Isothermal VaporâLiquid Equilibrium Data and Thermodynamic

Article pubs.acs.org/jced

Isothermal Vapor−Liquid Equilibrium Data and Thermodynamic Modeling for Binary Systems of Perfluorobutane (R610) + (Methane or Hydrogen Sulfide) at (293, 313, and 333) K Mulamba Marc Tshibangu,† Alain Valtz,‡ Caleb Narasigadu,† Christophe Coquelet,†,‡ and Deresh Ramjugernath*,† †

Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus, Durban 4041, South Africa ‡ CTP−Center for the Thermodynamics of Processes, MINES ParisTech, PSL Research University, Rue Saint Honoré, 77305 Fontainebleau, France ABSTRACT: Isothermal vapor−liquid equilibrium data for binary systems comprising perfluorobutane (R610) with methane (CH4) or hydrogen sulfide (H2S) were measured at isothermal conditions of approximately (293, 313, and 333) K, and pressures up to 9.837 MPa. The data were measured using a “static-analytic” apparatus equipped with a mobile pneumatic capillary sampler. The experimental data were correlated via the direct method using two sets of thermodynamic models. The Peng− Robinson equation of state incorporating the Mathias−Copeman α function, with the Wong−Sandler mixing rule utilizing the nonrandom two-liquid activity coefficient model, was used for the correlation of the CH4 + C4F10 system, while the Soave−Redlich−Kwong equation of state incorporating the Mathias−Copeman α function, with the modified Huron−Vidal first-order mixing rule utilizing the nonrandom two-liquid activity coefficient model was used for the H2S + C4F10 system.

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INTRODUCTION The atypical behavior of fluorochemicals, such as perfluorocarbons, has generated great interest within the Thermodynamics Research Unit at the University of KwaZulu-Natal, CTP Mines-ParisTech, and collaborating chemical industries. This has resulted in an investigative program to understand the potential use of these materials as physical solvents for flue gas cleaning. Fluorochemicals have found application as cleaning agents at display manufacturing plants; as blood substitutes, surfactants and anesthetics in the medical sector; as replacements for ozone-unfriendly substances such as chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs) in refrigeration industries; as plasma etching agents in semiconductor manufacturing; as a dielectric medium in highvoltage switching stations; and as solvents in the chemical industry.1 As part of the investigative program, phase equilibria measurements and thermodynamic modeling have already been undertaken for a number of binary systems, e.g., C2H6 + C4F10,2 CO2 + C4F10,3 and NO + C4F10 4 and CO + C4F10.4 To the best of our knowledge, vapor−liquid equilibrium (VLE) data for the binary systems of C4F10 + CH4 or H2S have not been published in open literature to date. Consequently, the current study concerns isothermal vapor− liquid equilibrium data for binary systems containing perfluorobutane (R610) with methane (CH4) or hydrogen © 2014 American Chemical Society

sulfide (H2S) at temperatures of approximately (293, 313, and 333) K. The experimental data were correlated with the Peng− Robinson equation of state (EoS)5 incorporating the Mathias− Copeman α function,6 and the Wong−Sandler mixing rule7 utilizing the nonrandom two-liquid activity coefficient model8 (abbreviated as PR-MC-WS-NRTL) for the CH4 + C4F10 system. For the H2S + C4F10 system, the Soave−Redlich− Kwong equation of state9 incorporating the Mathias−Copeman α function6 and the modified Huron−Vidal first-order mixing rule10 utilizing the NRTL activity coefficient model8 (abbreviated as SRK-MC-MHV1-NRTL) was used.

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EXPERIMENTAL SECTION Chemicals. The components perfluorobutane (C4F10), methane, and hydrogen sulfide were supplied in gas cylinders and were used in this study without further purification. Gas chromatograph (GC) analysis of the gaseous components did not reveal any significant impurities. Table 1 lists the supplier information and purities of the chemicals. Experimental Equipment. The experimental apparatus used in the measurements is based on the “static-analytic” method and is similar to that described by Laugier and Received: June 2, 2014 Accepted: August 14, 2014 Published: September 2, 2014 2865

dx.doi.org/10.1021/je500496y | J. Chem. Eng. Data 2014, 59, 2865−2871

Journal of Chemical & Engineering Data

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accelerate component transfer to the equilibrium cell, the bath temperature is set to approximately 273 K and perfluorobutane, the least volatile component, is then easily loaded due to a pressure differential. The bath temperature is thereafter set to a desired value, and the more volatile component (either CH4 or H2S) is charged to a desired pressure value corresponding to the first measurement. The stirrer is switched on and adjusted to ensure sufficient stirring and the system left to equilibrate. Equilibrium is characterized by the measured temperature and pressure remaining constant (within their measured uncertainty) for approximately 10 min. At the equilibrium state, samples of respective phases are withdrawn and analyzed using a mobile ROLSI pneumatic sampler12 and a gas chromatograph, respectively. At least five samples are withdrawn, and repeatability is achieved to within 1 %. A new equilibrium point is achieved by addition of the more volatile (either CH4 or H2S) component into the equilibrium cell. This procedure is repeated until the whole composition range is covered for a desired isotherm. After completion of one isotherm, the cell is cleaned and the procedure is repeated for each run at different temperatures. Data Reduction. The experimental VLE data were correlated using in-house software developed at CTP MINES-ParisTech. The experimental data were correlated via the direct method using two thermodynamic models. The first model which comprised the Peng−Robinson equation of state5 with the Mathias−Copeman α function6 and the Wong− Sandler mixing rule7 utilizing the NRTL activity coefficient model8 was used for the CH4 + C4F10 system. The H2S + C4F10 system was correlated using the Soave−Redlich−Kwong equation of state9 with the Mathias−Copeman α function6 and the MHV1 mixing rule10 utilizing the NRTL activity coefficient model.8 The critical properties and acentric factors for each of the pure compounds and which were used in the modeling are listed in Table 2.

Table 1. Specifications for Chemicals Used in This Study compound

CAS no.

supplier

volume fraction

C4F10 CH4 H2S

355-25-9 74-82-8 7783-06-4

NECSA (Pretoria, South Africa) Air Liquide (Paris, France) Air Liquide

0.9800 0.9999 0.9950

Richon.11 The entire experimental apparatus was housed inside a fume hood and consisted of a constant-volume equilibrium cell constructed from titanium alloy. The equilibrium cell was equipped with two sapphire windows facilitating direct observation of the liquid level, as well as viewing of phases in equilibrium and observation of the supercritical state (if it existed). Furthermore, the equilibrium cell was equipped with fitting valves for charging/discharging of its contents and provisions for temperature and pressure measurement. Isothermal measurement was achieved by immersion of the equilibrium cell in a thermoregulated liquid bath. For accurate temperature measurement, two platinum resistant temperature probes (Pt-100 Ω, Thermoset, Maizières-les-Metz, France) were inserted within thermowells drilled into the body of the equilibrium cell. One probe was placed near the top of the equilibrium cell corresponding to the vapor phase and the other near the base of the equilibrium cell corresponding to the liquid phase. The location of the probes was set to monitor if there were any temperature gradients within the bath. The temperature probes were intermittently calibrated against a standard probe (25 Ω, Hart Scientific 5628, Norwick, U.K.) certified by the Laboratoire National d’Essais (Paris, France) following the International Temperature Scale 1990 Protocol. The resulting uncertainty in the temperature measurement is estimated to be within 0.02 K (k = 2) for both probes. Pressure measurement was via a pressure transducer (model PTX611, Druck, Labége, France) encased in a heat regulated block maintained at 353 K. The temperature regulation was via a proportional−integral−derivative (PID) controller (model 6100, WEST, Gurnee, IL, USA). The pressure transducer was intermittently calibrated against a reference pressure transducer (model PACE 5000, Druck). The uncertainty in the pressure measurement is estimated to be within 0.0012 MPa (k = 2). Temperature and pressure data logging were both achieved via an online HP data acquisition unit (HP34970A, Agilent, Santa Clara, CA, USA) linked to a personal computer via an RS-232 connection port. Analysis of the equilibrium phase samples was undertaken using a GC (model CP-3800, Varian, Grenoble, France) configured with a thermal conductivity detector (TCD). Separation of the components was achieved using a 5 % Krytox/Carboblack B 60/80 mesh column purchased from Restek, Lisses, France. The GC detector was calibrated by repeated injections of known amounts of each pure component (separately) into the injector of the GC using a gastight syringe (SGE, Ringwood, Australia). The uncertainty in the equilibrium phase composition is estimated to be less than 0.006 for both the vapor and liquid mole fractions for the CH4 + C4F10 and H2S + C4F10 systems. The sampling of phases was achieved using a mobile ROLSI pneumatic sampler12 (ARMINES patent, Paris, France). Experimental Procedure. At room temperature, the equilibrium cell with its associated lines is initially cleaned with ethanol and evacuated using a vacuum pump. To

Table 2. Critical Properties and Acentric Factorsa

a

compound

Tc/K

Pc/ MPa

ω

C4F10 H2S CH4

385.84 451.70 190.60

2.289 1.9049 4.6002

0.385 0.4943 0.008

Values taken from ref 16.

The simplex algorithm was employed for the VLE data regression using the flash calculation objective function, which is expressed as follows: 2 ⎡N 100 ⎢ ⎛⎜ xexp − xcal ⎞⎟ F= + ∑ N ⎢⎢ 1 ⎜⎝ xexp ⎟⎠ ⎣

⎛ y − y ⎞2 ⎤ exp cal ⎟ ⎥ ∑ ⎜⎜ yexp ⎟⎠ ⎥⎥ 1 ⎝ ⎦ N

(1)

where N is the number of data points, xexp and xcal are the experimental and calculated liquid mole fractions; yexp and ycal, the experimental and calculated vapor mole fractions, respectively. Each isotherm measured for both systems was individually modeled. Thereafter, all isotherms were modeled simultaneously in a temperature-dependent form to facilitate phase equilibrium predictions for isotherms that were not measured. The mathematical form of the temperature dependence is defined by 2866



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gij − gjj = aij + bijT

Table 4. Experimental VLE Data for the CH4 (1) + C4F10 (2) Systema

(2)

where (gij − gjj) is the reduced NRTL parameter and T is the temperature in K. A statistical analysis of the experimental VLE data involving determination of the bias, the mean relative deviation (MRD), the root mean squared deviation (RMSD), or absolute average deviations (AAD) helps quantify the fit of the model to the experimental data, with lower values indicating a closer fit of the model to the experimental data. In this study, the bias was calculated for both the vapor and liquid mole fractions. The bias deviations are defined by bias (U /%) = (100/N ) ∑ ((Uexp − Ucal)/Uexp)

P/MPa 0.473 2.015 3.988 6.587 8.058 5.188 2.914 8.901 10.276 10.655 9.562

(3)

where N is the number of data points and U = x1 or y1. Relative volatility, which is used in distillation column design to provide an indication of the ease or difficulty of separating components in a mixture, can be calculated using the following equation. αij =

y /xi yi /xi Ki = i = Kj yj /xj (1 − yi )/(1 − xi)

1.052 1.853 2.687 3.924 4.788 5.603 6.459 7.447 8.432 9.446 9.837

(4)

Critical Point Determination. The critical coordinates for binary mixtures and the region near the critical phase behavior can be approximated using extended scaling laws as presented by Ungerer et al.13 and previously used by El Ahmar et al.2 and Valtz et al.3 In fact, the critical region of the P−x diagram is represented by complementing the scaling law with a linear term which is expressed as y − x = λ1(Pc − P) + μ(Pc − P)β

(5)

y+x − xc = λ 2(Pc − P) 2

(6)

7.753 1.321 2.168 2.839 3.704 4.541 5.301 6.017 6.743 7.368 8.466 8.138

where y and x are the vapor and liquid mole fractions; λ1, λ2, and μ are adjustable coefficients regressed from a set of P−x−y experimental data below the critical point; β is a constant; and (Pc, xc) are the critical coordinates.

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RESULT AND DISCUSSION The experimental vapor pressures for H2S of Reid et al.14 and vapor pressures for C4F10 of El Ahmar et al.2 were both fitted to the Peng−Robinson and Soave−Redlich−Kwong equations of states, respectively, to obtain the correlated Mathias−Copeman α function parameters. The correlated Mathias−Copeman α function parameters for C4F10 are available in El Ahmar et al.2, and those for H2S are reported in Table 3. The experimental isothermal VLE data for the CH4 + C4F10 and H2S + C4F10 systems are presented in Tables 4 and 5, respectively. The experimental and the modeled data for both systems are graphically compared in the form of P−x−y phase diagrams in Figures 1−3 and Figures 4−6 for the CH4 + C4F10

a

H2S (PR EoS)

H2S (SRK EoS)

c1 c2 c3

0.507 0.008 0.342

0.641 −0.183 0.513

y1 0.423 0.803 0.867 0.875 0.858 0.875 0.847 0.846 0.804 0.773 0.834 0.467 0.626 0.699 0.754 0.767 0.774 0.775 0.768 0.749 0.706 0.665 0.619 0.336 0.499 0.563 0.618 0.635 0.646 0.648 0.645 0.634 0.547 0.597

a

x1, y1: liquid and vapor mole fractions; uncertainty u (T,k=2) = 0.02 K; u (P,k=2) = 0.0012 MPa; and u (x1,y1) = 0.006.

and H2S + C4F10 systems, respectively. The correlated parameters for the CH4 + C4F10 system fitted with the PRMC-WS-NRTL model in temperature-independent and temperature-dependent forms are reported in Tables 6 and 7, respectively. Although some authors15 have reported that the Mathias−Copeman α function is known to be problematic since it increases with increasing temperature in the supercritical region, this undesired characteristic did not affect the modeling results in this case. This can be seen in Figures 1−3 where the experimental and modeled data agree favorably well near the critical region. However, one should note that, at supercritical temperatures, the Mathias−Copeman adjustable parameters c2 and c3 are set to zero and c1 becomes equal to the m parameter in the original Soave α function, which can be correlated using the acentric factor. For the H2S + C4F10 system, the correlated parameters for the SRK-MC-MHV1-NRTL model are reported in Tables 8 and 9 for the temperature-independent and temperaturedependent forms, respectively.

Table 3. Mathias−Copeman Parameters for the PR and SRK EoSa coefficient

x1 T/K = 293.05 0.012 0.085 0.181 0.307 0.393 0.234 0.123 0.434 0.552 0.606 0.483 T/K = 313.09 0.029 0.061 0.092 0.149 0.191 0.226 0.268 0.318 0.379 0.467 0.519 T/K = 332.97 0.355 0.029 0.064 0.094 0.133 0.169 0.203 0.239 0.279 0.316 0.435 0.380

Regressed from measured vapor pressure data in ref 14. 2867



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Table 5. Experimental VLE Data for the H2S (1) + C4F10 (2) Systema P/MPa 0.394 0.533 0.679 0.834 0.965 1.119 1.301 1.426 1.639 2.010 1.863 2.014 2.015 2.014 1.844 1.906 1.987 0.721 0.923 1.112 1.343 1.553 1.769 2.153 2.481 2.899 3.155 3.202 2.958 3.222 3.228 3.242 3.239 1.163 1.487 1.989 2.464 2.907 3.303 3.931 4.203 4.769 4.602 4.861 4.874 4.708

x1 T/K = 293.08 0.027 0.051 0.081 0.108 0.131 0.168 0.213 0.249 0.319 0.570 0.433 0.683 0.718 0.970 0.997 0.991 0.982 T/K = 313.00 0.043 0.069 0.095 0.130 0.159 0.196 0.268 0.355 0.507 0.672 0.760 0.996 0.957 0.952 0.930 0.931 T/K = 333.03 0.052 0.088 0.149 0.215 0.284 0.349 0.479 0.554 0.771 0.692 0.915 0.892 0.976

y1 0.396 0.555 0.644 0.706 0.747 0.780 0.810 0.819 0.840 0.879 0.859 0.884 0.894 0.891 0.972 0.943 0.907

Figure 1. Phase diagram (P−x−y) for the CH4 (1) + C4F10 (2) system: ⧫, 293.05 K , PR-MC-WS-NRTL model; *, mixture critical point.

0.395 0.508 0.573 0.635 0.676 0.715 0.763 0.796 0.826 0.853 0.865 0.981 0.895 0.890 0.888 0.883

Figure 2. Phase diagram (P−x−y) for the CH4 (1) + C4F10 (2) system: ▲, 313.09 K , PR-MC-WS-NRTL model; *, mixture critical point.

0.324 0.435 0.547 0.625 0.675 0.714 0.748 0.768 0.841 0.807 0.890 0.878 0.933

Figure 3. Phase diagram (P−x−y) for the CH4 (1) + C4F10 (2) system: ●, 332.97 K; , PR-MC-WS-NRTL model; *, mixture critical point.

For the 293 K isotherm, as pressure was increased (at approximately 1.987 MPa), the phenomena of vapor−liquid− liquid equilibrium were suspected, but no analysis was undertaken at these conditions due to the use of an opaque thermoregulated liquid bath in the experimental apparatus setup. This made analysis of multiple liquid phases nearly impossible as one has to periodically remove the cell from the thermoregulated liquid bath to observe the state of phases in equilibrium. The change of the environment affected the equilibrium cell temperature, and therefore one could see the second liquid phase disappear as the equilibrium cell temper-

a

x1, y1: liquid and vapor mole fraction; uncertainty u (T, k = 2) = 0.02 K; u (P, k = 2) = 0.0012 MPa; u (x1, y1) = 0.006.

The H2S + C4F10 system exhibited azeotropic behavior for both the (313 and 333) K isotherms, with azeotropic compositions of x1 = 0.87 and 0.86, respectively. At these conditions, conventional distillation cannot be used to separate the mixture into high-purity compounds and alternative methods such as pressure-swing distillation would have to be investigated. 2868



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Table 7. Model Parameters Regressed for the PR-MC-WSNRTL Model in a Temperature-Dependent Form for the CH4 (1) + C4F10 (2) System a12/(J·mol−1) a21/(J·mol−1) b12/(J·mol−1·K) b21/(J·mol−1·K) kij

48354 −3080 −107 17.6 0.60

Table 8. Model Parameters Regressed for the SRK-MCMHV1-NRTL Model in a Temperature-Independent Form for the H2S (1) + C4F10 (2) System for given T/K

Figure 4. Phase diagram (P−x−y) for the H2S (1) + C4F10 (2) system: ⧫, 293.08 K; , SRK-MC-MHV1-NRTL model.

parameters

293.08

313.00

333.03

(g12 − g22)/(J·mol−1) (g21 − g11)/(J·mol−1)

10819 1106

10467 757

10700 494

Table 9. Model Parameters Regressed for the SRK-MCMHV1-NRTL Model in a Temperature-Dependent Form for the H2S (1) + C4F10 (2) System a12/(J·mol−1) a21/(J·mol−1) b12/(J·mol−1·K) b21/(J·mol−1·K)

ature varied from 293.08 K to approximately 298.15 K. A transparent thermoregulated liquid bath would have facilitated the measurement for the VLLE data point. The relative volatilities were calculated for both systems using their respective set of thermodynamic models. The results obtained are graphically compared to the experimental data in Figures 7 and 8. As can be seen in Figure 7 for the CH4 + C4F10

Figure 5. Phase diagram (P−x−y) for the H2S (1) + C4F10 (2) system: ▲, 313.00 K; , SRK-MC-MHV1-NRTL model.

Figure 6. Phase diagram (P−x−y) for the H2S (1) + C4F10 (2) system: ●, 333.03 K; , SRK-MC-MHV1-NRTL model.

Figure 7. Plot of relative volatilities (α12) for the CH4 (1) + C4F10 (2) system: ⧫, 293.05 K; ▲, 313.09 K; ●, 332.97 K; , PR-MC-WSNRTL model. Error bands shown at 6 % for experimental data.

Table 6. Model Parameters Regressed for the PR-MC-WSNRTL Model in a Temperature-Independent Form for the CH4 (1) + C4F10 (2) System

system, there is generally an agreement between the measured and the calculated relative volatilities at 293.05 K, but the data at (313.09 and 332.97) K exhibit a significant disparity as compared to the calculated values, with an improvement in model representation as pressure increases. For the H2S + C4F10 system, there is good agreement between the calculated and the experimental relative volatilities for the three isotherms measured at (293.08, 313, and 333.03) K, as shown in Figure 8.

for given T/K parameters

293.05

313.09

332.97

(g12 − g22)/(J·mol−1) (g21 − g11)/(J·mol−1) kij

16649 1956 0.60

14414 2235 0.60

12164 2574 0.61

1275 226.5 35.42 141.8

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measured and calculated VLE data; this could be due to there being insufficient experimental data near the critical region. A comparison between the VLE data measured for the CH4 + C4F10 and the H2S + C4F10 systems, with the VLE data for the CO2 + C4F10 system of Valtz et al.,.3 was undertaken to check the selectivity of C4F10 for CO2 relative to CH4 and H2S. The results are presented in Figures 9 and 10. From these

Figure 8. Plot of relative volatilities (α12) for the H2S (1) + C4F10 (2) system: ⧫, 293.08 K; ▲, 313 K; ●, 333.03 K; , SRK-MC-MHV1NRTL model. Error bands shown at 6 % for experimental data.

The bias deviations were determined between the experimental and calculated VLE data for both systems. The results obtained are reported in Tables 10 and 11. The high bias values Table 10. Deviation Bias U Obtained in Fitting Experimental VLE Data with the PR-MC-WS-NRTL Model for the CH4 (1) + C4F10 (2) System T/K

bias(x/%)

bias(y/%)

293.05 313.09 332.97

2.12 1.79 4.10

−2.12 −3.49 −2.76

Figure 9. Selectivity of C4F10 for CO2 relative to CH4. Phase diagrams (P−x−y) for the CH4 (1) + C4F10 (2) system: ⧫, 293.05 K; ▲, 313.09 K; ●, 332.97 K. , PR-MC-WS-NRTL model. Predicted VLE data for the CO2 (1) + C4F10 (2) system of Valtz et al.:3 ◊, 293.05 K; Δ, 313.09 K; ○, 332.97 K.

Table 11. Deviation Bias U Obtained in Fitting Experimental VLE Data with the SRK-MC-MHV1-NRTL Model for the H2S (1) + C4F10 (2) System T/K

bias(x/%)

bias(y/%)

293.08 313.00 333.03

−0.73 −2.00 −2.85

0.13 0.28 0.53

for the CH4 + C4F10 system in Table 10 indicate that the PRMC-WS-NRTL model does not describe the measured VLE data very well. The bias values in Table 11 which are for the H2S + C4F10 system are relatively low and therefore indicate that the SRK-MC-MHV1-NRTL model provides a close fit of the model to the experimental data. The mixture critical points for each isotherm measured for the CH4 + C4F10 system were calculated using the proposed procedure of Ungerer et al.13 The critical coordinates obtained are presented in Table 12 and graphically presented in Figures 1−6. The mixture critical points for isotherms measured at (313.09 and 332.97) K are in agreement with both the experimental and calculated VLE data. The mixture critical point for the 293.05 K isotherm does not correspond to the

Figure 10. Selectivity of C4F10 for CO2 relative to H2S. Phase diagrams (P−x−y) for the H2S (1) + C4F10 (2) system: ⧫, 293.08 K; ▲, 313.00 K; ●, 333.03 K. , SRK-MC-MHV1-NRTL model. Predicted VLE data for the CO2 (1) + C4F10 (2) system of Valtz et al.:3 ◊, 293.08 K; Δ, 313.00 K; ○, 333.03 K.

figures, one can observe that C4F10 has a strong selectivity for CO2 compared to CH4 at temperatures of approximately (293, 313, and 333) K. Figure 10 shows that there is a great probability that coabsorption of CO2 and H2S in C4F10 takes place at (293, 313, and 333) K. However, at temperatures higher than 333 K, C4F10 absorption selectivity for CO2 improves compared to H2S.

Table 12. Mixture Critical Points Using Scaling Laws and Experimental Data for the CH4 (1) + C4F10 (2) System T/K

Pc/MPa

x1,c

293.05 313.09 332.97

10.727 9.837 8.504

0.690 0.595 0.500

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CONCLUSION VLE data were measured for two binary systems, CH4 + C4F10 and H2S + C4F10 at (293, 313, and 333) K using an apparatus 2870



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based on the “static-analytic” method briefly described in the work. The expanded uncertainties in the measurements were within 0.02 K, 0.0012 MPa, and 0.006 for temperatures, pressures, and mole fractions, respectively. The VLE data were correlated via the direct method using two thermodynamics models. The Peng−Robinson equation of state with Mathias− Copeman α function and the Wong−Sandler mixing rule incorporating the NRTL activity coefficient model provided the most satisfactory fit to the measured VLE data for the CH4 + C4F10 system. For the H2S (1) + C4F10 (2) system, the Soave− Redlich−Kwong equation of state with the Mathias−Copeman α function and the modified Huron−Vidal first-order mixing rule incorporating the NRTL activity coefficient model gave good representation of the data measured at (293.08 and 313) K. However, for the isotherm measured at 333.03 K there is a disparity between the experimental and model fit for the VLE data near the critical region.

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(11) Laugier, S.; Richon, D. New apparatus to perform fast determinations of mixtures vapour-liquid equilibria up to 10 MPa and 423 K. Rev. Sci. Instrum. 1986, 57, 469−472. (12) Guilbot, P.; Valtz, A.; Legendre, H.; Richon, D. Rapid On-Line Sampler-Injector: A Reliable Tool for HT-HP Sampling and On-Line GC Analysis. Analusis 2000, 28, 426−431. (13) Ungerer, P.; Tavitian, B.; Boutin, A. Applications of molecular simulation in the oil and gas industryMonte Carlo methods; Edition Technip: Paris, 2005. (14) Reid, R. C.; Praustnitz, J. M.; Polling, B. E. The properties of gases and liquids; McGraw-Hill Book: New York, NY, USA, 1987. (15) Segura, H.; Kraska, T.; Mejía, A.; Wisniak, J.; Polishuk, I. Unnoticed Pitfalls of Soave-Type Alpha Functions in Cubic Equations of State. Ind. Eng. Chem. Res. 2003, 42, 5662−5673. (16) Dortmund Data Bank (DDB), version 2002; DDBST Software and Separation Technology: Oldenburg, Germany.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +27312603128. Fax: +27312601118. Funding

This work is based upon research supported by the South African Research Chairs Initiative of the Department of Science and Technology and National Research Foundation of South Africa. This work is also based on the research supported in part by the National Research Foundation of South Africa (Grant GUN: 80063). Notes

The authors declare no competing financial interest.

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REFERENCES

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