Ind. Eng. Chem. Res. 1988,27, 519-523
519
Correlations of Viscosity, Gas Solubility, and Density for Saskatchewan Heavy Oils Beverly Quail,' G. A. Hill,*+and Kamal N. Jha* Department of Chemical Engineering, University of Saskatchewan, Saskatoon, Saskatchewan, Canada S7N OWO, and Petroleum Division, Saskatchewan Research Council, Regina, Saskatchewan, Canada S4N 5x1
The complex chemical nature of crude oil has made it extremely difficult to develop reliable models capable of predicting physical properties. Yet the importance of crude oil as a source of energy or as a precursor in chemical synthesis makes it necessary that simple equations be available that engineers can use to accurately predict these properties. Three noncomponent equations are presented which were found t o accurately model the viscosity, density, and gas solubility of a wide range of Saskatchewan heavy oils. These equations were developed from previous work with extended terms to allow for additional independent parameters. The extended equations allow for variations in temperature, pressure, dissolved methane concentration, and dissolved carbon dioxide concentration. Heavy oil represents an important source of future energy supplies. Saskatchewan has a large quantity of this resource, estimated (Jha and Verma, 1982) to be as high as 3.4 X lo9 m3. Recovery of this oil is based on standard techniques (primary and secondary methods) as well as enhanced techniques (tertiary methods). Upon recovery the oil is treated and transported to suitable processing stations. In order to develop reasonable equipment designs and operating procedures for these steps, an engineer needs to have accurate and simple correlating techniques to predict the physical properties of the crude oil. In this work, an investigation of existing correlating techniques for viscosity, density, and gas solubility of crude oil was undertaken. A number of existing models were then applied to a large, experimental data base of Saskatchewan crude oil properties, The models were fit by using a least-squares technique and the residual errors were compared to determine the best-fitting models. In addition, the most successful models were extended to incorporate terms for pressure and/or dissolved gas concentrations of both carbon dioxide and methane. Finally, the best models have been used on data for a non-Saskatchewanheavy oil. The data of Miller and Jones (1981) for a Wilmington heavy oil were extracted from their graphical presentation and fit by the techniques mentioned above.
Background A great deal of effort has been traditionally applied to the development of models to predict the physical properties of various materials. Models range from completely empirical (best fit curves) to completely theoretical (based on a hypothetical, physical explanation and then usually requiring the fitting of coefficient terms). The importance of these correlations is that they allow the prediction of properties for use in engineering calculations for such phenomena as pressure drop in pipes, fluid motion in oil reservoirs, or phase changes in distillation columns. Because crude oil is a complex mixture of hundreds of chemical compounds, however, it is a difficult if not impossible task to find a single model to correlate even one property of every crude oil. For instance, a crude oil composed mostly of aromatics might have quite a different viscosity vs temperature relationship than that of a crude oil composed mostly of saturates. In this regard, fundamental efforts now under way to develop component-related models (see for instance Peng et al. (1987)) show of Saskatchewan. Saskatchewan Research Council.
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great promise for eventually improving the accuracy of predicting crude oil properties when detailed experimental knowledge of component types and concentrations is known. However, even this information is usually not readily available, so an engineer must rely on more generally applicable equations. Quail (1985) assembled a wide range of correlating equations previously reported in the literature. Noncomponent equations were then tested against a large base of experimental, physical property data on Saskatchewan heavy oils. Three correlations were found to be most suitable. For viscosity, an empirical equation presented by Beggs and Robinson (1975) was found to be most accurate. This equation includes a term for specific gravity and is given by the following equation: - 1010'c~1+(~~z~.r))T~2 -1 (1) bd
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For gas solubility, an empirical form suggested by Mehrotra and Svrcek (1982) based on a simple quadratic equation was found to be most suitable: Sol = C 1 + C2P C 3 ( P / T )+ C , ( P / T ) 2 (2)
+
Finally, for density the simple linear equation reported earlier by Rojas (1977) was used: p = C 1 - C2T (3)
Results and Discussion Experimental. The experimental procedures for measuring viscosity, density, and solubility have been previously reported (Jha, 1986). The data base consisted of 59 heavy crude oil samples taken from different producing areas/subareas of Saskatchewan. Of all the sources, the most complete set of data was generated for an area called Senlac and appears in Table I. Data were used for both checking the applicability of different correlations and for extending the best correlations to include other parameters such as pressure and/or concentrations of dissolved gases. Correlations. The program used to fit the models to the data was called ZXSSQ and is marketed by IMSL, Houston. This program uses the Levenberg-Marquardt method of least-squares minimization. The program accuracy was tested against sample data and other more limited curve-fitting software and always reproduced those results exactly. The program was then used to determine the best coefficients in each of the tested models to fit the experimental data base. The best fit curves for each model were then compared based on the absolute average deviation (AAD) which was just the sum of the difference between 0 1988 American Chemical Society
520 Ind. Eng. Chem. Res., Vol. 27, No. 3, 1988 Table I. Physical Properties of Senlac Oil expt
temp, K
pressure, MPa
[CO,] exptl
solubility, mol %, eq 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56
293.1 303.1 313.1 353.1 383.1 413.1 301.1 301.1 301.1 301.1 301.1 301.1 301.1 301.1 301.1 383.1 383.1 301.4 301.4 301.4 301.4 301.4 301.4 301.4 301.4 301.4 301.4 301.4 301.4 301.4 383.1 383.1 383.1 383.1 383.1 383.1 383.1 301.1 301.1 301.1 301.1 301.4 301.4 301.4 301.4 301.4 301.4 301.4 301.4 301.4 301.4 301.4 301.4 301.4 301.4 301.4
0.10 0.10 0.10 0.10 0.10 0.10 0.10 2.07 3.45 4.82 6.88 10.88 3.28 5.52 7.58 4.16 12.24 7.90 7.92 5.95 5.96 3.67 3.68 3.10 12.10 10.00 8.50 7.60 5.80 5.80 4.69 6.21 7.58 11.45 13.96 17.13 12.24 4.48 5.17 6.89 8.27 12.76 8.38 5.38 12.27 8.83 5.93 5.17 7.52 10.48 14.07 6.89 14.89 12.07 9.21 8.27
0 0 0 0 0 0 0 0 0 0 0 0 36.13b 56.74b 60.90b 24.96* 53.76b 36.13 36.13 36.13 36.13 36.13 36.13 36.13 60.90 60.90 60.90 60.90 56.74 56.74 24.96 24.96 24.96 53.76 53.76 53.76 53.76 0 34.78 55.30 59.62 0 0 0 34.78 34.78 34.78 34.78 55.30 55.30 55.30 55.30 59.62 59.62 59.62 59.62
