How to Calculate Cryogenic Hydrogen Boil-Off Rate
Liquid hydrogen (LH₂) storage tanks are never perfectly adiabatic. Even with multilayer insulation, penetrations, and vapor-cooled shields tuned for performance, a residual heat leak slowly vaporises product. Quantifying that boil-off rate allows operators to dimension vent stacks, reclaim compressors, and revenue forecasts while also validating whether insulation upgrades deliver the promised benefit. This walkthrough formalises the calculation so engineering, commercial, and regulatory stakeholders can read from the same playbook.
We begin by defining the energy balance that links heat ingress to mass loss. Next we catalogue the variables, units, and reference data required for a rigorous calculation. The article then derives the governing equations, lays out a repeatable workflow for assembling measurements, and explains how to validate outputs against tank telemetry. Finally, we describe limitations and stress cases so you know when to escalate to computational fluid dynamics or transient boil-off simulations. Use the embedded calculator alongside storage planning tools such as the hydrogen backup storage sizing calculator and volumetric modelling covered in the cushion gas walkthrough to build a full storage strategy.
Definition and scope
Boil-off rate (BOR) expresses how many kilograms of liquid hydrogen vaporise per unit time because of unavoidable heat ingress. The metric is typically normalised to kg/day for commercial discussions or kg/hour when coordinating vent recovery hardware. We restrict the scope to steady-state heat leaks rather than rapid transients during filling or pump-down. The method applies to double-walled vacuum-insulated tanks, spherical dewars, and horizontal bullet tanks alike so long as the variables are measured consistently.
Operators often cite BOR as a percentage of stored mass per day. That framing is convenient for revenue protection but obscures the underlying energy balance. Keeping the raw kg/day figure front and centre ensures you can trace how each heat ingress pathway contributes to loss and reveals whether mitigation investments—improved insulation, vapor-cooled shields, or active recirculation—actually close the gap.
Variables, symbols, and units
Collect the following inputs before attempting the calculation. Maintaining SI units avoids conversion errors:
- A – External surface area exchanging heat with the environment (square metres). Include heads, shell, nozzle collars, and saddles if they bypass insulation.
- q̇ – Average heat flux through the insulation (watts per square metre). Obtain from boil-off tests, guarded hot plate measurements, or manufacturer data adjusted for actual vacuum levels.
- Q̇aux – Additional parasitic heat loads (watts). Represents penetrations, supports, pump columns, or mixer motors that bypass the primary insulation envelope.
- L – Latent heat of vaporisation for hydrogen at tank pressure (kilojoules per kilogram). Draw from thermophysical property tables; LH₂ at 1 bar uses 446 kJ/kg, while higher pressures reduce latent heat slightly.
- minv – Stored hydrogen mass (kilograms). Optional, used when translating BOR into percent-of-inventory metrics.
- BOR – Daily boil-off rate (kilograms per day).
Ensure heat flux measurements reflect the actual temperature gradient between ambient and bulk liquid. Sensors mounted on radiation shields or inner shells provide better fidelity than ambient probes alone. When q̇ varies markedly across surfaces—roof vs. cylindrical body, for example—calculate a weighted average or run the calculation separately for each zone before summing results.
Governing equations
The energy balance is straightforward: steady heat ingress divides by latent heat to reveal mass loss. Converting to daily terms yields:
Total heat ingress (watts): Q̇tot = A × q̇ + Q̇aux
Mass boil-off rate (kilograms per second): ṁ = Q̇tot ÷ (L × 1,000)
Daily boil-off (kilograms per day): BOR = ṁ × 86,400
Percent inventory loss per day (optional): f = BOR ÷ minv
Multiplying latent heat by 1,000 converts kJ/kg to J/kg, aligning with watts (J/s). The optional fraction f is dimensionless; multiply by 100 for a percent. Resist the temptation to embed percent conversions into equations—the calculator and workflow already format outputs for you, limiting rounding risk.
Step-by-step workflow
1. Establish geometry and thermal boundaries
Derive surface area from as-built drawings or laser scans. Include saddles, stiffening rings, or support skirts that bridge vacuum gaps. Document whether shields or foam cover those surfaces because they may justify lower q̇. Capture ambient temperature ranges and solar loads for each season; design calculations often assume 20 °C ambient but field conditions can swing 15 °C either direction.
2. Quantify heat flux
Combine insulation manufacturer data, vacuum quality, and test boil-off runs to estimate q̇. If boil-off trials are available, invert the equations to solve for q̇ and use that as your baseline. When using design data, apply correction factors for degraded multilayer insulation, settling, or moisture ingress. Keep seasonal values handy so you can run worst-case scenarios without rebuilding the entire model.
3. Capture parasitic loads
Inventory penetrations and moving equipment. Pump columns, sample lines, level gauge tubes, and mixer shafts each act as heat bridges. Estimate their steady-state wattage using conduction formulas or manufacturer data and add to Q̇aux. For intermittent loads—purges or valve actuation—convert duty cycles into an equivalent continuous watt load so the daily total reflects average behaviour.
4. Select latent heat
Choose L based on actual tank pressure. Use the same source across studies to avoid discrepancies. If you operate near 3 bar for transfer pressure, latent heat drops to roughly 425 kJ/kg; plug that into the formula rather than relying on 1 bar values. Document sources for auditability.
5. Compute and interpret BOR
Multiply A by q̇, add Q̇aux, divide by latent heat, then scale to kg/day. Translate to percent of inventory if you need to brief commercial teams. Compare the output with tank telemetry and historical vent flows to flag anomalies.
Validation techniques
Validation hinges on reconciling the calculated BOR with empirical data. Track tank mass using differential pressure transmitters or weigh cells if installed. Integrate boil-off mass flow meters or reclaim compressor throughput to build an empirical BOR curve. Compare the calculated BOR against rolling averages from telemetry; deviations beyond ±10% warrant investigation. Tie the workflow into commercial models such as the hydrogen throughput guide so delivery commitments reflect true losses.
Stress-test assumptions seasonally. Higher ambient temperatures raise heat flux; cold weather may reduce BOR but introduce stratification. When you apply insulation retrofits, re-run the calculation and log the before/after BOR along with field data so asset managers can quantify avoided venting.
Limitations and escalation triggers
The steady-state model assumes uniform heat flux and ignores transient effects during fill, pump start-ups, or rapid drawdown. Stratification, sloshing, and pressure-control sequences can temporarily boost BOR; treat those separately with dynamic simulations. Likewise, insulation damage or vacuum loss introduces time-varying heat ingress that requires continuous monitoring rather than a static calculation.
The equations also omit radiative gains through open hatches and conductive spikes during maintenance when manways are opened. Record such events in operational logs and exclude them from steady BOR comparisons. When deviations persist despite accurate inputs, deploy infrared thermography or helium leak detection to isolate problem zones before they escalate into safety risks.
Embed: Cryogenic hydrogen boil-off rate calculator
Enter surface area, heat flux, latent heat, and optional parasitic loads to quantify daily boil-off in kilograms and express the loss as a share of inventory when needed.