Viscosity blending equations

[mbeychok]

Calculating the viscosity blending index of a liquid consisting of two or more liquids having different viscosities is a two step procedure. The first step involves calculation of the Viscosity Blending Index (VBI) of each component of the blend using the following equation (known as a Refutas equation):


(1) VBI = 14.534 × ln[ln(v + 0.8)] + 10.975

where v is the viscosity in centistokes and ln is the natural logarithm (Log_e).

The second step involves using this equation:

(2) VBI_Blend = [w_A × VBI_A] + [w_B × VBI_B] + ... + [w_X × VBI_X]

where w is the weight fraction (i.e., % ÷ 100) of each component of the blend. In using the above blending equation, it is necessary that all viscosities are determined at the same temperature, for example, 100 ^oC.

(Reference: Robert E. Maples (2000), Petroleum Refinery Process Economics, 2nd Edition, Pennwell Books, ISBN 0-87814-779-9)

Once the viscosity blending number of a blend is obtained with equation (2), the viscosity of the blend can be determined 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.

[crook]

I would like to thank Mr. Milt Beychok on behalf of all the readers of CE's Chemical Engineering section . Although I am not a chemical engineer, I am sure that your articles are benefiting many chemical engineers.

[moodyengine]

Many thanks for this valuable equations.

but i had a challenge question from my manager which is; we can't blend two oils with the same type but the viscosity is different, for example we can't blend an ISO 100 turbine oil from ISO 460 and ISO 68, WHY?

[gohm]

Thank you for posting this! Could you illustrate this with some industrial examples of practical use?

[Dieselman]

Maybe I'm missing something, but it seems Refutas can be simplified somewhat:
(1) VBI = ln[ln(v + 0.8)] + 0.75513

Note than 10.975/14.534 = 0.75513

(2) VBI_Blend = [w_A × VBI_A] + [w_B × VBI_B] + ... + [w_X × VBI_X]
(same as before)

(3) v = exp[exp(VBN_Blend - 0.75513)] - 0.8

Milt, did I miss something?