VaporâLiquid Equilibrium (PTxy) Measurements and Modeling for the

Article pubs.acs.org/jced

Vapor−Liquid Equilibrium (PTxy) Measurements and Modeling for the CO−C2H4 Binary System Elise El Ahmar,*,† Alain Valtz,† Nicolas Ferrando,‡ Christophe Coquelet,†,§ and Pascal Mougin‡ †

MINES ParisTech, CEP/TEPCentre Energétique et Procédés, 35 Rue Saint Honoré, 77305 Fontainebleau, France IFP Energies nouvelles, 1 et 4 avenue de Bois Préau, 92852 Rueil-Malmaison, France § Thermodynamics Research Unit, School of Chemical Engineering, University of KwaZulu-Natal, Howard College Campus, Durban, 4041, South Africa ‡

ABSTRACT: In this work, vapor−liquid equilibrium data of the carbon monoxide−ethylene binary system have been measured at five isotherms ranging from (233.73 to 273.18) K, with pressure ranging from (1.4 to 6.1) MPa. The measurements were performed using a “static-analytic” apparatus, equipped with two pneumatic rapid on-line sampler−injector (ROLSI) capillary samplers, with phase analysis via gas chromatography. The uncertainties in the measurements were within ± 0.02 K, ± 0.6 kPa, and ± 0.003 for temperature, pressure, and mole fractions, respectively. The measured data are correlated using two models, the Peng− Robinson equation of state with the generalized α function and the van der Waals mixing rules and the Soave−Redlich−Kwong equation of state coupled with the Twu et al. α function and mixing rules.

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Apparatus Description. The apparatus used (Figure 1) in the experiments is based on the “static-analytic” method and has been previously described by Valtz et al.6,7 and Soo et al.8 Internal cell pressures are measured using a pressure transducer: (Druck, type PTX 611, range: (0 to 10) MPa). A dead weight pressure balance (Desgranges & Huot 5202S) is used for the pressure transducer calibration with the following uncertainties (u(P, k = 2) = 0.6 kPa). The temperature measurement was done via two platinum resistance thermometers probes (Pt-100 Ω) which are situated within each flange. The temperature probes were calibrated against a standard probe (25 Ohms, TINSLEY) which was certified by the Laboratoire National d’Essai (Paris, France). Uncertainties in the temperature measurement are estimated to be within (u(T, k = 2) = 0.02 K) for both probes. A Gas Chromatograph (GC; Varian, model: CP 3800) equipped with a thermal conductivity detector (TCD) was used to analyze the equilibrium phase samples and determine the compositions. For each equilibrium condition, at least five samples of both the vapor and liquid phases are withdrawn using the ROLSI samplers (Mines Paristech, France) and analyzed to check for repeatability of measurements. The column used in the gas chromatograph was supplied by Resteck, France (HaySep D 80/100 mesh, 1.8 m × 1/8” Silcosteel). Calibration of the detector was done by repeated

INTRODUCTION Accurate knowledge of phase equilibrium of systems involving ethylene and various light compounds is necessary to design many units in industrial polymerization plants. Due to specific legislations on the final products, the carbon monoxide content in the produced ethylene effluent should be more specifically controlled. The optimization of separation units thus requires a good knowledge of phase equilibrium of the carbon monoxide plus ethylene system. To understand the thermodynamic behavior of this binary system for which, to the best of our knowledge, no data are available in the open literature, a study of the properties of vapor−liquid equilibrium (VLE) has been initiated. So, isothermal measurements of P−T−x−y data (pressure− temperature−liquid and vapor composition) for this system are undertaken at five temperatures. For each isotherm, a critical point is determined. The measured data are correlated with the Peng−Robinson (PR) equation of state (EoS)1 with the generalized α function2 and the van der Waals mixing rules3 and the Soave−Redlich−Kwong (SRK) EoS2,4 using the Twu et al. α function and mixing rules.5 Relative volatility curves as well as the critical point loci are calculated for the system and presented in the paper.

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EXPERIMENTAL SETUP Materials. Carbon monoxide (CO, CAS Registry No.: 63008-0) and ethylene (C2H4, CAS Registry No.: 74-85-1) were purchased from Air Liquide (France) with a certified volume purity greater than 99.9 %. © 2012 American Chemical Society

Received: June 4, 2012 Accepted: August 30, 2012 Published: September 24, 2012 2744

dx.doi.org/10.1021/je300599p | J. Chem. Eng. Data 2012, 57, 2744−2749

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Figure 1. Schematic representation of vapor−liquid equilibrium measurement apparatus. C, gas chromatography; EC, equilibrium cell; FV, feeding valve; LB, liquid bath; LS, liquid ROLSI sampler−injector; PP, platinum resistance thermometer probe; PrC, carbon monoxide cylinder; PT, pressure transducer; RC, ethylene cylinder; SM, sampler monitoring; ST, sapphire tube; TC1 and TC2, thermal press; TR, temperature regulator; VS, vapor ROLSI sampler−injector; VSS, variable speed stirrer; VP, vacuum pump.

injection of known amounts of each pure component into the gas chromatograph using a syringe. The estimated uncertainties in the equilibrium phase composition is less than 0.003 for both vapor and liquid mole fractions.

In this expression:

MODELING VLE Data Modeling. The experimental VLE data are correlated using two equations of state (EoS's): 1. The Peng−Robinson (PR) EoS (eq 1) with the generalized α function (eq 6) and the van der Waals mixing rules (eq 3) as implemented in the in-house software developed at CEP/TEP:

and

ac, i = 0.457235

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⎞ ⎛ a (v − b) = RT ⎜P + 2 2 ⎟ (v + 2bv − b ) ⎠ ⎝

∑ ∑ xixj i

j

(6)

m = 0.374640 + 1.542260ω − 0.26992ω 2

(7)

where ω is the acentric factor of the compound (0.048 and 0.086 for carbon monoxide and ethylene, respectively9). 2. The Soave−Redlich−Kwong (SRK) EoS (eq 8) with the Twu et al. α function (eq 9) and mixing rules (eq 10), as implemented in the commercial process simulator PRO/ II (v.8.3, SimSci-Esscor):

(1)

⎛ ⎞ a ⎜P + ⎟(v − b) = RT (v − b)v ⎠ ⎝

(2)

(8)

The Twu α function is given by: α(T ) = TR C3(C2 − 1)exp[C1(1 − TRC2C3)]

(9)

where C1, C2, and C3 are three adjustable parameters (Table 1), and the Twu mixing rules are the following: Table 1. Pure Compound Parameters for the Twu et al. α Function (eq 9) in the SRK EoS

aiaj (1 − kij) (3)

with:

ai(T ) = ac, i ·αi(T )

(5)

where TR = T/Tc is the reduced temperature, and:

where xi, Tc,i, and Pc,i are the molar fraction, the critical temperature, and critical pressure of the ith compound [the critical temperature is (132.92 and 282.34) K for carbon monoxide and ethylene, respectively, and the critical pressure (3.499 and 5.041) MPa9]. The attractive term is given by: a(T ) =

Pc, i

αi(T ) = [1 + m(1 − TR1/2)]2

where P is the pressure, R the ideal gas constant, T the temperature, and v the molar volume. The term b stands for the covolume and a for the attractive term, respectively, given by: ⎛ RTc, i ⎞ ⎟⎟ b = ∑ xibi = ∑ xi⎜⎜0.077796 Pc, i ⎠ ⎝ i i

R2Tc,2i

carbon monoxide ethylene

(4) 2745

C1

C2

C3

0.20792 0.21307

0.86069 0.87009

1.7188 2


Journal of Chemical & Engineering Data a (T ) =

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kij = 1.68·10−3T − 0.368

∑ ∑ xixj(aiaj)1/2 (1 − kij) i

+

(15)

j

∑ xi

The kij values effectively used for our calculations with the PR model are determined with this equation. For the SRK EoS, two binary interaction parameters (kij and kji) of the Twu mixing rules (eq 10) are fitted to match experimental bubble pressures. To reduce the number of adjustable parameters, they are assumed to be temperatureindependent, and the other binary parameters of this mixing rules (cij and cji) are kept equal to zero. Results are given in Table 4. To quantify the fit of the models to the experimental data, the deviations, AADU and BIASU, were determined for both the liquid and the vapor phase mole fractions. The deviations are defined by:

[∑j Hij1/3Gij1/3(aiaj)1/6 xj]3

i

∑j Gijxj

(10)

with

Hij = kij − kji

(11)

and Gij = exp( −cijHij)

(12)

Note that eqs 10 and 11 slightly differ from the original Twu’s formulation, since here kij is not divided by temperature. With parameters given in Table 1, the Twu α function accurately correlates pure CO and pure ethylene vapor pressures (average absolute deviation less than 1 % compared to reference values of the DIPPR database9). The Twu mixing rule involves asymmetric binary interaction parameters (kij ≠ kji) which allows an accurate representation of polar/nonpolar systems. It has been developed to reproduce both infinite dilution domain and phase behavior throughout finite range concentrations. The Twu mixing rules are an evolution of the Panagiotopoulos and Reid mixing rules10 which are known to be thermodynamically inconsistent for multicomponent mixtures, since it is not invariant to dividing a component into a number of identical subcomponents.11 These improved mixing rules allow solving this problem. Critical Point Determination. The critical loci of binary mixtures and the near-critical phase behavior have been approximated by the use of extended scaling laws, as previously proposed.12,13 Using the experimental data particularly close to the critical point, it is possible to calculate the critical point coordinates (Pc, xc) using the following expressions: y+x − xc = λ1(Pc − P) 2

(13)

y − x = λ 2(Pc − P) + μ(Pc − P)β

(14)

AADU = (100/N ) ∑ |(Ucal − Uexp)/Uexp|

(16)

BIASU = (100/N ) ∑ ((Uexp − Ucal)/Uexp)

(17)

where N is the number of data points, and U = x1 or y1. These indicators, which give information about the agreement between models and experimental results, are presented in Table 5. Considering all the investigated temperatures, the average AADU for liquid and vapor phase CO compositions are equal to 7.8 %and 8.1 %, respectively, for the PR EoS and equal to 5.9 % and 7.4 %, respectively, for the SRK EoS. For each temperature, the maximal deviation is systematically obtained for the most diluted experimental point for which CO composition is particularly low. Thus, the SRK Eos model coupled with the Twu et al. α function and mixing rules represents the experimental data better than the PR EoS with the generalized α function and van der Waals mixing rules, especially near the critical point. The best criteria to check the good reliability of the data is to compare the experimental and calculated relative volatility (αij).16 The relative volatilities are computed from the model and compared to the experimental values. Figure 3 shows the composition dependency of relative volatility for the five isotherms measured. The error bands associated to this property are obtained from a propagation of error analysis as described in ref 16. There is generally a good agreement between the experimental relative volatility and those calculated using the SRK EoS with the proposed interaction parameters. The PR EoS did not fare as well, with representation becoming increasingly worse as temperature is decreased. Again, the maximal deviations for each isotherm are obtained for the highest dilution experimental point. The values of adjustable parameters and the coordinates of the critical point are given in Table 6. Figure 4 shows the PT diagram for the system, with the pure component vapor pressure curves, the critical point values, and critical locus calculated with PR and SRK EoS. Procedures to calculate critical points using EoS’s were initially proposed by Heidemann and Khalil17 and Michelsen and Heidemann.18 They assumed that the stability criterion for an isothermal variation (between an initial state and a very close new state) can be described by a minimization of the molar Helmholtz energy:

where x and y stand for molar fraction in the liquid and vapor phases, respectively, and β = 0.325 is a characteristic universal exponent.14 Pc, xc (critical coordinates) and λ1, λ2, μ (adjustable coefficients) are regressed from a set of coexistence points (P, x, y) below the critical point. Equation 13 concerns the mean composition evolution between the vapor and liquid compositions with pressure. Equation 13 uses the scaling laws equations and evolution of (y−x) with pressure.

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RESULTS The experimental VLE data are presented in Table 2 and Figure 2a,b for all five isotherms, that is, (233.73, 243.08, 253.22, 263.22, and 273.18) K. A classical phase diagram (type I according to Van Konynenburg and Scott15) with a single critical point is observed for each temperature. For each isotherm, the adjusted binary interaction parameter (kij) in the PR EoS for the CO (1) + C2H4 (2) system is presented in Table 3. It appears that the best fit of experimental VLE data is obtained using a temperature dependence of this parameter. The discrete kij values are then linearly correlated with temperature:

A − A0 −

∑ μi0 Δni ≥ 0 i

2746

(18)


2747

a

10 10 11 5 5 12 6 5 6 7 6 5 5 6

0 0.0005 0.0017 0.0034 0.0100 0.0186 0.0416 0.0623 0.0811 0.1029 0.1244 0.1525 0.1687 0.1921 0.1928

x1

5·10−6 1·10−5 6·10−5 1·10−4 1·10−4 1·10−4 8·10−5 1·10−4 5·10−4 4·10−4 9·10−4 9·10−4 2·10−3 1·10−3 2·10−3 2·10−3 1·10−3 2·10−3 7·10−4 1·10−3 2·10−3 1·10−3 5 5 5 6 5 5 5 6 5 5 5 5 4 5 4 5 4 5 5 5 5 5 y1

6 5 7 6 6 6 6 6 7 5 5 6 6 6

0 0.0030 0.0095 0.0191 0.0506 0.0844 0.1615 0.2050 0.2379 0.2630 0.2730 0.2750 0.2700 0.2530 0.2500

δy1 0 1·10−5 2·10−4 2·10−4 5·10−4 5·10−4 7·10−4 1·10−3 8·10−4 1·10−3 1·10−3 1·10−3 1·10−3 1·10−3 1·10−3

2·10−6 4·10−6 5·10−6 2·10−5 2·10−5 8·10−5 2·10−4 9·10−5 2·10−4 8·10−4 1·10−3 3·10−4 6·10−4 1·10−3 4·10−4 9·10−4 1·10−3 5·10−4 7·10−4

4.1020 4.1638 4.2528 4.3910 4.7277 5.0665 5.4138 5.7533 5.8604 5.9701 6.0115 6.0208 6.0294

P/MPa

7 5 5 5 6 5 6 5 5 5 5 5 6 7 5 5 5 6 5

0 0.0045 0.0198 0.0277 0.0588 0.0840 0.1298 0.2030 0.2920 0.3840 0.4384 0.4766 0.4950 0.5075 0.5042 0.4971 0.4878 0.4760 0.4599 0.4386

y1

nx 7 6 6 4 5 6 5 5 6 6 5 4

8·10−6 3·10−4 3·10−4 4·10−4 4·10−4 5·10−4 1·10−3 2·10−3 1·10−3 5·10−4 3·10−4 8·10−4 5·10−4 6·10−4 1·10−4 6·10−4 2·10−3 9·10−4 9·10−4

δy1

x1 0 0.0021 0.0053 0.0099 0.0230 0.0371 0.0534 0.0721 0.0783 0.0875 0.0927 0.0949 0.0975

2.5348 2.5433 2.5876 2.7364 2.8666 3.2172 3.696 4.2512 4.8275 5.4114 6.0057 6.5193 7.0432 7.1982 7.4141 7.5958 7.7887

P/MPa

0 2·10−5 1·10−5 1·10−4 2·10−4 1·10−4 5·10−4 5·10−4 3·10−4 6·10−4 5·10−4 5·10−4 3·10−4

7 5 6 6 5 11 5 5 5 5 5 6 6 6 5 5

nx 0 0.0003 0.0016 0.0062 0.0104 0.0228 0.0401 0.0607 0.0864 0.1113 0.1403 0.1676 0.1992 0.2120 0.2290 0.2460 0.2730

x1

δx1

ny

0 0.0004 0.0017 0.0024 0.0053 0.0079 0.0132 0.0237 0.0393 0.0655 0.0993 0.1340 0.1715 0.2069 0.2360 0.2696 0.2848 0.3020 0.3227 0.3444

ny

δx1 0 4·10−6 1·10−5 1·10−5 8·10−5 9·10−5 2·10−4 2·10−4 5·10−4 3·10−4 4·10−4 4·10−4 9·10−4 6·10−4 6·10−4

0 9 5 5 6 5 9 6 7 6 6 5 5 5 5 5 5 5 5 5

x1

T = 273.18 K

6·10−5 6·10−4 7·10−4 7·10−4 6·10−4 8·10−4 8·10−4 1·10−3 1·10−3 2·10−3 8·10−4 1·10−3 6·10−4 1·10−3 2·10−4 1·10−3 2·10−3 7·10−4 1·10−3 1·10−3 8·10−4 8·10−4

1.9323 1.9436 1.9846 2.0088 2.0968 2.1741 2.3258 2.6217 3.0885 3.7966 4.5929 5.4664 6.2935 6.993 7.5005 7.9219 8.1105 8.286 8.4505 8.5596

nx

0 0.0173 0.0664 0.1196 0.1752 0.1720 0.2577 0.3638 0.4760 0.5370 0.5670 0.5905 0.5940 0.5995 0.5990 0.5926 0.5860 0.5750 0.5682 0.5540 0.5360 0.5251 0.5167 T = 263.22 K

P/MPa

δx1

δy1

T = 243.08 K y1

δx1 ny

T = 233.73 K

7 6 6 5 11 6 5 5 8 8 4 4

ny

0 3·10−6 1·10−5 6·10−5 1·10−4 2·10−4 2·10−4 3·10−4 4·10−4 6·10−4 5·10−4 7·10−4 9·10−4 1·10−3 1·10−3 1·10−3 1·10−3

δx1

T = 253.22 K

Uncertainty: u(T, k = 2) = 0.02 K; u(P, k = 2) = 0.6 kPa; u(x,y) = 0.003. x,y: liquid and vapor mole fraction; nx,ny: number of taken samples; δx, δy: standard deviation).

nx

0 0.0010 0.0045 0.0088 0.0138 0.0136 0.0236 0.0411 0.0712 0.1040 0.1476 0.1935 0.1955 0.2360 0.2680 0.3020 0.3110 0.3340 0.3490 0.3667 0.3870 0.4080 0.4180

3.2475 3.2635 3.2983 3.3507 3.5391 3.7860 4.3624 4.8727 5.3143 5.8027 6.2308 6.6641 6.8438 7.008 7.013

5 5 5 6 5 5 9 9 6 5 5 5 5 5 5 5 6 5 4 5 5 7

1.4760 1.5106 1.6159 1.7291 1.8598 1.8649 2.1414 2.6144 3.4055 4.2278 5.2417 6.2375 6.2731 6.8651 7.3746 7.8872 8.0469 8.3726 8.5775 8.7608 8.9424 9.0132 9.0283

x1

P/MPa

nx

P/MPa

Table 2. Experimental VLE Pressures and Phase Compositionsa for CO (1) + C2H4 (2) System

y1 0 0.0078 0.0185 0.0334 0.0668 0.0967 0.1188 0.1330 0.1335 0.1322 0.1312 0.1296 0.1280

5 5 5 5 5 5 6 5 5 6 6 5 6 5 5 7

ny

y1 0 0.0025 0.0141 0.0505 0.0787 0.1505 0.2250 0.2870 0.3369 0.3750 0.3970 0.4070 0.4053 0.4003 0.3920 0.3756 0.3560

δy1

0 4·10−5 8·10−5 3·10−4 7·10−4 4·10−4 6·10−4 4·10−4 5·10−4 8·10−4 8·10−4 4·10−4 1·10−3

δy1

0 2·10−5 3·10−5 3·10−4 4·10−4 5·10−4 2·10−3 2·10−3 7·10−4 1·10−3 1·10−3 1·10−3 9·10−4 7·10−4 1·10−3 7·10−4 1·10−3

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Figure 3. Plot of relative volatility (αij) against mole fraction for the CO (1) + C2H4 (2) system (○, 233.73 K; *, 243.08 K; □, 253.22 K; △, 263.22 K; ◇, 273.18 K; , SRK EoS; ···, PR EoS. Error bands: ± 8 % for experimental results. (Δaij/aij) = ∑i(Δni̅ /ni).

Table 6. Adjustable Parameters and Calculated Critical Point Coordinates

Figure 2. (a) Phase diagrams (P−x−y) for the CO (1) + C2H4 (2) system at (a) ○, 233.73 K; *, 243.08 K and (b) □, 253.22 K; △, 263.22 K; ◇, 273.18 K. ◆, critical point value; , SRK EoS; ···, PR EoS.

T/K

μ·103

λ1·104

λ2·104

Pc/MPa

xc

233.73 243.08 253.22 263.22 273.18

265 246 220 196 120

89 131 −40 −485 −636

−217 −453 −260 −370 −505

9.085 8.611 7.836 7.037 6.046

0.468 0.407 0.320 0.226 0.115

Table 3. Binary Interaction Parameter in the PR EoS for the CO (1) + C2H4 (2) System T/K kij

233.73 0.029

243.08 0.046

253.22 0.045

263.22 0.058

273.18 0.106

Table 4. Binary Interaction Parameters Regressed for the Twu Mixing Rule (eq 8) in the SRK EoS for the CO (i) + C2H4 (j) System CO (i) + C2H4 (j)

kij

kji

cij

cji

0.0701

−0.0914

0

0

Figure 4. PT diagram for the CO (1) + C2H4 (2) system. ⧫, critical point value for pure component; ▲, critical point value for the binary system using the scaling laws. Curve ACO (CO pure component vapor pressure) and Curve B−C2H4 (C2H4 pure component vapor pressure): , critical loci calculated with the SRK EoS; ···, critical loci calculated with the PR EoS.

The critical point corresponds to the limit of stability. They developed an algorithm to calculate the critical point with a van der Waals type EoS, combined with the classical mixing rules. Stockfleth and Dohrn19 improved this method by generalizing the previous algorithm. The Stockfleth and Dohrn method19 was used in this work to calculate the critical locus.

Figure 4 clearly exhibits that the PR model does not describe the critical region as well as the SRK model, which seems to

Table 5. Relative Deviation AADU and BIASU Obtained in Fitting Experimental VLE Data with PR and SRK EoS PR EoS

SRK EoS

T/K

Bias x (%)

Bias y (%)

AAD x (%)

AAD y (%)

Bias x (%)

Bias y (%)

AAD x (%)

AAD y (%)

233.73 243.08 253.22 263.22 273.18 average

−0.5 1.1 3.7 7.2 −1.1 2.1

0.2 3.2 5.5 7.5 3.9 4.1

8.3 8.1 8.8 8.0 6.3 7.9

4.1 7.2 8.4 11.7 8.8 8.0

2.9 1.8 1.8 4.4 −8.0 0.6

3.2 3.5 4 5.6 −1.9 2.9

3.9 4.6 4.8 8.4 8.0 5.9

4.2 6.2 7.2 11.5 7.8 7.4

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(7) Valtz, A.; Coquelet, C.; Baba-Ahmed, A.; Richon, D. Vapor-liquid equilibrium data for the CO2 + 1,1,1,2,3,3,3-heptafluoropropane (R227ea) system at temperatures from 276.01 to 367.30 K and pressures up to 7.4 MPa. Fluid Phase Equilib. 2003, 207, 53−67. (8) Soo, C. B.; El Ahmar, E.; Coquelet, C.; Ramjugernath, D.; Richon, D. Vapor-liquid equilibrium measurements and modeling of the n-butane + ethanol system from 323 to 423 K. Fluid Phase Equilib. 2009, 286, 71−79. (9) Rowley, R. L.; Wilding, W. V.; Oscarson, J. L.; Yang, Y.; Zundel, N. A.; Daubert, T. E.; Danner, R. P. DIPPR Data Compilation of Pure Compounds Properties, Design Institute for Physical Properties, AIChE: New York, NY, 2003. (10) Panagiotopoulos, A. Z.; Reid, R. C. A new mixing rule for cubic equations of state of highly polar asymmetric systems; ACS Symposium Series 300; American Chemical Society: Washington, DC, 1986; pp 571−582. (11) Michelsen, M. L.; Kistenmacher, H. On composition-dependant interaction coefficients. Fluid Phase Equilib. 1990, 58, 229−230. (12) Sengers, J. V.; Kayser, R. F.; Peters, C. J.; White, H. J., Jr. Equation of state for fluids and fluid mixtures; Elsevier: New York, 2000. (13) Ungerer, P.; Tavitian, B.; Boutin, A. Applications of molecular simulation in the oil and gas industry - Monte Carlo methods; Technip: Paris, 2005. (14) Barrat, J. L.; Hansen, J. P. Basic Concepts for Simple and Complex Liquids; Cambridge University Publication: New York, 2003. (15) Van Konynenburg, P. H.; Scott, R. L. Critical lines and phase equilibria in binary van der Waals mixtures. Philos. Trans. R. Soc. London, Ser. A 1980, 298, 495−540. (16) El Ahmar, E.; Valtz, A.; Coquelet, C.; Ramjugernath, D. Isothermal Vapor-Liquid Equilibrium Data for the Perfluorobutane (R610) + Ethane System at Temperatures from 263 to 353 K. J. Chem. Eng. Data 2011, 56, 1918−24. (17) Heidemann, R. A.; Khalil, A. M. The calculation of critical points. AIChE J. 1980, 26, 769−779. (18) Michelsen, M. L.; Heidemann, R. A. Calculation of critical points from cubic two constant equations of state. AIChE J. 1981, 27, 521−523. (19) Stockfleth, R.; Dohrn, R. An algorithm for calculating critical points in multicomponent mixtures which can easily be implemented in existing programs to calculate phase equilibria. Fluid Phase Equilib. 1998, 145, 43−52.

handle the entire diagram reasonably well. As mentioned before, while using the PR EoS, we have considered a temperature-dependent binary interaction parameter. This allows an overall good prediction of a large part of the phase diagram, but it is probably not sufficient to accurately reproduce both infinite dilution domain and critical point domain. While using the SRK EoS, we have considered composition-dependent parameters through the Twu mixing rule, which involves asymmetric binary interaction parameters (kij ≠ kji). Such an approach allows a better prediction of this both domains simultaneously. Using the scaling laws with the experimental data, we have predicted the mixture critical point. Of course, this prediction is dependent on the numbers of data point available, but the estimation seems to be close to the reality.

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CONCLUSIONS In this paper, experimental VLE data for the CO + C2H4 system are presented at five temperatures. These data cover the entire composition range, from CO infinite dilution to critical point. Experimental data for this system have not been previously reported in the open literature. The experimental setup using a “static-analytic” method is completely described, and the uncertainties concerning the apparatus calibration are also given. The experimental data were modeled with the PR EoS with the generalized α function and van der Waals mixing rules, and with the SRK EoS coupled with the Twu et al. α function and mixing rule. This last model (SRK) is found able to accurately correlate experimental data with a reduced number of adjustable parameters, and can be used to predict relative volatility with reasonable accuracy. The critical loci for the binary mixture and the near-critical phase behavior have been approximated by the use of extended scaling laws.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +33 1 64694980. Fax: +33 1 64694968. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge L. Avaullée (Total Petrochemicals) for fruitful discussions. They would also like to acknowledge the CARNOT MINES Institute.

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REFERENCES

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