In the Laboratory
Use of Kinematic Viscosity Data for the Evaluation of the Molecular Weight of Petroleum Oils rez J. A. Maroto* and M. Quesada-Pe Departamento de Física, Escuela Politecnica Superior de Linares, Universidad de Ja en, C/Alfonso X el Sabio, 28, 23700 Linares (Ja en), Spain *
[email protected] ndez A. J. Ortiz-Herna Departamento de Química Inorg anica y Org anica, Escuela Polit ecnica Superior de Linares, Universidad de Ja en, C/Alfonso X el Sabio, 28, 23700 Linares (Ja en), Spain
A classic laboratory experiment designed for an introductory-level laboratory course in physical chemistry consists of the measurement of kinematic viscosity versus temperature (1-4). This experiment is usually devised to check certain phenomenological relationships such as the Walter equation (5) and the Guzman-Andrade equation (6, 7). However, students rarely have the opportunity to obtain relevant information from the relationships. In a recent article (8), Maroto and de las Nieves carried out a theoretical analysis of the ASTM standard D 2502-04, which is a standard test method to estimate the molecular weight (relative molecular mass) of petroleum oils from viscosity measurements (9). This standard is applicable to samples with molecular weights in the range from 250 to 700 and is intended for use with average petroleum fractions. However, this test method uses a viscosity-molecular weight chart (provided by the ASTM standard) that involves interpolation errors. Maroto and de las Nieves proposed a new set of analytical equations that, added to the original equations used in the design of the chart, permits an analytical evaluation of the molecular weight of the sample. Maroto and de las Nieves also proved that the new set of equations fits the data provided by the chart in a wide interval that covers the majority of commercial oils. Finally, the authors designed a PC program based on the set of equations to make the evaluation of molecular weight of petroleum oils easier for engineers and professionals. This program can be downloaded free of charge from the Internet (10). The density and dynamic viscosity of three commercial petroleum oils are measured at different temperatures. From these data, the values of the kinematic viscosity are obtained. In this way, certain shortcomings of the capillary viscometer, mentioned in some articles published in this Journal (1, 2), can be avoided. Then, the use of the ASTM standard D 341-03 (11) permits us to carry out a simple numerical analysis that properly fits the kinematic viscosity and provides the input data required by the set of equations mentioned above, which finally allows the estimation of the mean molecular weight of the petroleum oils. In addition, the mean molecular weight of the samples was straightforwardly measured by using gas chromatography to test the validity of the results based on the measurements of viscosity. An excellent agreement between the values of the mean molecular weight of the petroleum oils provided by the set of equations that fits the
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data of the chart of the ASTM standard D 2502-04 and those obtained from gas chromatography measurements was found. From a didactic point of view, the main aim of this article is to propose a new laboratory procedure for the evaluation of the mean molecular weight of petroleum oils with high accuracy. In addition, the use of ASTM standards and commercial lubricating oils can motivate the students during their laboratory work because they carry out measurements and evaluations similar to those performed in the petroleum industry. Theory Viscosity-Temperature Relationships Petroleum fractions are complex mixtures of cyclic and noncyclic hydrocarbons. Thus, the viscosity-temperature equations for pure hydrocarbons have been applied for petroleum fractions. The Walter (5) equation (eq 1) standardized for liquid hydrocarbons by the ASTM standard D 341-03 (11) and the Guzman-Andrade equation (6, 7) (eq 2 are typical empirical viscosity-temperature correlations developed for pure hydrocarbons and are also applied to their mixtures: log logðν þ 0:7Þ ¼ A - B log T (1Þ
D η ¼ exp C þ T
(2Þ
where ν is the kinematic viscosity, η is the dynamic viscosity, T is the absolute temperature, and A, B, C, and D are positive constants. Evaluation of Molecular Weights of Petroleum Oils The ASTM standard D 2502-04 provides a means of calculating the mean molecular weight of petroleum oils from kinematic viscosity measurements (9). This standard is applicable to samples with molecular weight in the range from 250 to 700 and is intended for use with average petroleum fractions. It should not be applied to oils that represent extremes of composition or possess an exceptionally narrow molecular weight range and is based on a set of equations proposed by Hirschler (12), which were used for the design of a viscosity molecular weight chart. This chart is used in practice for the evaluation of the mean molecular weight of a petroleum oil
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r 2010 American Chemical Society and Division of Chemical Education, Inc. pubs.acs.org/jchemeduc Vol. 87 No. 3 March 2010 10.1021/ed800090h Published on Web 02/09/2010
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In the Laboratory
from the kinematic viscosities at 100 °F (37.78 °C) and 210 °F (98.89 °C). It must be noted that Hirschler designed the chart after studying numerous experimental data previously published as no fundamental theory exists for the transport properties of liquids. Nevertheless, to design the chart, Hirschler used a set of equations that fitted the data in an approximate way. The set of equations uses the viscosity slope factor (VSF), which is defined as VSF ¼ H ½νð100 °FÞ - H ½νð210 °FÞ
(3Þ
where ν(100 °F) and ν(210 °F) are the kinematic viscosities evaluated at 100 °F and 210 °F, respectively, and H(ν) is a function, partially based on the Walter equation that takes the following form (4Þ H ðνÞ ¼ 870 log log½ðν=ðm2 s - 1 Þ þ 0:6 þ 154 The mean molecular weight (Mr) can be expressed as a function of the above parameters by Mr ¼ 180 þ SfH ½νð100 °FÞ þ 60g
(5Þ
where S is a function that depends on VSF. Values of S were tabulated for all integer values of the VSF from 190 to 319, although Hirschler found an analytical form for S that fits the tabulated values in a reasonable way. Recently, Maroto and de las Nieves (8) proposed the following equation for S that fits the tabulated values of S versus the VSF with higher accuracy: S ¼ 3:562 - 0:01129ðVSFÞ - 1:857 10 - 5 ðVSFÞ2 þ 6:843 10 - 8 ðVSFÞ3
(6Þ
Maroto and de las Nieves demonstrated that the new set of eqs 3-6 fits the data in a wide interval that covers the majority of commercial oils. Equations 3-6 permit an analytical evaluation of the mean molecular weight of a petroleum oil from the kinematic viscosities at 100 °F and 210 °F. Experiment The apparatus used in this work is composed of the following components: • • • • • • • •
Mohr density balance (PHYWE) Rotary viscometer (SELECTA ST-DIGIT) Gas chromatograph (Varian model Star 3400 CX) Immersion thermostat (PHYWE A 100) Bath for thermostat and distilled water Digital thermometer Petroleum oils (Repsol YPF) Diverse glass beakers
The density of the petroleum oils is determined as a function of the temperature by using a Mohr density balance and an immersion thermostat. The dynamic viscosity of the petroleum oils is determined as a function of the temperature by using a rotary viscometer and an immersion thermostat. The mean molecular weight of the petroleum oils is measured by gas chromatography (GC) (13). Oil samples are distillated under vacuum (1 mmHg) and GC analyses are performed with a Varian Model Star 3400 CX equipped with a FID and a Varian 8200 CX programmable injector. Several commercial petroleum oils manufactured by REPSOL YPF are examined. These petroleum oils are usually used 324
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as lubricants in motor vehicles. REPSOL YPF provided the density and dynamic viscosity values of the oils versus the temperature and these data were used to verify the experimental measurements. Discussion The students measure the densities of the petroleum oils versus the absolute temperature in 5 K steps from 303 to 343 K. A linear decrease of the density of the three petroleum oils with temperature can be observed. This is a classic behavior in this kind of system (14). These data are in good agreement with the data provided by Repsol YPF. The students also measure the dynamic viscosity of the petroleum oils versus the absolute temperature in 5 K steps from 303 to 343 K. A reduction of the dynamic viscosity of the three petroleum oils with temperature is evident, which is a known behavior of liquids and, particularly, of petroleum oils (14). These data were used to evaluate the natural logarithm of the dynamic viscosity of the petroleum oils versus the inverse of the absolute temperature. The three petroleum oils display linear trends in good agreement with the predictions of the Guzman-Andrade equation (eq 2). The kinematic viscosity is the dynamic viscosity divided by the density. The students plot the double logarithm of the kinematic viscosity plus 0.7 versus the logarithm of the absolute temperature. The three petroleum oils display linear relationships in good agreement with the predictions of the Walter equation (eq 1). This equation is used to fit the experimental data and to obtain the values of the parameters A and B. Finally, the students use both these data and eqs 3-6 to evaluate the mean molecular weight of the petroleum oils. The results of this evaluation are shown in Table 1. A PC program (10) can compute these results. It must be noted that the petroleum oils TDI have different mean molecular weights in SAE-30 and Elite spite of similar log log (ν þ 0.7) values. Yet the slopes of log log (ν þ 0.7) versus log T are somewhat different. This result emphasizes that the evaluation of the mean molecular weight of petroleum oils by means of viscosity measurements requires a high degree of accuracy in the viscosity measurements, which has been noted by experts of petroleum industry (15). The values of the VSF calculated from eq 3 are shown in Table 1. These are within the 190-319 interval for which it was previously demonstrated that the set of eqs 3-6 fits the data provided by the chart of the ASTM standard D 2502-04 (8). The mean molecular weights of the petroleum oils measured by gas chromatography are also shown in Table 1. The values of the mean molecular weight provided by this experimental technique have errors of ∼5%. The values of the mean molecular weights of the petroleum oils provided by the set of eqs 3-6 and the experimental data provided by the gas chromatography technique differ by less 3%. We can conclude that the set of eqs 3-6 provides good predictions of the mean molecular weights of the petroleum oils. We prefer measurements of both density and dynamic viscosity (in order to obtain the kinematic viscosity) instead of carrying out direct measurements of kinematic viscosity (by using a glass capillary viscometer). A rotary viscometer, unlike a glass capillary viscometer, has several advantages (16): measurements under steady-state conditions, multiple measurements with the same sample at different shear rates, and continuous measurement on materials whose properties may be a function of temperature.
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r 2010 American Chemical Society and Division of Chemical Education, Inc.
In the Laboratory Table 1. Mean Molecular Weight and Viscosity Slope Factor of the Lubricating Oils Calcd Mean Molecular Weighta
Viscosity Slope Factor (VSF)b
Exptl Mean Molecular Weightc
Serie 3 SAE - 30 TDI 15W40 Elite
542.4
238.4
543
640.3
217.8
625
Matic ATF
535.2
221.0
529
Lubricant Oil
a
Data from eqs 3-6. chromatography.
b
Data from eq 3.
c
Data measured by gas
A glass capillary viscometer for kinematic viscosity measurements requires a visual detection of the meniscus crossing the timing lines (1, 15). From a didactic point of view, the measurement process can be tedious especially in the case of slowly moving liquids (1). The use of a rotary viscometer for this experiment, carried out in a student laboratory and requiring accurate measurements, is therefore highly recommended. A new instrument (survismeter) that permits simultaneous measurements of surface tension, interfacial tension, and kinematic viscosity has been described (17); this instrument should be tested for use in an introductory-level laboratory course in physical chemistry. Conclusions A classic laboratory experiment, namely, the evaluation of kinematic viscosity versus the temperature, is revised and improved for educational purposes. The analysis of such data can provide an accurate estimate of the mean molecular weight of petroleum oils. Students can easily determine a relevant parameter, which makes viscosity measurements more attractive. The use of ASTM standards as well as commercial lubricating oils is also a valuable incentive of the experiment.
1. Victoria, L.; Arenas, A.; Molina, C. J. Chem. Educ. 2004, 81, 1333. 2. Bhattacharyya, B.; Majumdar, D. J. Chem. Educ. 1973, 50, 194. 3. Daignault, L. G.; Jackman, D. C.; Rillema, D. P. J. Chem. Educ. 1990, 67, 81. 4. Urian, R. C.; Khundar, L. R. J. Chem. Educ. 1998, 75, 1135. 5. Walter, C. Erdol Teer 1931, 7, 382. 6. Guzman, J. de An. Soc. Esp. Fis. Quim. 1913, 2, 353. 7. Andrade, E. N. da C. Phil. Mag. 1934, 17, 497. 8. Maroto, J. A.; de las Nieves, F. J. Petrol. Chem. 2007, 47, 87. 9. ASTM D 2502-04. Standard Test Method for Estimation of Molecular Weight ( Relative Molecular Mass) of Petroleum Oils from Viscosity Measurements; ASTM Committee on Standards: Philadelphia, PA, 2004. 10. For the PC program named PEMO-PC.EXE. see http://www4. ujaen.es/~jamaroto/programs.html (accessed Dec 2009). 11. ASTM D 341-03. Viscosity-Temperature Charts for Liquid Petroleum Products; ASTM Committee on Standards: Philadelphia, PA, 2003. 12. Hirschler, A. E. J. Inst. Pet. 1946, 32, 133. 13. ASTM D 2878-05. Estimating Apparent Vapor Pressures and Molecular Weights of Lubricating Oils; ASTM Committee on Standards: Philadelphia, PA, 2005. 14. Gomez, J. V. Oil Gas J. 1989, 27, 66. 15. Lane, J. L.; Henderson, K. O. Viscosity Measurement: So Easy, Yet So Difficult; http://www.astm.org/SNEWS/JUNE_2004/ lanhen_jun04.html (accessed Dec 2009). 16. Viswanath, D. S.; Ghosh, T. K.; Prasad, D. H. L.; Dutt, N. V. K.; Rani, K. Y. Viscosity of Liquids. Theory, Estimation, Experiment and Data; Springer: Dordrecht, The Netherlands, 2007; p 61. 17. Singh, M.; Pak, J. Anal. Environ. Chem. 2007, 8, 82.
Supporting Information Available
Acknowledgment The authors are grateful to REPSOL YPF for providing experimental data of the three petroleum oils analyzed in this work.
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Literature Cited
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Student handout including experimental procedures, assessment tasks, and some postlab questions and notes for the instructor. This material is available via the Internet at http://pubs.acs.org.
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