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# Weight of heavy fuel oil2

## Weight of heavy fuel oil

(OP)
Hello everybody:

As an exercise, in our power plant I am trying to calculate the engines specific fuel consumption via an alternative procedure, in order to corroborate the proper operation of the fuel mass flow meters.

I will try to put it as clear as I can do.

Heavy fuel oil: Bunker C (distillate Nº 6), density @ 15ºC = 996,6 kg/m³ = 3,77 kg/gallon, LHV = 17.374 BTU/lb (9.652 kcal/kg).

Point One = Storage day tank:
Temperature of fuel: 98º C.
Volume of fuel delivered: 46,23 m³.
Volume Correction Factor at this temperature: 0,9480.
Corrected volume @ 15º C: 46,23x0,9480 = 43,83 m³.

Point two = engines inlet:
Temperature of fuel: 120º C.
º API = 11,3 , this gives a density of 990,3 kg/m³ and a weight of 3,74 kg/gallon (8,25 lb/gallon).
Mass of fuel (measured by the fuel mass flow meters): 43.655 kg.
Volume Correction Factor at this temperature: 0,9340.
Corrected volume @ 15º C: 46,23x0,9340 = 43,18 m³.

And here comes my confusion. What value do I have to use in order to calculate the density ( and then the weight) of the fuel at the inlet of the engines?

Density = 43.655 kg/46,23 m³ or divide by 43,83 m³ or 43,18 m³.

According with the data displayed on the PLC, the density is 943 kg/m³ = 3,57 kg/gallon (this is almost 43.655 kg/46,23 m³).

Any comment on this subject, particularly the  interpretation of the ºAPI values (specific gravity, Volume Correction Factor) are welcome.

### RE: Weight of heavy fuel oil

At first sight:

Question: why do you apply the volume correction factor at 120 Celsius to 46.23 m3, which is the volume measured at 98 Celsius ?

Degrees API are related to the specific gravity 60/60oF = 15.56oC, which is dimensionless, not to a density [kg/m3]. By definition:

oAPI = [(141.5÷Spgr60/60) - 131.5]

The mass at 15 Celsius as measured by the flow meter: 43,655 kg.
The mass using the density and the corrected volume in the day tank: 996.6 × 43.83 = 43,681 kg.

The difference (instrument error) related to the tank measurement is:

100 × (43,681-43,655) ÷ 43,681 = 0.06% !

### RE: Weight of heavy fuel oil

I assume that you periodically sample the fuel from the supply to the engine e.g. from the mixer tank in the high pressure circuit, and measure its actual 15degC density.

In which case you need simply log the temperature at the fuel flow meters, calculate the density at these temperatures and thence determine the mass of fuel; it then, of course, doesn't matter what the fuel temperature is at the engine since the mass rate will be unaffected.
The link below takes you to a couple of useful spreadsheets for viscosity and for density. The density sheet allows you to determine the density at the flowmeters from the density at 15degC by reverse API calculation.

Of course, if you have only a conventional viscometer for fuel oil heater control, then you can only find the density from the samples and you are then limited by the frequency of sampling.

But, if it is a 7829 Viscomaster digital viscometer it will not only report the true kinematic viscosity, but it will also report (via RS232/485) the Ignition Index, the density at 15degC, at 98degC and at operating temperature (e.g. 120degC) and the kinematic viscosity at 100degC.
You can log this data to a spreadsheet and if you also input your flowmeter data and temperature you could automate the mass flow calculation.

I assume that you do not rely on the fuel suppliers certificate for the density nor on samples "as received" but do frequently sample and measure the density.

Fuel in storage will generally stratify to some degree so the fuel density will progressively decrease as the fuel is used.
The variation might not be significant but much depends on how the fuels are managed in storage and if different batches of fuel are kept segregated.
Density (and viscosity and hence fuel temperature at the engine) may vary significantly from one batch to another and as fuel is consmed.

Nor can one rely of the data in the suppliers fuel certificates because even oil majors tend to quote the generic properties and others may quote "typical" or "less than". It is difficult to determine when, if ever, the fuel certificate declares the actual properties of the fuel supplied (one test agency reports that over 50% of fuels sampled reveal a density error of more than 3kg/m3 from the certificate value).

Then too fuel oil may be adulterated between the source and storage (most commonly with water but also with waste chemicals).

If you follow this link you will find two spreadsheets useful for both the viscosity and density calculations:
http://www.viscoanalyser.com/page8.html

PS: volumetric flowmeters are usually calibrated at a set of reference conditions.
If the operating temperature was declared to be 98degC when calibrated and they operate at this temperature then the volume flow total will be as calibrated.
If not, then the meters will have an inherent error due to temperature and may register a greater volume flow than is correct (due to the expansion of the measuring chamber but possibly offset by increased slip flow). You may need to clarify with the manufacturer how the meters were calibrated and if the temperature errors are significant or not.

### RE: Weight of heavy fuel oil

Sorry, there is a PS:
fuel oil is usually measured by volume and sold by weight. The amount invoiced will thus depend on the nominal density value used.

There are many ways in which the weight of fuel supplied can be over-estimated and the most common are false temperature and false density statements.

Reconciling fuel used with fuel supplied (especially if some extra water has been added) may prove difficult.
The low cost of heavy fuel oils often means a lack of instrumentation and in turn this means the client is vulnerable to genuine errors and deliberate frauds.
At one power plant the engineers had to drain off the entire fuel stock because "it contained so much water you could shower in it".

### RE: Weight of heavy fuel oil

(OP)
Hello everybody:

25362: About your question, from the day tank a volume of 46,23 m³ @ 98º C is leaving the tank with a density of around 940 kg/m³. This same volume goes a few meters to the booster unit, where it is measured by the flow meter. After this, the fuel is heated up to 120º C prior to the entrance to the engines. That is why I think I have to consider to work with the corrected original volume of fuel (46,23 m³) because at this point the fuel has a temperature of 120º C, a different density value and a different volume.

In your post you state that the value displayed by the flow meter is at 15º C. Do I have to think that this value is a corrected one?

I still feel a little bit confused

### RE: Weight of heavy fuel oil

Regarding the flow meter I shouldn't have written a temperature, since the flow meter gives you a mass value, the same at any temperature. 15 Celsius was just mentioned as an indication to compare with the density and volume at this temperature.

As for the correction, the volume is not any more 42.63 m3 when heated to 120 Celsius. Thus the correction is not applicable to this volume but to a volume
42.63×0.9480÷0.9430 = 42.86 m3
which, when multiplied by the correction factor, results in the same volume at 15 Celsius as before.

### RE: Weight of heavy fuel oil

(OP)
Hello everybody:

According to the data, the last calculation should be:
volume of fuel at 120º C = 46,23x0,9480÷0,9340 = 46,92 m³, multiplied by the correction factor at 120º C gives 43,83 m³; the same value of the volume supplied by the day tank at 98º C.

Just before the inlet to the engines, chemical lab personnel took samples of fuel and then obtain 11,3º API @ 40º C, which in turn gives a specific gravity of 990,9 (a density of 990,9 kg/m³) and a weight of 3,75 kg/gallon (8,27 lb/gallon).

Then, the mass of fuel is: 43,83x990,9 = 43.431 kg

### RE: Weight of heavy fuel oil

(OP)
Hello everybody:

I am sorry for the delay, but here go for you a constellation. Gracias !

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