Optimization of liquid–liquid equilibria of the type 2 ternary systems (water + valeric acid + aromatic solvent): Modeling through SERLAS

Fluid Phase Equilibria 415 (2016) 110e124

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Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d

Optimization of liquideliquid equilibria of the type 2 ternary systems (water þ valeric acid þ aromatic solvent): Modeling through SERLAS Aynur Senol Department of Chemical Engineering, Faculty of Engineering, Istanbul University, 34320 Avcilar, Istanbul, Turkey

a r t i c l e i n f o

a b s t r a c t

Article history: Received 28 September 2015 Received in revised form 25 January 2016 Accepted 28 January 2016 Available online 2 February 2016

The study covers the liquideliquid equilibrium (LLE) of the type 2 ternary systems (water þ valeric acid þ aromatic solvent) measured at T ¼ (298.2 ± 0.1) K and P ¼ (101.3 ± 0.7) kPa. The extraction efficiency of valeric acid by the aromatic solvents is better for xylene and chlorobenzene as compared to benzyl ether and 1-phenyl ethanol. An optimization algorithm utilizing the derivative variation method has been applied to the prediction of the optimization range of a type 2 LLE system. The capability of the proposed six optimization factors and two six-parameter models to represent conformably the optimum extraction field has been rigorously tested regarding the variation profile of the derivatives of the optimized quantity. A solvation energy relation SERLAS involving six physical descriptors has been implemented on the relevant systems, and checked for consistency in reproducing the observed performance. The deviation statistics obtained for SERLAS testify its ability to simulate accurately the observed performance with a mean error of 5.1%. The predictive capability of the UNIFAC-original model has been also studied. © 2016 Elsevier B.V. All rights reserved.

Keywords: Liquideliquid equilibria Valeric acid Aromatic solvent Optimization Modeling

1. Introduction An expanding field of scientific research is increasingly concerned with solvent extraction of carboxylic acids from aqueous fermentation solutions prompting the search for more benign solvents [1e6]. From an efficiency standpoint, various conventional organic solvents and specific ionic liquids are being investigated for a wide variety of separation and extraction processes involving liquideliquid phase behavior. Characterization of liquideliquid equilibrium (LLE) in system containing a carboxylic acid is very much dependent on the nature of acid, the concentration of acid, the type of organic solvent, the swing effect of a mixed solvent and the third phase formation, which can influence controllably the phase equilibria [7e12]. It is intuitive that the type of a LLE system will be the most promising factor in controlling the phase equilibria [1,13,14]. The gathered information for the equilibrium properties of a ternary LLE system is critical to identifying the molecular interactions between the components with specific molecular structures, allowing the choice of most suitable solvents for the acid recovery [1e12]. Especially, phase diagrams allow a global overview

E-mail address: [email protected]. http://dx.doi.org/10.1016/j.fluid.2016.01.050 0378-3812/© 2016 Elsevier B.V. All rights reserved.

of the phase behavior of the ternary LLE systems under study. As classified by Treybal [13] and Prausnitz [14], type 1 and type 2 are most common ternary LLE systems which are actually encountered in practice due to a high phase stability favoring easy separation. A ternary LLE mixture of type 2 presents a partial miscibility in two pairs of compounds, while a system of type 1 has one partially miscible pair with a defined plait point. This phenomenon should have a significant impact on the implementation of a selected extraction method utilizing the type 2 LLE system composed of (water þ valeric acid þ aromatic solvent). As continuation of the previous study [7,10e12,15], the present work aims at generating new LLE data for the extraction of valeric acid from water at T ¼ 298.2 K and P ¼ 101.3 kPa using inert (xylene, Tb ¼ 417 K), polar (chlorobenzene, Tb ¼ 405 K), non-protic (benzyl ether, Tb ¼ 561.5 K) and protic (1-phenyl ethanol, Tb ¼ 477 K) aromatic solvents. It may be desirable to use a higheboiling solvent that does not have to be distilled so long as no azeotropes appear. Regarding the technical and economic merits of high boiling aromatic solvents during the regeneration by distillation, the selection of xylene, chlorobenzene, benzyl ether and 1-phenyl ethanol of higher boiling temperatures than water was made. As well, the employed protonedonating and eaccepting oxygenated solvents benzyl ether and 1-phenyl ethanol have lower vapor pressures than

A. Senol / Fluid Phase Equilibria 415 (2016) 110e124

valeric acid (Tb ¼ 458 K). In particular, solvents used in the present extraction systems should have low cost, low toxicity and rather high boiling temperature properties than water, while their viscosities and densities should be close to those of water. However, they should be applicable to numerous extraction systems while still being general with regard to the solubility properties, along with giving proper LLE data for the excellent design and productive operation of the related extraction equipment. As the phase behavior is affected by the choice of the solvent, and it is highly unlikely that any particular liquid will exhibit all of the properties desirable for solvent extraction, the final choice of a solvent is in most cases a compromise between various properties and parameters, viz. selectivity, distribution coefficient, insolubility of the solvent, recoverability, density, viscosity, interfacial tension, vapor pressure, freezing point, toxicity, flammability, chemical reactivity and cost [13,14]. From this point of view, the selected protic and non-protic aromatics may constitute an advantageous alternative as extractive solvents for valeric acid. LLE data for the present ternary systems are not available in the open literature. The equilibrium properties of the studied ternary systems, typically exhibiting no plait point, are used to elucidate the phase behavior of the components in terms of their structural and hydrogen bonding characteristics, aspiring at a better understanding of the main interactions between the aromatic solvent and the distributed acid that control the liquideliquid equilibrium of the considered systems. It is expected that the effect of temperature should be accustomed to a regular change in the immiscibility of the two-phases region so long as no phase change appears in the type 2 LLE system, therefore, the phase equilibrium at different temperatures will be accordingly considered redundant and not studied here. 1.1. Overview of thermodynamic models for LLE systems Modeling the phase equilibria of LLE systems containing an aromatic solvent and an aliphatic acid is still challenging because of their complex aggregation through hydrogen bonding and dipoleedipole interaction. Traditionally, LLE can be accurately calculated by the popular thermodynamic approaches known as LSER (linear solvation energy relationship) [16,17], the excess Gibbs energy based models Wilson, NRTL, UNIQUAC, ASOG, UNIFAC-original and UNIFACeDortmund [18e23], and PengeRobinson and RedlicheKnowneSoave cubic equations of state (EOS) [19,20,23], which have found use to varying degrees. Many researchers have attempted to evaluate the capability of the NRTL, UNIQUAC and electrolyte-NRTL (e-NRTL) models to predict the ternary LLE of systems using binary (and pure) component data [24,25]. The prediction of ternary LLE from binary data only is known to be difficult since a suitable solution to the interaction-parameter estimation problem is required for the later models, but unexpectedly, their predictive capabilities even for systems containing ionic liquids (ILs) were surprisingly good [25]. Group contribution methods are extensively used in the chemical industry, especially during the development of chemical processes [19,20,23], and the UNIFACeoriginal model [26e28] stands out because its parameter matrix is the most comprehensive one being obtained from extensive series of revisions and extensions of the VLE or LLE dataefitted parameters. To improve its predictive capability several modified UNIFAC models have been proposed, such as UNIFACeDortmund [22], UNIFACeLyngby [29] and AeUNIFAC [30e32]. The group contribution with association equation of state (GCAEOS) and the A-UNIFAC model were applied successfully to represent the phase equilibria of the ternary LLE system in the downstream separation process [32]. Despite of a high flexibility of GCAEOS and AeUNIFAC, taking into account association effects

111

between groups, a rigorous validation of the formulated association frameworks require an extension of the parameter matrix applicable to different kinds of LLE systems and their further analysis. To enable a possible extension of excess Gibbs energy dependent algorithms, new classes of EOS have been developed originally from the statistical fluid theory to improve the accuracy of phase equilibrium calculations for systems with multiple associating sites, namely, the associated perturbed anisotropic chain theory (APACT), the statistical associating fluid theory (SAFT), the lattice quasiechemical hole model (HM), cubicepluseassociation equation of state (CPAeEOS), and conductor-like screening model for real solvents (COSMOeRS) [33e49]. In spite of the difference in the physical interaction terms of the EOS, it was found reasonable results in the description of association equilibria through these approaches, being in agreement with the experimental data [33,36,43,44,47e52]. Numerous EOS models suitable for associating fluids have been developed using the concepts of three theories categorized as: a) perturbation theory of Wertheim (SAFT, CPAeEOS models); b) chemical theory which accounts for the formation of various oligomers through a chemical interaction (AEOS model of Anderko, APACT); c) latticeefluid quasiechemical theory (hole model, HM) [33e43]. In summary, these models include a physical term accounting for the deviations due to physical forces and an association term accounting for the effect of hydrogen bonding. Typically, the physical term is either a cubic EOS or a complex nonecubic EOS with two or more adjustable parameters (APACT, SAFT, HM models). While the association term, based on different principles of related theories, aims to capture the physics of the hydrogen bond. In fact, EOS models are widely used for the prediction of LLE and VLE in various electrolyte and non-electrolyte systems. In this context, Tang et al. [51] have selected PerturbedChain SAFT (PC-SAFT) and First-order Mean Spherical Approximation SAFT (FMSA-SAFT) models to calculate the complex phase equilibrium depending on equal-area method, and found that they are more theoretically rigorous and applicable to both homogeneous and inhomogeneous fluids. As noted by Oliveira et al. [52], water solubility in biodiesel has been successfully modeled through CPA-EOS with global average deviations inferior to 7% for the ester systems. Another predictive model, that has been gained importance recently, is COSMO-RS [45e50]. This model combines quantum chemistry, based on the dielectric continuum model known as COSMO (Conductor-like Screening Model), with iterative cycles of statistical thermodynamics to reduce the thermodynamics of the mixture to the interaction of a mixture of individual surface segments (chemical potential determination) [45e50]. This a priori solvent profiling method allows for an efficient prescreening of a great set of solvents [53]. The set of COSMO-RS equations gives the chemical potential of all components in a mixture and allows the estimation of several thermophysical properties and phase behavior of pure fluids and mixtures, namely activity coefficients, distribution ratios, and phase equilibria, among others. Logically, as COSMO-RS treats solvents with their real molecular structures, such an approach cannot be used for solvent molecular design. Therefore, Zhou et al. [53] introduce a new kind of solvent descriptor obtained from quantum chemical calculations and determine the contributions of common molecular (UNIFAC) subgroups to these descriptors. However, the ability of COSMO-RS as a predictive tool to describe the liquidliquid equilibria of ternary systems composed of ionic liquids and hydrocarbons has been thoroughly evaluated by Ferreira et al. [50]. Another purely predictive approach is the asymmetric framework developed by Simoni et al. [54,55] for predicting liquideliquid equilibrium of ionic liquid-mixed-solvent systems in which different phases have different degrees of electrolyte dissociation,

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A. Senol / Fluid Phase Equilibria 415 (2016) 110e124

and are thus represented by different Gibbs energy models. In view of the results obtained by Simoni et al. [55], an asymmetric NRTL/e-NRTL model provides better predictions of ternary LLE for systems containing ILs and water than standard symmetric models. Nevertheless, the UNIFACeoriginal model is always being opted for the prediction of the phase equilibria since its extended parameter matrix is applicable to different kinds of LLE systems [26e28]. Recently, several extended versions of the LSER approach proposed by Senol [7,8,56e61] have been especially intended for the correlative description of the phase equilibria of LLE and VLE systems. In principle, a reliable thermodynamic model should have a sound mathematical basis. However, ternary systems of type 2 are difficult to model predictively. As noted by Prausnitz and coeworkers [20,62], standard mean-field excess Gibbs energy models usually fail to solve the complex LLE near the binary mutual solubility regions of a type 2 system due to the fluctuations in composition nearby these limits. Thus, thermodynamic modeling the phase equilibria of ternary LLE mixtures with two partially miscible pairs of compounds is still in its deficiency. Here, we have examined the efficacy of using SERLAS (solvation energy relation for liquid associated systems) model to estimate the properties of a type 2 ternary system [7,8,59e61]. The model incorporates the simultaneous impact of six molecular descriptors, i.e., the thermodynamic factor, the Hildebrand solubility parameter and the solvatochromic parameters of hydrogen bonding [7,8,59e61]. The predictive capability of the UNIFAC-original model [26e28] has been also studied. The reliability analysis of both models has been performed statistically.

1.2. Optimization scheme for extraction equilibria This work primarily has focused on optimizing analytically the extraction conditions of a type 2 LLE system on the basis of the derivative variation method proposed by Senol [59e61,63]. Typically, the derivative variation method is based on analyzing the non-linear variation profile of the first order derivatives of the optimization factor in question [63]. Previously, the method has been successfully applied to a wide variety of LLE systems exhibiting the phase behavior of type 1 [59e61]. However, this article explores the application of a specially designed optimization algorithm to the more complicated type 2 ternary systems for the prediction of the optimum LLE by means of the derivative variation techniques. Intuitively, for these systems, the appearance of optimum conditions can be very sensitive to the limiting mutual solubility of the binaries and the overall composition of coexisting phases, even when irregular contribution of the solute concentration to the optimized quantity is observed along the working range. Here, it will be discussed the optimum conditions for an efficient acid extraction as the locus of the proposed six optimization factors being used as the optimization criteria for a type 2 LLE system. This is followed by the presentation of the formulated optimization structure and its application to relevant systems. In general, the examined optimization algorithm gives a realistic picture of whether an optimum point exists and how its values can be determined. Inevitably, the optimization algorithm calls for the use the derivatives of the optimized quantity to identify the optimum extraction field of relevant systems. The overall optimization structure is expected to be physically definable on a fundamental basis, rational and applicable to numerous LLE systems. Analysis is limited to the phase behavior of a type 2 ternary system. The optimization scheme for the type 2 LLE systems is interpreted from an integration perspective of four independent variables and will be discussed in more detail in Section 4.

2. Theoretical 2.1. Summary of the SERLAS model The SERLAS model given by Eq. (1) is a LSER-based solvation approach that is particularly well suited for a correlative description of the properties of types 1 and 2 ternary systems [7,8,59e61]. The model is briefly summarized below along with introducing the special calculations to achieve reliable solution. Here we have appropriately adapted SERLAS to estimate typical properties of a type 2 LLE system such as the separation factor (S), the modified distribution ratio (DM), the modified separation factor (SM) and the solventedependent optimization factor (OF) given by Eqs. (2)e(5). Basically, the Pr property (log mean) in Eq. (1) is made up of two balancing terms, i.e. the Pr0 term (log mean) accounted for the limiting observed property at the composition limit of the distributed acid x2 ¼ 0 and an integration term involving six physical descriptors of the components, namely, the thermodynamic factor GL, the modified Hildebrand solubility parameter d*H and the modified solvatochromic parameters p*, d* a*, and b* [7,8,59e61]. Following Marcus et al. [16,17], we select the combined polarity/ polarizability solvatochromic index pþd to be an independent descriptor accounting for the differences in the component polar00 00 izability. F1 ¼ ðx3  x03 Þ=ðx03  x003 Þ and 00 00 00 F2 ¼ ðx3 =ðx2 þ x3 ÞÞ  ðx03 =ðx02 þ x03 ÞÞ are correction factors in Eq. (1) that account for the limiting condition x2 ¼ 0 for which Pr ¼ Pr0.

Pr ¼ F1 Pr0 þ F2

Xh  k  k CG;k ðGL Þk þ CH;k dH þ Cp;k p* k

 k  k i þ Cb;k b* þ Ca;k a*

(1)

 00  0  x x D2 ¼  200  20  S¼ D1 x1 x1

(2)

 00 00   00  x þ x3 = 1  x3    DM ¼  20 x2 þ x03 = 1  x03

(3)

SM ¼

D2 þ D3 D1 þ D3 00

OF ¼

SR ¼

00 00

x2 x02

þ x30 x10

x1 x01

þ

x3 x1 x03 x01

00

00

00

(4)

x x

3 1 00 00

¼

D2 þ SR D1 þ SR

x3 x1 ¼ D3  D1 x03 x01

(5)

(5a)

where x'' and x' stand for the solvent-rich and water-rich compositions of water (1), acid (2) and solvent (3), respectively. D is the 00 00 distribution coefficient of the component, D1 ¼ x1 =x01 , D2 ¼ x2 =x02 00 and D3 ¼ x3 =x03 . CG, CH, Cp, Cb and Ca are the adjustable coefficients of Eq. (1). The Pr0 properties, referred to the mutual solubility region x2 ¼ 0, are defined as follows.

S0 ¼

DM0

00  00 x03 x01  x003 x001 00  00  x03 1  x03  ¼ 0  x03 1  x003

(6)

(7)

A. Senol / Fluid Phase Equilibria 415 (2016) 110e124

SM0

 00  0  x03 x03     00   ¼ 00 x01 x001 þ x03 x003

OF0 ¼

SR0 00

x01 x001 00

SR0 ¼

þ SR0

(8)

(9)

00

x03 x01 x003 x001

(9a)

where x03 and x01 represent the mole fractions of mutual solubility of solvent (3) and water (1) for the region x2 ¼ 0, respectively. As evident, S0 and DM0 quantities are identical in the nature by reason of reducing the complexity of Eq. (1). Here, S and DM are extraction factors characterizing the selectivity for the solvent and the degree of the acid distribution between the coexisting phases, respectively. While SM somewhat is a measure of the relative increase in the solvent capacity, and the OF factor represents the distribution effect of the solvents on the extraction degree of the solute. Here SR is related to the solventdependent distribution ratios to account for their cumulative rate of change. These extraction factors have been discussed further previously [59e61]. DM was selected instead of D to eliminate dealing with zero log value for D ¼ 1. The presence of compositions of overall components in the structure of SM and OF categorizes these factors as perceptible criteria adequate for modeling optimum extraction [59e61]. Considering the general case of a type 1 LLE system, the above mentioned quantities are varying between two indicators circumscribing the validation limits of prediction over the entire working range from x2 ¼ 0 to the plait point (x2 ¼ xpp) for which S ¼ DM ¼ SM ¼ OF ¼ 1. However, for the type 2 LLE systems the variation profile of the quantities in question is restricted between the concentration limits x2 ¼ 0 and x3 ¼ 0, in which the prediction is validated. When implementing SERLAS, several computational procedures including the characterization and the determination of all individual variables and model parameters had to be carried out initially. Typically, thermodynamic factors GL relative to the organic phase are determined due to the UNIFACeDortmund model [22] using the derivative approaches of Mori et al. [64,65], as described in detail in the previous work [7,8]. This requires a special subprogram to be added to the main algorithm to first calculate the thermodynamic factors, however, the calculations can be very sensitive to numerical stability. Next, other model variables represented by the modified molecular indices d*H , p*, a*, and b* are obtained from the corresponding solubility and solvatochromic parameters (dH,i, pi, di, ai, bi) of the individual components due to the procedures reported previously [7,8,59e61]. Subsequently, SERLAS is applied to the regression of the model coefficients Ci (CG, CH, Cp, Cb and Ca) for the expansion degree k ¼ 1 to demonstrate its attractive application to a type 2 ternary system. We conclude with a demonstration of the simulating performance of SERLAS with five adjustable coefficients Ci attributed to the S, DM, SM and OF quantities. It is clear that the quality of calculations is intimately connected to the numerical characterization of the Ci coefficients definable for the entire working range. Potentially, SERLAS, Eq. (1), captures the physics of hydrogen bond formation and dipoleedipole interaction associated with the limiting properties at the mutual solubility regions. This computational method is expected to be fundamentally in accordance with the boundary constraints and insensitive to the temperature and pressure conditions at which equilibrium is calculated. In Eq. (1), the effect of temperature is incorporated into the GL quantity, where the temperaturedependent interaction parameters across a larger temperature

113

range are introduced to the UNIFAC-Dortmund model to account for the real behavior (activity coefficients) as a function of temperature. Consequently, the SERLAS model clarifies the simultaneous impact of solvatochromic indicators, solubility and thermodynamic factors of associating components on the extraction equilibria of relevant systems. However, it is clear that the SERLAS model captures the underlying physical situation, which includes the physical characteristics of association such as group interaction parameters, hydrogen bonding indices, dipoleedipole interaction indicators, thermodynamic factors and solubility parameters of components. In this perspective, the model provides considerable improvement for a reliable calculation of the properties of the LLE systems, being in accordance with the boundary constraints and the behavior of the physical event; thus, the model may be considered as an attractive alternative to the common excess Gibbs energy based predictive models. 3. Experimental The chemicals xylene, chlorobenzene, benzyl ether, 1-phenyl ethanol and valeric acid all of analytical grade with stated mass fraction purities higher than 0.99 (GC) were furnished by Fluka. The purities of the compounds were verified by their densities and refractive indexes measured by Anton Paar densimeter Model DMA 4500 and a refractive index unit Model RXA 170 at T ¼ (298.2 ± 0.1) K and P ¼ (101.3 ± 0.7) kPa. The atmospheric pressure was measured by Fortin's mercury barometer with an average uncertainty of ±0.7 kPa. Table 1 presents a brief summary of the measured and literature values of the density and refractive index properties and the observed experimental uncertainties. All the chemicals were used as received without any further purification. Twice redistilled water was used in all experiments. The experimental binodal (solubility) curves and the mutual solubilities of the (water þ solvent) and (water þ valeric acid) binaries were determined by the cloud point method using an equilibrium glass cell equipped with a magnetic stirrer and a water jacket to maintain isothermal conditions [7,8,10e12]. The sample temperature in the cell was kept constant at T ¼ (298.2 ± 0.1) K by means of a thermostated water bath (Julago Labortechnik GMBHGermany) equipped with a temperature controller. Solubility curves were obtained by addition of the acid from a Metrohm microburette to a heterogeneous mixtures of (water þ solvent) located within the immiscibility gap until a permanent homogeneity became visible, which did not disappear when further agitated. The composition of each component was determined by weighing with a Sartorius scale accurate to within ±104 g. The transition point from an appearance to a disappearance of the heterogeneity was obtained visually. The reliability of the method depends on the precision of the microburette and is limited by the visual inspection of the transition across the apparatus. Similarly, the mutual solubilities of partially miscible liquid pairs (water þ solvent) and (water þ valeric acid) were determined by the cloud point method at T ¼ (298.2 ± 0.1) K and P ¼ (101.3 ± 0.7) kPa using the apparatus described above. It is recognized from three independent replicated measurements of the mutual solubilities of relevant systems that the cloud point compositions of (water þ aromatic solvent or valeric acid) binaries and the solubility curves remain in an acceptable narrow band with 1e5% standard deviation. Concentration determinations by the cloud point method were made with an uncertainty of ±0.0007 mole fraction. Current binary mutual solubilities of (water þ valeric acid) and (water þ solvent) are in agreement with the reported literature data [3,60,66]. The previous reported mutual solubility of water in benzyl ether [66] has been necessarily

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A. Senol / Fluid Phase Equilibria 415 (2016) 110e124

Table 1 Experimental and literature data for the densities d298 (g cm3) and refractive indexes nD,298 of components at T ¼ 298.2 K and P ¼ 101.3 kPa.a Component

d

Xylene Chlorobenzene Benzyl ether 1-Phenyl ethanol Valeric acid a b c d e f

Density d298 (g cm3)

Purityc

Refractive index nD,298

Exp.

Lit.b

Exp.

Lit.b

Mass fr.

0.85923 1.10108 1.03932 1.00648 0.93504

0.8567 1.1009 1.0425 1.0090e 0.9345

1.49435 1.52165 1.56019 1.52467 1.40718

1.4933 1.5240 1.5620 1.5225f 1.4060

0.99 0.99 0.99 0.99 0.99

Standard uncertainties u are u(d298) ¼ 0.0001 g cm-3, u(nD,298) ¼ 0.0001, u(T) ¼ 0.1 K, u(P) ¼ 0.7 kPa. Due to Riddick et al. [72]. The purities refer to the mass fraction. A mixture of isomers as provided by the supplier (Fluka). Due to Barega et al. [73]. Due to Hern
andez-Fern
andez et al. [74].

rearranged according to the cloud point-dependent three experimental replicates. The tie lines are determined by analysis of the conjugate phases in which a ternary mixture of known compositions of water, acid and solvent situated inside the two-phase region is separated. Samples of ternary mixtures prepared by mass within the heterogeneous gap were introduced into the extraction cell and agitated for 2 h, and then left for 1 h to settle down into raffinate (aqueous) and extract (solvent) layers. The compositions of liquid samples withdrawn from the conjugate phases were analyzed by HewlettePackard GC Analyzer 6890 equipped with FI and TC detectors. A 15 m long HP Plot Q column (0.32 mm i.d., 0.2 mm film thickness) for TCD, and HP-Innowax polyethylene glycol capillary column (30 m long, 0.32 mm i.d., 0.5 mm film thickness) for FID were utilized to separate organic components of samples at fixed oven programs suitable for each ternary. The detector temperature was kept at T ¼ 523.2 K, while the injection port temperature was held at T ¼ 473.2 K. Injections were performed on the split 1/100 mode. Nitrogen was used as a carrier at a rate of 1 cm3 min1. The endpoint compositions of the tie-lines were determined at T ¼ (298.2 ± 0.1) K and P ¼ (101.3 ± 0.7) kPa. 4. Results and discussion 4.1. Evaluation of LLE data for the extraction of valeric acid The experimental tie lines and solubility (binodal) curves of the ternary systems composed of (water þ valeric acid þ aromatic solvent) are plotted in Fig. 1aed, where xi stands for the mole fraction of the ith component. Table 2 presents the tie-line com00 positions of the aqueous (x0i ) and solvent (xi ) phases obtained for each LLE system, and also the mutual solubility compositions of (water þ aromatic solvent) and (water þ valeric acid) binaries at T ¼ 298.2 K and P ¼ 101.3 kPa. Table 2 also presents a brief summary of the estimated results for the thermodynamic factor GL and excess Gibbs energy function GE (J mol1) pertaining to the organic phase species. A comparison of the experimental tie-lines with the predicted ones through UNIFAC-original for the studied systems is provided in Fig. 1aed. The ternary phase diagrams given in Fig. 1aed display typical characteristics of the type 2 LLE systems represented by two partially miscible liquid pairs (water þ aromatic solvent) and (water þ valeric acid) and solubility curves exhibiting no plait point. The lower (down) part of the binodal curve at the water-rich phase lies close to the left-side corner of the phase diagram due to a low solubility displayed by valeric acid on water, indicating the fact that water does not adequately act as a cosolvent. Together with this, the addition of valeric acid to the (water þ aromatic solvent) mixture works in favor of slightly increasing the water miscibility in the solvent-rich

phase, as evident from the upper part of the binodal curves. Moreover, the phase diagrams are characterized by the tie lines with positive slopes where the tie-line gradient for each system increases proportionally with the amount of valeric acid. The mutual solubilities between two coexisting phases also increase as the global acid content increases. Conventionally, this trend could be attributable to the predominant interactions taking place favorably in the solvent-rich phase when compared with the waterrich one. Inspection of the slopes of the tie-lines and the polynomial character of the solubility curves from Fig. 1aed and Table 2 reveals that the distribution of valeric acid onto the (water þ aromatic solvent) two-phase mixture is intimately connected to the polarity and hydrogen bonding ability of high boiling aromatic solvents. The area of the two-phase heterogeneous region for the studied systems decreases in the order: 1-phenyl ethanol < benzyl ether < chlorobenzene < xylene. This implies that the existence of a hydroxyl group (OH) in the structure of 1-phenyl ethanol is likely responsible for a decrease in the immiscibility gap on the phase diagram leading to a large water solubility in the solvent-rich phase of the system containing 1-phenyl ethanol, as depicted in Fig. 1aed. As a result, water is most soluble in the (1-phenyl ethanol þ valeric acid) mixture and least soluble in the (xylene þ valeric acid) mixture. This is perhaps not surprising, considering the small dielectric constant and dipole moment of xylene. Further, a resonance electron effect between aromatic p ring and hydroxyl group in 1-phenyl ethanol or ether group in benzyl ether would likely give rise to the reduction of the overall area of the two-phase region for the oxygenated aromatics as opposed to the non-protic aromatics xylene and chlorobenzene which functional groups are less capable of interacting with water molecules. As evident from Table 2 and Fig. 1aed, the solubility of valeric acid in water is reduced much more readily in the system containing non-protic xylene or chlorobenzene, as compared to the oxygenated aromatic solvents. However, this behavior is related to the simultaneous effect of several specific solvent characteristics such as the polarity and the steric hindrance probably varying dependently with the functional group configuration in the solvent structure that may affect the aggregation of fluids in an unexpected way. When increasing the acid content in the global composition, however, the interaction forces in the solvent-rich phase are dominated by the interactions preferably between the acid and the aromatic solvent leading to a considerable increase of the tie-line slope, being indicative of a favorable acid separation into the organic phase. It is apparent from the phase diagrams that an appropriate reduction of the polarity (dielectric constant) and/or the steric hindrance relative to the aromatic solvent makes the packing between the acid and solvent molecules more appreciable to proceed, as expected from the observed increase in both the immiscibility gap and the tie-line

A. Senol / Fluid Phase Equilibria 415 (2016) 110e124

115

Valeric acid 0 .0 0 0.2 5

1

0 .5 0

x 0 .7 5

1

x

0 .5 0

0 .7 5

1.0 0

1.0 0

1.00

XY

0 0.0

0.75

5 0.2

0 0.0

0.50

Water 0.00

0.25

0.50

0.0 0 1

0.2 5

0.7 5

x

0.5 0

0.2 5 0 .5 0

1

1.0 0

x 0 .7 5

x3

Water

0.00

0 0 .0

BE

5 0.2

1.0 0

0 0.5

0 0.0

1.00

x2

5 0.2

0.75

5 0.7

0 0.5

x2

0.50

0 1.0

(d)

5 0.7

0.25

CB

1.00

Valeric acid

0 1.0

0 .0 0

Valeric acid

Water 0.00

0.75

x3

x3

(c)

x2

5 0.2

0.25

0 0.5

x2

0 0.5

Water 0.00

5 0.7

5 0.7

0.2 5

(b)

0 1.0

(a)

0 1.0

0 .0 0

Valeric acid

0.25

0.50

0.75

1.00

1-PE

x3

Fig. 1. Liquideliquid equilibria (mole fraction) for the systems (x1 water þ x2 valeric acid þ x3 solvent); B experimental solubility curve; : experimental tieelines (solid line); ◊ UNIFACepredicted end compositions (dashed line); a. xylene (XY), b. chlorobenze (CB), c. benzyl ether (BE), d. 1-phenyl ethanol (1-PE).

slopes. Unfortunately, there is a lack of experimental data reflecting the range of the steric hindrance provided by the aromatic solvent in solution; however, here the geometric structure of the solvent molecule is thought to be an appropriate reference about the expected magnitude of the steric effect along the entire composition range. Specifically, here most important physical quantities selected to characterize the packing of fluids are the dielectric constant, the dipole moment, the ionizing strength and the geometry of the component molecules. Besides the binodal curves and the tie lines assessment to discuss the phase diagrams, it should further evaluate the solvent selectivity (S) and distribution coefficient (D). Generally, the key parameters selectivity and distribution coefficient for determining the best solvent for the separation are calculated from liquideliquid equilibrium measurements for the system of components concerned (including the solvent). Analogous to the relative volatility in distillation, the separation factor (selectivity) must exceed unity, i.e., the greater the selectivity value away from unity the better for separation to take place. If the selectivity is unity, no separation is

possible. The distribution coefficient however is not required to be larger than unity, but the larger the distribution coefficient the smaller the amount of solvent which will be required for the extraction [13,14,19,23]. However, as mentioned above, a quantitative knowledge of the immiscibility regions, the binodal curves and the tie lines is essential to interpret the phase diagrams. But a further evaluation of the distribution coefficient (D), the solvent selectivity (S) and the modified separation factors (SM, DM and OF) is necessarily required, since they provide a quantitative description of the degree of the acid distribution between the coexisting phases. The values of the extraction factors S, SM, DM and OF as a function of the independent 00 00 variable xiv ¼ x2 =x3 are summarized in Table 3. The distribution 00 coefficients of the carboxylic acid D2 ¼ x2 =x02 , defined by the corresponding slopes of the tie lines in Fig. 1aed, clearly show that valeric acid is much more soluble in the organic phase than the aqueous phase for all of the solvents studied, yielding D2 > 1. Similarly, the selectivity (or separation factor, S) values, defined in the mole-fraction scale as the ratio of distribution coefficients of the

A. Senol / Fluid Phase Equilibria 415 (2016) 110e124

Table 2 Thermodynamic factors GL, excess Gibbs energy function GE (J mol1) and experi0 0 0 mental tieeline compositions (mole fraction)a of the conjugate solutions (x1 , x2 , x3 ) 00 00 00 and (x1 , x2 , x3 ) for the systems water x1 þ valeric acid x2 þ solvent x3 at T ¼ 298.2 K and P ¼ 101.3 kPa.

0

x1

0

x2

GLb

Solvent-rich phase 0

x3

00

x1

00

x2

GE (J mol1)c

00

x3

Water (1) þ valeric acid (2) þ xylene (3) 0.9998d 0.0000 0.0002 0.0105d 0.0000 0.9895 0.9918e 0.0082 0.0000 0.4752e 0.5248 0.0000 0.9977 0.0017 0.0006 0.0355 0.0391 0.9254 0.9957 0.0037 0.0006 0.0658 0.0866 0.8476 0.9951 0.0043 0.0006 0.1159 0.1654 0.7187 0.9940 0.0055 0.0005 0.1692 0.2826 0.5482 0.9927 0.0068 0.0005 0.2472 0.3891 0.3637 0.9918 0.0078 0.0004 0.3314 0.4827 0.1859 Water (1) þ valeric acid (2) þ chlorobenzene (3) d d 0.9999 0.0000 0.0001 0.0154 0.0000 0.9846 0.9918e 0.0082 0.0000 0.4752e 0.5248 0.0000 0.9966 0.0029 0.0005 0.0446 0.0535 0.9019 0.9948 0.0048 0.0004 0.0879 0.1323 0.7798 0.9934 0.0062 0.0004 0.1312 0.2496 0.6192 0.9925 0.0072 0.0003 0.1943 0.3701 0.4296 0.9917 0.0081 0.0002 0.3055 0.4852 0.2093 Water (1) þ valeric acid (2) þ benzyl ether (3) d d 0.9996 0.0000 0.0004 0.0632 0.0000 0.9368 0.9918e 0.0082 0.0000 0.4752e 0.5248 0.0000 0.9948 0.0047 0.0005 0.1585 0.1475 0.6940 0.9931 0.0065 0.0004 0.1915 0.2306 0.5779 0.9922 0.0074 0.0004 0.2625 0.3134 0.4241 0.9918 0.0078 0.0004 0.3235 0.3792 0.2973 0.9916 0.0081 0.0003 0.3745 0.4528 0.1727 Water (1) þ valeric acid (2) þ 1-phenyl ethanol (3) d d 0.9960 0.0000 0.0040 0.2346 0.0000 0.7654 0.9918e 0.0082 0.0000 0.4752e 0.5248 0.0000 0.9929 0.0033 0.0038 0.2675 0.0597 0.6728 0.9926 0.0042 0.0032 0.2745 0.1213 0.6042 0.9923 0.0052 0.0025 0.2985 0.1986 0.5029 0.9921 0.0058 0.0021 0.3287 0.2817 0.3896 0.9919 0.0064 0.0017 0.3854 0.3948 0.2198

b

Xylene

0.9888 0.9774 0.9646 0.9578 0.9722 1.0069

545.5 960.3 1481.2 1806.5 2006.3 1932.6

0.9619 0.9320 0.9731 0.9528 1.0202

570.5 1088.0 1499.9 1774.1 1870.5

Chlorobenzene

Benzyl ether

1-Phenyl ethanol 0.9866 0.9758 0.9625 0.9560 0.9658

1575.3 1832.3 2192.6 2320.7 2195.4

0.9635 0.9306 0.8995 0.8844 0.9193

1309.3 1364.2 1471.6 1568.7 1661.6

a Standard uncertainties of the measured quantities through relevant equipment u are u(x) ¼ 0.0002, u(T) ¼ 0.1 K, u(P) ¼ 0.7 kPa. b Thermodynamic factors derived from the UNIFACeDortmund model [22,64,65]. c Excess Gibbs energy function for the organic phase according to the UNIP FACeDortmund model [22], GE ¼ RT i xi lngi ðJ mol1 Þ. d Mutual solubility value referred to the region x2 ¼ 0. e Mutual solubility value referred to the region x3 ¼ 0.

00

00

0.000 0.042 0.102 0.230 0.516 1.070 2.597 0.000b 0.059 0.170 0.403 0.875 2.318 0.000b 0.213 0.399 0.739 1.275 2.622 0.000b 0.089 0.201 0.395 0.723 1.796

DM

S

SM

OF

471095.60 5617.91 1424.71 641.02 306.32 161.99 100.12 639287.10 2862.99 796.25 345.55 188.28 105.80 37042.14 528.58 277.49 164.11 117.36 89.98 812.38 314.11 246.91 182.81 138.92 97.09

471095.60 646.40 354.18 330.26 301.85 229.79 185.21 639287.10 412.23 311.94 304.82 266.83 194.45 37042.14 196.97 183.98 160.08 149.05 148.02 812.38 67.15 104.43 126.98 146.59 158.76

0.999998 1.0149 1.0165 1.0320 1.0467 1.0783 1.1323 0.999998 1.0102 1.0141 1.0239 1.0383 1.0589 0.999973 1.0225 1.0244 1.0397 1.0649 1.0964 0.998771 1.1005 1.1513 1.1881 1.2595 1.4727

0.999798 1.4182 1.2498 1.2746 1.2742 1.3141 1.3955 0.999898 1.2279 1.1594 1.1961 1.1855 1.1847 0.999573 1.1411 1.1266 1.1499 1.1989 1.2549 0.994801 1.3715 1.5449 1.6231 1.7806 2.2108

a Standard uncertainties of the measured quantities through relevant equipment u are u(x) ¼ 0.0002, u(T) ¼ 0.1 K, u(P) ¼ 0.7 kPa. b Properties corresponding to the mutual solubility region x2 ¼ 0 (i.e., xiv ¼ 0; DM ¼ DM0; S ¼ S0; SM ¼ SM0; OF ¼ OF0).

800

600

400

200

00

acid (2) to water (1) S ¼ ðx2 =x02 Þ=ðx1 =x01 Þ, are superior to 1 due to the positive slope of the tie lines. It is apparent from the selectivity data presented in Table 3 that the lowest S values exhibit valeric acid in the (water þ 1-phenyl ethanol). The non-protic xylene and chlorobenzene give S values about 2e3 times larger as compared to the oxygenated solvents (Fig. 1aed and Table 3). The same remarks hold for the modified extraction factors DM, SM and OF of these solvents given in Figs. 2 and 3 and Table 3. As seen in Table 3 and 00 00 Fig. 2, the increase in the independent variable xiv ¼ x2 =x3 leads to a considerable decrease in the selectivity S value due to the observed increase of water concentration in the solvent phase. A decrease of the modified distribution ratio DM with increasing xiv is also observed, but the range of decreasing is larger than that observed with the selectivity. On the other hand, as illustrated in Fig. 3 and Table 3, both SM and OF factors exhibit a continual increase against a proportional increase of xiv value, which variation profiles are about equally strongly dependent on the overall organic phase composition. The only exception is the OF factor for xylene, representing a non-regular functionality between OF and xiv, as shown in Fig. 3 and Table 3. It is concluded from Figs. 1e3 and Table 3 that replacing the protic solvent (1-phenyl ethanol) with the non-protic one (xylene,

00

xiv ¼ x2 =x3

System

0

1000

DM

Water-rich phase

Table 3 Experimental values of modified distribution ratio (DM), separation factor (S), modified separation factor (SM) and solvent dependent optimization factor (OF) 00 00 varying against the independent variable xiv ¼ x2 =x3 for the systems (water þ valeric acid þ solvent) at T ¼ 298.2 K and P ¼ 101.3 kPa.a

S

116

100

10 0.0

0.4

0.8

1.2

1.6

x iv = x2'' /x3''

2.0

2.4

2.8

Fig. 2. Variation of separation factors S and DM with the independent variable 00 00 xiv ¼ x2 =x3 for the systems (water þ valeric acid þ solvent). Experimental, xylene, C chlorobenzene, : benzyl ether, - 1-phenyl ethanol. Solid line theoretical through SERLAS, Eq. (1).

A. Senol / Fluid Phase Equilibria 415 (2016) 110e124

2.4

OF

2.0

1.6

1.2

0.8

SM

1.4

1.2

1.0

0.8 0.0

0.4

0.8

1.2

1.6

x iv = x2'' /x3''

2.0

2.4

2.8

Fig. 3. Variation of modified separation factor (SM) and optimization factor (OF) against 00 00 the independent variable xiv ¼ x2 =x3 for the systems (water þ valeric acid þ solvent). Experimental, xylene, C chlorobenzene, : benzyl ether, - 1-phenyl ethanol. Solid line theoretical through SERLAS, Eq. (1).

chlorobenzene, benzyl ether) always results in a corresponding increase of the tie-line gradients, the two-phase heterogeneous region and the selectivity values. However, the existence of protonaccepting groups such as aromatic p ring on xylene and chlorobenzene and ether (CeOeC) group on benzyl ether categorize these solvent structures as more hydrophobic and more capable of dipoleedipole association with the acid as compared to protic 1phenyl ethanol. As well, the large ionizing strength of valeric acid (pKa ¼ 4.842) makes it structure a more susceptible to dipoleedipole interaction with the non-protic solvents. Particularly, 1-phenyl ethanol contains both proton-accepting (aromatic p ring) and edonating (hydroxyl, OH) functional groups, being capable of intramolecular hydrogen bonding, thereby causing an interactive effect of formation of dimers or oligomers. This would call for the assumption that the aggregation should presumably reduce the distribution of valeric acid in 1-phenyl ethanol. These concepts can be verified by the results from Figs. 1e3 and Tables 2 and 3, manifesting the fact that the controlling factor for the physical extraction of valeric acid is its relatively high hydrophobicity. Another important factor affecting the extraction equilibria is the polarity of the solvent. As can be seen from Figs. 1e3 and Table 3, the extraction efficiency of valeric acid by the aromatic solvent decreases in the order, xylene > chlorobenzene > benzyl ether > 1phenyl ethanol. From the selectivity and distribution ratio data given in Figs. 1e3 and Table 3, one may conclude that the separation of valeric acid from water by extraction with a high boiling aromatic solvent is feasible, yielding D2 > 1, S > 60, DM > 80, SM > 1 and OF > 1. Furthermore, 1-phenyl ethanol is less favorable solvating agent for valeric acid as compared to non-protic xylene and chlorobenzene

117

yielding the largest S, SM, DM and OF factors. However, as discussed above, the physical factors predominantly influencing the solvent extraction of valeric acid are the degrees of hydrophobicity and polarity of the aromatic solvent and the transferred acid and the ability of these components to dipoleedipole interaction and hydrogen bonding. In conclusion, the observed features in the phase behavior of the considered systems like the large D, S, SM, DM and OF extraction factors being superior to unity and a preferable selectivity in favor of the solvent phase are encouraging issues toward the use of aromatic solvents in the liquideliquid extraction of valeric acid, as might be expected. This tendency can be verified by analyzing the variation profile of relevant quantities given in Figs. 1e3 and Table 3. The tie lines of relevant ternary systems were also predicted by the UNIFACeoriginal model [26e28]. Depending on the thermodynamic isoeactivity criterion of liquideliquid phase equilibrium 00 00 (x0i g0i ¼ xi gi ), the LevenbergeMarquardt multivariable algorithm was executed to solve implicit LLE equations [67]. Fig. 1aed presents a quantitative assessment of the tie-line predictions achieved for UNIFACeoriginal, yielding an overall mean deviation of the tieline composition of 28.9% for all of the studied systems. From Fig. 1, the modeled tie-line slopes for chlorobenzene are slightly less accurate than those predicted for other aromatics. Consequently, UNIFACeoriginal provides a relatively precise prediction of the phase equilibria of relevant systems and a reliable description of the high solubilities of the acid favorably in the solvent phase, therefore, it is the preeminent predictive method selected for this study. 4.2. Reliability analysis of SERLAS Comparisons of experimental and calculated LLE data for the studied systems (water þ valeric acid þ aromatic solvent) are used to analyze statistically the reliability of SERLAS and UNIFACeoriginal models in terms of the mean relative error  P   (e ¼ ð100=NÞ N  Y Þ=Y ðY ð%Þ) and i;obs i;mod i;obs i¼1 P 2 0:5 ). rootemeanesquare deviation (s ¼ ð N i¼1 ðYi;obs  Yi;mod Þ =NÞ To do this, firstly the application of SERLAS (Eq. (1)) to the type 2 ternary systems generates the following model parameters CG, CH, Cp, Cb and Ca. The coefficients Ci of Eq. (1) are regressed by means of the linpack algorithm [68] using the values of six molecular descriptors (GL, dH, p, b, a, d) listed in Tables 2 and 4. It is worthwhile to mention here that, though d can be treated as an independent physical descriptor, the integration index p þ d is selected to be a model variable only to obtain a suitable solution to the parameter estimation problem including the determination of five substancedependent coefficients. The resulting coefficients Ci relative to S, DM, SM and OF properties, as well as the statistical deviation factors e and s of Eq. (1) are presented in Table 5. It should be emphasized that the model coefficients Ci determined in this way are not exactly Table 4 Hildebrand solubility parameter dH (MPa0.5) and solvatochromic parameters (p, b, a, d) of compounds. Compound

pa,b

ba,b

aa,b

dHc,d (MPa0.5)

da,b

Xylene Chlorobenzene Benzyl ether 1-Phenyl ethanol Valeric acid Water

0.51 0.71 0.69 0.99 0.54 1.09

0.12 0.07 0.30 0.52 0.45 0.47

0 0 0 0.35 0.56 1.17

18.0 19.4 33.5 24.5 22.1 47.9

1 1 1 1 0 0

a b c d

Due Due Due Due

to to to to

Kamlet et al. [16]. Marcus [17]. Riddick et al. [72]. Barton [75].

118

A. Senol / Fluid Phase Equilibria 415 (2016) 110e124

Table 5 Coefficients Ci (CG, CH, Cp, Cb, Ca) of SERLAS model, Eq. (1), and rootemeanesquare deviation (s)a and mean relative error (e)a evaluated for different properties Pr (S, DM, SM, OF) of the systems (water þ valeric acid þ aromatic solvent). System

CG

CH

Cp

Cb

Pr ¼ ln(S); Pr0 ¼ ln(S0)b; s(S); eðSÞ Xylene ðs ¼ 75:2; e ¼ 21:4%Þ 0.75184  102 0.20457  103 0.42129  103 0.89303  103 Chlorobenzene ðs ¼ 25:3; e ¼ 7:2%Þ 0.22890  102 0.61569  105 0.64515  102 0.63898  103 Benzyl ether ðs ¼ 5:1; e ¼ 2:5%Þ 0.32885  103 0.24456  103 0.72179  103 0.15509  104 1-Phenyl ethanol ðs ¼ 16:9; e ¼ 10:6%Þ 0.25452  103 0.13822  103 0.34350  104 0.32885  104 Pr ¼ ln(DM); Pr0 ¼ ln(DM0)b; s(DM); eðDM Þ Xylene ðs ¼ 49:6; e ¼ 12:6%Þ 0.10197  103 0.20705  103 0.84897  103 0.62868  103 Chlorobenzene ðs ¼ 46:5; e ¼ 6:7%Þ 0.34849  102 0.56552  106 0.11611  103 0.57959  103 Benzyl ether ðs ¼ 9:0; e ¼ 3:3%Þ 0.28313  103 0.18006  103 0.52084  103 0.14648  104 1-Phenyl ethanol ðs ¼ 18:3; e ¼ 7:3%Þ 0.19121  103 0.80068  104 0.20098  104 0.17168  104 Pr ¼ ln(SM); Pr0 ¼ ln(SM0)c; s(SM); eðSM Þ Xylene ðs ¼ 0:010; e ¼ 0:6%Þ 0.34030  101 0.83468  105 0.16130  102 0.37221  102 Chlorobenzene ðs ¼ 0:003; e ¼ 0:2%Þ 0.47430  100 0.18099  106 0.97177  100 0.91002  101 Benzyl ether ðs ¼ 0:013; e ¼ 0:8%Þ 0.46247  101 0.30844  105 0.35222  101 0.30468  102 1-Phenyl ethanol ðs ¼ 0:018; e ¼ 1:2%Þ 0.33305  102 0.14299  104 0.37177  103 0.34016  103 Pr ¼ ln(OF); Pr0 ¼ ln(OF0)d; s(OF); eðOF Þ Xylene ðs ¼ 0:046; e ¼ 3:3%Þ 0.13916  102 0.23649  104 0.13008  103 0.39329  102 Chlorobenzene ðs ¼ 0:016; e ¼ 1:3%Þ 0.26429  101 0.30659  105 0.11506  102 0.22158  101 Benzyl ether ðs ¼ 0:004; e ¼ 0:3%Þ 0.21933  102 0.11197  104 0.33533  102 0.11938  103 1-Phenyl ethanol ðs ¼ 0:045; e ¼ 2:3%Þ 0.64869  102 0.29501  104 0.75678  103 0.70894  103   P P N 2 0:5 a   e ¼ ð100=NÞ N . i¼1 ðYi;obs  Yi;mod Þ=Yi;obs ð%Þ; s ¼ ½ i¼1 ðYi;obs  Yi;mod Þ =N b S0 ¼ DM0 ¼ 471095.60 (xylene); S0 ¼ DM0 ¼ 639287.10 (chlorobenzene); S0 ¼ DM0 ¼ 37042.14 (benzyl ether); S0 ¼ DM0 ¼ 812.38 (1-phenyl ethanol). c SM0 ¼ 0.999998 (xylene); SM0 ¼ 0.999998 (chlorobenzene); SM0 ¼ 0.999973 (benzyl ether); SM0 ¼ 0.998771 (1-phenyl ethanol). d OF0 ¼ 0.999798 (xylene); OF0 ¼ 0.999898 (chlorobenzene); OF0 ¼ 0.999573 (benzyl ether); OF0 ¼ 0.994801 (1-phenyl ethanol).

unique, so they cannot be adequately intended for a generalized estimation covering other systems. As shown in Table 5, the CG, Cp, Cb and Ca coefficients pertained to GL, p*, a*, and b* are larger than the CH coefficient of the solubility (d*H ) term, so terms in GL, p*, a*, and b* turn out to be dominant in Eq. (1). The terms in p* and b* of Eq. (1) make generally negative contributions, since their coefficients Cp and Cb are almost invariably negative. While the first and last terms in GL and a* of Eq. (1) make relatively large positive contributions to the modeled quantity. As well, the d*H term in Eq. (1) is about constantly positive regarding the sign of CH coefficient, but it cannot provide a physical explanation for its relatively small contribution to the modeled property. As evident from Figs. 1e3 and Table 5, both SERLAS and UNIFACeoriginal models yield a fair distribution verifying the goodnesseofefit relative to D, S, DM, SM and OF factors. Inspection of Figs. 2 and 3 and Table 5 reveals that SERLAS, Eq. (1), reproduces accurately the observed performance with the overall mean deviations of eðSÞ ¼ 10:4% (s(S) ¼ 30.6), eðDM Þ ¼ 7:4% (s(DM) ¼ 30.8), eðSM Þ ¼ 0:7% (s(SM) ¼ 0.011), eðOF Þ ¼ 1:8% (s(OF) ¼ 0.028) for all of the systems studied. Actually, as depicted in Figs. 2 and 3, SERLAS simulates satisfactorily the variation profile of the observed factors S, DM, SM and OF whose calculated values allow illustratively to confirm a rigorous validation of the considered model structure. It turns out from Fig. 1aed that UNIFACeoriginal predicts moderately precisely the extraction equilibria of relevant systems, yielding mean deviations of eðSÞ ¼ 40:6% (s(S) ¼ 127.5), eðDM Þ ¼ 45:9% (s(DM) ¼ 285.7), eðSM Þ ¼ 3:8% (s(SM) ¼ 0.06), eðOF Þ ¼ 10:1% (s(OF) ¼ 0.20). As shown in Figs. 1e3 and Table 5, SERLAS proved to be slightly more accurate yielding e ¼ 5:1% (s ¼ 15.4) as compared to e ¼ 25:1% (s ¼ 103.4) for the UNIFACeoriginal model with regard to S, DM, SM and OF. As illustrated in Figs. 1e3, the graphical confidence tests are also examined to characterize both visually and quantitatively whether the calculated quantity tends to a regular solution to the physical behavior in the whole working range or not. It is recognized from Figs. 1e3 that SERLAS most accurately correlates S, DM and OF properties of the studied systems and is similar in accuracy

Ca 0.65681 0.33169 0.70699 0.12462

   

103 103 103 104

0.85820 0.31531 0.57291 0.75467

   

103 103 103 103

0.25394 0.45528 0.79293 0.13100

   

102 101 101 103

0.10887 0.68911 0.40909 0.26487

   

103 101 102 103

to the UNIFAC-original prediction of SM. UNIFAC-original provides fairly accurate binodal curves and tie-lines (Fig. 1), but due to the better estimation of S, DM, SM and OF factors SERLAS does better in this regard. Based on Figs. 2 and 3 and Table 5 one may conclude that SERLAS actually provides useful results and reliable estimates for the correlative description of the phase behavior of the type 2 systems depending on the LSER principles. The deviation statistics obtained for SERLAS testify its ability to simulate accurately the observed performance with a mean error of 5.1%, thus, from this perspective it is presumed to be an attractive alternative to the excess Gibbs energy predictive models. The use of molecular indices of compounds very different in structure will allow an improved calculative description of the real behavior of various kinds of mixtures based on SERLAS. At the same time the large set of molecular descriptors guarantees a large range of applicability of SERLAS to more complex systems, like the liquideliquid phase separation of parabens by water-ethanol mixture for which the ternary phase diagrams contain five different regions [69,70]. These advantages should allow a more reliable design of separation processes, and selection of valuable solvents for extraction.

4.3. Prediction of optimum LLE of a type 2 ternary system This study shows promise for extending application of the derivative variation method to more complex type 2 ternary systems following the optimization algorithm of Senol [71]. The algorithm is described briefly below, along with a discussion how computational procedures have been improved for proceeding a more effectively prediction of the optimum point. The goal is to analyze the effectiveness with which the present optimization structure can identify the optimum extraction field of a type 2 ternary system with respect to six optimization factors being used as the optimization criteria. To achieve this goal, the distribution ratiodependent factor (X1), the selectivity-dependent factor (X2), the overall selectivity-dependent factor (X3) and the solvent ratiodependent extraction factor (X4) have been contemplated as the base variables compiling in the optimization algorithm [71].

A. Senol / Fluid Phase Equilibria 415 (2016) 110e124

X1 ¼

SA0

DM S S O ; X2 ¼ ; X3 ¼ M ; X4 ¼ F SA0 SA0 SA0 SA0

 W DA02 xA 02 x02 ¼ ¼ W DA01 xA 01 x01

119

(10)

(11)

where SA0 represents the separation factor for the mutual solubility W A W region x3 ¼ 0; DA01 ¼ xA 01 =x01 and DA02 ¼ x02 =x02 are the distribution ratios of water and acid for the mutual solubility region x3 ¼ 0; W A W xA 01 and x01 , and x02 and x02 stand for the mole fractions of water (subscript 01) and acid (subscript 02) in the acid-rich (superscript A) and water-rich (superscript W) phases in the absence of solvent (x3 ¼ 0). Before proceeding the optimization algorithm, several functionally symmetric combinations for the contribution of X1, X2, X3 and X4 are used for interpreting the Y ¼ f(X1, X2, X3, X4) curves, where Y designates the selected optimization factor. Inevitably, this requires a quantitative knowledge of X1, X2, X3 and X4 variables along the working range and Y0 for x3 ¼ 0, so that the optimum value of Y can be quantified. As a second step in applying the optimization approach to the relevant systems, we consider here six functional forms of the optimization factor Y given by Eqs. (12)e(14) to be adequately assessed for this purpose [71]. These mathematical expressions are fundamental to implement the optimization algorithm.

Y ¼ lnðX1 X2 X3 X4 Þ; Y ¼ X1 X2 X3 X4

(12)

Y ¼ lnðX1 X2 X3 Þ; Y ¼ X1 X2 X3

(13)

Y ¼ lnðX1 X2 X4 Þ; Y ¼ X1 X2 X4

(14)

As marked in Eqs. (13) and (14), either X3 or X4 variable is excluded from Y, since both variables exhibit about equally strongly contributions to Y. This is a stringent test of the capability of Y factors to represent the optimum conditions through analyzing the non-linear variation profile of the first order derivatives of the quantity in question. The large advantage of using Eqs. (12)e(14) is that, in principle, inclusion of compositions of overall components in the Y factor makes the later a perceptible criterion adequate for modeling optimum extraction. Thus, all six forms of Y have been independently checked for the optimum point by processing the derivative variation method [59e61,63,71]. As summarized by Senol [71], the method searches for the supreme point by analyzing the variation profile of the derivatives of Y factors vs the indepen00 dent variable x2 (solvent phase acid concentration) to obtain a 00 minimum of Y which obeys the conditions given by dY=dx2 ¼ 0 and 00 d2 ðYÞ=dðx2 Þ2 > 0. If there is not validated any supreme point over the whole working range corresponding to zero derivative value, as in the case of 1-phenyl ethanol (Fig. 4aeb), then optimum conditions are verified by analyzing the variation profile of the slopes of the observed curve. Conventionally, the reference optimum point is located in the section where the largest changes in the slope of the derivative curve dY/dx ¼ f(x) appear. However, the calculation procedures are analogous for all the selected Y factors, allowing a continuous predictive process to proceed, In general, to avoid the effect of an unexpected irregularity in the data distribution, the algorithm analyzes continuously point by point the overall working range and then terminates when a complete solution to the optimum point is being realized. But unexpectedly, if more than one position for the optimum point will eventually appear then the linearization of the upper and lower parts of the derivative curve

Fig. 4. Plot of the optimization factors Y (a. Y ¼ ln(X1X2X3X4), b. Y ¼ X1X2X3X4) due to 00 Eq. (12) against the solvent phase acid concentration x2 for the systems 00 (water þ valeric acid þ solvent). Variation of observed Y with x2 , xylene, C chlo00 robenzene, : benzyl ether, - 1-phenyl ethanol. Variation of observed dY=dx2 with 00 x2 , xylene, B chlorobenzene, benzyl ether, , 1-phenyl ethanol.

and the determination of their intercepting point should be carried out. In fact, using conventional searching techniques based solely on a supreme point can lead to the erroneous conclusion that any optimum point does not exist if no zero derivative value is found, neglecting the slope analysis of the non-linear section of the derivative curve as a test case for achieving an optimum point which actually occurs at that section. Considering the potential practical application of the above Y factors, procedurally, the optimization algorithm first calculates the 00 dY=dx2 derivatives for all the data points included and then analyzes the nonelinear variation profile of the Y derivatives restricted between two composition limits x2 ¼ 0 and x3 ¼ 0, circumscribing the validation limits of calculation. At the lower composition limit x2 ¼ 0, an indefinable character of the Y function would likely proceed since SA0 tends to go zero. In contrast, at the upper

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A. Senol / Fluid Phase Equilibria 415 (2016) 110e124

composition limit x3 ¼ 0, X02 ¼ 1, X03 ¼ 1, X04 ¼ 1 and Y0 ¼ ln(DA01) for logarithmic approaches and Y0 ¼ DA01 for non-logarithmic apW proaches, where DA01 ¼ xA 01 =x01 ¼ 0:47913 is the distribution ratio of water pertaining to the mutual solubility region x3 ¼ 0, xA 01 and xW represent the mole fractions of water in the acid-rich (extract) 01 and water-rich (raffinate) phases in the absence of solvent (x3 ¼ 0). As a final step, the algorithm identifies the supreme point (minimum) of Y which must appear at the prescribed values of the first and second order Y derivatives, as noted above. If this is not the case obeying a zero value derivative variation then the slope analysis of the derivative curve including the determination of the deviation (gradient) profile in the slopes of neighboring derivatives throughout the working range needs to be necessarily performed. Logically, when the derivatives of Y are invariably either positive or negative, the largest changes in the slope of the derivative curve dY/ dx ¼ f(x) will separate the location of the optimum point. Again, if no suitable solution to the optimum conditions is found with the slope variation test, then the intersection of the asymptotically drawing lines relative to the linearized upper and lower sections of the derivative curve dY/dx ¼ f(x) is selected to be dominant in specifying the optimum extraction field. A geometrical interpolation of conditions attributed to the intercepting point through drawing a parallel line to the axis will result in the optimization range reflecting the extremely changes in the slope of the observed derivative curve. This is the common strategy for analyzing a type 2 LLE system by the derivative variation method using Eqs. (12)e(14), as depicted in Figs. 4e6. Inspection of Figs. 4e6 reveals that the Y factor is varying with 00 the independent variable x2 through the non-linear function exhibiting an irregular pocket-type divergence of Y between the composition limits x2 ¼ 0 and x3 ¼ 0 with a prescribed minimum point. As can be seen from Figs. 4e6, this type of variation is prevalent for the considered systems, allowing the observed de00 rivative dY=dx2 to change its sign at the optimum point. Seemly, these figures show that a zero value derivative variation of the Y 00 factor against x2 is strictly followed along the working range, being indicative of the suitability of the optimization algorithm for describing the optimum LLE range of the studied systems. The only exception is the Y property of 1-phenyl ethanol (Fig. 4aeb) which derivatives tend to vary smoothly without a change in the sign of 00 dY=dx2 . For this problematic case where no solution to the supreme point is found, the location of the optimum point is validated by the section corresponding to the largest changes in the slope of the observed derivative curve, as illustrated in Fig. 4aeb. It can be deduced from Fig. 4aeb that the optimum point will eventually fall into that prescribed section representing extremely changes in the derivative slopes. An overview of Figs. 4e6 manifests the fact that the conditions pertained to the lefte and righteside regions of the optimum point are practically less convenient for an effective extraction process, as might be expected. The observed optimization conditions due to the derivative variation method depending on Eqs. (12)e(14) are briefly summarized in Table 6. Another important case is the predictive description of the optimum extraction range in a type 2 LLE system through a generalized approach. In the previous work [71], the author of this article has reported two six-parameter models formulated on the basis of the factorial design analysis of Xi, XiXj and XiXjXk variables and found that the experimental X1, X2, X3 and X4 variables are about equally strongly contributed to the modeled log-basis quantity Y ¼ ln(X1X2X3X4), being used for the prediction of the optimum conditions. The resulting six parameters approaches given by Eqs. (15) and (16) are thought to be equivalently effective in modeling of the optimum conditions.

Fig. 5. Plot of the optimization factors Y (a. Y ¼ ln(X1X2X3), b. Y ¼ X1X2X3) due to Eq. 00 (13) against the solvent phase acid concentration x2 for the systems (water þ valeric 00 acid þ solvent). Variation of observed Y with x2 , xylene, C chlorobenzene, : benzyl 00 00 ether, - 1-phenyl ethanol. Variation of observed dY=dx2 with x2 , xylene, B chlorobenzene, benzyl ether, , 1-phenyl ethanol.

Y ¼ lnðX1 X2 X3 X4 Þ ¼ lnðX01 X02 X03 X04 Þ þ A1 X1 X2 þ A2 X1 X3 þ A3 X1 X4 þ A4 X2 X3 þ A5 X2 X4 þ A6 X3 X4 (15) Y ¼ lnðX1 X2 X3 X4 Þ ¼ lnðX01 X02 X03 X04 Þ þ A01 X1 X2 X3 þ A02 X1 X2 X4 þ A03 X1 þ A04 X2 þ A05 X3 þ A06 X4 (16) where Y0 ¼ ln(X01X02X03X04) stands for the Y value related to the mutual solubility region x3 ¼ 0. At the composition limit x3 ¼ 0, W X02 ¼ X03 ¼ X04 ¼ 1 and Y0 ¼ ln(DA01), DA01 ¼ xA 01 =x01 ¼ 0:47913 for

A. Senol / Fluid Phase Equilibria 415 (2016) 110e124

121

0

Y (modeled)

-3

-6

-9

a

-12 0

Y (modeled)

-3

-6

-9

b

-12 -12

-9

-6

-3

0

Y (observed) Fig. 7. Comparison of the observed property with the modeled performance through six-parameter Eqs. (15) and (16) for relevant ternary systems: a. Eq. (15); b. : Eq. (16).

Fig. 6. Plot of the optimization factors Y (a. Y ¼ ln(X1X2X4), b. Y ¼ X1X2X4) due to Eq. 00 (14) against the solvent phase acid concentration x2 for the systems (water þ valeric 00 acid þ solvent). Variation of observed Y with x2 , xylene, C chlorobenzene, : benzyl 00 00 ether, - 1-phenyl ethanol. Variation of observed dY=dx2 with x2 , xylene, B chlorobenzene, benzyl ether, , 1-phenyl ethanol.

reveals that both Eqs. (15) and (16) are able to simulate satisfactorily the variation profile of the observed performance with mean deviations of eðYÞ ¼ 4:8% and s(Y) ¼ 0.147 for Eq. (15), and eðYÞ ¼ 3:7% and s(Y) ¼ 0.117 for Eq. (16), considering all of the systems studied. Fig. 7 clearly shows that both models reproduce very well a pocket-like divergence of Y nearby the optimum point along with providing similar predictions, although model structures are somewhat different. To illustrate the capability of Eqs. (15) and (16) for complex calculations of the optimum point, we have stringently probed the derivative variation method applied to these equations. When the optimization conditions described above are exactly achieved, the algorithm terminates. As a result, the modeled

Table 6 00 Observed optimization ranges of Y and x2 a variables evaluated for the systems (water þ valeric acid þ aromatic solvent). System

Y ¼ ln(X1X2X3X4)

Xylene Chlorobenzene Benzyl ether 1-Phenyl ethanol

8.71 8.55 9.56 8.85

a

(0.389)a (0.376) (0.379) (0.282)

Y ¼ X1X2X3X4 0.00017 0.00019 0.00007 0.00014

(0.389)a (0.376) (0.379) (0.282)

Y ¼ ln(X1X2X3) 4.08 3.82 4.85 4.53

(0.389)a (0.376) (0.379) (0.282)

Y ¼ X1X2X3 0.0168 0.0218 0.0078 0.0108

(0.389)a (0.376) (0.379) (0.282)

Y ¼ ln(X1X2X4) 3.89 3.69 4.73 4.19

(0.389)a (0.376) (0.379) (0.282)

Y ¼ X1X2X4 0.0205 0.0250 0.0088 0.0152

(0.389)a (0.376) (0.379) (0.282)

00

The optimum value of the solvent phase acid mole fraction x2 is given in parenthesis.

W x3 ¼ 0, xA 01 and x01 represent the mole fractions of water in the acidrich (extract) and water-rich (raffinate) for the region x3 ¼ 0. Ai and A0i are the adjustable coefficients. Fig. 7 and Table 7 present a quantitative assessment of estimations achieved for Eqs. (15) and (16) in terms of the regressed model coefficients Ai and A0i , respectively. Inspection of Fig. 7 and Table 7

optimum values due to Eqs. (15) and (16) coincide with the observed ones listed in Table 7. In fact, these models are applicable to any LLE system of type 2.

122

A. Senol / Fluid Phase Equilibria 415 (2016) 110e124

Table 7 Coefficients Ai of the optimization factor Y ¼ ln(X1X2X3X4)a, modeled through six parameters Eqs. (15) and (16), and mean relative error (e) and rootemeanesquare deviation (s) evaluated for the systems (water þ valeric acid þ solvent). System Equation (15) Xylene ðs ¼ 0:170; e ¼ 2:87%Þ Chlorobenzene ðs ¼ 0:008; e ¼ 0:006%Þ Benzyl ether ðs ¼ 0:403; e ¼ 16:21%Þ 1-Phenyl ethanol ðs ¼ 0:009; e ¼ 0:007%Þ Equation (16) Xylene ðs ¼ 0:073; e ¼ 0:53%Þ Chlorobenzene ðs ¼ 0:021; e ¼ 0:04%Þ Benzyl ether ðs ¼ 0:371; e ¼ 14:24%Þ 1-Phenyl ethanol ðs ¼ 0:005; e ¼ 0:003%Þ

A2

A1

A3

A4

A5

A6

0.369555 0.108798 0.245849 0.125882

   

102 102 103 103

0.835748 0.703793 0.830449 0.426889

   

105 102 105 105

0.786533 0.431576 0.115343 0.206393

   

105 104 106 105

0.180724 0.366177 0.153285 0.760544

   

106 105 105 104

0.145754 0.222312 0.540739 0.101162

   

106 105 105 104

0.177180 0.289212 0.805052 0.668368

   

107 107 107 105

0.201171 0.239638 0.135539 0.200066

   

105 104 106 105

0.127056 0.873713 0.541355 0.147977

   

105 103 105 104

0.894367 0.374136 0.850175 0.130045

   

102 102 103 103

0.329479 0.104554 0.452574 0.534717

   

102 103 103 102

0.185352 0.870774 0.413638 0.363069

   

106 105 106 103

0.166620 0.102604 0.283407 0.858236

   

106 106 106 104

a W For the composition limit x3 ¼ 0, X02 ¼ 1, X03 ¼ 1, X04 ¼ 1 and Y0 ¼ ln(X01X02X03X04) ¼ ln(DA01), DA01 ¼ xA 01 =x01 ¼ 0:47913 is the distribution ratio of water for the mutual W represent the mole fractions of water in the acid-rich (extract) and water-rich (raffinate) phases in the absence of solvent (x ¼ 0). solubility region x3 ¼ 0, xA and x 3 01 01

5. Conclusions LLE data for the systems (water þ valeric acid þ xylene or chlorobenzene or benzyl ether or 1-phenyl ethanol) were determined at T ¼ 298.2 K and atmospheric pressure. The SERLAS model in the present investigations is particularly well suited to the calculation of LLE of the type 2 ternary systems. The performed optimization algorithm predicts reliably the optimum conditions. The study leads to the following conclusions:  The equilibrium distribution of valeric acid onto (water þ aromatic solvent) twoephase system is better for xylene and chlorobenzene as compared to benzyl ether and 1phenyl ethanol. The extraction factors D, S, DM, SM, and OF characterizing the partition of the acid between water and the aromatic solvent are superior to unity and the solubility curve for each examined ternary system is almost vestigial for the aqueous phase. The aromatic solvents must therefore be considered as satisfactory for separation of valeric acid.  The evaluated Y quantities and their derivatives given by Eqs. (12)e(14) provide an analytical structure for prediction of the optimum extraction field of relevant systems through processing the derivative variation method. The developed optimization structure is applicable to any LLE system of type 2 so long as the Y derivatives are definable in the whole working range. The proposed six-parameter approaches, Eqs. (15) and (16), are able to predict the optimum conditions of complex liquideliquid systems exhibiting the phase behavior of type 2.  The experimental data are correlated accurately by SERLAS and satisfactorily predicted by UNIFAC-original. Particularly, SERLAS is reasonably precise in reproducing the observed performance with an overall mean error of 5.1%. The calculations from SERLAS confirm a physical significance for the selected model structure and its applicable extension. In principle, inclusion of physical characteristics of association in Eq. (1) such as group contribution and dipoleedipole interaction parameters, hydrogen bonding and solubility indices and thermodynamic factors of components, combined with the boundary constraints of the physical event, provides considerable improvement for a reliable calculation of the properties of type 2 LLE systems. The results presented show that SERLAS yields a fair distribution verifying the goodnesseofefit relative to S, DM, SM and OF factors, along with tending to a regular solution to the physical behavior in the whole working range. In conclusion, the use of the LSER principles coupled with the boundary constraints should provide a good potential in the phase equilibrium modeling of the complex type 2 LLE systems. The SERLAS model

works very well for a special equilibrium case where aromatic solvents are being used for the separation of valeric acid. Acknowledgments This study was supported by the Research Fund of Istanbul University (project number 33167). References [1] J. Wisniak, A. Tamir, LiquideLiquid Equilibrium and Extraction: a Literature Source Book, Elsevier, Amsterdam, 1980e1981. [2] A. Arce, A. Blanco, P. Souza, I. Vidal, Liquideliquid equilibria of the ternary system water þ propanoic acid þ methyl isobutyl ketone at various temperatures, J. Chem. Eng. Data 38 (1993) 201e203. [3] T.M. Letcher, G.G. Redhi, Phase equilibria for liquid mixtures of (butanenitrile þ a carboxylic acid þ water) at 298.15 K, Fluid Phase Equilib. 193 (2002) 123e133. [4] N.A. Darwish, M.A. Abdulkarim, I. Ashour, A.M. Dwaidar, F.S. Athamneh, Liquideliquid equilibrium for the system water þ acetic acid þ 1-heptanol at 278.1, 293.1, 303.1 and 313.1 K, Fluid Phase Equilib. 200 (2002) 277e285. [5] J.A. Briones, J.C. Mullins, M.C. Thies, Liquideliquid equilibria for the oleic acideb-sitosterolewater system at elevated temperatures and pressures, Ind. Eng. Chem. Res. 33 (1994) 151e156. [6] A.S. Kertes, C.J. King, Extraction chemistry of fermentation product carboxylic acids, J. Biotechnol. Bioeng. 28 (1986) 269e282. [7] A. Senol, Liquideliquid equilibria for ternary systems of (water þ carboxylic acid þ 1-octanol) at 293.15 K. Modeling phase equilibria using a solvatochromic approach, Fluid Phase Equilib. 227 (2005) 87e96. [8] A. Senol, Phase equilibrium for ternary liquid systems of water þ carboxylic acid þ chlorinated hydrocarbon. Thermodynamic modeling through SERLAS, Chem. Eng. Commun. 193 (2006) 402e416. [9] G. Maurer, Modeling the liquideliquid equilibrium for the recovery of carboxylic acids from aqueous solutions, Fluid Phase Equilib. 241 (2006) 86e95. [10] A. Senol, Liquideliquid equilibria for systems of (water þ carboxylic acid þ methylcyclohexanol) at 293.15 K. Modeling considerations, J. Chem. Eng. Data 49 (2004) 1815e1820. [11] A. Senol, Liquideliquid equilibria for mixtures of (water þ carboxylic acid þ 1octanol/Alamine 336) at 293.15 K, J. Chem. Eng. Data 50 (2005) 713e718. [12] A. Senol, Liquideliquid equilibria for the system (water þ carboxylic acid þ chloroform). Thermodynamic modeling, Fluid Phase Equilib. 243 (2006) 51e56. [13] R.E. Treybal, Liquid Extraction, second ed., McGraw-Hill, New York, 1963. [14] J.M. Prausnitz, T. Anderson, E. Grens, C. Eckert, R. Hsieh, J.P. O'Connell, Computer Calculations for Multicomponent VaporeLiquid and LiquideLiquid Equilibria, PrenticeeHall Inc., Englewood Cliffs, New Jersey, 1980. [15] A. Senol, Extraction equilibria of valeric acid using (Alamine 336/diluent) and conventional solvent systems. Modeling considerations, Chem. Eng. Process 41 (2002) 681e692. [16] M.J. Kamlet, R.M. Doherty, M.H. Abraham, Y. Marcus, R.W. Taft, Linear solvation energy relationships. 46. An improved equation for correlation and prediction of octanol/water partition coefficients of organic nonelectrolytes (including strong hydrogen bond donor solutes), J. Phys. Chem. 92 (1988) 5244e5255. [17] Y. Marcus, Linear solvation energy relationships. Correlation and prediction of the distribution of organic solutes between water and immiscible organic solvents, J. Phys. Chem. 95 (1991) 8886e8891. [18] V. Brandani, F. Evangelista, Correlation and prediction of enthalpies of mixing for systems containing alcohols with UNIQUAC associatedesolution theory, Ind. Eng. Chem. Res. 26 (1987) 2423e2430.

A. Senol / Fluid Phase Equilibria 415 (2016) 110e124 [19] S.I. Sandler, Chemical, Biochemical, and Engineering Thermodynamics, John Wiley, New York, 2006. [20] J.M. Prausnitz, R.N. Lictenthaler, E.G. de Azevedo, Molecular Thermodynamics of Fluid-phase Equilibria, third ed., PrenticeeHall Inc., New Jersey, 1999. [21] K. Tochigi, D. Tiegs, J. Gmehling, K. Kojima, Determination of new ASOG parameters, J. Chem. Eng. Jpn. 23 (1990) 453e463. [22] J. Gmehling, J. Li, M. Schiller, A modified UNIFAC model. 2. Present parameter matrix and results for different thermodynamic properties, Ind. Eng. Chem. Res. 32 (1993) 178e193. [23] S.I. Sandler, Models for Thermodynamic and Phase Equilibria Calculations (Chemical Industries), Marcel Dekker, New York, 1993. [24] C.-C. Chen, Y. Song, Generalized electrolyte-NRTL model for mixed-solvent electrolyte systems, AIChE J. 50 (2004) 1928e1941. [25] L.D. Simoni, Y. Lin, J.F. Brennecke, M.A. Stadtherr, Modeling liquid-liquid equilibrium of ionic liquid systems with NRTL, electrolyte-NRTL, and UNIQUAC, Ind. Eng. Chem. Res. 47 (2008) 256e272. [26] Aa Fredenslund, UNIFAC and related group-contribution models for phase equilibria, Fluid Phase Equilib. 52 (1989) 135e150. [27] J. Gmehling, P. Rasmussen, Aa Fredenslund, Vaporeliquid equilibriums by UNIFAC group contribution. Revision and extension 2, Ind. Eng. Chem. Process Des. Dev. 21 (1982) 118e127. [28] T. Magnussen, P. Rasmussen, Aa Fredenslund, UNIFAC parameter table for prediction of liquideliquid equilibriums, Ind. Eng. Chem. Process Des. Dev. 20 (1981) 331e339. [29] B.L. Larsen, P. Rasmussen, Aa Fredenslund, A modified UNIFAC groupcontribution model for the prediction of phase equilibria and heats of mixing, Ind. Eng. Chem. Res. 26 (1987) 2274e2286. [30] A.C. Mengarelli, E.A. Brignole, S.B. Bottini, Activity coefficients of associating mixtures by group contribution, Fluid Phase Equilib. 163 (1999) 195e207. [31] O. Ferreira, E.A. Macedo, S.B. Bottini, Extension of the A-UNIFAC model to mixtures of cross- and self-associating compounds, Fluid Phase Equilib. 227 (2005) 165e176.
s, P. Hegel, S.B. Bottini, E.A. Brignole, Phase equilibria [32] A.E. Andreatta, L.M. Casa in ternary mixtures of methyl oleate, glycerol, and methanol, Ind. Eng. Chem. Res. 47 (2008) 5157e5164. ~e
, M. SaleseCruz, C. Leibovici, J.P. O'Connell, Mathe[33] R. Gani, N. MuroeSun matical and numerical analysis of classes of property models, Fluid Phase Equilib. 250 (2006) 1e32. [34] I.G. Economou, M.D. Donohue, Equation of state with multiple associating sites for water and water-hydrocarbon mixtures, Ind. Eng. Chem. Res. 31 (1992) 2388e2394. [35] I.V. Prikhodko, T.M. Letcher, T.W. de Loos, Liquidliquid equilibrium modeling of ternary hydrocarbon þ water þ alkanol systems, Ind. Eng. Chem. Res. 36 (1997) 4391e4396. [36] E.A. Müller, K.E. Gubbins, Molecular-based equations of state for associating fluids: a review of SAFT and related approaches, Ind. Eng. Chem. Res. 40 (2001) 2193e2211. [37] S.eT. Lin, S.I. Sandler, A priori phase equilibrium prediction from a segment contribution solvation model, Ind. Eng. Chem. Res. 41 (2002) 899e913. [38] I. Tsivintzelis, G.S. Dritsas, C. Panayiotou, An alternative approach to nonrandomness in solution thermodynamics, Ind. Eng. Chem. Res. 45 (2006) 7264e7274. [39] A. Tihic, G.M. Kontogeorgis, N. von Solms, M.L. Michelsen, Applications of the simplified perturbed-chain SAFT equation of state using an extended parameter table, Fluid Phase Equilib. 248 (2006) 29e43. [40] C. Lundstrøm, M.L. Michelsen, G.M. Kontogeorgis, K.S. Pedersen, H. Sørensen, Comparison of the SRK and CPA equations of state for physical properties of water and methanol, Fluid Phase Equilib. 247 (2006) 149e157. [41] I.V. Yakoumis, G.M. Kontogeorgis, E.C. Voutsas, D.P. Tassios, Vapor-liquid equilibria for alcohol/hydrocarbon systems using the CPA Equation of State, Fluid Phase Equilib. 130 (1997) 31e47. [42] A. Anderko, J.M. Prausnitz, On the relationship between the equilibrium constants of consecutive association reactions, Fluid Phase Equilib. 95 (1994) 59e71. [43] J. Gross, G. Sadowski, Perturbed-chain SAFT: an equation of state based on a perturbation theory for chain molecules, Ind. Eng. Chem. Res. 40 (2001) 1244e1260. [44] J. Mi, C. Zhong, Y.G. Li, Y. Tang, Prediction of global VLE for mixtures with improved renormalization group theory, AIChE J. 52 (2006) 342e353. [45] A. Klamt, F. Eckert, COSMO-RS: a novel and efficient method for the a priori prediction of thermophysical data of liquids, Fluid Phase Equilib. 172 (2000) 43e72. [46] M. Diedqenhofen, A. Klamt, COSMO-RS as a tool for property prediction of IL mixtures: a review, Fluid Phase Equilib. 294 (2010) 31e38. [47] A. Klamt, F. Eckert, W. Arlt, COSMO-RS: an alternative to simulation for calculating thermodynamic properties of liquid mixtures, Annu. Rev. Chem. Biomol. Eng 1 (2010) 101e122. [48] J. Palomar, J.S. Torrecilla, V.R. Ferro, F. Rodríguez, Development of an a priori ionic liquid design tool. 2. Ionic liquid selection through the prediction of COSMO-RS molecular descriptor by inverse neural network, Ind. Eng. Chem. Res. 48 (2009) 2257e2265. [49] A.R. Ferreira, M.G. Freire, J.C. Ribeiro, F.M. Lopes, J.G. Crespo, J.A.P. Coutinho, An overview of the liquidliquid equilibria of (ionic liquid þ hydrocarbon) binary systems and their modeling by the conductor-like screening model for real solvents, Ind. Eng. Chem. Res. 50 (2011) 5279e5294.

123

[50] A.R. Ferreira, M.G. Freire, J.C. Ribeiro, F.M. Lopes, J.G. Crespo, J.A.P. Coutinho, Overview of the liquidliquid equilibria of ternary systems composed of ionic liquid and aromatic and aliphatic hydrocarbons, and their modeling by COSMO-RS, Ind. Eng. Chem. Res. 51 (2012) 3483e3507. [51] Y. Tang, G. Stephenson, E. Zhao, M. Agrawal, S. Saha, Calculations of complex phase equilibrium by equal-area method, AIChE J. 58 (2012) 591e599. [52] M.B. Oliveira, F.R. Varanda, I.M. Marrucho, A.J. Queimada, J.A.P. Coutinho, Prediction of water solubility in biodiesel with the CPA equation of state, Ind. Eng. Chem. Res. 47 (2008) 4278e4285. [53] T. Zhou, K. McBride, X. Zhang, Z. Qi, K. Sundmacher, Integrated solvent and process design exemplified for a DielseAlder reaction, AIChE J. 61 (2015) 147e158. [54] L.D. Simoni, J.F. Brennecke, M.A. Stadtherr, Asymmetric framework for predicting liquideliquid equilibrium of ionic liquid-mixed-solvent systems. 1. Theory, phase stability analysis, and parameter estimation, Ind. Eng. Chem. Res. 48 (2009) 7246e7256. [55] L.D. Simoni, A. Chapeaux, J.F. Brennecke, M.A. Stadtherr, Asymmetric framework for predicting liquid-liquid equilibrium of ionic liquid-mixed-solvent systems. 2. Prediction of ternary systems, Ind. Eng. Chem. Res. 48 (2009) 7257e7265. [56] A. Senol, Effect of diluent on amine extraction of acetic acid. Modeling considerations, Ind. Eng. Chem. Res. 43 (2004) 6496e6506. [57] A. Senol, Solvation model for estimating the properties of (vapour þ liquid) equilibrium, J. Chem. Thermodyn. 40 (2008) 1295e1304. [58] A. Senol, M. Lalikoglu, M. Bilgin, Modeling extraction equilibria of butyric acid distributed between water and tri-n-butyl amine/diluent or tri-n-butyl phosphate/diluent system. Extension of the LSER approach, Fluid Phase Equilib. 385 (2015) 153e165. [59] A. Senol, Liquideliquid equilibria for mixtures of (water þ pyruvic acid þ alcohol/Alamine). Modeling and optimization of extraction, J. Chem. Eng. Data 58 (2013) 528e536. [60] A. Senol, B. Baslioglu, Phase equilibria of ternary systems (water þ pyruvic acid þ high boiling alcohol). Thermodynamic modeling and optimization of extraction, J. Chem. Thermodyn. 55 (2012) 92e101. [61] A. Senol, Optimum extraction equilibria of the systems (water þ carboxylic acid þ 1-hexanol/Alamine). Thermodynamic modeling, Fluid Phase Equilib. 360 (2013) 77e87. [62] B.H. Lee, Y. Qin, J.M. Prausnitz, Thermodynamic representation of ternary liquideliquid equilibria near-to and far-from the plait point, Fluid Phase Equilib. 240 (2006) 67e72. [63] A. Senol, Optimal extractive separation of chromium(VI) from acidic chloride and nitrate media by commercial amines. Equilibrium modeling through linear solvation energy relation, Ind. Eng. Chem. Res. 52 (2013) 16321e16334. [64] R. Taylor, H. Kooijman, Composition derivatives of activity coefficient models (for the estimation of thermodynamic factors in diffusion), Chem. Eng. Commun. 102 (1991) 87e106. [65] H. Mori, A. Oda, C. Ito, T. Aragaki, F.Z. Liu, Thermodynamic factors derived from group contribution activity coefficient models, J. Chem. Eng. Jpn. 29 (1996) 396e398. [66] A. Senol, L. Sevgili, Phase equilibria for ternary liquid systems of (water þ tetrahydrofuran þ nonprotic aromatic solvent) at T ¼ 298.2 K, J. Chem. Thermodyn. 38 (2006) 578e584. [67] Aa Fredenslund, M.L. Michelsen, J.M. Sørensen, in: 2nd International Conference on Phase Equilibria and Fluid Properties, Berlin, March, 1980. [68] D.M. Himmelblau, J. Riggs, Basic Principles and Calculations in Chemical Engineering, eighth ed., PrenticeeHall Inc., Englewood Cliffs, New Jersey, 2012. [69] H. Yang, Å.C. Rasmuson, Ternary phase diagrams of ethyl paraben and propyl parabenin ethanol aqueous solvents, Fluid Phase Equilib. 376 (2014) 69e75. [70] H. Yang, Å.C. Rasmuson, Phase equilibrium and mechanisms of crystallization in liquideliquid phase separating system, Fluid Phase Equilib. 385 (2015) 120e128. [71] A. Senol, Optimization and modeling of extraction equilibria of the type 2 ternary systems containing (water þ isovaleric acid þ solvent), J. Chem. Thermodyn. 91 (2015) 211e224. [72] J.A. Riddick, W.B. Bunger, T.K. Sakano, Organic Solvents. Physical Properties and Methods of Purification, fourth ed., WilleyeInterscience, New York, 1986. [73] E.W. Barega, E. Zondervan, A.B. de Haan, Experimental density, viscosity, interfacial tension and water solubility of ethyl benzeneea-methyl benzyl alcoholewater system, J. Chem. Thermodyn. 63 (2013) 31e37.
ndez, A.P. de los Ríos, D. Go
mez, M. Rubio, F. Tom
[74] F.J. Hern
andez-Ferna asAlonso, G. Víllora, Ternary liquideliquid equilibria for mixtures of an ionic liquid þ n-hexane þ an organic compound involved in the kinetic resolution of rac-1-phenyl ethanol (rac-1-phenyl ethanol, vinyl propionate, rac-1-phenylethyl propionate or propionic acid) at 298.2 K and atmospheric pressure, Fluid Phase Equilib. 263 (2008) 190e198. [75] A.F.M. Barton, Solubility parameters, Chem. Rev. 75 (1975) 731e753.

Nomenclature Ai: Coefficient Ci: Coefficient of Eq. (1) D: Distribution coefficient DM: Modified distribution ratio

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DM0: The value of DM at the extraction x2 ¼ 0   P limit   e: Mean relative error, e ¼ ð100=NÞ N i¼1 ðYi;obs  Yi;mod Þ=Yi;obs ð%Þ F: Correction factor as defined by Eq. (1) GE: Excess Gibbs energy function (J mol1) N: Number of observations OF: Optimization factor OF0: The value of OF at the extraction limit x2 ¼ 0 Pr: Property as defined by Eq. (1) Pr0: Property as defined by Eq. (1) R: Gas constant (J mol1 K1) S: Separation factor S0: The value of S at the extraction limit x2 ¼ 0 SM: Modified separation factor SM0: The value of SM at the extraction limit x2 ¼ 0 SR: Solvent-dependent composition ratio SR0: The value of SR at the extraction limit x2 ¼ 0 T: Temperature (K) V: The molar volume of a solute (cm3 mol1) x0: Mole fraction of mutual solubility of a component x0i : Mole fraction of a component in the aqueous phase 00 xi : Mole fraction of a component in the solvent phase 00 00 xiv: Dimensionless independent variable (xiv ¼ x2 =x3 )

X: Independent variable Y: Variable Greek letters

a; a*: Solvatochromic parameters b; b*: Solvatochromic parameters GL: Thermodynamic factor g: Activity coefficient of a component in the solvent phase d: Solvatochromic parameter dH; d*H : Hildebrand solubility parameters (MPa0.5) p; p*: Solvatochromic parameters P s: Rootmeansquare deviation, s ¼ ½ Ni¼1 ðYi;obs  Yi;mod Þ2 =N0:5 Subscript max: Maximum mod: Modeled property obs: Observed property