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
| $\nu$ | : | Kinematic viscosity |
| $ x $ | : | Mass fraction |
| $ v $ | : | Volume fraction |
Gambill Method
Gambill (1959) proposed the following equation for estimating the kinematic viscosity of a two liquid mixture.
$$ \displaystyle \nu^{1/3} = x_a\nu_a^{1/3} + x_b\nu_b^{1/3} $$
Refutas Equation
Mass Basis
Refutas (2000) proposed a method by which the kinematic viscosity $ \left(\nu \right) $ 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.
$$ \displaystyle \text{VBN}_i = 14.534 \times \ln\left(\ln\left(\nu_i + 0.8\right)\right) + 10.975 $$
The VBN of the liquid mixture is then calculated as follows:
$$ \displaystyle \text{VBN}_{\text{mixture}} = \sum_{i = 0}^{N} x_i \times \text{VBN}_i $$
The kinematic viscosity of the mixture can then be estimated using the viscosity blending number of the mixture using the equation below.
$$ \displaystyle \nu_{\text{mixture}} = \exp \left(\exp \left(\frac{\text{VBN}_{\text{mixture}} - 10.975}{14.534}\right)\right) - 0.8 $$
Volumetric Basis
Chevron developed an alternative formulation for the viscosity blend index in which the volume fraction of each component may be used.
$$ \displaystyle \text{VBN}_i = \ln (\nu_i) / \ln (1000 \times \nu_i ) $$
The VBN of each volumetric component can then be used to calculate the VBI of the mixture as follows.
$$ \displaystyle \text{VBN}_{\text{mixture}} = \sum_{i = 0}^{N} v_i \times \text{VBN}_i $$
Using $ \text{VBN}_{\text{mixture}} $ 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.
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