Predicting the Viscosity of Pure Light Hydrocarbons
Authors: Eakin B.E. , Ellington R.T. 
Published: December 2007

Abstract
The following equation, which describes the viscosity of methane, ethane, propane and n-butane in the vapor, liquid and dense-fluid regions for densities up to 2.4 times the critical density, is presented.
The atmospheric-pressure viscosity can be reprevented satisfactorily by Sutherland's equation for which values of the necessary constants are given. The equation represents the data on these materials over the entire region with a standard deviation of 1.6 per cent for 288 points. Except in the immediate vicinity of the critical density, the largest difference between predicted and observed viscosity was 4.3 per cent. To facilitate calculations, the equation is presented as a single curve of, evaluated for a gas of zero molecular weight. By modification of the co-ordinates, the curve becomes a straight line. The factor for converting the curve value of to that for the actual gas is a linear function of molecular weight, and is also plotted.

Introduction
The pressures at which fluids are produced, transferred and processed have increased steadily in the petroleum and chemical industries. This has resulted in increased interest in the effect of pressure on the thermodynamic and transport properties of fluids. The relationships derived from simple kinetic theory often may be applied in estimating gas properties for low and moderate pressures. These have the advantage of simplicity, a fact which has frequently led to use beyond the range of proper applicability. At high pressures and low temperatures, these relationships may be greatly in error, and other means of calculation are needed for the dense gas and liquid regions.
The thermodynamic properties of fluids have been studied extensively, both theoretically and experimentally. The volumetric behavior of a large number of fluids has been measured experimentally to high pressures for wide ranges of temperature. It is more difficult, however, to obtain accurate experimental values for transport properties, and detailed data have been obtained for very few fluids for extensive ranges of temperature and pressure. This situation has greatly handicapped correlation efforts.
Because of the limited data available on transport properties and the complex relationships which exist between the transport and thermodynamic properties, generally one of three methods has been applied to represent these properties for pure fluids.Tabulations of each transport property at selected pressure andtemperature intervals.Equations for each transport property of each fluid which relatethese properties to PVT behavior.Generalized co-ordinate chart for each transport property, frequently with serious restrictions as to accuracy.
The methods are listed in order of decreasing accuracy. The first and second methods are limited to pure components and certain commonly occurring mixtures such as air for conditions other than atmospheric pressure. Equations have been developed from kinetic theory which quite accurately represent the temperature dependence of viscosity of gases and liquids at low pressures. Special equations have been developed to calculate the effects of pressure and temperature on viscosity of steam and nitrogen, but these equations are empirical and different for each fluid. No single equation is presenting available for accurate prediction of viscosity in both the liquid and gas phases, for any fluid.
The third method is based on van der Waals' theory, of corresponding states. Uyehara and Watson presented a plot of vs, with lines of constant which is generally accurate within 10 per cent, but in the critical region errors may be as large as 30 per cent. Carr and Comings, Mayland and Egly used, and as parameters and developed generalized correlations for gases, and Carr extended his to include mixtures. For natural gases Carr's chart is generally accurate within 3 per cent, but is less accurate for heavier hydrocarbons or other gases.
The purpose of this study was to examine the viscosity-pressure-temperature data on the light hydrocarbons in their liquid, gas and dense-fluid regions, and to develop an equation which relates viscosity to the state properties. The form of the equation should be such that it will approach the kinetic-theory relationships for temperature dependence of viscosity for gases at low pressures, and for liquids at high densities.

Background
Most efforts it development of general relationships for prediction of fluid viscosities are based on equating the expression for momentum transfer per unit area, or shear force, developed by use of a molecular model to the defining equation for a continuous Newtonian fluid.
JPT
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