Refrigerated ammonia storage with boil-off reliquefaction

Protects divisions against a zero denominator.

Lower limit in the input guard and gauge pressure of an atmospheric tank.

Unit value used in the CRF, the tank count and the Customized switch.

Converts a percent into a fraction.

Converts a fraction into a percent.

Kilograms per tonne.

Hours per day, to turn a daily boil-off into an hourly rate.

Days per year: boil-off and throughput are daily rates.

Hours per year.

MWh per kWh.

kWh per MWh.

USD per million USD.

kJ per kWh, to turn kJ/h into kW.

Reference case 1: IEA 2019 terminal tank cost (34,100 t for 68 MUSD), 4 % O&M, IRENA large-tank boil-off of 0.04 %/day.

Reference case 2: IEA Global Hydrogen Review 2024 terminal tank cost (36,700 t for 115 MUSD), 3 % O&M, terminal-tank boil-off of 0.01 %/day.

Lowest valid reference-case code, used by the input guard.

Highest valid reference-case code, used by the input guard.

Reliquefaction cycle 1: single-stage vapour-compression cycle on the boil-off gas (Ji et al. 2025).

Reliquefaction cycle 2: Linde-Hampson open cycle on the boil-off gas (Ji et al. 2025).

Smallest ammonia output accepted: a small modular green ammonia plant. Below 5 kt stored the CAPEX is extrapolated and flagged.

Largest ammonia output accepted: a world-scale ammonia train.

Shortest storage autonomy accepted, one day of output.

Longest storage autonomy accepted, covering an export terminal waiting on ship arrivals.

Lowest throughput load factor accepted. Below half load the tank is oversized for the flow and the fixed cost per tonne stops being representative.

A plant cannot ship more than its nameplate output.

Highest real discount rate accepted.

Numerical floor of the scaled specific CAPEX. With 50,000 t tanks at most, the law never goes below about 1,580 EUR/t, so the floor never binds inside the declared domain.

Numerical ceiling of the scaled specific CAPEX. The smallest tank of the domain (10 t) gives about 20,500 EUR/t in case 1 and 36,000 EUR/t in case 2, so the ceiling never binds inside the declared domain.

Ceiling on the content of one tank. The working capacity is split into the smallest whole number of tanks that keeps each one at or below it.

Market range IRENA Part II quotes storage sizes up to 60 kt (see irena_partII_max_storage_size_t).

Upper end of the ammonia storage sizes covered by IRENA Part II. Used only to show how large each tank is against it; the split into tanks uses the stricter 50 kt.

At or above this stored quantity the refrigerated atmospheric tank is the standard choice, and it is the only regime this calculator prices from a source.

Below this stored quantity, pressurised spheres or bullets are the norm. Between 1.5 and 5 kt both regimes are used (transition zone).

Lower end of the storage pressure of a pressurised ammonia vessel at ambient temperature, shown when the stored quantity is below the refrigerated threshold.

Upper end of the same pressure range.

Indicative steel mass of refrigerated storage, the reason refrigerated tanks win at scale. Not used in the cost.

Indicative steel mass if the same quantity were stored pressurised: 16 times more steel per tonne, which is why pressurised storage stays small. Not used in the cost.

Daily evaporation of the stored liquid, as a share of the working capacity, in case 1. The model keeps the tank full all year, a conservative reading.

Daily evaporation of the stored liquid in case 2 (IEA 2024 terminal tank).

Electricity per kg of boil-off gas reliquefied with cycle 1.

Electricity per kg of boil-off gas reliquefied with cycle 2.

Heat that evaporates one kg of liquid ammonia at -33 C. The boil-off rate times this value is the heat leaking into the tank, which the reliquefaction loop pumps back out.

Market range About 1,370 kJ/kg at 1 atm; physical property.

Size of the tank whose cost anchors case 1. The law scales the cost of each tank from this size.

CAPEX of the case 1 reference tank, in 2019 USD. IEA does not itemise it; the calculator reads it as the installed cost of a tank, owner's contingency excluded.

Market range About 1,700-2,000 USD/t stored at 34-57 kt (IEA 2019); 3,130 USD/t at 36.7 kt (IEA 2024); 600-1,000 USD/t (Morgan 2013 via IRENA).

Second IEA tank point, used only to derive the scaling exponent (shown as a check output).

CAPEX of the second IEA tank point, used only to derive the scaling exponent.

Exponent of the per-tank power law: the cost of one tank grows as its content to the power 0.7, so the cost per tonne stored falls as content to the power -0.3. Applied to the case 2 anchor as well, which IEA 2024 does not contradict but does not confirm.

Size of the tank whose cost anchors case 2.

CAPEX of the case 2 reference tank, as printed in USD. It is converted at the same 2019 exchange rate as case 1 and is not deflated to 2019, so part of its 57 % premium over IEA 2019 is price inflation between the two reports.

Low end of the Morgan cost curve reproduced by IRENA, shown as a benchmark next to the model's specific CAPEX in USD. Different currency year (2013 study) and scope: the comparison is qualitative.

High end of the same curve, benchmark only.

Fixed O&M of the tank farm in case 1, as a share of CAPEX a year. Excludes the reliquefaction electricity, which is priced separately.

Fixed O&M in case 2.

IEA's discount rate, the default of the discount-rate input and the basis of the reference CRF output, which shows the IEA annuity factor whatever rate you set.

Service life of the tank farm, used for the annuity and exported to project mode as the replacement interval. Refrigerated steel tanks are built for this order of life.

Converts the euro storage cost back into 2019 USD, to set it next to IRENA's rest-of-plant lump and the Morgan curve.

Converts the IEA tank CAPEX from USD into EUR. Both cases use the 2019 rate, so the calculator is in 2019 euros.

Low end of the lump in which the small modular green ammonia calculator (#482) buries storage. Benchmark for the storage cost in USD, and the reason for the double-count rule.

High end of the same lump. The output 'share of #482 rest-of-plant' divides the storage cost by it.

Turns the reliquefaction electricity per tonne of ammonia into kWh per kg of hydrogen carried, the unit of the IEA terminal electricity figures.

Working capacity = ammonia output x storage days, split into the fewest tanks of at most 50 kt. Boil-off = capacity x daily boil-off rate, reliquefied by an electric loop. Tank CAPEX = number of tanks x reference tank CAPEX x (tank content / reference content)^0.7. Storage cost = (CAPEX x CRF + fixed O&M + reliquefaction electricity) / tonnes of ammonia shipped through storage a year.

Only the refrigerated atmospheric tank (-33 C, full containment, API 625 / EN 14620) is priced. Below 5 kt stored the sources favour pressurised spheres or bullets at 16-18 bar, for which no source found prints a CAPEX: the calculator still returns a number, extrapolated from the refrigerated law, and raises the flag 'CAPEX extrapolated'. That number is not defended.

Boil-off is computed on the full working capacity every day of the year, whatever the throughput. Real inventory cycles between full and the heel, so this overstates the boil-off and the electricity a little; both weigh under 2 % of the cost.

The small modular green ammonia calculator (#482) includes a rest-of-plant lump of 5-30 USD/t that already covers ammonia storage. When this calculator is chained to it, remove the storage share of that lump, or set #482's rest of plant to its low end, so storage is not counted twice.

Constant 2019 euros: both IEA tank costs are converted at the 2019 ECB rate and not escalated. The discount rate is applied as a real rate, as IEA does, and no cost line is escalated, so real and constant money match. Case 2's USD are not deflated to 2019, which leaves case 2 high by the price inflation between the two reports.