Disagreement between ASTM D1250 table 53b and calculation 1

[jmw]

I have had the following problem raised that someone may be able to help with.
I publish a density calculation spreadsheet (see link below).

I have been queried as to why my calculation results disagree with the 53b tables:
"Why isn't Dens09 produce the exact entries of table 53B?"

After some discussion we get to the following position:
"I wanted to calculate density as a function of temperature for petroleum products having a density range 620-1100 kg/m3. So i looked around the internet and the 1st application I found was yours.[JMW: he means Dens09.xls found on

http://www.viscoanalyser.com

and follow the "Downloads" link]

So I try using it but I soon discovered that the values of table ASTM D1250, vol VIII, table 53B cannot be reproduced.

So I looked further and I came across one piece of freeware and one shareware that can do the calculation and produce the exact values of table 53B.

I decided to write my own routine in MS excel to do the calculation and for this I used the quidelines of API 11.1 (American Petroleum Instiute).
The values I got however out of my routine were identical to yours.

So I try to find out where the problem is and maybe try to fix it."

So that is the question that stumped me; why do some solutions give values that correspond exactly with the tables and some, following the API guidelines not?

Can anyone help?

By the way, the freeware is Bcalc from Shell, it is a bunker fuel blending program.
The DNV Bunkermaster II program gives answers very similar to those of Dens09/xls - I say near, it quotes density to one decimal place and dens09.xls displays 2 decimal places.

The calculations in Dens06.xls actually mimic the calculation of base density used in flow/density computers which are used with fiscal inline density meters used in the oil industry... so I guess it should be important to understand why and what to do.


JMW

http://www.ViscoAnalyser.com

 

[BigInch]

I'm guessing bigtime here. Isn't ASTM a temperature only compensation and API a temperature and pressure compensation?

"Make everything as simple as possible, but not simpler." - Albert Einstein (1879-1955)
***************

http://virtualpipeline.spaces.live.com/

 

[jmw]

Both density and viscosity are affected by both temperature and pressure but the pressure effects aren't significant at low pressures.

So yes, here is a pressure correction defined but which isn't applied in my spreadsheet because in many cases it isn't necessary.

The problem here is agreement between the temperature only calculation and the tables but it is certainly worth me double checking, the obvious being missed is common glitch.

(I've got 272 pages of standard to re-read and the tables!)

JMW

http://www.ViscoAnalyser.com

 

[BigInch]

Right, not much difference until you get to 1000 psi or so.
Have fun. Let me know if you think there's something I can do.

"Make everything as simple as possible, but not simpler." - Albert Einstein (1879-1955)
***************

http://virtualpipeline.spaces.live.com/

 

[jmw]

I've been having some fun here, (I'm curious as to why this question didn't come up earlier):
Table 53B plots the observed densities (As column headers)and the the measurement temperatures using soft glass hydrometers with the volume correction for the glass built into the tables, and against each temperature the base density corresponding to the line density (column header value).

I ran my spreadsheet and got these results:

User Line Density Line Temp º C Base Density
745.6 673.00 95.00 746.88
727.9 673.00 75.00 728.89
722.2 667.00 75.00 723.13
739.9 667.00 95.00 741.19
747.1 693.00 75.00 748.11
730.3 675.00 75.00 730.81
764.6 693.00 95.00 765.89
747.5 675.00 95.00 748.78
913.7 873.00 75.00 914.94
950.6 873.00 130.00 953.07
1071.5 1033.00 75.00 1073.03
1074.9 1013.00 111.00 1077.31

Sorry, the four columns are not aligned with the headers but I'm sure that isn't going to be a problem.

"User" is the observed reading at the line temperature.
"Base density is the table column header i.e. the measured density at the observed temperature.

the final column is the calculated base density.

Compare first and fourth columns.
These are not small errors, not by my reckoning anyway, and always lower than the table values.

I'd have thought these were significant differences in the oil industry.

What ASTM D1250 says is (the interesting point is the opening section (1): “Scope”):

“Hence, the published implementation procedures are the primary standard, the distributed subroutines are the secondary standard, and the published tables are produced for convenience.”

Suggesting that:
[ul][li]they encountered errors when compiling the standard[/li]
[li] they anticipated differences between the tables and calculation [/li]
[li]whatever the calculated density, that is what we will all agree the density is irrespective of whether the calculation is right, the tables are right, neither is right[/li]
[li]The tables show density to 1 decimal place, implying we ought to agree at 1 decimal place? but we don't.[/li][/ul]

The standard calls for minimum iterations 1000 and maximum change <0.0001. Going to 10000 and 0.00001 doesn't change the calculation results at two decimal places.

Note that an inline density meter for fiscal duty will measure to 0.1kg/m3 or better.

I am now scouring the standard for any indication of what an acceptable deviation between tables and calculation is.



JMW

http://www.ViscoAnalyser.com

 

[jmw]

My correspondent on this problem has found a possible solution so any comments on this would be appreciated.

This is the interpretation we now arrive at:

The tables are arranged in columns with the column header being the observed/reported density at some temperature.
By following the table down until the measurement temperature is found, the base density is then read from the appropriate column.

The tables have a built in correction for hydrometer readings at temperatures other than the calibration temperature. That means that the column header is the actual value read off the hydrometer; the correction is in the base density values and not in the observed density. Hence the column header is not the true density at the measurement temperature.

What the calculation in Dens09.xls does is start with a true density at the measurement temperature (because it is based on vibrating tube density meters which are calibrated not only across a range of densities but also across a range of pressures and temperatures, hence they report the true density at the measurement temperature.

Not for me to say, but the tables ought surely, today when there are so many different ways to measure density at various temperatures, ought to apply the correction to the measured value rather than the base density so that the value used for the column headers is the true density? or is there some compelling reason not to do this? Well, OK, yes. What correction do you apply if you don't know what temperature to correct for I suppose but then the tables could be better arranged to tabulate the data with base density as the column header and the line density to be found against the measurement temperature.

Historical reasons is the answer, in other words or am I wrong?

I still have to validate what Excel does in iteration if the iteration limit is reached before the divergence limit (I have a query posted in the spreadsheets forum on this).

JMW

http://www.ViscoAnalyser.com

 

[protechWT]

Hi, many years ago I was a member of D2 and the relevant API MPM ch17 subcommittees. From memory, there was always a discrepancy at various densities - the standard was written in cobol I think and the "variations" only came apparent after people started using Sharp PC6 basic calculators and noticed a difference in the 4th and 5th decimal.

As you know there are four subroutine ranges in the B tables - products - and these were empirically derived from a couple of years observations of the various crude import streams around 1978 to 1982 and extrapolated to products. So AFIK the raw data was derived from many different crude densities and observed thermal cooefficients and then a few products - not lubes, table D - were also observed. There were notable diffs between resids, gasoils and gasolines - not the aromatics in D1555 - but for simplicity in custody transfer, fiscalisation and duties, it was agreed to roll out one product table, with at the time, negligible flaws. Participants included major oil cos, USCustoms and various interested parties. Most of the people involved are probably out of the business now but I remember a few names if you're interested - email me and I'll give you some leads.

The tables were always a compromise because of the 0.5 rounding that was necessary to reduce the size of the computations to one manageable booklet. There are a couple of oil companies which produced and printed their own tables to 0.1 density and degsF, and this resulted in a shelf of telephone books with only marginal increase (or decrease) in accuracy so after 10 years these were abandoned. I did an arbitration once where all data was referred back to volume 10 and 11 subroutines but the fiscal difference was always very minor and the real errors were always gross temperature and liquid level, not cumulative rounding. Sidewall bulges in 500kBbl steel lakes are more of a problem than density errors.

Here is my 1998 attempt to make the API60/60/Density15C conversion incorporate the density ranges.

c8: API number to 1 decimal, range name is REQUEST

e8: @ROUND(141.5/(131.5+REQUEST),4)

f8: @ROUND(@IF(E8<0.5549,E8+0.0002,@IF(E8<0.5859,E8+0.0001,@IF(E8<0.6249,E8,@IF(E8<0.6799,E8-0.0001,@IF(E8<0.7399,E8-0.0002,@IF(E8<0.7929,E8-0.0003,@IF(E8<0.8599,E8-0.0004,@IF(E8<0.9539,E8-0.0005,@IF(E8<1.0489,E8-0.0006,0))))))))),4)

we're working in vac not air. It doesn't help that the former soviet countries use density at 20C/68F - there was ASTM work begun on a table 20, to provide for relative densities at 68F but it was fraught with issues of which density data to use for products, fuel oil observations from Baytown or Constantia?
BRgds
WT

 

[byrdo]

More Help needed on this topic; Can someone help answer this:

Why does ASTM D 1250 use 8.328 lb/gal as the density of water at 60F. Based on all of my reference books, 8.3372 lb/gal is the correct density for water at 60F. This is driving me crazy because I get a different density when converting from Spec Gravity than given in 1250-80 Vol XI/XII. Does this have something to do with apparent density vs observed density?

Matt

 

[jmw]

ProtechWT,
thanks for our post and information. I may well come back to you for some further information and advise.

Since I started this spreadsheet solution i have had some invaluable collaboration which has resulted in the current version "Density 12Mb rev 01.xls" (to be found on the downloads page of the

http://www.Viscoanalyser.com

web site) and i gather that it is seeing some use out there with at least one Bunker Survey company using it and reporting good results when sued with marine fuel oils. I get periodic requests for for the password so I assume either some people are modifying the spreadsheet sill further or they simply want to make it anonymous. Fair enough.

However, a further iteration is in the works and I'd appreciate any feedback, bearing in mind this is intended to be a practical, rather than exact interpretation of the standards:
The next change is to include the pressure correction.
I am going to assume that in most cases the density will be measured online using such devices as vibrating element sensors, coriolis, vibrating tube and vibrating fork etc. where density may be measured under analyser conditions but where these conditions may vary from other process conditions eg meter runs, so no hydrometer corrections for the observed and alternative conditions but since I still need to go via the base conditions, if I want the alternative conditions then I don't need hydrometer corrections for the base temperature and pressure conditions but I will if the user wants to compare to lab measurements at atmospheric pressure.

All well and good, and I guess I can come up with a suitable combination of calculations and sequence but the big difference here is the lack of real data to check against. hen doing the temperature density conversions there were always the tables to compare to but I now need some reference data to compare for pressure corrections. I did manage to obtain a small set of data from one of the oil companies some time ago but if anyone can point me to any such data please do.

Byfro, I hope someone can answer your question for you and for me.

JMW

http://www.ViscoAnalyser.com