Compressed Liquid Densities and Excess Volumes of CO2 + Decane

Compressed Liquid Densities and Excess Molar Volumes of CO2 + Hexan-1-ol Mixtures from (313 to 363) K and Pressures up to 25 MPa. Abel Zúñiga-Moreno...
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1030

J. Chem. Eng. Data 2005, 50, 1030-1037

Compressed Liquid Densities and Excess Volumes of CO2 + Decane Mixtures from (313 to 363) K and Pressures up to 25 MPa Abel Zu ´n ˜ iga-Moreno, Luis A. Galicia-Luna,* and Luis E. Camacho-Camacho Instituto Polite´cnico Nacional, ESIQIE, Laboratorio de Termodina´mica, Edif. Z, Secc. 6, 1er piso, UPALM Zacatenco, 07738 Lindavista, Me´xico, D.F., Me´xico

Experimental liquid densities of decane and of CO2 (1) + decane (2) binary mixtures (at five different compositions, x1 ) 0.0551, 0.2369, 0.4536, 0.8114, and 0.9663) were measured from (313 to 363) K and at pressures up to 25 MPa. The densities of decane were fitted to the Benedict-Webb-Rubin-Starling equation of state (BWRS EoS). Excess molar volumes are calculated by using decane densities calculated from the BWRS EoS and CO2 densities calculated from the Span-Wagner EoS.

Introduction

Table 1. Purity and Origin of Pure Compounds

Sulfur content lower limits in fuels have become a source of new investigations all around the world. At present, a hydrotreating process is used to obtain low sulfur content fuels; however, energy and hydrogen consumption will make this process undesirable. Alternative processes, such as extraction using supercritical fluids and ionic liquids, are needed. An attempt to develop a new sulfur extraction process was recently made by Huang et al.1 They used dodecane and thiophene as a model diesel to perform sulfur extraction using ionic liquids. This work is part of a project focused on sulfur compound extraction from commercial fuels using supercritical carbon dioxide2,3 to fulfill sulfur content regulations.1 Because decane is a component present in fuels, it can be used as a model fuel as Huang et al.1 did with dodecane. The development of supercritical fluid extraction processes is strongly dependent on accurate thermodynamic data as PVT properties and phase equilibria of pure compounds and mixtures. In this work, the volumetric behavior of CO2 + decane were determined as basic information for process development and as part of a systematic study.2,3 This system has been previously reported in the literature. Cullick and Mathis4 measured the density of CO2 (1) + decane (2) from (310 to 403) K and (7 to 30) MPa and at x1 ) 0.15, 0.301, 0.505, 0.649, and 0.85. Bessie´res et al.5 measured the density of this system from (308.15 to 368.15 K) and (20 to 40) MPa and at x1 ) 0.16, 0.22, 0.34, 0.49, 0.70, and 0.85. In this work, new experimental densities for decane and for CO2 (1) + decane (2) mixtures from (313 to 363) K and up to 25 MPa at x1 ) 0.0551, 0.2369, 0.4536, 0.8114, and 0.9663 are reported.

compound

certified purity

supplier

decane CO2 water nitrogen

99 + mole % anhydrous 99.995 mole % 99.95 mole % (HPLC) 99.998 mole %

Aldrich Air Products-Infra Aldrich Air Products-Infra

previously.6-9 The measuring cell consists of a vibrating tube (Hastelloy C-276 U-tube) containing a sample of approximately 1 cm3. The pressure measurements are made directly in the equilibrium cell (Figure 1) by means of a 25 MPa Sedeme pressure transducer. The pressure transducer is thermoregulated at a specific value and calibrated periodically. The temperature was measured by two platinum probes located at the top of the sapphire cell and in the vibrating tube densimeter (VTD). The calibration of the vibrating tube was performed using water and nitrogen as the reference compounds. Density values for

Experimental Section Materials. The sources and purities of the various compounds are given in Table 1. These materials were used without any further purification, except for careful degassing of water and decane. Apparatus and Procedure. The apparatus and experimental procedure used in this work have been described * To whom correspondence should be addressed. E-mail: [email protected]. Phone: +52 55-5729-6000, ext 55133. Fax: +52 55-5586-2728.

Figure 1. Flow diagram of the apparatus: AB air bath, CA cathetometer, DMA 60 period meter, DPI 145 digital indicator of pressure, EC equilibrium cell, GC gas compressor, LB liquid bath, MC measurement cell, MR magnetic rod, PI Isco pump, PT pressure transducer, PTPi platinum probe i, TD digital indicator of temperature F250, Vi shut-off valve i, VSE variable-speed engine, VP vacuum pump, VTD vibrating tube densimeter, O window.

10.1021/je050020m CCC: $30.25 © 2005 American Chemical Society Published on Web 04/26/2005

Journal of Chemical and Engineering Data, Vol. 50, No. 3, 2005 1031 Table 2. BWRS EOS Adjusted Parameters for Decane parameter

decane

B0/cm3‚mol-1 A0/bar‚cm6‚mol-2 C0/bar‚K2‚cm6‚mol-2 D0/bar‚K3‚cm6‚mol-2 E0/bar‚K4‚cm6‚mol-2 b/cm6‚mol-2

653.40 4.9923 × 107 2.82531 × 1012 -5.470013 × 1014 -1.954206 × 1017 129 382.289 2.77188 × 109 4.89128 × 1011 -7.00804 × 1014 3.39814 × 107 10 090.4141

a/bar‚cm9‚mol-3 d/bar‚K‚cm9‚mol-3 c/bar‚K2‚cm9‚mol-3 R/cm9‚mol-3 u/cm6‚mol-2

Table 3. Coefficients for the Lemmon-Span EoS14 for Decane coefficient

decane

n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12

1.0461 -2.4807 0.74372 -0.52579 0.15315 0.00032865 0.84178 0.055424 -0.73555 -0.18507 -0.020775 0.012335

Figure 2. Relative deviations between experimental densities of decane and those calculated with the BWRS EoS and the Lemmon-Span EoS at the following temperatures: b, 313.09 K; 1, 323.03 K; 9, 332.95 K; [, 342.80; 2, 352.71 K; b, 362.63 K. Closed and open symbols are for deviations using the BWRS EoS and the Lemmon-Span EoS, respectively.

water and nitrogen were obtained from the equations proposed by Wagner and Pruβ10 and Span et al.,11 respectively. Details about the calibrating procedures of the platinum temperature probes and the pressure transducer were given in a previous article.12 The estimated uncertainties of the experimental quantities presented in this work are T/K ) (0.03, P/MPa ) (0.008, and F/kg‚m-3 ) (0.2 for liquid density in the range of the reported data, in a similar fashion as previously reported data.7-9 Loading of the Measurement Cell. A detailed procedure of the loading of the measurement cell is presented in preceding papers.6,9 The samples with the desired compositions are prepared by successive loadings6 of the pure compounds in a sapphire feeding cell with a maximum volume of 12 cm3. The amounts of the compounds are

determined by weighing carried out with an uncertainty of (10-7 kg with a Sartorius comparator balance (MCA1200), which was periodically calibrated with a standard mass of 1 kg class E1. The resulting uncertainty for the mole fraction composition of the mixtures is lower than (10-4. Theory. The BWRS EoS13 was used to correlate the densities of decane. The following expression was used: 2 3 4 RT (B0RT - A0 - C0/T + D0/T - E0/T ) P) + V V2

+

(bRT - a - d/T) V3

+

R(a + d/T)

+ V6 c(1 + u/V2) exp(-u/V2) V3T2

(1)

where V is the molar volume and the units for the corresponding constants are shown in Table 2.

Table 4. Experimental Densities of Decane P/MPa

F/kg‚m-3

T/K ) 313.09 1.048 715.63 2.010 716.43 2.997 717.28 4.060 718.18 5.029 718.98 6.019 719.80 7.016 720.64 8.050 721.47 9.000 722.24 10.029 723.06 11.016 723.85 12.012 724.63 13.027 725.40 14.011 726.15 15.010 726.91 16.030 727.65 17.016 728.38 18.037 729.10 19.000 729.81 20.019 730.50 21.014 731.21 22.032 731.92 23.021 732.62 24.016 733.33 25.012 734.06

P/MPa

F/kg‚m-3

T/K ) 323.03 1.025 707.94 2.017 708.85 3.015 709.76 4.018 710.65 5.022 711.53 6.021 712.41 7.018 713.31 8.022 714.15 9.016 715.01 10.012 715.84 11.022 716.67 12.015 717.51 13.020 718.33 14.011 719.12 15.010 719.90 16.019 720.71 17.010 721.46 18.013 722.22 19.033 723.00 20.022 723.74 21.014 724.45 22.023 725.22 23.025 725.93 24.016 726.68 25.021 727.42

P/MPa

F/kg‚m-3

T/K ) 332.95 1.022 700.40 2.005 701.33 3.025 702.32 4.025 703.25 5.018 704.20 6.018 705.12 7.019 706.08 8.023 706.96 9.021 707.89 10.017 708.78 11.033 709.68 12.023 710.54 13.009 711.42 14.016 712.21 15.025 713.05 16.011 713.87 17.017 714.69 18.016 715.50 19.015 716.28 20.029 717.09 21.001 717.84 22.034 718.63 23.017 719.41 24.023 720.18 25.002 720.95

P/MPa

F/kg‚m-3

T/K ) 342.80 1.014 692.56 2.027 693.64 3.016 694.64 4.020 695.65 5.016 696.67 6.019 697.68 7.026 698.66 8.022 699.65 9.014 700.58 10.017 701.53 11.022 702.48 12.021 703.39 13.011 704.27 14.013 705.16 15.025 706.05 16.019 706.94 17.010 707.79 18.023 708.61 19.030 709.47 20.008 710.25 21.017 711.10 22.035 711.92 23.004 712.73 24.008 713.53 25.103 714.44

P/MPa

F/kg‚m-3

T/K ) 352.71 2.132 3.053 4.028 5.028 6.065 7.007 8.041 9.064 10.047 11.019 12.012 13.031 14.010 15.014 16.012 17.008 17.959 19.020 20.044 21.044 22.024 23.009 24.014 25.000

686.04 687.07 688.15 689.19 690.28 691.26 692.36 693.40 694.38 695.38 696.31 697.31 698.18 699.14 700.05 700.95 701.80 702.70 703.60 704.46 705.31 706.13 707.00 707.86

P/MPa

F/kg‚m-3

T/K ) 362.63 2.054 3.010 4.132 5.020 6.026 7.042 8.057 9.014 10.034 10.999 12.014 13.025 13.992 15.019 16.004 17.008 18.002 19.037 20.027 21.030 22.003 23.027 24.046 25.011

678.23 679.34 680.68 681.68 682.79 683.95 685.06 686.08 687.17 688.24 689.26 690.26 691.22 692.24 693.18 694.11 695.04 696.02 696.93 697.80 698.73 699.61 700.55 701.39

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Journal of Chemical and Engineering Data, Vol. 50, No. 3, 2005

Table 5. Comparison of Densities between Literature Data and Calculated Values by the BWRS EoS 100(Fref 5 - FBWRS) T/K

P/MPa

308.15 318.15 328.15 338.15 348.15 358.15 368.15 308.15 318.15 328.15 338.15 348.15 358.15 368.15 308.15 318.15 328.15 338.15 348.15 358.15 368.15

20 20 20 20 20 20 20 30 30 30 30 30 30 30 40 40 40 40 40 40 40

F/kg‚m-3

(ref 5)

734.79 727.82 720.92 714.02 707.19 700.30 693.35 741.46 734.79 728.22 721.72 715.26 708.80 702.31 747.57 741.14 734.84 728.65 722.52 716.42 710.33

Fref 5 0.127 0.104 0.090 0.076 0.069 0.050 0.020 0.105 0.075 0.055 0.040 0.027 0.008 -0.020 0.064 0.024 -0.004 -0.022 -0.039 -0.059 -0.083

Figure 3. Experimental and calculated densities of decane: b, this work at 20 MPa; O, Bessie`res et al.5 at 20 MPa; 0, Bessie`res et al.5 at 30 MPa; 3, Bessie`res et al.5 at 40 MPa;-, BWRS EoS.

was calculated from the expression

[ ( )]

The equation of state proposed by Lemmon and Span14 was used to calculate the densities reported here. Density

P ) FRT 1 + δ

∂Rr ∂δ

(2)

τ

Table 6. Experimental Densities and Excess Molar Volumes of the CO2 (1) + Decane (2) Mixture P/MPa

F/kg‚m-3

VE/cm3‚mol-1

P/MPa

F/kg‚m-3

2.005 3.035 4.061 5.063 6.029 7.028 7.998 9.019 10.010 11.032 12.046 13.029 14.011 15.013 15.992 16.999 18.044 19.030 19.999 21.031 22.015 23.023 24.060 25.026

T/K ) 313.10 717.94 718.98 719.88 720.72 721.55 722.42 723.25 724.09 724.92 725.72 726.55 727.32 728.10 728.84 729.58 730.32 731.13 731.85 732.57 733.30 734.00 734.74 735.50 736.20

-62.13 -37.65 -25.45 -18.13 -13.20 -9.24 -5.84 -2.05 -1.00 -0.69 -0.54 -0.43 -0.36 -0.29 -0.24 -0.19 -0.16 -0.12 -0.10 -0.06 -0.04 -0.02 0.00 0.01

1.989 3.015 3.984 5.002 6.010 7.043 8.018 9.009 10.008 11.036 11.995 13.035 14.026 15.008 16.035 17.008 18.019 18.994 20.009 21.010 21.987 23.060 23.980 25.055

x1 ) 0.0551 T/K ) 323.05 710.33 711.28 712.18 713.14 714.04 714.97 715.86 716.73 717.66 718.47 719.35 720.16 721.01 721.76 722.62 723.40 724.22 724.89 725.73 726.47 727.22 728.04 728.74 729.61

2.043 3.006 4.043 5.044 6.046 6.984 8.003 8.999 10.007 11.044 11.996 13.021 13.997 15.043 16.022 17.001 17.984 19.042 20.017 21.054 22.022 23.029 24.018 25.025

T/K ) 342.86 694.82 695.92 696.93 697.98 699.02 699.98 701.00 702.09 702.98 703.97 704.89 705.84 706.74 707.69 708.54 709.54 710.28 711.19 712.03 713.10 713.72 714.55 715.37 716.21

-68.64 -43.98 -30.47 -22.68 -17.42 -13.84 -10.86 -8.61 -6.71 -5.15 -3.98 -3.00 -2.30 -1.78 -1.43 -1.22 -0.99 -0.84 -0.72 -0.67 -0.54 -0.47 -0.41 -0.36

2.008 3.010 4.018 5.014 6.015 7.011 8.024 8.988 10.035 11.021 12.025 13.009 14.003 15.017 16.009 17.043 18.011 18.999 19.980 21.012 22.017 23.034 24.044 24.991

T/K ) 352.78 686.89 688.04 689.18 690.28 691.42 692.46 693.62 694.56 695.65 696.68 697.67 698.59 699.60 700.50 701.58 702.49 703.38 704.26 705.14 706.06 706.96 707.84 708.75 709.57

F/kg‚m-3

VE/cm3‚mol-1

P/MPa

VE/cm3‚mol-1

-65.47 -39.99 -27.88 -20.12 -14.91 -10.98 -8.06 -5.55 -3.38 -1.88 -1.27 -0.92 -0.74 -0.60 -0.50 -0.43 -0.37 -0.29 -0.26 -0.21 -0.18 -0.15 -0.12 -0.11

1.997 3.024 4.011 5.040 6.062 7.009 7.978 9.037 9.992 11.032 12.013 13.027 14.018 15.021 15.997 16.998 18.031 19.004 20.002 21.014 22.027 23.014 24.057 25.048

T/K ) 332.94 702.61 703.63 704.59 705.62 706.62 707.53 708.43 709.44 710.31 711.27 712.13 713.03 713.89 714.75 715.59 716.44 717.29 718.07 718.88 719.68 720.50 721.30 722.11 722.92

-67.83 -41.78 -29.24 -21.35 -16.09 -12.53 -9.69 -7.22 -5.38 -3.75 -2.60 -1.83 -1.38 -1.09 -0.89 -0.75 -0.63 -0.53 -0.46 -0.39 -0.34 -0.29 -0.25 -0.22

-72.53 -45.70 -32.19 -24.15 -18.74 -14.86 -11.92 -9.68 -7.75 -6.29 -5.05 -4.04 -3.24 -2.58 -2.14 -1.74 -1.46 -1.24 -1.06 -0.91 -0.80 -0.69 -0.61 -0.55

2.031 3.029 4.134 5.034 6.050 7.045 8.030 9.020 10.044 11.025 11.987 13.025 14.075 15.026 16.020 17.003 18.032 19.030 19.998 21.052 22.028 22.996 24.036 25.008

T/K ) 362.66 678.97 680.17 681.50 682.58 683.77 684.91 686.02 687.12 688.25 689.34 690.35 691.46 692.50 693.52 694.47 695.45 696.46 697.38 698.32 699.32 700.22 701.10 702.10 702.93

-74.09 -47.11 -32.42 -25.22 -19.65 -15.75 -12.83 -10.54 -8.64 -7.18 -5.98 -4.91 -4.01 -3.37 -2.79 -2.34 -1.97 -1.67 -1.44 -1.24 -1.08 -0.95 -0.84 -0.73

Journal of Chemical and Engineering Data, Vol. 50, No. 3, 2005 1033 Table 7. Experimental Densities and Excess Molar Volumes of the CO2 (1) + Decane (2) Mixture F/kg‚m-3

P/MPa

VE/cm3‚mol-1

5.020 6.029 7.015 8.019 9.012 10.012 11.018 12.009 13.016 14.019 15.006 16.017 17.006 18.008 19.016 20.000 21.019 22.002 23.007 24.008 25.013

T/K ) 313.10 728.09 729.09 730.07 731.05 732.01 732.96 733.88 734.80 735.72 736.60 737.46 738.34 739.17 740.01 740.85 741.67 742.51 743.29 744.12 744.96 745.78

-79.24 -56.88 -40.04 -24.88 -9.00 -4.35 -3.08 -2.41 -1.96 -1.63 -1.38 -1.16 -0.99 -0.84 -0.70 -0.59 -0.49 -0.40 -0.32 -0.26 -0.20

5.031 6.026 7.029 8.006 9.030 10.017 11.019 12.003 13.017 14.013 15.021 16.004 17.018 18.016 19.005 20.000 21.023 22.008 23.029 23.992 25.008

T/K ) 342.87 702.48 703.70 704.93 706.09 707.28 708.40 709.54 710.62 711.73 712.79 713.84 714.86 715.90 716.89 717.86 718.83 719.83 720.78 721.76 722.74 723.65

-97.71 -75.13 -58.70 -46.52 -36.45 -28.62 -22.10 -16.91 -12.74 -9.72 -7.56 -6.09 -4.99 -4.19 -3.58 -3.09 -2.69 -2.36 -2.08 -1.87 -1.65

F/kg‚m-3

P/MPa

x1 ) 0.2369 T/K ) 323.06 719.60 720.66 721.73 722.80 723.79 724.84 725.81 726.78 727.75 728.70 729.63 730.54 731.46 732.36 733.24 734.11 735.00 735.85 736.71 737.58 738.42

5.014 6.022 7.021 8.020 9.010 10.030 11.018 12.021 13.001 14.021 15.014 16.010 17.006 18.028 19.016 20.015 21.027 22.023 23.022 24.006 25.004

VE/cm3‚mol-1

P/MPa

-86.24 -63.92 -47.59 -34.66 -23.85 -14.29 -8.15 -5.35 -4.01 -3.17 -2.61 -2.19 -1.87 -1.60 -1.39 -1.20 -1.04 -0.90 -0.78 -0.68 -0.59

5.026 6.015 7.019 8.020 9.017 10.015 11.009 12.015 13.015 14.011 15.003 16.019 17.015 18.026 19.022 20.012 21.024 22.021 23.010 24.025 25.028

T/K ) 352.79 6.023 7.016 8.017 9.014 10.006 11.019 12.015 13.014 14.010 15.002 16.000 17.020 18.006 19.014 19.955 21.069 22.042 23.032 24.057 24.999

695.17 696.39 697.70 698.95 700.10 701.32 702.48 703.71 704.77 705.93 707.03 708.08 709.15 710.21 711.22 712.30 713.30 714.28 715.33 716.29

where Rr(δ, τ) is given by14

n8δ τ

exp

+ n9δτ

3.625

3 14.5

n11δ τ

exp exp

-δ2

-δ3

4 3.625

+ n10δ τ

4 12.0

+ n12δ τ

exp

exp

-δ2

-δ3

+

-80.15 -63.56 -50.96 -41.14 -33.26 -26.73 -21.46 -17.16 -13.70 -11.02 -8.95 -7.33 -6.15 -5.22 -4.53 -3.86 -3.39 -2.99 -2.65 -2.39

5.978 7.016 8.020 9.035 10.044 11.011 12.005 13.039 14.013 15.072 16.012 17.009 18.008 19.020 20.006 21.068 22.007 23.055 24.030 25.056

c1 + c2P c3 - (c4/T + c5/T1/3) + P

S)

∑ i

(3)

where δ ) F/Fc and τ ) Tc/T. Constants n1 to n12 are listed in Table 3. To make comparisons with reported literature data,4,5 we propose a five-parameter empirical equation to correlate the densities of decane and those of the CO2 + decane mixtures.

ν)

T/K ) 332.94 711.09 712.23 713.38 714.47 715.56 716.65 717.69 718.74 719.76 720.77 721.75 722.73 723.70 724.66 725.60 726.51 727.44 728.35 729.26 730.17 731.08

-92.08 -69.98 -53.62 -41.11 -31.11 -22.87 -16.15 -11.07 -7.81 -5.85 -4.62 -3.76 -3.15 -2.68 -2.31 -2.00 -1.75 -1.54 -1.35 -1.19 -1.05

T/K ) 362.65

n5δ3τ0.25 + n6δ7τ0.875 + n7δ2τ0.625 exp-δ + -δ

VE/cm3‚mol-1

-85.64 -67.84 -54.99 -44.90 -36.89 -30.64 -25.32 -20.75 -17.22 -14.07 -11.82 -9.89 -8.34 -7.10 -6.12 -5.27 -4.65 -4.08 -3.63 -3.23

686.43 687.86 689.21 690.58 691.88 693.13 694.38 695.64 696.82 698.07 699.18 700.33 701.44 702.57 703.64 704.82 705.81 706.93 707.95 709.02

densities of decane reported in this work. The MarquardtLevenberg least-squares optimization was used with the following objective function, S:

Rr(δ, τ) ) n1δτ0.25 + n2δτ1.125 + n3δτ1.5 + n4δ2τ1.375 + 5 1.75

F/kg‚m-3

(4)

where different sets of c1, c2, c3, c4, and c5 were obtained by fitting experimental data for the different compositions of the mixtures and for decane reported in this work. Results and Discussion Densities of decane are reported in Table 4. The parameters of the BWRS EoS13 were fitted to the experimental

[

]

Fexptl - Fcalcd i i Fexptl i

2

(5)

The BWRS EoS13 adjusted parameters for decane are reported in Table 2. Densities of decane from the BWRS EoS were calculated with a standard deviation of 0.0242%. Relative deviations using eqs 1 and 2 are plotted in Figure 2. The average absolute deviation in density using the Lemmon-Span EoS14 was about 0.01%. Data for decane from this work and from Bessie´res et al.5 at 20 MPa are plotted in Figure 3; good agreement between both sets of data is observed. The adjusted parameters for the BWRS EoS13 were tested by predicting the densities of decane reported by Bessie´res et al.5 at (30 and 40) MPa. These results are plotted in Figure 3, and the corresponding deviations are reported in Table 5. The predicted values are in good agreement with experimental data. In Tables 6 to 10, compressed liquid densities and excess molar volumes for the CO2 + decane mixtures at temperatures from (313 to 363) K and pressures up to 25 MPa at five different compositions are presented.

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Journal of Chemical and Engineering Data, Vol. 50, No. 3, 2005

Table 8. Experimental Densities and Excess Molar Volumes of the CO2 (1) + Decane (2) Mixture P/MPa

F/kg‚m-3

VE/cm3‚mol-1

7.015 8.024 9.021 10.024 11.020 12.022 13.012 14.017 15.020 16.020 17.013 18.019 19.014 20.018 21.018 22.006 23.003 24.023 25.010

T/K ) 313.11 742.30 743.57 744.82 746.02 747.22 748.39 749.55 750.69 751.81 752.93 753.99 755.06 756.08 757.13 758.18 759.18 760.18 761.23 762.23

-76.55 -47.38 -16.96 -8.18 -5.80 -4.52 -3.68 -3.05 -2.57 -2.18 -1.86 -1.58 -1.34 -1.14 -0.96 -0.80 -0.65 -0.53 -0.42

7.027 8.024 9.027 10.014 11.025 12.015 13.006 14.013 15.001 16.029 17.019 18.026 19.018 20.000 21.007 22.021 23.032 24.017 25.029

T/K ) 342.87 711.28 712.92 714.50 716.02 717.56 719.02 720.46 721.87 723.23 724.63 725.94 727.26 728.54 729.75 731.02 732.28 733.50 734.70 735.91

-112.01 -88.29 -69.46 -54.46 -41.91 -31.95 -24.16 -18.33 -14.29 -11.36 -9.34 -7.83 -6.68 -5.77 -5.03 -4.41 -3.88 -3.45 -3.07

P/MPa

7.029 8.017 9.018 10.024 11.019 12.025 13.003 14.027 15.001 16.024 17.010 18.030 19.000 20.028 21.001 22.020 23.012 24.021 25.029

F/kg‚m-3 x1 ) 0.4536 T/K ) 323.06 732.05 733.42 734.79 736.13 737.41 738.69 739.89 741.16 742.33 743.53 744.68 745.84 746.93 748.09 749.17 750.24 751.33 752.42 753.51

x 1W1 + x 2W2 Fmix

P/MPa

-90.66 -66.22 -45.30 -27.24 -15.40 -10.06 -7.51 -5.91 -4.88 -4.07 -3.47 -2.97 -2.58 -2.24 -1.95 -1.69 -1.47 -1.28 -1.11

7.015 8.025 9.016 10.023 11.014 12.001 13.045 13.998 15.000 16.032 17.018 18.021 19.012 20.002 21.028 22.021 23.009 24.026 25.022

T/K ) 352.80 8.029 9.011 10.022 11.012 12.018 13.013 14.019 15.017 16.008 17.028 18.018 19.024 20.015 21.003 22.029 23.006 24.025 25.013

702.49 704.17 705.86 707.47 709.07 710.62 712.14 713.63 715.06 716.51 717.90 719.28 720.60 721.91 723.29 724.51 725.86 727.09

The excess volumes were calculated over the complete temperature and pressure intervals according to the relation

VE )

VE/cm3‚mol-1

- (x1V1 + x2V2)

(6)

where VE is the molar excess volume, Fmix is the density of the mixture, V1 and V2 are the pure component molar volumes at the measured temperature and pressure of the mixture, W1 and W2 are the molecular weights of CO2 and decane, respectively, and x1 and x2 are the mole fractions of CO2 and decane, respectively. Densities of decane were calculated in the reported range of pressure and temperature by using the BWRS EoS with the parameters reported in Table 2. The equation of state proposed by Span and Wagner15 was used to calculate the molar volumes of CO2. The uncertainty in the excess molar volumes is estimated to be (0.15%. A typical behavior of the excess molar volume for this type of mixture is shown in Figure 4, where the excess molar volumes is plotted as a function of x1 at 362.65 K at different pressures. The excess molar volume becomes less negative with increasing pressure, as previously reported.5 The reliability of the measurements has been checked by comparing the data calculated through the proposed empirical equation of state fitted to data reported in this work and data from other authors.4 To compare our experimental data with those reported in the literature,

F/kg‚m-3 T/K ) 332.94 721.74 723.26 724.72 726.15 727.55 728.90 730.28 731.55 732.81 734.14 735.36 736.57 737.79 738.93 740.14 741.29 742.44 743.58 744.71

VE/cm3‚mol-1

-102.46 -78.30 -59.30 -43.39 -30.62 -21.08 -14.59 -11.04 -8.65 -7.01 -5.87 -4.99 -4.30 -3.73 -3.25 -2.86 -2.53 -2.23 -1.97

T/K ) 362.66 -96.80 -78.32 -63.05 -50.85 -40.69 -32.49 -25.85 -20.71 -16.80 -13.76 -11.51 -9.75 -8.38 -7.28 -6.36 -5.62 -4.98 -4.45

9.024 10.012 11.031 12.002 13.028 14.008 15.024 16.000 17.017 18.002 19.030 20.001 21.029 22.014 23.024 24.006 25.025

693.68 695.47 697.25 698.93 700.66 702.25 703.87 705.42 706.96 708.44 709.94 711.37 712.80 714.18 715.57 716.91 718.29

-85.54 -70.49 -57.88 -47.99 -39.35 -32.54 -26.77 -22.29 -18.55 -15.66 -13.26 -11.45 -9.89 -8.67 -7.63 -6.79 -6.04

densities for the mixtures reported here and those reported by Cullick and Mathis4 were correlated at constant composition using eq 4. The obtained parameters, temperature and pressure intervals, data points used for the correlation, and the different statistical values used to evaluate the correlations are reported in Tables 11 and 12. Densities reported by Bessie´res et al.5 at 20 MPa were taken as a

Figure 4. Excess molar volumes of the carbon dioxide (1) + decane (2) binary mixtures at 362.65 K reported in this work: b, 15 MPa; O, 16 MPa; 1, 17 MPa; 3, 18 MPa; 9, 19 MPa; 0, 20 MPa; [, 21 MPa; ], 22 MPa; 2, 23 MPa; 4, 24 MPa; b, 25 Mpa;-, trend.

Journal of Chemical and Engineering Data, Vol. 50, No. 3, 2005 1035 Table 9. Experimental Densities and Excess Molar Volumes of the CO2 (1) + Decane (2) Mixture P/MPa

F/kg‚m-3

VE/cm3‚mol-1

12.053 13.017 14.021 15.103 15.990 16.981 17.993 19.038 20.009 21.018 22.020 22.999 24.019 25.017

T/K ) 313.12 782.82 785.68 788.54 791.51 793.84 796.39 798.92 801.45 803.73 806.06 808.29 810.42 812.60 814.70

-6.76 -5.41 -4.39 -3.56 -3.02 -2.52 -2.09 -1.72 -1.43 -1.16 -0.93 -0.73 -0.54 -0.38

13.020 14.001 15.022 16.041 17.013 18.018 19.020 20.008 21.023 22.003 23.041 24.026 25.034

T/K ) 342.84 721.51 726.31 730.92 735.26 739.14 742.96 746.57 749.98 753.35 756.46 759.67 762.58 765.48

-39.52 -29.67 -22.50 -17.59 -14.27 -11.75 -9.85 -8.39 -7.19 -6.25 -5.42 -4.76 -4.18

P/MPa

12.005 13.009 14.026 15.008 16.046 17.018 18.002 19.025 20.031 21.047 21.988 22.999 24.016 25.054

F/kg‚m-3 x1 ) 0.8114 T/K ) 323.04 762.12 765.56 769.00 772.02 775.13 777.99 780.75 783.58 786.22 788.86 791.16 793.66 796.11 798.55

VE/cm3‚mol-1

P/MPa

-16.20 -11.65 -8.97 -7.21 -5.88 -4.93 -4.17 -3.53 -3.00 -2.56 -2.19 -1.87 -1.58 -1.32

12.008 13.051 14.018 15.048 15.985 17.015 18.008 19.002 20.017 21.018 22.044 23.040 24.008 25.047

T/K ) 352.76 14.034 15.050 15.994 17.009 18.024 19.033 20.039 21.009 22.013 23.004 24.035 25.042

T/K ) 332.91 740.55 744.82 748.57 752.37 755.64 759.04 762.27 765.33 768.38 771.25 774.13 776.83 779.40 782.09

VE/cm3‚mol-1

-34.85 -23.56 -17.34 -13.21 -10.70 -8.70 -7.28 -6.16 -5.25 -4.51 -3.89 -3.38 -2.95 -2.55

T/K ) 362.63 -41.53 -32.67 -26.38 -21.26 -17.43 -14.54 -12.29 -10.58 -9.14 -7.97 -6.97 -6.14

701.72 707.51 712.45 717.35 722.02 726.33 730.42 734.16 737.84 741.32 744.84 748.08

F/kg‚m-3

15.022 16.023 17.027 18.027 19.028 20.026 21.017 22.023 23.019 24.030 25.024

681.16 688.18 694.15 699.67 704.83 709.67 714.17 718.48 722.51 726.42 730.11

-42.19 -34.60 -28.49 -23.69 -19.89 -16.89 -14.50 -12.53 -10.92 -9.58 -8.46

Table 10. Experimental Densities and Excess Molar Volumes of the CO2 (1) + Decane (2) Mixture P/MPa

F/kg‚m-3

VE/cm3‚mol-1

11.029 12.037 13.049 14.020 15.013 16.007 17.027 17.984 19.037 20.002 21.015 22.023 23.021 24.063 24.976

T/K ) 313.11 714.21 738.68 758.54 774.43 788.48 800.98 812.43 822.21 832.11 840.48 848.66 856.28 863.40 870.36 876.18

-2.43 -1.68 -1.35 -1.17 -1.05 -0.99 -0.94 -0.91 -0.90 -0.89 -0.88 -0.88 -0.88 -0.88 -0.88

13.528 14.029 15.026 16.019 17.025 18.035 19.000 20.022 21.024 22.022 23.022 24.017 25.006

T/K ) 342.79 503.61 528.33 569.49 603.24 631.60 657.54 674.01 691.29 706.16 719.34 731.24 741.98 751.96

-10.75 -9.40 -7.02 -5.43 -4.36 -3.84 -3.01 -2.55 -2.20 -1.91 -1.68 -1.49 -1.34

P/MPa

11.016 12.030 13.015 14.007 15.021 16.018 17.026 18.010 19.001 20.025 21.021 22.023 23.026 24.036 25.030

F/kg‚m-3 x1 ) 0.9663 T/K ) 323.04 580.54 636.15 672.02 698.83 721.04 739.12 754.76 768.22 780.23 791.43 801.33 810.55 819.05 827.07 834.47

VE/cm3‚mol-1

P/MPa

-9.15 -4.59 -2.91 -2.10 -1.68 -1.42 -1.25 -1.14 -1.06 -0.99 -0.94 -0.90 -0.86 -0.84 -0.82

12.005 12.511 13.003 14.015 15.026 16.035 17.018 18.016 19.002 20.033 21.022 22.029 23.010 24.016 25.006

T/K ) 352.75 14.010 15.010 16.020 17.024 18.026 19.015 20.016 21.018 22.006 23.021 24.018 25.017

449.95 494.40 532.74 566.61 594.54 618.22 638.64 656.61 672.26 686.58 699.34 710.94

reference, and then the densities at the same temperature and pressure were calculated for the different compositions reported here and in ref 4 with the parameters reported in Tables 11 and 12 for eq 4. Good agreement exists among the three sets of data, as shown in Figure 5.

F/kg‚m-3 T/K ) 332.94 511.90 544.43 571.24 614.37 648.23 674.85 695.62 713.48 728.62 742.59 754.63 765.58 775.39 784.64 793.10

VE/cm3‚mol-1

-11.54 -9.37 -7.59 -5.05 -3.77 -3.00 -2.47 -2.09 -1.80 -1.58 -1.42 -1.27 -1.16 -1.06 -0.98

T/K ) 362.65 -11.82 -9.99 -8.11 -6.78 -5.61 -4.71 -3.97 -3.40 -2.94 -2.55 -2.24 -1.98

15.510 16.012 17.007 18.010 19.013 20.015 21.029 22.007 23.022 24.015 25.028

452.61 471.04 504.42 534.34 561.23 585.01 606.13 624.31 641.03 655.59 669.28

-10.63 -9.92 -8.45 -7.14 -6.11 -5.26 -4.54 -3.97 -3.46 -3.03 -2.68

Conclusions In this work, we reported new compressed liquid densities of decane and CO2 + decane mixtures covering the whole interval of composition at temperatures from (313

1036

Journal of Chemical and Engineering Data, Vol. 50, No. 3, 2005

Table 11. Parameters for Equation 4 for Data Reported in This Worka Tmin/K Tmax/K Pmin/MPa Pmax/MPa Fmin/kg‚m-3 Fmax/kg‚m-3 data points c1/MPa‚kg-1‚m3 c2/kg-1‚m3 c3/MPa c4/K‚MPa c5/MPa‚K1/3 AAD/%b bias/%c SDV/%d RMS/%e a

x(

1

x1 ) 0

x1 ) 0.0551

x1 ) 0.2369

x1 ) 0.4536

x1 ) 0.8114

x1 ) 0.9663

313.09 352.62 1.014 25.103 678.23 734.06 148 0.159724 1.195 × 10-3 -190.319 29 515.986 -2707.4836 0.0068 -1.72 × 10-6 1.56 × 10-4 0.0087

313.10 362.66 1.989 25.055 678.97 736.20 144 0.154668 1.191 × 10-3 -202.930 31 299.251 -2808.8628 0.0057 -1.09 × 10-6 1.07 × 10-4 0.0074

313.10 362.65 5.014 25.056 686.43 745.78 124 0.135714 1.174 × 10-3 -211.409 30 770.939 -2768.9001 0.0047 -7.64 × 10-7 8.34 × 10-5 0.0062

313.11 362.66 7.015 25.029 693.68 762.23 111 0.103402 1.152 × 10-3 -234.490 31 843.812 -2797.1328 0.0068 -1.55 × 10-6 1.71 × 10-4 0.0088

313.12 362.63 12.053 25.054 681.16 814.17 78 0.021617 1.129 × 10-3 -346.673 46 306.191 -3463.6413 0.0646 -1.46 × 10-4 1.73 × 10-2 0.0854

313.11 362.65 11.029 25.028 449.95 876.18 81 -0.004692 1.058 × 10-3 -180.882 14 652.310 -1504.5692 0.4591 -7.53 × 10-3 8.33 × 10-1 0.6147

n n %∆V ) 100((Vexptl - Vcalcd)/Vexptl). b AAD ) (1/n)∑i)1 |%∆Vi|. c bias ) (1/n)∑i)1 (%∆Vi).

d

SDV )

n /n)∑i)1 (%∆Vi)2.

n (%∆Vi-bias)2. e RMS ) x1/(n-1)∑i)1

Table 12. Parameters for Equation 4 for Data Reported in Reference 4 Tmin/K Tmax/K Pmin/MPa Pmax/MPa Fmin/kg‚m-3 Fmax/kg‚m-3 data points c1/MPa‚kg-1‚m3 c2/kg-1‚m3 c3/MPa c4/K‚MPa c5/MPa‚K1/3 AAD/% bias/% SDV/% RMS/%

x1 ) 0.150

x1 ) 0.301

x1 ) 0.505

x1 ) 0.850

310.93 403.08 6.72 34.68 652.40 749.30 20 0.102223 1.230 × 10-3 -147.053 21 191.465 -1957.6624 0.0702 -1.41 × 10-4 1.07 × 10-2 0.0838

310.92 403.08 6.76 34.51 650.08 757.80 20 0.094339 1.211 × 10-3 -135.888 17 752.385 -1771.6752 0.0697 -1.31 × 10-4 9.65 × 10-3 0.0809

311.25 402.94 6.93 30.94 652.80 778.00 17 0.070276 1.173 × 10-3 -205.707 26 986.365 -2333.1702 0.0736 -1.20 × 10-4 7.27 × 10-3 0.0776

312.46 402.80 8.72 28.03 571.60 836.80 13 0.006335 1.137 × 10-3 -295.456 38 034.189 -2856.8387 0.2168 -1.42 × 10-3 1.07 × 10-1 0.2667

to 363) K and pressures up to 25 MPa. Densities of decane at (30 and 40) MPa were predicted successfully using the parameters determined here for the BWRS EoS. Good agreement was found for experimental densities with those calculated with the equation proposed by Lemmon and Span.14 A simple empirical equation was used successfully

to correlate the densities of CO2 + decane mixtures at constant composition. Acknowledgment Special thanks are given to F. F. Betancourt-Ca´rdenas for his help and Erick W. Lemmon for his useful comments and for providing us with his unpublished equation. Literature Cited

Figure 5. Comparison with data reported by Bessie`res et al.5 and Cullick and Mathis4 at 20 MPa: b, this work at 318.15 K; O, Bessie`res et al.5 at 318.15 K; shaded O, Cullick and Mathis4 at 318.15 K; 9, this work at 338.15 K; 0, Bessie`res et al.5 at 338.15 K; shaded 0, Cullick and Mathis4 at 338.15 K; 2, this work at 358.15 K; 4, Bessie`res et al.5 at 358.15 K; shaded 4, Cullick and Mathis4 at 358.15 K.

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Journal of Chemical and Engineering Data, Vol. 50, No. 3, 2005 1037 (8) Zu´n˜iga-Moreno, A.; Galicia-Luna, L. A. Densities of 1-Propanol and 2-Propanol via a Vibrating Tube Densimeter from 310 to 363 K and up to 25 MPa. J. Chem. Eng. Data 2002, 47, 155-160. (9) Zu´n˜iga-Moreno, A.; Galicia-Luna, L. A.; Horstmann, S.; Ihmels, C.; Fischer, K. Compressed Liquid Densities and Excess Volumes for the Binary Systems Carbon Dioxide + 1-Propanol and Carbon Dioxide + 2-Propanol Using a Vibrating Tube Densimeter up to 25 MPa. J. Chem. Eng. Data 2002, 47, 1418-1424. (10) Wagner, W.; Pruβ, A. The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use. J. Phys. Chem. Ref. Data 2002, 31, 387-535. (11) Span, R.; Lemmon, E. W.; Jacobsen, R. T.; Wagner, W. A Reference Quality Equation of State for Nitrogen. Int. J. Thermophys. 1998, 19, 1121-1132. (12) Galicia-Luna, L. A.; Ortega-Rodrı´guez, A.; Richon, D. New Apparatus for the Fast Determination of High-Pressure Vapor-

Liquid Equilibria of Mixtures and of Accurate Critical Pressures. J. Chem. Eng. Data 2000, 45, 265-271 (13) Starling, K. E. Thermo Data Refined for LPG, Part 1: Equation of state and computer prediction. Hydrocarbon Process. 1971, 50, 101-104. (14) Lemmon, E. W.; Span, R. Short Fundamental Equations of State for Industrial Fluids. To be submitted for publication in J. Chem. Eng. Data. (15) Span, R.; Wagner, W. A New Equation of State For Carbon Dioxide Covering the Fluid Region from the Triple-Point Temperature to 1100 K at Pressures up to 800 MPa. J. Phys. Chem. Ref. Data 1996, 25, 1509-1596. Received for review January 14, 2005. Accepted March 21, 2005. We thank CONACYT and IPN for their financial support.

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