Tanker
Cargo Calculations  ASTM Tables Usage & Procedure of Calculations
Series
I  TABLE 5 & 6  FOR API, ^{O}F, 60^{O}F


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, ^{o}F,^{ }60^{o}F


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/cm^{3} DENSITY, ^{o}C,^{ }15^{o}C


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 125080  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 60^{o}F to
Relative Density 60/60^{o}F and to Density at 15^{o}C


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 60/60^{o}F
to API Gravity at 60^{o}F and to Density at 15^{o}C


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 15^{o}C 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 60^{o}F :


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 60/60^{o}F :


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 waterpaste 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 D_{A}
(the Corrected liquid sounding at the aft bulkhead position); D_{A} = D + {f(Y  (H x f))}


where:


D is the observed liquid sounding;


f is the Trim factor
( T_{S} / L_{S} );


T_{S} 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;


L_{S} is the vessel's
Length Between Perpendiculars.


Step 2:


Calculate C_{t} (the Tank constant); C_{t} = L_{S} / ( 2 x T_{S} x L_{t} ) (where L_{t}
is the Length of the Cargo Tank).


Step 3:


Calculate the 'k'
coefficient; k = D_{A} x C_{t }


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 D_{X}
(the wedge sounding). D_{X}
= D_{A} / 2


Step 6:


Enter the cargo tank calibration
tables with D_{X}, without applying trim corrections to
equivalent volume V_{O}.


Step 7:


Calculate the liquid wedge volume V_{1}; V_{1} = V_{O} 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.

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