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# Liquid viscosity blending

**Liquid viscosity blending** calculations to determine the viscosity of a blend of two or more liquids having different viscosities are best performed by using what is known as the Refutas equation ^{[1]}^{[2]} in a three-step procedure.

## The three step equations

The first step is to calculate the Viscosity Blending Index (VBI) of each component of the liquid blend using the following equation:

- (1)
**VBN = 14.534 × ln[ln(***v*+ 0.8)] + 10.975

where **v** is the viscosity in square millimeters per second (mm²/s) or centistokes (cSt) and **ln** is the natural logarithm (log_{e}). It is important that the viscosity of each component of the blend be obtained at the same temperature.

The next step is to calculate the VBN of the blend, using this equation:

- (2)
**VBN**_{Blend}= [*w*_{A}× VBN_{A}] + [*w*_{B}× VBN_{B}] + ... + [*w*_{X}× VBN_{X}]

where **w** is the weight fraction (i.e., weight % ÷ 100) of each component of the blend.

Once the viscosity blending number of a blend has been calculated using equation (2), the third and final step is to determine the viscosity of the blend by using the invert of equation (1):

- (3)
**v = e**^{e(VBN - 10.975) ÷ 14.534}− 0.8

where **VBN** is the viscosity blending number of the blend and **e** is the transcendental number 2.71828, also known as Euler's number.

## References

- ↑ Robert E. Maples (2000).
*Petroleum Refinery Process Economics*, 2nd Edition. Pennwell Books. ISBN 0-87814-779-9. - ↑ C.T. Baird (1989),
*Guide to Petroleum Product Blending*, HPI Consultants, Inc. HPI website