Fluid-Phase Equilibria in the Binary System Trifluoromethane + 1

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Ind. Eng. Chem. Res. 2011, 50, 213–220

213

Fluid-Phase Equilibria in the Binary System Trifluoromethane + 1-Phenyltetradecane Cristina Bogatu,† Dan Geana˘,‡ Anca Dut¸a˘,† Wim Poot,§ and Theo W. de Loos*,§ The Centre Product Design for Sustainable Energy, TransilVania UniVersity of BrasoV, 50 Iuliu Maniu Street, 500036 BrasoV, Romania, Applied Physical Chemistry and Electrochemistry Department, Faculty of Applied Chemistry and Materials Science, Politehnica UniVersity of Bucharest, 1-7 Gh Polizu Street, 011061 Bucharest, Romania, and Laboratory for Engineering Thermodynamics, Process and Energy Department, Delft UniVersity of Technology, Leeghwaterstraat 44, 2628CA Delft, The Netherlands

In this study, the phase behavior of an asymmetric system consisting of the refrigerant, trifluoromethane, and 1-phenyltetradecane, a lubricant from the family of alkylbenzenes, is investigated. Equilibrium data were obtained using a synthetic method in the temperature range 253.34-370 K and pressures up to12 MPa. The investigated system exhibits type III phase behavior, according to the classification of van Konynenburg and Scott. The new experimental data were modeled with two cubic equations-of-state, Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR), and were coupled with classical van der Waals mixing rules. A single set of binary parameters was used to predict the global phase behavior of the system for a large range of pressure and temperature. Although the model is simple, it is able to represent correctly the complex phase equilibria of the system studied in this work. 1. Introduction In refrigeration cycles the most important component is the refrigerant, but a small quantity of oil must be added to lubricate the sliding parts of the compressor and to ensure protection against the wear. During functioning the two components can interact due to the oil migration from the compressor to other parts of the system such as the evaporator, the condenser, or the expansion devices. Therefore, the performance of the refrigeration system is determined by the properties of the two components separately (refrigerant and oil), but also by the properties of the lubricant-refrigerant mixture.1,2 As a consequence, fluid-phase equilibrium data for these mixtures are required as important properties for the good functioning of the refrigeration cycle and to avoid compressor failure. These data can be obtained from experimental investigations, but this is time-consuming and expensive. With the use of different thermodynamic models like the ones described in refs 3-7, predictions of the global behavior can be done. However, these models also require experimental data to tune the adjustable parameters of the model. In the modern refrigeration cycles, refrigerants from the family of the hydrofluorocarbons are used with synthetic oils like polyolesters or polyalkylene glycols, polyalfaolefins, polyvinylethers, or alkylbenzenes (phenylalkanes). Among these, alkylbenzenes, which can be considered as synthetic aromatic hydrocarbon oils, are used for special applications at very low temperature. To understand the phase behavior of refrigerant-oil systems, it is interesting to study the phase behavior of the hydrofluorocarbon (HFC) refrigerants with members of the homologous series of the n-alkylbenzenes.8 Such systems belong to the class of asymmetric, highly nonideal systems, with a significant difference in the size of the molecules. According to the clas-

sification of van Konynenburg and Scott, asymmetric systems can develop type II, III, IV, or V phase behavior.9 This paper continues our study on the high-pressure phase behavior of systems consisting of trifluoromethane and different alkylbenzenes. Our previously published papers10-13 concerned the fluid-phase behavior of the systems consisting of CHF3 and phenylpropane, isobutylbenzene, or 1-phenyloctane. The aim of this paper is to add new experimental equilibrium data of the system of trifluoromethane and 1-phenyltetradecane and to predict the global phase behavior of this system using a simple model based on cubic equations of state (EoSs). We tested two EoSs: the SRK and PR EoS coupled with van der Waals mixing rules and one single set of binary interaction parameters to represent the topology of the phase behavior. Although the model is relatively simple, the results showed good agreement between the model and our experimental data. 2. Experimental Section 2.1. Chemicals. The trifluoromethane, CHF3 (R-23) (purity >99.995%), was provided by Praxair and the phenyltetradecane, phC14 (purity of 99.8%), was from Fluka. The chemicals were used without further purification. Some properties of these compounds are given in Table 1. 2.2. Experimental Apparatus and Procedure. The measurements were carried out using the so-called Cailletet apparatus according to the synthetic method. A detailed description of the experimental setup is given elsewhere.18,19 In this apparatus, pressures up to 15 MPa can be applied and the temperature can vary from 240 to 510 K. Mixtures with known overall composition, previously degassed, are confined Table 1. Chemicals Used and Some Properties name

* To whom correspondence should be addressed. E-mail: [email protected]. † Transilvania University of Brasov. ‡ Politehnica University of Bucharest. § Delft University of Technology.

formula

Tb (K) a

Tm (K)

b

a

ω

191.7 117.97 299.3 4.858 0.267d trifluoromethane CHF3 1-phenyltetradecane C6H5-C14H29 632.15b 289.15b 800.29c 1.415c 0.869d a Reference 14. ence 17.

a

Pc Tc (K) (MPa)

Reference 15. c According to Nikitin et al.16

10.1021/ie101008w  2011 American Chemical Society Published on Web 08/02/2010

a

d

Refer-

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over mercury in the top end of the Cailletet tube. The tube is mounted in a thermostat with circulating ethanol, water, or silicon oil depending on the temperature range of interest. The temperature of the thermostat liquid is kept at the desired value with accuracy better than 0.03 K at temperatures up to 370 K. The measurements consist of visually observing the phase transitions when the pressure is slowly changed at constant temperature or the temperature is slowly varied at constant pressure. The pressure is measured with a dead-weight pressure gauge (type De Wit, accuracy of (0.003 MPa) or in the case of the measurements of liquid-liquid-vapor equilibria with a manometer (Heise; uncertainty, (0.01 MPa), previously calibrated against the dead weight gauge. A platinum resistance thermometer (Pt-100), calibrated against a standard thermometer, records the temperature of the thermostat liquid near the sample with accuracy within 0.01 K.18,19 The error in the mole fraction of trifluoromethane is estimated to be less than 0.001. 3. Results For the investigated system, vapor-liquid equilibria (VLE), liquid-liquid equilibria (LLE), solid-liquid-liquid equilibria (SLLE), liquid-liquid-vapor equilibria (LLVE), and the corresponding critical end point were measured for compositions x (trifluoromethane) ) 0.0525-0.3011, temperatures T ) 253.34-370 K and pressures up to 12 MPa. The experimental data are given in Tables 2-5, and the results are plotted in Figure 1. The vapor pressure data and the critical point of trifluoromethane (Table 2) were measured and the data agrees within the experimental uncertainty with literature.20-22 At mole fractions higher than x(trifluoromethane) ) 0.3059, no bubble point could be measured because the system shows at these compositions, a liquid-liquid phase split. From experimental data in Figure 1, P-x cross sections were constructed by interpolation and plotted in Figure 2 for five different temperatures. For temperatures below the temperature of the upper critical end point (UCEP), the bubble point curves end in the three-phase equilibrium line. The three-phase line separates the L2V region from the upper two-phase regions: L1L2 and L1V (very narrow, not experimental accessible for the studied system). As can be seen the liquid-liquid immicibility region is very large, so the composition of the vapor phase is almost pure trifluoromethane. At the temperature of UCEP, the narrow L1V region will disappear and with increasing temperature, the two regions L1L2 and L2V join in one single LV region. The liquid-liquid-vapor curve (LLV) ends at a high temperature in an upper critical end point (UCEP L2 + L1 ) V). In this point, the two critical phases are the vapor phase and the liquid phase L1, richer in trifluoromethane. The critical phase coexists with the liquid L2, richer in 1-phenyltetradecane (the heavy component). This implies that the investigated system exhibits type III phase behavior according to the classification of fluid phase behavior of van Konynenburg and Scott.9 The LLVE points and the coordinates of the critical end point are given in Table 4. For this system, there are no available data for comparation, so far. In the P-T projection, type III phase behavior is characterized by the presence of a discontinuous critical line: one branch originates in the critical point of the heavy component and goes to higher pressures and temperatures, while the other branch connects the critical point of the light component with the UCEP.9,23,24 Because of the relatively high value of the melting point of the 1-phenyltetradecane (Table 1), a solid phase occurs in the

Table 2. Vapour-Liquid Equilibria in the System [x Trifluoromethane + (1 - x) 1-Phenyltetradecane]: Bubble-Point Pressure as a Function of Temperature at Constant Mole Fraction of Trifluoromethane x (CHF3)

T (K)

P (MPa)

T (K)

P (MPa)

T (K)

P (MPa)

0.0526

303.34 313.72 323.44 283.56 288.45 296.43 303.46 283.53 293.65 303.53 313.47 278.57 283.59 293.58 303.41 283.48 286.47 287.7 288.49 289.45 288.44 293.50 298.55 308.55 294.17 303.71 313.46 298.39 303.43 313.53 368.64 358.57 348.55 338.54 328.49 253.34 258.27 263.18 268.17

0.657 0.732 0.791 1.501 1.616 1.806 1.966 2.016 2.341 2.666 3.001 2.419 2.639 3.099 3.554 3.142 3.307 3.376 3.427 3.482 3.579 3.905 4.239 4.875 4.216 4.894 5.549 4.705 5.066 5.75 8.978 8.578 8.113 7.598 7.048 1.405 1.635 1.89 2.175

333.66 343.64 354.09 313.45 323.56 333.54 343.52 323.41 333.45 343.51 353.56 313.44 323.43 333.46 343.44 293.5 303.45 313.41 323.43 333.51 318.71 328.5 348.54 358.59 323.46 333.6 343.62 323.57 333.62 343.63 321.94 315.58 308.39 304.52 300.73 273.20 278.33 283.31 288.35

0.866 0.936 1.001 2.201 2.431 2.666 2.881 3.331 3.656 3.956 4.246 4.004 4.474 4.905 5.329 3.711 4.306 4.882 5.442 5.977 5.48 6.03 7.049 7.489 6.164 6.754 7.274 6.38 6.961 7.491 6.633 6.238 5.798 5.703 6.148 2.500 2.865 3.260 3.695

363.61 368.66

1.061 1.091

353.52 368.71

3.086 3.381

363.55 368.6

4.526 4.651

353.49 363.49 369.59

5.704 6.05 6.214

343.51 353.55 363.62 368.57

6.457 6.912 7.307 7.492

368.67 338.47

7.889 6.575

353.61 368.72

7.754 8.389

353.57 368.56

7.971 8.616

298.14 295.85 294.21 292.69 290.55 293.29 298.95a

6.647 7.648 8.648 9.648 11.898 4.175 4.790a

0.1501

0.1955

0.2454

0.2802

0.2909

0.3011 0.3059 0.3106

1.000

a

Critical point (L ) V).

Table 3. Liquid-Liquid Equilibria in the System [x Trifluoromethane + (1 - x) 1-Phenyltetradecane] and Liquid-liquid Upper Solution Pressures as a Function of Temperature at Constant Mole Fraction of Trifluoromethane: Phase Boundaries at Constant Mole Fraction of Trifluoromethane x (CHF3)

T (K)

P (MPa)

T (K)

P (MPa

T (K)

P (MPa)

0.2909

280.78 281.18 281.50 293.7 290.84 368.64 358.57 348.55 338.54 x28.49

11.649 8.899 7.649 5.401 6.65 8.978 8.578 8.113 7.598 7.048

281.85 282.81 283.85 289.18 287.67 321.94 315.58 308.39 304.52 300.73

6.899 5.149 4.049 7.65 8.901 6.633 6.238 5.798 5.703 6.148

284.15

3.649

286.18 285.15 298.14 295.85 294.21 292.69 290.55

10.4 11.9 6.647 7.648 8.648 9.648 11.898

0.3059 0.3106

temperature range of the measurements. The presence of the solid phase of 1-phenyltetradecane complicates the phase diagram, and at low temperatures hides partially the three-phase LLV equilibrium line and LL phase boundary lines.25 Thus, the three-phase line (LLV) will end at lower temperatures in a quadruple point: SLLV (Table 5). In this point a solid phase coexists in equilibrium with a vapor phase and two liquid phases. From the quadruple point a three-phase equilibrium line, solid-liquid-liquid (SLLE) (measured at x (trifluoromethane) ) 0.2800) originates and emerges to higher pressure with a steep slope. This curve is also depicted in Figure 1. At the quadruple

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Table 5. Solid-Liquid-Liquid Equilibrium Pressure in the System [x Trifluoromethane + (1 - x) 1-Phenyltetradecane] x(CHF3)

T (K)

P (MPa)

T (K)

P (MPa)

0.2802

281.12 280.71 280.39 280.21

9.402 7.401 6.401 5.401

279.96 279.77 279.53

4.402 3.402 2.953b

b

Quadruple point SLLV.

Figure 1. The experimental isopleths for the system [x trifluoromethane + (1 - x) 1-phenyltetradecane]: LLV line (s), critical end point L2 + (L1 ) V) (0), solid-liquid-liquid-vapor quadruple point (9); vapor-liquid equilibria at x ) 0.0525 (+), 0.1500 (∆), 0.1954 (9), 0.2453 (2), 0.2800 (b), 0.2909 (1), 0.3011 (+), 0.3059 ([); liquid-liquid equilibria at x ) 0.2909 (3), 0.3059 (]), 0.3106 (O); solid-liquid-liquid equilibria (---).

Figure 3. Liquid-liquid equilibria in the system [x trifluoromethane + (1 - x) 1-phenyltetradecane]: isobaric T-x diagrams at 6 MPa ()), 8 MPa (2), 10 MPa ([), solid-liquid-liquid point (b).

Figure 2. Vapor-liquid equilibria in the system [x trifluoromethane + (1 - x) 1-phenyltetradecane]: isothermal bubble point curves at 288 (O), 298 (2), 310 (9), 330 (+), and 360 K (3); LLV points (b), LLV equilibria (---). Table 4. Liquid-Liquid-Vapour Equilibrium Pressure in the System [x Trifluoromethane + (1 - x) 1-Phenyltetradecane] T (K) 278.57 283.45 288.43 a

P (MPa) 2.877 3.267 3.697

T (K) 293.5 298.48 299.31

P (MPa) 4.187 4.719 4.802

T (K) 299.38

P (MPa) a

4.824a

UCEP L2 + L1 ) V.

point, two other three-phase solid-liquid-vapor (SLV) lines meet, not measured in this work. At mole fractions of trifluoromethane below 0.3059, the liquid-liquid isopleths originate in the liquid-liquid-vapor line and go very steep to high pressures. For the sample with composition of x (trifluoromethane) ) 0.3059, the liquid-liquid isopleth joins the corresponding liquid-vapor equilibrium line almost in the UCEP and this composition corresponds almost to the critical composition (L1 ) V) at the UCEP. For mixtures richer in trifluoromethane the isopleths move toward higher pressures and temperatures and show a minimum in pressure. For mixtures in the range of very low concentrations of 1-phenyltetradecane (1.5-5% phC14),

liquid-liquid-vapor and solid-liquid-liquid equilibrium could be observed at lower pressure and temperature and also a liquid-liquid demixing above the critical end point. However no-phase boundary data (vapor-liquid, liquid-liquid, or liquid-fluid) could be measured, probably because the phase boundary curves are located at compositions very close to pure trifluoromethane in the range of temperature and pressure investigated. Particularly interesting is the sample with composition x (trifluoromethane) ) 0.2909. At this composition the LL phase boundary intersects the SLL line in the point corresponding to a pressure P ) 8.899 MPa and temperature T ) 281.18 K. Only solid-liquid equilibria (SLE) could be measured at higher pressures. In the region between the SLL line and the LL line for x ) 0.3059 it is very difficult to determine which kind of equilibrium (LLE or SLE) occurs. Moreover, the liquid-liquid/ solid immiscibility region is narrower than in the case of other homologous members from the family of alkylbenzenes with lower numbers of carbon atoms. This can be explained by the large asymmetry of the investigated system.10-13 Figure 3 shows the isobaric liquid-liquid equilibrium lines for three different pressures. For the investigated range of concentrations, the T-x lines separate the liquid-liquid region at low temperature from the homogeneous liquid region positioned at intermediate temperatures. Further, as the temperature increases at a given composition, a liquid demixing is observed, and finally, at temperatures high enough, a one single liquid phase results. As can be observed, the T-x curves end in the SLL three-phase line, at low temperatures in the point assigned with filled circle (b) in Figure 3. The composition of the coexisting liquid or fluid phase could not be measured as mentioned before. For the same reason no liquid-liquid/fluid critical point could be measured. This fact is in accordance with the topology of type III phase behavior, characteristic for asymmetric binary systems with large differences in the size of the molecules of the components.19,21-23

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4. Modeling The SRK and PR EoSs coupled with two parameter conventional (van der Waals) mixing rules (2PCMR) were used to model the high pressure phase behavior of the investigated system. The model was chosen based on results previously obtained for other asymmetric binary systems, of trifluoromethane and other members of the alkylbenzene family.10-12 Moreover, the good modeling capability of this simple model for highly nonideal systems (type I-V phase behavior) is mentioned elsewhere.26-28 The binary interaction parameters, k12 and l12 can be used in a k-l global phase diagram (klGPD, see Figure 2 in ref 27) representing all possible types of phase behavior that an equation of state can predict for a particular binary system. The two EoSs are described by eqs 1 and 6, respectively. P)

a(T) RT V-b V(V + b)

(1)

where the two constants, a and b, for SRK EoS are a ) 0.42748

R2TC2 R(T) PC

(2)

RTC PC

(3)

b ) 0.08664

R(TR,ω) ) [1 + mSRK(1 - TR0.5)]2

(4)

mSRK ) 0.480 + 1.574ω - 0.176ω2

(5)

a(T) RT V-b V(V + b) + b(V - b)

(6)

P)

R2TC2 R(T) PC

(7)

RTC PC

(8)

b ) 0.077796

R(TR,ω) ) [1 + mPR(1 - TR0.5)]2

(9)

mPR ) 0.37464 - 1.54226ω - 0.26992ω2

(10)

The two parameters conventional mixing rules (2PCMR), derived from the van der Waals (vdW) one fluid approximation, are presented in eqs 11 -14: a)

∑ ∑xxa

(11)

∑ ∑xxb

(12)

i j ij

i

b)

j

i j ij

i

j

where: aij ) √aiaj(1 - kij) bij )

bi + bj (1 - lij) 2

interaction parameters T (K)

EoS

k12

l12

AADP (%)

Nexpt

288

PR SRK PR SRK PR SRK PR SRK PR SRK

0.1694 0.1692 0.1677 0.1696 0.1677 0.1695 0.1681 0.1697 0.1688 0.1695

-0.0060 -0.0062 -0.0065 -0.0061 -0.0065 -0.0064 -0.0060 -0.0062 -0.0052 -0.0062

0.62 0.33 0.58 0.22 1.07 0.69 1.02 0.53 0.90 0.43

5

298 310 330 360

(13) (14)

The two EoSs together with the mixing rules were integrated in the software package PHEQ developed by Geana˘ and Rus29

7 9 9 9

and used to model the phase behavior. Prediction of the critical lines is done using the Heidemann and Khalil method.30,31 These models were applied to the experimental data in two steps. First, the VLE data for five different temperatures (288, 298, 310, 330, 360 K) were correlated, and at each temperature a set of interaction parameters was obtained. In the next step, we try a semipredictive approach of the model (as described in refs 12, 32, 33), by introducing a single set of temperature independent parameters in the EoS to predict the critical and subcritical phase behavior in a large range of pressures and temperatures. A similar procedure was applied with good results for modeling other binary systems of trifluoromethane and members of alkylbenyenes (phenyloctane, phenylpropane, isobutylbenzene) and the results are presented elsewhere.10-12 To evaluate the quality of correlations, average absolute deviation in bubble-point pressure AADP was calculated, given by AADP (%) )

where the two constants, a and b, for PR EoS are a ) 0.45724

Table 6. Interaction Parameters and Average Absolute Deviation in Bubble-Point Pressure (AADP) for the System [x trifluoromethane + (1 - x) 1-phenyltetradecane], Obtained by Correlation

1 Nexpt

Nexpt

∑ i)1

|

Pexpt - Pcalcd i i Pexpt i

|

100

(15)

The values of the k12 and l12 parameters and the AADP values for five temperatures positioned below and above the temperature of UCEP, obtained in the VLE data correlation procedure are listed in Table 6. The results prove the quantitative applicability of the cubic EoS to correlate the VLE data. As can be observed, the interaction parameters are not strongly temperature dependent. On the basis of this fact, the single set of parameters was established by averaging the k12 and l12 values in the fitted temperature range. The resulting set of parameters is k12 ) 0.1695, l12 ) -0.0062 for the SRK EoS and k12 ) 0.168, l12 ) -0.006 for the PR EoS. These sets of parameters were introduced in the two EoSs, and predictions of the system’s phase behavior were done. The predictions of the liquid-liquid-vapor curve and critical curve with the SRK and PR EoS coupled with two-parameter mixing rules and a single set of binary parameters are compared as P-T projections in Figure 4. As can be seen similar critical curves are predicted; the PR EoS gives lower critical pressures than SRK, at the same temperatures. Similar to our previous work,11,12 the predicted behavior represents in both cases, type III phase behavior,9 in agreement with the experimental findings. The second branch of critical line originates in the critical point of the heavy component (1phenyltetradecane) and goes to high pressure and temperature without a minimum or maximum in pressure or temperature. This fact is characteristic for asymmetric systems with a large immiscibility region, developing type III phase behavior.27 For the system in study there are no critical data available for comparison.

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Figure 4. P-T diagram of the system [x trifluoromethane + (1 - x) 1-phenyltetradecane]. Comparison of the predictions with a single set of parameters with SRK/2PCMR (k12 ) 0.1695, l12 ) -0.0062) and PR/ 2PCMR (k12 ) 0.168, l12 ) -0.006): critical points of 1-phenyltetradecane (b); critical end point (2); quadruple point SLLV (9); LLV line (9s2); PR/2PCMR predicted critical line (light line); SRK/2PCMR predicted critical line (heavy line).

217

Figure 6. Comparison of predicted results with SRK/2PCMR (k12 ) 0.1695, l12 ) -0.0062) (s), with our experimental phase equilibrium data for the system [x trifluoromethane + (1 - x) 1-phenyltetradecane] at T ) 288 K (O). Table 7. Comparison of AADP of the Correlations at Different Temperatures (a) with the Predictions with One Single Set of Parameters (b) and SRK EoS T (K)

Nexpt

AADPa (%)

AADPb (%)

288 298 310 330 360

7 11 10 11 10

0.33 0.22 0.69 0.53 0.43

0.48 0.27 0.77 0.56 0.45

a Obtained in the bubble P optimization procedure of the VLE data. Calculations with a single set of interaction parameters: k12 ) 0.1695, l12 ) -0.0062.

b

Figure 5. Comparison of predicted results with SRK/2PCMR (k12 ) 0.15, l12 ) -0.013) (s), with our experimental phase equilibrium data for the system [x trifluoromethane + (1 - x) 1-phenyltetradecane]: 310 (9); 330 (2); 360 K (b).

Further, SRK/vdW and PR/vdW calculations with the single set of parameters were done for the new experimental VLE and LLE data, for temperatures between 288 and 360 K (Figure 5 and Figure 6). As can be seen the predictions with a single set of parameters are in good agreement with the experiments for both VLE and LLE data. The absolute average deviations in bubble-point pressure (AADP) obtained with the single set of parameters (k12 ) 0.1695, l12 ) -0.0062) and results of correlation of the experimental isothermal data with SRK/van der Waals mixing rules at each temperature are presented in Table 7. It can be observed that the predictions with a single set of binary parameters are in agreement with the results from the correlations, proving the applicability of the SRK/vdW model for describing the phase behavior of the investigated system. Figure 6 shows that the mole fraction of CHF3 of liquid phase L1 in the calculated P-x diagrams is very close to 1, so the L1V region is very narrow (not shown in the diagram) in accordance with experimental data. It must be noted that the liquid-liquid immiscibility region is larger than for other

Figure 7. P-T projection of the three phase equilibrium line for the system [x trifluoromethane + (1 - x) 1-phenyltetradecane]: experimental LLV (O), measured UCEP, L2 + (L1 ) V) (∆), measured quadruple point (9), SRK/ vdW predictions (k12 ) 0.1695, l12 ) -0.0062) (s), predicted UCEP (2).

systems involving alkylbenzenes with lower molar weight, as heavy component,10-12 as a result of the increasing asymmetry of these systems with the increase of the molar mass of the alkylbenzene. Moreover, our studies10-12 have shown an increase of the interaction parameter, k12, in the binary systems CHF3 + alkylbenzenes (phenylalkanes) from 1-phenylpropane to 1-phenyltetradecane. Thus, k12 can be considered to be a measure of the system’s asymmetry.

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Figure 8. T-x-y diagram for the system [x trifluoromethane + (1 - x) 1-phenyltetradecane] at P ) 6 MPa. Experimental data (0) vs SRK predictions (k12 ) 0.1695, l12 ) -0.0062) (s).

Figure 9. T-x-y diagram for the system [x trifluoromethane + (1 - x) 1-phenyltetradecane] at P ) 10 MPa. Experimental data (0) vs SRK predictions (k12 ) 0.1695, l12 ) -0.0062) (s).

In addition, Figure 7 compares the predictions using the SRK/ vdW model with experimental LLVE data. The three phase equilibrium line is limited at low temperatures by the quadruple point, SLLV (not calculated in this work). In this case the model is less accurate, but the results can be satisfactorily considered. A good prediction of the UCEP is observed. The quality of predictions is also tested for isobaric T-x diagrams. Figure 8 and Figure 9 present a comparison of our VLE and LLE experimental data with calculation results when the SRK/vdW model is applied. The predictions cover the whole range of temperature and mole fractions, while the measured region is limited. As can be seen, the predictions describe very well our data at relatively low pressures, while for the LLE points of the higher pressure isobars (Figure 9) less good results are obtained. To have the global view of the phase behavior for the whole range of concentrations and large domain of temperature and pressure, predictions with the SRK/vdW model based on a single set of parameters at constant mixture composition were done. The results are plotted and compared as P-T isopleths. In Figure 10 and Figure 11, two isopleths for x (trifluoromethane) ) 0.3106 and x (trifluoromethane) ) 0.2909, respectively, are given, the first not intersecting the LLV line, and the second

Figure 10. The isopleth for the system [x trifluoromethane + (1 - x) 1-phenyltetradecane] at x ) 0.3106. Experimental data vs SRK predictions (k12 ) 0.1695, l12 ) -0.0062): experimental data (O); predicted LLV line (•••); predicted isopleth (s); predicted critical point for mixture (b).

Figure 11. The isopleth for the system [x trifluoromethane + (1 - x) 1-phenyltetradecane] at x ) 0.2909. Experimental data vs SRK predictions (k12 ) 0.1695, l12 ) -0.0062): experimental data (O); predicted LLV line (•••); predicted isopleth (s); predicted critical point for mixture (b).

Figure 12. Experimental isopleths vs SRK predictions (k12 ) 0.1695, l12 ) -0.0062) for the system [x trifluoromethane + (1 - x) 1-phenyloctane]: LLV line (s), solid-liquid-liquid-vapor quadruple point (9); vapor-liquid equilibria at x ) 0.0525 (+), 0.1500 (/), 0.1954 (9), 0.2453 (2), 0.2800 (b), 0.2909 (∆), 0.3011 (×), 0.3059 ([); liquid-liquid equilibria at x ) 0.2909 (∆), 0.3059 ()), 0.3106 (0); solid-liquid-liquid equilibria (O), predicted isopleths (s).

crossing the LLV line with two branches, one for VLE and the other for LLE. Figure 12 presents a comparison of all

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experimental isopleths with the corresponding predicted data over the entire investigated P-T domain. It is of importance to point out the quality of the predicted VLE data. The agreement with our experiments is almost perfect not only for certain isopleths, but for the whole range of concentrations. As comparation, LL equilibria are slightly worse described by the tested model, especially in the vicinity of the SLL phase boundary, but the quality of the predictions can be considered satisfactory. These results confirm the predicted behavior as was illustrated in the T-x diagrams. Similar results are obtained when using the PR EoS coupled with van der Waals mixing rules and the averaged set of parameters (k12 ) 0.168, l12 ) -0.006). The topology of the phase behavior is also good for both critical and subcritical regions. 5. Conclusions High pressure phase behavior of the system consisting of trifluoromethane and 1-phenyltetradecane was investigated in the temperature range 253.34-370 K and pressures up to 12 MPa. According to the general classification of van Konynenburg and Scott, the system develops type III phase behavior, characteristic for asymmetric systems with a large region of immiscibility. The new measured data were modeled using PR and SRK EoSs coupled with two parameters van der Waals mixing rules integrated in the PHEQ software package. One set of interaction parameters, optimized in the VLE correlation procedure was introduced in the EoS, and the model was applied in a semipredictive approach to describe the critical and subcritical behavior of the binary system. Comparison of the experimental data with predictions proved that a relatively simple model based on cubic EoS and van der Waals mixing rules is able to predict the topology of phase behavior for highly asymmetric systems, like the investigated one. Nomenclature EoS ) equation of state a,b ) equation of state parameters k12, l12 ) binary interaction parameters m ) parameter in the equation of state, depending on the acentric factor PR ) Peng-Robinson equation of state SRK ) Soave-Redlich-Kwong equation of state HFC ) hydrofluorocarbons phC14 ) phenyltetradecane T ) temperature P ) pressure UCEP ) upper critical end point Pc ) critical pressure Tc ) critical temperature Tm ) melting temperature Tb ) boiling temperature AADP ) absolute average deviation in pressure x,y ) mole fractions Nexpt ) number of experimental points VLE ) vapor-liquid equilibria LLE ) liquid-liquid equilibria LLVE ) vapor-liquid-liquid equilibria SLLE ) solid-solid-vpour equilibria SLLV ) quadruple point 2PCMR ) two parameters conventional (van der Waals) mixing rules vdW ) van der Waals

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Greek Letters ω ) acentric factor R(T) ) temperature dependence function of parameter a in the equation of state

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ReceiVed for reView May 3, 2010 ReVised manuscript receiVed June 29, 2010 Accepted July 12, 2010 IE101008W