Extractive Separation of Pentanedioic Acid by Amberlite LA-2 in

Article pubs.acs.org/jced

Extractive Separation of Pentanedioic Acid by Amberlite LA‑2 in Various Solvents Hasan Uslu,*,†,‡ Hisham S. Bamufleh,‡ Amit Keshav,§ Dharm Pal,§ and Göksel Demir∥ †

Beykent University, Engineering & Architecture Faculty, Chemical Engineering Department, 34500 Istanbul, Turkey Department of Chemical & Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah 21589, Saudi Arabia § Department of Chemical Engineering, National Institute of Technology, Raipur, Chhattisgarh 492010, India ∥ Department of Urban and Regional Planning, Architecture Faculty, Kırklareli University, 39020 Kırklareli, Turkey ‡

S Supporting Information *

ABSTRACT: Reactive extraction of pentanedioic acid using Amberlite LA-2 in different diluents, such as hexane, methylbenzene, kerosene, 4-methyl-2-pentanone, 2,6-dimethyl4-heptanone, n-hexanone, 3-methyl-1-butanol, n-octanol, nnonanol, and n-decanol, respectively, was studied. At lower amine concentrations, KD values of less than 1 were obtained but it improves as amine concentration was raised. Increase in amine concentration was found to increase the KD by 80−85% in inert diluents (hexane, methylbenzene and kerosene). In the chosen ketones, the extraction percentage follows the following trend 4methyl-2-pentanone > DIBK > n-hexanone. Among the various diluents used, higher KD was obtained when alcohols were used as diluents. Mass action equilibria, linear solvation energy relationship modeling, and differential evolution (DE) was applied for estimating the model parameter and compare the model values with the experimental results of extraction equilibria.

1. INTRODUCTION Pentanedioic acid is an important dicarboxylic organic acid. It is produced in the body by metabolism of amino acid using tryptophan and tryphophern. Naturally, it occurs in green sugar beets and in water extracts of crude wool. To produce pentanedioic acid (via butyrolactone) potassium cyanide is reacted to form potassium carboxylate-nitrile which gives diacid after hydrolysis. Otherwise, pentanedioic can also be produce by hydrolysis, followed by oxidation of dihydropyran.1 It is also produced in 4−9% in the production of adipic acid2 along with succinic and adipic acid. Denitrification of adipic acid mother liquor (through oxidiation of cyclohexanol with nitric acid using catalyst), the waste in the form of succinic and pentanedioic acid is produced. This waste is usually discarded and it is important that these acids must be recovered before discharge. Numerous techniques have been applied to recover adipic, succinic, and pentanedioic acid from the waste stream looking at the advantage that the pentanedioic acid is more soluble than the corresponding linear dicarboxylic acids such as adipic and succinic acid (50%). According to Konno et al.3 adipic acid may be extracted, for example, with cyclohexanol and cyclohexanone. According to Nishikido et al.,4 pentanedioic and succinic acid form adducts with urea, from which adipic acid can be separated. The conversion of pentanedioic and succinic acids into imides and their separation has also been described.5 © XXXX American Chemical Society

The reaction with alkyl amine converts pentanedioic and succinic acid into amides, which are then separated from adipic acid. Mims,6 describes the esterification of dicarboxylic acids and the workup and separation of the resultant esters. Various crystallization processes have also been described in the literature. For the recovery of adipic acid from the byproducts, Moore7 describes a simple cooling crystallization. Experiments have shown, however, that the efficiency of such a process is unsatisfactory for carrying out on a technical scale because the quantity which crystallizes is too small, a large quantity of succinic acid crystallizes at the same time, heavy deposits cake to the walls of the vessels and cooling coils, and the speed of crystallization is too low because the solution frequently remains supersaturated even after about 3 h. Pentanedioic acid has wide number of uses. It finds application in the polymers like, polyester polyols, polyamines. Pentanedioic acid and its derivatives is also used for the production of 1,5-pentanediol (plasticizer). Mc Namara et al.1 has demonstrated the improvement in the oral bioavailability of the API in dogs by crystalline molecular complex of Received: February 17, 2016 Accepted: June 7, 2016

A

DOI: 10.1021/acs.jced.6b00141 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Table 1. Experimental Results for Pentandioic Acid Extraction by Amberlite LA-2 in Diluents

3-methyl-1-butanol

n-octanol

n-nonanol

n-decanol

methylbenzene

kerosene

methyl ethyl ketone

diisobutyl ketone

n-hexane

2-hexanone

a

Caqb (mol·kg−1)

pH

Camine (mol·kg−1)

KD

E%

Z

0.27 0.25 0.17 0.14 0.11 0.10 0.35 0.26 0.20 0.15 0.10 0.06 0.41 0.31 0.26 0.21 0.13 0.07 0.41 0.34 0.28 0.21 0.16 0.10 0.43 0.36 0.30 0.21 0.15 0.10 0.52 0.45 0.37 0.30 0.22 0.15 0.27 0.24 0.21 0.16 0.12 0.09 0.40 0.34 0.27 0.20 0.15 0.09 0.48 0.45 0.38 0.32 0.25 0.18 0.53 0.47 0.40 0.34 0.26 0.19

2.66 2.67 2.76 2.8 2.85 2.87 2.60 2.67 2.72 2.79 2.87 2.99 2.57 2.63 2.67 2.71 2.82 2.95 2.57 2.61 2.65 2.71 2.77 2.87 2.56 2.59 2.63 2.71 2.79 2.87 2.51 2.55 2.59 2.63 2.70 2.79 2.66 2.68 2.71 2.77 2.83 2.90 2.57 2.61 2.66 2.72 2.79 2.90 2.53 2.55 2.58 2.62 2.67 2.75 2.51 2.54 2.57 2.61 2.67 2.73

0.24 0.47 0.71 0.94 1.18 1.41 0.24 0.47 0.71 0.94 1.18 1.41 0.24 0.47 0.71 0.94 1.18 1.41 0.24 0.47 0.71 0.94 1.18 1.41 0.24 0.47 0.71 0.94 1.18 1.41 0.24 0.47 0.71 0.94 1.18 1.41 0.24 0.47 0.71 0.94 1.18 1.41 0.24 0.47 0.71 0.94 1.18 1.41 0.24 0.47 0.71 0.94 1.18 1.41 0.24 0.47 0.71 0.94 1.18 1.41

2.09 2.37 3.81 5.00 6.32 7.47 1.42 2.24 3.23 4.62 7.09 13.45 1.03 1.67 2.22 3.05 5.60 10.54 1.06 1.47 1.97 2.94 4.37 7.47 0.93 1.32 1.82 2.90 4.45 7.47 0.59 0.87 1.24 1.77 2.73 4.56 2.10 2.46 3.06 4.21 5.89 7.89 1.08 1.45 2.12 3.10 4.65 7.96 0.73 0.88 1.19 1.65 2.37 3.62 0.58 0.78 1.12 1.47 2.17 3.30

68.95 71.54 80.06 84.03 86.89 88.68 60.40 70.43 77.33 82.95 88.14 93.36 52.86 64.09 70.25 76.32 85.46 91.69 53.44 61.26 67.74 75.68 82.14 88.68 50.25 58.60 65.96 75.41 82.41 88.68 39.86 48.60 57.17 65.40 74.31 82.77 69.04 72.28 76.41 81.59 86.09 89.21 54.01 60.88 69.32 76.60 83.04 89.30 44.60 48.89 56.12 63.80 71.54 79.24 39.47 46.16 54.68 61.26 69.78 77.69

2.41 1.25 0.94 0.74 0.61 0.52 2.09 1.23 0.91 0.73 0.62 0.55 1.81 1.11 0.82 0.67 0.60 0.54 1.83 1.06 0.79 0.66 0.58 0.52 1.71 1.01 0.77 0.66 0.58 0.52 1.33 0.83 0.66 0.57 0.52 0.49 2.41 1.27 0.89 0.72 0.61 0.53 1.85 1.05 0.81 0.67 0.59 0.53 1.50 0.83 0.64 0.55 0.50 0.46 1.31 0.78 0.63 0.53 0.49 0.46

B



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Table 1. continued a

Caq is the concentration of acid in the aqueous phase after extraction. Camine is the concentration of amine in the organic phase. KD is the distribution coefficient. E is the extraction efficiency. Z is the loading factor. bStandard uncertainties u are u(Caq) = 0.01, u(pH) = 0.1.

Erlenmeyer flaks. Sample were equilibrated for 6 h in a constant temperature water bath shaker at 298 K at 40 rpm speed. Then, samples were kept for settling for at least 2 h at the same temperature in a incubator. Equilibrium time (6 h) was determined by few preliminary tests, which is the sufficient time for the achievement of equilibrium. Concentration of acid left in the aqueous phase at equilibrium has been determined by titration with 0.1 N NaOH. During titration, analysis relative uncertainty was within ±3%. Organic phase acid concentration was determined by mass balance.

pentanedioic. So, it has been important to look out for a technique to recover the acid from the waste stream. In the literature organic solvents like oxygen-bearing and hydrocarbon extractants; organo phosphorus compounds; high molecular weight aliphatic amines have been reported for the recovery of carboxylic acids. However, in case of separation from dilute streams, conventional solvents such as ketones, ethers, aliphatic hydrocarbons etc. were found not effective due to low distribution coefficients obtained. Relative few studies on effect of type of diluents on the extractive recovery of carboxylic acid have been found in the literature. However, there is no work reported on the extraction of pentanedioic acid. Reactive extraction of dicarboxylic acid such as oxalic, malonic, succinic, and adipic acids using different amines has been widely studied in the literature.8−11 Zhou et al.,8 performed batch extraction experiments of several saturated aliphatic dicarboxylic acids namely oxalic, malonic, succinic, and adipic acids by a tertiary amine extractant in 1-octanol. 1:2 Acid:amine complexation was observed and was quantitatively shown by FT-IR spectral analysis. Extraction ability of the aicds was found to depend on pKa1 values of the acids. They concluded that stronger acids can obtain greater extraction abilities in TOA/1-octanol systems. Hong and Hong9 studied the reactive extraction of succinic acid from aqueous solutions with various tertiary amines dissolved in 1-octanol and nheptane, as a function of the acid concentration and the chain length of tertiary amine. In reactive extraction with tertiary amines in 1-octanol, the extractability and loading was found proportional to the chain length of amine. Uslu and Kirbaslar11 studied the reactive extraction of malic acid from aqueous solution using a secondary amine (Amberlite LA-2) in five different esters (dimethyl phthalate, dimethyl adipate, dimethyl succinate, dimethyl glutarate, diethyl carbonate), five different alcohols (3-methyl-1-butanol, hexan-1-ol, octan-1-ol, nonan-1ol, decan-1-ol) and two different ketones (2,6-dimethyl-4heptanone (DIBK), 4-methyl-2-pentanone (MIBK)) and found that 3-methyl-1-butanol as diluents provided the highest extraction efficiency value of 98.82%. In the present paper, effect of different diluents (n-hexane, methylbenzene(toluene), kerosene, 4-methyl-2-pentanone (MIBK), 2,6-dimethyl-4-heptanone (DIBK), n-hexanone, 3methyl-1-butanol(isoamyl alcohol), n-octanol, n-nonanol and ndecanol) on the recovery of pentanedioic acid was studied using Amberlite LA-2 (secondary amine) as extractant. Amberlite LA-2 (secondary amine) was used as extractant. Concentration of Amberlite LA-2 was varied from 0.24 to 1.41 mol/L in various diluents. Acid concentration was fixed to be 0.83 mol/L.

3. THEORY In the present paper, an attempt has been made to visualize the effect of concentration of Amberlite LA-2 and effect of various diluents for the reactive extraction of pentanedioic acid. Mass action equilibria modeling was explained based on the uptake of acid ([HA]aq) by chemical complexation between acid and Amberlite LA-2 ([T]org) is not certain as here in this case high concentrations of acid and amine have been employed. However, it can be assumed that acid could form different types of complexations with amine depending on the type of interaction such as K11

[HA]aq + [T]org ↔ [T: HA]org

(1)

K 21

[HA]aq + [T: HA]org ← → [T: (HA)2 ]org

(2)

K n1

[HA]aq + [T: (HA)n − 1]org ← → [T: (HA)n ]org

(3)

Complexation of acid with Amberlite LA-2 determines the type of complex formation (1:1, 2:1, or 3:1 of acid:Amberlite LA-2). For (n:1) complexation, equilibrium constant (KEn) can be defined as KEn =

[T: (HA)n ]org [T]o;org [HA]naq

(4)

KEn is the function of the natureof the acid and the solvation efficiency of the used diluent. Degree of extraction (E%) in term of KD can be calculated as E% =

KD × 100 1 + KD

(5)

Further, loading ratio (z) is the measure of extent of loading of the organic phase (amine + diluent) with carboxylic acid and can be formulated as z=

2. MATERIALS AND METHOD 2.1. Materials. Amberlite LA-2 (density = 0.83 g/mL, CAS No.: 11128-96-4), pentanedioic acid (moleculer weight = 132.11 g/mol, CAS No: 110-94-1) and the diluents were purchased from the Sigma-Aldrich Company. Chemicals used were with purities >98% and were used as received. 2.2. Methods. Initial concentration of aqueous acid was prepared as 0.84 mol·kg−1 (8% in mass). Aqueous and organic phases were taken in equal volumes (30 mL each) in an

[HA]org [T]o;org

(6)

In eq 6, the extractability of the acid (strength of the acid−base interaction) and its aqueous concentration12−14 will govern the z value. Using loading ratio in the organic phase, z, the stoichiometry of the overall extraction reaction can be predicted. In the present case, because in most of the cases, high loadings were obtained, this signifies that more than 1:1 acid−amine complexation is possible and there is possibility of different associations. C



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4. RESULTS AND DISCUSSION 4.1. Effect of Extractant and Diluents on Reactive Extraction of Pentanedioic Acid. Effect of Amberlite LA-2 concentration on the reactive extraction in various dilutents, nhexane, methylbenzene, kerosene, methyl isobutyl ketone, diisobutyl ketone, n-hexanone, 3-methyl-1-butanol, n-octanol, n-nonanol, and n-decanol, respectively, were presented in Table 1 and Figures 1−3.

study, K D values are less than 1. At higher amine concentrations, approximately, double extraction was obtained in Amberlite LA-2−methylbenzene system compared to Amberlite LA-2−hexane system. Amberlite LA-2−kerosene solvent system provides intermediate KD values when compare with Amberlite LA-2−methylbenzene and Amberlite LA-2− hexane system. At lower amine concentrations, KD values of less than 1 were obtained but it improves as amine concentration was raised. The highest KD of 4.56 was obtained at higher amine concentration employed. In all the three diluents, increase in amine concentration was found to increase the KD by 80−85% in the range of amine concentrations employed in the present study. Loading ratios were found to be high at low amine concentration but reduces to about 0.5 as amine concentration was raised. Maximum loading ratio between 1 and 2 was obtained in the Amberlite LA-2 and hexane, kerosene, and methylbenzene systems, respectively. Methyl isobutyl ketone (MIBK), diisobutyl ketone (DIBK), and n-hexanone belong to the category of ketones. In the chosen ketones, the extraction percentage follows the following trend MIBK > DIBK > n-hexanone (Figure 2). In all the ketones, increase in Amberlite LA-2 concentration was found to increase KD. KD increases from 2.10 to 7.89, 1.08 to 7.96, and 0.58 to 3.30 as Amberlite LA-2 concentration was raised from 0.57 to 0.74, 0.44 to 074, and 0.31 to 0.64 mol·kg−1, respectively, in MIBK, DIBK, and n-hexanone. Highest E% (89.21%) was obtained using 0.75 mol/L Amberlite LA-2 in MIBK. Loading was found to lower down as the concentration of Amberlite LA-2 was raised. A 65−70% decrease in loading was observed as Amberlite LA-2 concentration was raised in the three diluents, respectively. Though at higher amine concentrations higher extractions were obtained in MIBK compared to DIBK, however, at higher concentration there is no significant difference in KD among the two. A 58−72% lower KD was observed in n-hexanone compared to MIBK. There is a uniform decrease in all Amberlite LA-2 concentrations in among nhexanone and MIBK. The trend in extraction follows the increase in water solubility of the diluents where there is possibility that Amberlite LA-2−pentanedioic acid complex may be transferred in association with water molecule (solubility of MIBK = 18.1 g·dm−3, DIBK = 0.43 g·dm−3, and n-hexanone = 14 g·dm−3). Also, the low viscosity of MIBK could have provided higher solvation of the complexes. (viscosity of MIBK = 0.58 cP, DIBK = 1.05 cP, and nhexanone =0.63 cP). Study reported that the close values of Hansen solubility parameter (polarity (δp), dispersion (δd), and hydrogen bonding (δh)) values of a diluent (here, MIBK) and solute (here, pentanedioic acid) could also provide the evidence of more solubility of amine−acid complexes. Higher δp values of MIBK (δp = 3) compared to other two diluents (DIBK, δp = 1.8) could provide evidence of higher solvation of acid−amine complexes MIBK. Four different alcohols (3-methyl-1-butanol, n-octanol, nnonanol, and n-decanol) were used with Amberlite LA-2 as solvent system. KD increases from 70 to 90% as the concentration of Amberlite LA-2 was raised in the range employed in the study. Lower alcohols provide higher KD at all amine concentrations (with exception of high amine concentration in 3-methyl-1-butanol, where value lower than the other alcohols were obtained but it may be due to experimental error). KD as high as 13.45 (using 1.41 mol·kg−1 Amberlite LA-

Figure 1. Effect of amine concentration on the KD for reactive extraction of pentandioic acid using various diluents.



Hexane being aliphatic hydrocarbon, solvates the acid-amine complex based on dispersion forces, provides lowest KD. At all amine concentrations, KD < 1 suggests that Amberlite LA-2− hexane system is poor solvent system for extraction of pentanedioic acid. Methylbenzene provides higher KD than hexane but still at lower amine concentrations employed in the D



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Figure 4. Comparison between experimental and model points in the extraction of pentandioic acid using Amberlite LA-2 in (a) alcohols and (b) MIBK, hexane, and kerosene.

Table 2. LSER Model Equation for Extraction of Pentandioic Acid Using Amberlite LA-2 in Various Diluents amine concentration (mol·kg−1)

model equations

RSMD

0.24

ln KD = − 0.439 + 0.334(π * + 0.996δ) − 1.338β + 2.264α

1.79

0.47

ln KD = − 0.147 + 0.097(π * + 5.198δ) − 1.179β + 2.261α

0.71

ln KD = 0.168 + 0.133(π * + 3.478δ) − 0.929β + 2.030α

0.94

ln KD = 0.522 + 0.293(π * + 1.571δ) − 0.694β + 1.687α

1.18

ln KD = 0.919 − 0.124(π * − 5.989δ) − 0.909β + 2.117α

1.41

ln KD = 1.404 − 0.287(π * − 2.879δ) − 0.582β + 1.841α

R2

solvatochromic parameters, respectively. An “ideal inert” diluent’s extraction constant is represented by the KD0. The ability of the solvent to donate a proton in a solvent to solute hydrogen bond is described by solvatochromic parameter α scale of solvent HBA (hydrogen-bond donor) acidities. The β scale of HBA (hydrogen-bond acceptor) basicities is a measure of ability to accept a proton (donate an electron pair) by the solvent’s in a solute to solvent hydrogen bond, respectively. Parameters p, s, d, and a are regression coefficients. The values of solvatochromic parameters π*, δ, α, and β have been found for the diluents used in the study. The solubility parameter, δh, has no significant effect on the values of the objective function. Therefore, eq 7 reduces to

2) could be achieved. Among the various diluents used, higher KD were obtained when alcohols were used as diluents. 4.2. Modeling. To find out the best model for the reactive extraction of pentanedioic acid using Amberlite LA-2, two different models were applied. Mass action equilibria have been considered as base model and the experimental data is subject to two different models for verification. 4.2.1. Linear Solvation Energy Relationship Modeling. To describe the effect of diluents on the distribution coefficients, KD, the linear solvation energy relationship (LSER) model15−17 was used ln KD = ln KD0 + P(δ h)2 /100 + s(π * + dδ) + bβ + aα (7)

where Hildebrand’s solubility parameter was denoted by δh and the solute + solvent, dipole + dipole, and dipole + induced dipole interactions were measured by π*, d, and δ

ln KD = ln KD0 + s(π * + dδ) + bβ + aα E

(8)



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Table 3. Differential Evolution Model Parameters for Extraction of Pentandioic Acid Using Amberlite LA-2 in Various Diluents diluent

KD

KDCalculated

isoamy lalcohol

2.09 2.37 3.81 5 6.32 7.47 1.42 2.24 3.23 4.62 7.09 13.45 1.03 1.67 2.22 3.05 5.6 10.54 1.06 1.47 1.97 2.94 4.37 7.47 0.93 1.32 1.82 2.9 4.45 7.47

1.25 1.89 2.62 3.60 4.81 5.78 0.37 2.03 2.92 4.37 7.09 13.45 0.26 0.85 1.59 2.89 5.60 10.54 0.28 0.73 1.46 2.77 3.76 5.57 0.25 0.66 1.47 2.75 4.30 5.56

n-octanol

n-nonanol

n-decanol

methylbenzene

statistical check RMSD = 1.25 NRMS D = 0.27 R2 = 0.714 Q2 = 0.592

RMSD = 0.85 NRMSD = 0.11 R2 = 0.992 Q2 = 0.984

RMSD = 0.52 NRMSD = 0.05 R2 = 0.974 Q2 = 0.970

RMSD = 0.95 NRMSD = 0.18 R2 = 0.832 Q2 = 0.811

RMSD = 0.88 NRMSD = 0.16 R2 = 0.857 Q2 = 0.845

KECalculated

nCalculated

1.069 1.249 1.556 1.804 2.021 2.163 1.140 1.214 1.400 1.562 1.876 2.427 0.787 0.957 0.973 1.149 1.640 2.183 0.832 0.806 0.850 1.112 1.228 1.515 0.645 0.663 0.829 1.052 1.274 1.499

1.50 1.47 1.43 1.47 1.36 1.36 1.49 1.48 0.96 1.41 0.50 0.50 1.50 1.48 1.48 1.41 0.50 0.50 1.47 1.48 1.38 1.49 0.58 0.59 1.43 1.43 1.30 1.05 0.54 0.63

diluent kerosene

methyl ethyl ketone

diizo butyl ketone

n-hekzan

2-hekzanone

KD

KDCalculated

0.59 0.87 1.24 1.77 2.73 4.56 2.1 2.46 3.06 4.21 5.89 7.89 1.08 1.45 2.12 3.1 4.65 7.96 0.73 0.88 1.19 1.65 2.37 3.62 0.58 0.78 1.12 1.47 2.17 3.3

0.83 0.41 0.68 1.75 2.98 4.56 0.54 1.35 2.21 4.04 5.89 7.89 0.89 0.73 1.68 3.06 4.65 7.96 0.19 0.49 1.29 1.57 2.37 3.62 0.17 0.42 0.72 1.42 2.17 3.30

statistical check RMSD = 32 NRMS D = 0.08 R2 = 0.944 Q2 = 0.941

RMSD = 0.85 NRMSD = 0.11 R2 = 0.969 Q2 = 0.824

RMSD = 0.35 NRMSD = 0.05 R2 = 0.977 Q2 = 0.970

RMSD = 0.27 NRMSD = 0.08 R2 = 0.924 Q2 = 0.849

RMSD = 0.27 NRMSD = 0.08 R2 = 0.911 Q2 = 0.831

KECalculated

nCalculated

0.307 0.251 0.411 0.629 0.922 1.346 1.462 1.348 1.307 1.469 1.690 1.894 0.799 0.764 0.993 1.204 1.454 1.903 0.458 0.268 0.345 1.342 0.780 1.115 0.339 0.199 1.642 1.228 0.692 1.022

1.50 1.50 1.31 1.10 0.50 0.50 1.45 1.39 1.49 1.16 0.50 0.50 1.39 1.43 1.39 1.40 0.50 0.50 1.47 1.29 1.50 0.50 0.50 0.50 1.47 1.42 1.43 0.43 0.50 0.50

search for the most appropriate strategy and to tune its associated parameter values. However, certain guidelines have been available for choosing the parameters such as population size should be 5−10 times the values of dimension of each vector; the scaling factor can be chosen initially to be 0.5, and crossover rate may be chosen as 0.9 in the initial guess. Assuming the objective function is to be minimized; having D dimension, the scaling factor and crossover rate is specified to carry out the process of optimization. Steps performed while exercising differential evolution is explained below. Step 1: Population Generation. Here, we generate (PnxD) random numbers between the entire ranges of the function; now by mapping random numbers over the range, we generate Pn random vectors each of dimension D. The range used here must be linearized from 0 to 1 Step 2: Target Vector Selection. Random numbers are generated from 0 to 1. By using linear mapping rule it is to be decided which population member from Pn is to be selected as target vector (Xi). Step 3: Determination of Weighted Difference. From the population of Pn, it is to be decided two members are selected at random (X1, X2). Vector difference between the two members is evaluated and the result is multiplied to weight factor (W), therefore

Model predicted results were compared with experimental data (Figure 4). Root-mean-square deviation (RMSD) and normalized root-mean-square deviation (NRMSD) has been applied to check the consistency of model with the experimental values. RMSD and NRMSD for n-octanol, ndecanol, 3-methyl-1-butanol, n-nonanol, methyl isobutyl ketone, methylbenzene, n-hexane, and kerosene was obtained to be 1.78, 0.46, 1.25, 0.34, 0.14, 0.05, 0.23, 0.22 and 0.22, 0.06, 0.14, 0.03, 0.02, 0.01, 0.06, 0.06, respectively. Computed R2 values of the fit of equation is obtained to be 0.81, 0.95, 0.79, 0.99, 0.99, 0.98, 0.94, and 0.97 for reactive extraction using extractant in n-octanol, n-decanol, 3-methyl-1-butanol, nnonanol, methyl isobutyl ketone, methylbenzene, n-hexane, and kerosene, respectively. It can be seen that there was a good description of the distribution of pentanedioic acid using LSER model with coefficient of linear regression value of 0.99. Thus, LSER model successfully predict the equilibrium behavior of pentanedioic acid extraction using Amberlite LA-2 in various diluents. Model parameter equation was presented in Table 2. 4.2.2. Differential Evolution Modeling. Differential evolution (DE) is a population-based efficient and powerful optimization technique that can be widely applied in many engineering problems.18 Many vector generation strategies exist in DE, however, a few could be suitable for solving a particular problem.19 In DE, three critical control parameters are involved, that is, population size, scaling factor, and crossover rate. The optimization performance of the DE may influence significantly by these parameters. Thus, for solving a specific optimization problem at hand, a trial-and-error is required to

weighted difference = W (X1 − X 2)

Step 4: Noisy Random Vector. Here, third random vector is to be selected from the population of Pn. This random vector F



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(X3) to be added to the weighted difference to obtain noisy random vector (X′3), hence

2. Methylbenzene provides higher KD than hexane, but still, at lower amine concentrations employed in the study, KD values are less than 1. 3. Amberlite LA-2-kerosene solvent system provides intermediate KD values when compare with Amberlite LA-2-methylbenzene and Amberlite LA-2-hexane system. 4. Loading ratios were found to be high at low amine concentration but reduces to about 0.5 as amine concentration was raised 5. In the chosen ketones, the extraction percentage follows the following trend MIBK > DIBK > n-hexanone 6. Though at higher amine concentrations higher extractions were obtained in MIBK compared to DIBK, however at higher concentration there is no significant difference in KD among the two. 7. KD increases from 70 to 90% as Amberlite LA-2 concentration was raised in the four different alcohols (3-methyl-1-butanol, n-octanol, n-nonanol, and n-decanol) were used with Amberlite LA-2 as solvent system. 8. KD as high as 13.45 (using 1.41 mol/L Amberlite LA-2) could be achieved when alcohols were used as diluents. 9. Data obtained experimentally were compared with modeled values. A good account of the distribution of pentanedioic acid using different models with coefficient of linear regression value of 0.99 for LSER Model. 10. KE and n values have been calculated using DE approach using the program built up in MATLAB.

noisy random vector(X ′3 ) = (X3) + W (X1 − X 2)

The program methodology is as follows: 1. Initialize all DE parameters like size of population, crossover ratio, weight factor, number of iterations, number of variables, and boundary value of variables. 2. Initialize population matrix of size 1 more than number of variables with random values between minimum and maximum values of parameters. 3. Initialize best population member ever and best population member ever to gain speed. 4. After initialization, evaluate the best by starting with first population member and comparing it with other members. Save the location of best member evaluated. 5. Fill the population matrix with best members. For this, save the old population matrix, select a random member that will compete with the old population member, shuffle its location in case of success. By the end of iterations, population matrix will be filled with best population members. 6. Perform crossover. Select the vectors which are allowed to enter the new population. Check the cost of the competing member. Replace the old member with the new one and update the objective function’s value in case of success. 7. Return the value of best member, weight factor, crossover ratio, and population. 8. Repeat steps 5 to 8 until desired value of objective function is achieved. To find the equilibrium complexation constant (KE) and number of reacting molecules (n) eq 4 have been used as the model equation. The program for evaluating the minimum of the objective function is given in Annexure 1 minimization of the objective function based on least-squares error is done to obtain the values of the parameters and are listed in Table 3. Root-mean-square deviation (RMSD) and normalized rootmean-square deviation (NRMSD) has been applied to check the consistency of model with the experimental values. RMSD and NRMSD for 3-methyl-1-butanol, n-octanol, n-nonanol, ndecanol, methylbenzene, kerosene, methyl isobutyl ketone, diisobutyl ketone, n-hexane, and n-hexanone, was obtained to be 1.22, 0.46, 0.52, 0.95, 0.88, 0.32, 0.85, 0.35, 0.27, 0.27 and 0.27, 0.03, 0.05, 0.18, 0.16, 0.08, 0.11, 0.05, 0.08, 0.09, respectively. Computed R2 values of the fit of equation is obtained to be 0.94, 0.86, 0.97, 0.92, 0.91, 0.95, 0.96, 0.99, 0.98, and 0.97 for reactive extraction using extractant in 3-methyl-1butanol, n-octanol, n-nonanol, n-decanol, methylbenzene, kerosene, methyl isobutyl ketone, diisobutyl ketone, n-hexane, and n-hexanone, respectively.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00141. Program for finding the minimum of the objective function. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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5. CONCLUSION Reactive extraction studied using Amberlite LA-2 in various categories of diluents (hexane, methylbenzene, kerosene, methyl isobutyl ketone, diisobutyl ketone, n-hexanone, 3methyl-1-butanol, n-octanol, n-nonanol, and n-decanol) reveal that 1. KD < 1 suggests that Amberlite LA-2-hexane system is a poor solvent system for extraction of pentanedioic acid. G



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Extractive Separation of Pentanedioic Acid by Amberlite LA-2 in

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