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# 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)

where

The second step involves using this equation:

(2)

where

(Reference: Robert E. Maples (2000),

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)

where

(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.
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.

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?

😔😔😔

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?

😔😔😔

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

Maybe I'm missing something, but it seems Refutas can be simplified somewhat:

(1)

(2)

(3)

Milt, did I miss something?

(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?

**😕**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

mbeychokCalculating 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

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.

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,

BuachaillAbroad

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

thanx........... i ws messed up wid it

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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Hi 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?

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?