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# Liquid viscosity blending

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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 (loge). 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)   VBNBlend = [wA × VBNA] + [wB × VBNB] + ... + [wX × VBNX]

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 = ee(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

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