By pressure hydrometer — ASTM D 1657
The measurement of density by hydrometer has been the standard method for many years. It is a simple procedure but is probably the least accurate of all. In this method, the hydrometer, containing a thermometer, is floated in a sample of the liquid within a transparent pressure container. The procedure involves warming to a standard temperature, usually 15°C, and the density is read directly from the immersed hydrometer.
8.3.2 Units of density
The density of LPG cargoes is usually expressed in terms of kilogrammes per cubic metre (kg/m3), kilogrammes per cubic deci-metre (kg/dm3) (equivalent to tonne/m3) or kilogrammes/litre (for all practical purposes equal to kg/dm3, 1 litre = 1.000028 dm3).
However, units of relative density, formerly called specific gravity, are still used at some terminals. Relative density is defined as the mass of a given volume of product at a given temperature divided by the mass of the same volume of water at a given temperature which may be different from the temperature given for the product. This wide definition of relative density requires a knowledge of the density of pure water at the given water temperature in order to determine the density of the product. Thus, the relative density 60°/60°F of a product denotes both product and water to be at the same given temperature of 60°F and may be converted to density at 60°F by multiplying by the density of water at 60°F (999.035 kg/m3). Similarly, a product specific gravity 15°/4°C may be converted to density at 15°C by multiplying by the density of water at 4°C (1,000.0 kg/m3).
8.4 SHIP/SHORE CALCULATION PROCEDURES 8.4.1 Outline of weight-in-air calculation
Procedures to calculate the weight-in-air of a cargo can vary in detail between ship and shore. It is not possible in this book to deal with every variation. There is, unfortunately, no internationally agreed standard but all calculation procedures should meet the following basic requirements.
• Account must be taken of liquid product on board before loading or left on board after discharge.
• Account must be taken of the vapour quantity. In determining the contribution of the vapour quantity to the total, the vapour is converted to a liquid equivalent.
• The mass of liquid or vapour is determined by multiplying the volume at a stated temperature by the density at the same temperature. If volume and density are not physically measured or calculated at the same temperature, they must be converted to the same temperature before multiplication.
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• The result of the foregoing multiplication is mass and may be converted to weight-in-air by an appropriate conversion factor found in published tables.
8.4.2 Procedures using standard temperature
The following is a widely practised procedure using Sl units when considering a standard temperature of 15°C.
(i) Find the average liquid and average vapour space temperatures (°C) and the vapour space pressure (barg or mbarg).
(ii) Read the liquid level and calculate the liquid volume (Vt) at tank conditions (t°C) using the ship's calibration tables and making corrections for temperature and the ship's list and trim (Vt in m3).
(iii) Obtain the liquid density noting the temperature at which it is determined and, by ASTM-IP Table 53, convert this to liquid density at 15°C (D15 in kg/m3). Note that in Table 53 density is given in kg/litre. For all practical purposes the values are equal to tonne/m3 and should be multiplied by 1,000 to obtain kg/m3.
(iv) Using the liquid density at 15°C (expressed in kg/litre) and the average liquid temperature, enter ASTM-IP Table 54 to derive the appropriate volume cor-rection factor to convert Vt to the volume at 15°C (V15 in m3).
(v) Calculate the liquid mass as Mliq (kg) = V15 x D15
(vi) Calculate the vapour volume at tank conditions (Vt) in m3 by subtracting the apparent liquid volume at calibration temperature from the tank total volume at calibration temperature and applying to the difference the necessary vapour space contraction factor.
(vii) Determine the vapour density at vapour space conditions (dvt) by the following calculation based upon the ideal gas laws.
where:— Ts standard temperature of 288 K (15°C)
Tv is average temperature of vapour in degrees Kelvin
Pv is absolute pressure of vapour space in bar
Ps is standard pressure of 1.013 bar
Mm is molecular mass of vapour mixture in kg/kmol (provided from industry tables or from shore)
I is ideal gaseous molar volume at standard temperature (288 K) and standard pressure (1.013 bar) = 23.645 m3/kmol.
[Note: An accurate knowledge of the vapour composition in deriving Mm is not necessary and the deviation of saturated liquid gas vapours from the ideal gas laws is usually ignored.]
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(viii) Calculate the vapour mass (m) as the product of vapour volume and vapour
density:m= Vt x Dvt (kg).
(ix) Add the liquid mass, Mliq, and the vapour mass, m, to give the total mass, MT;
Mt = Mliq + m (kg).
(x) Convert the total mass to weight-in-air by means of the appropriate conversion factor found by entering the left hand side of the short table in the introduction of ASTM-IP Table 56 with the liquid density at 15°C.
The above is the procedure for the static measurement of tanks when the calculation is based on the standard temperature of 15°C. It can apply either to shore tanks or the ship's tanks before and after cargo transfer, the net cargo transfer being the difference. In the case of ship tank measurement and shipboard calculations, the liquid density is supplied by the shore.
As already mentioned in 8.1.6, one of the difficulties in shore measurement is accounting accurately for the various vapour flows within the terminal. Some terminals, therefore, use a simplified approach in assessing the vapour quantity associated with the cargo transfer of refrigerated propane or butane. In this procedure the weight-in-air of the liquid change in the shore tank is evaluated from measurements before and after transfer and 0.43 per cent of the weight-in-air of the liquid transferred is subtracted to account for the vapour which replaces the liquid in the case of a tank being discharged or for the vapour displaced in the case of a tank being filled. Despite its simplicity, the procedure is a good approximation, although it is not recommended for custody transfer purposes. It assumes that the vapour is at the same temperature and pressure before and after transfer and that the difference in vapour volume before and after is the same as the difference in liquid volume. On this basis, the vapour mass to be accounted for will be related to the liquid mass transferred by the ratio of the density of vapour to that of liquid at the tank conditions. The vapour/liquid density ratio at atmospheric boiling point for pure propane is about 0.0040 and for n-butane, 0.0046. Thus, vapour weight-in-air = 0.43 per cent of liquid weight-in-air can be taken as a generalised figure for fully refrigerated propane, butane or their mixtures. This figure should not be used for other cargoes or for propane and butane at other than fully refrigerated condition, where substantially different vapour/liquid density relationships apply.
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8.4.3 Procedure using dynamic flow measurement
As a means of overcoming the uncertainties associated with static measurement of cargo on shore, which were discussed in 8.1.6, some modern terminals are being equipped with sophisticated liquid and vapour flow metering with associated in-line sampling. The equipment presently is expensive and requires complicated proving arrangements. However, this method allows flow rate and density to be continuously recorded at the flow temperature and, by combining these outputs electronically, mass flow rate can be provided and integrated to give total mass transferred. Nevertheless, it is likely that, until such systems have been proved reliable and have been widely accepted, shipboard static measurement will continue to be the basis of cargo quantification for cargo custody transfer purposes.
8.5 EXAMPLE — CARGO CALCULATION
The following example demonstrates the typical procedure outlined in 8.4.2 using the standard temperature of 15°C as applied to cargo in a ship's tank.
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