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 0878147799)
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.
(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 0878147799)
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.
Replies

crookI 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.

moodyengineMany 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?
😔😔😔 
gohmThank you for posting this! Could you illustrate this with some industrial examples of practical use?

DieselmanMaybe 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?
😕 
jasonmann42
Yes, you are not being consistent with your algebra. Your simplified equation (1) should read,DieselmanMaybe 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 
morganparkarmbeychokCalculating 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

BlackmotI 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.

BuachaillAbroadHi 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,
BuachaillAbroad 
dreshti sharmathanx........... i ws messed up wid it

crazygolfIn 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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Saher EfaraHi Guys,
is the viscosity of the blend will be results of the viscosities of the two fluids at the same temperature? Ie if the viscosities of two fluids at 25 c degree the output will be at the same temperatures or the factors values are related to the temp?
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