LiquidâLiquid Equilibria for Mixtures of (Water + Pyruvic Acid + Alcohol

Article pubs.acs.org/jced

Liquid−Liquid Equilibria for Mixtures of (Water + Pyruvic Acid + Alcohol/Alamine). Modeling and Optimization of Extraction Aynur Senol* Department of Chemical Engineering, Faculty of Engineering, Istanbul University, 34320 Avcilar, Istanbul, Turkey ABSTRACT: Extraction equilibria of the systems (water + pyruvic acid + alcohol/ Alamine 336) have been investigated at T = 293.2 K. The solvent mixture of 1-dodecanol/alamine yields the largest separation factors for the extraction of pyruvic acid. An analytical structure for optimum extraction has been developed as the locus of the proposed separation factors. The properties of extraction systems have been correlated by a solvation relation (SERLAS) with 5 and 10 parameters. The tie-lines of the present systems have been predicted by the universal functional activity coefficient (UNIFAC) original model. The reliability analysis of both models has been made statistically against the experimental extraction factors.

predicted by the UNIFAC-original model.12,13 Finally, an analytical structure for optimum extraction of piruvic acid on the basis of the proposed separation factors has been developed.

1. INTRODUCTION Regarding the technical merits of high boiling solvents during the regeneration, various solvents have been investigated in the fermentation industry to improve the efficient separation of organic acids from aqueous solutions.1 The extraction efficiency of a monocarboxylic acid can be improved through applying synergistic separation power of a solvent mixture of (alcohol + C8−C10 saturated aliphatic tertiary amines, e.g., Alamine 336), used as a commercial extractant for carboxylic acids.2,3 In this study, a solvent mixture of (heavy alcohol + 3 % by volume Alamine 336) is used as a high boiling solvent for separation of pyruvic (2-oxopropanoic) acid from water. The extractability of pyruvic acid from the aqueous solution has been investigated at T = 293.2 K, along with testing several alcohols mixed with Alamine 336 (3 % by volume). Heavy alcohols from various classes of aliphatic, aromatic, and cyclic types were selected (i.e., 1-dodecanol, 1-decanol, 1-hexanol, 1-phenylethanol, and cyclohexanol). All of the tested alcohols have higher boiling temperatures than water and pyruvic acid. The analysis is limited with an alcohol-containing solvent system, where the alcohol/amine solvent is being regarded as a coupled solvent. Due to the synergistic effect of physical and chemical interactions, the alcohol/amine solvent can improve the extraction efficiency of pyruvic acid. Liquid−liquid equilibrium (LLE) data for extraction of oxocarboxylic acids by high boiling solvents are scarce in the literature.4−7 Ion exchange, amine extraction, and reverse osmosis membrane are the most effective processes used for the recovery of pyruvic acid from the fermentation solutions.8 The properties of the present LLE systems have been correlated through a solvation relation SERLAS,5 which clarifies the impact of solvatochromic parameters of linear solvation energy relation (LSER)9,10 and the thermodynamic factors according to the UNIFAC-Dortmund model.11 As well, the tie-lines have been © 2013 American Chemical Society

2. THEORETICAL SECTION 2.1. Estimation of Extraction Equilibrium by SERLAS. The extraction equilibrium of 2-oxopropanoic acid has been correlated by the SERLAS model depending on the principles of LSER.9,10 LSER (eq 1) predicts the property XYZ in terms of five physical parameters. XYZ = XYZ0 + Vm/100 + s(π + dδ) + bβ + aα

(1)

XYZ0 is an adjustable parameter for the distributed solute. LSER includes a cavity term for the molar volume of the solute (Vm/100), a polarity/polarizability term [s(π + dδ)], and hydrogen bond donation aα (HBD) and acceptance bβ (HBA) terms. For estimating the properties of a liquid−liquid system, the SERLAS model with 5 and 10 parameters has been performed. The separation factor S (eq 2) and the modified distribution ratio DM (eq 3), all defined as the property Pr (log mean), can be expressed by eq 4, which incorporates the Pr0 property and a Σ term of several parameters. S=

D2 (x ″/x ′) = 2 2 D1 (x1″/x1′)

DM =

(x 2″ + x3″)/(1 − x3″) (x 2′ + x3′)/(1 − x3′)

(2)

(3)

Received: June 26, 2012 Accepted: January 29, 2013 Published: February 14, 2013 528

dx.doi.org/10.1021/je3012265 | J. Chem. Eng. Data 2013, 58, 528−536

Journal of Chemical & Engineering Data

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when either x2 = 0 for which Pr = Pr0 or x′ = x″ (i.e., the plait point compositions for which S = 1 and DM = 1). The evaluation of the thermodynamic factors (ΓL),14,15 the modified Hildebrand solubility parameter (δH*), and the modified solvatochromic parameters π*, α*, and β* is given elsewhere.5 In this study, ΓL values were predicted from the UNIFAC-Dortmund model using the derivative approaches for the activity coefficient of Mori et al.15 SERLAS (eq 4) was executed for two ranges of the degree of expansion k. For the expansion degrees k = 1 and k = 2, eq 4 is rearranged to the 5 parameter eq 5 and the 10 parameter eq 6, respectively.

Pr = F1Pr0 + F2·∑ [C Γ, k(ΓL)k + C H, k(δ H*)k + Cπ , k(π *)k k k

+ Cβ , k(β*) + Cα , k(α*)k ]

(4)

x″ and x′ represent solvent-rich and water-rich compositions of water (1), acid (2), and alcohol/amine solvent (3). The Pr0 properties referred to the mutual solubility region (x2 = 0) are defined as S0 = (x″03/x″01)/(x′03/x′01) and DM0 = [x″03/(1 − x″03)]/ [x03 ′ /(1 − x03 ′ )], where x03 and x01 represent the mole fractions of mutual solubility of solvent and water, respectively. To reduce the complexity of eq 4, S0 was selected to be equal to DM0. The correction factors, F1 = (x″03−x′01)/(x″03−x′03) and F2 = (x″3 /(x″2 + x3″)) − (x3′ /(x2′ + x3′ )), in eq 4 account for two limiting conditions

Pr = F1Pr0 + F2·[C Γ(ΓL) + C H(δ H*) + Cπ(π *) + Cβ(β*)

Table 1. Densities (d20) and Refractive Indexes (nD(20)) of Components at 101.33 kPa and 293.2 Ka density d20 (g·cm−3) component

d

pyruvic acid 1-hexanol cyclohexanol 1-phenylethanol 1-decanol 1-dodecanol

b

exptl

lit.

1.2668 0.8152 0.9621 1.0121 0.8289 0.8305

1.2670 0.8150 0.9624 1.0120 0.8290 0.8307

refractive index nD(20) b

exptl

lit.

1.4140 1.4180 1.4650 1.5268 1.4372 1.4430

1.4138 1.4178 1.4648 1.5270 1.4370 1.4428

+ Cα(α*)]

(5)

Pr = F1Pr0 + F2·[C Γ,1(ΓL) + C H,1(δ H*) + Cπ ,1(π *)

purityc mass fr.

+ Cβ ,1(β*) + Cα ,1(α*) + C Γ,2(ΓL)2 + C H,2(δ H*)2

≥0.99 ≥0.99 ≥0.99 ≥0.99 ≥0.99 ≥0.99

+ Cπ ,2(π *)2 + Cβ ,2(β*)2 + Cα ,2(α*)2 ]

(6)

2.2. Separation Factors for Optimizing an Extraction Process. In searching for the optimum extraction of a system including water, a solute and a solvent mixture, the following modified separation factor (SM) has been processed as an optimization criterion of extraction. Dk, Dj, and Di are the distribution coefficients of solute, water, and solvent, respectively.

Standard uncertainties u are u(d20) = 0.0001 g·cm−3, u(nD(20)) = 0.0002. bValues due to Riddick et al.17 cThe purities refer to the mass fraction. dAll materials were provided by Fluka. a

Figure 1. Liquid−liquid equilibria (mole fraction) for the systems x1 water + x2 pyruvic acid + x3 alcohol/Alamine (x1 = 1 − x2 − x3); ○, experimental solubility curve; ▲, experimental tie-lines (solid line); ◊, UNIFAC-predicted end compositions (dashed line); ⧫, plait point; (a) 1-dodecanol/Alamine, (b) 1-decanol/Alamine, (c) 1-hexanol/Alamine, (d) 1-phenylethanol/Alamine, (e) cyclohexanol/Alamine. 529


Journal of Chemical & Engineering Data SM =

Dk + ∏i Di Dj + ∏i Di

Article

Table 2. Thermodynamic Factors (ΓL), Excess Free Energy Function (GE), and Experimental Tie-Line Compositions (Mole Fraction) of the Conjugate Solutions, x′1, x′2, x″1 , and x″2 for the Systems Water x1 + Pyruvic Acid x2 + Alcohol/Alamine x3 (x3 = 1 − x1 − x2) at T = 293.2 Ka

( i ≠ k ; i ≠ j) (7)

Regarding eq 7, SM has a maximum for Dk > Dj in the range between xk = 0 and xk = xpp, where xpp is the mole fraction of a solute at the plait point. Because Dj is very small (Dk > Dj), two limiting values of SM are practically equal to 1 (i.e., for xk = 0, Dk = 0 and SM = SM0→1, and for xk = xpp, D = 1 and SM = 1). The location of the supreme (optimum) point is obtained by analyzing the derivatives of SM against an independent variable, xiv = x2″/x3″, regarding eq 8. d(SM) = 0; d(xiv)

d2(SM) d(xiv)2

water-rich x1′

⟨0 (8)

Dk − Dj Dj + ∏i Di

(9)

Because Dj is very small (Dk > Dj), practically FE = 0 for two limiting values of xk (i.e., for xk = 0, Dk = 0 and FE = FE0→0, and for xk = xpp, D = 1, and FE = 0). The optimum value of FE is defined by analyzing the derivatives of FE in terms of eq 10. d(FE) = 0; d(xiv)

d2(FE) d(xiv)2

⟨0 (10)

Consequently, characterization of the supreme (optimum) point requires an analytical solution of eqs 8 and 10. In this study, it has been evaluated only the variation of the observed SM and FE factors and their derivatives ranging between xiv = 0 and the plait point. The optimum conditions were obtained by applying a third-order polynomial function of the observed SM and FE factors against xiv. However, for reproducing SM factors by SERLAS, it has been processed eq 11, where D1, D2, and D3 are the distribution coefficients of water, acid, and alcohol/amine, respectively. SM =

D2 + D3 D1 + D3

x2′

x1″

x2″

ΓL

b

Water (1) + Pyruvic Acid (2) + 1-Dodecanol/Alamine (3) 0 0.1154d 0 0.9999d 0.9803 0.0172 0.1215 0.0928 1.0347 0.9573 0.0375 0.1422 0.1941 1.0728 0.9199 0.0725 0.1523 0.3582 1.1290 0.8793 0.1094 0.1637 0.4662 1.1536 0.8417 0.1445 0.1779 0.5487 1.1546 0.8151 0.1704 0.1803 0.5893 1.1474 Plait pointe: (x1 = 0.4048; x2 = 0.5567; x3 = 0.0385) Water (1) + Pyruvic Acid (2) + 1-Decanol/Alamine (3) 0 0.1502d 0 0.9999d 0.9794 0.0175 0.1613 0.0906 1.0277 0.9525 0.0402 0.1766 0.2093 1.0622 0.9209 0.0696 0.1915 0.3612 1.0972 0.8976 0.0912 0.2001 0.4302 1.1054 0.8574 0.1283 0.2107 0.4978 1.1045 Plait pointe: (x1 = 0.4324; x2 = 0.5284; x3 = 0.0392) Water (1) + Pyruvic Acid (2) + 1-Hexanol/Alamine (3) 0 0.1595d 0 0.9982d 0.9709 0.0256 0.1797 0.0382 1.0069 0.9502 0.0454 0.1975 0.0691 1.0123 0.9140 0.0802 0.2201 0.1146 1.0196 0.8621 0.1284 0.2575 0.1712 1.0273 0.8063 0.1823 0.2915 0.2151 1.0317 0.7294 0.2513 0.3393 0.2764 1.0346 Plait pointe: (x1 = 0.4752; x2 = 0.3641; x3 = 0.1607) Water (1) + Pyruvic Acid (2) + 1-Phenylethanol/Alamine (3) 0 0.2122d 0 0.9972d 0.9702 0.0221 0.2362 0.0420 1.0046 0.9524 0.0374 0.2555 0.0733 1.0079 0.9288 0.0591 0.2815 0.1188 1.0128 0.9111 0.0753 0.3019 0.1559 1.0168 0.8803 0.1056 0.3271 0.1987 1.0219 0.8549 0.1295 0.3678 0.2318 1.0275 Plait pointe: (x1 = 0.5887; x2 = 0.2538; x3 = 0.1575) Water (1) + Pyruvic Acid (2) + Cyclohexanol/Alamine (3) 0 0.3915d 0 0.9965d 0.9811 0.0124 0.4055 0.0316 1.0054 0.9607 0.0298 0.4360 0.0675 1.0117 0.9430 0.0455 0.4605 0.0943 1.0167 0.9186 0.0688 0.4912 0.1305 1.0240 0.9023 0.0815 0.5123 0.1488 1.0285 0.8752 0.0995 0.5278 0.1654 1.0330 Plait pointe: (x1 = 0.6831; x2 = 0.1751; x3 = 0.1418)

Due to regressing with very small SM values, the following extraction factor (FE) may be used instead of SM. FE = 100|SM − 1| = 100

(GE)c

solvent-rich

(11)

For the possible lower extraction limit (x2 = 0), the corresponding SM0 and FE0 values are defined as SM0 = (x03 ″ /x03 ′ )/ [(x01 ″ /x01 ′ ) + (x03 ″ /x03 ′ )] and FE0 = 100|SM0 − 1|. For x2 = xpp, SM = 1 and FE = 0. Consequently, for optimizing an extraction process, the design strategy based on SM and FE factors and their derivatives eqs 8 and 10, ranging from x2 = 0 to x2 = xpp, should be utilized.

3. EXPERIMENTAL SECTION The tested compounds 1-dodecanol, 1-decanol, 1-hexanol, 1-phenylethanol, cyclohexanol, and pyruvic acid of analytical grade (99 %, GC) were supplied by Fluka (Netherlands). Alamine 336 (Henkel Co., USA), a C8−C10 saturated straight-chain tertiary amine mixture, is a pale yellow liquid, practically insoluble in water, with an average molecular weight of 392 g·mol−1 and a density of 0.81 g·cm−3. The volume percent of Alamine 336 in the solvent mixture was restricted at 3 %. All of the chemicals were used as received. The experimental and literature properties of components are given in Table 1. The purity of the chemicals was checked on the basis of their densities and refractive indexes at 293.2 K. Refractive indexes and densities were measured with

J·mol−1

1244.9 1808.8 2295.3 2355.9 2195.2 2043.4

1341.2 1848.8 2147.8 2137.4 2011.5

1018.7 1214.7 1450.0 1697.5 1830.9 1892.1

1196.2 1302.6 1415.3 1473.1 1505.2 1519.1

−145.7 −154.8 −168.5 −188.1 −198.1 −205.0

a

Standard uncertainties u are u(T) = 0.1 K and u(x) = 0.0002. Thermodynamic factors14,15 derived from the UNIFAC-Dortmund model. cExcess Gibbs free energy function for the organic phase according to the UNIFAC-Dortmund model, GE/(J·mol−1) = R(T/K)∑ixi ln γi. d Mutual solubility value. eThe plait point composition due to the method of Treybal et al.19 b

Anton Paar densimeter (model DMA 4500) integrated with a refractive index unit (model RXA 170) both in ± 10−5 precision. An equilibrium glass cell of a 75 mL volume including a water jacket to maintain isothermal conditions at T = 293.2 ± 0.1 K was used to determine the mutual solubility of components and the solubility curves by the cloud point method.5 The method is 530



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solubility of water is much more reduced in the system containing 1-dodecanol/Alamine. As well, the mutual solubility of n-alcohol/Alamine and water decreases with increasing the carbon chain length of n-alcohol (Table 2). As depicted in Figure 1a−e, the area of the two-phase heterogeneous region increases in the order, cyclohexanol < 1-phenylethanol < 1-hexanol < 1-decanol < 1-dodecanol. This indicates the fact that a ring-included alcohol structure is responsible for a decrease in the area of the two-phase region, being the smallest for cyclohexanol/Alamine. As evident from the slope of the observed tie-lines in Figure 1a−e (i.e., the distribution coefficient of acid, D2 = x2″/x2′ ), pyruvic acid yields D2 > 1 for all of the alcohols studied. Figure 2 and Table 3 show that the separation of pyruvic acid by an alcohol/Alamine solvent is feasible, yielding S > 1.

based on titrating heterogeneous mixtures of (water + solvent) with acid until the transition point from heterogeneity to homogeneity is reached. Solubility curves were obtained by using the Metrohm microburet with an accuracy of ± 0.01 cm3. All mixtures were prepared by weighing with a Sartorius scale accurate to within ± 10−4 g. Concentration determinations by the cloud point method were made with an uncertainty of ± 0.0005 mole fraction. To obtain the end-points of tie-lines, mixtures of water, acid, and alcohol/Alamine lying within the heterogeneous gap were stirred for 3 h in the extraction cell5 and then left for 2 h to settle down into aqueous and solvent layers. The compositions of the conjugate phases were analyzed by Hewlett-Packard GC analyzer 6890, equipped with HP-Innowax polyethylene glycol capillary column (FI detector) and HP Plot Q column (TC detector). The detector and the injection port temperatures were kept at T = 523.2 K and T = 473.2 K, respectively. Nitrogen was used as a carrier at a rate of 1 cm3·min−1. Concentrations of the end compositions of tie-lines were determined with an uncertainty of ± 0.0002 mole fraction. Figure 1a−e represents the experimentally defined solubility curves, tie-lines, and plait points of the systems studied at T = 293.2 K.

Table 3. Modified Distribution Ratio (DM), Separation Factor (S), Modified Separation Factor (SM), and Extraction Factor (FE) Varying against the Independent Variable xiv for the Systems (Water + Pyruvic Acid + Alcohol/Alamine) obsa solvent system

4. RESULTS AND DISCUSSION 4.1. Factors Affecting the Extraction Equilibria of Pyruvic Acid. The mutual solubility of water and solvent, the solubility isotherms, and the observed and calculated tie-lines through the UNIFAC original of the considered systems are plotted on the two-axis phase diagrams in Figure 1a−e, where the left side of the plait point represents the aqueous phase composition, while the right side one designates the solvent phase composition. The experimental tie-line compositions x′i and x″i of aqueous and solvent phases are given in Table 2. The thermodynamic factors (ΓL) and excess Gibbs free energy function (GE/J·mol−1) of the organic phase species, and the plait point compositions according to the Treybal method are also tabulated. Figure 1a−e and Table 2 show that the distribution of pyruvic acid in (water + alcohol/Alamine) mixture is strongly dependent on the nature of alcohol. Table 2 shows that the

1-dodecanol/ Alamine

1-decanol/ Alamine

1-hexanol/ Alamine

1-phenylethanol /Alamine

cyclohexanol/ Alamine

Figure 2. Variation of separation factor (S) with the solvent-phase acid mole fraction (x2′ ) for the systems (water + pyruvic acid + alcohol/ Alamine). Experimental: ▲, 1-dodecanol; ★, 1-decanol; ◊, 1-hexanol; ○, 1-phenylethanol; +, cyclohexanol. Theoretical through SERLAS; solid line eq 5, dashed line eq 6.

xiv = x″2 /x″3 b

DM

S b

76647.4

SM b

FE b

0.99999

0.0013b

0

76647.4

0.12 0.29 0.73 1.26 2.01 2.56 0b

207.57 59.42 20.57 10.88 7.05 5.68 56572.2b

43.53 34.85 29.84 22.89 17.97 15.63 56572.2b

1.0168 1.0393 1.0739 1.1237 1.1791 1.2009 0.99998b

1.68 3.93 7.39 12.37 17.91 20.09 0.0018b

0.12 0.34 0.81 1.16 1.71 0b

161.12 44.59 18.32 12.25 7.70 2922.3b

31.44 28.08 24.96 21.16 15.79 2922.3b

1.0208 1.0596 1.1053 1.1352 1.1762 0.99966b

2.08 5.96 10.53 13.52 17.62 0.0342b

0.05 0.09 0.17 0.30 0.44 0.72 0b

128.91 60.18 26.94 12.44 7.14 3.89 1322.2b

8.06 7.32 5.93 4.46 3.26 2.36 1322.2b

1.0058 1.0079 1.0103 1.0171 1.0188 1.0311 0.99924b

0.58 0.79 1.03 1.71 1.88 3.11 0.0756b

0.06 0.11 0.20 0.29 0.42 0.58 0b

91.42 47.08 24.90 16.92 10.54 7.15 442.5b

7.81 7.31 6.63 6.25 5.06 4.16 442.5b

1.0176 1.0256 1.0342 1.0433 1.0444 1.0521 0.99774b

1.76 2.56 3.42 4.33 4.44 5.21 0.2255b

0.06 0.14 0.21 0.35 0.44 0.54

71.50 28.23 16.86 9.93 7.43 5.32

6.17 4.99 4.24 3.55 3.22 2.76

1.0245 1.0344 1.0404 1.0446 1.0585 1.0832

2.45 3.44 4.04 4.46 5.85 8.32

a

Observed performance. bProperties corresponding to the mutual solubility region x2 = 0 (i.e., xiv = 0; DM = DM0; S = S0; SM = SM0; FE = FE0). 531



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These findings are attributed to the large hydrophobicity of 1-dodecanol having the longest R-chain structure. Further, the existence of a proton-accepting aromatic π ring and donating hydroxyl (OH) functional groups in the 1-phenylethanol structure results in a formation of intramolecular hydrogen bonding, thereby causing an effect of decreasing the extraction power. Due to the carbonyl (CO) and carboxyl (COOH) groups on the acid structure, pyruvic acid is more hydrophilic and less capable of association with a ring-included alcohol solvent. This would call for the assumption that the main controlling factor of the acid extraction is the range of hydrophobicity and polarity of alcohol and pyruvic acid. By the analysis of Figures 1 to 4 and Table 3 this tendency can be verified. The end compositions of tie-lines have been predicted by the UNIFAC-original model,12,13 yielding a mean error (e/%) with ̅ regard to x2 variable of 33.4% considering all of the systems studied. Figure 1a−e presents a quantitative assessment of predictions achieved for the UNIFAC-original model. The predicted capability of UNIFAC-original model proved to be slightly less accurate for 1-phenylethanol as compared to other alcohols. Probably, a modified interaction parameter for the aromatic π system in 1-phenylethanol may improve the accuracy of the model estimates. 4.2. Reliability Analysis of Existing Models. The reliability of both SERLAS and UNIFAC-original models has been analyzed statistically against the observed performance in N terms of the mean relative error (e/% ̅ = (100/N)∑i=1|(Yi,obs − Yi,mod )/Yi,obs|) and root-mean-square deviation (σ). The coefficients Ci of both eqs 5 and 6 have been regressed by the linpack algorithm16 using the thermodynamic factors and solvatochromic parameters from Tables 2 and 4. Table 5 shows

Cyclohexanol/Alamine and 1-phenylethanol/Alamine yield the lowest separation factors (S) as compared to n-alcohol/Alamine. The same remarks hold for the modified factors SM, DM, and FE of these solvents given in Table 3. It is apparent from Figures 2 to 4

Figure 3. Plot of distribution ratio (DM) against the solvent-phase acid mole fraction (x2′ ) for the systems (water + pyruvic acid + alcohol/ Alamine). Experimental: ▲, 1-dodecanol; ★, 1-decanol; ◊, 1-hexanol; ○, 1-phenylethanol; +, cyclohexanol. Modeled through SERLAS, solid line eq 5, dashed line eq 6.

Table 4. Hildebrand Solubility Parameter (δH) and Solvatochromic Parameters (π, β, α, δ) of Compounds compound

πa,b

βa,b

αa,b

δHc,d/ (MPa0.5)

δ′a,b

pyruvic acid 1-dodecanol 1-decanol 1-hexanol 1-phenylethanole cyclohexanol water

0.62 0.42 0.40 0.40 0.99 0.45 1.09

0.45 0.45 0.45 0.45 0.52 0.51 0.47

0.60 0.33 0.33 0.33 0.35 0.31 1.17

23.6 17.6 19.4 21.9 24.8 23.3 47.9

0.0 0.0 0.0 0.0 1.0 0.0 0.0

a Values due to Kamlet et al.9 bValues due to Marcus.10 cValues due to Riddick et al.17 dValues due to Barton.18 eParameters of phenylmethanol.

the regressed C coefficients for S, DM, and SM properties, as well as the mean deviations (e)̅ and (σ) of 5 parameter eq 5 and 10 parameter eq 6. Figures 1 to 4 and Table 5 present the consistency of predictions achieved for the existing models in terms of S, DM, and SM factors. From the statistical results in Table 5, it is concluded that SERLAS is reasonably accurate, yielding the overall deviations of e(S) = 8.03 % (σ(S) = 2.40), ̅ e(D ) = 6.60 % (σ(D ) = 6.40), and e (S M ̅ M ̅ M) = 0.57 % (σ(SM) = 0.0083) for eq 5, and e(S) = 5.47 % (σ(S) = 1.16), e(D ̅ ̅ M) = 7.09 % (σ(DM) = 4.87), and e(S ̅ M) = 0.40 % (σ(SM) = 0.0052) for eq 6, considering all of the systems studied. Equation 6 is slightly more accurate yielding e ̅ = 4.3 % (σ = 2.01) as compared to e ̅ = 5.2 % (σ = 2.94) for eq 5, and e ̅ = 38.7 % (σ = 51.93) for the UNIFACoriginal model with regard to S, DM, and SM properties. Figures 2 to 4 also manifest the fact that SERLAS accurately conforms the trend of variation of S, DM, and SM quantities. 4.3. Evaluation of Optimum Extraction Conditions. Regarding Figures 5 to 8, it turns out that a hump type divergence

Figure 4. Plot of modified separation factor (SM) against the solventphase acid mole fraction (x2″) for the systems (water + pyruvic acid + alcohol/Alamine). Experimental: ▲, 1-dodecanol; ★, 1-decanol; ◊, 1-hexanol; ○, 1-phenylethanol; +, cyclohexanol. Modeled through SERLAS, solid line eq 5, dashed line eq 6.

and Table 3 that the most appropriate solvent for the separation of pyruvic acid is 1-dodecanol/Alamine, yielding the largest S, SM, DM, and FE factors. Cyclohexanol/Alamine and 1-phenylethanol/ Alamine are less favorable solvents for pyruvic acid. Referring to Table 3 and Figures 1 to 4, it turns out that the extraction degree of pyruvic acid in the alcohol/Alamine solvent decreases in the order, cyclohexanol < 1-phenylethanol < 1-hexanol < 1-decanol < 1-dodecanol. Similar large extraction degrees for n-alcohol were obtained in a previous work,7 where 1-octanol/Alamine 336 was used as the solvent for the extraction of a monocarboxylic acid. 532



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Table 5. Coefficients Ci of 5 Parameter eq 5 and 10 Parameter eq 6 and Root-Mean-Square Deviations (σ) and Mean Relative Errors (e/̅ %)a Evaluated for Different Properties Pr (Separation Factor S, Distribution Ratio DM, Modified Separation Factor SM) of the Systems (Water + Pyruvic Acid + Alcohol/Alamine) solvent system

CΓ,1

CH,1

Cπ,1

Cβ,1

Cα,1

CΓ,2

CH,2

Cπ,2

Cβ,2

Cα,2

Pr = ln(S); Pr0 = ln(S0) ; σ(S); e(S) ̅ b

1-dodecanol/Alamine (σ = 8.80; e ̅ = 16.3 %) Fd (σ = 0.72; e ̅ = 2.2 %) Td 1-decanol/Alamine (σ = 2.14; e ̅ = 6.3 %) F (σ = 4.28; e ̅ = 13.9 %) T 1-hexanol/Alamine (σ = 0.33; e ̅ = 3.8 %) F (σ = 0.29; e ̅ = 3.6 %) T 1-phenylethanol/Alamine (σ = 0.51; e ̅ = 6.3 %) F (σ = 0.35; e ̅ = 4.4 %) T cyclohexanol/Alamine (σ = 0.41; e ̅ = 7.4 %) F (σ = 0.16; e ̅ = 3.2 %) T 1-dodecanol/Alamine (σ = 16.26; e ̅ = 11.3 %) Fd (σ = 0.32; e ̅ = 1.3 %) Td 1-decanol/Alamine (σ = 6.62; e ̅ = 8.6 %) F (σ = 18.78; e ̅ = 22.1 %) T 1-hexanol/Alamine (σ = 3.29; e ̅ = 2.8 %) F (σ = 2.54; e ̅ = 3.0 %) T 1-phenylethanol/Alamine (σ = 4.20; e ̅ = 5.6 %) F (σ = 1.98; e ̅ = 4.2 %) T cyclohexanol/Alamine (σ = 1.61; e ̅ = 4.7 %) F (σ = 0.72; e ̅ = 4.8 %) T 1-dodecanol/Alamine (σ = 0.024; e ̅ = 1.7 %) Fd (σ = 0.003; e ̅ = 0.24 %) Td 1-decanol/Alamine (σ = 0.003; e ̅ = 0.17 %) F (σ = 0.007; e ̅ = 0.52 %) T 1-hexanol/Alamine (σ = 0.003; e ̅ = 0.20 %) F (σ = 0.005; e ̅ = 0.38 %) T 1-phenylethanol/Alamine (σ = 0.004; e ̅ = 0.32 %) F (σ = 0.002; e ̅ = 0.20 %) T cyclohexanol/Alamine (σ = 0.009; e ̅ = 0.49 %) F (σ = 0.009; e ̅ = 0.68 %) T

−42.47 46.28

0.13·10−2 −0.15·10−4

1924.41 89.01

−1006.22 225.62

−1385.47 31.98

−38.53

−206.93

−261.88

−1491.63

610.40

−49.53 −3272.58

0.12·10−3 −0.56·10−3

44.37 944.53

43.44 −569.19

64.82 −2496.40

1637.86

1499.12

−1103.52

40881.2

1008.78

38.38 −1.19

−0.12·10−4 0.21·10−4

−257.59 94.01

−121.65 128.52

220.25 22.39

−6.97

−57.50

−20.57

−881.29

−2.60

165.17 185.28

0.69·10−4 0.78·10−4

80.28 −496.17

−751.22 23.78

−116.07 95.89

−4.91

360.64

74.01

−2521.67

−583.26

−320.95 −284.38

−0.31·10−4 0.96·10−5

549.14 730.53 −220.83 128.50 554.05 394.45 151.42 Pr = ln(DM); Pr0 = ln(DM0)b; σ(DM); e(D ̅ M)

−182.96

−442.12

−1015.48

35.20

−20.15 36.63

0.90·10−3 −0.79·10−5

1296.21 −10.35

−659.44 66.61

−980.92 −94.71

−20.66

−102.49

26.60

−175.70

341.46

−45.85 −5360.61

0.16·10−3 −0.91·10−3

10.59 1526.91

110.70 −809.20

33.05 −4026.28

2689.23

2442.35

−1651.87

−61.60 −17.89

0.50·10−5 −0.13·10−4

425.96 −18.36

113.84 −41.24

−356.07 −10.49

−20.14

22.96

65.59

1008.06

−61.38

−133.14 −194.21

−0.52·10−4 −0.75·10−4

−60.56 479.83

539.95 −1.27

107.84 −68.52

17.33

−326.89

−132.96

2129.98

546.79

14.05 458.44

0.25·10−5 0.17·10−4

−29.32 −37.60 12.21 −199.35 −515.08 −820.26 −22.90 Pr = ln(SM); Pr0 = ln(SM0)c; σ(SM); e(S ̅ M)

339.22

170.91

−711.96

−314.99

−8.57 9.48

0.13·10−3 0.46·10−5

205.61 −5.82

−88.47 −46.91

−143.74 −31.53

−6.71

−11.77

99.94

230.88

8.53

−8.66 134.07

−0.24·10−5 0.22·10−4

9.29 −29.56

20.65 4.10

5.65 89.21

−70.36

−59.47

11.33

−1531.14

15.80

−1.46 0.60

0.15·10−5 0.10·10−5

10.70 −6.32

1.98 −1.27

−8.33 −1.43

1.07

2.31

4.14

−9.73

1.54

1.12 4.02

−0.43·10−6 0.20·10−5

2.77 −8.84

−8.46 −2.07

−1.35 −0.34

−0.0067

7.03

3.42

−49.16

−9.98

25.68 −26.83

0.39·10−5 −0.28·10−5

−50.71 10.62

−61.45 54.63

25.71 −7.85

10.83

−21.12

18.21

142.49

30.52

66501.4

1312.25

b N e/% 56572.23 for 1-decanol; S0 = DM0 = 2922.28 (1-hexanol); S0 = ̅ = (100/N)∑i=1|(Yi,obs − Yi,mod)/Yi,obs|. S0 = DM0 = 76647.44 for 1-dodecanol; DM0 = 1322.19 (1-phenylethanol); S0 = DM0 = 442.53 (cyclohexanol). cSM0 = 0.99999 (1-dodecanol); SM0 = 0.99998 (1-decanol); SM0 = 0.99966 (1-hexanol); SM0 = 0.99924 (1-phenylethanol); SM0 = 0.99774 (cyclohexanol). dF = coefficients of 5 parameter eq 5; T = coefficients of 10 parameter eq 6. a

is a favorable type of variation of SM and FE quantities in the range from x2 = 0 (SM = SM0→1, FE = FE0→0) to x2 = xpp (SM = 1, FE = 0). As evident from these figures, the variation of the observed SM and FE factors with xiv = x″2 /x″3 exhibits a strong maximum, which leads to the observed derivatives, d(SM)/d(xiv) and d(FE)/d(xiv), changing their sign at the maximum point. Here, for interpolating

the optimum value of SM or FE, the evaluation of the maximum point based on experiments has been utilized. Figures 5 to 8 show that a zero value derivative variation of the observed SM and FE factors against xiv is reproduced. The derivatives change the sign at the maximum point. The optimization structure has been simplified through presuming that the experimental SM and FE 533



Article

Figure 5. Plot of modified separation factor (SM) against xiv for the systems (water + pyruvic acid + alcohol/Alamine). Variation of observed SM with xiv: ◊, 1-hexanol; ○, 1-phenylethanol; +, cyclohexanol, dashed line polynomial fit through eq 12. Variation of observed (d(SM)/d(xiv)) with xiv: ⧫, 1-hexanol; ●, 1-phenylethanol; ×, cyclohexanol.

Figure 7. Plot of extraction factors (FE and SM) vs xiv for the system (water + pyruvic acid + 1-decanol/Alamine). Variation of observed factors FE (★) and SM (⧫) with xiv. Variation of observed derivatives (d(FE)/d(xiv)) (×) and (d(SM)/d(xiv)) (◊) against xiv; dashed line polynomial fit through eq 12 for SM and eq 13 for FE.

Figure 6. Plot of extraction factor (FE) against xiv for the systems (water + pyruvic acid + alcohol/Alamine). Variation of observed FE with xiv: ◊, 1-hexanol; ○, 1-phenylethanol; +, cyclohexanol, dashed line polynomial fit through eq 13. Variation of observed (d(FE)/d(xiv)) with xiv: ⧫, 1-hexanol; ●, 1-phenylethanol; ×, cyclohexanol.

Figure 8. Plot of extraction factors (FE and SM) vs xiv for the system (water + pyruvic acid + 1-dodecanol/Alamine). Variation of observed factors FE (●) and SM (▲) with xiv. Variation of observed derivatives (d(FE)/d(xiv)) (○) and (d(SM)/d(xiv)) (△) against xiv; dashed line polynomial fit through eq 12 for SM and eq 13 for FE.

factors can be well-defined by a third-order polynomial expansion term, SM = p3(xiv) and FE = p3(xiv). The final approaches, eqs 12 and 13, will reflect reasonably optimum conditions.

3

3

SM =

k

∑ ak(xiv) k=0

2

3

= a0 + a1(xiv) + a 2(xiv) + a3(xiv)

FE = p3 (xiv) =

(12)

∑ ai′(xiv)i i=0

534

(13)



Article

Table 6. Coefficients ak of Polynomial Equation eq 12 and Mean Relative Errors (e/̅ %) and Optimum Conditions in Terms of SM Factor for the Systems (Water + Pyruvic Acid + Alcohol/Alamine) optimum conditionb

a

a

solvent system

a0

a1

a2

a3

e(S ̅ M) /%

xiv,max

SM,max

1-dodecanol/Alamine 1-decanol/Alamine 1-hexanol/Alamine 1-phenylethanol/Alamine cyclohexanol/Alamine

1.00204 1.00990 1.00195 1.00794 1.00754

0.11690 0.11628 0.05011 0.13088 0.14471

−0.01648 −0.00868 −0.01105 −0.08447 0.02203

0.00058 0.0 −0.00505 0.0 −0.11657

0.23 0.53 0.12 0.38 0.67

4.74 6.69 1.23 0.63 0.72

1.24765 1.39933 1.03747 1.05687 1.07964

b N e/% ̅ = (100/N)Σi=1|(SM,obs − SM,mod)/SM,obs|. Values evaluated in terms of eqs 8 and 12.

e̅

In this study, only eq 12 has been processed. The coefficients ak of eq 12 and the obtained optimum values of the SM factor are given in Table 6. The same remarks hold for the FE factor through analyzing eq 13 for a maximum. Consequently, the dimensionless factors SM and FE, and their derivatives, eqs 8 and 10, appear to be a perceptible optimization structure for analyzing an extraction system. This analytical structure is seen to improve the data fit.

F FE FE0 GE N p Pr Pr0 R S SM SM0 T Vm x0 x′i x″i xiv xpp Y

5. CONCLUSIONS LLE data for the systems (water + pyruvic acid + alcohol/ Alamine) were determined at T = 293.2 K. Table 3 shows that the selected solvents are appropriate separation agents for pyruvic acid. Among the tested alcohol/Alamine solvents, 1-dodecanol/ Alamine yields the largest separation factors. It is apparent from Table 5 that the SERLAS model with 5 and 10 parameters is presumably an effective tool for fitting LLE data, yielding an overall error of e ̅ = 4.7 % (σ = 2.48) in terms of S, DM, and SM factors. Regarding the mean errors of e ̅ = 4.3 % (σ = 2.01) for eq 6, and e ̅ = 5.2 % (σ = 2.94) for eq 5, it is concluded that SERLAS becomes a powerful method for modeling the properties of alcohol-containing extraction systems. The capability of SERLAS (eq 4) to reproduce a hump-type variation of SM quantity actually should provide an analytical structure for optimum extraction. Especially, an important concern is whether the design strategy based on SERLAS is applicable to any extraction system. As evident from Figures 2 to 4, the proposed model accurately matches the trend of variation of S, DM and SM factors. Figures 5 to 8 manifest the fact that the proposed analytical structure depending on SM and FE factors and their derivatives, eqs 8 and 10, is an effective tool for optimizing an extraction process. In fact, the optimization structure with the related derivative approaches is applicable to any extraction system.

■

Greek Letters

α; α* β, β* ΓL γ δ δH; δH* π, π* σ

max maximum mod modeled property obs observed property

AUTHOR INFORMATION

■

*E-mail: [email protected]. Fax: 90 212 4737180. Funding

The author is grateful to the Research Fund of Istanbul University for the technical support of this study (Project No. BYP-146/06012003).

REFERENCES

(1) Wisniak, J.; Tamir, A. Liquid-Liquid Equilibrium and Extraction: A Literature Source Book; Elsevier: Amsterdam, Netherlands, 1980−1981. (2) Kertes, A. S.; King, C. J. Extraction Chemistry of Fermentation Product Carboxylic Acids. Biotechnol. Bioeng. 1986, 28, 269−282. (3) Tamada, J. A.; Kertes, A. S.; King, C. J. Extraction of Carboxylic Acids with Amine Extractants. 1. Equilibria and Law of Mass Action Modeling. Ind. Eng. Chem. Res. 1990, 29, 1319−1326. (4) Letcher, T. M.; Redhi, G. G. Phase Equilibria for Mixtures of (Butanenitrile + a Carboxylic Acid + Water) at 298.15 K. Fluid Phase Equiib. 2002, 193, 123−133. (5) Senol, A. Liquid−Liquid Equilibria for Ternary Systems of (Water + Carboxylic Acid + 1-Octanol) at 293.15 K: Modeling Phase Equilibria

Notes

The authors declare no competing financial interest.

a C D DM

Solvatochromic parameters Solvatochromic parameters Thermodynamic factor Activity coefficient of a component in the organic phase Solvatochromic parameter Hildebrand solubility parameters (MPa0.5) Solvatochromic parameters Root-mean-square deviation, σ = (∑Ni=1(Yi,obs − Yi,mod)2/ N)1/2

Subscripts

Corresponding Author

■

N Mean relative error, e/% ̅ = (100/N)∑i=1|(Yi,obs − Yi,mod)/ Yi,obs| Correction factor as defined in eq 4 Extraction factor The value of FE at the extraction limit x2 = 0 Excess Gibbs free energy function (J·mol−1) Number of observations Polynomial function Property as defined in eq 4 Property as defined in eq 4 Gas constant (J·mol−1·K−1) Separation factor Modified separation factor The value of SM at the extraction limit x2 = 0 Temperature (K) Molar volume of a solute (m3·mol−1) Mole fraction of mutual solubility of a component Mole fraction of a component in the aqueous phase Mole fraction of a component in the solvent phase Dimensionless independent variable (xiv = x″2 /x″3 ) Mole fraction of a solute at the plait point Independent variable

NOMENCLATURE Coefficient of polynomial function Coefficient defined in eq 4 Distribution coefficient Modified distribution ratio 535



Article

Using a Solvatochromic Approach. Fluid Phase Equilib. 2005, 227, 87− 96. (6) Senol, A. Influence of Diluent on Amine Extraction of Pyruvic Acid Using Alamine System. Chem. Eng. Process 2006, 45, 755−763. (7) Senol, A. Liquid-Liquid Equilibria for Mixtures of (Water + Carboxylic Acid + 1-Octanol/Alamine 336) at 293.15 K. J. Chem. Eng. Data 2005, 50 (2), 713−718. (8) Ma, C. Q.; Li, J. C.; Qiu, J. H.; Wang, M.; Xu, P. Recovery of Pyruvic Acid from Biotransformation Solutions. Appl. Microbiol. Biotechnol. 2006, 70, 308−314. (9) Kamlet, M. J.; Doherty, R. M.; Abraham, M. H.; Marcus, Y.; Taft, R. W. 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. 1988, 92, 5244−5255. (10) Marcus, Y. Linear Solvation Energy Relationships: Correlation and Prediction of the Distribution of Organic Solutes between Water and Immiscible Organic Solvents. J. Phys. Chem. 1991, 95, 8886−8891. (11) Gmehling, J.; Li, J.; Schiller, M. Modified UNIFAC Model: 2. Present Parameter Matrix and Results for Different Thermodynamic Properties. Ind. Eng. Chem. Res. 1993, 32, 178−193. (12) Gmehling, J.; Rasmussen, P.; Fredenslund, A. Vapor-Liquid Equilibria by UNIFAC Group Contribution: Revision and Extension 2. Ind. Eng. Chem. Process Des. Dev. 1982, 21, 118−127. (13) Magnussen, T.; Rasmussen, P.; Fredenslund, A. UNIFAC Parameter Table for Prediction of Liquid-Liquid Equilibria. Ind. Eng. Chem. Process Des. Dev. 1981, 20, 331−339. (14) Taylor, R.; Kooijman, H. Composition Derivatives of Activity Coefficient Models (for the Estimation of Thermodynamic Factors in Diffusion). Chem. Eng. Commun. 1991, 102, 87−106. (15) Mori, H.; Oda, A.; Ito, C.; Aragaki, T.; Liu, F. Z. Thermodynamic Factors Derived from Group Contribution Activity Coefficient Models. J. Chem. Eng. Jpn. 1996, 29, 396−398. (16) Himmelblau, D. M. Basic Principles and Calculations in Chemical Engineering, 5th ed.; Prentice-Hall, Inc.: New York, 1989. (17) Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic Solvents. Physical Properties and Methods of Purification, 4th ed.; WileyInterscience: New York, 1986. (18) Barton, A. F. M. Solubility Parameters. Chem. Rev. 1975, 75, 731− 753. (19) Treybal, R. E.; Weber, L. D.; Duley, J. F. The System Acetone + Water + 1,1,2-Trichloroethane. Ternary Liquid and Binary Vapor Equilibria. Ind. Eng. Chem. 1948, 38, 817−821.

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LiquidâLiquid Equilibria for Mixtures of (Water + Pyruvic Acid + Alcohol

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