Cargo calculation methods are essential for ensuring the accuracy and efficiency of shipping operations. These methods involve various techniques for measuring cargo volume and weight, which are critical for compliance and cost management. Proper calculation not only facilitates accurate billing but also helps in optimizing storage and transport logistics.
Furthermore, understanding molecular weights and sampling procedures can enhance the reliability of these calculations. By utilizing effective cargo calculation methods, businesses can minimize discrepancies and improve overall supply chain performance. Ultimately, these practices contribute to a smoother and more reliable shipping process.
General
Liquefied gas cargoes are measured and calculated in a similar manner to that of other bulk liquid cargoes such as crude oils and petroleum products. However, as liquefied gases are carried as boiling liquids in a closed containment system the quantity of vapor has also to be measured when calculating the total quantity onboard.
It is common practice for gas tankers on a regular trade to retain onboard a quantity of liquid (heel) in order to keep tanks cool on the ballast passage. In this way the vessel arrives at the load port ready to commence loading with no cool down time necessary. At the load port the new cargo is added to the heel. Similarly if the ship has arrived with un-cooled tanks a quantity is usually put onboard for tank cool down purposes. It is therefore extremely important that a full survey of all tanks is carried out before and after every operation.
Measurement
Temperature. Cargo being loaded may arrive at the manifold at various temperatures during loading. This may be due to cargo being taken from different shore tanks or the initial cooling of ship/shore lines. It is possible that because of this some stratification in the vessel’s tanks can occur. It is very important therefore that temperatures are taken at all available points in order to accurately assess the actual average liquid temperature. Ships temperature sensors are usually provided at a number of different levels. This is equally important for vapor temperature where temperatures in the tank dome are usually higher than that of the vapor near the surface of the liquid. The positions of temperature probes must be accurately known in order that only those actually submerged in the liquid are used for liquid temperature and similarly for vapor temperature.
- Density.
- Density is by definition measured in vacuum at 15 °C.
- Density × Volume M3 (at 15 °C gives metric tonnes in vacuum).
The measurement of liquid gas density requires laboratory facilities or equipment not available on ships. Modem terminals usually calculate this form from an analysis of liquid composition obtained from a gas liquid chromatograph. The results of this are provided to the ship in order to carry out the cargo calculations.
It is necessary to correct the density for the actual observed temperature of the cargo. For specialized chemical gases the storage facility normally provides their own density table for the cargo showing the density for a range of temperatures. Some ports provide the density at a standard temperature of 60 °F or 15 °C. This has to be corrected to the density for the observed cargo temperature. Density can be quoted as either being in air or in vacuum. For a density quoted in vacuum subtract 0,0011 to obtain the density in air, i. e. 0,5074 in vacuum corresponds to a density of 0,5063 in air.
Cargo’s quantities worked out in vacuum are always heavier than those worked out in air. Liquid gas quantification is more commonly expressed in terms of weight in air and indeed this is a requirement of most customs authorities. It is extremely important that when a density is provided to the Vessel it is ascertained whether the density is in air or vacuum.
Liquid Level. The liquid level is read direct from the tank level gauge on the tank dome. The remote readout must not be used for cargo calculations. It is necessary to apply corrections to this figure before entering the tables. These corrections are for tape shrinkage and float immersion. The float gauge tape passes through the cold vapor space and depending on the space temperature contracts thus indicating a higher liquid level than actually present. Float immersion will depend on the density of the cargo and this will usually be different from the manufacturer’s initial determination. A small correction is necessary for both these items to obtain the correct gauge reading before entering the tables.
Liquid Volume. All ships are provided with a calibration table for each tank by means of which the tank’s liquid (and vapor) volume can be calculated from the measurement of the liquid level. These tables are obtained from careful measurement of the tanks during the ship’s construction. These tables normally refer to an upright vessel with no list. Corrections are therefore necessary for trim and list and these will be included with the tank calibration tables. Instruction for use will be included with the tables.
The cargo tank volume will have been calculated at ambient temperature and the tables calculated for a standard temperature of say 20 °C. Cold cargo temperature will result in tank shrinkage and a reduction in volume. A correction therefore is necessary and this is normally expressed as the Tank Shrinkage factor.
Vapor Quantity. The volume of vapor is found by subtracting the volume of liquid from the tanks 100 %
capacity. This is at the calibration temperature for the tank before the Volume Correction Factor has been applied. It is necessary to apply a Volume Correction Factor (tank shrinkage factor) to this figure and this correction is obtained using the average vapor temperature.
Calculation
On completion of measurement calculation of the total cargo quantity can be carried out. There is no internationally agreed standard for gas Measurement and calculation of cargo on gas carrierscargo calculations and procedures can vary particularly with the chemical gases. In the absence of any instructions concerning calculations the following procedure using the standard temperature of 15 °C which is widely used should be followed.
Calculation Procedure (Typical)
a Determine by measurement the average liquid and vapor space temperature (degrees C) and the vapor space pressure (barg or mbarg).
b Read the tank liquid level and calculate the liquid volume (Vi) at tank conditions using the ship’s calibration tables for that tank and making all necessary corrections for temperatures, list and trim.
c Determine the liquid density noting the temperature at which it is determined and using ASTM table 53 & convert this to liquid density at 15 °C.
d Using the liquid density at 15 °C and the measured average liquid temperature, enter ASTM table 54 to derive the appropriate volume correction factor to convert to the volume at 15 °C.
e Calculate the liquid mass. Volume × Density.
f Calculate the vapor volume at tank conditions by subtracting the apparent liquid volume (liquid quantity before applying tank shrinkage factor) from the tank total volume.
NB ASTM tables 53 & 54 have been revised for densities in the range 610,0 to 1076,0.
Kg/m3 however below this range covering LPG no revision has been carried out and ASTM-IP tables 53 & 54 are to be used.
g Using the average vapor temperature correct the apparent volume of vapor for tank shrinkage.
h Determine the vapor density at vapor space conditions using the following formula.
Where:
- Ts – is standard temperature of 288 K.
- Tv – is average temperature of vapor in K.
- Pv – is absolute pressure of vapor space in bars.
- Ps – standard pressure of 1,013 bar.
- Mm – is molecular mass of vapor mixture in Kg/K mol (sometimes called molecular weight).
- I – is ideal gaseous molar volume at standard temperature (288 K) and standard pressure (1,013 bar). This is 23,645 m I K mol.
Calculate the vapor mass by multiplying vapor volume and vapor density.
j Add the liquid mass and the vapor mass to give the total cargo mass in the tank.
k Convert the total to weight in air.
Example Calculation
The following numeral example demonstrates in detail the typical procedure for the calculation of the contents of a ship’s tank.
| Table 1. Measurement Data Tank No. 3 Port Product – Propane | |
|---|---|
| Gauge reading | 10,020 metres |
| Ship’s Trim | 2,0 metres by stern |
| Ship’s List | 0,5 degrees to port |
| Average liquid temperature | -43 °C |
| Average vapor temperature | -38 °C |
| Vapor space pressure | 59 mbarg |
| Molecular weight of liquid | 44,097 |
| Density of liquid | 511 Kg/m3 |
| Table 2. From Ship’s Calibration Tables for 3P Tank | |
|---|---|
| Tank gauge reading | 10 020 mm |
| Correction for trim | – 127 mm |
| Correction for list | + 46 mm |
| Level gauge correction | + 1 mm |
| Float immersion correction | 0 mm |
| Corrected liquid depth | 9 940 mm |
| Liquid volume (uncorrected) | 5441,88 m |
| 100 % tank volume | 9893,63 m |
| Vapor volume (uncorrected) | 4451,75 m |
| Tank shrinkage factor (liquid) | 0,99773 (- 43 °C) |
| Tank shrinkage factor (vapor) | 0,99791 (- 38 °C) |
| Table 3. Liquid Calculation | |
|---|---|
| Volume of liquid (uncorrected) | 5441,88 m |
| Tank shrinkage factor | x 0,99773 |
| Volume of liquid at – 43 °C | 5429,52 m |
| VRF from – 43 °C to 15 °C (table 54) | × 1,145 |
| Volume of liquid at 15 °C | 6216,8 m |
| Liquid density at 15 °C (from shore) | × 511 Kg/m |
| Mass of liquid | 3 176 785 Kg |
| Table 4. Vapor Calculation | |
|---|---|
| Volume of liquid (uncorrected) | 5441,88 m |
| 100 % tank volume | 9893,63 m |
| Vapor volume (uncorrected) | 4451,75 m |
| Tank shrinkage factor | × 0,99791 |
| Volume of vapor at – 38 °C | 4442,45 m |
| Density of vapor at – 38 °C | – |
| Mass of Vapor | 10 613 Kg |
| Table 5. Total Mass | |
|---|---|
| Mass of liquid | 3 176 785 kg |
| Mass of vapor | 10 613 kg |
| Total Mass | 3 187 398 Kg |
Weight in Air. Factor for converting mass to weight in air for liquid of 511 Kg/m density at 15 °C (Table 56) × 0,99775.
Total weight in air: 3 180 226 Kg = 3180,23 mt
Cargo Documentation
The transportation of Chemical Composition and Physical Properties of Liquefied Gasesliquefied gases is subject to the same commercial documentation as applies to oil cargoes. Documents accompanying a liquid gas cargo will generally include the following.
Bill of Lading. This is the most important document. It is a receipt for the cargo on board and is normally signed by the Master on behalf of the ship owner or time charterer. It will state the quantity of cargo shipped, that it was received onboard in apparently good order and condition and will indicate the terms and conditions under which the ship will carry the cargo to its destination. In some ports which operate early departure procedures the Agents will sign the Bills and the Master will be required to furnish the agents with a letter authorizing them to do this.
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The Bill of Lading is usually issued in three «originals» of equal standing, each separately stamped and signed. One of these goes to the shipper, one to the carrier (ship owner or time charterer) and one to the intended receiver of the cargo. A copy will be retained onboard and normally the Master will only deliver the cargo on presentation of the receivers «original». This is issued by the loading terminal and is the cargo quantities declared as loaded usually established by an independent surveyor.
Certificate of quality. This provides the product specification and quality in terms of physical characteristics and component constituents. It is again issued by the loading terminal.
Certificate of Origin. This is a document issued by the manufacturer or shipper, countersigned by the custom’s authorities and attesting to the country in which the cargo was produced.
Time Sheet. This records all timing details of the ship’s movements and operations from the ships entry to its final departure from the port. This is usually prepared by the vessel’s agents and is countersigned by the Master. Its purpose is to provide an agreed statement of facts relating to timing of events and any delays.
Cargo Manifest. This document is again usually prepared by the vessel’s agents at the loading port and lists the cargo according to the Bill of Lading(s) and the disposition of the cargo within the ship. Its purpose is to provide readily available data for Customs authorities etc., at the discharge port.
Certificate of Tank Fitness. This is issued by independent chemists or surveyors where particular tank conditions are required prior to loading.
Certificate of Inhibitor Addition. Certain gases require an inhibitor added for transportation and the certificate will show the quantity added and the length of time the inhibitor will last for.
Molecular Weights
The following are the molecular weights for various standard gases. In the absence of data from the loading terminal these figures should be used for calculating the vapor mass.
| Table 6. Molecular weights for various standard gases | |
|---|---|
| Ammonia | 17,05 |
| Butadiene | 54,10 |
| Butane | 58,12 |
| Butene | 56,10 |
| Chlorine | 70,91 |
| Ethane | 30,10 |
| Ethylene | 28,05 |
| Methane | 16,04 |
| Methyl Chloride | 50,49 |
| Propane | 44,10 |
| Propylene | 42,08 |
| R12 | 120,92 |
| R22 | 86,48 |
| Sulphur Dioxid | 64,07 |
| Vinyl Chloride | 62,50 |
Sampling
Cargo is normally sampled by shippers’ or receivers’ personnel, or by authorized petroleum inspectors. The responsible officer must, however, be present when sampling is carried out to ensure that samples are taken from correct sampling points and that this is performed in a correct and safe manner. He is to also make a proper record of the samples taken as these may be of considerable value subsequently. A good rule is to request samples to be taken from the liquid shore connections at the start of loading to safeguard against possible contamination of shore transfer lines. The following precautions are to be observed when sampling Liquid Cargo Transportation – Safety and Operational Efficiencycargo liquid or vapor.
Liquid Samples
a) The sample container must be completely clean and compatible with the cargo to be sampled and is to be able to withstand the extremes of temperature and pressure anticipated.
b) Sample containers must be purged of air by pure nitrogen before use with flammable cargoes.
c) If the sample is to be representative its container has to be purged thoroughly with cargo from the sampling connection. Sufficient cargo must be passed through the container to cool it down to liquid temperature. If the cargo is a mixture (which is often the case) the most volatile components will evaporate more rapidly than the heavier fractions as the container is cooled down; this will leave the sample with a higher concentration of the heavy fraction than present in the cargo, and it will therefore be unrepresentative. To counteract this, sample containers are to be turned with the vent valve downwards during cool down, to drain off the liquid that first collects. For the same reason, samples from the bottom of cargo tanks at the beginning of, or just after, loading may not be representative. It is recommended that the cargo is circulated using the cargo pump, if possible, before taking bottom samples.
d) It is imperative that sufficient ullage or vapor space is left in the sample container to allow for the liquid expansion that will occur when the temperature increases to ambient. Ullage is obtained by holding the full sample container upright after disconnecting it from the sample connection and draining some liquid by opening the bottom valve for a moment.
e) Unless the sample container is free of cargo vapor, it should not be stored in an unventilated space.
f) Gloves, goggles and protective clothing must be worn when sampling cold cargoes.
g) If the cargo is toxic, a suitable respirator, or preferably self-contained breathing apparatus, must be worn. If sampling in an enclosed space, a respirator is unsuitable, due to the possibility of asphyxiation, then breathing apparatus is necessary.
h) If electrical equipment is used when taking samples this is to be of the certified-safe type.
Vapor Samples
a) The precautions given in “Liquid Samples” (a), (b), (c), (fl, (g) and (h) are to be observed when sampling cargo vapor or inert gas.
b) Plastic sample bags are sometimes used for collecting vapor samples. These must be handled carefully, never used for liquid samples and always purged after use.
