n‐hexane||Hydrocarbon||308.2||4.60|||
|Water + phosphoric acid + cyclohexane||Hydrocarbon, cycloalkane||308.2||15.30|||
|Water + phosphoric acid + methyl cyclohexane||Hydrocarbon, cycloalkane||308.2||43.10|||
|Water + phosphoric acid + toluene||Hydrocarbon, aromatic hydrocarbon||308.2||26.50|||
|Water + phosphoric acid + ethyl benzene||Hydrocarbon, aromatic hydrocarbon||298.2||32.70|||
|Water + phosphoric acid + isopropyl benzene||Hydrocarbon, aromatic hydrocarbon||298.2||23.70|||
|Water + phosphoric acid + dichloromethane (DCM)||Halogenated aliphatic hydrocarbon||298.2||1.04|||
|Water + phosphoric acid + DCM + 10 wt% NaCl||Halogenated aliphatic hydrocarbon + salt||298.2||2.20|||
|Water + phosphoric acid + DCM + 10 wt% CaCl2||Halogenated aliphatic hydrocarbon + salt||298.2||1.39|||
|Water + phosphoric acid + 1,2‐dichloroethane (DCE)||Halogenated aliphatic hydrocarbon||298.2||1.10|||
|Water + phosphoric acid + DCE + 10 wt% NaCl||Halogenated aliphatic hydrocarbon + salt||298.2||2.35|||
|Water + phosphoric acid + DCE + 10 wt% CaCl2||Halogenated aliphatic hydrocarbon + salt||298.2||2.13|||
|Water + phosphoric acid + methyl isobutyl ketone||Ketone||308.2||1.26|||
|Water + phosphoric acid + methyl isoamyl ketone||Ketone||298.2||11.00|||
|Water + phosphoric acid + methyl ethyl ketone||Ketone||308.2||0.91|||
In addition, the presence of dissolved salt changes the phase equilibrium behavior of a mixture significantly [28–31]. Recently, Govindarajan and Sabarathinam , Mohsen‐Nia et al. , and Santos et al.  have investigated effects of some inorganic salts such as Na2SO4, ZnSO4, (NH4)2SO4, NaCl, KCl, KBr, and NaNO3 on the ternary liquid‐liquid equilibria data. Similarly, by considering the importance of the salting effect on the extraction of phosphoric acid from aqueous mixtures, it is worthwhile to study LLE of mixtures of (water + phosphoric acid + solvent + salt). In particular, as can be seen in Table 2, maximum values of separation factor for (water + phosphoric acid + DCM + 10 wt% NaCl and 10 wt% CaCl2) solutions are improved compared with those in the absence of added salts .
Although solvents with high separation are considered as potential candidates to carry out the extraction, due to the economic, environmental, and technical factors, the suitable solvent at optimum conditions is proposed to be chosen for the extraction of phosphoric acid from aqueous mixtures. Meanwhile, it seems that the measurement of the (liquid + liquid) equilibrium data of the mixtures with a mixed solvent has become the turning point topic of the chemistry investigations in recent years [11, 35–42]. As an illustration, Figure 3 compares distribution coefficients of phosphoric acid for three quaternary systems of (water + phosphoric acid + mixed solvent (25% DCM + 75% DCE) or (50% DCM + 50% DCE) or (75% DCM + 25% DCE)) . The results confirm the different effects of the dichloromethane as co‐solvent on 1,2‐dichloroethane for the extraction of phosphoric acid from aqueous mixtures. The comparison between the experimental separation factors obtained for the mixed solvent (DCM + DCE) with various ratios also indicates that mixed solvent (25% DCM, 75% DCE) has a higher separation factor than the other mixed solvents at
Besides, it is anticipated that the magnetic, electromagnetic, and ultrasonic fields as external factors can affect LLE data by influencing solvents properties such as polarity and permittivity, especially for polar solvents. Therefore, the application of them to the phase separation in the solvent extraction process has been considered from the technical and economical viewpoints. For studying this purpose, the effect of the applied different fields on phase behavior of several ternary systems has been obtained and reported [43–48]. There are a number of effective potentials for future research to evaluate the effects of the magnetic, electromagnetic, and ultrasonic fields on the extraction of phosphoric acid from aqueous mixtures.
The linear solvation energy relationship (LSER) models  such as Kamlet (Eq. (1)) and Katritzky (Eq. (2)) equations [50, 51] were used to correlate separation factor for several ternary LLE systems with phosphoric acid, reporting in references [16, 19, 24]. Kamlet LSER model with the solvatochromic parameters is defined according to the following equation:
Katritzky  introduced a multiparameter polarity scale with combination of Riechardt's solvent polarity, , the dielectric constant,
The LSER model values showed a good regression of the experimental data for all investigated systems. The temperature susceptibility coefficient,
4. LLE correlation
Various thermodynamic models with different abilities can be used to accurately describe the multicomponent LLE systems. Aided by these activity coefficient equations and a parameter fit, it is possible to reproduce the measurement and control the data. The non‐random two‐liquid (NRTL)  and the universal quasi‐chemical (UNIQUAC)  methods have been successfully applied for the correlation of many ternary and quaternary liquid‐liquid phase equilibrium solutions [12, 16–19, 24–26], while a group contribution approach (UNIFAC)  may be utilized to predict the LLE mixtures.
4.1. NRTL equation
The basic idea in NRTL equation follows from the concept of local composition which was used by Renon and Prausnitz . Renon's equation is applicable to partially miscible liquid mixtures, and for the binary mixtures the excess Gibbs energy is
The significance of
For strongly nonideal mixtures and especially for partially immiscible systems , the NRTL equation often provides a good representation of experimental data if care is exercised in data reduction to obtain the adjustable parameters.
The equations discussed are readily to as many components as desired without any additional assumptions and without introducing any constants other than those obtained from binary data. For a solution of
The activity coefficient for any component
Eqs. (8) and (11) contain only parameters obtained from binary data. The experimental tie line LLE data of multicomponent mixtures can be correlated using the NRTL model within well‐known simulation software such as Aspen Plus. The quality of the correlation is measured by the root‐mean‐square deviation (RMSD) . Many NRTL LLE values for the ternary and quaternary systems containing water, phosphoric acid, and solvent have appeared in the available literature [11, 16, 17]. For example, in Figure 3, the calculated NRTL data have been used to plot and show the variation of distribution coefficients of acid for (water + phosphoric acid + mixed‐solvent (DCM + DCE)) system at temperature
4.2. UNIQUAC equation
A critical examination of the derivation of the NRTL equation shows that this equation is more suitable for
For a binary mixture,
where the coordination number
For each binary mixture, there are two adjustable parameters,
For a multicomponent system, the UNIQUAC equation for the molar excess Gibbs energy is given by the sum of
where segment fraction
The activity coefficient for any component
The molecular interaction‐based model of UNIQUAC successfully has correlated many LLE data of ternary and quaternary systems [10, 15–17, 24] within Aspen Plus—for example, see Table 5; however, as previously mentioned, during the last 10 years, many LLE‐based algorithm—GA, SA, and BA—have been developed and introduced in the literature [57, 60, 61]. Recently, a study on
4.3. GMDH‐type neural network
It is observed that usually LLE measurements are successfully correlated using common models such as NRTL and UNIQUAC. However, these conventional thermodynamic methods for data prediction of complex systems are tedious and involve a certain amount of empiricism. Recently, a new prediction method, the group method of data handling, was developed to predict LLE and VLE data in order to avoid these limitations [64, 65]. Namely, the GMDH tie line data for the ternary system of water + phosphoric acid + dichloromethane have been illustrated in Table 1 [10, 26]. Furthermore, the reliability of the presented tie line results can be tested through the Othmer‐Tobias  and Bachman  correlation equations.
We gratefully acknowledge the financial support from the Research Council of Firoozabad Branch, Islamic Azad University.
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