Figure 8.1 Cargo calculations — correction for trim
It is usual for tank calibration tables to be presented assuming that the ship is on an even keel. Accordingly, where the tank gauge is not situated at the tank's geometric centre and if the ship is trimmed, a correction to the measured liquid level is necessary in order to enter the calibration table to get the correct liquid volume. This deviation from the correct liquid level is indicated on the diagram by the distance between the gauge-float and the even-keel liquid level.
8.2.2 List correction
Figure 8.2 shows a prismatic tank on a ship which is listed to port. In other words the ship's port side draft is greater than the starboard side draft. As can be seen, with the ship in the listed condition, the liquid level in the tank remains parallel to the waterline. Accordingly, and taking the port side tank as an example, at the outer bulkhead the liquid level rises by the amount a/a'. However, if the ship was upright, the liquid level would be as shown by the dashed line on the diagram.
Figure 8.2 Cargo calculations — correction for list
It is usual for tank calibration tables to be established assuming the ship to be upright (having a zero list). Accordingly, where the tank gauge is not situated centrally and if the ship is listed, a correction to the measured liquid level is necessary in order to enter the calibration table to get the correct liquid volume. This deviation from the correct liquid level is indicated on the diagram by the distance between the gauge-float and liquid level shown for the ship in the upright position.
8.2.3 Tape correction
Float gauge tapes pass through cold vapour spaces and, depending on temperature, will contract and indicate a greater ullage in the vapour space — so leading to a lesser indication of liquid level. This correction, therefore, adds to the indicated liquid level.
8.2.4 Float correction
The zero reading of a float gauge is determined by the manufacturer but is normally at 50 per cent float immersion. If the cargo liquid has a temperature and density different from that assumed for the manufacturer's zero determination, a small correction for float immersion will be required.
8.2.5 Tank shell contraction and expansion
The cargo tank, having been calibrated at an ambient temperature, has a smaller volume at a cold cargo temperature due to contraction of the tank material. If the liquid temperature is different from the vapour space temperature, it is usual to apply separate correction factors to the liquid and vapour space tank volumes.
8.3 MEASUREMENT OF DENSITY 8.3.1 Density measurement methods
Since liquefied gases are boiling liquids, the measurement of density requires laboratory equipment not available on ships. Cargo liquid density is measured on shore and the results are provided to the ship for its cargo calculations.
There are four principal methods of liquid density measurement. These are described below.
By calculation from an analysis of liquid composition
Liquid composition analysis is the most accurate method of density measurement and is increasingly used in modern terminals. The liquid composition is usually obtained by a gas liquid chromatograph which is an instrument requiring expert operation. The density is calculated from this analysis by means of one of two formulae: the Francis Formula or the Costald Equation. The Francis Formula is the simpler but is applicable only to LPG temperature ranges and loses some accuracy in the case of LPG mixtures and chemical gases. The Costald Equation is more complicated but provides accurate results when calculating the density of LNG, chemical gas and mixed gas cargoes. Calculations using these formulae are usually carried out by a programmed hand calculator or small computer. Apart from the greater accuracy obtainable by these formulae, the methods also have the virtue of providing a density at any required temperature without introducing the inaccuracy of generalised conversion tables.
By density meters
Shore tank density may be measured by density meters which operate using various physical principles. The differing types are listed below.
• Differential pressure across the height of a known vertical liquid column
• Resonant frequency of a vibrating element immersed in the liquid
• Buoyancy of a body immersed in the liquid
• Variation of electrical capacitance of an immersed probe, or
• The variation of the speed of ultrasonic signals within the liquid In such cases the density is measured at shore tank temperature and requires con-
version to a standard temperature, usually 15°C, or to the ship's tank temperature, depending on the calculation procedure used.
By in-line densitometer
The use of a densitometer involves diverting a portion of the product flow in a pipeline through the instrument. The instrument contains a vibrating element and, as in the static density meter using this principle, the resonant frequency of the vibrating element is related to the density of the liquid. Each densitometer requires careful initial calibration. Corrections need to be applied to its correlations between frequency and density for pressures, temperatures and for products differing from the calibration values. The overall accuracy is considered to be ±0.2 per cent and is similar to that achieved from compositional analysis. The instrument is particularly appropriate for use with liquid cargo flow measurement since the corrected output of the densitometer may be combined with the output of the volume flow measurement to give mass flow. This can then be integrated over the whole transfer period to give directly the total liquid mass transferred.
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