Ind. Eng. Chem. Res 1991, 30, 420-427
420
Hayden, L. V.; O'Connell, J. P. A Generalized Method for Predicting Second Virial Coefficients. Ind. Eng. Chem. Process Des. Deu.
Acknowledgment We are indebted to the Italian Minister0 dell'universiti e della Ricerca Scientifica e Tecnologica for financial support. Registry No. H C H O , 50-00-0; M e O H , 67-56-1. Literature Cited Abrams, D. S.; Prausnitz, J. M. Statistical Thermodynamics of Liquid Mixtures: A New Expression for the Excess Gibbs Energy of Partly or Completely Miscible Systems. AIChE J . 1975,21,62. Bondi, A. Physical Properties of Molecular Crystals, Liquids & Gases; John Wiley & Sons: New York, 1968;pp 450-471. Brandani, V.; Di Giacomo, G. Effect of Small Amounts of Methanol on the Vapour-Liquid Equilibrium for the Water-Formaldehyde System. Fluid Phase Equilib. 1985,24,307. Brandani, V.; Di Giacomo, G.; Foscolo, P. U. Isothermal VaporLiquid Equilibria for the Water-Formaldehyde System. A Predictive Thermodynamic Model. Ind. Eng. Chem. Process Des. Dev. 1980,19,179. Brandani, V.; Di Giacomo, G.; Mucciante, V. A Test for the Thermodynamic Consistency of VLE Data for the Systems WaterFormaldehyde and Methanol-Formaldehyde. Ind. Eng. Chem. Res. 1987,26, 1162. Brelvi, S. W.; O'Connell, J. P. Corresponding States Correlations for Liquid Compressibility and Partial Molar Volumes of Gases a t Infinite Dilution in Liquids. AIChE J . 1972,18, 1239. Bryant, W. M.; Thompson, J. B. Chemical Thermodynamics of Polymerization of Formaldehyde in an Aqueous Environment. J . Polym. Sci.: Part A-1 1971,9, 2523. Hall, M. W.; Piret, E. L. Distillation Principles of Formaldehyde Solutions. Ind. Eng. Chem. 1949,41,1277.
1975,14,209. Ikonomou, G. D.; Donohue, M. D. Extension of the Associated Perturbed Anisotropic Chain Theory to Mixtures with More Than One Associating Component. Fluid Phase Equilib. 1988,39,129. Kogan, L. V.; Ogorodnikov, S. K. Liquid-Vapor Equilibrium in the Formaldehyde-Methanol System. Zh. Prikl. Khim. 1980,53,115. Maurer, G. Vapor-Liquid Equilibrium of Formaldehyde- and Water-Containing Multicomponent Mixtures. AIChE J. 1986,32,
932. Maurer, G.; Prausnitz, J. M. On the Derivation and Extension of the UNIQUAC Equation. Fluid Phase Equilib. 1978,2,91. Molzahn, M.; Wolf, D. Distillation, Absorption and Extraction-Is There Any Scope for Research Left? Ger. Chem. Eng. 1982,5,
221. Nothnagel, K. H.; Abrams, D. S.; Prausnitz, J. M. Generalized Correlation for Fugacity Coefficients in Mixtures a t Moderate Pressures. Application of Chemical Theory of Vapor Imperfections. Ind. Eng. Chem. Process Des. Dev 1973,12,25. Prausnitz, J. M.; Eckert, C. A,; Orye, R. V.; O'Connell, J. P. Computer Calculations for Multicomponent Vapor-Liquid Equilibria; Prentice-Hall: Englewood Cliffs, NJ, 1967;p 218. Prausnitz, J. M.; Anderson, T. F.; Grens, E. A.; Eckert, C. A.; Hsieh, R. O'Connell, J. P. Computer Caculations for Multicomponent Vapor-Liquid and Liquid-Liquid Equilibria; Prentice-Hall: Englewood Cliffs, NJ, 1980;pp 221-270. Spencer, C. F.; Danner, R. P. Improved Equation for Prediction of Saturated Liquid Density. J . Chem. Eng. Data. 1972,17, 236. Walker, J. F. Formaldehyde; ACS Monograph Series; American Chemical Society: Washington, DC, 1964;p 103.
Received for review April 9, 1990 Revised manuscript received July 16, 1990 Accepted August 1, 1990
A Generalized Viscosity Equation for Pure Heavy Hydrocarbons Ani1 K.Mehrotra Department of Chemical and Petroleum Engineering, The University of Calgary, Calgary, Alberta, Canada T2N 1N4
A new method is presented for the correlation and prediction of the viscosity of pure heavy hydrocarbons listed in API Research Project 42. The 273 heavy hydrocarbons in the database include branched/unbranched paraffins and olefins together with a variety of complex nonfused/fused aromatic and naphthenic compounds. A generalized one-parameter viscosity-temperature equation, log ( k + 0.8) = 100(O.OIT)b,is proposed (overall AAD < 7-1070) for all heavy hydrocarbons in the database. For each hydrocarbon, an optimum value of parameter b is provided. It is shown that parameter b varies linearly with the logarithm of molar mass as well as the inverse of boiling temperature (at 10 mmHg). This important observation leads to the development of a predictive method for the liquid-phase viscosity of pure heavy hydrocarbons. Numerous correlative and predictive methods for liquid viscosity and its variation with temperature have been proposed in the literature. A review of viscosity prediction methods is given by Reid et al. (1986). The TRAPP method (Ely and Hanley, 1981) for viscosity calculation uses a simple n-alkane, such as methane or propane, as the reference fluid in the corresponding states framework. Twu (1985) presented a method for the viscosity of petroleum fractions, which uses n-alkanes as the reference substances and requires boiling point and specific gravity as input parameters. However, the use of an n-alkane as the reference fluid in methods based on the corresponding states principle gives inadequate viscosity predictions for most non-paraffinic hydrocarbons (Johnson et al., 1987; Pedersen et al., 1984; Teja and Rice, 1981). Instead, as shown by Johnson et al. (1987) and Mehrotra and Svrcek 0888-5885/91/2630-0420$02.50/0
(1987), the use of a non-paraffinic hydrocarbon as the reference fluid give satisfactory predictions for the viscosity of bitumens, which are mixtures of mostly aromatic and naphthenic compounds. Bitumens from oil sands of Alberta (Canada) are extremely complex and viscous crude oils comprising high molecular weight polymeric asphaltenes and resins (Strausz, 1989). The SARA chemical analysis of bitumens and heavy oils is performed routinely to divide the constituent hydrocarbons into four groups: saturates, aromatics, resins, and asphaltenes. Most of the saturate fraction (14-28 mass %) of Alberta bitumens is composed of alkylcycloalkanes, involving one- to six-ring structures. The n-alkanes and other paraffinic hydrocarbons that exist in abundance in conventional crude oils are almost totally nonexistent in bitumens. The aromatic fraction (13-30 0 1991 American Chemical Society
Ind. Eng. Chem. Res., Vol. 30, No. 2, 1991 421 mass %) consists of roughly equal proportions of monoaromatic and di- or multiringed aromatic compounds. The resin fraction (40-48 mass % ), the most abundant of the four groups, is a highly complex mixture of heterocycles and carboxylic acids. The asphaltene fraction (16-25 mass 90)can have a number-average molar mass of 3600 g/mol, with individual molecules exceeding 17 000 g/mol. A typical asphaltene molecular structure in bitumens involves an aromatic core surrounded by n-alkyl branched and/or unbranched chains (Strausz, 1989). In this paper, a different approach is presented for correlation and prediction of the viscosity of pure heavy hydrocarbons. A two-parameter equation, proposed originally by Walther (19311, is used as the starting point in modeling the effect of temperature on the viscosity of pure heavy hydrocarbons listed in API Research Project 42 (API, 1966). An excellent representation of the viscosity of all heavy hydrocarbons is accomplished with a modified Walther Correlation. Next, an interdependence of the two parameters for all hydrocarbons is recognized and used to derive a generalized one-parameter viscosity-temperature relationship. The single parameter in the generalized viscosity equation is shown to be related directly to the molar mass and boiling temperature of pure heavy hydrocarbons.
Database This study examines the variation of viscosity with temperature for 273 pure heavy hydrocarbons, all of which have a molar mass exceeding 100 g/mol. Many of these compounds have chemical structures that are similar to the type of compounds found in bitumens and heavy oils. These pure compounds, each of which is designated by a PSU number or code in API (1966), are classified into the following six groups: (a) n-paraffins and 1-olefins, (b) branched paraffins and olefins, (c) fused ring aromatics, (d) nonfused aromatics, (e) fused-ring naphthenes, and (0 nonfused naphthenes. Table I identifies all of the heavy hydrocarbon compounds included in the database by their PSU number (the name and molar mass are given in supplementary material). In API (1966), three to five viscosity measurements are provided for most compounds over a typical temperature range of 0-98.9 O C . For solids and very heavy hydrocarbons, such as PSU 205 (n-tetratetracontane) in Table Ia, viscosity data are given in API (1966) at higher temperatures (up to 135 “C). For approximately 20 compounds, however, viscosity data were not available, and in some cases they were found to be inconsistent (possible typographical errors). The compounds, for which only two viscosity measurements were reported, were also excluded from the database. API (1966) lists several other useful properties including molar mass and the boiling temperature under vacuum (typically 1-10 mmHg) for most heavy hydrocarbons. Of the 25 straight-chain n-paraffin and 1-olefin compounds (ranging from CllHZ2to Cg4Hlw),only 3 could not be included in the database due to the aforementioned reasons. The branched paraffin and olefin compounds in API (1966) range from CloHzzto C50H102.The nonfused aromatic compounds consist of one or more benzene rings interconnected by alkyl chains. The fused ring aromatics, on the other hand, have benzene-ringed structures sharing common carbon bonds. The naphthenic compounds involve cyclic (saturated cyclohexane) structures as opposed to benzene rings in the aromatic family of compounds. Otherwise, they have chemical structures that are similar in certain ways to the aromatic compounds. The compounds with dual functionality were listed in API (1966)
under both the aromatic and naphthenic categories, and such compounds have been highlighted in Table I, c and d.
Viscosity-Temperature Relationships Svrcek and Mehrotra (1988) evaluated several viscosity correlations and showed the following two-parameter Walther (1931) correlation to give the best overall results for bitumens: log log ( p + 0.7) = bl + bz log T (1) where p is the dynamic viscosity in mPa-s at temperature T i n K. Parameters bl and b2 are two empirical constants that are evaluated from viscosity measurements. It is noted that the ASTM viscosity-temperature chart D341 (ASTM, 1981) is also based on a similar correlation for the kinematic viscosity of heavy crude oils. In an anti-logarithmic form, eq 1 is log ( p + 0.7) = 10blTb2 (2) Equation 1has been tested extensively for the viscosity of bitumens, bitumen fractions, and reconstituted binary mixtures of bitumen fractions (Eastick and Mehrotra, 1990; Mehrotra, 1990; Mehrotra et al., 1989). For all of the above-noted viscous liquids and liquid mixtures, eq 1 was demonstrated to correlate viscosity-temperature data over a wide range of temperatures (10-200 O C ) and viscosities from 1 to 1 x IO6 mPa.s. Mehrotra (1990) extended the applicability of eq 1 to the viscosity of toluene-diluted bitumen and bitumen fractions. A minor variation of eq 1, replacing constant 0.7 with 0.8, enabled correlation of the low viscosity (> 1 mPa-s. The modified two-parameter viscosity correlation is log log ( p + 0.8) = bl + bz log T (3) Another well-known viscosity-temperature correlation, the three-parameter Antoine equation, was used in API (1966) to correlate the data for most heavy hydrocarbons. The Antoine correlation is log p = B / ( T - C ) - A (4) where p is in mPa-s and T in K. The values of the three parameters A , B, and C for most heavy hydrocarbons were provided in API (1966).
Discussion of Results Correlation of Viscosity-Temperature Data for Each Compound. (1) Results with Equation 1. The viscosity-temperature data for each compound were regressed individually by using eq 1, with the results summarized in Table I. The average absolute deviations (AADs) in Table I are very satisfactory as they are generally below 4-590. In Table 11, the overall AAD for the six families of hydrocarbons ranges from 1.2% for fusedring aromatics to 1.9% for n-paraffins and 1-olefins. Note that the dual functionality aromatic-naphthenic compounds have been included in both categories, Table 11, as was done in API (1966). A cross-plot of the two parameters, bl and bz in eq 1,for all database compounds is presented as Figure 1. Also shown in Figure 1 are the parameter values for several bitumens (Svrcek and Mehrotra, 1988) and the five fractions or “cuts” of Cold Lake bitumen (Mehrotra et al., 1989). The points denoting the bitumens are confined to a small region of the graph. In spite of some scatter, the points for bitumen fractions and the pure compounds
422 Ind. Eng. Chem. Res., Vol. 30, No. 2, 1991 Table I. Results for Heavy Hydrocarbons generalized one-parameter
empirical two-parameter PSU
eq 1 AAD,"%
565 528 566 529 530 531 589 532 533 534 590
6.4 4.3 4.7 3.4 3.9 2.0 3.2
549 550 581 546 547 512 555 556 582 545 583 557 500 642 510 643 511 588 591 554 163 584 26 25
3.4 3.1 1.7
1
2 3 524 560 516 521' 522' 517' 538 513 571 631 633 235 50 1 503 506 502 119 89 126' 18 128
130' 87 10 206 567 568 606 646 652 625' 592' 576' 616
1.8
2.6 1.8 1.6
1.1 1.1
3.3 2.7 2.7 2.3 2.7 1.3 1.7 2.5 1.6 0.5 1.4 1.8 1.2 2.1 2.6 2.6 0.2 1.5 2.2 2.1 1.2 2.0 0.6
1.6 0.6 0.6 1.4 0.3 2.3 2.1 1.6 0.4 15.5 0.6 1.3 0.2 1.5 2.5 3.9 4.7 0.9 0.3 0.5 0.8 1.6 2.8 0.4 1.2 0.9 1.1
3.2 0.3 0.9 1.1 0.0
0.1
b,
eq 3 b2 AAD," %
11.269 10.775 10.798 10.516 10.528 10.491 10.237 10.285 10.110 10.140 10.073
-4.800 -4.548 -4.573 -4.413 -4.433 -4.375 -4.285 -4.269 -4.213 -4.191 -4.175
2.4 1.6 1.8
12.007 11.426 11.368 12.299 11.617 10.788 10.186 9.940 10.152 11.453 9.984 11.573 10.984 10.898 10.609 10.715 10.729 9.621 9.896 11.753 10.431 9.359 9.992 10.137 9.940 10.030 9.874
-5.179 -4.944 -4.830 -5.152 -4.892 -4.504 -4.223 -4.084 -4.197 -4.732 -4.093 -4.747 -4.486 -4.447 -4.326 -4.358 -4.371 -3.907 -4.023 -4.760 -4.221 -3.770 -4.040 -4.087 -3.997 -4.031 -3.966
9.601 11.779 10.139 10.047 9.435 10.917 10.008 10.725 9.823 12.489 11.342 11.375 11.914 11.500 10.989 11.375 10.956 11.564 10.586 10.464 10.061 10.538 10.126 10.494 9.721
-3.980 -4.789 -4.166 -4.126 -3.902 -4.446 -4.169 -4.457 -4.054 -4.924 -4.447 -4.620 -4.782 -4.624 -4.470 -4.612 -4.348 -4.575 -4.202 -4.182 -3.994 -4.160 -4.073 -4.191 -3.837
0.1 3.3 2.0 1.6 0.8 1.4 0.6 0.2 0.2 0.5 16.0
10.270 10.229 11.055 12.091 11.697 10.980 10.282 11.836 11.529
-4.247 -4.262 -4.540 -4.868 -4.764 -4.412 -4.218 -4.675 -4.528
0.5 0.2
1.2
1.5 0.7 1.2 0.6 0.9 0.8 0.6 1.2 1.1 2.2
1.2 1.5 1.1 1.1
1.3 0.7 0.5 0.5 0.3 0.9 0.2 0.4 0.1 0.4 0.5 1.0 1.2 1.4 0.2 0.5 1.1 1.1
0.6 1.1
1.1
2.7 0.7 0.2 0.9 4.8 5.5 1.7 0.7 0.4 0.2 0.6 1.9 0.2
1.2
4.7 3.8 1.7 0.4 0.1 0.2
empirical two-parameter
T b
-5.472 -5.178 -5.279 -5.041 -5.118 -4.884 -4.962 -4.768 -4.853 -4.664 -4.719
eq 1 AAD,"% PSU AAD,'% (a) n-Paraffins and 1-Olefins 6.8 535 0.8 7.2 536 1.6 7.6 537 0.7 7.5 609 1.0 7.8 540 0.7 5.0 619 1.8 8.4 176 0.1 5.2 197 0.1 8.3 220 0.1 5.3 190 0.1 5.8 205 0.1
(c) Nonfused 5.3 8.0 5.7 6.0 11.0 1.6 8.6 4.8 8.4 5.7 21.3 5.1 15.6 8.0 1.8 5.5 15.7 0.9 10.6 5.1 4.2 12.9 1.2 5.5 1.0
-4.700 -4.824 -4.550 -4.149 -4.420 -4.104 -4.531 -3.804 -3.727
(d) Fused-Ring 6.2 3.9 3.8 15.7 6.9 5.3 4.8 3.2 4.5
eq 3 b2 AAD,'%
10.085 9.944 9.959 9.840 9.735 9.853 8.989 8.704 8.957 8.496 8.575
-4.150 -4.104 -4.083 -4.021 -3.966 -3.976 -3.593 -3.455 -3.537 -3.352 -3.350
0.2 0.6 0.2 0.5 0.2 1.3 0.1 0.1 0.0 0.0 0.2
-4.558 -4.622 -4.477 -4.404 -4.338 -4.151 -3.949 -3.823 -3.736 -3.725 -3.564
3.4 5.9 3.4 3.6 3.6 2.3 1.9 1.3 1.1 1.4 1.5
9.851 10.793 10.397 10.001 9.997 10.071 10.789 10.314 9.185 10.233 10.928 9.764 9.874 11.348 9.639 10.080 9.681 9.402 9.437 9.296 9.307 9.451 9.191 8.948 10.539 8.390 8.769
-3.953 -4.330 -4.170 -4.023 -4.017 -4.049 -4.325 -4.138 -3.685 -4.085 -4.354 -3.908 -3.959 -4.506 -3.852 -4.007 -3.865 -3.749 -3.759 -3.696 -3.695 -3.735 -3.646 -3.540 -4.106 -3.282 -3.430
0.4 2.1 0.6 1.0 0.4 0.9 0.4 1.1 0.1 2.5 0.2 0.5 0.4 0.3 0.5 0.9 1.7 1.7 0.9 0.5 0.3 3.7 0.5 0.5 2.5 0.3 0.7
-4.061 -4.059 -4.053 -4.114 -4.900 -4.120 -4.053 -4.062 -4.036 -3.957 -3.910 -4.012 -4.046 -3.826 -3.981 -3.872 -3.961 -3.944 -3.916 -3.883 -3.853 -3.771 -3.843 -3.800 -3.445 -3.610 -3.604
2.0 5.8 2.6 2.3 1.1 1.6 4.5 1.6 4.4 2.9 10.9 2.1 1.4 17.7 2.5 3.8 2.7 5.8 3.3 3.8 2.3 3.9 4.0 5.3 24.6 6.2 3.4
1.2 2.0 0.2 0.5 0.2 0.5 0.9 1.2 0.9 1.6 0.4 3.3 0.1 0.9 0.9 0.5 2.6 0.8 1.7 2.3 1.7 0.7 0.3 0.3
10.259 10.658 9.302 9.609 9.927 10.142 10.166 10.220 9.822 9.312 9.120 10.311 10.212 10.058 10.079 9.859 10.611 10.830 9.886 10.097 10.406 9.663 9.358 8.963
-4.076 -4.222 -3.721 -3.840 -3.965 -4.048 -4.061 -4.084 -3.918 -3.733 -3.652 -4.112 -4.058 -4.025 -4.022 -3.911 -4.195 -4.272 -3.955 -4.015 -4.123 -3.834 -3.691 -3.519
0.9 1.4 0.1 0.2 0.1 0.1 0.3 0.6 0.7 0.8 0.1 2.4 0.6 0.8 0.3 0.5 3.2 1.3 0.8 1.5 0.4 0.2 0.7
-3.864 -3.790 -3.985 -3.977 -3.969 -3.961 -3.972 -3.983 -3.943 -4.045 -3.999 3.935 -3.872 -4.010 -3.952 -3.844 -3.749 -3.710 -4.003 -3.881 -3.811 -3.840 -3.736 -3.657
Aromatics 617* 0.8 645' 1.2 599 2.5 595' 0.7 597' 0.9 600' 2.8 601* 1.6 602' 1.0 604* 2.6
12.342 10.257 11.477 9.998 9.786 12.086 11.724 10.250 10.722
-4.854 -4.113 -4.609 -4.053 -3.957 -4.849 -4.701 -4.144 -4.313
1.5 2.1 1.2 0.4 0.2 1.4 0.8 0.6 1.5
-3.746 -4.048 -4.083 -4.268 -4.216 -4.062 -4.051 -4.220 -4.119
(b) Branched Paraffins and Olefins -5.917 4.1 4 1.0 -5.910 5.2 22 3.2 -5.422 6.2 23 1.6 -5.162 1.2 27 1.9 -5.230 4.1 51 1.o -4.951 5.6 53 1.9 -4.750 7.5 55 1.1 -4.548 67 2.1 7.8 -4.687 7.2 109 0.4 -4.756 0.7 210 3.4 -4.488 5.0 183 1.7 -4.586 2.3 5 1.0 -4.465 63 1.0 0.8 -4.438 184 1.2 0.2 -4.410 1.0 6 1.1 0.1 223 1.4 -4.358 -4.398 0.6 8 1.1 -4.283 5.5 7 2.4 -4.324 6.1 191 1.4 -4.347 1.1 107 0.9 -4.245 164 1.3 1.5 -4.112 4.0 211 4.3 -4.218 3.8 133 0.9 -4.163 2.1 134 0.5 -4.105 2.8 182 2.9 -4.092 1.1 58 0.5 -4.081 59 3.0 0.8 -4.663 -4.381 -4.556 -4.540 -4.651 -4.397 -4.836 -4.837 -4.629 -3.835 -3.654 -4.348 -4.076 -4.128 -4.371 -4.304 -3.820 -3.702 -3.831 -3.982 -3.845 -3.720 -4.116 -3.966 -3.752
bl
generalized one-parameter eq 8 b AAD," %
Aromatics 13 116 101 79 103 80 81 82 158 208 152 161 12 52 9 156 170 171 54 167 168 68 135 137
1.2
4.4 12.1
3.5 1.8 0.1 1.2 1.5 1.7 0.8 7.6 4.5 4.3 4.0 0.9 1.3 0.9 13.6 13.0 1.4 3.3 6.3 0.4 0.5 1.6
14.2 2.5 11.1
4.0 5.1 16.7 14.2 1.5 3.9
Ind. Eng. Chem. Res., Vol. 30, No. 2, 1991 423 Table I (Continued)
638 627 613 610 62@ 63gh 593b 614b 611b 559 64@ 236 174 *16b 120b 188
0.6 0.1 2.2 2.6 0.7 0.6 0.7 3.8 2.4 0.4 1.5 0.4 4.4 0.2 0.6 0.4
11.062 11.214 11.084 10.773 11.036 11.010 9.928 10.838 11.488 10.474 10.434 10.839 11.346 9.468 9.443 9.688
generalized empirical two-parameter one-parameter eq 3 eq 8 eq 1 eq 3 b, AAD,"% b AAD."% PSU AAD." % b, b, AAD," 70 (d) Fused-Ring Aromatics -4.412 0.7 -3.928 12.0 224 0.2 11.587 -4.477 0.1 -4.474 0.4 -3.969 6.5 226 0.5 11.334 -4.400 1.0 -4.432 1.1 -3.989 10.2 179 2.8 12.068 -4.653 3.0 -4.314 -4.018 6.7 230* 0.3 10.380 -4.055 1.6 0.2 -4.412 -3.995 7.4 146 0.4 0.2 0.3 9.926 -3.908 -4.387 -3.935 9.5 142b 1.3 0.6 0.1 10.209 -4.010 -3.989 0.2 -4.091 2.2 218b 0.3 0.4 11.303 -4.391 -3.946 9.1 165b 0.7 -4.325 2.8 0.5 11.884 -4.605 -4.034 6.9 232* 0.1 -4.612 1.4 11.542 -4.444 0.0 -4.001 -4.189 0.2 3.4 18gb 0.1 9.723 -3.827 0.1 -4.113 -3.705 9.4 144b 1.1 0.8 9.465 -3.709 0.7 -3.751 -4.274 0.5 10.888 -4.218 0.5 11.0 131 0.4 -4.508 -3.883 12.185 -4.677 4.0 9.9 121 0.4 0.3 -3.930 0.4 -3.775 9.927 -3.913 2.9 2.2 61 3.5 0.4 -3.773 -3.956 9.922 -3.900 4.0 2.2 173 4.6 0.1 -3.848 -3.862 0.3
551 608 580 525 520 518 523 539 514 573 548 564 572 634 632 505 542 504 552 553 509 111 19 110 88 128 112 115 113
3.4 0.3 1.6 1.4 1.5 1.1 0.9 2.1 2.2 2.3 1.8 0.2 1.9 4.6 0.5 0.4 2.2 2.5 2.0 2.0 2.7 2.3 3.4 4.1 2.8 0.5 1.9 4.2 2.0
8.817 9.875 -9.005 10.333 10.322 10.319 9.613 10.115 10.403 9.670 8.414 10.308 9.885 12.367 12.219 12.071 10.884 11.282 9.818 10.588 10.556 9.878 10.512 9.999 10.209 10.061 9.559 10.827 9.922
-3.760 -4.069 -3.774 -4.225 -4.195 -4.188 -3.944 -4.179 -4.292 -3.998 -3.472 -4.171 -4.049 -4.871 -4.816 -4.805 -4.424 -4.558 -3.913 -4.200 -4.233 -3.939 -4.152 -4.011 -4.079 -3.994 -3.793 -4.227 -3.927
1.7 0.0 1.0 0.3 0.4 0.2 0.7 0.6 0.5 0.9 0.8 1.0 0.6 5.2 0.2 0.4 0.7 1.0 1.2 1.2 1.6 1.6 2.7 1.7 1.9 0.4 1.2 3.7 1.4
-5.183 -4.600 -4.874 -4.460 -4.327 -4.305 -4.498 -4.674 -4.660 -4.657 -4.546 -4.242 -4.480 -3.647 -3.765 -3.899 -4.353 -4.221 -3.928 -3.817 -4.053 -3.936 -3.730 -4.058 -3.975 -3.845 -3.848 -3.472 -3.789
569 570 620 622 623 561 626 607 647 578 577 618 654 575 598 596 603 605 629 640 594 615 612 544 562 563
3.3 3.4 2.6 2.8 2.1 1.9 0.7 1.7 1.0 0.5 1.1 1.4 0.4 9.6 0.7 1.6 2.0 2.2 0.7 1.0 1.7 2.6 2.6 10.0 6.1 9.3
9.621 9.544 9.082 9.236 9.355 9.011 9.312 10.329 10.030 9.837 9.829 10.323 10.099 11.590 9.490 9.719 10.379 11.277 10.731 10.527 9.753 11.501 10.897 9.940 12.766 14.718
-3.985 -4.004 -3.812 -3.835 -3.849 -3.678 -3.788 -4.227 -4.079 -3.928 -3.941 -4.122 -4.040 -4.583 -3.825 -3.914 -4.183 -4.536 -4.299 -4.221 -3.911 -4.591 -4.359 -3.978 -4.955 -5.696
1.8 1.7 1.1 1.5 0.9 0.9 0.8 0.5 0.3 1.0 1.8 2.2 0.8 10.4 0.8 0.6 0.9 0.9 0.1 0.2 0.9 1.4 1.5 0.4 6.4 9.5
-4.693 -4.945 -4.910 -4.716 -4.542 -4.376 -4.323 -4.479 -4.336 -3.963 -4.048 -3.959 -4.003 -3.725 -4.151 -4.135 -4.155 -4.123 -4.038 -4.050 -4.049 -3.946 -3.996 -4.010 -3.995 -3.175
empirical two-parameter
~
PSU
eq 1 AAD," %
b,
(e) Nonfused Naphthenes 15.1 129 2.7 3.7 127 3.5 13.9 207 0.2 3.9 15 0.7 1.6 202 0.7 2.2 11 0.1 9.0 139 3.8 7.2 209 0.7 5.4 153 0.5 9.8 162 2.9 17.2 64 1.9 1.3 102 0.7 7.2 75 0.3 29.7 104 0.6 13.3 76 2.1 17.1 77 2.6 1.1 78 2.7 6.4 159 0.6 1.3 199 2.3 10.3 74 2.0 4.0 157 0.1 1.5 172 0.9 12.5 65 0.9 2.0 91 2.7 2.5 180 2.2 4.2 169 3.4 2.0 69 2.5 27.4 136 1.1 3.4 138 0.5
generalized one-parameter
T b
AAD.O%
-3.402 -3.437 -3.162 -3.566 -3.716 -3.650 -3.507 -3.325 -3.201 -3.702 -3.624 -3.362 -3.098 -3.707 -3.653
8.3 26.4 56.6 12.3 2.6 6.4 6.2 31.3 34.7 0.9 1.4 20.1 49.5 6.2 7.7
10.296 10.753 10.243 9.177 9.705 10.556 11.220 9.543 9.185 10.336 9.954 9.210 9.449 9.874 9.990 10.057 10.105 9.396 10.123 9.801 9.339 10.814 10.567 9.988 9.997 10.275 9.569 9.297 9.041
-4.054 -4.210 -3.997 -3.659 -3.862 -4.164 -4.418 -3.809 -3.659 -4.118 -3.986 -3.667 -3.767 -3.934 -3.980 -4.008 -4.030 -3.748 -4.000 -3.919 -3.717 -4.213 -4.164 -3.976 -3.993 -4.073 -3.792 -3.664 -3.547
2.1 3.0 0.3 0.3 0.1 0.4 3.0 0.4 0.3 2.0 1.0 0.3 0.2 0.1 1.3 1.8 1.8 0.1 1.7 1.2 0.4 0.7 0.4 2.0 1.4 2.7 1.8 0.7 0.3
-3.672 -3.537 -3.574 -3.937 -3.900 -3.729 -3.641 -3.951 -3.911 -3.918 -4.024 -3.908 -3.934 -3.921 -3.916 -3.926 -3.942 -3.946 -3.749 -3.995 -3.903 -3.477 -3.694 -3.902 -3.974 -3.813 -3.823 -3.724 -3.649
11.7 22.9 2.8 5.4 0.8 7.0 24.0 2.0 3.5 5.0 1.4 4.8 3.1 0.2 1.7 2.0 2.2 3.7 6.8 2.4 3.5 15.7 10.8 1.8 1.3 7.0 2.0 1.6 1.9
11.080 10.358 9.331 9.220 9.514 15.648 11.091 9.774 11.992 10.285 11.604 10.489 10.496 9.468 10.344 9.039 10.263 11.909 9.289 9.771 10.083 10.212 9.945 10.628 11.915 9.985
-4.329 -4.101 -3.712 -3.664 -3.777 -5.968 -4.325 -3.830 -4.654 -4.039 -4.515 -4.113 -4.127 -3.725 -4.068 -3.594 -4.083 -4.589 -3.662 -3.807 -3.980 '4.007 -3.854 -4.139 -4.594 -3.925
0.2 1.0 0.2 0.4 0.3 0.6 0.4
-3.473 -3.782 -3.888 -3.870 -3.856 -2.907 -3.484 -3.602 -3.354 -3.391 -3.353 -3.581 -3.666 -3.680 -3.689 -3.659 -3.889 -3.280 -3.887 -3.542 -3.731 -3.608 -3.729 -3.432 -3.216 -3.654
30.0 9.2 2.5 3.0 1.8 29.8 25.7 7.9 30.5 14.7 44.6 17.9 8.0 5.2 0.9 9.8 4.9 8.1 6.1 2.1 7.2 12.9 1.8 26.4 37.6
(0 Fused-Ring Naphthenes 10.7 11.9 13.5 12.8 11.2 12.9 9.6 4.3 4.6 1.0 2.5 4.8 1.1 26.4 6.5 4.9 0.8 8.5 4.5 3.9 3.6 15.3 8.3 0.9 7.4 67.0
196 237 108 118 175 200 228 231 166 216 225 219 125 143 141 229 178 155 193 145 181 177 132 192 -122 62
0.4
1.5 0.4 0.6 0.8 0.6 0.5 1.6 0.1 1.1 0.8 1.1 0.1 1.0 0.4 5.2 3.0 0.0 1.0 0.6 3.8 4.3 0.4 3.0 0.2 3.7
1.1
0.1 0.7 1.0 0.8 0.2 0.6 0.1 0.6 2.2 0.0 0.6 0.7 3.2 3.8 0.6 2.6 0.3 3.2
" AAD = ( l / N ) ~ N l p e-xpcalJ/perp. p bDual functional compounds listed in API (1966) under both aromatic and naphthenic categories.
8.8
424 Ind. Eng. Chem. Res., Vol. 30, No. 2, 1991 -3
T a b l e 11. Comparison of Average R e s u l t s f r o m E q u a t i o n s 1, 3. a n d 8 overall AAD," % generaltwo-parameter ized correlations method 22 54
ea 1 1.9 1.8
ea 3 0.8 0.9
eq 8 4.7 2.3
49 49 62 78
1.5 1.2 1.8 1.8
1.4 1.1 1.1 1.1
5.5 10.3 7.0 10.6
nb
hvdrocarbon familv n-paraffins, 1-olefins branched paraffins, olefins nonfused aromatics fused-ring aromatics nonfused naphthenes fused-ring naphthenes average
-5
-3
Branched Paraffins and Olefins -6
-4
-5
c\l
n
-3
Non-fused Aromatics
-6
L
a,
-w -4
a,
E
-5
0,
-3
0 -6
a
Overall AAI of compounds.
-3
-4
,
-4
-3
-5
Non-fused Naphthenes
-6
.'Cuts of Cold Lake bitumen Alberta bitumens
-4
OB
-5 Fused ring Naphthenes
L -4
-6
a,
9
-cI
fy
10
11
12
13
Parameter b l 0
-5
0
0
0
Unbranched/Branched "0 Paraffins and Olefins Nan-fused Aromatics Fused ring Aromatics Non-fused Naphthenes Fused ring Naphthenes
7
% @
6oooo
e
A
F i g u r e 2. Cross-correlation between the two parameters, b, and b2, in eq 3 for different families of pure heavy hydrocarbons.
-
+
-6 8
9
10
11
12
13
T a b l e 111. I n t e r d e p e n d e n c e of the T w o P a r a m e t e r s b 2 w i t h E q u a t i o n 5 ( b , = log 8 (log @ ) b 2 ) log 8 log Q hvdrocarbon familv n-paraffins, 1-olefins 2.312 -1.864 branched paraffins, olefins 1.299 -2.155 -2.521 nonfused aromatics -0.113 -1.013 -2.749 fused-ring aromatics -2.740 nonfused naphthenes -0.984 -2.847 fused-ring naphthenes -1.396
14
Parameter b l F i g u r e 1. Relationship between the two parameters of Walther viscosity correlation for pure heavy hydrocarbons and bitumen samples.
suggest linear trends in the parameter values. (2) Results with Equation 3. The above regression calculations were repeated for all compounds with eq 3, which has been shown to be superior for correlating the viscosity of lighter hydrocarbons such as toluene (Mehrotra, 1990). The values of parameters bl and b2 along with the AAD for each compound are given in Table I. The correlation of data for the lower viscosity compounds, which had shown larger errors with eq 1,is much improved with eq 3. The overall AADs obtained with eq 3, given in Table 11, range from 0.8% for n-paraffins and 1-olefins to 1.4% for nonfused aromatics. The results in Tables I and I1 clearly indicate an excellent representation of the viscosity-temperature data with eq 3 for all 273 heavy hydrocarbons. Cross-Correlation between the Two Parameters. Figure 2 shows the relationship between parameters bl and b2 in eq 3 for the last five families of pure hydrocarbons. Also plotted in Figure 2 is the "best-fit" line for each case, with the linear regression results summarized in Table 111. The regression coefficient, lrl, for each family of hydrocarbons in Table I11 is fairly impressive. Overall, these results indicate the possibility of a cross-correlation between the two parameters in eq 3. It is pointed out that any such trend in the values of the three parameters in the Antoine correlation (eq 4),in API (1966), could not be found. If a cross-correlation between the two parameters in eq 3 does exist, then the regression of viscosity-temperature
bl and Irl
1.00 0.99 0.98 0.98 0.97 0.98
data for each compound individually, as outlined in the previous section, may not be appropriate. That is, the viscosity-temperature regression calculations should be repeated by incorporating a suitable model for the interdependence of parameters bl and b2 in eq 3. Based on the results presented in Figure 2 and Table 111, it is reasonable to assume that parameters bl and bz in eq 3 for each family of pure hydrocarbons are related linearly by the following equation: b, = log 8 + (log @)bz (5) The constants log @ and log 8, obtained from correlating the parameters bl and b2 for all compounds in the six families of heavy hydrocarbons, are provided in Table 111. The following one-parameter viscosity-temperature correlation is obtained next by combining eq 3 with eq 5: log log ( p + 0.8) = [log 8 + b2 log @] + b2 log T (6) Equation 6 in an antilogarithmic form can be expressed as log
(p
+ 0.8) = 8(@7')b2 8 ( @ T ) b E
(7)
where b (=b2)is the only parameter that can be determined for any compound from one viscosity measurement, and 9 and 0 for each family of hydrocarbons are listed in Table 111. Generalized 0 and 8 for All Heavy Hydrocarbons. Next, regression calculations involving the entire viscosity-temperature data for all heavy hydrocarbons in the database were repeated with eq 7. All of the approximately
Ind. Eng. Chem. Res., Vol. 30, No. 2, 1991 425 105 104
L?
2
Equation 8 ....... Andrade, eq 9
103
E
.--wsVI; 102
8
ffl .->
101 100 10-1 -3
-4 -5 Parameter b
-6
0
F i g u r e 3. Sensitivity of calculated viscosities to parameter b in eq
8.
1300 individual viscosity-temperature data for the 273 compounds in Table I, as opposed to correlating parameters bl and b2 in the previous case, were used in these regression calculations. This approach was adopted to obtain a single set of @ and 8 values for all heavy hydrocarbons, instead of one pair for each family of hydrocarbons. It was found that the optimum, corresponding to the minimum in - pexp)/peXp]* for the entire set of data, was actually a fairly broad minimum. The "best" values of the generalized constants, log @ and log 0, were selected as -2.0 and +2.0, respectively. With these numerical values, eq 7 becomes log
(p
+ 0.8) = 100(O.OIT)b
(8)
The optimized values of the single parameter b in eq 8 and the corresponding AADs are given in Table I. Some of the dual aromatic-naphthenic functionality compounds have relatively larger AADs. In Table 11, the overall AADs range from 2-3 70 for branched paraffins and olefins to slightly over 10% for the fused-ring aromatic and naphthenic compounds. The AADs with the above one-parameter generalized approach, eq 8, are larger than those with the two-parameter correlation, eq 3. The AADs for most compounds in Table I, nonetheless, are under lo%, which is well within the accepted precision for viscosity measurements spanning several orders of magnitude. For comparison, the reliability of viscosity data for the less complex hydrocarbons in the TRC Handbook (1986) is believed to be only within 5-1570 (Ely and Hanley, 1981). The magnitude of deviations with eq 8 is indeed very satisfactory in view of the tremendous extent of generalization involving a wide spectrum of heavy hydrocarbons that range from simple n-alkanes to complex aromatic and naphthenic compounds. (1) Sensitivity Analyses. Figure 3 presents calculated viscosities, at three selected temperatures of 0,50, and 100 "C, over the range of parameter b for heavy hydrocarbons in the database. The hydrocarbon viscosities are most sensitive to the value of parameter b at lower temperatures. A t 0 OC, a hypothetical hydrocarbon with b = -3.0 is predicted to have a viscosity of approximately 80 000 mPaOs. At the same temperature, a viscosity of about 0.9 mPa.s is predicted for another hypothetical hydrocarbon with b = -6.0. At 100 "C,the viscosity values for these two hypothetical hydrocarbons are only about 83 and 0.3 mPa.s, respectively. Similarly at 0 O C , a viscosity of 62 mPa.s for another hydrocarbon with b = -4.0 is much lower than about 8OOOO mPa-s for the hydrocarbon with b = -3.0. This is an over 3 orders of magnitude difference in viscosity, and it indicates that the viscosities are fairly sen-
25 50 Temperature,
75
100
OC
F i g u r e 4. Comparison of viscosity-temperature trends for heavy hydrocarbons; the results from eq 8 compared to those from the Andrade correlation.
sitive to the parameter value over the range -3.0 1 b 1 -4.0, particularly a t lower temperatures. (2) Comparison of Equation 8 with the Andrade Correlation. The following Andrade equation is used commonly for correlating liquid viscosities log p = A B / T (9)
+
In Figure 4, predictions for the variation of viscosity with temperature are plotted for several values of parameter b in eq 8. Also plotted as dotted lines are the results obtained from correlating the viscosities with the Andrade correlation, eq 9. For hydrocarbons with low viscosities (i.e., hydrocarbons with b < -5.0), eq 9 gives reasonably satisfactory results. However, eq 9 does not provide an adequate representation of the effect of temperature on the viscosity of more viscous hydrocarbons, particularly with b > -4.0. Most of the compounds in Table I are actually quite viscous with b > -4.5; hence, the Andrade correlation is not suitable for representing the effect of temperature on the viscosity of heavier hydrocarbons. Dependence of P a r a m e t e r b on Hydrocarbon Properties. In this section, the single parameter b is demonstrated to be related to other hydrocarbon properties. The results will be useful in the development of a totally predictive method for the viscosity of heavy hydrocarbons. Of the several choices for hydrocarbon properties, the most desirable possibility would be to seek a relationship for parameter b in terms of the hydrocarbon critical properties. However, critical properties of the types of heavy hydrocarbons in the database are not readily available. For many of the heavy hydrocarbons considered here, it is doubtful if the critical properties could actually be determined without destroying their original chemical structure. Of the properties reported for the heavy hydrocarbons in API (1966), the two selected as suitable candidates in this study are the molar mass (M) and the boiling temperature at 10 mmHg, denoted here by Tb'O. (1) Dependence of Parameter b on Molar Mass ( M ) . Figure 5 presents the variation of parameter b with molar mass M for all heavy hydrocarbons. Also plotted for comparison are similar values of parameter b2 in eq 3, which are more widely scattered. In spite of the scatter in Figure 5 , the value of parameter b is noted to increase with an increase in molar mass. That is, the compounds with a larger molar mass are found to have a higher, less negative value of parameter b. A higher value of parameter b implies a more viscous hydrocarbon with a more prominent effect of temperature on its viscosity, as was shown in Figures 3 and 4.
426 Ind. Eng. Chem. Res., Vol. 30, No. 2, 1991
-3
Table IV. Dependence of Single Parameter b on Molar Mass ( M ) with Equation 10 ( b = Bmo B m , log M ) hvdrocarbon familv Bmn Bm, IrI
1
+
n-paraffins, l-olefins branched paraffins, olefins nonfused aromatics fused-ring aromatics nonfused naphthenes fused-ring naphthenes
-12.067 -10.976 -9.692 -9.309 -9.001 -9.513
3.110 2.668 2.261 2.185 2.350 2.248
0.98 0.96 0.87 0.82 0.90 0.87
-3 B
o
0
0
a
0
Equation 3 Equation 8
-4
-5
-6 I
100
200
400
Branched Paraffins and Olefiis
800
Molar Mass, g/mol
-4
Figure 5. Variation of parameter b in eq 8 and b2 in eq 3 with molar mass for all pure heavy hydrocarbons.
0 7
a L
-3, -4
-3
-6
-5
Non-fused Aromatics
-3
-6
Q)
4 '
-4
E
-5
u
-6
Y
-5
"
Q)
Branched Paraffins and Olefins
-3
-6
a
Fused ring Aromatics
-3 -4
-4
L
-3
-6
-4
Non-fused Aromatics
-3
Non-fused Naphthenes
-5
-6
-5
8
U
-3
-9
-5
Fused ring Naphthenes 2.0
2.5
I
-4
Non-fused Naphthenes
-3
-cY- I 100
200
300 400
-5
Figure 7. Relationship between parameter b and the inverse of
-6
boiling temperature a t 10 mmHg for five families of pure heavy hydrocarbons.
600 800
Molar Mass (M), g/mol Figure 6. Relationship between parameter b and molar mass for five families of pure heavy hydrocarbons.
Figure 6 shows the variation of parameter b with molar mass for each of the last five families of heavy hydrocarbons in the database. Here, the scatter is considerably reduced and the points appear to fall on straight lines. A few compounds in Table I, particularly in the fused-ring aromatic and naphthenic categories, gave unusually high AADs with eq 8. In obtaining a correlation between b and M , the few hydrocarbons with AAD > 20% were ignored. The b and M values for the remaining hydrocarbons were regressed with the following relationship: b = Bm, + Bm, log M (10) The results of regression calculations are summarized in Table IV and plotted as straight lines in Figure 6. For the unbranchedlbranched paraffins and olefins, the correlation coefficient Irl is close to 1.0, which is very satisfactory. For the other four families of hydrocarbons, the correlation coefficient varies between 0.82 and 0.90. However, this should be expected because the database includes several isomers with significantly different viscosities. The results in Table IV, nevertheless, clearly
suggest parameter b to depend on the molar mass of heavy hydrocarbons. (2) Parameter b and Boiling Temperature ( T b " ) . As mentioned previously, boiling temperatures for most heavy hydrocarbons at pressures typically ranging from 1 to 10 mmHg are listed in API (1966). The use of boiling point as a characterization parameter for hydrocarbons is common and appropriate. Boiling point is a property that is energy-related and varies fairly uniformly for compounds with a hydrocarbon family, particularly the paraffins. For example, the numerous commonly used critical properties correlations are expressed in terms of the boiling point. Figure 7 presents the variation of parameter b as a function of the inverse of boiling point TblO.Not shown in Figure 7 are similar, and considerably better, results for the case of n-paraffins and l-olefins, for which the trend was most impressive. Despite some scatter in Figure 7 , parameter b shows a definite linear trend for every family of pure hydrocarbons. Also shown are the best-fit lines for each group of hydrocarbons, which were obtained by fitting the results to the following equation: b = Bto + Bt1/Tblo (11) The values of Bt,, Bt,, and Irl for the six families of hydrocarbons are provided in Table V. The correlation coefficients for the two paraffinic and olefinic families of hydrocarbons are remarkable with Irl 1.0. For the remaining four families of aromatic and naphthenic hydrocarbons, the Irl values are better than those obtained with
Ind. Eng. Chem. Res., Vol. 30, No. 2, 1991 427 Table V. Dependence of Single Parameter b on Boiling Temperature (Tb") with Equation 11 ( b = B t , BtI/Tb") hvdrocarbon familv Btn Bti Irl
+
n-paraffins, 1-olefins branched paraffins, olefins nonfused aromatics fused-ring aromatics nonfused naphthenes fused-ring naphthenes
-1.391 -1.559 -1.656 -1.722 -1.683 -1.994
-1.381 -1.298 -1.187 -1.099 -1.155 -0.947
0.99 0.99 0.94 0.86 0.90 0.83
eq 10 and given in Table IV. The results in Tables IV and V clearly indicate that eq 10 or eq 11 can be used to predict the viscosity parameter b for branched and unbranched paraffins and olefins from their molar mass or boiling temperature. For most aromatic and naphthenic heavy hydrocarbons, on the other hand, parameter b can be estimated from eq 10 or eq 11 for obtaining viscosity predictions that would be well within an order of magnitude of experimental viscosities. It is noted that the available viscosity calculation methods give unsatisfactory predictions for these heavy aromatic and naphthenic hydrocarbons.
Conclusions The effect of temperature on the viscosity of 273 heavy hydrocarbons listed in API Research Report 42 was correlated very well with eq 3, the two-parameter equation (overall AAD C 1-2%). A linear relationship between the two parameters, b, and b,, was identified and used to derive eq 8, the one-parameter generalized viscosity equation that is valid for all compounds in the six families of heavy hydrocarbons considered in this study. The viscosity predictions from eq 8 were shown to be well within 10% of the data for most compounds. Also, the predicted trends for the effect of temperature on the viscosity of heavy hydrocarbons were superior to those from the Andrade correlation. Parameter b in the above equation was expressed in terms of the hydrocarbon molar mass and boiling temperature, resulting in a predictive procedure for the viscosity of paraffinic, olefinic, aromatic, and naphthenic heavy hydrocarbons. Acknowledgment
I thank Mr. K. Ham and Mr. R. Rundle for their assistance. Financial support was provided by the Natural Sciences and Engineering Research Council of Canada (NSERC). Nomenclature AAD = average absolute deviation, % A , B , C = empirical constants in eqs 4 and 9 Bm,, Bm, = regression constants in eq 10 Bt,, Btl = regression constants in eq 11 bl, b2 = empirical constants in eqs 1-3 b = single parameter in eqs 7 and 8 M = molar mass, g/mol n = number of compounds N = number of viscosity data points Irl = correlation coefficient T = absolute temperature, K T blo = boiling temperature at 10 mmHg, K
Greek Symbols
dynamic viscosity, mPa.s CP = generalized viscosity constant for heavy hydrocarbons e = generalized viscosity constant for heavy hydrocarbons
1=
Subscripts
cal = calculated, predicted exp = experimental Abbreviations
API = American Petroleum Institute ASTM = American Society for Testing and Material PSU = heavy hydrocarbon code in API Research Report 42 TRC = Thermodynamic Research Center
Supplementary Material Available: The name and molar mass of all pure heavy hydrocarbons included in the database and listed in Table I (6 pages). Ordering information is given on any current masthead page. Literature Cited API. Properties of Hydrocarbons of High Molecular Weights; API Research Project 42; American Petroleum Institute: Washington, DC, 1966. ASTM. Annual Book of ASTM Standards; American Society for Testing and Material: Philadelphia, PA, 1981; P a r t 23, p 205. Eastick, R. R.; Mehrotra, A. K. Viscosity Data and Correlation for Mixtures of Bitumen Fractions. Fuel Process. Technol. 1990,26, 25. Ely, J. F.; Hanley, H. J. M. A Computer Program for the Prediction of Viscosity and Thermal Conductivity in Hydrocarbon Mix-
tures; NBS Technical Note 1039; National Bureau of Standards: Washington, DC, 1981. Johnson, S. E.; Svrcek, W. Y.; Mehrotra, A. K. Viscosity Prediction of Athabasca Bitumen Using the Extended Principle of Corresponding States. Ind. Eng. Chem. Res. 1987,26, 2290. Mehrotra, A. K. Development of Mixing Rules for Predicting the Viscosity of Bitumen and Its Fractions Blended with Toluene. Can. J . Chem. Eng. 1990,68,839. Mehrotra, A. K.; Svrcek, W. Y. Corresponding States Method for Calculating Bitumen Viscosity. J. Can. Pet. Technol. 1987,26 (61, 60. Mehrotra, A. K.; Eastick, R. R.; Svrcek, W. Y. Viscosity of Cold Lake Bitumen and Its Fractions. Can. J . Chem. Eng. 1989, 67, 1004. Pedersen, K. S.; Fredensland, A,; Christensen, P. L.; Thomassen, P. Viscosity of Crude Oils. Chem. Eng. Sci. 1984, 39, 1011. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1986, Chapter 9. Strausz, 0. P. Bitumen and Heavy Oil Chemistry. In AOSTRA
Technical Handbook on Oil Sands, Bitumens and Heavy Oils; Hepler, L. G., Hsi, C., Eds.; Alberta Oil Sands Technology and Research Authority: Edmonton, Canada, 1989; Chapter 3. Svrcek, W. Y.; Mehrotra, A. K. One Parameter Correlation for Bitumen Viscosity. Chem. Eng. Res. Des. 1988, 66, 323. Teja, A. S.; Rice, P. Generalized Corresponding States Method for the Viscosities of Liquid Mixtures. Znd. Eng. Chem. Fundam. 1981, 20, 77. TRC. TRC Thermodynamic Tables-Hydrocarbons. Thermodynamic Research Center Handbook; Texas A & M University: College Station, 1986; Section C. Twu, C. H. Internally Consistent Correlation for Predicting Liquid Viscosities of Petroleum Fractions. Znd. Eng. Chem. Process Des. Dev. 1985, 24, 1287. Walther, C. The Evaluation of Viscosity Data. Erdol Teer 1931, 7, 382.
Received for review April 20, 1990 Revised manuscript received J u l y 2, 1990 Accepted J u l y 18, 1990
