Measuring the Level in Liquid Hydrogen Tanks: Considering Cryogenics, Density and Heat Input

→ Product category: H² Level measurement

 

Level measurement in a liquid hydrogen tank is one of the most demanding tasks in process instrumentation. Liquid hydrogen, abbreviated as LH₂, is stored at temperatures close to −253 °C. Even small amounts of heat input can vaporise part of the liquid, change the tank temperature and cause the pressure in the gas space to rise.

A level sensor must therefore do more than simply detect the position of a liquid surface. The measuring principle, process connection, materials, electrical feedthrough, tank insulation and calibration must be designed as a complete system. A probe that operates reliably under normal process conditions is not automatically suitable for temperatures close to 20 K.

Liquid hydrogen also has a very low density. As a result, even tall tanks generate only a small hydrostatic differential pressure. Changes in temperature and pressure affect the density, evaporation and, in some cases, the characteristics of the measuring principle itself.

Suitable measuring solutions requiring project-specific design can be found in the ICS category H² Level Measurement. Additional sensors for monitoring the temperature of hydrogen systems are grouped under H² Temperature Sensors.

Why is LH₂ level measurement so demanding?

Hydrogen must be cooled to approximately −253 °C in order to remain liquid at low pressure. An LH₂ tank therefore normally consists of an inner vessel and highly effective thermal insulation or a vacuum-insulated outer shell.

This creates several challenges for the measuring equipment:

• extremely low process temperature close to 20 K,
• low density of liquid hydrogen,
• very low density and high mobility of hydrogen gas,
• evaporation caused by unavoidable heat input,
• temperature stratification in the liquid and gas space,
• pressure changes during filling, storage and withdrawal,
• significant thermal contraction of probes, pipes and tank components,
• high requirements regarding leak tightness and material compatibility,
• limited accessibility after installation.

A sensor can also influence the tank itself. Every probe, electrical cable and mechanical feedthrough forms a potential thermal bridge from the ambient environment into the cryogenic interior. The measuring point must therefore not only be accurate, but also have the smallest possible thermal impact.

Distinguishing between level, volume and mass

A level sensor initially measures a height or an electrical quantity that depends on it. However, the quantities required for operation are often volume, filling percentage or mass. These quantities must not be treated as identical.

Level

The level describes the position of the liquid surface relative to a defined reference point. It is the direct output variable of many radar, capacitive and hydrostatic systems.

Volume

The volume is derived from the level and the tank geometry. In a cylindrical, spherical or horizontal tank, the relationship between level and volume is not linear across the entire measuring range. A tank characteristic curve or strapping table is required for the conversion.

Mass

The mass is calculated from the volume and the current density:

m = V × ρ

The density of LH₂ depends on temperature and pressure. An unchanged liquid level therefore does not correspond to exactly the same hydrogen mass under all operating conditions.

For reliable inventory calculation, several measured variables are therefore often combined:

• level,
• temperature of the liquid and gas space,
• tank pressure,
• tank geometry,
• thermodynamic density calculation.

Hydrostatic differential-pressure measurement

In hydrostatic measurement, the pressure at the lower tank connection is compared with the pressure in the gas space. The gas-space pressure acts on both sides of the differential-pressure measurement and is therefore largely compensated.

The differential pressure generated by the liquid is approximately:

Δp = ρ × g × h

Where:

• Δp: hydrostatic differential pressure,
• ρ: density of the liquid hydrogen,
• g: acceleration due to gravity,
• h: liquid level above the lower measuring connection.

Assuming a density of approximately 70.8 kg/m³ and a level of 4 m, the resulting pressure is only:

Δp = 70.8 kg/m³ × 9.81 m/s² × 4 m ≈ 2,778 Pa ≈ 27.8 mbar

Even a four-metre-high tank therefore produces only a small measuring span. Zero-point drift, installation height, temperature influence and additional liquid or gas columns can be significant in comparison.

Advantages of differential-pressure measurement

• direct physical relationship between differential pressure and level,
• measurement is also possible in closed and pressurised tanks,
• no long probe extending across the entire tank height is required,
• a continuous standard output signal is possible.

Particular difficulties with LH₂

• very small hydrostatic measuring span,
• density changes caused by temperature and pressure,
• phase changes in connecting lines,
• heat input through process connections and measuring lines,
• possible gas bubbles or liquid columns in unsuitable lines,
• demanding requirements for the temperature range of the measuring cell and pressure transmission system.

Conventional liquid-filled diaphragm seals or capillary systems must not be used without explicit confirmation of their suitability. Standard fill fluids can solidify at cryogenic temperatures, become highly viscous or lose their pressure-transmission properties.

In a project-specific differential-pressure solution, the process connections, thermal decoupling, line routing and position of the transmitter must therefore already be considered in the hydrostatic calculation.

Radar and microwave measurement

Radar measures the distance between an antenna and the liquid surface using reflected electromagnetic waves. The level is calculated from the known tank height and the measured distance.

The main advantage is that no long measuring probe has to extend down into the liquid. The additional heat input into the tank can therefore be lower than with a solid rod probe.

However, radar measurement is not automatically straightforward with liquid hydrogen. Hydrogen has only weak dielectric properties. The reflected measuring signal can therefore be weaker than with water, oil or many chemicals.

The following factors must be checked during the design process:

• dielectric contrast between LH₂ and hydrogen vapour,
• antenna and frequency concept,
• tank height and required measuring resolution,
• interference reflections caused by internals, pipes and the tank bottom,
• geometry of the process nozzle,
• cryogenic suitability of the antenna and process window,
• condensation or icing outside the cryogenic interior,
• unobstructed view of the liquid surface,
• movement and foaming during filling.

A standard radar transmitter for conventional storage tanks must not be used for LH₂ solely on the basis of its measuring range. The process connection, antenna system, leak tightness and thermal decoupling must be qualified for the specific tank design.

Guided microwave

With guided microwave measurement, the radar pulse is guided along a rod or cable probe. The method can detect reflections specifically at the phase boundary, but it introduces a probe over a large part of the tank height into the interior.

For LH₂, the heat input through the probe, thermal contraction, mechanical mounting and possible vibrations during filling and transport must be assessed.

Capacitive level measurement

Capacitive probes use the difference in electrical permittivity between liquid and gaseous hydrogen. Part of the probe is located in the gas space and another part in the liquid. As the level rises, the total capacitance changes.

Capacitive systems have been used for cryogenic liquids for many years. They enable both continuous measurements and multiple discrete switching points.

Advantages

• continuous measurement over a large part of the tank height,
• no moving parts,
• very slim probe designs are possible,
• multiple measuring segments or redundant electrodes can be implemented,
• direct detection of the liquid-gas boundary.

Factors to be considered

• small absolute difference in capacitance,
• change in dielectric constant with temperature and pressure,
• stray capacitance from cables and feedthroughs,
• thermal deformation and change in probe length,
• electrical insulation at cryogenic temperatures,
• end effects in the upper and lower probe areas,
• tank geometry and internal components,
• possible two-phase or foam zones.

The evaluation electronics should be positioned outside the cryogenic area wherever possible. The connection between the probe and the electronics must be electrically stable, hermetically sealed and protected against external interference.

Calibration with water or nitrogen can verify the basic behaviour, but it does not automatically replace an LH₂-specific characteristic curve. The dielectric properties and temperature conditions differ significantly.

Temperature-based level detection

Several temperature sensors can be arranged along a vertical probe. Sensors located in liquid hydrogen show different thermal behaviour from sensors in the gas space. This allows the position of the phase boundary to be determined approximately.

The method is particularly suitable for:

• discrete level points,
• additional plausibility checks,
• detection of temperature gradients,
• monitoring during filling and withdrawal,
• research and test facilities.

However, a temperature measuring chain does not automatically provide a high-resolution continuous level signal. Heat conduction along the probe, response time, sensor spacing and thermal stratification can broaden the detected transition zone.

The temperature sensors must be qualified for temperatures close to 20 K. A sensor with a specified lower measuring limit of −196 °C is not sufficient because LH₂ is approximately 57 K colder.

Tank weighing as an alternative measurement method

For smaller tanks or test facilities, the entire tank can be mounted on load cells. The mass of the hydrogen contained in the tank is calculated from the total mass minus the mass of the tank, piping and attached components.

Advantages

• no additional probe inside the cryogenic interior,
• direct determination of the contained mass,
• largely independent of density changes,
• suitable as a reference for other measuring methods.

Disadvantages

• forces from piping and expansion joints influence the measurement,
• the tank mounting must be designed for load cells,
• wind, vibration and acceleration influences,
• high requirements for large stationary tanks,
• buoyancy and pressure forces may require additional corrections.

For mobile tanks, weighing during transport is only of limited use. However, for stationary reference measurements, it can provide a valuable independent comparison value.

Heat input through sensors and feedthroughs

Every connection between the ambient environment and the inside of the tank conducts heat. These include:

• probe rods and thermowells,
• capillaries and impulse lines,
• electrical cables,
• flanges and process nozzles,
• connectors and hermetic feedthroughs,
• mechanical supports.

The heat input can locally vaporise LH₂ and create gas bubbles at the sensor. In hydrostatic or capacitive measurements, such local two-phase regions can affect the signal.

Measures for reducing heat input include:

• small heat-conducting cross-sections,
• the shortest possible metallic thermal bridges,
• thermal anchor points at suitable temperature stages,
• thin-walled probe designs,
• suitable materials and conductor alloys,
• integration into the vacuum and multilayer insulation,
• positioning the electronics outside the cryogenic area.

The smallest probe is not automatically the best. It must also be able to withstand pressure, vibration, transport loads and thermal contraction safely.

Materials, seals and thermal contraction

Materials change their dimensions and mechanical properties when cooled to 20 K. Different coefficients of thermal expansion can generate high stresses at flanges, solder joints, insulators and electrical feedthroughs.

The following factors must be assessed during material selection:

• toughness at cryogenic temperatures,
• hydrogen compatibility,
• weldability and weld quality,
• thermal contraction of the combined materials,
• permeation and permissible leakage rate,
• pressure-cycle and fatigue resistance,
• behaviour during warming and cooling cycles.

Elastomer seals can only be used at temperatures close to 20 K if they have been explicitly qualified for this purpose. Welded connections, metallic sealing systems or specially developed cryogenic feedthroughs are often preferred.

Cable insulation and electrical potting compounds must also withstand the complete temperature cycle. A design can be leak-tight at room temperature and still develop leaks during cooling because of different contraction rates.

Considering tank pressure and boil-off

Even with very effective insulation, heat enters an LH₂ tank. Part of the liquid evaporates and increases the amount of gas or the pressure inside the tank. This process is referred to as boil-off.

The tank pressure influences:

• the saturation temperature of the hydrogen,
• the density of the liquid,
• the density and condition of the gas space,
• the hydrostatic conversion,
• the mechanical load on the tank and sensor connections,
• venting and pressure-control processes.

In closed tanks, measuring only the lower absolute pressure is therefore not sufficient for level determination. Changes in gas-space pressure would incorrectly appear as changes in level. Differential-pressure measurement against the gas space or calculated pressure compensation using two sufficiently accurate pressure measurements is required.

For inventory calculation, the level, tank pressure and several temperature measuring points should be evaluated together. A single temperature value cannot completely represent pronounced stratification inside the tank.

Dead zones, blind zones and minimum level

No measuring system automatically detects the entire tank content from the lowest to the highest point. Typical limitations include:

• radar dead zone close to the antenna,
• interference reflections from the tank bottom,
• end effects of a capacitive probe,
• distance between the lower pressure connection and the actual tank bottom,
• unusable residual content below the withdrawal line,
• gas cushion above the maximum permissible level,
• internal components and baffles.

At least the following reference points must therefore be defined for scaling:

• mechanical tank zero point,
• sensor measuring zero point,
• usable minimum level,
• normal maximum operating level,
• independent overfill limit,
• total geometric tank volume.

A reading of “0%” does not necessarily mean that the tank is completely empty. Likewise, “100%” in a cryogenic tank must not correspond to the complete geometric volume because a defined gas space may be required for thermal expansion and operational control.

Calibration and density compensation

A reliable calibration must be matched to the measuring principle.

Differential-pressure measurement

The pressure transmitter can be checked electrically and metrologically using a pressure calibrator. However, this only checks the pressure measuring chain. Density, elevation, line routing and tank geometry must also be considered.

Capacitive measurement

The empty and full values, stray capacitance, temperature behaviour and, where applicable, several intermediate points must be checked. The characteristic curve may be nonlinear because of the tank geometry and electrode design.

Radar

The distance reference, tank height, blocking distance and false-signal suppression must be checked in the actual installation. Calibration outside the tank does not fully reproduce reflections caused by internal components.

Temperature measuring chain

Each measuring point must be calibrated or qualified for the cryogenic range. Cable resistance, self-heating and heat conduction along the probe must be considered.

A suitable density model is additionally required for mass calculation. A fixed density may be sufficient for a simple operating indication, but it results in systematic deviations when pressure and temperature conditions change.

Redundancy and overfill protection

Continuous level measurement should not automatically be the only protective measure against overfilling. Particularly in safety-critical LH₂ systems, separate functions may be required:

• continuous operating indication,
• independent high-level alarm,
• independent high-high level limit,
• shutdown or closure of the filling valve,
• plausibility checking using pressure, temperature or tank mass,
• diagnostics for cable breaks and sensor-signal faults.

Wherever possible, redundant sensors should not all have the same systematic failure cause. Two identical hydrostatic measurements, for example, can both be affected simultaneously by an incorrect density assumption.

A combination of different measuring principles can improve diagnostics, such as continuous capacitive measurement combined with an independent cryogenic level switch or tank weighing as a reference.

Systematic selection and planning procedure

1. Define the measuring objective: Distinguish between level, volume, mass, inventory management and overfill protection.
2. Record the tank data: Document the geometry, internal height, insulation, internal components and usable filling range.
3. Define the operating conditions: Consider temperature, pressure, filling, storage, withdrawal, warming and fault conditions.
4. Preselect the measuring principle: Compare differential pressure, radar, capacitance, temperature chain and weighing.
5. Calculate the measuring span: Consider the low LH₂ density in hydrostatic measurements.
6. Assess the heat input: Evaluate the thermal contribution of probes, cables, flanges and feedthroughs.
7. Select the materials: Check cryogenic toughness, H₂ compatibility and contraction.
8. Plan the process connections: Consider leak tightness, maintainability, dead spaces and vacuum integrity.
9. Define pressure and temperature compensation: Determine the required additional sensors and density model.
10. Define the signal and evaluation: Specify 4–20 mA, HART, digital bus or specialised electronics.
11. Plan redundancy: Separate the operating indication from independent overfill protection.
12. Create a calibration concept: Define factory testing, cold testing, tank characteristic curve and on-site testing.
13. Consider the lifecycle: Plan accessibility, replacement, leak testing and recalibration.

Typical errors in LH₂ level measuring points

Error	Possible consequence	Suitable corrective action
Standard sensor selected only on the basis of the measuring range	Failure at cryogenic temperature	Obtain complete confirmation of temperature, material and LH₂ suitability
Constant density used without temperature reference	Errors in mass and volume calculation	Compensate the density using pressure and temperature
Gas-space pressure not compensated	A pressure change is indicated as a level change	Measure the differential pressure relative to the gas space
Hydrostatic measuring span overestimated	Unsuitable or insufficiently accurate pressure range	Calculate the measuring span using the actual LH₂ density
Conventional diaphragm seal with standard fill fluid	Solidification or delayed pressure transmission	Use only a confirmed cryogenic system configuration
Solid probe used without a heat-balance calculation	Increased boil-off and local gas-bubble formation	Minimise heat conduction and provide thermal anchors
Capacitive probe tested only at room temperature	Incorrect characteristic curve under LH₂ conditions	Consider cryogenic temperature and calibration behaviour
Tank geometry scaled linearly	Incorrect volume indication in spherical or horizontal tanks	Store a tank characteristic curve or strapping table
Sensor with a lower limit of −196 °C used	Operation far outside the specification	Select a sensor suitable for temperatures close to −253 °C
Operating indication used as the sole overfill protection	No independent protective function	Provide a separate high-high level limit

Practical example: Level measurement in a closed LH₂ tank

A stationary, vacuum-insulated LH₂ tank has an effective measuring height of 4 m. The level is to be measured continuously for operational control. An independent overfill shutdown is also required.

The following requirements are defined for the preliminary design:

• continuous measuring range from 0 to 4 m,
• closed tank with variable gas-space pressure,
• density compensation for inventory calculation,
• the lowest possible additional heat input,
• independent high-high level limit,
• plausibility checking using temperature and pressure measurements.

Assessment of differential-pressure measurement

At a density of approximately 70.8 kg/m³, the maximum hydrostatic measuring span is only around 27.8 mbar. The required differential-pressure transmitter must therefore be capable of measuring a very small range with sufficient long-term stability.

The lower connection measures the liquid pressure, while the low-pressure side measures the gas-space pressure. Both connection paths are designed specifically for LH₂, heat input and possible phase transitions. A conventional diaphragm-seal fill system is not used unless its suitability for 20 K has been explicitly confirmed.

Assessment of a capacitive probe

A slim capacitive probe can measure the entire filling range. Its mechanical design ensures that thermal contraction and tank movement do not produce impermissible stresses. The electrical feedthrough is located in the tank cover and integrated into the vacuum insulation.

The characteristic curve is qualified using the empty value, several intermediate points and the full value. Temperature and tank pressure are measured in parallel so that density and possible dielectric influences can be considered.

Selected measuring concept

In this example, a project-specific capacitive LH₂ probe is used for the operating indication. An independent cryogenic point-level sensor triggers the high-high shutdown.

The tank pressure and several temperature measuring points are also recorded. The control system calculates the current volume and estimated hydrogen mass from the level, tank characteristic curve and thermodynamically determined density.

During commissioning, the measured values are compared with the filled mass or a reference weighing result. This allows installation errors, incorrect scaling and deviations in the tank characteristic curve to be identified.

Which products and solutions are suitable?

Project-specific H² level measurement solutions

The category H² Level Measurement includes solutions and components for level measurement in hydrogen systems. For liquid hydrogen, however, the suitability of each configuration must be explicitly confirmed for temperatures close to −253 °C, the low LH₂ density and the specific tank design.

Standard bypass level indicators with floats are not automatically suitable because of the very low LH₂ density and their frequently specified minimum temperature of only −196 °C. A special configuration may only be used if the temperature range, float buoyancy, materials and process connections have been verified for the specific project.

Special capacitive and microwave-based systems

Capacitive probes, guided microwave systems or radar may be used depending on the tank geometry and qualification. The decisive factors are the cryogenic design of the wetted components, the low dielectric reflection, the heat input and calibration under actual pressure and temperature conditions.

Selection based only on the measuring range, output signal or Ex approval is not sufficient.

Cryogenic H² temperature sensors

Temperature measurements in the liquid and gas space support density compensation, detection of stratification and assessment of boil-off. Suitable product groups and project-specific solutions can be found in the category H² Temperature Sensors.

For direct use in LH₂, the sensor must be explicitly specified down to approximately 20 K or −253 °C. A standard resistance thermometer with a lower operating limit of −196 °C is not sufficient for this purpose.

ICS Schneider Messtechnik provides support with selecting the measuring principle, performing hydrostatic calculations, designing materials and process connections, and defining temperature compensation, tank linearisation, signal processing and the calibration concept.

Conclusion

Level measurement in liquid hydrogen tanks requires a complete assessment of cryogenics, tank geometry, density, pressure and heat input. A standard sensor for conventional liquids cannot be adopted without modification.

Because of the low LH₂ density, hydrostatic differential-pressure measurement provides only a small measuring span. It requires reliable compensation of the gas-space pressure and a pressure-transmission system specifically designed for cryogenic operation.

Capacitive probes provide an established method for continuous measurement, but they must be qualified with regard to temperature, pressure, stray capacitance and heat conduction. Radar can reduce intrusion into the tank, but because of the weak dielectric properties of hydrogen, it requires application-specific assessment.

Temperature sensors provide important supplementary information, but they do not replace continuous level measurement in every application. For reliable inventory calculation, the level, tank characteristic curve, pressure, temperature and density must be evaluated together.

A good measuring concept minimises heat input, considers thermal contraction and uses suitable cryogenic materials and hermetic feedthroughs. The operating indication and independent overfill protection should be planned as separate functions.

Frequently asked questions about level measurement in liquid hydrogen tanks

At what temperature is liquid hydrogen stored?

At low pressure, the boiling point of hydrogen is approximately −253 °C or around 20 K. The exact state depends on the tank pressure.

Why is differential-pressure measurement difficult with LH₂?

Liquid hydrogen has a very low density. As a result, even a liquid column several metres high generates only a small differential pressure. Zero-point and temperature influences therefore become particularly relevant.

Can a standard pressure transmitter be used?

Only if the complete measuring arrangement is designed for the pressure span, cryogenic connections and thermal decoupling. The transmitter itself can be installed in a warmer area, but the pressure transmission system must be specially designed.

Is radar suitable for liquid hydrogen?

Radar may be suitable in principle. However, because of the weak dielectric properties of hydrogen and the extreme temperature, the specific combination of frequency, antenna, process connection and tank geometry must be qualified.

Why are capacitive probes used?

They have no moving parts and can continuously detect the liquid-gas boundary over a wide measuring range. Temperature and pressure influences on the capacitance must be considered during calibration.

Can a sensor rated down to −196 °C be used for LH₂?

No. Liquid hydrogen is at approximately −253 °C and therefore significantly below −196 °C. The sensor, feedthrough and all materials used must be specified for the actual LH₂ temperature range.

How is the hydrogen mass calculated from the level?

First, the level is converted into a volume using the tank characteristic curve. This volume is then multiplied by the liquid density determined from temperature and pressure.

Why does a measuring probe cause additional boil-off?

The probe and its cables conduct heat from the ambient environment into the tank. This heat can locally vaporise hydrogen and thereby increase boil-off.

Is continuous level measurement sufficient as overfill protection?

An independent point-level function should be provided in safety-critical systems. This ensures that a failure of the continuous measurement does not automatically result in the loss of overfill protection.