Recent Topics
Thoughts on the GM strike?
by Vern_in_IL - 09/19/19 09:37 PM
tropical storm imelda blows up everynight?
by motor_oil_madman - 09/19/19 09:12 PM
2017 Corvette / Mobil 1 ESP 0w40 / 5.2k mi
by dparm - 09/19/19 08:57 PM
2019 Lexus UX 250h
by Direct_Rejection - 09/19/19 08:56 PM
Gas theft
by tahoe_hybrid - 09/19/19 08:04 PM
Aisin 09G transmission fluid?
by sloinker - 09/19/19 07:44 PM
Oil for 2005 BMW X3
by Nyquist - 09/19/19 07:34 PM
Golden Eagles Take Down Deer and Wolves
by buster - 09/19/19 07:31 PM
P21S Windshield Washer Booster
by mclasser - 09/19/19 06:30 PM
Why warm up oil before a UOA sample is taken?
by paulri - 09/19/19 06:21 PM
Selling the 97 Camry V6 again
by PandaBear - 09/19/19 05:15 PM
FRAM Orange Cans
by KevGuy - 09/19/19 05:13 PM
Hill billy down spout
by P10crew - 09/19/19 05:04 PM
Colt Ceases Civilian AR-15 Production
by billt460 - 09/19/19 04:50 PM
Amsoil “synthetic technology”
by spiderbypass - 09/19/19 03:15 PM
Oil Change Special @ Firestone
by Mad_Hatter - 09/19/19 01:05 PM
Newest Members
Srfridd, V1313, Ecan89, ProBest, Zolton
69333 Registered Users
Who's Online Now
83 registered members (ACC, 330indy, 4WD, AdditiveOCD, 2002 Maxima SE, 10 invisible), 1,714 guests, and 21 spiders.
Key: Admin, Global Mod, Mod
Forum Statistics
Forums67
Topics294,799
Posts5,066,829
Members69,333
Most Online3,532
Jul 30th, 2019
Donate to BITOG
Print Thread
Hop To
Page 2 of 2 1 2
Re: Calculator for viscosity mixing based on the Lederer - Roegiers equation [Re: Gokhan] #5198359 08/27/19 08:49 PM
Joined: Jun 2003
Posts: 2,008
E
edhackett Online Content
Online Content
E
Joined: Jun 2003
Posts: 2,008
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 [email protected]) [PDS [email protected], 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



Last edited by MolaKule; 08/28/19 01:07 AM.

Never attribute to engineers that into which politicians, lawyers, accountants, and marketeers have poked their fingers.
Re: Calculator for viscosity mixing based on the Lederer - Roegiers equation [Re: Gokhan] #5199994 08/29/19 03:54 PM
Joined: Jun 2003
Posts: 2,008
E
edhackett Online Content
Online Content
E
Joined: Jun 2003
Posts: 2,008
I received a PM from Gokhan and he indicated that he would like someone else to do the calculations using his calculator at this time. I'll excuse myself from doing the calculations as I've seen the results and don't want to chance introducing any unintentional bias into choosing a value for alpha.

Garak, MolaKule, Shannow, or anyone else who would like to plug in the numbers, please feel free to do so.

Ed


Never attribute to engineers that into which politicians, lawyers, accountants, and marketeers have poked their fingers.
Re: Calculator for viscosity mixing based on the Lederer - Roegiers equation [Re: Gokhan] #5201755 08/31/19 10:48 PM
Joined: Dec 2010
Posts: 4,465
G
Gokhan Offline OP
OP Offline
G
Joined: Dec 2010
Posts: 4,465
Great work, Ed!

I was able to get to it briefly.

I tested both spreadsheet calculators in my original post -- the first one using only the kinematic viscosities (KV) and the second one also using the densities. The error in using the simpler calculator was between +0.00% and +0.06% -- always very slightly overestimating the KV of the mix -- and it's obviously entirely negligible given the accuracy of the KV values. Therefore, from now on, I will only use the Lederer - Roegiers formula, which is

n = n1^x1_effective * n2^x2_effective

with

x1_effective = x1 / (x1 + x2 * alpha)
x2_effective = x2 * alpha / (x1 + x2 * alpha)

so that I plug in the KV values into the n's instead of bothering to convert them into the dynamic viscosity (DV).

Using alpha = 1, here are the results for the KV100 of the mix in cSt. I calculated them both using the Blackstone values (first column) and PDS values (second column).

Code
Mix #    Lab      PDS

 1	 9.80    10.53
 2	10.91    11.90
 3	 8.79     9.33
 4	15.30    16.38
 5	10.75    12.15
 6	11.89    12.85
 7	14.89    16.35
 8	 9.50    10.10
 9	16.00    17.73
10	12.68    13.97
11	10.41    11.49
12	14.83    15.59
13	13.70    14.53


As far as the alpha is concerned, it can only be determined empirically. When the experimental results are presented, we can calculate the alpha to see if it makes sense.

A concern that remains is the accuracy of the Blackstone KV measurements. Typical commercial viscometers seem to have an accuracy around ±3%. Therefore, we shouldn't expect an agreement with the theory beyond about ±4%, which is about ±0.4 cSt, when two different oils with measured viscosities are mixed. In fact Wear Check told me that the error in a single KV measurement is "less than ±0.5 cSt," which is consistent with this observation: accuracy around ±0.3 cSt for a single oil and ±0.3 cSt × √2 ~ ±0.4 cSt for two different oils mixed together.


2020 Toyota Prius Prime XLE plug-in hybrid, 2ZR-FXE engine, ~ 0,000 M
TGMO 0W-16 SN Japan
OEM spin-on oil filter Japan
Re: Calculator for viscosity mixing based on the Lederer - Roegiers equation [Re: Gokhan] #5202742 09/02/19 11:18 AM
Joined: Jun 2003
Posts: 2,008
E
edhackett Online Content
Online Content
E
Joined: Jun 2003
Posts: 2,008
Originally Posted by Gokhan

Using alpha = 1, here are the results for the KV100 of the mix in cSt. I calculated them both using the Blackstone values (first column) and PDS values (second column).

Code
Mix #    Lab      PDS

 1	 9.80    10.53
 2	10.91    11.90
 3	 8.79    9.33
 4	15.30    16.38
 5	10.75    12.15
 6	11.89    12.85
 7	14.89    16.35
 8	 9.50    10.10
 9	16.00    17.73
10	12.68    13.97
11	10.41    11.49
12	14.83    15.59
13	13.70    14.53


Here's the Widman data including the lab values for the mixes:

Code
Mix #    Lab   PDS      Lab Actual

 1	9.77    10.49   10.14
 2	10.89   11.86   11.11
 3	8.77    9.30    8.95
 4	15.21   16.31   15.08
 5	10.69   12.10   10.61
 6	11.73   12.64   11.38
 7	14.75   16.17   14.66
 8	9.42    10.00   9.37
 9	15.96   17.68   14.86
10	12.65   13.93   12.20
11	10.40   11.49   10.12
12	14.69   15.45   14.44
13	13.63   14.42   13.12


OK, you statisticians, have fun!

Ed

Last edited by MolaKule; 09/08/19 05:15 PM.

Never attribute to engineers that into which politicians, lawyers, accountants, and marketeers have poked their fingers.
Re: Calculator for viscosity mixing based on the Lederer - Roegiers equation [Re: edhackett] #5202938 09/02/19 04:06 PM
Joined: Jun 2003
Posts: 2,008
E
edhackett Online Content
Online Content
E
Joined: Jun 2003
Posts: 2,008
Darn it, friggin dyslexia! Even after checking the table twice, I managed a Typo. The measured viscosity of mix #7 should read 14.75 not 17.75. Could one of the moderators please correct the table?

Ed


Never attribute to engineers that into which politicians, lawyers, accountants, and marketeers have poked their fingers.
Re: Calculator for viscosity mixing based on the Lederer - Roegiers equation [Re: Gokhan] #5210611 09/12/19 01:46 AM
Joined: Dec 2010
Posts: 4,465
G
Gokhan Offline OP
OP Offline
G
Joined: Dec 2010
Posts: 4,465
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!


2020 Toyota Prius Prime XLE plug-in hybrid, 2ZR-FXE engine, ~ 0,000 M
TGMO 0W-16 SN Japan
OEM spin-on oil filter Japan
Re: Calculator for viscosity mixing based on the Lederer - Roegiers equation [Re: Gokhan] #5211354 09/13/19 03:07 AM
Joined: Sep 2019
Posts: 58
L
Lowflyer Offline
Offline
L
Joined: Sep 2019
Posts: 58
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?


On the arduous way...to learn...English.
Page 2 of 2 1 2
Previous Thread
Index
Next Thread

BOB IS THE OIL GUY® Powered by UBB.threads™