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Hydrogen liquefaction

Screening of specific liquefaction energy and levelized cost of liquefaction (EUR/kg) for turning gaseous H2 into LH2 at -253 C.

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11

Cost of liquefaction

Delivered electricity price to the liquefaction plant.

EUR/MWh

Real discount rate used to compute the capital recovery factor.

Economic life for levelized cost. IDEALHY uses 20 years; DOE liquefier lifetime is 40 years.

years

Annual fixed O&M as a fraction of total CAPEX. IDEALHY assumes 4%.

Levelized cost of liquefaction (LCOL)

Plant-gate cost to turn 1 kg of gaseous H2 into LH2

…EUR/kg

LCOL breakdown: capital share

Annuity contribution to LCOL (~43% at the IDEALHY point)

…EUR/kg

LCOL breakdown: electricity share

Electricity contribution to LCOL (~39% at the IDEALHY point)

…EUR/kg

Total project CAPEX

Installed cost plus indirect/owner factor (zero here: source is all-in)

…EUR

Scaled specific CAPEX

Installed plant cost intensity after the HDSAM 0.8-power scale curve

…EUR/(kg/day)
LCOL cost breakdown

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LCOL vs electricity price

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Energy & efficiency

Refrigeration cycle. Selects reference specific liquefaction energy and reference CAPEX intensity.

Specific liquefaction energy (plant SEC)

Electricity drawn per kg of LH2 (process + plant auxiliaries), at nameplate

…kWh/kg

Second-law (exergetic) efficiency

Reversible Carnot floor (2.88 kWh/kg) divided by actual plant SEC

…%

Reversible (Carnot) energy floor

Second-law minimum work to liquefy H2 from 20 bar

…kWh/kg

Effective electricity consumption (part-load adjusted)

Plant SEC scaled by a screening part-load penalty

…kWh/kg
Sensitivity to operating hours

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Throughput

Nameplate liquefaction capacity in tonnes of LH2 per day.

Full-load operating hours per year. 8000 h ~ 91% load factor (IDEALHY base case).

Annual operating hours

Full-load equivalent operating hours per year

…h/year

Annual LH2 output

Liquefied hydrogen delivered at the plant gate

…t/year

Annual electricity input

Refrigeration plant electrical demand based on effective SEC

…MWh/year
LCOL vs plant capacity

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Delivery

Price of the gaseous H2 feed, used to value process/leakage losses (feed/LH2 ratio ~1.017).

EUR/kg

Delivered cost incl. boil-off allowance

LCOL plus a downstream holding-loss penalty (0.1-0.2 %/day)

…EUR/kg

About

Calculator context

Screening calculator for a cryogenic hydrogen liquefaction plant that cools gaseous H2 (typ. 20-80 bar, ambient) down to liquid hydrogen (LH2) at about -253 C (20-23 K) using a refrigeration cycle (Claude/precooled, Brayton-Nelium or mixed-refrigerant). It is physically distinct from mechanical compression (which only raises pressure) and from salt-cavern storage. Two deliverables: (A) the specific liquefaction energy of the plant (kWh of electricity per kg of LH2, bundling the refrigeration process and plant auxiliaries) together with its second-law (exergetic) efficiency relative to the 2.88 kWh/kg reversible Carnot floor; and (B) the plant-gate levelized cost of liquefaction (LCOL) via a standard annualized-cost / annual-output build-up: annualized CAPEX (capital recovery factor on a HDSAM-style 0.8-power scaling curve), fixed O&M, electricity, and a feed-hydrogen loss term. A boil-off allowance (~0.1-0.2 %/day) is exposed as a downstream holding-loss penalty on top of the plant-gate cost. Calibrated against the IDEALHY economic model (1.72 EUR/kg at 50 t/day, 8000 h/yr, 100 EUR/MWh) and cross-checked against DOE Record 19001. Excludes upstream H2 production and downstream delivery.

Model

77 variables — inputs, calculations and outputs, with their dependencies.

77 variables shown of 77
VariableValueUnitDepends on
1——
50t/day—
8000h/year—
100EUR/MWh—
2EUR/kg—
0.1ratio—
20years—
0.04ratio—
VariableFormulaUnitDepends on
if((<=0)+(<=0)+(>)+(<0)+(<0)+(<0)+(<=0)+(<0)+(<)+(>)>0,1,0)bool
/max(,)—
clamp(+*(-),,)—
*kg/day
/max(,)kg/h
if(==,,if(==,,))EUR/(kg/day)
*(+)EUR
if(<,/max(,),(*(+)^)/max((+)^-,))—
*EUR/year
*EUR/year
*kg/year
*(-)*EUR/year
*/*kg/year
*/max(,)EUR/kg
VariableFormulaUnitDepends on
*h/year
if(==,,if(==,,))kWh/kg
*kWh/kg
*kWh/kg
clamp(/max(,)*,,)%
*/max(,)kg/year
/max(,)t/year
*/max(,)MWh/year
clamp(*(/max(,))^(-),,)EUR/(kg/day)
*EUR
*(+)EUR
*EUR
*EUR
*EUR
*EUR/year
+++EUR/year
/max(,)EUR/kg
/max(,)EUR/kg
/max(,)EUR/kg
+EUR/kg

Assumptions

35 assumptions used in the calculations

  • Prevents division-by-zero and NaN propagation in edge cases.

    Market range Not applicable (numerical parameter).

    0.000001
    Numerical stability constant for division guards.

  • Avoids inline literals in DSL expressions per spec.

    Market range Exact.

    0
    Numeric constant.

  • Avoids inline literals in DSL expressions per spec.

    Market range Exact.

    1
    Numeric constant.

  • Calendar-year hours, used for the load factor.

    Market range 8760 (non-leap year); 8784 (leap year).

    8760h/year
    Calendar-year hours convention.

  • Converts daily nameplate throughput to annual via operating hours.

    Market range Exact.

    24h/day
    Hours per day.

  • Converts kWh-based specific consumption to MWh for cost accounting.

    Market range Exact.

    1000kWh/MWh
    Unit conversion.

  • Converts tonnes per day to kg per day for production and CAPEX intensity.

    Market range Exact.

    1000kg/t
    Unit conversion.

  • Converts ratios to percent and percent rates to fractions.

    Market range Exact.

    100
    Percent conversion factor.

  • Required because the DSL has no strings.

    Market range Not applicable.

    1
    Numeric selector encoding.

  • Required because the DSL has no strings.

    Market range Not applicable.

    2
    Numeric selector encoding.

  • Required because the DSL has no strings.

    Market range Not applicable.

    3
    Numeric selector encoding.

  • Validates the selector domain.

    1
    Input validation bound.

  • Validates the selector domain.

    3
    Input validation bound.

  • Captures the rise in specific energy when the liquefier runs below full load.

    0.3
    Screening part-load penalty coefficient.

  • Prevents part-load operation from improving on the nameplate specific energy.

    Market range 1 (by definition).

    1
    Clamp lower bound for the penalty factor.

  • Avoids unrealistically large penalties at low operating hours in a screening model.

    1.4
    Clamp upper bound for the penalty factor.

  • Thermodynamic reference for the second-law efficiency.

    2.88kWh/kg
    Reversible (Carnot) minimum liquefaction work.

  • Reference plant SEC for the Claude/precooled cycle.

    6.76kWh/kg
    Full-plant specific liquefaction energy (process + auxiliaries).

  • Reference plant SEC for the Brayton (Nelium) cycle.

    7.5kWh/kg
    Full-plant specific liquefaction energy.

  • Reference plant SEC for conventional / mixed-refrigerant liquefiers in operation today.

    12kWh/kg
    Full-plant specific liquefaction energy.

  • Reference size at which the specific CAPEX equals the reference value.

    50t/day
    Scale-curve reference capacity.

  • Economy-of-scale exponent for total liquefier CAPEX; specific CAPEX scales as C^(0.8-1).

    0.8
    HDSAM installed liquefier cost exponent.

  • Reference installed CAPEX intensity for the Claude/precooled cycle.

    2100EUR/(kg/day)
    Specific installed CAPEX at reference size.

  • Reference installed CAPEX intensity for the Brayton (Nelium) cycle.

    2300EUR/(kg/day)
    Specific installed CAPEX at reference size.

  • Reference installed CAPEX intensity for conventional / mixed-refrigerant plants.

    1900EUR/(kg/day)
    Specific installed CAPEX at reference size.

  • Prevents unrealistically low specific CAPEX from extrapolating the scale curve to very large sizes.

    1200EUR/(kg/day)
    Clamp minimum for scaled specific CAPEX.

  • Prevents unrealistically high specific CAPEX when scaling to very small sizes.

    6000EUR/(kg/day)
    Clamp maximum for scaled specific CAPEX.

  • The cascade is kept for readability but the factor is zero since the source cost is already installed.

    Market range 0 here; 0.2-0.8 if starting from bare-equipment cost.

    0
    Installation factor on equipment cost.

  • Kept for readability but zero because the reference CAPEX is all-in.

    Market range 0 here; 0.1-0.5 if starting from a narrower scope.

    0
    Indirect + owner cost factor on installed cost.

  • Cold box and heat exchangers are a major share of liquefier cost.

    0.45
    Equipment cost allocation share.

  • Compression machinery is the second major share of liquefier cost.

    0.4
    Equipment cost allocation share.

  • Remaining balance-of-plant share of liquefier cost.

    0.15
    Equipment cost allocation share.

  • Values the gaseous H2 lost in the liquefaction process.

    1.017kg feed/kg LH2
    Feed-to-product hydrogen ratio.

  • Continuous evaporation of LH2 in storage/transport.

    0.2%/day
    Boil-off rate.

  • Holding duration over which boil-off accumulates.

    10day
    AI

Sources

Primary reference

Stolzenburg et al., Efficient Liquefaction of Hydrogen: Results of the IDEALHY Project (2013); DOE Hydrogen and Fuel Cells Program Record 19001 (2019).