scope:

Viscosity is a measure of the ability of a fluid to resist shear. When the shear stress on any differential volume element of flowing fluid is proportional to the velocity gradient in the direction perpendicular to the direction of flow, the fluid is called a Newtonian fluid.

The methods presented in this chapter are for Newtonian fluids and should not be expected to maintain their accuracy for non-Newtonian fluids. Almost all gases and most hydrocarbon liquids are Newtonian fluids. Very heavy asphalts with low UOP K's exhibit non-Newtonian behavior. Some other common non-Newtonian fluids are polymers, pastes, slurries, waxy oils, and some silicate esters.

Viscosity is a function of temperature, pressure, and molecular species. For non-Newtonian fluids, the viscosity is also a function of the local velocity gradient.

The absolute viscosity is defined as the shear stress at a point divided by the velocity gradient at that point. The unit of absolute viscosity is the poise, which is equal to 1 gram per (centimeter)(second).

The kinematic viscosity is defined as the ratio of the absolute viscosity to the density, both at the same temperature and pressure. The unit of kinematic viscosity corresponding to the poise is the stoke. which is equal to 1 square centimeter per second. The conversion from absolute to kinematic viscosity is given by the following equation:

Where:

ν = kinematic viscosity, in stokes

µ = absolute viscosity, in poises

ρ = density, in vacuo, in grams per cubic centimeter

The units centipoise (0.01 poise) and centistoke (0.01 stoke) are used most frequently.

Saybolt Universal viscosity is the efflux time in seconds for a 60-milliliter sample to flow through a standard orifice in the bottom of a tube. Saybolt Furol viscosity is determined in the same manner as Saybolt Universal viscosity except that a larger orifice is used. The orifice and tube geometry are specified in standards of the American Society for Testing and Materials.

Viscosity of Liquid Systems

Conversions between the more common engineering units of viscosity are given in Chapter 1. Conversions of kinematic viscosity data to Saybolt Universal seconds and to Saybolt Furol seconds are given in Procedures 11A1.1 and 11A1.2, respectively. The relationships between other viscosity scales and kinematic viscosity are shown in Procedure 11A1.6.

The viscosity-temperature behavior for approximately 300 pure liquid hydrocarbons can be determined from the correlating equation given in Procedure 11A2.1. Using viscosity data at the two temperatures, the viscosity-temperature behavior can be estimated using Procedure 11A4.4. Viscosity data at 100 F and 210 F are given in Chapter 1 for a number of hydrocarbons and the more common nonhydrocarbons. The viscosities of compounds for which no experimental data exist can be estimated by a group contribution method given in Procedure 11A2.3. Liquid viscosities of defined mixtures can be predicted with Procedure 11A3.1.

Several methods are presented to determine the viscosity-temperature relationship for petroleum fractions. Procedure 11A4.1 can be used to calculate viscosity if a measured viscosity at 100 F is known.

Procedure 11A4.2 can be used to predict liquid viscosity if no experimental measurements are available. Procedure 11A4.2 predicts the viscosity at two temperatures, 100 F and 210 F. The viscosity at any other temperature can then be determined by using Procedure 11A4.4. Procedure 11A4.5 is used to mathematically estimate the viscosity of liquid blends of petroleum fractions. Procedure 11A4.6 is used to determine the viscosity of multicomponent blends of pure hydrocarbons with petroleum fractions or multicomponent blends of petroleum fractions.

There is no general method for predicting the effect of pressure on the liquid viscosity of all types of hydrocarbons. For low-molecular-weight hydrocarbons, Procedure 11A5.1 may be used to predict viscosity at elevated pressures provided the critical pressure, critical temperature, and acentric factor are known, and provided either a value of the viscosity at the critical point or a liquid viscosity value at another temperature and pressure is known. Procedure 11A5.5 is given to estimate the effect of pressure on the viscosity of high-molecular-weight pure and mixed hydrocarbons. Procedure 11A5.5 should be used for the effect of pressure on the viscosity of petroleum fractions.

The viscosity index of an oil is an empirical number indicating the effect of a change in temperature on viscosity. It can be calculated using Procedure 11A6.1. The liquid viscosity of pure and mixed hydrocarbons containing dissolved gases is given by Procedure 11A7.1.

Viscosity of Gaseous Systems

In contrast with the viscosities of liquids, viscosities of gases increase with increasing temperature and with increasing pressure.

The viscosities predicted by the methods of this chapter should not be used at pressures below approximately 0.2 pound per square inch absolute.

The viscosity-temperature behavior for approximately 300 pure gaseous hydrocarbons can be determined from the correlating equation given in Procedure 11B1.1. The viscosities of other pure gases at reduced pressures below 0.6 are estimated by Procedure 11B1.3.

The viscosities of mixtures of known composition at reduced pressures below 0.6 are estimated by Procedure 11B2.1 in conjunction with Procedure 11B1.1 or Procedure 11B1.3. A more rapid but less precise approximation is given by Procedure 11B3.1. Procedure 11B3.1 is not recommended except as a rough approximation for gaseous hydrocarbon mixtures of undefined composition.

For reduced pressures above 0.6, the effect of pressure on viscosity can be estimated using Procedure 11B4.1.

Viscosity of Nonhydrocarbons

The viscosity of liquid and gaseous hydrogen is plotted in Figure 11C1.1. Procedure 11C1.2 correlates the effect of pressure on the viscosity of nonhydrocarbon gases. Procedures 11B2.1 and 11B4.1 are also applicable for calculating the viscosities of gaseous mixtures containing nonhydrocarbons at low and high pressure, respectively.

Summary of Viscosity Calculation Methods

Figure 11-0.1 gives a schematic diagram showing which procedure(s) should be used for calculating hydrocarbon viscosities for any particular case.

Computerized Subroutines Available in Chapter 16

Chapter 16 of the API Technical Data Book contains subprograms for all the predictive methods in Chapter 11. The subprograms are written in standard Fortran code and can be incorporated into computer packages prepared by the user. Subprograms are available either on tape or on diskette and are purchased separately from the Technical Data Book.

A list of the subprograms that accompany the chapter 11 procedures is shown in the table below.

Alternate Computer Method for Viscosity of Liquid and Vapor Hydrocarbon Systems

Ely and Hanley (33) proposed an extended corresponding states method applicable to all hydrocarbon fluid phases as pure compounds or defined mixtures. This method is available as a generalized computer method called SUPERTRAPP, distributed by the National Institute of Standards and Technology. (A copy of the program can be obtained from the U.S. Department of Commerce, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, MD 20899.) Input parameters for the method include the critical temperature, critical pressure, critical volume, acentric factor, molecular weight, vapor pressure data, and saturated liquid density data of each component of interest. Large errors near the bubble point of the fluid may be obtained because the method will sometimes converge to a solution in the wrong phase. However, the method can be modified to predict viscosity in a specified phase. The average errors for the SUPERTRAPP program were comparable to the Technical Data Book procedure for any of the categories evaluated. The main advantage of the program is the ability to handle phase changes or large pressure variations with one method. Our analysis of the program is shown in the table below.

Because this is proprietary software, the equations and computer algorithms are not included in the API Technical Data Book. However, it is a viable alternate computer method for viscosity calculations. The method is quite complex for desktop calculations.

A method similar to SUPERTRAPP is being developed for undefined mixtures, either in the vapor or liquid phase. The method is not available for distribution at this time, but may be in the near future. Contact the National Institute of Standards and Technology for additional information.