Measurements and Correlation of Liquid–Liquid Equilibria for the

Article pubs.acs.org/jced

Measurements and Correlation of Liquid−Liquid Equilibria for the Ternary System Water + Cyclohexanol + Cyclohexanone Xing Gong,† Qinbo Wang,*,† Fuqiong Lei,† and Binwei Shen‡ †

Department of Chemical Engineering, Hunan University, Changsha, 410082 Hunan, P. R. China Zhejiang Shuyang Chemical Co., Ltd., Quzhou, 324000 Zhejiang, P. R. China

‡

ABSTRACT: Liquid−liquid equilibrium (LLE) data of the ternary system water + cyclohexanol + cyclohexanone was measured from (303.2 to 333.2) K. The reliability of the experimental tie-line data was confirmed by applying the Othmer− Tobias and the Bachman equations. The equilibrium data were correlated with the nonrandom two-liquid (NRTL) and universal quasichemical activity coefficient (UNIQUAC) models. The calculated LLE data for the ternary system agreed well with the experimental data. The root-mean-square deviations (rmsd’s) obtained comparing calculated and experimental two-phase compositions are 0.46 % for the NRTL model and 0.44 % for the UNIQUAC model. The obtained interaction parameters can be used in the calculation of LLE for the ternary system water + cyclohexanol + cyclohexanone as well as for the design, simulation, and optimization of the related separation process.

1. INTRODUCTION Adipic acid is an important bulk chemical, whose production is necessary for the manufacture of nylon 66, polyesters, resins, plasticizers, and other products.1 Currently, adipic acid is manufactured by the oxidation of KA oil (mixture of cyclohexanol and cyclohexanone) using nitric acid as a oxidant. Thus, this process leads to a substantial amount of undesirable NOx, which is commonly believed to cause global warming and ozone depletion.2 In recent years, a green method of production of adipic acid was proposed.3 In this process, cyclohexanol and cyclohexanone are oxidized to adipic acid in high yield with aqueous 30 % H2O2, and no organic solvent is used. Hydrogen peroxide is an ideal oxidant because of its high oxygen content and water is the sole theoretical coproduct.4 This method is clean, safe, and costeffective, and no operational problems are foreseen for a largescale version of this green process. During the oxidation process, the reaction mixture would split into two liquid phases due to the existence of water, that is, an upper phase containing unconverted cyclohexanol and cyclohexanone and a lower phase containing adipic acid, water, and byproducts. Thus, it is very essential to obtain the thermodynamic data of ternary system water + cyclohexanol + cyclohexanone, which is important for the simulation, design, and optimization of related separation operations. In the present study, the liquid−liquid equilibrium (LLE) data are determined for the water + cyclohexanol + cyclohexanone system at temperatures from 303.2 K to 333.2 K. The Othmer− Tobias and the Bachman equations5,6 were used to check the reliability of the obtained tie-lie data. The experimental data were correlated with the nonrandom two-liquid (NRTL) model of Renon and Prausnitz7 and universal quasichemical (UNIQUAC) model of Abrams and Prausnitz 8 to obtain interaction parameters. These experimental data and model parameters © 2014 American Chemical Society

might be used in the calculation of LLE for the ternary system water + cyclohexanol + cyclohexanone as well as for the design and optimization of the related separation process which is an ongoing part of our work.

2. EXPERIMENTAL SECTION 2.1. Materials. The suppliers and the mass fraction of the used chemical reagents were shown in Table 1, including Table 1. Suppliers and Mass Fractions of the Chemical Reagent component

suppliers

mass fraction

analysis method

cyclohexanol cyclohexanone chlorobenzene N,N-dimethylformamide water

Aladdin Chemistry Co. Aladdin Chemistry Co. Aladdin Chemistry Co. Aladdin Chemistry Co. Hangzhou Wahaha Group Co.

> 0.990 > 0.990 > 0.990 > 0.990 > 0.999

GCa GCa GCa GCa KFb

a

Gas chromatograph. bKarl Fischer method.

cyclohexanol, cyclohexanone, chlorobenzene, N,N-dimethylformamide, and water. All of the chemicals were used in the experiment without further purification. The purity (in mass fraction) of these chemicals were checked by gas chromatography and found to be greater than 0.99. The water content of cyclohexanol and cyclohexanone was checked by a Karl Fischer titrator. The results of this titration (in mass fraction) were 0.0021 and 0.0025 for cyclohexanol and cyclohexanone, respectively. Received: January 28, 2014 Accepted: March 7, 2014 Published: March 19, 2014 1651

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2.2. Apparatus and Procedures. The experimental apparatus and sampling methods used in this work was described in detail by Wang et al.9 and our recent work.10 Briefly, the equilibrium experiments were carried out in glass bottles with approximately 250 mL. The temperature was controlled by a regulator with a precision of 0.1 K. For each run, the prepared mixture were charged into the glass bottle and heated to the desired temperature. After reaching the desired temperature, the liquid mixture was stirred for at least 2 h; then the mixture would be left undisturbed in the following several hours. To verify the attainment of liquid−liquid equilibrium, the two liquid phases would be sampled once an hour, and the phase composition was determined. It was found that 2 h after stopping stirring was enough for the prepared mixture to reach liquid− liquid equilibrium, because repetitive measurements during the following several hours indicated the results were reproducible with ± 3 %. For assurance, after stopping stirring at each temperature, the solution was kept undisturbed and isothermal for at least 18 h to ensure that the solution reached liquid−liquid equilibrium. 2.3. Analysis. In each measurement, about 3 mL of the solution was sampled for each phase. The samples were diluted with N,N-dimethylformamide and analyzed by the gas chromatograph (KeXiao GC1690) equipped with a flame ionization detector (FID) and a capillary column (30 m long, 0.32 mm i.d.). The internal standard method was used, and chlorobenzene was chosen as the internal standard substance. The mass fraction of cyclohexanol and cyclohexanone was measured by the gas chromatograph, and the concentration of water was determined by the normalized calculation. The uncertainty in temperature was ± 0.1 K. To verify the reliability and reproducibility of the GC analysis method, five cyclohexanol + cyclohexanone solutions of known concentration were analyzed. Their deviations of the actual composition and the measured composition were calibrated with working curves, which were obtained from sets of gravimetrically prepared standard solutions covering the whole composition range. The five solutions were measured at least five times. The standard uncertainty of cyclohexanol in mass fraction was determined to be 0.0006, and that for cyclohexanone was determined to be 0.0004.

Table 2. Experimental LLE Data on Mass Fraction (w) of the Ternary System Water (1) + Cyclohexanol (2) + Cyclohexanone (3) at (303.2 to 333.2) K and Pressure p = 101.3 kPaa organic phase

⎛ 1 − W23 ⎞ ⎛ 1 − W11 ⎞ ln⎜ ⎟ = A + B ln⎜ ⎟ ⎝ W11 ⎠ ⎝ W23 ⎠

(1)

W23 = m + n(W23/W11)

(2)

T/K

w1

w2

w3

w1

w2

w3

303.2

0.0809 0.0967 0.1120 0.1214 0.1263 0.1317 0.1327 0.1335 0.1272 0.0837 0.0984 0.1111 0.1194 0.1260 0.1322 0.1311 0.1382 0.1327 0.0890 0.1024 0.1163 0.1255 0.1312 0.1359 0.1353 0.1372 0.1373 0.0943 0.1070 0.1179 0.1267 0.1280 0.1371 0.1373 0.1384 0.1366

0.1055 0.1868 0.2833 0.3539 0.4433 0.5259 0.6140 0.6981 0.7843 0.0911 0.1843 0.2761 0.3624 0.4442 0.5255 0.6112 0.6915 0.7773 0.0979 0.1719 0.2675 0.3360 0.4375 0.5152 0.6149 0.6910 0.7703 0.0968 0.1807 0.2735 0.3578 0.4441 0.5181 0.6080 0.6940 0.7748

0.8136 0.7165 0.6047 0.5248 0.4304 0.3425 0.2533 0.1684 0.0885 0.8252 0.7173 0.6128 0.5182 0.4298 0.3423 0.2577 0.1703 0.0900 0.8131 0.7257 0.6163 0.5385 0.4314 0.3490 0.2498 0.1718 0.0923 0.8089 0.7123 0.6086 0.5155 0.4279 0.3448 0.2547 0.1676 0.0886

0.9152 0.9188 0.9225 0.9282 0.9325 0.9372 0.9427 0.9503 0.9549 0.9251 0.9274 0.9314 0.9352 0.9396 0.9432 0.9482 0.9540 0.9590 0.9309 0.9318 0.9364 0.9396 0.9438 0.9480 0.9517 0.9562 0.9614 0.9331 0.9362 0.9398 0.9414 0.9448 0.9504 0.9539 0.9576 0.9614

0.0071 0.0127 0.0178 0.0211 0.0248 0.0282 0.0311 0.0326 0.0357 0.0063 0.0111 0.0157 0.0191 0.0224 0.0258 0.0285 0.0305 0.0326 0.0056 0.0105 0.0147 0.0180 0.0211 0.0239 0.0271 0.0294 0.0310 0.0056 0.0099 0.0140 0.0177 0.0212 0.0232 0.0260 0.0287 0.0313

0.0776 0.0685 0.0598 0.0507 0.0427 0.0346 0.0263 0.0171 0.0094 0.0685 0.0614 0.0529 0.0457 0.0380 0.0310 0.0233 0.0155 0.0084 0.0634 0.0578 0.0489 0.0423 0.0351 0.0281 0.0212 0.0144 0.0076 0.0613 0.0538 0.0462 0.0409 0.0341 0.0264 0.0201 0.0137 0.0073

313.2

323.2

333.2

3. RESULTS AND DISCUSSION 3.1. Experimental Results. LLE data of the ternary system water (1) + cyclohexanol (2) + cyclohexanone (3) at (303.2, 313.2, 323.2, and 333.2) K and atmospheric pressure are shown in Table 2, and the experimental data of the ternary system at different temperatures are plotted in Figure 1. All concentrations are listed in mass fraction. The Othmer−Tobias equation5 (eq 1) and the Bachman equation6 (eq 2) were used to check the reliability of experimental results at each temperature. The equations are listed as:

aqueous phase

a

Standard uncertainties u are u(T) = 0.1 K, ur(p) = 0.05, u(w2) = 0.0006, and u(w3) = 0.0004.

By fitting the experimental data with eqs 1 and 2, the parameters of Othmer−Tobias and the Bachman equations are linear regressed and listed in Table 3. The Othmer−Tobias and the Bachman plots are also presented in Figures 2 and 3, respectively. As can be seen from Table 3, the correlation factors, R2, were all close to unity, indicating a high degree of consistency of the experimental determined data. 3.2. Correlation of Experimental Data. Theoretically, the mole fractions of the organic phase and the aqueous phase can be determined using the following equations:

γiEx iE = γiOx iO

where A, B, m, and n are the parameters of the Othmer−Tobias equation and the Bachman equation, respectively. W23 is the mass fraction of cyclohexanone in the organic phase. W11 is the mass fraction of water in aqueous phase. 1652

(2a)

∑ xiE = 1

(3)

∑ xiO = 1

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Figure 1. LLE of the water (1) + cyclohexanol (2) + cyclohexanone (3) system at different temperatures: ●---●, experimental data tie line; ○---○, calculated data tie line using the NRTL model; △---△, calculated data tie line using the UNIQUAC model. wi is the mass fraction of component i in water (1) + cyclohexanol (2) + cyclohexanone (3) solvent mixtures.

Table 3. Parameters of the Othmer−Tobias Equation and Bachman Equation for the Ternary System Water (1) + Cyclohexanol (2) + Cyclohexanone (3) Othmer−Tobias equation T/K

A

B

303.2 313.2 323.2 333.2

−13.37 −15.00 −15.87 −16.86

−5.147 −5.519 −5.675 −5.957

R

2a

0.978 0.974 0.983 0.979

Bachman equation m

n

R2a

0.009 0.007 0.006 0.006

0.906 0.917 0.924 0.927

0.999 0.999 0.999 0.999

a 2

R is the linear correlation coefficient.

where xiE and xiO are the mole fraction of component i in the aqueous phase and organic phase and γiE and γiO are the corresponding activity coefficients of component i in the aqueous phase and organic phase. To calculate the activity coefficients is the key to solve the set of equations. In this work, NRTL and UNIQUAC models were used. For a solution of m-components, the NRTL activity coefficient equation is: 3

ln γi =

∑ j = 1 τjiGjixj 3 ∑k = 1 Gkixk

Figure 2. Othmer−Tobias plots of the ternary system water (1) + cyclohexanol (2) + cyclohexanone (3) system at (303.2 to 333.2) K: ■, 303.2 K; ●, 313.2 K; ▲, 323.2 K; ▼, 333.2 K.

xjGij 3 j = 1 ∑k = 1 Gkjxk 3

τij = aij + bij(T /K)−1

+ ∑

3 ⎛ ∑k = 1 xkτkjGkj ⎞ ⎟ × ⎜⎜τij − 3 ⎟ G x ∑ ⎝ k = 1 kj k ⎠

τij ≠ τji

τii = 0

Gij = exp( −ηijτij)

ηij = ηji (6)

where xi is the mole fraction of the component i and γi is the activity coefficient of component i, and T is the absolute temperature.

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where ψi and θi represent the volume fraction and the area fraction of component i, respectively. aij and bij are UNIQUAC model parameters needed to be regressed. The pure component structural parameters11,12 (r and q) are listed in Table 4. By using NRTL and UNIQUAC model, the experimental data was correlated, and the model parameters were optimized. The optimum algorithm applied in the parameter estimation program was the Nelder−Mead Simplex approach,13 which had been introduced in detail in the work of Wang et al.9 and Lei et al.10 Function f minsearch in the optimization toolbox of Matlab (Mathwork, MA) uses the Nelder−Mead Simplex approach and can be employed for the minimization of the objective function, which is calculated by minimizing the differences between the experimental and the calculated results for each component over all of the measured LLE data of the ternary system. The objective function (OF) used in this case was exp cal 2 OF = min ∑ ∑ ∑ ∑ (xijkt − xijkt )

Figure 3. Bachman plots of the ternary system water (1) + cyclohexanol (2) + cyclohexanone (3) system at (303.2 to 333.2) K: □, 303.2 K; ○, 313.2 K; △, 323.2 K; ◊, 333.2 K.

t

compound

r

q

0.920 4.274 4.114

1.400 3.284 3.340

ψi xi

+

ψ θ z qi ln i + li − i xi 2 ψi 3

t

3 j=1

− qi ln(∑ θτ j ji) + qi − qi ∑ j=1

j=1

θτ j ij 3

∑k = 1 θkτkj

(7)

where lj = ψi =

⎛Z⎞ ⎜ ⎟(r − q ) − (r − 1) j j ⎝2⎠ j xiri m ∑i = 1 xiri

θi =

(8)

xiqi m ∑i = 1 xiqi

k

j

(11)

i

where N is the number of tie-lines. To obtain a unique set of parameters valid for all the range of temperatures studied, a simultaneous regression of all experimental LLE data of this system was carried out. Tables 5 and 6 listed the optimized NRTL and UNIQUAC parameters obtained in a simultaneous correlation of all data assuming temperatureindependent parameters. As shown in Tables 5 and 6, the RMSD values for NRTL model and UNIQUAC model were 0.46 % and 0.44 %, respectively. It indicates that LLE data of the ternary system water + cyclohexanol + cyclohexanone are reasonably correlated by the NRTL and UNIQUAC models. Figure 1 compares experimental data and composition of tie-line calculated from NRTL and UNIQUAC model with fitted parameters at 303.2 K, 313.2 K, 323.2 K, and 333.2 K, respectively. As can be seen from Figure 1, we can conclude that both the NRTL and UNIQUAC models can be used to predict the liquid−liquid equilibrium for the ternary system of water + cyclohexanol + cyclohexanone.

∑ xjlj

3

(10)

i

exp cal 2 RMSD = 100(∑ ∑ ∑ ∑ (xijkt − xijkt ) /6N )1/2

The activity coefficient equation for the UNIQUAC model of Abrams and Prausnitz is: ln γi = ln

j

cal where xexp ijkt and xijkt are the experimental and calculated mole fractions. The subscripts i, j, k, and t denote component, phase, tie-line, and temperature, respectively. In this work, the root-mean-square deviation (RMSD) in the phase composition was calculated as

Table 4. Pure Component Structural Parameters for UNIQUAC Equation water cyclohexanol cyclohexanone

k

⎛ bij ⎞ τij = exp⎜aij + ⎟ T⎠ ⎝ (9)

Table 5. Optimized Temperature-Independent NRTL Binary Interaction Parameters for the Ternary System Water (1) + Cyclohexanol (2) + Cyclohexanone (3) i

j

aij

aji

bij

bji

ηij = ηji

RMSD

water water cyclohexanol

cyclohexanol cyclohexanone cyclohexanone

6.91 6.21 0.26

3.26 7.12 3.30

−739.4 −691.4 −106.0

4981.1 2939.8 −934.8

0.17 0.16 0.33

0.46 %

Table 6. Optimized Temperature-Independent UNIQUAC Binary Interaction Parameters for the Ternary System Water (1) + Cyclohexanol (2) + Cyclohexanone (3) i

j

aij

aji

bij

bji

RMSD

water water cyclohexanol

cyclohexanol cyclohexanone cyclohexanone

−2.83 −1.13 −1.77

1.64 0.58 1.67

686.85 343.07 430.23

−515.84 −488.54 −501.21

0.44 %

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4. CONCLUSIONS Liquid−liquid equilibrium (LLE) data for the ternary system water + cyclohexanol + cyclohexanone have been measured at (303.2 to 333.2) K under atmospheric pressure. The reliability of the experimental data was ascertained by Othmer−Tobias and Bachman equations. The NRTL and UNIQUAC models were used to correlate the experimental LLE data. A unique set of optimum NRTL parameters at (303.2 to 333.2) K were determined. The obtained interaction parameters can be used in the calculation of LLE for the ternary system water + cyclohexanol + cyclohexanone as well as for the design and optimization of the related separation process.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

The project was granted financial support from Key S&T Special Project of Zhejiang Province (2012C13007-2) and the Fundamental Research Funds for the Central Universities. Notes

The authors declare no competing financial interest.

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REFERENCES

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