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Cited by 132Spacecraft and Cryogenic TechnologiesHeat transfer and supercritical fluidsHeat Transfer and Boiling Studies

Modelling of Liquid Hydrogen Boil-Off

Open access
Al Ghafri, Saif Z. S., Swanger, Adam, Jusko, Vincent, Siahvashi, Arman, Perez, Fernando, Johns, Michael L., May, Eric F.·2022·Energies
DOI 10.3390/en15031149
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Abstract

A model has been developed and implemented in the software package BoilFAST that allows for reliable calculations of the self-pressurization and boil-off losses for liquid hydrogen in different tank geometries and thermal insulation systems. The model accounts for the heat transfer from the vapor to the liquid phase, incorporates realistic heat transfer mechanisms, and uses reference equations of state to calculate thermodynamic properties. The model is validated by testing against a variety of scenarios using multiple sets of industrially relevant data for liquid hydrogen (LH2), including self-pressurization and densification data obtained from an LH2 storage tank at NASA’s Kennedy Space Centre. The model exhibits excellent agreement with experimental and industrial data across a range of simulated conditions, including zero boil-off in microgravity environments, self-pressurization of a stored mass of LH2, and boil-off from a previously pressurized tank as it is being relieved of vapor.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper presents BoilFAST, an extended superheated-vapor (SHV) non-equilibrium model for liquid hydrogen boil-off and self-pressurization, validated against large-scale LH2 storage data. It shows good agreement with NASA Kennedy, NASA Glenn, and LLNL experiments across different tank geometries, fill levels, and heat fluxes.

Key findings

  • For NASA Kennedy’s 125 m³ horizontal IRAS tank, BoilFAST reproduced 33% and 67% fill duty-cycle pressurization/depressurization and a 46% fill densification to hydrogen’s triple point; average \(U_L\) and \(U_V\) were 0.0066 W·m⁻²·K⁻¹ and \(U_{VL}\) was 0.6 W·m⁻²·K⁻¹.
  • For NASA Glenn’s 4.89 m³ ellipsoidal tank at 83–84% fill, self-pressurization under heat fluxes of 0.35, 2, and 3.5 W/m² was in excellent agreement; \(U_{VL}\) = 1.04 W/m²/K, with stratification observed especially at 3.5 W/m².
  • For the LLNL 12.5 m³ Dewar with relief pressure 310 kPa and initial 10.2 m³ LH2, BoilFAST matched summer/winter liquid-volume changes and variable heat ingress; \(U_V\) and \(U_L\) = 0.0045 W·m⁻²·K⁻¹ and \(U_{VL}\) = 0.15 W/m²/K.
  • The model accounts for ortho–para hydrogen spin isomer composition; at 20.3 K the equilibrium para-hydrogen content is 99.8%, and a warmer vapor can drive endothermic para-to-ortho conversion.

Methods

  • Extended SHV non-equilibrium model implemented in BoilFAST: solves phase energy balances with heat ingress to liquid and vapor, vapor–liquid heat transfer, and boil-off/relief mass transfer; uses Leachman reference Helmholtz equations of state for parahydrogen, orthohydrogen, and normal hydrogen, plus equilibrium ortho–para ratio equations.
  • Validated against multiple LH2 datasets: NASA Kennedy 125 m³ IRAS tank (33%, 67% duty-cycle; 46% densification), NASA Glenn 4.89 m³ tank (83–84% full; heat fluxes 0.35–3.5 W/m²), and LLNL 12.5 m³ Dewar (relief 310 kPa; initial 10.2 m³).
  • Heat transfer coefficients \(U_L\) and \(U_V\) were estimated from correlations or adjusted to match data; \(U_{VL}\) was fitted to experimental vapor temperature data.

Limitations

  • Stated: \(U_{VL}\) was determined empirically from a fit to experimental vapor temperature data and “will be resolved in future work”; the model assumes the liquid phase is saturated and thermally homogeneous, so it cannot represent liquid thermal stratification.
  • Stated future improvements: calculate vapor–liquid heat transfer coefficients for different tank geometries and insulation systems, describe liquid thermal stratification, and simulate filling/draining operations.
  • Evident from the text: in some cases insufficient tank construction details required adjusting \(U_L\) and/or \(U_V\) to match BOG data; for NASA Glenn, insulation thickness was not stated and existing correlations could not be used, so coefficients were estimated from measured heat fluxes and ambient temperatures. Validation is limited to the specific tanks and conditions tested.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.3390/en15031149

Cites

87 of 87 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

10 of 81 cited sources checked · 4 supported · 1 flagged · accuracy not yet measured

  • Premisecitation

    This tank incorporates an Integrated Refrigeration and Storage (IRAS) system, which maintains the liquid in a zero boil-off state through the use of an internal cryogenic heat exchanger connected to an external Brayton cycle refrigerator.

    “This tank incorporates an Integrated Refrigeration and Storage (IRAS) system [75], which maintains the liquid in a zero boil-off state through the use of an internal cryogenic heat exchanger connected to an external Brayton cycle refrigerator.”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [75] Notardonato, 2017, Zero boil-off methods for large-scale liquid hydrogen tanks using integrated refrigeration and storage, IOP Conf. Ser. Mater. Sci. Eng. source
  • Premisecitation

    Liquefaction processes use heterogeneous catalysts to ensure this equilibrium ratio is attained to prevent the exothermic ortho-to para-hydrogen conversion from occurring during storage.

    “Liquefaction processes use heterogeneous catalysts to ensure this equilibrium ratio is attained to prevent the exothermic ortho-to para-hydrogen conversion from occurring during storage [66].”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [66] Skaugen, 2020, Comparing exergy losses and evaluating the potential of catalyst-filled plate-fin and spiral-wound heat exchangers in a large-scale Claude hydrogen liquefaction process, Int. J. Hydrogen Energy source
  • Findingown data

    A model has been developed and implemented in BoilFAST that allows reliable calculations of self-pressurization and boil-off losses for liquid hydrogen in different tank geometries and thermal insulation systems.

    “A model has been developed and implemented in the software package BoilFAST that allows for reliable calculations of the self-pressurization and boil-off losses for liquid hydrogen in different tank geometries and thermal insulation systems.”
    Quote in the paperSubstantial claim
  • Findingnone given

    The model accounts for heat transfer from the vapor to the liquid phase.

    “The model accounts for the heat transfer from the vapor to the liquid phase, incorporates realistic heat transfer mechanisms, and uses reference equations of state to calculate thermodynamic properties.”
    Quote in the paperSubstantial claim
  • Findingreasoning

    The sensor located at a height of 162 cm is located approximately in the centre of the vapor space.

    “The tank has an internal height of 183 cm, thus the sensor located at a height of 162 cm is located approximately in the centre of the vapor space.”
    Quote in the paperNot a substantial claim
  • May combine two claims. 30
  • Classified as probably not a substantial claim. 35
  • The quote only partly states this claim. 1

  • May combine two claims.

    Premisecitation

    Many studies have investigated how to minimize boil-off losses and empirically determined that top fill (spray) is the most effective way to reduce transfer losses during loading, but the underlying physics remains poorly understood.

    “While many studies [71][72][73][74][75][76][77][78][79][80][81][82][83][84] have investigated how to minimize boil-off losses and empirically determined that top fill (spray) is the most effective way to reduce transfer losses during loading, the underlying physics remains poorly understood.”
    Quote in the paperSubstantial claim1 of 3 sources checked
    • cites [71] Moran, M., and Nyland, T.E.D. (1992, January 6–8). Hydrogen no-vent testing in a 5 cubic foot (142 L) tank using spray nozzle and spray bar liquid injection. Proceedings of the 28th Joint Propulsion Conference and Exhibit: American Institute of Aeronautics and Astronautics, Nashville, TN, USA. source
    • cites [72] Moran, M.E., Nyland, T.W., and Driscoll, S.L. (1992). Hydrogen No-Vent Fill Testing in a 34 Liter (1.2 Cubic Foot) Tank. source
    • cites [73] Chato, D. (1993, January 1). Ground testing for the no-vent fill of cryogenic tanks—Results of tests for a 71 cubic foot tank. Proceedings of the 29th Joint Propulsion Conference and Exhibit: American Institute of Aeronautics and Astronautics, Monterey, CA, USA. source

      The Conclusions (page unavailable) say that both the spray bar and bottom-orifice configurations maintained reasonable tank pressures and that there were few differences between their fills. Rather than finding spray fill most effective, the paper reports successful no-vent fills with both configurations; it also says its equilibrium model predicted both with good accuracy, while noting that low-gravity performance remained unproven. (LLM, conf=0.86)

      Checked by a reasoning model — may be wrong.

      Experimental — accuracy not yet measured

  • Probably not a substantial claim: may not pass S1 (asserted), S3 (load-bearing), S4 (based). The quote only partly states this claim.

    Findingnone given

    For Figure 4b, the measured temperature from sensor TT10 was lower than that estimated because the liquid also thermally stratified.

    “For Figure 4b, sensor TT10, located at the 61% fill level [78], was closest to the vapor liquid interface (approximately 13 cm below); the measured temperature was lower tha”
    Quote in the paperNot a substantial claim2 of 2 sources checked
    • cites [78] Swanger, 2017, Large scale production of densified hydrogen to the triple point and below, IOP Conf. Ser. Mater. Sci. Eng. source
    • cites [75] Notardonato, 2017, Zero boil-off methods for large-scale liquid hydrogen tanks using integrated refrigeration and storage, IOP Conf. Ser. Mater. Sci. Eng. source

      Section 5 (page unavailable) reports liquid-temperature stratification and mentions TT10 in a 67% fill-level test. It does not identify TT10 as being at the 61% fill level or 13 cm below the interface, nor does it compare TT10’s measured temperature with an estimate or attribute such a difference to stratification. (LLM, conf=0.78)

      Experimental — accuracy not yet measured

  • May combine two claims.

    Premisecitation

    The mean effective thermal conductivity of this IRAS MLI system was 0.14 mW·m−1·K−1; this value was used in Equation (14).

    “The mean effective thermal conductivity of this IRAS MLI system was 0.14 mW•m -1 •K -1 ; this value was used in Equation ( 14).”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [89] Fesmire, 2018, Cylindrical cryogenic calorimeter testing of six types of multilayer insulation systems, Cryogenics source

      The Conclusion (p. 18) reports effective thermal conductivities for MLI systems, but does not identify an IRAS MLI system or give its mean conductivity as 0.14 mW·m−1·K−1. Searches for “IRAS” and “0.14 mW/mK” found no passage establishing that value; the paper’s use of 0.00014 is in different units. Whether the citing authors used a value in their Equation (14) is not established by this source. (LLM, conf=0.76)

      Experimental — accuracy not yet measured

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductcitation

    Recently, the model's performance was compared against BOG data obtained for ternary mixtures of methane, ethane, and nitrogen using our apparatus and an LNG mixture used as rocket fuel conducted at Kennedy Space Centre (NASA).

    “Recently [86], the model's performance was compared against BOG data obtained for ternary mixtures of methane, ethane, and nitrogen using our apparatus [58] and an LNG mixture used as rocket fuel conducted at Kennedy Space Centre (NASA) [87].”
    Quote in the paperNot a substantial claim2 of 3 sources checked
    • cites [86] Ghafri, 2021, Advanced Boil-Off Gas Studies of Liquefied Natural Gas used for the Space and Energy Industries, Acta Astronaut source
    • cites [58] Perez, 2021, Measurements of boil-off gas and stratification in cryogenic liquid nitrogen with implications for the storage and transport of liquefied natural gas, Energy source
    • cites [87] Rose, L., Swanger, A.M., Notardonato, W.U., Fesmire, J.E., Gleeson, J., and Carro, R. (2019, January 21–25). Integrated Refrigeration and Storage of LNG for Compositional Stability. Proceedings of the Cryogenic Engineering Conference and International Cryogenic Materials Conference, Hartford, CT, USA. source

      The Introduction identifies a NASA Kennedy Space Center research program studying LNG as a potential rocket fuel. But the Discussion and future experimental investigations section says LNG had not yet been delivered and the first LNG boiloff test had not begun. This paper therefore does not provide the LNG boiloff data implied by the citation. (LLM, conf=0.90)

      Experimental — accuracy not yet measured

  • May combine two claims.

    Premisecitation

    This model is flexible with regards to the fluid type, utilises reference Helmholtz equations of state for the thermodynamic property calculations and has physically-based parameters that are anchored by high-quality experimental data for pure fluids measured using a custom BOG apparatus.

    “This model is flexible with regards to the fluid type, utilises reference Helmholtz equations of state [60,61] for the thermodynamic property calculations and, most importantly, has physically-based parameters that are anchored by high-quality experimental data for pure fluids measured using a custom BOG apparatus.”
    Quote in the paperSubstantial claim1 of 2 sources checked
    • cites [60] Kunz, 2012, The GERG-2008 Wide-Range Equation of State for Natural Gases and Other Mixtures: An Expansion of GERG-2004, J. Chem. Eng. Data source
    • cites [61] Monika, 2019, EOS-LNG: A Fundamental Equation of State for the Calculation of Thermodynamic Properties of Liquefied Natural Gases, J. Phys. Chem. Ref. Data source

      Split into 3 atoms — 2 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

      Experimental — accuracy not yet measured

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationcitation

    This capability of the model to simulate storage at sub-atmospheric pressures is highly relevant to LH2 applications in microgravity environments, including the cryogenic storage systems needed for future long-term space missions.

    “This capability of the model to simulate storage at sub-atmospheric pressures is highly relevant to LH 2 applications in microgravity environments, including the cryogenic storage systems needed for future long-term space missions [90].”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [90] Tesny, E.M., and Hauser, D.M. (2019). Thermal Modeling of Zero Boil Off Tank Experiment. AIAA Propulsion and Energy 2019 Forum, American Institute of Aeronautics and Astronautics. source

      The Background (page unavailable) says cryogenic-fluid storage in microgravity is crucial for future long-term space missions, and Future Work proposes comparing the model’s results with a cryogen in microgravity. Our copy does not establish that the model can simulate storage at sub-atmospheric pressures or specifically address LH2; the experiment used perfluoro-normal-pentane. (LLM, conf=0.84)

      Experimental — accuracy not yet measured

  • May combine two claims.

    Findingown data

    The model exhibits excellent agreement with experimental and industrial data across a range of simulated conditions, including zero boil-off in microgravity environments, self-pressurization of a stored mass of LH2, and boil-off from a previously pressurized tank as it is being relieved of vapor.

    “The model exhibits excellent agreement with experimental and industrial data across a range of simulated conditions, including zero boil-off in microgravity environments, self-pressurization of a stored mass of LH 2 , and boil-off from a previously pressurized tank as it is being relieved of vapor.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Findingnone given

    The model uses reference equations of state to calculate thermodynamic properties.

    “The model accounts for the heat transfer from the vapor to the liquid phase, incorporates realistic heat transfer mechanisms, and uses reference equations of state to calculate thermodynamic properties.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The liquid temperature estimation closely aligns with the experimental results for the densification experiment, except for an irregularity in the data occurring in the range of 125 to 250 h, which was caused by temporary issues with the refrigeration system.

    “The liquid temperature estimation closely aligns with the experimental results, except for an irregularity in the data occurring in the range of 125 to 250 h, which was caused by temporary issues with the refrigeration system.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Overall, the BoilFAST calculations are in good agreement with the experimental data for both the 33% and 67% fill experiments.

    “Overall, the BoilFAST calculations are in good agreement with the experimental dat for both the 33% (Figure 4a) and 67% (Figure 4b) fill experiments.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim.

    Findingnone given

    The model is flexible with regards to the spin isomer composition of the hydrogen in each phase, tank geometry, and associated heat transfer, allowing the simulation of a wide range of scenarios.

    “The model is flexible with regards to the spin isomer composition of the hydrogen in each phase, tank geometry, and associated heat transfer, allowing the simulation of a wide range of scenarios.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingreasoning

    The sensor at a height of 139 cm is close to the liquid-vapor interface and is well represented by the model's liquid temperature estimation.

    “As a result, the sensor at a height of 139 cm is close to the liquid-vapor interface and is well represented by the model's liquid temperature estimation.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S4 (based).

    Findingnone given

    A vapor-liquid heat transfer coefficient, UVL = 1.04 W/m2/K, was chosen as this best.

    “A vaporliquid heat transfer coefficient, U VL = 1.04 W/m 2 /K, was chosen as this best”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingreasoning

    Good agreement exists between the SHV model and each of the sources from all of the comparisons listed above.

    “Good agreement exists between the SHV model and each of the sources from all of the comparisons listed above.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    The model represents the pressurization and subsequent depressurization for both experiments, well only slightly deviating in the pressurization rate during the initial heat leak and at the activation of the IRAS.

    “The model represent the pressurization and subsequent depressurization for both experiments, well onl slightly deviating in the pressurization rate during the initial heat leak and at the activa tion of the IRAS.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The resulting BoilFAST simulation matched the experimental data well, capturing the variable heat ingress rate evident in the slightly non-linear experimental data.

    “The resulting simulation matched the experimental data well, capturing the variable heat ingress rate evident in the slightly non-linear experimental data.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The resultant pressure decline in the tank is also well represented, with the same deviation observed in the middle of the experiment.

    “The resultant pressure decline in the tank is also well represented, with the same deviation observed in the middle of the experiment.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

    Findingnone given

    At the initial tank pressure of 111 kPa, hydrogen has a saturation temperature of 20.6 K and para-hydrogen content of 99.8%.

    “At the initial tank pressure of 111 kPa, hydrogen has a saturation temperature of 20.6 K and para-hydrogen content of 99.8%.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

    Premisecitation

    Liquid hydrogen will play a key role in the transition away from fossil fuels.

    “Liquid hydrogen (LH 2 ) [1][2][3] will play a key role in this transition [4] as it is clean-burning and can function as a store of energy generated from zero-or low-carbon sources, such as renewables or natural gas combined with carbon capture and storage.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [4] Dong, 2018, CO2 emissions, economic and population growth, and renewable energy: Empirical evidence across regions, Energy Econ. source

  • May combine two claims.

    Premisecitation

    The temperature difference between the volume of stored liquid and the ambient environment ensures that heat ingress into the LH2 is inevitable, which can cause it to evaporate.

    “The resulting temperature difference between the volume of stored liquid and the ambient environment ensures that heat ingress into the LH 2 is inevitable, which can cause it to evaporate [8].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [8] Wang, 2021, Numerical investigation on subcooled pool film boiling of liquid hydrogen in different gravities, Int. J. Hydrogen Energy source

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    The evaporated vapor is termed boil-off gas (BOG) and its generation leads to a pressure increase in the relevant storage tank in a process known as self-pressurization, necessitating venting of the tank into the atmosphere and loss of valuable hydrogen.

    “The evaporated vapor is termed boil-off gas (BOG) [9][10][11][12][13] and its generation leads to a pressure increase in the relevant storage tank in a process known as self-pressurization, necessitating venting of the tank into the atmosphere and loss of valuable hydrogen.”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites [9] Tan, 2016, Enhancement of energy performance in a boil-off gas re-liquefaction system of LNG carriers using ejectors, Energy Convers. Manag. source
    • cites [10] Lin, 2018, An approach to estimating the boil-off rate of LNG in type C independent tank for floating storage and regasification unit under different filling ratio, Appl. Therm. Eng. source
    • cites [11] Querol, 2010, Boil off gas (BOG) management in Spanish liquid natural gas (LNG) terminals, Appl. Energy source

  • May combine two claims.

    Premisecitation

    Heat ingress causes the vapor temperature to increase faster than that of the liquid due to the vapor's higher thermal diffusivity, resulting in heat conduction across the vapor-liquid interface and a temperature gradient in the top layer of the liquid phase with the interface at a higher temperature than the bulk liquid (thermal stratification).

    “Additionally, heat ingress causes the vapor temperature to increase faster than that of the liquid due to the vapor's higher thermal diffusivity (α = κ/ρ•c p ), resulting in heat conduction across the vapor-liquid interface, and thus a temperature gradient in the top layer of the liquid phase with the interface at a higher temperature than the bulk liquid: this is known as thermal stratification [”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [15] Kang, 2018, Experimental investigation of thermal stratification in cryogenic tanks, Exp. Therm. Fluid Sci. source
    • cites [16] Gursu, 1993, Analysis and Optimization of Thermal Stratification and Self-Pressurization Effects in Liquid Hydrogen Storage Systems—Part 1: Model Development, J. Energy Resour. Technol. source
    • cites [17] Choi, 2017, Numerical analysis of convective flow and thermal stratification in a cryogenic storage tank, Numer. Heat Transf. Part A Appl. source

  • May combine two claims.

    Premisecitation

    Depending on the insulation quality and the tank's surface-to-volume ratio, BOG generation can be on the order of 0.4% per day for a 50 m3 cryogenic tank and 0.06% per day for a 20,000 m3 LH2 tank.

    “Depending on the insulation quality and the tank's surface-to-volume ratio, BOG generation can be on the order of 0.4% per day for a 50 m 3 cryogenic tank and 0.06% per day for a 20,000 m 3 LH 2 tank [14].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [14] Verfondern, K. (2007). Safety Considerations on Liquid Hydrogen, Forschungszentrum Jülich GmbH.

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    If the warmer stratified layers enter the rocket propellant feed system, pump cavitation can occur, which could potentially destroy the rocket.

    “If the warmer stratified layers enter the rocket propellant feed system, pump cavitation can occur, which could potentially destroy the rocket [35].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [35] Tatom, J.W., Brown, W.H., Knight, L.H., and Coxe, E.F. (1964). Analysis of Thermal Stratification of Liquid Hydrogen in Rocket Propellant Tanks, Springer. source

  • May combine two claims.

    Study design and conductreasoning

    It was not possible to use existing correlations to estimate the ambient-vapor and ambient-liquid heat transfer coefficients in this case as there are insufficient details concerning the insulation system used and uncertainty as to how the use of the electrical resistance heaters can be incorporated into such calculations.

    “It was not possible to use existing correlations to estimate these values in this case as there are insufficient details concerning the insulation system used and uncertainly as to how the use of the electrical resistance heaters can be incorporated into such calculations.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    The liquid temperature estimated by the model is the saturation value corresponding to the tank pressure, which will always be higher than temperatures measured by sensors immersed in the bulk liquid phase due to stratification.

    “The liquid temperature estimated by the model is the saturation value corresponding to the tank pressure, which will always be higher than temperatures measured by sensors immersed in the bulk liquid phase (below the interface) due to stratification.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: The liquid phase is saturated and thermally homogenous.

  • Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.

    Interpretationreasoning

    An accurate and robust BOG model is required to model the storage of LH2 in rockets and spacecraft, and thereby verify the performance of newly designed LH2 storage systems.

    “An accurate and robust BOG model is thus required to model the storage of LH 2 in rockets and spacecraft, and thereby verify the performance of newly designed LH 2 storage systems.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Huerta and Vesovic expanded the non-equilibrium model to include more realistic heat transfer mechanisms in the vapor phase.

    “This was then expanded by Huerta and Vesovic [39] to include more realistic heat transfer mechanisms in the vapor phase.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [39] Huerta, 2019, A realistic vapour phase heat transfer model for the weathering of LNG stored in large tanks, Energy source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Study design and conductcitation

    The model calculations were also compared against literature data reported by the Gas Research Institute for six different LNG weathering tests, and those reported by Harper and Powars for a self-pressurization test from 283 kPa to 1585 kPa in an advanced on-vehicle LNG fuel system.

    “The model calculations were also compared against literature data reported by the Gas Research Institute [56] for six different LNG weathering tests, and those reported by Harper and Powars [57] for a self-pressurization test from 283 kPa to 1585 kPa in an advanced on-vehicle LNG fuel system.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [56] Kountz, K.J. (1999). Weathering of On-Board Storage Tanks. Project Final Report, Institute of Gas Technology. IGT Project 32034-02.

      Not checked in the free run.

    • cites [57] Harper, G., and Powars, C. (2021, December 16). Advanced Liquid Natural Gas Onboard Storage System, Available online: https://www.osti.gov/biblio/835120-advanced-liquid-natural-gas-onboard-storage-system.

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    In the authors' previous work modelling LNG boil-off, a U_VL of 4.0 W/m2/K produced the best match for the experiment.

    “In our previous work modelling LNG boil-off [59], we found that a U VL of 4.0 W/m 2 /K produced the best match for the experiment.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [59] Perez, 2021, Advanced Boil-Off Gas Studies for Liquefied Natural Gas, Appl. Therm. Eng. source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    Both models consider heat ingress in the vapor and liquid phases separately and enable heat transfer between the two phases across the interfacial surface area.

    “Both models consider heat ingress in the vapor and liquid phases separately and enable heat transfer between the two phases across the interfacial surface area.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [44] Migliore, 2017, A non-equilibrium approach to modelling the weathering of stored Liquefied Natural Gas (LNG), Energy source
    • cites [39] Huerta, 2019, A realistic vapour phase heat transfer model for the weathering of LNG stored in large tanks, Energy source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Migliore et al. developed a non-equilibrium numerical model that allows for the vapor phase to be at a higher temperature than the liquid phase.

    “Migliore et al. [44] developed a non-equilibrium numerical model that allows for the vapor phase to be at a higher temperature than the liquid phase.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [44] Migliore, 2017, A non-equilibrium approach to modelling the weathering of stored Liquefied Natural Gas (LNG), Energy source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    At absolute zero, all the hydrogen molecules must be in a rotational ground state and thus 100% para-hydrogen.

    “At absolute zero, all the hydrogen molecules must be in a rotational ground state and thus 100% para-hydrogen [65].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [65] Boeva, 2017, Low-temperature ortho–para hydrogen conversion catalyzed by gold nanoparticles: Particle size does not affect the rate, Int. J. Hydrogen Energy source

  • May combine two claims.

    Study design and conductcitation

    The model has also been compared against the self-pressurization calculations reported by Wang et al. for a horizontal storage tank, and the BOG calculations of Migliore et al. for a standard LNG storage vertical tank with a 165,000 m3 capacity.

    “The model has also been compared against the self-pressurization calculations reported by Wang et al. [46] for a horizontal storage tank, and the BOG calculations of Migliore et al. [44] for a standard LNG storage vertical tank with a 165,000 m 3 capacity.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [46] Wang, 2020, Non-equilibrium thermodynamic model for liquefied natural gas storage tanks, Energy source
    • cites [44] Migliore, 2017, A non-equilibrium approach to modelling the weathering of stored Liquefied Natural Gas (LNG), Energy source

  • Probably not a substantial claim: may not pass S2 (checkable). May combine two claims.

    Premisecitation

    Tools that can accurately estimate BOG production are particularly important in the context of industrial-scale LH2 storage, as the capital expense to design and implement such systems is large, and experimental testing at a relevant pilot-scale can be cost-prohibitive with the results obtained making it difficult to translate to full-scale if their description is entirely empirical.

    “Tools that can accurately estimate BOG production are particularly important in the context of industrial-scale LH 2 storage, as the capital expense to design and implement such systems is large, and experimental testing at a relevant pilot-scale can be cost-prohibitive with the results obtained making it difficult to translate to full-scale if their description is entirely empirical [27,28].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [27] Petitpas, 2018, Simulation of boil-off losses during transfer at a LH2 based hydrogen refueling station, Int. J. Hydrogen Energy source
    • cites [28] Zuo, 2019, Thermal stratification suppression in reduced or zero boil-off hydrogen tank by self-spinning spray bar, Int. J. Hydrogen Energy source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Appreciable temperature gradients (thermal stratification) may exist within the fluid contained by the vessel.

    “It was also shown that appreciable temperature gradients (thermal stratification) may exist within the fluid contained by the vessel.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [7] Petitpas, G. (2018). Boil-Off Losses along the LH2 Pathway, Lawrence Livermore National Laboratory. source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    The tank is insulated with two blankets of MLI, each having seventeen Mylar layers; however, the thickness of the insulation layer was not stated by Hasan et al.

    “The tank is insulated with two blankets of MLI, each having seventeen Mylar layers; however, the thickness of the insulation layer was not stated by Hasan et al. [53].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [53] Hasan, M.M., Lin, C.S., van Dresar, N.T., and Park, F. (1991, January 1). Self-pressurization of a flightweight liquid hydrogen storage tank subjected to low heat flux. Proceedings of the ASME/AIChE National Heat Transfer Conference, Minneapolis, MN, USA.

  • Probably not a substantial claim: may not pass S2 (checkable).

    Premisecitation

    A high-fidelity, physically-based BOG model would allow developers to iterate through full-scale vessel layouts completely within the design space, enabling cost and time savings by better informing decisions on the overall development path and strategy.

    “A high-fidelity, physically-based BOG model would allow developers to iterate through full-scale vessel layouts completely within the design space, enabling cost and time savings by better informing decisions on the overall development path and strategy [7].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [7] Petitpas, G. (2018). Boil-Off Losses along the LH2 Pathway, Lawrence Livermore National Laboratory. source

  • Classified as probably not a substantial claim.

    Premisecitation

    Schaffer found that the payload weight of the cryogenic propulsion stages is considerably influenced by the boil-off rate.

    “The impact of boil-off limitations on future long-term Mars missions is described in detail by Schaffer [37], who found that the payload weight of the cryogenic propulsion stages is considerably influenced by the boil-off rate.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [37] Schaffer, M. (2012). A Study of Cryogenic Propulsive Stages for Human Exploration beyond Low Earth Orbit, International Astronautical Federation.

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationnone given

    The deviation in Test 2 potentially reflects that the heat flux at the beginning of the experiment was initially slightly larger than the average value.

    “Some deviation exists with the data's curvature in Test 2 (2 W/m 2 ); however, this potentially reflects that the heat flux at the beginning of the experiment was initially slightly larger than the average value.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Wang et al. proposed a non-equilibrium model to simulate LNG during storage and refuelling.

    “More recently, a non-equilibrium model was proposed by Wang et al. [46] to simulate LNG during storage and refuelling.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [46] Wang, 2020, Non-equilibrium thermodynamic model for liquefied natural gas storage tanks, Energy source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Petitpas presented a model to estimate the boil-off losses based on their experimental data.

    “Petitpas also presented a model to estimate the boil-off losses based on their experimental data.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [27] Petitpas, 2018, Simulation of boil-off losses during transfer at a LH2 based hydrogen refueling station, Int. J. Hydrogen Energy source

  • May combine two claims.

    Premisecitation

    These models were developed for LNG mixtures in specific scenarios and limited experimental or industrial data were available to verify simulations conducted using these models.

    “However, these models were developed for LNG mixtures in specific scenarios and limited experimental or industrial data were available to verify simulations conducted using these models [56,57].”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [56] Kountz, K.J. (1999). Weathering of On-Board Storage Tanks. Project Final Report, Institute of Gas Technology. IGT Project 32034-02.

      Not checked in the free run.

    • cites [57] Harper, G., and Powars, C. (2021, December 16). Advanced Liquid Natural Gas Onboard Storage System, Available online: https://www.osti.gov/biblio/835120-advanced-liquid-natural-gas-onboard-storage-system.

      Not checked in the free run.

  • Classified as probably not a substantial claim. May combine two claims.

    Premisereasoning

    Several proposals based on exploiting the endothermic para-ortho conversion for cooling purposes and/or to reduce boil-off have been considered; these efforts would be facilitated by a BOG model able to account for a vapor that is not at compositional or thermal equilibrium with the liquid.

    “Several proposals based on exploiting the endothermic para-ortho conversion for cooling purposes and/or to reduce boil-off [67][68][69][70] have been considered; these efforts would be facilitated by a BOG model able to account for a vapor that is not at compositional or thermal equilibrium with the liquid.”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites [67] Petitpas, 2014, Para-H2 to ortho-H2 conversion in a full-scale automotive cryogenic pressurized hydrogen storage up to 345 bar, Int. J. Hydrogen Energy source
    • cites [68] Ubaid, 2014, Effect of para–ortho conversion on hydrogen storage system performance, Int. J. Hydrogen Energy source
    • cites [69] Peng, 2013, Enhanced dormancy due to para-to-ortho hydrogen conversion in insulated cryogenic pressure vessels for automotive applications, Int. J. Hydrogen Energy source

  • May combine two claims.

    Premisecitation

    Petitpas's model ignores the insulation in the energy balance and assumes a constant rate of heat ingress into the tank.

    “This model ignores the insulation in the energy balance, instead assuming a constant rate of heat ingress into the tank; 50 W was found to yield the closest estimate to the experimental data.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [27] Petitpas, 2018, Simulation of boil-off losses during transfer at a LH2 based hydrogen refueling station, Int. J. Hydrogen Energy source

  • Classified as probably not a substantial claim.

    Study design and conductnone given

    Here, the industrial and experimental data of LH2 boil-off and tank self-pressurization are compared with corresponding estimations made using BoilFAST to validate its use for liquid hydrogen storage applications.

    “Here, the industrial and experimental data of LH 2 boil-off and tank self-pressurization are compared with corresponding estimations made using BoilFAST to validate its use for liquid hydrogen storage applications.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Throughout the Petitpas experiment, the system remained static, meaning no mass transfer across the system boundary occurred.

    “Throughout the experiment, the system remained 'static', meaning no mass transfer across the system boundary (such as refuelling) occurred.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [27] Petitpas, 2018, Simulation of boil-off losses during transfer at a LH2 based hydrogen refueling station, Int. J. Hydrogen Energy source

  • May combine two claims.

    Premisecitation

    The stratified mass is unusable as fuel and becomes a liability to the payload capacity of the rocket.

    “Additionally, as this stratified mass is unusable as fuel, it becomes a liability to the payload capacity of the rocket [36].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [36] Joseph, 2016, Effect of Insulation Thickness on Pressure Evolution and Thermal Stratification in a Cryogenic Tank, Appl. Therm. Eng. source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Designs incorporating multi-layer insulation, minimal tank thermal connection points, and deployable sun shields have been proposed to reduce the impact of boil-off.

    “To reduce the impact of boil-off, designs incorporating multi-layer insulation, minimal tank thermal connection points, and deployable sun shields have been proposed [37].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [37] Schaffer, M. (2012). A Study of Cryogenic Propulsive Stages for Human Exploration beyond Low Earth Orbit, International Astronautical Federation.

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Premisecitation

    Many computational fluid dynamics (CFD) and thermodynamic boil-off models have been developed for cryogenic liquids such as liquefied natural gas (LNG), including models based on heat ingress and subsequent BOG rates and those accounting for heat transfer between the vapor and liquid phases.

    “Many computational fluid dynamics (CFD) and thermodynamic boil-off models have been developed for cryogenic liquids such as liquefied natural gas (LNG), including models based on heat ingress and subsequent BOG rates and those accounting for heat transfer between the vapor and liquid phases [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55].”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites [38] Miana, 2016, Comparison of evaporation rate and heat flow models for prediction of Liquefied Natural Gas (LNG) ageing during ship transportation, Fuel source
    • cites [39] Huerta, 2019, A realistic vapour phase heat transfer model for the weathering of LNG stored in large tanks, Energy source
    • cites [40] Miana, 2010, Calculation models for prediction of Liquefied Natural Gas (LNG) ageing during ship transportation, Appl. Energy source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Study design and conductcitation

    In our related work, we tested and validated the SHV model against our experimental data for pure liquid nitrogen and LNG-like binary mixtures of methane and ethane.

    “In our related work [58,59], we tested and validated the SHV model against our experimental data for pure liquid nitrogen [58] and LNG-like binary mixtures of methane and ethane [59].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [58] Perez, 2021, Measurements of boil-off gas and stratification in cryogenic liquid nitrogen with implications for the storage and transport of liquefied natural gas, Energy source
    • cites [59] Perez, 2021, Advanced Boil-Off Gas Studies for Liquefied Natural Gas, Appl. Therm. Eng. source

  • Probably not a substantial claim: may not pass S4 (based).

    Premisenone given

    These models tend to use cubic equations of state for thermodynamic calculations, which are not optimised for the most accurate description of LNG, let alone liquid hydrogen.

    “Furthermore, these models tend to use cubic equations of state for thermodynamic calculations, which are not optimised for the most accurate description of LNG, let alone liquid hydrogen.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Interpretationreasoning

    To correctly use this model for the description of liquid hydrogen storage and boil-off, it must adequately capture the influence of conversions between the two spin isomers, orthohydrogen and parahydrogen.

    “However, to correctly use this model for the description of liquid hydrogen storage and boil-off, it must adequately capture the influence of conversions between the two spin isomers, orthohydrogen.and parahydrogen.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    We have previously presented a boil-off model based on a superheated vapor assumption similar to the non-equilibrium methods presented in the literature.

    “We have previously [58,59] presented a boil-off model based on a superheated vapor assumption similar to the non-equilibrium methods presented in the literature.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [58] Perez, 2021, Measurements of boil-off gas and stratification in cryogenic liquid nitrogen with implications for the storage and transport of liquefied natural gas, Energy source
    • cites [59] Perez, 2021, Advanced Boil-Off Gas Studies for Liquefied Natural Gas, Appl. Therm. Eng. source

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    Currently, the space industry is an important user of LH2, with long duration storage of cryogenic hydrogen being essential in orbital transfer vehicles, the upper stages of rockets, and deep space exploration probes.

    “Currently, the space industry is an important user of LH 2 , with long duration storage of cryogenic hydrogen being essential in orbital transfer vehicles, the upper stages of rockets, and deep space exploration probes [29][30][31][32][33][34].”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites [29] Haberbusch, 2004, Thermally optimized zero boil-off densified cryogen storage system for space, Cryogenics source
    • cites [30] Majumdar, 2008, Numerical modeling of propellant boil-off in a cryogenic storage tank, AIP Conf. Proc. source
    • cites [31] Bailey, T.E., and Fearn, R.F. (1964). Analytical and Experimental Determination of Liquid-Hydrogen Temperature Stratification, Springer. source
55 of 55

  • The authors state this as an assumption.

    The liquid phase is saturated and thermally homogenous.

    “The SHV model currently implemented in BoilFAST assumes the liquid phase is saturated and thermally homogenous.”

  • The authors state this as an assumption.

    The initial liquid and vapor in the tank are a saturated liquid in equilibrium with the vapor phase.

    “The initial conditions of the liquid and vapor in the tank are defined based on the system pressure, assuming a saturated liquid in equilibrium with the vapor phase.”

  • The authors state this as an assumption.

    The vapor temperature is the average temperature for the vapor phase.

    “The vapor temperature is taken to be the average temperature for the vapor phase.”

  • The authors state this as an assumption.

    During self-pressurization, no venting occurs (n_relief is zero) during the pressure build-up stage.

    “This ensures that n relief is zero (no venting) during the pressure build-up stage (i.e., n F,j-1 -n L -n V = 0 for all time steps).”

  • The paper relies on this without support.

    At liquid hydrogen storage conditions, the equilibrium fraction of parahydrogen is around 99.8% (at the normal boiling point of 20.3 K).

    “In particular, at the cryogenic storage conditions where liquid hydrogen is stored, the equilibrium fraction of parahydrogen is around 99.8%.”
    “For liquid hydrogen at its normal boiling point (20.3K), the equilibrium para-hydrogen content is 99.8%.”
5 of 5

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Energy-balance equations use rates where the text describes changes per time step

    Minor

    Equations (6) and (7) put enthalpy derivatives on the left, but the text says their right-hand sides equal total enthalpy changes over a time step. A derivative is a rate, not a total change; the heat and boil-off terms would need to be expressed as rates for these equations to be consistent.

1 of 1

Cites

Flagged first, then by citations

Research works printed but not linked: 1

  1. Migliore, C. (2016). Modelling the Weathering Process of Stored Liquefied Natural Gas (LNG), Imperial College London. · DOI · Paper page

Cited by

Sorted by citations

Related

Authors
Al Ghafri, S. Z. S., Swanger, A., Jusko, V., Siahvashi, A., Perez, F., Johns, M. L., & May, E. F.
Affiliations
  • Fluid Sciences and Resources Division, Department of Chemical Engineering, Faculty of Engineering and Mathematical Sciences, The University of Western Australia, Crawley, WA 6009, Australia
  • Kennedy Space Center (US)
  • The University of Western Australia (AU)
Corresponding author
May, Eric F.
ORCID
Venue
Energies
Publisher
MDPI AG
Published
2022-02-04
Volume
15
Issue
3
Pages
1149
ISSN
1996-1073 (ISSN-L)
DOI
10.3390/en15031149
OpenAlex
W4210351193
Cited by
131
References
84
Citations by year
2026: 35 · 2025: 45 · 2024: 28 · 2023: 19 · 2022: 4
FWCI
10.68
Type
journal article
Language
en
Open access
Licence
Locations
  • Energies (publishedVersion, cc-by)
  • RePEc: Research Papers in Economics (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • UWA Profiles and Research Repository (UWA) (submittedVersion, cc-by)
Topics
  • Physical Sciences › Engineering › Aerospace Engineering › Spacecraft and Cryogenic Technologies
  • Physical Sciences › Engineering › Computational Mechanics › Heat transfer and supercritical fluids
  • Physical Sciences › Engineering › Mechanical Engineering › Heat Transfer and Boiling Studies
Keywords
liquid hydrogen, boil-off, self-pressurization, cryogenic storage tanks, heat transfer, equation of state, thermal insulation, tank geometry

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-30.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-30.

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