Measurement and correlation of isobaric vapor-liquid equilibrium for the binary system of cyclopentane and tetrahydrofuran

THERMODYNAMICS

^IDepartment of Chemistry, Dezhou University, Dezhou 253023, PR China

^IIKey Laboratory of Coordination Chemistry and Functional Materials in Universities of Shandong, (Dezhou University), Dezhou 253023, PR China. E-mail: [e-mail]

ABSTRACT

Isobaric vapor-liquid equilibrium (VLE) data for the cyclopentane and tetrahydrofuran (THF) system were measured at 101.3 kPa by using an equilibrium still. Thermodynamic consistency of the experimental data was confirmed by means of the Herington method. The experimental data were correlated and calculated by the Margules, Van Laar and Wilson activity-coefficient models, respectively. The Wilson and Van Laar activity-coefficient models are better than the Margules activity-coefficient model based on the average absolute deviations of temperature and the vapor-phase composition. For the Wilson and Van Laar activity-coefficient models the average absolute deviations between the experimental and the calculated values were 0.24 K and 0.23 K for the boiling point, and 0.0040 for vapor-phase composition, respectively. These agree well with the experimental data. Therefore, it was shown that the Wilson and Van Laar activity-coefficient models satisfactorily correlate the experimental results of the cyclopentane and tetrahydrofuran system.

Keywords: Cyclopentane; Tetrahydrofuran; Vapor-liquid equilibrium.

INTRODUCTION

In industrial production processes, solvent recovery is one of the problems that needs to be solved urgently due to environmental protection and production costs (Slater et al., 2012). Currently, distillation is extensively used for the separation of a great number of liquid mixtures and clearly dominates separation processes, accounting for more applications than all of the other solvent separation processes such as extraction, adsorption, filtration and membrane technologies (Humphrey, 1995; Ramzan et al., 2008; Mohsen-Nia and Memarzadeh, 2010). For the correct design of separation processes, it is essential to obtain accurate and quantitative information on the phase equilibrium of binary or multicomponent mixtures (Aucejo et al., 2006; Ovejero et al., 2007).

Cyclopentane and tetrahydrofuran are solvents employed in many processes. Several processes in chemical industries produce mixtures of cyclopentane and tetrahydrofuran, so vapor-liquid equilibrium data of cyclopentane and tetrahydrofuran are indispensable for separation of them. However, so far, no relevant isobaric VLE data are available for cyclopentane and tetrahydrofuran in the open literature. In this paper, we present isobaric vapor - liquid equilibrium measurements for the mixture of cyclopentane and tetrahydrofuran at 101.3 kPa. The vapor-liquid equilibrium data have been correlated with the Margules (Margules, 1895), Van Laar (Van Laar, 1910) and Wilson (Wilson, 1964) activity-coefficient models.

MATERIALS AND METHODS

Materials

Chemicals used: all the reagents were analytical purity grade. Cyclopentane was purchased from Tianjin University Ke Wei Company and tetrahydrofuran was purchased from Tianjin Chemical Reagent Third Plant. The purity of the chemicals was checked by gas chromatography (>0.997 mass %), so no further purification was needed. The water content in the chemicals was determined using a Karl-Fischer titration method (<0.03 mass %). The purity of the chemicals was further confirmed by comparing the experimental densities, the refractive indexes and the normal boiling points with those reported (Ma, 2005; Cheng, 2007), as listed in Table 1. The accuracies in density, and refractive index measurements are ±2.0×10^-5 g/cm³ and ±0.00001, respectively.

Apparatus and Procedure

An equilibrium still, the same as in the previous work (Li and Bai, 2012; Li et al., 2013), was employed to measure isobaric VLE data at 101.3 kPa and is shown in Figure 1. The temperature was controlled by a small voltage adjuster. A mercury thermometer calibrated by Shanghai Metrology Institution was used for temperature measurement within an accuracy of ±0.01 °C.

The temperature uncertainties in this work, combining both the errors from calibration and repeatability of the measurements, are not higher than ±0.06 K. The actual atmospheric pressure was measured by a mercury barometer with an accuracy of ±0.1 kPa. Since the atmospheric pressure changed slightly during the experiments, the boiling temperatures at the actual pressure were corrected to 101.3 kPa according to the literature (Hiaki and Kawai, 1999).

The analytical work was carried out using a gas chromatograph (SP-6890) equipped with a thermal conductivity detector (TCD) connected to a data acquisition system. The TCD was repeatedly calibrated by introducing known amounts of each pure compound through a syringe into the injector of the gas chromatograph. Taking into account the uncertainties due to calibrations and dispersions of the analyses (at least five for each sample), the resulting uncertainties in vapor and liquid mole fractions are estimated to be 0.0001 in mole fraction.

The still was operated at constant pressure until equilibrium was reached. When constant temperature and pressure were obtained for 30 min or longer, it was assumed that the vapor and liquid phases had achieved balance. To verify the equilibrium conditions, we analyzed the vapor until the variation of the mole fraction of the vapor phase composition was less than 0.0001. Then, samples of liquid and condensate were taken for analysis.

Verification of the Apparatus

In order to verify the reliability of the device, the atmospheric VLE data of the cyclohexane + ethanol binary system were measured by this device and compared with literature data (Yuan et al., 1963) as shown in Figure 2. As can be seen from Figure 2, the measured VLE data were in good agreement with the literature data, so the device can be used to measure the VLE of the binary system cyclopentane and tetrahydrofuran at 101.3 kPa.

RESULTS AND DISCUSSION

Experimental Data

Table 2 shows the values of the quantities that characterize the equilibrium states of the liquid and vapor phases, , and at a pressure of = 101.3 kPa. The corresponding phase diagram is shown in Figure 3 and Figure 4. As can be seen from Figure 3, there is no intercrossing point between the bubble point curve and the dew point curve over the entire composition range, which reveals that no azeotrope exists in the cyclopentane + THF binary system.

Thermodynamic Consistency Verification

Thermodynamic consistency of the experimental results was checked by means of two tests: (1) the point-to-point van Ness method (Van Ness et al., 1973) and (2) the Herington method (Herington, 1951).

The thermodynamic consistency of the experimental results was checked using the van Ness method, described by Fredenslund et al. (1977) using a third-order Legendre polynomial for the excess free energies. According to this test, experimental data are considered to be consistent if the average deviation in () is smaller than 0.01. All the experimental data are consistent, as one can see in Table 3.

Experimental errors may cause deviations of the activity coefficients obtained from the experimental VLE data via the Gibbs-Duhem equation (Smith et al., 2001). Therefore, the Herington method was used to check the thermodynamic consistency.

where . and were the highest and the lowest boiling point in the system, respectively, in K. According to the Herington method, the experimental data are consistent if Herington's was less than 10. The calculation result was that, which indicated that all experimental data were in accordance with thermodynamic consistency.

Correlation of the Binary Vapor-Liquid Equilibrium

The activity coefficients were calculated from the equation

At low pressure, the assumption of ideal behavior is adopted for the vapor (Chen, et al. 1993). The fugacity coefficients and are equal to unity. Therefore, Eq. (1) can be simplified to

where is the activity coefficient of component . , and are total pressure of the system and the liquid and vapor phase mole fractions in the equilibrium. ,are the fugacity coefficients of component in the vapor mixtures and at saturation, respectively. is the saturated vapor pressure of pure component at the system temperature, calculated with the Antoine equation

where , , and are Antoine constants and is the temperature in Kelvin. The Antoine constants for cyclopentane and THF were obtained from the literature (Ma, 2005), and are presented in Table 4.

Because the experiment was carried out at 101.3 kPa, the vapor phase could be regarded as an ideal gas, and the boiling point difference between cyclopentane and THF was not more than 30 K, so the parameters of the activity-coefficient models could be regarded as constant values. In order to find parameters of the equations, the activity coefficients were correlated with the Margules, Van Laar and Wilson equations. Estimation of the parameters of the equations was based on minimization of the following objective function :

where is the number of data points and the number of components in the mixture. The experimental and calculated values are denoted by the superscripts '' and '', respectively. is calculated with Equation (1) and is calculated with the Margules, Van Laar and Wilson equations. The parameters of the activity-coefficient models obtained through a simplex search are shown in Table 4. These were then used to calculate and under the corresponding liquid compositions and pressure (101.3 kPa). The temperatures and vapor-phase compositions obtained from the theoretical calculations using the three activity-coefficient models were compared with the experimental data. The comparative results are shown in Table 2. The average absolute deviations of temperature and the vapor-phase compositions between the experimental and the calculated values obtained from the Margules, Van Laar and Wilson models, together with the correlated interaction parameters, are shown in Table 5.

It can be seen from Table 5 that the average absolute deviations between the experimental and the calculated values using the Wilson and Van Laar activity-coefficient models were 0.24 K and 0.23 K for the boiling point and 0.0040 for vapor-phase composition, respectively. However, by the Margules activity-coefficient models the average absolute deviations of temperature and the vapor-phase compositions were 0.41 and 0.0113. When these results are compared, it can be seen that the Wilson and Van Laar activity-coefficient model is better than the Margules activity-coefficient model based on the average absolute deviations of and .

CONCLUSIONS

The VLE data for the binary system cyclopentane and tetrahydrofuran at 101.3 kPa are reported in this article. No azeotrope was found in the binary system. The VLE data were verified and were in accordance with the consistency of thermodynamics. They were correlated by the Margules, Van Laar and Wilson activity-coefficient models and the corresponding binary interaction parameters of the three activity-coefficient models were obtained. The average absolute deviations of temperature and the vapor-phase compositions between the experimental and the calculated values using the Wilson and Van Laar activity-coefficient models were 0.24 K and 0.23 K for the boiling point and 0.0040 for the vapor-phase composition, which are better than those obtained by the Margules activity-coefficient model. Therefore, the Wilson and Van Laar activity-coefficient models correlate the experimental results of cyclopentane and tetrahydrofuran system satisfactorily.

Submitted: March 21, 2013

Revised: June 25, 2013

Accepted: July 31, 2013

* To whom correspondence should be addressed

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Measurement and correlation of isobaric vapor-liquid equilibrium for the binary system of cyclopentane and tetrahydrofuran

Yumei Li ^{I, II}

Publication Dates

• Publication in this collection
  17 Sept 2014
• Date of issue
  Sept 2014

History

• Received
  21 Mar 2013
• Accepted
  31 July 2013
• Reviewed
  25 June 2013