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Jon Watson
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Density measurement by hydrometer.... discrepancies?
I produced a spreadsheet (download from www.viscoanalyser.com download page: Density 12MD.xls).
A user contacted me to say it was inaccurate.
He measured 740.6kg/m3 at 33degC and from tables got a base density of 755.4kg/m3.
The spreadsheet said 755.53kg/m3.
He then said that an industry program also gave 755.4kg/m3.
I discovered that the DNV PS program BunkerMaster also gave 755.4 kg/m3.
This was a puzzle.
My spreadsheet, which is calculation based, does indeed give 755.53kg/m3.
I then decided to try incrementing the density values either side of the observed density and found some odd results.
Table 53B is produced by calculation from empirical data such that it has 0.25degC temperature increments and 2.0kg.m3 density increments and we are allowed to interpolate the density but not the temperature.
So I went to my copy of 53B (which is reproduced in the May 2004 Manual of Petroleum Measurement Standards).
The two observed density columns of interest are 739 and 741 kg/m3.
At 33degC the corresponding values are 754.9 and 755.9kg/m3 so when I interpolate from the tables I get a base density of 755.5 kg/m3, not 755.4kg/m3.
I tabulated some results:
33°C 739.0 739.2 739.4 739.6 739.8 740.0 740.2 740.4 740.6 740.47 740.8 741.0
53B (RMI) 754.9 755.1 755.3 755.5 755.7 755.9 756.1 756.3 756.5 n/a 756.7 756.9
53B (GM) n/a n/a n/a n/a n/a n/a n/a n/a 756.4 n/a n/a n/a
Oil Survey 754.9 754.9 755.4 755.4 755.9 755.9 755.9 756.4 756.4 n/a 756.9 756.9
DNV PS BunkerMst 754.9 754.9 755.4 755.4 755.9 755.9 755.9 756.4 756.4 n/a 756.9 756.9
Density 12MD.xls 754.95 755.14 755.34 755.54 755.74 755.94 756.13 756.33 756.53 756.40 756.73 756.92
Density 12MD.xls (rounded) 754.9 755.1 755.3 755.5 755.7 755.9 756.1 756.3 756.5 n/a 756.7 756.9
(I hope you can get the table format back...cut and apset into word or excel maybe?)
This showed that the two programs do the same thing and they limit the density increment to 0.5kg/m3 steps.
Any observed density from 740.3 to 740.7 gives the same answer - 755.4kg/m3.
This posed two questions:
Why not interpolate as permitted by the MPMS in which case the answer would have been 755.5kg/m3?
I guess the industry does not want people actually calculating things, especially during bunkering, and it would make sense to expand the tables by interpolation. SO all the operator does is round the observed density to the nearest value and read of the result. No calculations and not interpolations. I guess 0.5kg/m3 is a reasonale compromise increment.
So am I right? Are the tables used in the industry pre-interpolated versions of the original 53B? or is there some other explanation entirely?
i.e. instead of observed densities 739 and 741 we would have added columns of calculated interpolations at 0.5 kg/m3 intervals i.e. at 739.5, 740.0 and 740.5.
That would means the 740.6 observed value would be rounded to 740.5 and the base density is then 755.43 (by calculation) and 755.4 in these pre-interpolate tables that I guess may be being used.
In this way a base density of 755.53 has been parleyed down to 755.4kg/m3.
Posted: 1/15/2010 10:51:01 AM
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Jon Watson
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RE:Density measurement by hydrometer.... discrepancies?
Panic over.
I have been advised that a great many use one or other of this type of program and the results are "good enough".
A simple way the mechanism can work is for the hydrometer reading to be rounded to the nearest 0.5 and hat would account for the answers.
Doing the same rounding before entering the hydrometer reading would allow the spreadsheet to reproduce the same results as the programs.
Of course, whether this remains "good enough" is a question.
A number of the larger shipping companies have fitted coriolis meters on their vessels and they potentially measure density to fiscal standards.
That means that they will be working to two decimal places and the current use of hydrometers will seem rather coarse in comparison.
I suggest this is going to require some careful thought when it comes to litigation and the industry has a history of mutual suspicion between suppliers and vessels that such differences will not help.
There will be a suspicion amongst some suppliers that any time the density they quote is higher than the density the vessel quotes, the vessel will challenge their readings but any time the density they quote is lower than the vessel readings there will be silence.
The industry will need to sort out how to resolve these disputes not just where the two readings are within repeatability and reproducibility limits of each other, but where major differences emerge.
Posted: 1/21/2010 9:29:29 AM
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