Linear Solvation Energy Relationship (LSER) Modeling and Kinetic

Using acid−base titration with 0.1 N NaOH (with a relative uncertainty of 1%) and .... to eq 20:23 where X1 is the mole fraction of the first solven...
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Ind. Eng. Chem. Res. 2006, 45, 5788-5795

Linear Solvation Energy Relationship (LSER) Modeling and Kinetic Studies on Propionic Acid Reactive Extraction Using Alamine 336 in a Toluene Solution Hasan Uslu* I˙ stanbul UniVersity, Engineering Faculty, Chemical Engineering Department, I˙ stanbul 34850, Turkey

Organic solutions of amines are being used increasingly to separate organic acids from aqueous mixture solutions via reactive extraction. The design of an amine extraction process requires kinetic data for the acid + amine + solvent system that is used. Kinetic studies for the extraction of propionic acid from aqueous solution with Alamine 336 diluted in toluene were conducted using a stirred cell for kinetic studies. Equilibria for propionic acid extraction by Alamine 336 in toluene as a diluent have been determined. All measurements were conducted at a temperature of 298.15 K. The extent to which the organic phase may be loaded with propionic acid is expressed as a loading ratio (Z). Calculations based on the stoichiometry of the reactive extraction and the equilibria that are involved indicated that more propionic acid is transferred to the organic phase than would be expected from the 1:1 stoichiometry of the reaction. The equilibrium data were also interpreted by a proposed mechanism of three reactions of complexation by which 1:1 and 2:1 acid-amine complexes are formed. The kinetics of extraction of propionic acid by Alamine 336 in toluene has also been determined. The results of the liquid-liquid equilibrium measurements were correlated by a linear solvation energy relationship (LSER) model, which takes into account physical interactions. From the regression coefficients, information on the solvent-solute interaction is obtained and solvation models are proposed. 1. Introduction Propionic acid is a general sales grade and may be used to produce numerous esters, salts, and other derivatives for use in the plastics, coatings, agricultural chemicals, food, flavor, and perfume industries. Propionic acid is a carboxylic acid. The recovery of carboxylic acids from diluent aqueous solutions, such as a fermentation broth or a wastewater stream that has an acid concentration of 99.5% purity) as a diluent). Alamine was used as supplied. 3.1. Kinetic Studies. Propionic acid (Fluka, Product No. 1150593, >99% purity) was dissolved in water to prepare the solutions with initial concentrations of acid (∼8% (1.17 mol/ L)). A comparatively low concentration range was used, because, in the practical case of acid recovery from fermentation broths, the acid concentrations are not expected to be high; equal volumes of an aqueous propionic acid solution and an organic solution of Alamine 336 were stirred for 2 h, which preliminary tests have demonstrated to be a sufficient time for equilibration. The stirring was performed in glass flasks that were immersed in a water bath at a temperature of 298.15 K. A stirred cell with a diameter of 0.07 m , a height of 0.1 m, and a flat bottom was used for the kinetic studies. An aqueous solution of propionic acid of known concentration (half of the volume of the stirred cell) was first placed in the vessel. The position of the four-blade paddle double stirrer (0.058 m in diameter and 0.01 mm in width) was adjusted to 1 cm below and above the interface. A fixed volume of the organic extractant mixture was then added and stirred. Using acid-base titration with 0.1 N NaOH (with a relative uncertainty of 1%) and phenolphthalein as an indicator, the acid concentration in the aqueous phase was determined periodically. The concentration of propionic acid in the organic phase was determined by mass balance.19 Acid analysis was checked against the material balance; the uncertainty in the results was 3%. 3.2. Equilibrium Studies. An initial concentration of propionic acid (1.17 mol/L) and different concentrations of organic phases (toluene that contained different concentrations of Alamine 336) of known concentrations were equilibrated in a temperature-controlled shaker bath for 3 h. After equilibration, both phases were separated and the aqueous phase was analyzed. The reactive component that used to determine the concentration of propionic acid was Alamine 336; the aqueous phase was titrated with 0.1 N NaOH, and phenolphthalein was used as an indicator. The acid concentrations in the organic phase were calculated by mass balance.17,18 4. Results and Discussion 4.1. Extraction Equilibria and Kinetics. Experiments were conducted to describe the physical and chemical equilibria for carboxylic acid. There is only a very slight effect, if any, of temperature in the range of 20-90 °C on the distribution ratio of carboxylic acid into alcohols, ketones, diethyl carbinol, and ethers.19 The physical equilibrium distribution coefficients were measured at 25 °C in toluene. The results are shown in Figure 1. The chemical equilibrium distribution coefficients were measured at a temperature of 25 °C for Alamine 336 concentra-

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Figure 1. Distribution coefficient of propionic acid with various ratios of Alamine 336 in toluene. Table 1. Molar Concentration of Amine in the Organic Phase, Molar Concentration of Acid in the Aqueous Phase, Molar Concentration of Acid in the Organic Phase, Distribution Coefficient, Loading Factor, and Extraction Efficiency for the Extraction of Propionic Acid with Alamine 336 in Toluene Solutiona

a

molar concentration of amine in organic phase, Ce,org (mol/L)

molar concentration of acid in aqueous phase, Ca (mol/L)

molar concentration of acid in organic phase, Ca,org (mol/L)

distribution coefficient, KD

loading factor, Z

extraction efficiency, E

2.19 1.85 1.58 1.37 1.05 0.55 0.32

0.018 0.021 0.024 0.033 0.048 0.074 0.211

1.151 1.149 1.146 1.137 1.122 1.096 0.959

63.944 54.714 47.750 34.454 23.375 14.811 4.545

0.526 0.621 0.725 0.830 1.069 1.992 2.997

98.462 98.205 97.949 97.179 95.897 93.675 81.966

The diluent used in this table of data was toluene.

tions of 0.32, 0.55, 1.05, 1.37, 1.58, 1.85, and 2.19 mol/L in toluene. The chemical equilibrium distribution coefficients are shown in Figure 1 and Table 1. Extraction efficiencies are represented in Figure 2. The extraction efficiency increased as the Alamine 336 concentration increased. The degree of extraction has been reported to increase up to an Alamine 336 concentration of 2.19 mol/L and then remain constant. In Figure 3, a plot of the logarithm of ([BHL]0/[HL]w) versus the logarithm of [B]0 should yield a straight line with a slope of unity. However, the slope is less than unity (0.8), which implies that the organic phase extracts more acid than would be expected on the basis of a 1:1 complex. The value of z is dependent on the extractability of the acid and its aqueous concentration, and it is independent of the amine content in an inert diluent:

z)

[HL]0 [B]i,0

(11)

The stoichiometry of the overall extraction reaction is dependent on the loading ratio in the organic phase, z. If the organic phase is not highly concentrated, i.e., at very low loading ratios (z < 0.5), the 1:1 complex is formed and a plot of z/(1 - z) versus

[HL]w is a straight line whose slope gives the complexation constant, KE1:

z ) KE1[HL]w 1-z

(12)

A straight line of the plot of eq 12 is shown in Figure 4 with a slope of 1.091. Hence, the equilibrium complexation constant for the 1:1 acid:amine complex at 25 °C for the extraction of propionic acid with Alamine 336 dissolved in toluene, for low concentrations of propionic acid in the organic phase, is KE1 ) 1.091 m3/kmol. For higher loading ratios, the 2:1 acid:amine complex is formed, and a plot of z/(2 - z) versus [HLW]2 should yield a straight line, whose slope gives the complexation constant for the 2:1 complex (KE2). KE2 is determined using eq 10:

z ) KE2[HL]w2 2-z

(13)

The straight-line plot of eq 13 is shown in Figure 5 with a slope of 16.884. Hence, the equilibrium complexation constant for the 2:1 complex at 25 °C for the extraction of propionic acid with Alamine 336 dissolved in toluene is KE2 ) 16.884 (m3/ kmol)2.

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Figure 2. Extraction efficiency of propionic acid with various ratios of Alamine 336 in toluene.

Figure 3. Distribution coefficient of propionic acid in Alamine 336 dissolved in toluene, as a function of the free amine concentration in the organic phase.

The value of the physical mass transfer coefficient kL is required to confirm the regime of extraction. This was obtained by conducting physical extraction (diluent only) of the propionic acid from water. For a batch process, a differential mass balance yields the following equation:

Vaq

dCorg ) kLAC(C* org - Corg) dt

(14)

Integration of this equation yields

kL )

Vaq ACt

∫0C

dCorg C*org - Corg

org

(15)

The value of kL evaluated using eq 15 for different speeds of agitation is plotted in Figure 6. The regression relation between

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Figure 4. Estimation of equilibrium complexation constant KE1 of propionic acid.

Figure 5. Estimation of equilibrium complexation constant KE2 of propionic acid.

the mass-transfer coefficient and the speed of agitation obtained by a statistical analysis data is given below.

kL ) 1.76 × 10-4N4.1

(16)

The reaction between propionic acid and Alamine 336 is reversible, particularly under conditions of high loading in the organic phase. To avoid problems due to this reversibility, only initial rates were considered for evaluation of the kinetics.

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Figure 6. Effect of various of speed agitation on the mass-transfer coefficient.

The effect of agitation on the extraction of propionic acid by Alamine 336 is determined by the mechanism that is proposed for use.20,21 The speed of agitation was varied over a range of 0.44-1.8 rev/s. In this range, the liquid/liquid interface was flat and the interfacial area for extraction was equal to the geometric area. 4.2. LSER Model. According to Kamlet et al.,22 the linear solvation energy relationship (LSER) that measures property XYZ, in terms of solvent properties, is

P(δh)2 0 XYZ ) XYZ + + s(π* + dδ) 100

(17)

P(δh)2 + s(π* + dδ) + bβ + aR 100

toluene

π*

β

R

δ

0.54

0.11

0

1

significantly. Thus, eq 18 reduces to

ln KD ) ln K0D + s(π* + dδ) + bβ + aR

(18)

where the parameters π*, δ, R, and β refer to the diluent, and KD represents the partitioning coefficients for an ideal inert diluent. The second term of eq 18, which contains the solubility parameter δh, does not affect the values of the objective function

(19)

Bizek, Horacek, and Kousova calculated the solvatochromic parameters of the solvent mixtures according to eq 20:23

SP12 ) X1SP1 + (1 - X2)SP2

where δh is the Hildebrand’s solubility parameter and π*, d, and δ are the solvatochromic parameters that measure the solute + solvent, dipole + dipole, and dipole + induced dipole interactions, respectively. The solvatochromic parameter R scale of solvent HBD (hydrogen-bond donor) acidities describes the ability of the solvent to donate a proton in a solvent-to-solute hydrogen bond. The β scale of HBA (hydrogen-bond acceptor) basicities provides a measure of the solvent’s ability to accept a proton (donate an electron pair) in a solute-to-solvent hydrogen bond. The coefficients p, s, d, a, and b include the solute properties; p, s, d, and a are regression coefficients. The values of the solvatochromic parameters π*, δ, R, and β have been found for several hundreds of compounds. Equation 17 can be adopted to describe the effect of diluents on the values of partitioning coefficients KD, in the form

ln KD ) ln K0D +

Table 2. Solvatochromic Parameters (Hydrogen-Bond Donor Acidities (π* and δ) and Hydrogen-Bond Acceptor Basicities (r and β) for Diluent Mixtures

(20)

where X1 is the mole fraction of the first solvent and X2 is the mole fraction of the second solvent. SP1 is the solvatochromic parameters of the first solvent and SP2 is the solvatochromic parameters of the second solvent in solvent mixtures. 4.3. LSER Model Results. As mentioned previously, the work of Kamlet et al.22 gives the values of solvatochromic parameters for several hundreds of compounds. Knowing the values of the parameters KD, s, d, b, and a for the given extraction system (Alamine 336 + aqueous propionic acid in this case), eq 19 allows one to estimate the partitioning coefficients for a wide range of diluents, for which a comparatively narrow confidence interval has been observed. The values of the solvatochromic parameters of toluene were taken from Table 2;23 the remaining parameters were fitted to the experimental results. Experimental results are compared to the model predictions in Table 3 and Figure 7. This gives a final correlation that indicates a good description of the distribution of propionic acid over a wide concentration range. For the optimal estimation of the model parameters, a regression-technique-assisted computer program (ANALYSE) was used to minimize the deviation between the model prediction and the experimental data. All predicted partition coefficients agree well with each other, and the agreements

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Figure 7. Comparison of the variation of the partitioning coefficient (KD) with the concentration of Alamine 336 (Ce,org) and LSER model predictions (KD′): ([) experimental data and (-b-) model data. Table 3. Molar Concentration of Amine in the Organic Phase, Experimental Results, and Model Results, for a Comparison of the Experimental Results and Model Predictionsa Distribution Coefficient, KD molar concentration of amine in organic phase, Ce,org (mol/L)

experimental results, KD

model results, KD′

2.19 1.85 1.58 1.37 1.05 0.55 0.32

63.994 54.714 47.750 34.454 23.375 14.811 4.545

70.822 52.433 38.894 28.641 28.718 13.053 5.432

a

The diluent used in this table of data was toluene.

between the predictions and measurements also are acceptable, considering the experimental uncertainty. The estimated values of parameters of the model are presented in Table 4. The experimental data shows a good correlation to the calculated values. It is been concluded that, using this model, the distribution coefficients of propionic acid between water and an amine + toluene system can be described. The system constants in Tables 2-4 reveal that the partition coefficients are strongly correlated to a solute’s partition coefficient, which means that the organic solute-amine partitioning equilibrium of a solute is strongly affected by the cavity effect and dispersive solute/amine interactions. The solute hydrogen acidity and basicity, a and b, also show a significant correlation with the partition coefficient. This confirms that the organic solvent serves as both a hydrogen donor and a hydrogen acceptor. The relative size of the standardized system constants (β), which are the regression coefficients derived from standardized dependent variables, relays information pertaining to the

relative importance of different types of solute/solvent interactions. This suggests that the strength of the interaction decreases from dispersive interactions to hydrogen bonding, to solute/ solvent σ/π electron pair interactions, to solute/solvent dipolarity/ polarizability interactions. The values of the distributions coefficients can be correlated with the solvatochromic parameters of the toluene π*, δ, R, and β, according to eq 19. The resulting fitting curves are included in Figure 7. The resulting LSER regression is

ln KD ) 5.004 + 114.1392 (π* - 0.4614δ) + 0R - 105.3173β (21) This equation was used to predict the value of ln KD for the organic solutes, which had been studied by Hilal et al.24 5. Conclusion The objective of this study was to determine the extractability of propionic acid by Alamine 336 that has been dissolved in toluene. Some physical and chemical equilibria for propionic acid extraction by Alamine 336 in toluene as a diluent have been determined. The loading of the extractant (Z) is defined as the total concentration of acid in the organic phase, divided by the total concentration of amine in the organic phase. Calculations based on the stoichiometry of the reactive extraction and the equilibria involved indicated that more propionic acid is transferred to the organic phase than would be expected from a 1:1 stoichiometry of the reaction. The extraction equilibrium was interpreted as a result of consecutive formation of two acid-amine species with stoichiometries of 1:1 and 2:1. Equilibrium complexation constants

Table 4. Values of the LSER Model Parameters (S, d, b, a), the Coefficient of Linear Regression (R2), and the Standard Error (SE) models

ln K0D

S

LSER model parameters

5.004

114.1392

LSER Model Parameters d a - 0.4614

0

b

coefficient of linear regression, R2

standard error, SE

-105.3173

0.88

0.33

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(K11 and K21) have been determinated. The mass-transfer coefficients (kL) were obtained by diffusion. Note Added after ASAP Publication. The version of this paper that was published on the Web July 12, 2006 had errors regarding the in-text equations for eqs 15-20. The correct version was published on the Web July 12, 2006. Literature Cited (1) Baniel, A. M.; Blumberg, R.; Hadju, K. Recovery of acids from aqueous solutions. U.S. Patent No. 4,275,234, June 23, 1981. (2) Hong, Y. K.; Hong, W. H. Reactive extraction of lactic acid with mixed tertiary amine extractants. Biotechnol. Technol. 1999, 13, 915. (3) Kertes, A. S.; King, C. J.; Extraction chemistry of fermentation product carboxylic acids. Biotechnol. Bioeng. 1986, 28, 269. (4) Ricker, N. L.; Pittman, E. F.; King, C. J. Solvent extraction with amines for recovery of acetic acid from dilute aqueous industrial streams. J. Sep. Process. Technol. 1980, 1, 23. (5) I˙ nci, I˙ . Extraction of of aqueous solution of gluconic acid with organic solutions of Alamine 336. Chem. Biochem. Eng. Q. 2002, 16, 185. (6) Yang, S. T.; White, S. A.; Hsu, S. T. Extraction of Carboxylic Acids with Tertiary and Quaternary Amines: Effect of pH. Ind. Eng. Chem. Res. 1991, 30, 1335. (7) Kyuchoukov, G.; Marinova, M.; Molinier, J.; Albet, J.; Malmary, G. Extraction of Lactic Acid by Means of a Mixed Extractant. Ind. Eng. Chem. Res. 2001, 40, 5635. (8) Wennersten, R. The Extraction of Malic Acid from Fermentation Broth Using a Solution of Tertiary Amine. J. Chem. Technol. Biotechnol. 1983, 33, 85-94. (9) Han, D. H.; Hong, W. H. Reactive extraction of lactic acid with trioctylamine/methylene chloride/n-hexane. Sep. Sci. Technol. 1996, 31, 1123. (10) San-Martin, M.; Pazos, C.; Coca, J. Reactive extraction of lactic acid with Alamine 336 in the presence of salts and lactose. J. Chem. Technol. Biotechnol. 1992, 54, 1. (11) Senol, A. Extraction Equilibria of Formic, Levulinic and Acetic Acids Using (Alamine 336/Diluent) and Conventional Solvent Systems: Modelling Consideration. J. Chem. Eng. Jpn. 1999, 32, 717. (12) Kirsch T.; Maurer G.; Distribution of Oxalic Acid Between Water and Tri-n-Octylamine. Ind. Eng. Chem. Res. 1996, 35, 1722.

(13) Chaikorski, A. A.; Niklskii, B. P.; Mikhailov, B. A. Complex Formation in Nonaqueous Solutions X. Interaction of Tridecylamine with Citric Acid. SoV. Radiochem. 1966, 152. (14) Inci, I.; Uslu H.; Extraction of Glycolic Acid from Aqueous Solutions by Trioctyl Methylammonium Chloride and Organic Solvents. J. Chem. Eng. Data 2005, 50, 536. (15) Inci I.; Liquid-Liquid Equilibria of Gluconic Acid Between Water and Tri-n-Octlyamine in various Diluents. Asian J. Chem. 2002, 14, 1711. (16) San-Martin, M.; Pazos, C.; Coca, J. Reactive extraction of lactic acid with Alamine 336. J. Chem. Technol. Biotechnol. 1996, 65, 281. (17) Tamada, J. A.; King, C. J. Extraction of Carboxylic Acids with Amine Extractants. 2. Chemical Interactions and Interpretation of Data. Ind. Eng. Chem. Res. 1990, 29, 1327. (18) 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. (19) Doraiswamy, L. K.; Sharma, M. M. Fluid-Fluid-Solid-Reactions, First Edition; Heterogeneous Reaction: Analysis, Examples, and Reactor Design, Vol. 2; Wiley: New York, 1984; p 17. (20) Wasewar, K. L.; Heesink, A. B. M.; Versteeg, G. F.; Pangarkar, V. G. Reactive extraction of lactic acid using Alamine 336 in MIBK: equilibria and kinetics. J. Biotechnol. 2002, 97, 59. (21) Wasewar, K. L.; Yawalkar, A. A.; Moulijn, J. A.; Pangarkar, V. G. Fermantation of Glucose to Lactic Acid Coupled with Reactive Extraction. A Review. Ind. Eng. Chem. Res. 2004, 43, 5969. (22) Kamlet, M. J.; Abboud, J.-L. M.; Abraham, M. H.; Taft, R. W. Linear Solvation Energy Relationships. 23. A Comprehensive Collection of the Solvatochromic Parameters, π*, R, and β, and Some Methods for Simplifying the Generalized Solvatochromic Equation. J. Org. Chem. 1983, 48, 2877. (23) Bizek, V.; Horacek, J.; Kousova, M. Amine Extraction of Citric Acid: Effect of Diluent. Chem. Eng. Sci. 1993, 48, 1447. (24) Hilal, S. H.; Karickhoff, S. W.; Carreira, L. A. Prediction of the solubility, activity coefficient and liquid/liquid partition coefficient of organic compounds. QSAR Comb. Sci. 2004, 23, 709-720.

ReceiVed for reView April 11, 2006 ReVised manuscript receiVed June 3, 2006 Accepted June 10, 2006 IE060453Y