I n d . Eng. Chem. Res. 1995,34,4140-4144
4140
CORRELATIONS
Prediction of Viscosity of Heavy Petroleum Fractions and Crude Oils Using a Corresponding States Method Hassan M. Moharam and Mohamed A. Fahim* Department of Chemical and Petroleum Engineering, United Arab Emirates University, P.O. Box 17555, Al-Ain, United Arab Emirates
A new corresponding states model for predicting the viscosity of heavy crude oils and petroleum fractions is proposed in this work. The model uses decane and eicosane as reference components for petroleum fractions of average molecular weight higher than 142. The viscosity of a component or fraction may be obtained from the viscosities of these two reference fluids (decane and eicosane) a t the same reduced temperature and reduced pressure using the molecular weight as an interpolation parameter. This model showed better accuracy in predicting the viscosity than the model that uses one reference (methane) or two references (methane and decane), when the molecular weight is higher than 142. The present model, when tested on 187 data points for 29 undefined heavy petroleum fractions from 15 worldwide crudes, yielded an overall deviation of 5.3%. Testing of the model on 53 data points for seven crude oils from offshore Abu Dhabi yielded an average absolute deviation of 5.9%.
Introduction To develop reasonable equipment designs and operating conditions, an engineer needs t o have an accurate and simple correlation t o estimate the physical properties. For this reason, a great deal of effort has been put to the development of estimation models. These models range from completely empirical (best-fit curves) to completely theoretical (based on physical explanation and then usually requiring the fitting of coefficient terms). Viscosity is one of the important properties since fluid flow, heat transfer, and mass transfer calculations depend on accurate viscosity estimates. Petroleum crude oils and fractions are typically complex mixtures, and the physical and chemical properties vary considerably depending on the composition of the constituents. For instance, the viscosity of a crude oil or a fraction composed mostly of aromatics might have quite a different temperature dependence than that composed mostly of saturates. Developing a viscosity estimation correlation accounting for all the composition details is dificult, if not impossible. Useful viscosity prediction methods are most conveniently based on parameters such as boiling temperatures and specific gravities that are commonly used to characterize each fraction. A review of viscosity estimation methods is given by Reid et al. (1987). It presents the most general methods and concludes that none are particularly reliable and that all are empirical. Many of the currently available methods with a more theoretical foundation are based on the corresponding states principle, which states that dimensionless properties of all fluids have the same numerical values at the same reduced conditions. These methods require a knowledge of the properties of, a t least, one reference fluid. Hanley (1976) developed an extended corresponding states method t o calculate transport properties of mixtures. The reference fluid (methane) viscosity was correlated as a function of temperature and density 0888-5885/95I2634-414O$Q9.00/0
(Hanley et al., 1975). For fluids that do not correspond with the reference fluid, Hanley derived a correction factor. The method of Ely and Hanley (1981) has been applied by Baltatu (1982) to estimate the viscosities of petroleum fractions. However, the application is restricted to petroleum fractions with low boiling points. Pedersen et al. (1984) used a new parameter to account for the molecular size and density effects. An improvement of the model was proposed by Pedersen and Fredenslund (1987). The major difficulty in using methane as a reference fluid is that its normal freezing point is at reduced temperature (T,) of 0.476, which is above that of many other hydrocarbons. Also, the difficulty in extrapolating methane viscosities to high reduced densities and the noncorrespondence of methane with several other hydrocarbons at high reduced densities pose additional problems (Monnery et al., 1991). Sherman et al. (1989) have used propane as a reference fluid. An alternative formulation of the corresponding states principle, based on the properties of two reference fluids, has been proposed by Teja and Rice (1981) and Teja et al. (1985). However, all these methods use the acentric factor as an interpolation parameter of reference fluids properties. Petersen et al. (1991) used the molecular weight as an interpolation parameter instead of the acentric factor having observed that, for heavy petroleum fractions, the acentric factor decreases with increasing molecular weight. Other interpolation parameters were proposed by Willman and Teja (1988). The model of Petersen et al. (1991) yields accurate predictions of light petroleum fraction viscosities; however, its application to heavy fractions may give inaccurate predictions. In addition, the prediction by this model is restricted to the condition of reduced temperature, T, > 0.476. The technique of using two reference components offers a substantial advantage over other corresponding states methods in that no density iterations are required in the calculations. Furthermore, the ability t o change reference fluids allows the method to be extended to
0 1995 American Chemical Society
Ind.Eng. Chem. Res., Vol. 34, No. 11, 1995 4141 fluids that are not usually amenable to corresponding states treatments. It is the purpose of the present work t o describe a n extension to the model of Petersen et al. (19911, by using decane and eicosane as the two reference fluids, to obtain more accurate predictions for the heavy fractions and t o relax the restriction on reduced temperature Tr > 0.476 to Tr > 0.4 so that many of the heavy crude oils and fractions will be covered. Methane and decane as reference fluids are still used for light fractions. Eicosane was chosen because most petroleum fractions of practical interest have average molecular weights in the range between the molecular weights of methane and eicosane and because its viscosity data are available in literature.
Table 1. Correlation Constants for Equation 10
v
V,(cm3/mol)
Vr
(2)
=r / ~ c
The following expression is used t o evaluate the critical viscosity (Pedersen et al., 1989) 7, = ~ W 1 1 2 p c 2 / 3 T c - 1 1 6
(3)
where C is a constant and MW is the molecular weight. From eqs 1-3, the following equation may be derived for the determination of viscosity: (4) where
In this work, the reference fluids selected for this model were decane and eicosane for the crude oils and fractions with molecular weights above 142. The interpolation parameter used is the molecular weight, similar to Petersen et al. (1991). Viscosity of the Reference Components. The viscosity of the reference componentsat their saturation pressures can be calculated using the following equation (Orbey and Sandler, 1993): l n ( ~ s L l ~ r= e fk>ln(vR) VR
(6)
where
lo9
1 + D(APJ2.118? I= 1
(9)
+ CUM,
where D = [0.3257/(1.0039 - Tr2.573)o.29061 - 0.2086; h p r = (P - P, ypC;A = 0.9991 - [ 4.674 10-41 (1.0523Tr-0.0f;877 - 1.0513)]; C = -0.07921 2.16161: - 13.4040Tr2 44.1706Tr3 - 84.8291Tr4 96.1209Tr5 - 59.8127Tr6 15.6719Tr7;u is the acentric factor; and P, is the vapor pressure that can be calculated using the Antoine equation. Characterization of Undefined Petroleum Fractions. Since petroleum fractions consist of a variety of components, and very few compositional data exist for such fractions, they are best treated as a single pseudocomponent. Boiling temperature and specific gravity can then be used to characterize each fraction. In the present work, the Riazi-Daubert correlation (1980) was used for the determination of the characterization parameters T,, P,, and Mw. The correlation can be expressed as
+ +
+
Q,
=
AT;^
+
(10)
where Q, is any physical property, Tb is the boiling point in Rankine, y is the specific gravity, and A, B , and C are correlation constants and are shown in Table 1. Other characterization methods are available from Ahmed (1989). Characterization of Crude Oils. Application of the proposed model to crude oils requires mixing rules. In the case of the partially defined crude oils, the composition of the crude is known until C7+,which can be characterized using the Riazi-Daubert correlation. For the critical temperature of a mixture, The rule of Li (Reid et al., 1987) can be used. The rule has the following form:
where zi are mole fractions of component i. The critical pressure of a mixture, P,,,, can be calculated using the Mo and Gubbins (Petersen et al., 1991) relation:
and k were
+ 1.4010(TdT) + 0.2406(TdT>2 (7) lz = 0.143 + 0.0046316 = 0 . 0 0 0 0 0 4 0 5 T ~ (8)
VR
C -1.0164 0.3596 2.3201 -1.683
eicosane) = 0.226 mPa-S. The methods of Mehrotra (1991) and Allan and Teja (1991) can also be used. Lucas has suggested a correlation to calculate the effect of high pressure on the liquid viscosity (Reid et al., 1987). The equation has the following form:
VSL
where 8 is the interpolation parameter and subscripts r and c indicate reduced and critical properties, respectively. The reduced viscosity vr is determined from
where
1.6607 x 19.0623 5.53029 x 1.7842 x
T,(K) P, (MPa)
The Model The corresponding states model based on two reference (methane-decane) components (Teja and Rice, 1981; Teja et al., 1985) is given by
B 2.1962 0.58848 -2.3125 2.3829
A
MW
= 1.6866
Vref
(for decane) = 0.228 mPa.S and
Vref
(for
P
cm
=
(12)
4142 Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 Table 2. Comparison of the Results of the Present Model with Previous Models for Petroleum Fractions with MW at T, > 0.476
142
av absolute deviation (8) no. of fractns
crude oil
no. of data pts
3 3 3 2
Arab Berri Arab Heavy Arab Medium Boscan California Iranian Export Light Valley Minas (Sumatra) Oklahoma Pennsylvania Safania (Saudi Arabia) Stabilized Arabian Waxy Wyoming (U.S.)
31 30 30 2 3 5 2 4 4 3 2 2
1
2 2 3 2 2 1 1 1
Overall
range of range of mid-bp ("C) temp ("C)
2
1 5
28
126
range of kinematic Pedersen model viscos x lo6 (mz/s)
range of MW
Petersen model
present model
232-399 232-399 232-399 247-290 188 178-223 213-253 211-310 188-238 188-238 201 196 217 188-238
60-200 60-200 60-200 99 40-100 38-99 54-99 54-299 40-100 40-100 54-99 54-99 54 40-100
179-304 178-299 178-299 177-206 144 145-173 158-181 167-238 148-178 153-185 160 156 164 148-180
0.4278-2.1597 0.4413-2.0427 0.4350-1.9917 1.0200-1.5100 0.6480-1.1800 0.5300-1.1700 1.1100-1.2000 0.6680-1.4100 0.6110-1.0900 0.6180-1.4000 0.6480-1.0200 0.6150-0.9450 1.1300 0.6210-1.4200
23.3 19.6 21.7 5.5 5.7 18.7 5.7 18.5 9.9 5.6 11.6 15.5 17.3 6.6
40.7 33.7 36.3 10.7 2.2 13.8 7.2 24.6 4.6 4.0 6.2 8.9 21.1 4.6
4.0 4.1 4.6 10.3 1.2 11.6 6.7 4.9 4.4 4.4 3.7 7.5 10.6 2.9
178-399
38-200
144-304
0.4278-2.1597
18.5
29.2
4.6
Table 3. Comparison of the Results of the Present Model with Previous Models for Petroleum Fractions with MW at T, < 0.476
Arab Berri Arab Heavy Arab Medium Boscan Iranian Export Light Valley Midway Special Minas (Sumatra) Oklahoma Pennsylvania Safania (Saudi Arabia) Stabilized Arabian Waxy Wyoming (US.)
range of mid-bp ("C)
range of temp ("C)
range of MW
range of kinematic viscos x lo6 (m2/s)
av absol dev for present model ( 8 )
3 3 3 2 1 2
13 13 14 4 1 3
1
1 5
232-399 232-399 232-399 247 -290 223 213-253 245 211-310 238 238 201 196 217 238
40-120 40-130 40-130 38-54 38 38-54 38-54 38-54 40-60 40 38 38 38 40
179-304 178-299 178-299 177-206 173 158-181 175 167-238 178 185 160 156 164 180
1.3982-6.1833 1.4542-5.6636 1.4237-6.7765 1.8200-4.8000 1.4700 1.5200-2.4700 1.7000-2.2300 1.3800-4.0000 1.4300-1.9300 1.9000 1.2500 1.1600 1.5000 1.9300
7.0 4.6 6.0 18.1 13.4 3.4 2.1 11.4 2.5 3.8 6.4 18.4 8.6 1.7
196-399
38-130
156-304
1.1600-6.7765
6.4
3 1
2 1 1
1 1
1 1
Overall
142
no. of data pts
no. of fractns
crude oil
>
1
1
1 1
25
61
Table 4. Composition of the Seven Crude Oils from Offshore Abu Dhabi ~
crude oilno. 1 2 3 4 5
6 7
H2S 1.16 0.60 1.93 0.68 3.68 0.00 1.40
Nz 0.25 0.24 0.17 0.32 0.43 0.21 0.77
COz 2.19 1.53 0.65 3.69 3.47 0.34 1.99
c1 16.33 13.16 12.59 21.55 19.49 20.04 17.38
CZ 6.29 6.38 6.05 8.6 8.28 7.93 6.42
composition (mol 8 ) C3 I-Cd Cd 7.48 1.56 4.53 7.62 1.69 5.08 6.51 0.70 3.56 7.66 1.14 5.26 6.85 1.16 3.14 8.00 1.93 4.67 7.62 1.25 4.37
The mixture molecular weight found by Petersen et al. (1991) is as follows: MW, = MW,
+ 0.00867358(MW,'~56079-
~
Cl+ I-Cs 1.63 2.46 1.46 2.19 1.91 2.52 2.19
CS 2.73 3.19 3.06 2.88 2.27 3.35 2.34
c6
3.58 6.37 1.14 2.62 2.42 5.08 5.14
C7+ 52.27 51.68 62.18 43.41 46.9 45.93 49.13
MW 249 275 230 243 246 230 267
Y 0.8803 0.8764 0.8766 0.8687 0.8764 0.8606 0.8912
used correlation has the form
(14)
MW,1.56079)(13) where N
N
MW, = &MW?/&MWi i
2
N
MW, = &MWi I
As an acceptable approximation, The modified Racket's equation of Spencer and Adler (1978) was used to predict the densities of the petroleum fraction so as to convert the dynamic viscosity to kinematic viscosity. The
where VL is the saturated liquid volume and ZRAis Racket's constant. In case of petroleum fractions, Racket's constant was back calculated from the fraction specific gravity at standard conditions.
Results and Discussion The results presented in this study comprised 240 data points for heavy crude oils and undefined petroleum fractions. Undefined Petroleum Fractions. The present model has been applied to predict the viscosities for 187 experimental points of 29 undefined petroleum fractions
Ind. Eng. Chem. Res., Vol. 34, No. 11, 1995 4143 Table 5. Comparison of the Results of the Present Model with Previous Models for Crude Oils % deviation
T(K)
p(p,pa)
exp 103(pa.s) "
Petersen present model
model
6.5 7.7 8.5 9.0 10.5 12.1 13.9 15.9 18.0 18.9 19.2 12.8
42.9 42.4 42.1 41.9 41.3 40.7 40.1 39.5 38.8 38.5 38.5 40.6
11.2 9.0 7.7 6.7 4.4 2.0 -0.3 -2.7 -5.1 -6.0 -6.1 5.6
5.5 8.4 11.4 13.3 15.4 17.5 19.4 13.0
35.1 35.1 34.7 34.6 34.5 34.3 34.4 34.7
6.1 2.7 -1.3 -3.0 -4.5 -6.2 -6.9 4.4
Crude 3 0.826 -0.9 0.807 1.2 0.782 4.0 0.761 6.7 0.739 9.6 0.717 12.6 0.695 12.8 0.673 19.2 8.7
35.8 36.1 36.4 36.8 37.1 37.5 37.9 38.3 37.0
3.7 2.8 1.6 0.8 -0.1 -0.8 -1.4 -1.8 1.6
12.9 13.1 13.9 15.3 15.5 15.7 15.8 16.0 14.8
10.0 7.0 3.6 -0.4 -0.7 -1.2 -1.7 -2.2 3.3
15.9 10.1 3.9 -2.9 -3.6 -4.3 -5.1 -5.9 6.5
5.4 6.4 7.5 9.1 10.0 11.3 8.3
41.3 39.3 36.8 33.7 32.0 30.0 35.5
22.6 17.5 11.4 4.7 1.0 -2.5
40.0 38.8 37.5 36.1 34.6 34.4
12.7 8.4 3.8 -1.0 -5.4 -5.8 6.2
1
model .
wuae I
374.8
34.46 31.02 28.95 27.57 24.13 20.68 17.24 13.79 10.34 8.96 8.69
1.236 1.190 1.163 1.144 1.099 1.053 1.008 0.963 0.918 0.900 0.897
34.46 27.57 20.68 17.24 13.79 10.34 7.86
Crude 2 0.908 0.847 0.781 0.750 0.720 0.688 0.668
%AAD 360.9
%AAD 388.2
34.46 31.46 27.57 24.13 20.68 17.24 136.1 10.27
%AAD 388.2
34.46 27.57 20.68 13.79 13.10 12.40 11.71 10.97
Crude 4 0.848 0.766 0.687 0.610 0.603 0.595 0.587 0.579
34.46 27.57 20.68 13.79 10.34 6.85
Crude 5 1.174 1.069 0.961 0.854 0.801 0.750
%AAD 383.2
%AAD 385.9
34.46 27.57 20.68 13.79 6.89 6.21
%AAD 385.4
%AAD Overall % AAD
34.46 27.57 20.68 13.79 10.34 8.96 8.21
Crude 6 1.154 -15.2 1.071 -1.7 2.5 0.987 7.5 0.903 13.6 0.821 14.2 0.813 9.1 Crude 7 -11.8 0.901 -7.8 0.841 -3.0 0.782 0.723 2.8 5.7 0.692 0.681 7.1 0.675 7.9 6.6 10.8
40.0 31.1 30.5 30.1 29.6 29.2 29.1 29.1 29.8 31.2
10.0
0.9 -3.0 -6.8 -10.4 -12.3 -12.8 -13.0 8.5 5.9
from 15 world crudes. The data were obtained from Beg et al. (1988). Table 2 shows a comparison of the results of the average absolute deviations for the present model with earlier models. The first model uses methane as a single reference component (Pedersen et al., 1987), and the- second uses methane-decane as two reference components (Petersen, 1991). The comparison shows that using decane and eicosane as reference fluids for the range MW > 142 gives better results than the other two models. The reason for having to use decaneeicosane as the two reference components in the range MW > 142 is that the molecular weight of decane equals 142. The deviations are shown merely to illustrate that large errors occur when methane, as a single reference, or methane-decane as two reference components is used in the corresponding states model to predict the viscosity of heavy petroleum fractions. For comparison, the 127 data points in Table 2 satisfy the limitation of using methane as reference component that has T, > 0.476. For this set of data, the present models give 4.6%as an average absolute deviation. The corresponding values for the Pedersen model and Petersen model are 18.5 and 29.2%,respectively. The results of the application of the present model t o 61 data points with 0.4 < T, < 0.476 shown in Table 3. The other two models are not applicable in this range of T,. The average absolute deviation for this set of data is 6.4%. Crude Oils. The model was tested against 53 experimental points of seven different crude oils from offshore Abu Dhabi. Table 4 contains the compositions of the samples of the crude oils as well as the molecular weights and the specific gravities of its C7+ fractions. The viscosities of the subsurface samples at the crude oil reservoir temperatures were measured over a wide range of pressures in a rolling ball viscometer, and the results were obtained from Abu Dhabi Marine Operating Co. (ADMA-OPCO). Comparison of the results of the present model with that of Pedersen and Petersen is shown in Table 5. The overall average absolute deviation of the present model is 5.9%. The corresponding value for the Pedersen model is 10.8%and for the Petersen model 31.2%. The results in Table 5 indicate a systematic trend in the percent deviation with pressure. The deviations for both the present method and the method of Petersen are positive a t higher pressures and negative at lower pressures, while the results from the Pedersen method show an opposite trend. Both of the methods, the present and that of Petersen, use the Lucas equation to calculate the effect of high pressure on the liquid viscosity of decane and eicosane for the earlier and decane for the later. The Pedersen model does not use the Lucas equation. These trends may result from the inadequacy of the Lucas equation for the calculation of the effect of high pressure on liquid viscosity, especially at higher pressures. In spite of the inaccuracies introduced by the estimation of the intermediate correlating parameters, such as critical temperature, critical pressure, and molecular weight, the results are very satisfactory and, in fact, the new model, when applied to heavy hydrocarbons and petroleum fractions, is more accurate than many other models currently in use.
Conclusions A corresponding states viscosity model for heavy hydrocarbons and petroleum fractions (MW > 1421,
4144 Ind. Eng. Chem. Res., Vol. 34,No. 11, 1995
using decane and eicosane as the reference fluids, has been applied for a variety of world crude oil fractions. Agreement between experimental and predicted viscosities is good in most cases. The present model performs better than earlier published models that use only methane or methane and decane as reference components for heavy fractions. The new model extends the range of prediction since it relaxes the limitation imposed on reduced temperature T,> 0.476 to T,> 0.4, which is suitable for application with heavy petroleum fractions. Furthermore, the model when tested on 187 data points for undefined heavy petroleum fractions from 15 worldwide crudes yields an overall deviation of 5.3%. Similarly, a test of the model on 53 data points for seven crude oils from offshore Abu Dhabi yielded an average absolute deviation of 5.9%.
Acknowledgment We acknowledge the management of Abu Dhabi Marine Operating Co. (ADMA-OPCO)for providing the viscosity data used in this work. Nomenclature K = parameter defined in eq 5 k = parameter defined in eq 8 MW = molecular weight P = pressure Pvp= vapor pressure T = temperature VL = saturated liquid volume z = mole fraction ZRA= Racket’s constant Subscripts
b = boiling point c = critical property m = hydrocarbon mixture or crude oil r = reduced property ref = reference SL = saturated liquid x = crude oil or petroleum fraction Greek Letters = dynamic viscosity
6 = interpolation parameter in eq 1 w = acentric factor p = any physical property in eq 10 y = specific gravity q5 = parameter in eq 11
Baltatu, M. E. Prediction of the liquid viscosity of petroleum fractions. Ind. Eng. Chem. Process Res. Dev. 1982,21, 192195. Beg, S. A.; Amin, M. B.; Hussain, I. Generalized kinematic viscosity-temperature correlation for undefined petroleum fractions. Chem. Eng. J . 1988,38,123-136. Ely, J. F.; Hanley, H. J. Prediction of transport properties. 1. Viscosity of fluids and mixtures. Ind. Eng. Chem. Fundam. 1981,20,323-332. Hanley, H. J. M. Prediction of viscosity and thermal conductivity coefficients of mixtures. Cryogenics 1976,16, 643-651. Hanley, H. J. M.; McCarty, R. D.; Haynes, W. M. Equation for the viscosity and thermal conductivity coefficients of methane. Cryogenics 1975,15, 413-415. Mehrotra, A. K. Generalized viscosity equation for pure heavy hydrocarbons. Ind. Eng. Chem. Res. 1991,30,420-427. Monnery, W. D.; Mehrotra, A. K.; Svrcek, W. Y. Modified shape factors for improved viscosity predictions using corresponding states. Can. J . Chem. Eng. 1991,69,1213-1219. Orbey, H.; Sandler, S. I. The prediction of the viscosity of liquid hydrocarbons and their mixtures as a function of temperature and pressure. Can. J . Chem. Eng. 1993,71, 437-446. Pedersen, K. S.; Fredenslund, A. Aq improved corresponding states model for the prediction of the oil and gas viscosities and thermal conductivities. Chem. Eng. Sei. 1987,42,182-186. Pedersen, K. S.; Fredenslund, A,; Christensen, P. L.; Thomassen, P. viscosity of crude oils. Chem. Eng. Sei. 1984,39,1011-1016. Pedersen, K.S.; Thomassen, P.; Fredenslund, Aa. The properties of oils and natural gases; Gulf Publishing Inc.: Houston, TX, 1989. Petersen, K. A,; Knudsen, K.; Fredenslund, Aa. Prediction of viscosities of hydrocarbon mixtures. Fluid Phase Equilib. 1991, 70, 293-308. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The properties of gases and liquids, 4th ed.; McGraw-Hill: New York, 1987; Chapter 9. Riazi, M. R.; Daubert, T., E. Simplify property prediction. Hydrocarbon Process. 1980,59 (March), 115-116. Sherman, G. J.; Magee, J. W.; Ely, J. F. PVT Relationship in a carbon dioxide-rich mixture with ethane. Int. J . Thermophys. 1989,10,47-59. Spencer, C . ;Adler, S. A critical review of equations for predicting saturated liquid density. J . Chem. Eng. Data 1978,23, 81-89. Teja, A. S.; Rice, P. Generalized corresponding states method for the viscosities of liquid mixtures. Ind. Eng. Chem. Fundam. 1981,20,77-81. Teja, A. S.; Thurner, P. A.; Pasumarti, B. The calculation of transport properties of mixtures for synfuels process design. Ind. Eng. Chem. Process Des. Dev. 1985,24,344-394. Willman, B.; Teja, A. S. Characteristic viscosity as a third parameter in corresponding states calculations of transport mixtures. Part 11. Undefined mixtures. Chem. Eng. J . 1988,37, 71-78.
Received for review January 17, 1995 Revised manuscript received J u n e 1, 1995 Accepted J u n e 14, 1995@
Literature Cited Ahmed, T. Hydrocarbon phase behavior; Gulf Publishing Co., Houston, TX, 1989; Chapter 2. Allan, J. M.; Teja, A. S. Correlation and prediction of the viscosity of defined and undefined hydrocarbon liquids. Can. J . Chem. Eng. 1991,69,986-991.
IE950050Q
@
Abstract published i n Advance A C S Abstracts, October 1,
1995.
