Antoine Vapor Pressure Correlation: Generalization and Prediction of Coefficients of Normal Alkanes
Vol. 5(4), pp. 37-46, August 2014 DOI 10.5897/JCEMS2014.0182 Article Number: FF7E25546435 Journal of Chemical Engineering and Materials ISSN 2141-6605 Copyright © 2014 Science Author(s) retain the copyright of this article http://www.academicjournals.org/JCEMS
Full Length Research Paper
Antoine vapor pressure correlation: Generalization and prediction of coefficients of normal Alkanes
A. A. Rabah
Department of Chemical Engineering, University of Khartoum, P.O. Box 321, Khartoum, Sudan.
Received 7 June, 2014; Accepted 21 July, 2014.
This work presents two developments in Antoine vapor pressure correlation: (1) Generalization of the correlation using the principle of corresponding state; (2) Prediction of the Antoine coefficients form molecular weight. The coefficients of the generalized correlation are correlated to molecular weight 2 (r =0.99) for the group of normal alkanes (C1 to C20). The method is validated using experimental data obtained from reliable literature covering 169 vapor pressure data points covering 11 fluids. The method reproduced the experimental data with a grand absolute average percent deviation (AAPD) of 2.93 while the original Antoine correlation reproduced the same data with 1.90. The method provides a simple procedure for the prediction of Antoine coefficients. On the other hand, the developments, significantly reduces the number of coefficients of C1 to C20 from (3×20=) 60 to (3×3=) 9. This saves the labor work needed for storage and processing of the large number of coefficients values.
Key words: Antoine coefficients, normal alkanes, vapor pressure.
INTRODUCTION
Normal alkanes (n-CnH n+2) are the basic compositions B 2 ln P s A (1) of reservoir fluids (dry gas, wet gas, gas condensate, C T volatile oil or black oil). The vapor pressure is the most important physical property needed by engineers, s 1.5 3 6 1 ln P a b c d e 1 (2) scientific researcher and students in the field of oil and gas industry. In this field the bubble and dew point Where τ = 1-Tr. pressures are most needed for reservoir development and simulation. There exist a number of correlations of Antoine correlation [Equation (1)] is most widely used one vapor pressure of pure fluids. These include Antoine however; the constant A, B and C are specific to each [Antoine, 1988] correlation (Equation 1) and Wagner fluid. Hence a large data bank is needed for each fluid (1973) correlation (Equation 2) among other which are coefficients. On the other hand, by numerical basically extensions or modifications of these two computation, large memory is needed to store and correlations: process the values of the coefficients. Wagner correlation
E-mail: [email protected]. Author(s) agree that this article remain permanently open access under the terms of the Creative Commons Attribution License 4.0 International License 38 J. Chem. Eng. Mater. Sci.
8 8 8
7 7 7
6 6 6
5 5 5
4 4 4 A' A' 3 3 B' 3 A' B' C' B' C' 2 2 2 C' Coefficeints A', B', C'
1 1 1
0 0 0
-1 -1 -1 0 100 200 3000 250 500 75010 20 30 40 50 M Tc Pc
Figure 1. Variation of Antoine equation coefficients with physical constants.
[Equation (2)] is similar to Antoine correlation in term of dependency acentric factor is shown earlier. Hence coefficient specific fluid however, it has a wide range of Equation (4) becomes: validity down to Tr = 0.5 (Edalat et al., 1993). Edalat et al. (1993) have generalized Wagner y y(T,T ,T ,M ,) (5) correlation [Equation (2)] for hydrocarbons by correlating b c its coefficients to accentric factor. The accentric factor is calculated using Pitzer Equation (3): Using the principles of corresponding state Equation (1) is reduced to Equation (6) as: s log Pr Tr0.7 1 (3) s P B ln A (6) The generalized Wagner correlation is reported to yield P C T vapor pressure for n-Alkane with an average error of c r 6.53%. B C T A A ln P , B , C and T (7) c T T r T GENERALIZATION OF ANTOINE CORRELATION c c c
As mentioned earlier Antoine coefficients are function of The accentric factor is a function of vapor pressure as type of fluid as: given by Equation (3) and the normal boiling point Tb can be predicted from vapor pressure equation. Hence these y fluid (4) parameters (Tc; Pc; Tb; ω) are independent of the coefficients. Hence Equation (5) becomes: Where y represent any of the coefficients A; B; C. Figure 1 shows the variation of the coefficients with physical y y M (8) parameters. It can be seen that there is a clear dependency of the Antoine coefficients on critical temperature and pressure and molecular weight. The Where y′ represents the modified coefficients A′, B', C'. Rabah 39
Table 1. Physical constants of n-Alkanes (Reid et al., 1987; Danesh, 1998).
No Name Chemical formula M Tc (K) Pc (bar) ω
C1 Methane CH4 16.043 190.56 46.99 0.0115
C2 Ethane C2H6 30.070 305.32 48.72 0.0995
C3 Propane C3H8 44.097 369.83 42.48 0.1523
nC4 n-Butane C4H10 58.124 425.12 37.96 0.2002
nC5 n-Pentane C5H12 72.151 469.70 33.70 0.2515
nC6 nhexane C6H14 86.178 507.60 30.25 0.3013
nC7 n-heptane C7H16 100.204 540.20 27.40 0.3495
nC8 n-octane C8H18 114.231 568.70 24.90 0.3996
nC9 n-nonane C9H20 128.259 594.60 22.90 0.4435
nC10 n-decane C10H22 142.286 617.70 21.10 0.4923
nC11 n-undecane C11H24 156.313 639.00 19.49 0.5303
nC12 n-dodecane C12H26 170.340 658.00 18.20 0.5764
nC13 n-tridecane C13H28 184.367 675.00 16.80 0.6174
nC14 n-tertadecane C14H30 198.394 693.00 15.70 0.6430
nC15 n-pentadecane C15H32 212.421 708.00 14.80 0.6863
nC16 n-hexadecane C16H34 226.448 723.00 14.00 0.7174
nC17 n-heptadecane C17H36 240.475 736.00 13.40 0.7697
nC18 n-octadecane C18H38 254.502 747.00 12.70 0.8114
nC19 n-nonadecae C19H40 268.529 758.00 12.10 0.8522
nC20 n-eicosane C20H42 282.556 768.00 11.60 0.9069
DATA BANK AND REGRESSION ANALYSIS coefficients are needed. For Antoine correlation there are (20×3=) 60 coefficients values needed. The coefficients of Equation (1) and their range of application Tmin and Tmax as well as the physical parameters (M, Tc, Pc, ω) for the group under VALIDATION OF THE PROCEDURE consideration are obtained from Reid et al. (1987). The data on physical parameter is cross-checked with that To compare the generalized Antoine correlation and the available in Danesh (1998) and VDI (2007). Tables 1 and Antoine correlation to experimental data, numerous 2 show the physical parameters and coefficients of quality measurements based on statistical error analysis Equation (1) for n-Alkane (C1 to nC20). Experimental are computed. These include the percent deviation (PD), vapor pressure data for model validation is obtained from the average absolute percent deviation (AAPD), the different sources as shown in Table 4. minimum absolute percent deviation (APDmin), the Using critical properties (Table 1), coefficients data of maximum absolute percent deviation (APDmax) and the Equation (1) (Table 2) and Equation (7), the coefficients grand average AAPD (Rabah and Mohamed, 2010a, b). of the generalized Antoine correlation Equation (6) are The percent deviation is defined as: calculated for normal Alkanes of C1 to C20. Figure 2 shows the best fit (r2 = 0:99) of the coefficients of X exp.i X cal,i Equation (8) to molecular weight. The regression PDi (10) assumed the following equations: X exp,i
y M M 2 (9) The average absolute percent deviation (AAPD) is o 1 2 defined as:
where y′ represents the coefficients A′, B′ and C′. The 1 values of the constants βo, β1 and β2, of Equation (9) are AAPD PD (11) 2 i given in Table 3 together with correlation coefficient (r ). N The correlation coefficient for each parameter is about 0.99. The generalized Antoine correlation has Where Xexp is the experimental value, Xcal is the significantly reduced the number of coefficients needed. calculated value, N is the number of the data points and i For example for C1 to C20 there is only (3×3=) 9 is a dummy index. 40 J. Chem. Eng. Mater. Sci.
Table 2. Antoine correlation coefficients of n-Alkanes (Reid et al., 1987).
Generalized Antoine Antoine Compound Trmin Trmax A' B' C' A B C
C1 4.754 4.712 -0.038 15.224 897.84 -7.16 0.49 0.63
C2 5.157 4.950 -0.056 15.664 1511.42 -17.16 0.44 0.65
C3 5.357 5.063 -0.068 15.726 1872.46 -25.16 0.46 0.67
nC4 5.421 5.069 -0.081 15.678 2154.90 -34.42 0.47 0.69
nC5 5.696 5.274 -0.085 15.833 2477.07 -39.94 0.49 0.70
nC6 5.807 5.314 -0.096 15.837 2697.55 -48.78 0.50 0.72
nC7 5.943 5.389 -0.105 15.874 2911.32 -56.51 0.51 0.73
nC8 6.108 5.487 -0.112 15.943 3120.29 -63.63 0.53 0.75
nC9 6.216 5.536 -0.120 15.967 3291.45 -71.33 0.54 0.76
nC10 6.342 5.596 -0.127 16.011 3456.80 -78.67 0.55 0.77
nC11 6.464 5.656 -0.134 16.054 3614.07 -85.45 0.56 0.78
nC12 6.592 5.736 -0.139 16.113 3774.56 -91.31 0.57 0.79
nC13 6.694 5.767 -0.147 16.136 3892.91 -98.93 0.58 0.80
nC14 6.774 5.784 -0.152 16.148 4008.52 -105.40 0.58 0.81
nC15 6.858 5.821 -0.158 16.172 4121.51 -111.80 0.59 0.81
nC16 6.925 5.830 -0.164 16.184 4214.91 -118.70 0.60 0.82
nC17 6.936 5.835 -0.168 16.151 4294.55 -124.00 0.59 0.78
nC18 6.961 5.839 -0.174 16.123 4361.79 -129.90 0.61 0.84
nC19 7.04 5.871 -0.179 16.153 4450.44 -135.60 0.62 0.85
nC20 7.397 6.094 -0.184 16.469 4680.46 -141.10 0.63 0.85
Table 3. β’s values of Equation (6).
Coefficients A' B' C'
βo 4.715 4.667 -0.032
β1 0.014 0.009 -0.001
β2 -1.784E-05 -1.431E-05 9.963E-07 r2 0.995 0.990 0.998
Table 4. AAPD of Antoine and generalized Antoine correlations.
Antoine Generalized Antoine Data Tmax Tmin Data Fluid AAPD APD APD AAPD APD APD source max min max min points K K % % % % % %
C1 [8],[9] 180 153 2.28 5.16 0.20 5.11 6.65 4.35 5
C2 [10],[11] 143 74 1.74 6.91 0.11 3.06 6.52 0.3 13
C3 [10],[12] 109 24 1.72 5.58 0.20 4.00 6.58 0.07 6
C4 [13],[12] 178 17 2.00 5.38 0.58 3.30 6.59 0.01 15
C5 [14],[10],[15] 153 57 1.15 5.81 0.35 2.87 6.56 0.32 21
C6 [13],[10],[15] 128 97 1.83 5.41 0.21 2.67 6.52 0.63 10
C7 [13],[16],[15] 400 270 1.68 5.83 0.71 2.00 6.05 0.06 29
C8 [13],[16],[15] 425 292 2.50 5.18 -0.23 2.08 3.66 0.31 9
C9 [17] 179 39 1.59 5.30 0.18 3.11 6.25 0.31 36
C10 [8],[17] 203 57 2.50 6.57 0.0 2.15 6.41 0.27 10
C12 [13] 247 91 1.85 6.88 0.20 1.84 6.73 0.08 15 Grand 1.90 5.82 0.23 2.93 6.23 0.61 169 Rabah 41
Table 5. AAPD of Antoine and generalized Antoine correlations (C1 to C3).
T Pexp Antoine Generalized Antoine No. K mmHg Pcal PD |PD| Pcal PD |PD|
C1 1 130.00 2755.78 2750.13 0.20 0.20 2572.64 6.65 6.65 2 140.00 4809.48 4767.96 0.86 0.86 4560.12 5.18 5.18 3 150.00 7800.78 7653.30 1.89 1.89 7454.96 4.43 4.43 4 160.00 11941.94 11547.04 3.31 3.31 11422.00 4.35 4.35 5 170.00 17464.00 16563.54 5.16 5.16 16599.59 4.95 4.95 AAPD 2.28 2.28 5.11 5.11
APDmax 5.16 5.16 6.65 6.65
APDmin 0.20 0.20 4.35 4.35
C2 1 184.56 759.98 762.86 -0.38 0.38 797.98 -5.00 5.00 2 200.00 1629.76 1635.49 -0.35 0.35 1695.45 -4.03 4.03 3 220.00 3691.64 3695.81 -0.11 0.11 3795.82 -2.82 2.82 4 240.00 7253.38 7214.67 0.53 0.53 7355.35 -1.41 1.41 5 260.00 12845.03 12614.53 1.79 1.79 12783.54 0.48 0.48 6 280.00 21059.11 20258.01 3.80 3.80 20427.72 3.00 3.00 7 300.00 32683.77 30424.81 6.91 6.91 30551.85 6.52 6.52 8 184.40 750.08 756.29 -0.83 0.83 791.20 -5.48 5.48 9 198.00 1500.15 1492.57 0.51 0.51 1548.94 -3.25 3.25 10 220.20 3750.38 3723.05 0.73 0.73 3823.48 -1.95 1.95 11 241.00 7500.75 7436.68 0.85 0.85 7579.19 -1.05 1.05 12 266.60 15001.50 14873.31 0.85 0.85 15046.39 -0.30 0.30 13 296.60 30003.00 28509.16 4.98 4.98 28647.16 4.52 4.52 AAPD 1.48 1.74 -0.83 3.06
APDmax 6.91 6.91 6.52 6.52
APDmin -0.83 0.11 -5.48 0.30
C3 C3 1 231.08 759.98 767.63 -1.01 1.01 810.02 -6.58 6.58 2 255.00 1959.05 1976.13 -0.87 0.87 2050.50 -4.67 4.67 3 280.00 4364.76 4391.69 -0.62 0.62 4496.22 -3.01 3.01 4 300.00 7334.31 7493.06 -2.16 2.16 7605.85 -3.70 3.70 5 320.00 11991.45 11890.77 0.84 0.84 11983.58 0.07 0.07 32 340.00 18239.57 17794.34 2.44 2.44 17824.88 2.27 2.27 33 362.45 27989.05 26428.24 5.58 5.58 26321.23 5.96 5.96 6 230.90 760.00 761.56 -0.20 0.20 803.72 -5.75 5.75 AAPD 0.50 1.72 -1.93 4.00
APDmax 5.58 5.58 5.96 6.58
APDmin -2.16 0.20 -6.58 0.07
Table 4 shows a summary of AAPD for some 11 fluids respectively. The error associated with generalized compromising about 169 vapor pressure data points from correlation is in the same order of the associated with the literature. All experimental data from literature is Antoine correlation. That is to say, the generalization is presented in Tables 5 to 9. Only the data that fall within not made at the expense of accuracy. the range of the correlation application is considered. The
range is set by the original Antoine correlation as given in Conclusion Table 2. Both Antoine and generalized Antoine correlations produced comparable results; with a The method is useful in the prediction of Antoine consistent grand average AAPD of about 1.90 and 2.93 coefficients; the prediction of the coefficients requires 42 J. Chem. Eng. Mater. Sci.
Table 6. AAPD of Antoine and generalized Antoine correlations (C4 to C5).
T Pexp Antoine Generalized Antoine No. K mmHg Pcal PD |PD| Pcal PD |PD|
C4 1 272.63 759.98 755.29 0.62 0.62 796.96 -4.87 4.87 2 295.00 1656.17 1642.77 0.81 0.81 1718.65 -3.77 3.77 3 320.00 3432.27 3389.63 1.24 1.24 3522.54 -2.63 2.63 4 345.00 6347.21 6224.17 1.94 1.94 6438.12 -1.43 1.43 5 370.00 10768.83 10439.58 3.06 3.06 10763.04 0.05 0.05 6 395.00 17127.96 16298.15 4.84 4.84 16764.17 2.12 2.12 7 270.00 686.69 682.70 0.58 0.58 721.24 -5.03 5.03 8 300.00 1936.02 1919.69 0.84 0.84 2005.26 -3.58 3.58 9 340.00 5652.12 5555.85 1.70 1.70 5751.46 -1.76 1.76 10 370.00 10763.58 10439.58 3.01 3.01 10763.04 0.01 0.01 11 400.00 18691.87 17687.00 5.38 5.38 18185.90 2.71 2.71 12 228.80 100.00 98.11 1.89 1.89 106.59 -6.59 6.59 13 241.80 200.00 196.66 1.67 1.67 211.31 -5.65 5.65 14 256.70 400.00 394.82 1.30 1.30 420.03 -5.01 5.01 15 272.50 760.00 751.57 1.11 1.11 793.08 -4.35 4.35 AAPD 2.00 2.00 -2.65 3.30
APDmax 5.38 5.38 2.71 6.59
APDmin 0.58 0.58 -6.59 0.01
C5 C5 1 309.20 759.83 769.55 -1.28 1.28 798.04 -5.03 5.03 2 335.00 1702.67 1719.17 -0.97 0.97 1763.86 -3.59 3.59 3 350.00 2557.76 2579.69 -0.86 0.86 2632.68 -2.93 2.93 4 365.00 3690.37 3728.62 -1.04 1.04 3787.01 -2.62 2.62 5 380.00 5160.52 5216.93 -1.09 1.09 5275.68 -2.23 2.23 6 395.00 7013.20 7095.05 -1.17 1.17 7146.71 -1.90 1.90 7 410.00 9368.44 9411.74 -0.46 0.46 9446.20 -0.83 0.83 8 425.00 12256.23 12213.02 0.35 0.35 12217.36 0.32 0.32 9 440.00 15774.08 15541.42 1.47 1.47 15499.83 1.74 1.74 10 469.60 25270.03 23800.90 5.81 5.81 23611.13 6.56 6.56 11 335.00 1702.67 1719.17 -0.97 0.97 1763.86 -3.59 3.59 12 350.00 2557.76 2579.69 -0.86 0.86 2632.68 -2.93 2.93 13 365.00 3690.37 3728.62 -1.04 1.04 3787.01 -2.62 2.62 14 380.00 5160.52 5216.93 -1.09 1.09 5275.68 -2.23 2.23 15 395.00 7013.20 7095.05 -1.17 1.17 7146.71 -1.90 1.90 16 410.00 9368.44 9411.74 -0.46 0.46 9446.20 -0.83 0.83 17 425.00 12256.23 12213.02 0.35 0.35 12217.36 0.32 0.32 18 440.00 15774.08 15541.42 1.47 1.47 15499.83 1.74 1.74 19 274.90 200.00 201.10 -0.55 0.55 212.39 -6.20 6.20 20 291.50 400.00 403.02 -0.76 0.76 421.61 -5.40 5.40 21 309.10 760.00 766.92 -0.91 0.91 795.35 -4.65 4.65 AAPD -0.25 1.15 -1.85 2.87
APDmax 5.81 5.81 6.56 6.56
APDmin -1.28 0.35 -6.20 0.32
only molecular weight. This piece of information is works otherwise needed to store and process the large available. Other hand Antoine correlation saves the labor number of Antoine correlation coefficients. Today, one Rabah 43
Table 7. AAPD of Antoine and generalized Antoine correlations (C6 to C7).
T Pexp Antoine Generalized Antoine No. K mmHg Pcal PD |PD| Pcal PD |PD|
C6 1 341.88 759.83 774.08 -1.88 1.88 793.84 -4.48 4.48 2 370.00 1710.17 1733.49 -1.36 1.36 1760.03 -2.92 2.92 3 385.00 2482.75 2521.98 -1.58 1.58 2549.27 -2.68 2.68 4 400.00 3487.85 3553.48 -1.88 1.88 3577.86 -2.58 2.58 5 415.00 4770.48 4868.20 -2.05 2.05 4884.49 -2.39 2.39 6 430.00 6405.64 6506.16 -1.57 1.57 6507.51 -1.59 1.59 7 445.00 8430.84 8506.37 -0.90 0.90 8484.19 -0.63 0.63 8 460.00 10928.59 10906.14 0.21 0.21 10850.03 0.72 0.72 9 475.00 13943.89 13740.47 1.46 1.46 13638.22 2.19 2.19 10 507.44 22734.77 21505.07 5.41 5.41 21252.89 6.52 6.52 AAPD -0.41 1.83 -0.78 2.67
APDmax 5.41 5.41 6.52 6.52
APDmin -2.05 0.21 -4.48 0.63
C7 1 372.32 780.20 770.57 1.23 1.23 785.96 -0.74 0.74 2 371.81 768.63 759.18 1.23 1.23 774.45 -0.76 0.76 3 371.24 755.75 746.44 1.23 1.23 761.59 -0.77 0.77 4 370.73 744.49 735.33 1.23 1.23 750.36 -0.79 0.79 5 370.18 732.53 723.51 1.23 1.23 738.41 -0.80 0.80 6 365.08 628.32 620.48 1.25 1.25 634.23 -0.94 0.94 7 357.86 501.15 494.80 1.27 1.27 506.92 -1.15 1.15 8 351.20 402.93 397.73 1.29 1.29 408.39 -1.36 1.36 9 344.97 325.42 321.18 1.30 1.30 330.52 -1.57 1.57 10 338.92 262.13 258.67 1.32 1.32 266.82 -1.79 1.79 11 333.90 217.54 214.65 1.33 1.33 221.86 -1.99 1.99 12 328.44 176.26 173.83 1.38 1.38 180.09 -2.17 2.17 13 324.37 149.76 147.71 1.37 1.37 153.31 -2.37 2.37 14 319.99 124.95 123.24 1.37 1.37 128.18 -2.59 2.59 15 315.68 104.00 102.55 1.40 1.40 106.89 -2.77 2.77 16 311.90 88.06 86.83 1.40 1.40 90.68 -2.97 2.97 17 309.11 77.65 76.52 1.45 1.45 80.04 -3.08 3.08 18 306.11 67.60 66.62 1.44 1.44 69.80 -3.26 3.26 19 302.81 57.88 56.99 1.54 1.54 59.82 -3.35 3.35 20 299.04 48.19 47.41 1.63 1.63 49.87 -3.49 3.49 21 371.60 759.83 754.45 0.71 0.71 769.67 -1.30 1.30 22 380.00 975.10 959.25 1.63 1.63 976.34 -0.13 0.13 23 400.00 1642.66 1620.82 1.33 1.33 1641.67 0.06 0.06 24 420.00 2617.76 2585.03 1.25 1.25 2607.54 0.39 0.39 25 440.00 3967.90 3926.90 1.03 1.03 3947.22 0.52 0.52 26 460.00 5408.04 5723.08 -5.83 5.83 5735.39 -6.05 6.05 27 480.00 8205.82 8049.30 1.91 1.91 8045.59 1.95 1.95 28 500.00 11348.63 10978.04 3.27 3.27 10948.03 3.53 3.53 29 520.00 15346.53 14576.72 5.02 5.02 14507.86 5.46 5.46 AAPD 1.28 1.68 -1.18 2.00
APDmax 5.02 5.83 5.46 6.05
APDmin -5.83 0.71 -6.05 0.06 44 J. Chem. Eng. Mater. Sci.
Table 8. AAPD of Antoine and generalized Antoine correlations (C8 to C9).
T Pexp Antoine Generalized Antoine No. K mmHg Pcal PD |PD| Pcal PD |PD|
C8 1 423.97 759.83 755.70 0.54 0.54 782.12 -2.93 2.93 2 435.00 1005.10 1003.27 0.18 0.18 1036.14 -3.09 3.09 3 455.00 1605.16 1608.85 -0.23 0.23 1655.91 -3.16 3.16 4 475.00 2535.25 2462.02 2.89 2.89 2526.59 0.34 0.34 5 495.00 3720.37 3619.27 2.72 2.72 3704.73 0.42 0.42 6 515.00 5378.04 5138.81 4.45 4.45 5248.44 2.41 2.41 7 535.00 7238.22 7078.97 2.20 2.20 7215.84 0.31 0.31 8 555.00 9900.99 9496.70 4.08 4.08 9663.55 2.40 2.40 9 575.00 13126.31 12446.32 5.18 5.18 12645.48 3.66 3.66 AAPD 2.45 2.50 0.04 2.08
APDmax 5.18 5.18 3.66 3.66
APDmin -0.23 0.18 -3.16 0.31
C9 1 151.79 780.11 772.62 0.96 0.96 799.49 -2.48 2.48 2 151.22 768.57 761.19 0.96 0.96 787.76 -2.50 2.50 3 150.58 755.57 748.33 0.96 0.96 774.55 -2.51 2.51 4 150.02 744.37 737.23 0.96 0.96 763.14 -2.52 2.52 5 149.41 732.45 725.36 0.97 0.97 750.96 -2.53 2.53 6 143.75 628.22 622.02 0.99 0.99 644.72 -2.63 2.63 7 135.74 501.05 495.99 1.01 1.01 515.00 -2.78 2.78 8 128.36 402.81 398.65 1.03 1.03 414.65 -2.94 2.94 9 121.43 325.27 321.87 1.04 1.04 335.38 -3.11 3.11 10 114.71 262.00 259.19 1.07 1.07 270.55 -3.26 3.26 11 109.14 217.40 215.02 1.09 1.09 224.80 -3.40 3.40 12 103.07 176.11 174.13 1.12 1.12 182.38 -3.56 3.56 13 98.55 149.63 147.94 1.13 1.13 155.16 -3.70 3.70 14 93.66 124.80 123.38 1.13 1.13 129.62 -3.86 3.86 15 88.86 103.86 102.63 1.19 1.19 107.99 -3.98 3.98 16 84.66 87.94 86.88 1.20 1.20 91.56 -4.11 4.11 17 81.55 77.52 76.57 1.23 1.23 80.78 -4.21 4.21 18 78.22 67.47 66.67 1.18 1.18 70.44 -4.40 4.40 19 74.55 57.73 57.01 1.24 1.24 60.32 -4.48 4.48 20 70.34 48.04 47.42 1.29 1.29 50.25 -4.61 4.61 21 423.97 759.83 755.70 0.54 0.54 782.12 -2.93 2.93 22 435.00 1005.10 1003.27 0.18 0.18 1036.14 -3.09 3.09 23 455.00 1605.16 1608.85 -0.23 0.23 1655.91 -3.16 3.16 24 475.00 2535.25 2462.02 2.89 2.89 2526.59 0.34 0.34 25 495.00 3720.37 3619.27 2.72 2.72 3704.73 0.42 0.42 26 515.00 5378.04 5138.81 4.45 4.45 5248.44 2.41 2.41 27 535.00 7238.22 7078.97 2.20 2.20 7215.84 0.31 0.31 28 555.00 9900.99 9496.70 4.08 4.08 9663.55 2.40 2.40 29 575.00 13126.31 12446.32 5.18 5.18 12645.48 3.66 3.66 30 324.20 20.00 18.94 5.30 5.30 20.25 -1.27 1.27 31 339.00 40.00 38.93 2.68 2.68 41.33 -3.33 3.33 32 348.50 60.00 59.36 1.07 1.07 62.78 -4.63 4.63 33 361.10 100.00 99.53 0.47 0.47 104.76 -4.76 4.76 34 380.50 200.00 203.16 -1.58 1.58 212.50 -6.25 6.25 35 401.20 400.00 396.52 0.87 0.87 412.45 -3.11 3.11 Rabah 45
Table 8. Contd.
36 423.80 760.00 752.30 1.01 1.01 778.63 -2.45 2.45 AAPD 1.49 1.59 -2.58 3.11
Table 9. AAPD of Antoine and generalized Antoine correlations (C10 to C12).
T Pexp Antoine Generalized Antoine No. K mmHg Pcal PD |PD| Pcal PD |PD|
C10 1 447.31 759.83 760.12 -0.04 0.04 770.87 -1.45 1.45 2 460.00 1057.61 1038.26 1.83 1.83 1051.35 0.59 0.59 3 480.00 1702.67 1630.66 4.23 4.23 1647.75 3.23 3.23 4 500.00 2467.75 2453.68 0.57 0.57 2474.93 -0.29 0.29 5 520.00 3592.86 3557.94 0.97 0.97 3583.15 0.27 0.27 6 540.00 5063.01 4995.67 1.33 1.33 5024.21 0.77 0.77 7 560.00 6953.20 6819.39 1.92 1.92 6850.17 1.48 1.48 8 580.00 9375.94 9080.70 3.15 3.15 9112.09 2.81 2.81 9 600.00 12376.24 11829.17 4.42 4.42 11859.02 4.18 4.18 10 617.60 15721.57 14687.97 6.57 6.57 14714.24 6.41 6.41 AAPD 2.50 2.50 1.80 2.15
APDmax 6.57 6.57 6.41 6.41
APDmin -0.04 0.04 -1.45 0.27
C12 1 363.00 9.87 9.19 6.88 6.88 9.20 6.73 6.73 2 377.60 19.74 18.67 5.40 5.40 18.68 5.34 5.34 3 394.70 39.48 39.28 0.51 0.51 39.25 0.57 0.57 4 405.10 59.22 59.34 -0.20 0.20 59.26 -0.08 0.08 5 419.20 98.69 99.56 -0.88 0.88 99.35 -0.67 0.67 6 440.20 197.39 199.14 -0.89 0.89 198.50 -0.56 0.56 7 464.00 394.77 397.49 -0.69 0.69 395.74 -0.24 0.24 8 489.20 750.08 755.08 -0.67 0.67 750.92 -0.11 0.11 9 377.60 20.00 18.67 6.64 6.64 18.68 6.58 6.58 10 394.70 40.00 39.28 1.81 1.81 39.25 1.86 1.86 11 405.10 60.00 59.34 1.11 1.11 59.26 1.23 1.23 12 419.20 100.00 99.56 0.44 0.44 99.35 0.65 0.65 13 440.20 200.00 199.14 0.43 0.43 198.50 0.75 0.75 14 464.00 400.00 397.49 0.63 0.63 395.74 1.06 1.06 15 489.20 760.00 755.08 0.65 0.65 750.92 1.19 1.19 AAPD 1.41 1.85 1.62 1.84
APDmax 6.88 6.88 6.73 6.73
APDmin -0.89 0.20 -0.67 0.08
may find the coefficient of same fluid varies from author correlation; M, molecular weight; P, pressure; r, to author. This makes the user always uncertain about correlation coefficient; T, temperature; y, a dummy the accuracy. This method shall contribute in building variable stands for the coefficients A, B,C. confidence in vapor pressure correlations. Greek symbols: ß, Coefficient of generalized Antoine correlation; τ, 1-Tr; ω, acentric factor. Nomenclature: A, Coefficient of Antoine correlation; B, coefficient of Antoine correlation; C, coefficient of Antoine Subscripts: c, Critical; r, reduced. 46 J. Chem. Eng. Mater. Sci.
8 Rabah AA, Mohamed S (2010b). A new three parameters equation of state. Scientia Trans. C: Chem. Chem. Eng. 17(2):1-15. Rabah AA, Mohamed SA (2010a). Prediction of Molar Volumes of the 7 Sudanese Reservoir Fluids. J. Thermodyn. 2010:1-9. doi:10.1155/2010/142475. Reid RC, Prausnitz JM, Poling BE (1987). The Properties of Gases and 6 Liquids, 4th ed., McGraw-Hill. VDI-Wärmeatlas, 10. Auflage (2007). VDI-Gesellschaft 5 Verfahrenstechnik (Hrsg.), Springer-Verlag, Heidelberg, Deutschland. Wagner W (1973). New vapor pressure measurement for Argon and Nitrogen and a new method for establishing rational vapor pressure 4 equation. Cryogenics 13:470-82.
A' 3 B' C' 2
1 Antoine Equation Coefficeints A', B', C' 0
-1 0 100 200 300 M
Figure 2. Dependency of generalized Antoine coefficients on molecular weight.
Superscripts: o, Degree; s, saturation.
REFERENCES
Antoine C (1988). Tensions des vapeurs; nouvelle relation entre les tensions et les températures" [Vapor Pressure: A new relationship between pressure and temperature], Comptes Rendus des Séances de l'Académie des Sciences (in French) 107:681–685. Danesh A (1998). PVT and Phase Behavior of Petroleum Reservoir Fluids, 2nd Edition, Elsevier Science, Amsterdam. Edalat E, Bozar-Jomehri RB, Mansoori GA (1993). Generalized equation predicts vapor pressure of hydrocarbons. Oil Gas. 1:39-40.