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Viscosity Extrapolation to 150°C #5436797 05/23/20 02:53 PM
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Boxnuts Offline OP
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In order to pursue Harman index, etc, calculations, the first step is to extrapolate the viscosity data to 150°C. But there have been warnings that the formula cannot be relied upon.

First some background.
Extrapolation is usually done with the help of online calculators and Apps for your phone or tablet. E.g. Widman.
The "standard" calculation of the variation of oil viscosity is based on the ASTM-Walther formula.
log(log(KV+0.7)) = A+B log T
Where
KV is the kinematic viscosity
T is the temp in Kelvin and A & B are constants unique to each oil.
This is the formula behind online calculators and the straight line graphs of log log data.
The advantage of this formula is that it only has two constants and therefore we only need two sets of data to solve for the constants A & B, usually the 40 and 100°C points. When you enter data into the calculator the first thing it does is solve for A& B and it then calculates for any other temperature.
The ASTM version with the 0.7 figure is said to be a good fit for light crudes and base stocks, however we are now interested in finished multigrades, PAO's, GTL's, etc.

So I have gone back to the fuller version of the formula which has another variable C instead of the 0.7.

This formula which I refer to as the Walther 3 formula is now
log(log(KV+C)) = A+B log T . To solve for A,B,C, 3 sets of data are now required.

So how do different C constants affect the extrapolation to 150 degs?

https://i.postimg.cc/1RHfdP4Y/Variable-C-Constants.png

The chart shows how an oil will deviate from the "standard" C=0.7 calc, when it's viscosity is calculated with different C constants.
Considerable deviations from standard are apparent at low and high temps. Percentage differences are shown because at full scale the deviation at high temperature would not be visible.
As can be seen at high temperatures negative deviations up to -10% can be expected for oils with high C const such as PAO oils, meaning the KV150 is 10% less than the standard calculation.
GTLs, and ANs are close to standard with less than ±4% difference. Oils with different viscosities will have different deviations from standard.
Other oils have been investigated and as an example this chart shows the variation of the C const in a range of oils from the Shear Thinning paper by Hugh Spikes et al.

https://i.postimg.cc/Qdwnp23f/1-to-17b-C-constants.png

Oils #1-#10 are simple base + VM
Oils #11-#17 are fully finished
Oils #1-11b-#17b are base oils + detergent inhibitor but no VM

It can be seen from these figures is that the effect of VM's is to lower the C constant while the "purer" oils have higher figures. The base oils without VM's are between 0.95 and 1.59 Oils #2 and #10 have extreme figures, presumably the effects of large amounts of VM's.
Finally, it would seem that there can be both positive and negative differences in extrapolation depending on the oil type, but if you are dealing with a finished oil and you don't know the C const, which is normally the case, as a rule of thumb calculate the KV150 as standard and add 10%.

Re: Viscosity Extrapolation to 150°C [Re: Boxnuts] #5439817 05/26/20 11:31 PM
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Gokhan Offline
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Hi there, you seem to have made a mistake. See column J in my spreadsheet in the HTFS thread. I only get a few percent difference from ASTM D341 for most oils except for oils #2 and #10. There is a link to my spreadsheet with the calculations there.


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Re: Viscosity Extrapolation to 150°C [Re: Gokhan] #5446888 06/05/20 12:44 PM
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Hi Gokhan

Thank you for your reply, straight to point as usual.

I was attempting to show the possible problems with extrapolating beyond the data points using the Walther astm341 simple formula.
I was comparing astm341 with the enhanced Walther 3 with variable C constants. So this is not the same as your spreadsheet.
The "error" figures you referred to in your spreadsheet are differences between the Vogel formula and astm341.
Fundamentally, the problem is Extrapolation, it's a journey into the unknown, nobody knows what is accurate.
I am looking for actual measured viscosity data that is above 100°C to try and determine which formula is best for extrapolation, so far I have found data for two reference oils up to 130 and 150°C. Initial figures indicate that the enhanced Walther 3 is close, astm341 not bad, and Vogel surprisingly less accurate. Two samples of cause does not prove anything, if anybody has more such data please tell me know where.

In the chart in the previous post I did get a cell ref wrong and got some high figures. Thank you for pointing that out. That's the problem with spreadsheets, get the first col/row wrong and they're all wrong.
It does seem there is no way to edit your own posts otherwise I could just update the chart, so I will have to delete it at source.

Thank you for pointing me towards your spreadsheet on shear thinning which I hadn't looked at before.
I no longer use the ASTM calculation for density. Other scientific papers including the Shear Thinning paper all use linear density extrapolation and together with my own analysis of published density data indicating that linear is the best fit. The difference is almost negligible but it's a lot easier and you don't have to solve quadratic equations. I use the TREND formula a lot, does everything in one go.

One thing that puzzles me. The theory is that base oils don't shear, if so, shouldn't the Harman index for the base oils #18 and #1-11 be close to 1.0, they appear to be 0.75 and 0.78 respectively, not what I would expect.

Re: Viscosity Extrapolation to 150°C [Re: Boxnuts] #5447346 06/06/20 12:08 AM
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Gokhan Offline
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Originally Posted by Boxnuts
One thing that puzzles me. The theory is that base oils don't shear, if so, shouldn't the Harman index for the base oils #18 and #1-11 be close to 1.0, they appear to be 0.75 and 0.78 respectively, not what I would expect.

Hi there, that's not what I got. See this older spreadsheet for example:

https://docs.google.com/spreadsheets/d/1kS-prIQdDC5Ul_k__yTAQuv7DRI4hjA4ha5WUtPHtE8/edit?usp=sharing

Note that the Vogel coefficients are for the dynamic viscosity, not the kinematic viscosity.

To extrapolate the density, I first calculated α in the exponential density formula from 40° C to 100° C using density = DV_Vogel / KV_measured. When I extrapolated the density to 150 °C, I used that α and the density from Vogel at 100 °C. When I extrapolated density to 15.6 °C (60 °F), I used that α and the density from Vogel at 40 °C.


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Re: Viscosity Extrapolation to 150°C [Re: Boxnuts] #5451428 06/11/20 03:32 PM
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userfriendly Offline
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Have a look at;

ASTM D5621, 2603,6022, 7109, 6278 and E1875

I posted HPL's 10W20 in their thread, as that pcmo might be of interest to this discussion.

Re: Viscosity Extrapolation to 150°C [Re: userfriendly] #5453473 06/14/20 07:25 AM
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Originally Posted by userfriendly
Have a look at;

ASTM D5621, 2603,6022, 7109, 6278 and E1875

I posted HPL's 10W20 in their thread, as that pcmo might be of interest to this discussion.

Hi
Sorry, You've lost me. What thread?

Re: Viscosity Extrapolation to 150°C [Re: Boxnuts] #5453494 06/14/20 07:49 AM
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Originally Posted by Boxnuts
Originally Posted by userfriendly
Have a look at;

ASTM D5621, 2603,6022, 7109, 6278 and E1875

I posted HPL's 10W20 in their thread, as that pcmo might be of interest to this discussion.

Hi
Sorry, You've lost me. What thread?


He's referring to this thread: A Trip to High Performance Lubricants

He's referring to the PCMO 10w-20 which has a KV100 of 8.89 cSt, KV40 of 57.42 cSt, and HTHS of 2.9 cP.

Here's the PDS for their PCMO line: High Performance Lubricants PCMO PDS

Here's the PDS for their HDEO line: High Performance Lubricants HDEO PDS


"He who is without oil, shall throw the first rod." - Compressions 9:1
Re: Viscosity Extrapolation to 150°C [Re: Boxnuts] #5453635 06/14/20 10:27 AM
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That's right.Basically a shear stable SAE20 for engines that don't need 0W or 5W winter performance.

www.researchgate.net/publications/3...rrelated_to_Hydraulic_System_Performance

Re: Viscosity Extrapolation to 150°C [Re: userfriendly] #5453649 06/14/20 10:42 AM
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Originally Posted by userfriendly
Have a look at;

ASTM D5621, 2603,6022, 7109, 6278 and E1875

I posted HPL's 10W20 in their thread, as that pcmo might be of interest to this discussion.

All the High-Performance Lubricants HPL PCMO and HDEO SAE grades are in my calculator:

HTFS (base-oil + DDI-package viscosity (full-shear viscosity) at 150 °C) and VII-content calculator


2020 Toyota Prius Prime XLE plug-in hybrid, 2ZR-FXE engine, ~ 65 mpg on regular gasoline, ~ 5,000 mi
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Re: Viscosity Extrapolation to 150°C [Re: Boxnuts] #5453712 06/14/20 12:25 PM
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Gokhan, does your calculator account for different SSI ratings of different viscosity index improvers? Obviously an oil with a VII that has an SSI of <20 would be more shear stable than one with an SSI of 50 at the same concentration.


"He who is without oil, shall throw the first rod." - Compressions 9:1
Re: Viscosity Extrapolation to 150°C [Re: Boxnuts] #5453717 06/14/20 12:45 PM
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researchgate.net/publication/323417763_temporary_and_Permanent_Viscosity_Loss_Correlated_to_Hydraulic_System_Performance

That is the link which drops out when I put the www. in www.researchgate.net

Re: Viscosity Extrapolation to 150°C [Re: RDY4WAR] #5453932 06/14/20 06:40 PM
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Gokhan Offline
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Originally Posted by RDY4WAR
Gokhan, does your calculator account for different SSI ratings of different viscosity index improvers? Obviously an oil with a VII that has an SSI of <20 would be more shear stable than one with an SSI of 50 at the same concentration.

The "VII" output in the calculator represents the temporary shear of the VII, not the actual VII content, which is given by the temporary shear stability of the VII (temporary-shear-stability index (temporary SSI)) and actual VII content. Note that the temporary SSI and permanent SSI are not related. Therefore, "VII" output gives the relative VII content only if the same VII is used. It is equal to (1 - A_Harman index) / 2, which is the temporary shear of the VII divided by a factor of 2.

"HTFS" output depends on the ratio of the actual temporary-shear rate and actual viscosity-boost rate of the VII, but these two are proportional and tend to cancel each other to an extent.

Usually the main sources of error are the errors in the data sheets from which the input values are taken and the ASTM D341 extrapolation, which doesn't work for a comb-type PMA VII for example.


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Re: Viscosity Extrapolation to 150°C [Re: userfriendly] #5453943 06/14/20 06:46 PM
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Originally Posted by userfriendly
researchgate.net/publication/323417763_temporary_and_Permanent_Viscosity_Loss_Correlated_to_Hydraulic_System_Performance

That is the link which drops out when I put the www. in www.researchgate.net

You need to use the [Linked Image] "insert link" button.

Temporary and permanent viscosity loss correlated to hydraulic-system performance


2020 Toyota Prius Prime XLE plug-in hybrid, 2ZR-FXE engine, ~ 65 mpg on regular gasoline, ~ 5,000 mi
TGMO 0W-16 SN/RC Japan
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