At this stage, the only figure available is that stated by the supplier on the BDR.

Table B shows the opening readings, before discharge, of the barge. The stated density of the product being 990kg/m3. From this it may be seen that the total observed volume is 1236.758m3, which relates to the standard volume at 15°C which is 1208.682m3. The VCF is taken from Table 54B for the measured temperature.

The total volumes delivered by the barge, both for observed and standard temperatures, can be found by subtracting the closing volumes from those at the start:

The observed volume transfer = 1236.758 - 144.949
= 1091.809 m3.
The standard volume transfer = 1208.682 - 141.861
= 1066.821 m3.

As already defined, density is the absolute relationship between mass and volume and not its weight to volume, by definition density is in vacuo. To convert weight in vacuo to weight in air, reference must be made to Table 56 of ISO 91-1. An extract of this table is shown in Table D.

The theoretical weight transferred in air:

= Density (kg/m3) * Standard volume at 15°C(m3)
x Factor = kg * kg/1000 = (MT)
= 990.0 x 1066.821 x 0.99895 = 1055043.7 kg
= 1055.044 MT

The value of 1055.044 MT represents the weight of fuel transferred in air, based uponthe density given on the BDR. In order to determine the actual weight transferred, the density of the fluid delivered must be determined. This determination can either be by on-board testing or after laboratory analysis.

Assuming that the density determined from a representative sample of the bunkering is 985.1 kg/m3, the actual weight transferred in air:

= 98.51 * 1066.821/1000 * 0.99895 = 1049.82 MT

If the density is not determined from a representative sample, the BDR should be signed only for volume. If the supplier insists on a signature for weight, add “for volume only - weight to be determined after density testing of a representative sample”.

Comment

The example calculation given for a fuel delivery changed the actual delivery from:

Opening Closing
1224.39 - 144.949 = 1079.44 Changes to 1049.82 MT a saving of 29.62 MT or $2962 at $100/MT

Table A) Extract of Table 54B of ISO 91-1 Generalised products factor for correcting volume to 15°C (VCF)

Table B) Barge opening readings. Table B shows the opening readings, before discharge, of the barge. The stated density of the product being 990kg/m3. From this it may be seen that the total observed volume is 1236.758m3, which relates to the standard volume at 15°C which is 1208.682m3. The VCF is taken from Table 54B (above) for the measured temperature.

Table C) Barge final readings

Table D) Extract of Table 56 of ISO 91-1