Bitumen Tonnage and Volume Conversions

Bitumen is loaded hot. In a tank, a bitutainer or a vessel compartment it is typically between 130 °C and 170 °C, because below that it is too viscous to pump. At those temperatures it has expanded significantly against its volume at ambient. A tank gauged as full of 30 m³ of hot bitumen does not contain 30 m³ worth of cold product, and it certainly does not contain 30 tonnes.

The physics is straightforward. Bitumen, like any liquid hydrocarbon, expands as it is heated. For bitumen the volumetric coefficient of thermal expansion is approximately 0.00061 per °C. Density therefore falls as temperature rises, following:

• ρ(T) = ρ15 / [ 1 + 0.00061 × (T − 15) ]

Take a typical paving bitumen with a density of 1.03 t/m³ at 15 °C. At 150 °C the expansion factor is 1 + 0.00061 × 135 = 1.0824, so the density has fallen to 0.952 t/m³. One tonne now occupies 1.051 m³ instead of 0.971 m³ — an 8.2 % increase in volume for exactly the same mass.

Where that 8 % turns into money

• Tank gauging at load port. An ullage or dip reading gives observed volume at observed temperature. Without a correction back to a reference temperature, it cannot be compared to a contract quantity.
• Discharge shortfall claims. Cargo loaded at 165 °C and discharged at 140 °C will gauge as a smaller volume even if not one kilogram is missing.
• Drum counts. Drums are filled hot. A drum filled to a fixed volume at 160 °C holds less mass than the same drum filled at 130 °C.
• Letters of credit. If the L/C says tonnes and the survey says cubic metres, the documents do not match and the bank has grounds to refuse.

Expansion, in one paragraph

Heat a hydrocarbon and its molecules move further apart. The material occupies more space; not one atom has been added or lost. For bitumen the fractional increase in volume is close to 0.00061 of itself for every degree Celsius — 0.061 % per °C, or about 0.00034 per °F. That is the volumetric coefficient of thermal expansion, and because density is mass divided by volume, it is also the rate at which density falls. The linear coefficient, if you ever need it for a joint or a coating rather than for a cargo, is roughly one third of it, near 0.00020 per °C.

Over the range bitumen is actually handled the effect is not small. From 15 °C to 150 °C is 135 degrees, so volume increases by 0.00061 × 135 = 8.24 %. Going the other way, from a loading temperature of 160 °C to a discharge temperature of 135 °C, the hot volume shrinks by 1.40 %. Those percentages get applied to cargo values that run into six figures, which is why they generate arguments rather than shrugs.

The two forms of the formula

• Density at any temperature, from density at 15 °C: ρ(T) = ρ15 / [ 1 + 0.00061 × (T − 15) ]
• Volume at 15 °C, from volume observed at temperature T: V15 = V(T) / [ 1 + 0.00061 × (T − 15) ]

The bracket is the same in both. Call it the expansion factor E. Its reciprocal, 1 / E, is the volume correction factor (VCF): the number a surveyor multiplies an observed volume by to express it at the base temperature. At 150 °C, E is 1.0824 and the VCF is 0.9239. At 160 °C, E is 1.0885 and the VCF is 0.9187. Mass is then the corrected volume multiplied by the density at the base temperature — and mass is the only quantity in the entire calculation that does not depend on how hot anything was.

An apparent shortage is not a shortage

The consequence deserves stating flatly, because it is the origin of most claims in this trade. A cargo measured by volume when hot and compared with a volume measured when cooler will always look short, and nothing will be missing. The mass is conserved; the space it occupies is not. A quantity claim built on two volumes at two temperatures is not a claim about cargo at all, it is a claim about arithmetic, and it collapses the moment both figures are corrected to the same base temperature.

The corollary matters just as much and is heard far less often. A real loss is invisible until you do the correction. A leaking valve, a heel left in a tank, a line flushed to slops, product pumped into the wrong shore tank — all of these are smaller than the temperature effect that is hiding them. Correcting to a common base temperature is not a formality that protects the seller. It is the only procedure that lets a buyer see an actual shortfall when there is one.

How the correction is applied, and by whose rules

Volume correction in the oil industry is not improvised. The general practice is API MPMS Chapter 11.1, published jointly with ASTM as ASTM D1250 — the Petroleum Measurement Tables. Those tables are the reason a parcel of gasoil can be gauged in one port and invoiced in another without an argument: they return a volume correction factor for a given observed temperature and a given density at the base temperature, with the coefficient of expansion derived from the density itself rather than assumed.

Bitumen is handled separately, and it is worth being honest about why rather than implying that the same tables cover it. The generalized tables were fitted to crude oils, refined products and lubricating oils — materials that are liquids at the base temperature. Bitumen is not. At 15 °C a paving grade is a semi-solid; you cannot pour it, gauge it, or measure its volume at all. The asphalt-specific practice is ASTM D4311 / D4311M, Standard Practice for Determining Asphalt Volume Correction to a Base Temperature, which corrects to 15 °C or to 60 °F and which tabulates a coefficient of expansion by density group rather than deriving one from a general equation. The 0.00061 per °C used throughout this page is the value in common commercial use for paving-grade material; where a survey is performed strictly to D4311, read the coefficient out of the table for the density group the cargo falls in rather than assuming this one.

Two honest caveats follow. Neither is a reason to avoid the correction. Both are reasons to name it in the contract.

• The volume at 15 °C is a bookkeeping figure, not a physical state. Nobody has ever gauged bitumen at 15 °C. It is an extrapolation to a common reference so that two parties can compare like with like, and it is entirely legitimate provided both parties extrapolate the same way. What is not legitimate is quoting it as though it were something a surveyor saw.
• Several coefficients are in commercial circulation. Values of 0.00060, 0.00061, 0.00063 and 0.00065 per °C all appear on real survey reports and in real supplier spreadsheets. They are not all wrong — they reflect different density groups, different source data and different vintages of practice — but over a 145 °C correction the spread between 0.00060 and 0.00065 is 0.67 %, about 6.6 tonnes in a thousand. That is larger than the measurement tolerance most contracts allow. A contract that names a coefficient has named a number. A contract that names ASTM D4311 has named a procedure, and a procedure is what survives a dispute.

Whichever route is chosen, require the quantity certificate to show the coefficient or the practice used, the observed temperature and the volume correction factor applied, not merely the final tonnage. A tonnage with no working behind it cannot be checked, and anything that cannot be checked will eventually be argued about.

Which reference temperature a contract should name

Four reference temperatures circulate in this trade and they are not interchangeable.

15 °C is the standard reference temperature for petroleum volume accounting outside the United States, and one of the two base temperatures in ASTM D4311. Almost every bulk oil contract in the world states corrected volume there. If a contract names one temperature, this is the one to name.

60 °F is the US customary equivalent and the other base temperature in ASTM D4311. It is not the same number: 60 °F is 15.56 °C. The gap is 0.56 °C, worth 0.034 % of volume — about 0.34 kg per tonne, or 1.7 tonnes on a 5,000 tonne cargo. Small, but free to get right and tedious to argue about afterwards.

25 °C is a laboratory temperature rather than an accounting one, which is precisely why it causes trouble. ASTM D70, the pycnometer method for the density of semi-solid asphalt binder, permits testing at 15.6 °C or at 25 °C. EN 15326 works at 25 °C. And penetration under ASTM D5 is run at 25 °C, so a bitumen laboratory already has a bath sitting at 25 °C and reports density there because it is convenient. The result is systematic: most Certificates of Analysis carry a density at 25 °C while most contracts correct volume to 15 °C, and somebody in the chain has to notice.

27 °C appears on Indian data sheets because 27 °C is the standard laboratory temperature in Indian standards; IS 1202 determines specific gravity there. A density at 27 °C is about 0.73 % below the same product’s density at 15 °C.

Converting between them is one multiplication. To move a density from a higher temperature down to 15 °C, multiply by the expansion factor for the gap: ρ15 = ρ(T) × [ 1 + 0.00061 × (T − 15) ]. From 25 °C the multiplier is 1.0061. From 27 °C it is 1.0073. From 60 °F it is 1.00034. Skipping that step on a 5,000 tonne cargo costs about 30 tonnes, which is worked through with the arithmetic further down this page.

Specific gravity is not density

A second trap sits in the same place on the same document. A certificate reporting specific gravity 1.030 at 25/25 °C has not reported a density of 1.030 g/cm³. Specific gravity is a ratio to water at the stated temperature, and water at 25 °C has a density of 0.9970 g/cm³, not 1.0000. The density is therefore 1.030 × 0.9970 = 1.0269 g/cm³ — 0.30 % below the printed figure. On a 5,000 tonne cargo that is 15 tonnes.

Note which way each error points. The missing water correction makes the density too high by 0.30 %; the missing 25 °C to 15 °C conversion makes it too low by 0.61 %. Applied to the same certificate they partly cancel and leave a residue of about 0.31 %, which looks like measurement noise and gets written off as such. That is why both mistakes survive for years in the same office. The fix is mechanical: read the units. A figure in g/cm³ or kg/m³ is a density. A dimensionless figure with two temperatures in its label is a relative density and needs the water correction before anything else is done to it.

What a capacity table is

A tank does not have a volume. It has a capacity table — also called a gauge table, a calibration table or a strapping table — which converts a liquid depth in that particular tank into a volume. The table is produced by physically calibrating the tank: measuring the circumference of each shell course with a steel tape, which is the strapping method covered by ISO 7507-1 and API MPMS Chapter 2.2A, or by the optical reference line, optical triangulation and electro-optical distance ranging methods in the later parts of ISO 7507. The calibration then deducts deadwood: every internal structure that displaces liquid instead of containing it.

Three consequences are worth knowing before you accept anybody’s gauge.

• The table belongs to one tank in one condition. It is invalidated by anything that changes the geometry: shell distortion, foundation settlement or tilt, a replaced datum plate, a new suction line, internal repair work. Bitumen tanks are full of heating coils, and coils are deadwood. Re-coiling a tank without recalibrating it leaves a table that reads high by the volume of steel that was added.
• The table has a date and usually an expiry. Most legal metrology and custody-transfer regimes require periodic recalibration. Asking for the calibration certificate, its date and the calibrating body is a routine request and a reasonable one. An expired table is a legitimate objection before loading and a useless one afterwards.
• The table was built at one shell temperature. It states the temperature the steel was at when it was calibrated, and that matters more for bitumen than for anything else in the oil business, for the reason two sections below.

Innage, ullage and the check that costs nothing

Innage, or a dip, is the depth of liquid measured from the datum plate on the tank bottom up to the surface. Ullage, or outage, is the distance measured downwards from a fixed reference point at the gauge hatch to that same surface. They are two routes to one number, and they are tied together by the reference height: innage plus ullage should equal the certified reference height of that tank, which appears on the calibration certificate and is usually marked at the hatch.

That identity is the most useful free check in the whole procedure. If a dip and an ullage taken at the same time do not sum to the reference height, one of them is wrong — and on a bitumen tank the usual reason is that the tape never reached the datum plate, because it landed on a heel of aged product on the floor. A tank that has been in bitumen service for years has a bottom that is not where the drawing puts it. Taking both readings and reconciling them, rather than taking one and trusting it, is the difference between a gauge and a guess.

Bitumen adds difficulties of its own. Hot binder coats the tape and blurs the cut, so the reading is taken from where the coating begins rather than from a clean line. A tank standing idle forms a surface skin stiff enough to hold a bob, which then measures the crust instead of the liquid. Automatic tank gauges — servo or radar, covered by ISO 4266 and API MPMS Chapter 3.1B — avoid the tape but contend with fume, condensate on the antenna and the same crust. Whatever the instrument, a reading that will appear on a custody-transfer certificate should be proved against a manual gauge at the time it is taken.

Resolution is worth stating in tonnes, because it explains how two competent people disagree honestly. In a 30 m diameter tank, one millimetre of depth is 0.71 m³, which at 160 °C is 0.67 tonnes of bitumen. A five millimetre difference of opinion about where the cut sits is three and a third tonnes. In a 12 m tank the same millimetre is 0.11 m³, about 107 kg. Argue about the tape as long as you like; the tank diameter decides what the argument is worth.

The chain from a dip to an invoice

This is why the answer to how much is in the tank is never a single number. Each step has a name, a published practice and an error attached to it.

1. The gauge. A dip or an ullage read to the millimetre from the certified reference point, under API MPMS Chapter 3.1A for manual gauging.
2. Total observed volume (TOV). The capacity table converts that depth into a volume at whatever temperature the product happens to be.
3. Gross observed volume (GOV). Free water and bottom sediment are deducted. Bitumen carries no free water at handling temperature, but a tank that has stood cold can hold condensate and a heel of aged product, and a heel is not your cargo.
4. Tank shell correction (CTSh). The capacity table was built for steel at one temperature; a shell full of 150 °C bitumen is a bigger tank than the table describes. API MPMS Chapter 12.1 is the calculation practice. Where shell temperature is not measured directly it is estimated from the liquid and ambient temperatures.
5. The temperature survey. Spot temperatures at several depths, volume-weighted, under API MPMS Chapter 7. This is the weakest number in the chain and it has its own section below.
6. Gross standard volume (GSV). Observed volume multiplied by the volume correction factor to bring it to the base temperature, under ASTM D4311 for asphalt.
7. Mass. GSV multiplied by the density at the base temperature, determined by ASTM D70 or an equivalent method and converted to the base temperature if it was measured somewhere else.
8. Weight in air or in vacuum. A cubic metre of bitumen displaces a cubic metre of air, and air at ambient conditions weighs about 1.2 kg per cubic metre, so the same cargo weighs roughly 0.12 % less on a scale than it would in a vacuum — around six tonnes on a 5,000 tonne parcel. API MPMS Chapter 11.5 governs the intraconversion of density, weight and volume. Commercial invoices are normally raised on weight in air; the contract should say so rather than leave it to be assumed.
9. The difference. Quantity transferred is the difference between an opening gauge and a closing gauge, never a single gauge. Errors that are constant — a mis-set datum, a heel on the floor, a shell correction at an unchanged temperature — cancel in the subtraction. Errors that are proportional, above all a wrong temperature or a wrong density, do not cancel and never will.

Nine steps and half a dozen published practices, and only the last of them produces something that can go on an invoice. A dip reading is a depth. A weight is the output of a calculation for which the depth is one input. Any document that presents the first as if it were the second has left out the eight steps in between, and the person who signed it is asking you to take those eight steps on trust.

Temperature is the weakest number in the calculation

Everything above assumes you know the temperature. In a bitumen tank you usually do not, to anything like the precision the arithmetic implies.

Bitumen tanks are heated by coils near the floor and lose heat through the shell and the surface, so they stratify. A tank that has stood without circulation can be 15 or 20 degrees hotter at the coils than at the surface, and the surface may carry a crust colder still. A single thermometer lowered through the top hatch measures the coldest part of the tank and is not a tank temperature by any definition. API MPMS Chapter 7 exists because of exactly this: it calls for spot temperatures at several depths, weighted to the volume each one represents.

The cost of getting it wrong is easy to state. At handling temperature, one degree of temperature error is about 0.056 % of the tonnage. Ten degrees — entirely achievable with one thermometer in a stratified tank — is about 0.55 %, or 5.5 tonnes in a thousand. That is bigger than the margin between most competing offers, and it is completely invisible on a certificate that reports a single temperature with no indication of how many readings produced it.

Three rules follow. Circulate the tank before gauging where the installation allows it, and have the fact recorded. Require the certificate to state the number of temperature readings and the depths at which they were taken, not just the average. And require a calibrated instrument with a current certificate, because a portable electronic thermometer that has not been checked in three years is an opinion with a digital display.

On a vessel, and on a truck

Ship’s tanks add two problems a shore tank does not have. First, a vessel is never level: ullages must be corrected for trim and list from the vessel’s own calibration tables, and small quantities in a trimmed tank need the wedge formula rather than the table. Second, there is cargo in the tank before loading and after discharge — on-board quantity before, remaining on board after — and for bitumen both figures run higher than for a clean product, because bitumen clings to steel and cools against it. Who owns the ROB, and who pays to heat it out, is a contract question best answered before the vessel is fixed rather than after it is empty. API MPMS Chapter 17 covers marine measurement, including the vessel experience factor — the historical ratio between a particular ship’s figures and shore figures, which is the tool for judging whether a difference on this voyage is unusual for this vessel.

The bill of lading quantity is normally the shore figure at the load port, and the ship’s figure will differ from it. That difference is a measurement difference until something else proves otherwise. A contract that treats any difference as a shortage has guaranteed itself a dispute on every single voyage.

A truck, a bitutainer or a container has a far better answer available: weigh it. A trade-verified weighbridge measures mass directly and the entire temperature question disappears, because mass does not expand. Tare and gross on the same instrument in the same session, driver out of the cab for both, and the difference is the cargo. For drummed cargo the quantity is the drum count multiplied by the verified net weight per drum, cross-checked against the verified gross mass declared for the container under SOLAS Chapter VI Regulation 2, less the container tare marked on the door and less the total drum tare. The only common in-line instrument that measures mass directly is a Coriolis meter, covered by API MPMS Chapter 5.6; it needs a heated and traced meter run for bitumen, but where one is installed it removes the temperature argument at source rather than correcting for it afterwards.

1. The discharge shortage that was not a shortage

A cargo of exactly 1,000.00 tonnes is loaded at 160 °C and discharged at 135 °C.

• At 160 °C: expansion factor 1 + 0.00061 × 145 = 1.08845; density 1.030 / 1.08845 = 0.94630 t/m³; volume 1,000 / 0.94630 = 1,056.75 m³.
• At 135 °C: expansion factor 1 + 0.00061 × 120 = 1.07320; density 1.030 / 1.07320 = 0.95975 t/m³; volume 1,000 / 0.95975 = 1,041.94 m³.

The cargo has lost 14.81 m³, 1.40 % of its volume, and not one kilogram of mass. Now watch the claim appear. The receiver gauges 1,041.94 m³ and multiplies by the density printed on the loading documents, 0.94630 t/m³, because that is the density figure he was given: 1,041.94 × 0.94630 = 985.99 tonnes. He writes to the seller claiming 14.01 tonnes short.

Multiply the same volume by the density at the temperature it was actually measured at, 0.95975 t/m³, and the answer is 1,000.00 tonnes. The error was never in the cargo. It was in pairing a volume from one temperature with a density from another.

2. The density measured in the wrong bath

A Certificate of Analysis reports density 1.0200 g/cm³ at 25 °C to ASTM D70. The contract corrects volume to 15 °C. A 5,000.00 tonne cargo has a gross standard volume at 15 °C of 4,872.24 m³.

• Correct: ρ₁₅ = 1.0200 × (1 + 0.00061 × 10) = 1.0200 × 1.0061 = 1.026222. Mass = 4,872.24 × 1.026222 = 5,000.00 tonnes.
• Wrong: mass = 4,872.24 × 1.0200 = 4,969.68 tonnes.

The gap is 30.32 tonnes, 0.61 %, produced by one omitted multiplication on a cargo where every physical measurement was taken correctly. The same error runs in reverse if the density was determined at 15 °C and applied to a volume observed at 25 °C.

Now add the second trap. Suppose the certificate had said relative density 1.0200 at 25/25 °C instead. That is a ratio against water at 25 °C, and water at 25 °C is 0.9970 g/cm³, so the density is 1.0200 × 0.9970 = 1.01694 g/cm³ — 0.30 % below the printed number. Converting that to 15 °C: 1.01694 × 1.0061 = 1.02314, which against the same 4,872.24 m³ gives 4,984.99 tonnes. Against the bare 1.0200 that somebody would otherwise have used, the net error is 0.31 %, or 15.3 tonnes on this cargo. The two mistakes point in opposite directions and mostly cancel, which is exactly why neither is ever noticed.

3. The coefficient nobody named

The same 1,056.75 m³ of hot bitumen at 160 °C, gauged by two surveyors using different expansion coefficients, both of which are in commercial use.

• At 0.00060 per °C: factor 1.08700; density 0.94756 t/m³; mass = 1,056.75 × 0.94756 = 1,001.34 tonnes.
• At 0.00065 per °C: factor 1.09425; density 0.94128 t/m³; mass = 1,056.75 × 0.94128 = 994.70 tonnes.

Same tank, same tape, same thermometer, same density at 15 °C, same cargo. 6.64 tonnes of difference, 0.67 %, generated entirely by a number nobody wrote into the contract. This is the argument for naming ASTM D4311 rather than a coefficient, and for requiring the certificate to state which coefficient was applied.

4. The drum filled by volume instead of by weight

A filling line meters 195 litres into each 200-litre drum, leaving a nominal headspace.

• Filled at 130 °C: density 1.030 / (1 + 0.00061 × 115) = 0.96248 kg/l, so the drum holds 187.68 kg.
• Filled at 160 °C: density 0.94630 kg/l, so the drum holds 184.53 kg.

Three and a bit kilograms per drum, 1.7 %, with nothing changed but the temperature of the product going in. Across the 80 drums in a 20-foot container that is 252 kg. Across 1,000 tonnes invoiced on a nominal 180 kg net it is roughly 17 tonnes. This is why drums are filled to weight on a scale rather than to a mark, why a nominal net weight should be verified by weighing a random sample of filled drums at load, and why the contract should say that invoiced quantity is net product weight established by weighing.

The same arithmetic explains a complaint that arrives every season. A drum filled with 195 litres at 160 °C and opened cold at 25 °C contains 195 × 1.0061 / 1.08845 = 180.2 litres. The surface has dropped by almost 15 litres and looks dished and short. It is not short. That is 7.6 % of volume that went away as the drum cooled, and all 184.53 kg is still in there. The only instrument that settles the question is a weighbridge.

5. The tank that is bigger when it is hot

A shore tank whose capacity table was built at 15 °C is holding bitumen at 150 °C, with an average shell temperature of 140 °C. Carbon steel expands by roughly 11.7 millionths of its length per °C, so its volume grows by about three times that, near 35 millionths per °C.

• Shell correction: 125 °C × 0.0000351 = 0.44 %.
• On a capacity-table reading of 2,000.00 m³ that is 8.8 m³ more product present than the cold table indicates — about 8.4 tonnes at the density prevailing.

This is the correction left out most often, because it is a property of the tank rather than of the cargo and because 0.44 % sounds like rounding. It is not rounding. It is the same order of magnitude as the tolerance the parties are arguing over. It also has one useful property: if the shell is at the same temperature for the opening and the closing gauge, it cancels in the difference. It stops cancelling the moment a loading runs overnight, or a tank is topped up hot after standing cool — which is precisely when somebody notices a discrepancy and reaches for the word shortage.

1. Name the quantity basis

State explicitly that quantity is determined on a weight basis in metric tonnes. Mass is invariant with temperature; volume is not. If for operational reasons quantity must be expressed as volume, the clause must also name the reference temperature (15 °C is the normal choice) and the correction practice used to get there.

2. Name where and how quantity is determined

Specify the point of determination — weighbridge at load point, shore tank gauging before and after loading, or vessel measurement — and who performs it. "Quantity as per independent surveyor's certificate at load port" is short, standard and enforceable.

3. Name the surveyor and who pays

Appoint an internationally recognised inspection company, name it in the contract, and state how the cost is split. What third-party inspection buys is that both sides are working from a report neither of them wrote, which is what removes the argument rather than merely recording it.

4. Agree a tolerance

Bulk cargoes normally carry a tolerance, commonly expressed as a percentage more or less at the seller's option. Without one, a routine measurement variance becomes a contractual breach.

5. Keep the documents consistent

The unit and the basis must be identical across the sales contract, the letter of credit, the commercial invoice, the packing list and the bill of lading. A discrepancy between "MT" on the invoice and "m³" on the survey report is one of the most common reasons a bank refuses documents under an L/C — and the cargo is already on the water by the time anyone notices.

6. Handle drummed cargo on its own terms

For drums, quantity is normally the drum count multiplied by the declared net weight per drum, verified by weighing a sample of drums. Make clear that the invoiced weight is net of drum tare, and record the tare on the packing list.

7. Choose the basis the cargo can actually be measured on

Which basis is right is not a matter of taste. It follows from how the cargo will physically move.

• Drums and jumbo bags. Weight, net of tare, established on a trade-verified weighbridge, with a random sample of filled units weighed individually. No temperature question arises at any point in the chain, which is why drummed trade produces so few quantity disputes relative to its volume.
• Bitutainers and tank containers. Weight, from a weighbridge before and after filling or discharge. Never from the unit’s nominal capacity: a rated volume tells you what a tank container can hold, not what is in it.
• Bulk vessel. Weight in air, from shore tank gauging at the load port corrected under a named practice, with the ship’s figures recorded on the certificate for reference but not governing. Provide for a load-port and a discharge-port survey, and state that a difference between them within an agreed percentage is deemed measurement variance rather than shortage.
• Road tanker into a plant. Weighbridge at both ends where the receiving plant has one, and a mass meter where it does not.
• Where a volume basis is genuinely unavoidable — some tenders, some excise regimes and some pipeline arrangements are written in cubic metres and cannot be renegotiated — the volume must be a corrected volume at a named base temperature, under a named correction practice, using a density from a named test method at a named test temperature. Four names. A volume with fewer than four names behind it is not a quantity.

8. Decide who measures, and pay them properly

Whoever owns the tape owns the number. If the seller gauges his own tank with his own thermometer and issues his own certificate, the buyer has not bought a quantity, he has bought the seller’s arithmetic — and it will be arithmetic that is defensible in every particular and consistently favourable at every rounding.

• Appoint an independent surveyor at the point where quantity is determined, name the company in the contract, and state the cost split. Require the report to be issued to both parties directly rather than passed on by one of them.
• Reserve the right to attend. A clause allowing the buyer or its representative to witness gauging costs nothing to write and is almost never exercised. Its value is that it exists and that the other side knows it exists.
• Take a discharge survey even where the load-port figure governs. It is the only way to detect a real loss, and it is the evidence a marine cargo underwriter will ask for. A load figure that is final for invoicing does not stop you from measuring at the other end.
• Do not let one party supply both the volume and the density unchecked. Density is the multiplier that converts one into the other, and a sealed retained sample lets it be verified later by a laboratory neither party controls.

9. The sentence that stops a temperature difference becoming a claim

All of the above condenses into one clause. Adapt the wording to your own contract and your own governing law, but the four elements — unit, weight basis, correction practice and an express statement about temperature — all need to be present.

“Quantity shall be determined and invoiced in metric tonnes, weight in air, as per the certificate of the independent inspector appointed under Clause [X] at the load port, which shall be final and binding for invoicing purposes save for fraud or manifest error. Where any volume figure is used for any purpose under this contract, observed volume shall be corrected to a base temperature of 15 °C in accordance with ASTM D4311, using the density at 15 °C stated on the batch Certificate of Analysis, determined in accordance with ASTM D70 and converted to 15 °C by the same practice. The observed temperature, the number and depth of temperature readings, the density and its test temperature, and the volume correction factor applied shall each be stated on the quantity certificate. A difference between volumes observed at different temperatures shall not of itself constitute a shortage or a shortfall in delivery.”

Each sentence does one job. The first fixes the unit and the basis and names who decides. The second fixes the correction and the density, closing the 25 °C gap described earlier in this page. The third makes the certificate show its working, so that the arithmetic can be checked by anybody rather than taken on trust. The fourth is the one that ends the argument before it begins: it states in terms that a volume difference caused by temperature is not a shortage, which removes the entire class of claim this page exists to explain. Nothing here is legal advice — the wording that works is the wording your own counsel approves under the law governing your contract.

10. What a quantity certificate has to show

A certificate stating a tonnage and nothing else is a conclusion, not evidence, and it cannot be checked by the person paying against it. Require the following on the face of the document, and read them when it arrives rather than when a dispute starts.

• Tank or vessel identity, with the reference and date of the capacity table used
• Opening and closing gauges, stated as innage or ullage, with the reference height check
• Observed temperature, with the number of readings and the depths at which they were taken
• Density, the test method, and the temperature at which it was determined
• The coefficient of expansion or the correction practice applied, and the resulting volume correction factor
• Total observed volume, gross observed volume and gross standard volume, shown separately rather than collapsed into one line
• Whether the mass is stated in air or in vacuum
• The surveyor, the date and place of attendance, and a signature with a name and a role

Every item on that list is a step in the chain set out further up this page. A certificate carrying all of them can be recalculated by a third party in fifteen minutes, which is the entire point of it.