• mbeychok

MemberOct 3, 2007

## Viscosity blending equations

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[sub]e[/sub]).

The second step involves using this equation:

(2) VBI[sub]Blend[/sub] = [w[sub]A[/sub] × VBI[sub]A[/sub]] + [w[sub]B[/sub] × VBI[sub]B[/sub]] + ... + [w[sub]X[/sub] × VBI[sub]X[/sub]]

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 [sup]o[/sup]C.

(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[sup]e[sup](VBN - 10.975) ÷ 14.534[/sup][/sup] - 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.
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Replies
• MemberOct 3, 2007

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.
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• MemberApr 21, 2008

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?
😔😔😔
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• MemberApr 22, 2008

Thank you for posting this! Could you illustrate this with some industrial examples of practical use?
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• MemberSep 5, 2008

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[sub]Blend[/sub] = [w[sub]A[/sub] × VBI[sub]A[/sub]] + [w[sub]B[/sub] × VBI[sub]B[/sub]] + ... + [w[sub]X[/sub] × VBI[sub]X[/sub]]
(same as before)

(3) v = exp[exp(VBN[sub]Blend[/sub] - 0.75513)] - 0.8

Milt, did I miss something?
😕
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• MemberMar 19, 2009

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[sub]Blend[/sub] = [w[sub]A[/sub] × VBI[sub]A[/sub]] + [w[sub]B[/sub] × VBI[sub]B[/sub]] + ... + [w[sub]X[/sub] × VBI[sub]X[/sub]]
(same as before)

(3) v = exp[exp(VBN[sub]Blend[/sub] - 0.75513)] - 0.8

Milt, did I miss something?
😕

=> (VBI/14.534) = ln[ln(v + 0.8)] + 0.75513,

not,

=> VBI = ln[ln(v + 0.8)] + 0.75513.

Just remember to be systematic when doing algebra.

Regards
Jason
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• MemberMar 22, 2009

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):

Hi Friend,

You can get it by applying mixing rule which is you need to the viscosity of pure component fraction and sum all those to get the mixture viscosity. Anyone please comment if there is any mistakes.

Other is yours.

Thanks
Parkar

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• MemberJun 8, 2009

I am looking for a reference to papers describing the applicability of the Refutas equation, in particular, to the original publication of the Refutas equation. Does anyone have a reference available that I can locate? Online or library, either way works just fine.
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• MemberJun 25, 2009

Hi guys,

For the equations, are there specific requirements?

For example, viscosity must be greater than x cSt, only applies for oil based liquids, etc.

I am trying to calculate the viscosity of a 50/50 Ethanol & Water blend (@ STP) but the calculations do not match my experimental results.

Thanks & please let me know you thoughts,
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• MemberJul 20, 2009

thanx........... i ws messed up wid it
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• MemberSep 9, 2009

In particular, to the original publication of the Refutas equation. Does anyone have a reference available that I can locate? Online or library, either way works just fine.

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