NEW EQUATION PREDICTS VISCOSITY OF UNKNOWN HYDROCARBON VAPORS

Joss Vicento Gomez
Maraven S.A.
Falcon, Venezuela

An empirical equation has been developed for predicting the dynamic viscosity of light and heavy undefined hydrocarbon vapors at atmospheric pressure. The equation uses molar mass and specific temperature as the input parameters.

The proposed correlation has been derived from experimental data for hydrocarbons with molar masses ranging from 16 to 480 g/g-mole, which covers the span between methane and most petroleum vacuum distillates. Moreover, the method allows smooth extrapolation beyond the experimental boundary of 480 g/g-mole, up to a molar mass of about 665 g/g-mole. This range embraces nearly all fractions commonly found in petroleum refining processes.

The lowest and highest temperatures at which the experimental data were obtained are 250 K. and 850 K., yet the functional form of the equation provides a smooth trend away from those limits. The average deviation of the method is about 1%, with a maximum deviation of 4%.

EXISTING METHODS

Among the transport properties needed by process engineers, viscosity is perhaps used most frequently. Its many uses in process engineering calculations include fluid-flow problems, heat and mass-transfer mixing, and sizing of process equipment and pipelines. This widespread use, coupled with the fact that experimental data on gas viscosity are scarce or unavailable in many cases, makes prediction methods very desirable tools.

At present, there are two major theoretical approaches for the estimation of low-pressure gas viscosity: the law of corresponding states and the Chapman-Enskog theory.

Methods for predicting low-pressure viscosities of pure, nonpolar gases (such as hydrocarbons) that are based on the law of corresponding states require knowing the molar mass and critical properties of the compound.1-12 Some techniques even require a knowledge of the molecular structure so that a "group contribution" parameter can be determined.9 10 The Chapman-Enskog-based methods, on the other hand, are somewhat more extensive in their requirements.13 14 These methods need, in addition to the molar mass, the Lennard-jones potentials for nonpolar molecules (the collision diameter and the characteristic energy) and the collision integral for viscosity as input parameters. For compounds whose Lennard-jones potentials are not available in literature, Chung, et al., propose correlations for their estimation, but these correlations also presuppose that critical properties are known.14 The method of Chung, et al., also makes use of Pitzer's acentric factor to account for molecular shapes.

Yet for all of their success with light, defined hydrocarbons gases, the above mentioned methods suffer from two serious drawbacks when applied to complex mixtures of heavy hydrocarbon vapors:

Their application is cumbersome, due to the extensive characterization work needed.
Viscosity predictions worsen as the molar mass increases.

To lessen the effort associated with theoretical routines, several authors and sources have advised the use of empirical graphical methods to compute low-pressure viscosities.15-20 Although convenient and accurate for many engineering purposes, these methods still exhibit some shortcomings. Nomographs, for instance, apply for numbers of light gases but not heavy gaseous fractions; while graphs have scales limited to a molar mass of 200 mole, or even lower. 15-20 Furthermore, the author has found that even the methods recommended by the American Petroleum Institute and by the Gas Processors Suppliers Association (GPSA) do not accurately reproduce the data for heavier vapors.18 20 This is perhaps because these graphs were developed for paraffin vapors, whereas actual heavy gaseous fractions are of a more complex nature.

Finally, graphical methods do not lend themselves to computer applications, thus they lose their appeal in an age of nimble calculations.

NEW METHOD

A new analytical relationship has been developed for predicting the dynamic viscosity of undefined hydrocarbon vapors at low pressure, as a function of their average molar mass, M, and specific temperature, T. The correlation was derived from properties of pure, light paraffins and actual petroleum fractions in the author's data base, taken from open literature and private sources.

Ranges for M and T in the data bank were:

M - 16.043-481 g/g-mole
T - 250-850 K.

Equation 1 fits vapor viscosity data over a wide span of temperatures. In the equation, coefficients A(M) and B(M) are functions of M (Equations) (9026 bytes). The square root of T is easily identifiable as coming from the kinetic theory of gases.

For the sake of accuracy, coefficients A(M) and B(M) were correlated not by single equations covering the entire range of values of M, but rather by a series of separate correlations, each one applicable in a particular domain of M. Both linear and nonlinear functions were employed for this task.

Table 1 (28906 bytes) shows the various relationships for A(M) and B(M), their range of application, and the constants for the equations.

Table 2 (12982 bytes) compares results from Equation 1 (9026 bytes) with those reported in open literature and private sources. As shown, predictions from the new method are quite accurate for gases as light as methane and as heavy as vacuum gas oil. The average deviation of the method is around 1%, with a maximum deviation of 4%.

Comparison with results from graphical methods has been avoided on purpose in Table 2 (12982 bytes), as it would require nonlinear interpolations in those graphs. Nevertheless, for those who go through the original sources, larger deviations from these methods with respect to reported values will be evident at a glance. 18-20 For mixtures of light gases with average molar masses in the range from 17 to 58 g/g-mole and containing nonhydrocarbons such as nitrogen, carbon dioxide, or hydrogen sulfide, reasonable viscosities can be computed using the new method. The technique involves solving the method proposed here for the average molar mass of the mixture then adding the appropriate correction factors for nonhydrocarbons, as obtained from the linear relationships shown in the GPSA graphs. 20

Viscosities from Equation 1 (9026 bytes) are valid for pressures up to 1 atm absolute. The crescendo trend of viscosity with temperature in Table 2 (12982 bytes) indicates that gases are found in a dilute state at such low pressures.

Nonetheless, at high reduced pressures, there are regions in which the viscosity behavior of gases resembles that of a liquid state (dense gas), displaying an actual decrease of viscosity with temperature. A generalized viscosity phase diagram for nonpolar gases has been developed by Lucas. 21 22 Should dense-gas viscosity have to be estimated, the low-pressure viscosity calculated by Equation 1 (9026 bytes) should be corrected by the effect of pressure. For that task, Reichenberg and Lucas have proposed suitable mathematical methods. 9 10 21 22

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