# Summary

For some engineering calculations, particularly in hydrocarbon processing, it is necessary to estimate the viscosity of a mixture (blend) of two or more components. This article presents the Gambill and Refutas methods, which are commonly used in petroleum refining for predicting the viscosity of oil blends.

# Definitions

: | Kinematic viscosity | |

: | Mass fraction | |

: | Volume fraction |

# Gambill Method

Gambill (1959) proposed the following equation for estimating the kinematic viscosity of a two liquid mixture.

# Refutas Equation

## Mass Basis

Refutas (2000) proposed a method by which the kinematic viscosity of a mixture of two or more liquids. In this method a Viscosity Blending Number (VBN) of each component is first calculated and then used to determine the VBN of the liquid mixture as shown below.

The VBN of the liquid mixture is then calculated as follows:

The kinematic viscosity of the mixture can then be estimated using the viscosity blending number of the mixture using the equation below.

## Volumetric Basis

Chevron developed an alternative formulation for the viscosity blend index in which the volume fraction of each component may be used.

The VBN of each volumetric component can then be used to calculate the VBI of the mixture as follows.

Using the viscosity of the mixture may then be calculated as shown previously.

# References

- Gambill, W.R., 1959,
*"How to estimate mixtures viscosities"*, Chemical Engineering, 66, pg 151-152. - Maples, R.E., 2000,
*"Petroleum Refinery Process Economics"*, PennWell, ISBN 978-0-87814-779-3.