Tanker Cargo Calculations - ASTM Tables Usage & Procedure of Calculations

Hi, In my recent meetings with a variety of Ship's officers, including some Engineers, who were interested in knowing more of this, I've realized that no training institute actually gives them a complete picture of Tanker cargo calculations.  It is really amusing to note that some of these people, I've had to prepare for vettings etc. or for that matter, just for preparing for the vessel, are senior officers on board. Anyhow, below is a concise effort to introduce all to these calculations. As usual, please feel free to contact self for more info, and share as much as you want. Do let me know, if something is not correct. One more note: The below is usually not applicable to Chemical cargoes in liquid bulk, since the ASTM tables are normally not applicable there.  Series I - TABLE 5 & 6 - FOR API, OF, 60OF
Volume I:		Generalized Crude Oils (Tables 5A & 6A)
Volume II:		Generalized Products (Tables 5B and 6B)
Volume III:		Individual and Special Applications (Table 6C)
Series II - TABLE 23 & 24 - FOR RELATIVE DENSITY, oF, 60oF
Volume IV:		Generalized Crude Oils (Tables 23A & 24A)
Volume V:		Generalized Products (Tables 23B and 24B)
Volume VI:		Individual and Special Applications (Table 24C)
Series III - TABLE 53 & 54 - FOR KG/cm3 DENSITY, oC, 15oC
Volume VII:		Generalized Crude Oils (Tables 53A & 54A)
Volume VIII:		Generalized Products (Tables 53B and 54B)
Volume IX:		Individual and Special Applications (Table 54C)
Volume X:		Background, Documentation, Program Listings
Volume XI / XII - ASTM D 1250-80 - API standard 2540 and IP Designation 200 apply
Volume XI - ENTRY WITH API GRAVITY
Table 1		Interrelation of Units of Measurement
Table 2		Temperature Conversions
Table 3		API Gravity at 60oF to Relative Density 60/60oF and to Density at 15oC
Table 4		U.S. Gallons at 60F and Barrels at 60F to Litres at 15C against API Gravity at 60F
Table 8		Pounds per US Gallon at 60F and US Gallons at 60F per pound against API Gravity at 60F
Table 9		Short Tons per 1000 US Gallons at 60F and Barrel at 60F against API Gravity at 60F
Table 10		US Gallons at 60F and Barrels at 60F per Short Ton against API Gravity at 60F
Table 11		Long Tons per 1000 US Gallons at 60F and per Barrel at 60F against API Gravity at 60F
Table 12		US Gallons at 60F and Barrels at 60F per Long Ton against API Gravity at 60F
Table 13		Metric Tons per 1000 US Gallons at 60F and per Barrel at 60F against API Gravity at 60F
Table 14		Cubic Metres at 15C per Short Ton and per Long Ton against API Gravity at 60F
Volume XII - ENTRY WITH RELATIVE DENSITY
Table 21		Relative Density 60/60oF to API Gravity at 60oF and to Density at 15oC
Table 22		US Gallons at 60F to Litres at 15C and Barrels at 60F to Cubic Metres at 15C
Table 26		Pounds per US Gallon at 60F and US Gallons at 60F per Pound against Relative Density 60/60F
Table 27		Short Tons per 1000 US Gallons at 60F and per Barrel at 60F against Relative Density 60/60F
Table 28		US Gallons at 60F and Barrels at 60F per Short Ton against Relative Density 60/60F
Table 29		Long Tons per 1000 US Gallons at 60F and per Barrel at 60F against Relative Density 60/60F
Table 30		US Gallons at 60F and Barrels At 60F per Long Ton against Relative Density 60/60F
Table 31		Cubic Metres at 15C per Short Ton and per Long Ton against Relative Density 60/60F
Table 33		Specific Gravity Reduction to 60F for Liquefied Petroleum Gases and Natural Gasoline
Table 34		Reduction of Volume to 60F against Specific Gravity 60/60F for Liquefied Petroleum Gases
Table 51		Density at 15C to Relative Density 60/60F and to API Gravity at 60F
Table 52		Barrels at 60F to Cubic Metres at 15C and Cubic Metres at 15C to Barrels at 60F
Table 56		Kilograms per Litre at 15C and Litres at 15C per Metric Ton against Density at 15C
Table 57		Short Tons and Long Tons per 1000 Litres at 15C against Density at 15C
Table 58		US Gallons and Barrels per Metric Ton against Density at 15C
Volume XIII:		LUBRICATING OILS, TABLES 5D & 6D
Volume XIV:		LUBRICATING OILS, TABLES 53D & 54D
Please remember that normally the density or API is provided by the terminal or surveyor in the load ports and what is used will be dependent on the region / port of loading. For example in USA / Canada, Persian Gulf, API usage is prevalent, while entire of Europe and Asia uses Density at 15C. However please ascertain, if Density at 15C is provided, whether it is in air or in vacuum. This is very important when finding out from Table 54, since the density provided there is in Air and hence same must be used. (Density at 15C in Air = Density at 15C in Vacuum - 0.0011
PROCEDURE OF CALCULATIONS
Working with Density at 15oC in air:
1)  Observed Ullage - apply corrections - get Corrected Ullage
2)  Observed Interface - apply corrections - get Corrected Interface
3)  From Corrected Ullage, find Total Observed Volume TOV (in cubic metres)
4)  From Corrected Interface, find Volume of Water (in cubic metres)
5)  TOV - Water = Gross Observed Volume (GOV) of Cargo (in cubic metres)
6)  Use Density at 15C and Observed Temperature (oC) and find Volume Correction Factor (VCF) from Table 54
7)  Gross Standard Volume (GSV) = GOV x VCF (cubic metres)
8)  Weight Correction Factor (WCF) = Density at 15C in vacuum - 0.0011 (or the Density at 15C in air)
9)  Weight in Air (Metric Ton) = GSV x WCF(Density at 15C in air)
10) Weight in Vaccum (Metric Ton) = GSV x Density at 15C in vacuum
Working with API Gravity at 60oF :
1)  Observed Ullage - apply corrections - get Corrected Ullage
2)  Observed Interface - apply corrections - get Corrected Interface
3)  From Corrected Ullage, find Gross Observed Volume (in US Barrels)
4)  From Corrected Interface, find Volume of Water (in US Barrels)
5)  GOV - Water = Observed Volume of Cargo (in US Barrels)
6)  Use API Gravity at 60F and Observed Temperature (oF) and find Volume Correction Factor (VCF) from Table 6
7)  Gross Standard Volume (GSV) = Observed Cargo Volume (Barrels) x VCF (in US Barrels)
8)  Find Weight Correction Factor (WCF) from Table 13
9)  Weight in Air (Metric Tons) = GSV x WCF
Working with Relative Density at 60/60oF :
1)  Observed Ullage - apply corrections - get Corrected Ullage
2)  Observed Interface - apply corrections - get Corrected Interface
3)  From Corrected Ullage, find Gross Observed Volume (in cubic metres)
4)  From Corrected Interface, find Volume of Water (in cubic metres)
5)  GOV - Water = Observed Volume of Cargo (in cubic metres)
6)  Use Relative Density at 60/60F and Observed Temperature (oF) and find Volume Correction Factor (VCF) from Table 24
7)  Gross Standard Volume (GSV) = Observed Cargo Volume (m3) x VCF (in m3)
8)  Weight in Air (Metric Ton) = GSV x Relative Density at 60/60F
Total observed volume (TOV)
The total volume of material measured in the tank including cargo (oil or chemical), free water (FW), entrained sediment and water (S&W), sediment and scale as measured at observed temperature and pressure.
Free water (FW)
Water layer existing as a separate phase in the tanks, normally detected by water-paste or interface detector and usually settled at the bottom of the cargo tank  depending on relative density of the cargo.
Sediment & Water (S&W or BS&W)
Entrained material within the oil bulk, including solid particles and dispersed water, also sometimes known as base sediment and water (BS&W). Expressed always as a percentage of the total cargo quantity, is found out be collecting average sample of the cargo inline during transfer and calculated by centrifuge technique in a laboratory.
Gross observed volume (GOV)
It is the Total Observed Volume (TOV) less free water (FW) and bottom sediment, being the measured volume of product and sediment &  water (S&W) at observed temperature and pressure. Bottom sediment are normally not present on board a chemical or clean oil product tanker and therefore not deducted whereas it may be present in a dirty oil carrier, but be very difficult to ascertain.
Gross standard volume (GSV)
It is the measured volume of product and S&W at standard conditions of 15°C and atmospheric pressure. In practice is the GSV the GOV multiplied by the volume correction factor (VCF) obtained from the appropriate ASTM/IP Petroleum Measurement Tables.
Net standard volume (NSV)
It is normally applicable only to Crude Oils. NSV is the GSV minus S&W, being a measurement of the dry oil quantity at standard conditions. For clean oil products and chemicals, the S&W is not normally included within the receiver's quality specifications.
The term Weight in Air  is that weight which a quantity of fluid appears to have when weighed in air against standard commercials weights so that each will have a mass (weight in vacuum) equal to the nominal mass associated with it.
The term Weight in Vacuum refers to the true mass of a fluid.
USE OF WEDGE FORMULA FOR OBQ / ROB CALCULATIONS & FREE WATER CALCULATIONS
The Wedge Formula is a mathematical mean being used to approximate the small quantities of liquid and solid cargo and free water on board prior to the vessel's loading and after her discharge, based on the dimensions of the individual cargo tank and vessel's trim. The Wedge Formula is to be used only when the oil liquid does not touch all bulkheads of the vessel's cargo tank, that is to say the liquid oil lying in small pools among the bottom sediment.
In order to standarise the OBQ/ROB calculations on board the Crude Oil carrying tanker vessels, the following geometric form of the Wedge Formula shall be used and this form of the formula assumes that the cargo tank is 'box shaped' with no internal 'deadwood' or pipeline systems, heating coils etc. that would impact the accuracy of the volume calculated from the sounding. Furthermore this wedge formula calculation makes the enormous assumption that any 'liquid' found in a cargo tank is in the form of a regular wedge shape with its base at the aft bulkhead of the cargo tank.
It is obvious that such a series of assumptions normally can invalidate the absolute accuracy of the calculation immediately given, amongst other issues, the shape of the wing tanks (the turn of the bilge) and in particular those wing tanks at the fore and aft parts of the vessel.
The calculation method for the Geometric edition of the Wedge Formula:
Assumption: Given the small angle involved with the trim of the vessel, then the 'Sine' of an angle can be considered as the same as the 'Tangent' (Tan) of an angle and consequently:
Step 1:
Correct the position of the sounding position with respect to the aft bulkhead of the cargo tank due to the trim of the vessel, distance = A
A = Tank Reference Height (Observed Height) x Tan X;
where X = the Trim angle of the vessel and;
Tan X = (Aft draft - Forward draft) / Length Between Perpendiculars (L.B.P.) of the vessel.
Step 2:
Determine the distance of the apex of the wedge from the aft bulkhead for obtaining information whether:
(1) should a Wedge Formula be used at all (kindly note that a wedge formula is not applicable if:      (a) the liquid surface covers the total cargo tank bottom or the calculated apex of the wedge is at or beyond the forward bulkhead of                the cargo tank or:      (b) it is sludge ROB volumes only);
And
(2) whether the wedge is a regular wedge (which can be checked by comparison with alternative soundings being taken).
S = Observed Sounding;
F  (Distance of the apex of the wedge from the sounding position) = S x Tan X;
E (Distance of the apex of the wedge to the aft bulkhead) = (F - A) + B;
where B is the distance on deck from the point of sounding to the aft bulkhead.
Step 3:
Determine the depth of the wedge at the aft bulkhead of the cargo tank, depth = D;  D = E x Tan X
Step 4:
Knowing D (sounding depth at the aft bulkhead) and E (the distance from the aft bulkhead to the apex of the wedge), then the area of the longitudial cross section of the wedge may be calculated,
thus as the area of a triangle = (Base x Height) / 2 then; (D x E) / 2 = cross sectional area of wedge.
Step 5:
Having obtained the cross sectional area of the wedge, the volume of the wedge is calculated by multiplication by the breadth of the cargo tank (please note that the breadth of the cargo tank should be measured at the bottom of the tank at the aft bulkhead position and not at deck level or elsewhere within the cargo tank).
Volume of the Wedge = Cross sectional Area x Breadth of Tank
Throughout this calculation it is very important that all distances are in metres. Do not use centimetres for the observed sounding.
Alternatives:
Regardless above stated requirement, an I.S.O. standard method is also available in the event that any Cargo Inspector do not accept the geometric edition of the wedge formula. This method depends upon the accuracy of the vessel's tank ullage calibration tables for the larger ullages / smaller soundings in the cargo tank. If the tank calibration tables are accurate for this region of the cargo tanks, then this method will give added accuracy to the general method of calculating tank residues after discharge.
This method is as follows:
Step 1:
Calculate DA (the Corrected liquid sounding at the aft bulkhead position);  DA = D + {f(Y - (H x f))}
where:
D is the observed liquid sounding;
f  is the Trim factor ( TS  / LS );
TS  is the vessel's trim;
Y is the distance of the sounding point to the aft bulkhead;
H is the reference height of the cargo tank;
LS  is the vessel's Length Between Perpendiculars.
Step 2:
Calculate Ct  (the Tank constant); Ct  =  LS  / ( 2 x TS  x Lt ) (where Lt is the Length of the Cargo Tank).
Step 3:
Calculate the 'k' coefficient;   k = DA  x Ct
if k > 0.5 wedge is not required to be carried out;
if k = 0.5 wedge must be carried out.
Step 4:
if k > 0.5 then calculate the volume of the liquid contained in the cargo tank from the calibration tables using the Observed sounding, D, applying the trim corrections.
Step 5:
if k = 0.5 then calculate DX (the wedge sounding).   DX = DA  / 2
Step 6:
Enter the cargo tank calibration tables with DX, without applying trim corrections to equivalent volume VO.
Step 7:
Calculate the liquid wedge volume V1;   V1 =  VO  x  2  x  k
In addition to above methods it should be noted that if the procedures as specified in the vessel's COW manual are being followed for the determination of the 'Dryness' of a cargo tank, namely, the sounding of the residues in four(4) differing locations within the cargo tank, then the foregoing methods of calculations can be avoided.
Assuming the shape of the individual cargo tanks is fairly regular / constant in a fore and aft direction and, notwithstanding the fact that the vessel will be significantly trimmed by the stern, then the four measurements, as suggested in the COW Manual guidelines, as obtained by sounding can be used to calculate an average sounding so as to obtain a single sounding. The single average sounding can be used directly in order to obtain an equivalent volume from the vessel's tank ullage calibration tables
Such a method will provide a clearer indication as to the type and nature of the residues on the cargo tank floor as well as provide much clearer indications as to the profile of the residues within the cargo tanks.