Correlation of the Viscosity of Light Paraffin Hydrocarbons And Their Mixtures in the Liquid and Gaseous Regions
Authors: Giddings J.G. , Kobayshi Riki 
Published: December 2007

Abstract
Residual viscosity, the viscosity at a given pressure and temperature minus the dilute gas viscosity at the same temperature, has been found to be independent of temperature for pure components and mixtures for simple molecules and light hydrocarbons. The residual viscosities for methane, ethane, propane and four mixtures were correlated as a function of reduced density and molecular weight.
Introduction
Earlier efforts in correlating the viscosity of light hydrocarbons and associated gases under pressure, primarily by some form of the corresponding states principle, have been reported elsewhere. The formal theory of corresponding states principle for viscosity from non-equilibrium statistical mechanical arguments for simple molecules has been developed by Helfand and Rice. The most serious obstacle to the development of a generalized corresponding states representation of viscosity data, even for simple molecules, has been the limited quantity of precise viscosity data of pure components and mixtures over a wide range of pressure and temperature conditions. Viscosity data on light hydrocarbons have recently been contributed by several laboratories. In the study of the viscosity of nitrogen, Michaels and Gibson observed that the viscosities of nitrogen as a function of density gave parallel isotherms. The same behavior has since been reported for other gases. The observed behavior indicates that the residual viscosity or the viscosity at a given pressure and temperature minus the dilute gas viscosity at the same temperature is a unique function of the density. Abas-Zade, Michaels and Botzen, and Michaels, Botzen, Friedman and Sengers, observed similar behavior for thermal conductivity, the residual thermal conductivity being defined in a manner parallel to that of residual viscosity. Thodos and co-workers applied the residual viscosity concept to the viscosity of pure monatomic and diatomic gases. Ellington and co-workers made the residual viscosity vs density plots for ethane and propane, but omitted the region below a residual viscosity of 15 micropoise and showed a systematic separation of the ethane isotherms in the low density region. Eakin correlated the residual viscosity of methane, ethane, propane and n-butane empirically as a function of density and molecular weight. Carmichael and Sage recently presented ethane residual viscosity vs density values in the gaseous liquid, and near critical regions as a single univariant function of density. Flynn, Hanks, Lemaire and Ross have contributed extremely accurate viscosity data to confirm that the residual viscosity concept is essentially correct, but may not be accurate within 0.1 per cent of the viscosity value for the gaseous state. The recent studies by Giddings indicate that the residual viscosity of methane, propane and each of four methane-propane mixtures are unique functions of density over the temperature and the density ranges studied.
QUALITATIVE AGREEMENT OF OBSERVED BEHAVIOR WITH THEORY
It is interesting to compare the residual viscosity concept with theory, since the residual viscosities will be subsequently correlated by means of a corresponding states theory. The Enskog dense-gas kinetic theory for rigid spherical molecules of finite size states that
An examination of Eq. 1 indicates that the residual viscosity of a given substance would not appear as a unique function of the density, but is a function of the dilute gas viscosity value at the temperature under consideration times a function of the density which is independent of the temperature. The theory of viscosity of dense fluids using the nonequilibrium statistical mechanical approach has been developed by Kirkwood and by Born and Green.
JPT
P. 679ˆ