Calculator for viscosity mixing based on the Lederer - Roegiers equation

I have finally got to calculate the empirical alpha values using the Blackstone KV100 for Oil 1, Oil 2, and Mix.

My conclusions in summary:

(1) Lederer - Roegiers equation when used with the proper alpha value works!

(2) Arrhenius equation and the Widman mixing calculator do not work!

(3) alpha values ranged from 0.42 to 1.46 in Ed's samples, greatly deviating from the Arrhenius equation and Widman mixing calculator, which assume alpha = 1.

(4) You need to have at least one measured sample to calculate the alpha empirically, from which you can calculate the viscosity for different mix ratios for the same two oils.

If you want to calculate the alpha for a given sample directly without trial and error, here is the formula:

beta = [ln(n / n2)] / [ln (n1 / n2)]

alpha = [x1 * (1 - beta)] / [ (1 - x1) * beta]

Note the parentheses. n1, n2, and n are the viscosities of Oil 1, Oil 2, and Mix, respectively. x1 is the fraction of Oil 1. Once you know the alpha for a given sample, you can calculate the viscosity for different fractions of the same two oils using:

n = n1^x1_effective * n2^x2_effective

x1_effective = x1 / (x1 + x2 * alpha)
x2_effective = 1 - x1_eff

Here are the average alpha values for Ed's samples, with the info in the parenthesis showing the approximate oil composition:

Code
Oil 1 Oil 2 alpha



M1 EP 0W-20 (~ PAO) M1 FS 0W-40 (~ GTL) 1.40

Castrol GTX UC 5W-30 (~ Gr II) Castrol GTX 20W-50 (~ Gr II) 0.86

M1 EP 0W-20 (~ PAO) Redline 50WT Race (~ PAO) 0.85

M1 FS 0W-40 (~ GTL) Redline 50WT (~ PAO) 0.42

Castrol GTX UC 5W-30 (~ Gr II) Rotella T5 10W-30 (~ Group II + GTL ?) 0.50

M1 EP 0W-20 (~PAO) Castrol GTX 20W-50 (~ Group II) 0.81

Redline 50WT Race (~ PAO) Valvoline SAE 30 ND (~ Group II) 1.46

Note that similar base oils result in alpha ~ 1 as expected but when you mix a PAO base oil even with a GTL base oil, alpha differs from 1 significantly.

Use these alpha values along with the spreadsheet provided in the original post for a lot more accurate estimates of the viscosity of the mix. Note that the order of the oils matters when you use a given alpha value -- do not exchange Oil 1 and Oil 2.

The actual empirical alpha values using the Blackstone KV100 for Oil 1, Oil 2, and Mix:

Code
Sample # alpha_empirical Name Average alpha_empirical



1 1.47 M1 EP 0W-20 - M1 FS 0W-40 1.40

2 1.41 M1 EP 0W-20 - M1 FS 0W-40

3 1.33 M1 EP 0W-20 - M1 FS 0W-40

4 0.86 GTX 5W-30 UC - GTX 20W-50 0.86

5 0.86 GTX 5W-30 UC - GTX 20W-50

6 0.79 M1 EP 0W-20 - Redline 50WT 0.85

7 0.88 M1 EP 0W-20 - Redline 50WT

8 0.89 M1 EP 0W-20 - Redline 50WT

9 0.39 M1 FS 0W-40 - Redline 50WT 0.42

10 0.45 M1 FS 0W-40 - Redline 50WT

11 0.50 GTX 5W-30 UC - Rotel. T5 10W-30 0.50

12 0.81 M1 EP 0W-20 - GTX 20W-50 0.81

13 1.46 Redline 50WT - Valvoline 30 ND 1.46

Last but not least, thank you very much, edhackett, for this great work! It's much appreciated!
 
Originally Posted by Gokhan
I just realized that the Widman viscosity-mixing calculator and similar calculators on the Internet are totally useless. They are very inaccurate.
I believe all of this, no problem. But may I ask how you realized, they are very inaccurate? The Counter-test, was?
 
I have finally got to calculate the empirical alpha values using the Blackstone KV100 for Oil 1, Oil 2, and Mix.

My conclusions in summary:

(1) Lederer - Roegiers equation when used with the proper alpha value works!

(2) Arrhenius equation and the Widman mixing calculator do not work!

(3) alpha values ranged from 0.42 to 1.46 in Ed's samples, greatly deviating from the Arrhenius equation and Widman mixing calculator, which assume alpha = 1.

(4) You need to have at least one measured sample to calculate the alpha empirically, from which you can calculate the viscosity for different mix ratios for the same two oils.

If you want to calculate the alpha for a given sample directly without trial and error, here is the formula:

beta = [ln(n / n2)] / [ln (n1 / n2)]

alpha = [x1 * (1 - beta)] / [ (1 - x1) * beta]

Note the parentheses. n1, n2, and n are the viscosities of Oil 1, Oil 2, and Mix, respectively. x1 is the fraction of Oil 1. Once you know the alpha for a given sample, you can calculate the viscosity for different fractions of the same two oils using:

n = n1^x1_effective * n2^x2_effective

x1_effective = x1 / (x1 + x2 * alpha)
x2_effective = 1 - x1_eff

Here are the average alpha values for Ed's samples, with the info in the parenthesis showing the approximate oil composition:

Code
Oil 1 Oil 2 alpha



M1 EP 0W-20 (~ PAO) M1 FS 0W-40 (~ GTL) 1.40

Castrol GTX UC 5W-30 (~ Gr II) Castrol GTX 20W-50 (~ Gr II) 0.86

M1 EP 0W-20 (~ PAO) Redline 50WT Race (~ PAO) 0.85

M1 FS 0W-40 (~ GTL) Redline 50WT (~ PAO) 0.42

Castrol GTX UC 5W-30 (~ Gr II) Rotella T5 10W-30 (~ Group II + GTL ?) 0.50

M1 EP 0W-20 (~PAO) Castrol GTX 20W-50 (~ Group II) 0.81

Redline 50WT Race (~ PAO) Valvoline SAE 30 ND (~ Group II) 1.46

Note that similar base oils result in alpha ~ 1 as expected but when you mix a PAO base oil even with a GTL base oil, alpha differs from 1 significantly.

Use these alpha values along with the spreadsheet provided in the original post for a lot more accurate estimates of the viscosity of the mix. Note that the order of the oils matters when you use a given alpha value -- do not exchange Oil 1 and Oil 2.

The actual empirical alpha values using the Blackstone KV100 for Oil 1, Oil 2, and Mix:

Code
Sample # alpha_empirical Name Average alpha_empirical



1 1.47 M1 EP 0W-20 - M1 FS 0W-40 1.40

2 1.41 M1 EP 0W-20 - M1 FS 0W-40

3 1.33 M1 EP 0W-20 - M1 FS 0W-40

4 0.86 GTX 5W-30 UC - GTX 20W-50 0.86

5 0.86 GTX 5W-30 UC - GTX 20W-50

6 0.79 M1 EP 0W-20 - Redline 50WT 0.85

7 0.88 M1 EP 0W-20 - Redline 50WT

8 0.89 M1 EP 0W-20 - Redline 50WT

9 0.39 M1 FS 0W-40 - Redline 50WT 0.42

10 0.45 M1 FS 0W-40 - Redline 50WT

11 0.50 GTX 5W-30 UC - Rotel. T5 10W-30 0.50

12 0.81 M1 EP 0W-20 - GTX 20W-50 0.81

13 1.46 Redline 50WT - Valvoline 30 ND 1.46

Last but not least, thank you very much, edhackett, for this great work! It's much appreciated!

Here are the data for the viscosity calculations. I tried to pick combinations that replicate common mixing practices seen on BITOG. The first is the classic 50:50 Mobil 1 0w-40 and 0W20. The rest simulated adding a quart of heavier oil to thicken things a bit, or a quart of thinner oil to thin things down a bit. There is also the practice of adding a quart of Redline as an "additive". Other mixes are intended to test the equations with differing base stocks and viscosity ranges.

As you can see, the measured viscosity varied significantly from the published "typical" viscosity in some cases. The data came from U.S.A. region PDS sheets published directly on the oil manufacture's web site. In the case of Castrol, the sheet for the GTX 20W-50 was dated 2012. The data for the Valvoline SAE 30 ND was from 2006, which was current when the oil used was purchased. The other oil's data are current.

These are the calculations I'd like to see run at a minimum:

Widman measured cSt.
Widman PDS cSt.

Gokhan's calculator measured dynamic viscosity, estimated alpha from tables in calculator(state number used).
Gohkan's calculator measured cSt., alpha 1.0 for all.
Gokhan's calculator measured cSt., estimated alpha from tables in calculator(state number used).
Gokhan's calculator PDS cSt., alpha 1.0 for all.
Gokhan's calculator PDS cSt., estimated alpha from tables in calculator(state number used).

Those combinations will allow us to see how much error is introduced by the difference in a measured viscosity vs, typical, the calculation methods, and the effect of adding an estimated alpha into the equation. Once all the data has been posted I'll post the measured values for the mixes. At that point, someone who likes to play with Excel can wrap it all up in a neat, informative table.

The oils:
Oil (Measured cSt@100C) [PDS cSt@100C, PDS density g/[email protected]]

Mobil 1 0W-20 EP(8.18) [8.6, 0.839]
Mobil 1 0W-40 FS (11.73) [12.9, 0.8456]
Castrol GTX 5W-30 ULTRACLEAN (9.56) [11.0, 0.862]
Castrol GTX 20W-50 (17.21) [18.09, 0.884]
Redline 50WT Race Oil (17.29) [19.2, 0.897]
Valvoline SAE 30 ND (10.86) [11.0, 0.889]
Rotella T5 10W-30 (11.34) [12, 0.869]

The mixes:
Oil 1(fraction) - Oil 2(fraction)

1. Mobil 1 0W-20(0.5) - Mobil 1 0W-40(0.5)
2. Mobil 1 0W-20(0.2) - Mobil 1 0W40 (0.8)
3. Mobil 1 0W-20(0.8) - Mobil 1 0W40(0.2)
4. Castrol GTX 5W-30((0.2) - Castrol GTX 20W-50(0.8)
5. Castrol GTX 5W-30((0.8) - Castrol GTX 20W-50(0.2)
6. Mobil 1 0W-20(0.5) - Redline 50WT Race(0.5)
7. Mobil 1 0W-20(0.2) - Redline 50WT Race(0.8)
8. Mobil 1 0W-20(0.8) - Redline 50WT Race(0.2)
9. Mobil 1 0W-40(0.2) - Redline 50WT Race(0.8)
10. Mobil 1 0W-40(0.8) - Redline 50WT Race(0.2)
11. Castrol GTX 5W-30(0.5) - Rotella T5 10W30(0.5)
12. Mobil 1 0W-20(0.2) - Castrol GTX 20W-50(0.8)
13. Redline 50WT Race(0.5) - Valvoline SAE30 ND(0.5)

Ed

I have finally got to calculate the empirical alpha values using the Blackstone KV100 for Oil 1, Oil 2, and Mix.

My conclusions in summary:

(1) Lederer - Roegiers equation when used with the proper alpha value works!

(2) Arrhenius equation and the Widman mixing calculator do not work!

(3) alpha values ranged from 0.42 to 1.46 in Ed's samples, greatly deviating from the Arrhenius equation and Widman mixing calculator, which assume alpha = 1.

(4) You need to have at least one measured sample to calculate the alpha empirically, from which you can calculate the viscosity for different mix ratios for the same two oils.

If you want to calculate the alpha for a given sample directly without trial and error, here is the formula:

beta = [ln(n / n2)] / [ln (n1 / n2)]

alpha = [x1 * (1 - beta)] / [ (1 - x1) * beta]

Note the parentheses. n1, n2, and n are the viscosities of Oil 1, Oil 2, and Mix, respectively. x1 is the fraction of Oil 1. Once you know the alpha for a given sample, you can calculate the viscosity for different fractions of the same two oils using:

n = n1^x1_effective * n2^x2_effective

x1_effective = x1 / (x1 + x2 * alpha)
x2_effective = 1 - x1_eff

Here are the average alpha values for Ed's samples, with the info in the parenthesis showing the approximate oil composition:

Code
Oil 1 Oil 2 alpha



M1 EP 0W-20 (~ PAO) M1 FS 0W-40 (~ GTL) 1.40

Castrol GTX UC 5W-30 (~ Gr II) Castrol GTX 20W-50 (~ Gr II) 0.86

M1 EP 0W-20 (~ PAO) Redline 50WT Race (~ PAO) 0.85

M1 FS 0W-40 (~ GTL) Redline 50WT (~ PAO) 0.42

Castrol GTX UC 5W-30 (~ Gr II) Rotella T5 10W-30 (~ Group II + GTL ?) 0.50

M1 EP 0W-20 (~PAO) Castrol GTX 20W-50 (~ Group II) 0.81

Redline 50WT Race (~ PAO) Valvoline SAE 30 ND (~ Group II) 1.46

Note that similar base oils result in alpha ~ 1 as expected but when you mix a PAO base oil even with a GTL base oil, alpha differs from 1 significantly.

Use these alpha values along with the spreadsheet provided in the original post for a lot more accurate estimates of the viscosity of the mix. Note that the order of the oils matters when you use a given alpha value -- do not exchange Oil 1 and Oil 2.

The actual empirical alpha values using the Blackstone KV100 for Oil 1, Oil 2, and Mix:

Code
Sample # alpha_empirical Name Average alpha_empirical



1 1.47 M1 EP 0W-20 - M1 FS 0W-40 1.40

2 1.41 M1 EP 0W-20 - M1 FS 0W-40

3 1.33 M1 EP 0W-20 - M1 FS 0W-40

4 0.86 GTX 5W-30 UC - GTX 20W-50 0.86

5 0.86 GTX 5W-30 UC - GTX 20W-50

6 0.79 M1 EP 0W-20 - Redline 50WT 0.85

7 0.88 M1 EP 0W-20 - Redline 50WT

8 0.89 M1 EP 0W-20 - Redline 50WT

9 0.39 M1 FS 0W-40 - Redline 50WT 0.42

10 0.45 M1 FS 0W-40 - Redline 50WT

11 0.50 GTX 5W-30 UC - Rotel. T5 10W-30 0.50

12 0.81 M1 EP 0W-20 - GTX 20W-50 0.81

13 1.46 Redline 50WT - Valvoline 30 ND 1.46

Last but not least, thank you very much, edhackett, for this great work! It's much appreciated!
how you get alpha value? Which formula you use ?
 
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