Absolute Pressure Control = Absolute Temperature Control

Neil Hartmann, CTO

 

Alicat absolute pressure controllers enable direction of cryogen pressures ensuring precise temperature.

Cryogens are loosely defined as gases which liquefy at or below 120°K under standard pressure (760 Torr).1 Cryogens are used for applications including cryopreservation, superconductivity and superfluidity. All of these applications share a need for temperatures under the previously mentioned 120°K temperature at standard pressure (760 Torr)

Liquid Nitrogen is a commonly used cryogen which is near the upper end of the cryogen temperature spectrum. Helium is perhaps the most well-known of cryogens, renowned for its proximity to absolute 0 (0 degrees Kelvin – Helium is typically 3-4 °K, depending on isotope and pressure).2

Figure 1: Graphs showing the interdependence of temperature and pressure for commonly used Cryogens.  Graph 1 shows an overview, while Graph 2 shows an expanded view of lower pressures

 

Pressure:100 torr760 torr1,000 torr10,000 torr
Helium-42.64 °K4.21 °K4.53 °K
p-Hydrogen14.99 °K20.27 °K21.23 °K
Neon 27.10 °K28.04 °K39.36 °K
Nitrogen63.49 °K77.36 °K79.76 °K108.39 °K
Argon 87.30 °K89.98 °K121.73 °K
Oxygen74.45 °K90.19 °K92.90 °K124.76 °K
Methane91.72 °K111.67°K115.11 °K155.69 °K

Table 1: Table showing the equilibrium temperatures at low, medium and high pressures for common Cryogens

 

Back Pressure Control

In systems where cryopreservation is the goal, researchers are concerned with maintenance of cryogen volumes as evaporation occurs. However, fluctuations in the atmospheric pressure can be the driving source of changes in Dewar pressure, as these are typically not fully closed systems. In an extreme example, boiloff from propellant storage tanks was estimated to cost $625,000 ($4.1M/year in inflation adjusted dollars) at NASA’s John F. Kennedy Space Center.3

Here, we analyze a more common volume; a 100L Dewar of liquid helium. Atmospheric pressure often fluctuates, commonly changing by +/- 25 Torr. In the case of a decrease in pressure, this will result in the vaporization of 0.874 Liquid Liters generating 25 standard cubic feet (or ~700 Standard Liters) of Helium gas. This translates to approximately $25 worth of liquid Helium.4 Given the current supply shortage of Helium, it’s unlikely that these prices will decrease in the future. Over a period of years this may amount to thousands of dollars in unnecessary loss. An Alicat Absolute Pressure Controller can be used to maintain a constant absolute pressure in the head space of a Dewar, ensuring minimal loss of cryogens. In addition to controlling the pressure, Alicat Mass Flow Controllers and Meters can measure the actual gas lost while controlling the pressure of the head space. Alicat’s totalizer function can also directly measure the mass escaping over time. This technique also allows the amount of cryogen remaining in the vessel to be inferred.

In the case where a Helium recovery system is utilized, the exhaust port of a back pressure controller would be connected directly to the recovery manifold (as opposed to venting to atmosphere). This system configuration is desirable for its low cost and simplicity, while allowing for precise back pressure control of cryogens.

Figure 1:Diagram of a typical system using an Alicat back pressure controller to control headspace cryogen pressure

 

Active Headspace Pressure Control

Faster, more flexible control of cryogen pressure and temperatures can be achieved using an active headspace pressure control scheme. Using the technique outlined above, the only source of positive pressure is boiloff due to heating of the cryogen itself. Therefore, utilizing pressure changes to control temperatures is dependent on the time to boiloff the necessary amount of cryogen, which is typically a slow process. Some users speed this pressure increase (and warming) with the use of a pressure builder coil. These coils expose a greater surface area of liquid cryogen, causing faster gas formation and pressure buildup.

Greater speed and control can be achieved by attaching a positive pressure source of warm gas, as well as a vacuum system to a Dual Valve Pressure Controller (PCD). This configuration allows for rapid introduction of warm gas, increasing system pressure. This in turn is assisted by an increased rate of boiloff as the cryogen shifts its equilibrium conditions. This rapidly increases cryogen temperature while maintaining precise control. Conversely, the pressure of the system can be lowered by venting to atmosphere or a vacuum. As the pressure decreases, cryogen temperature will decrease as well.

Figure 2: Diagram of a typical system using an Alicat differential pressure controller (PCD) to actively control headspace cryogen pressure

Some of these advanced techniques utilize an Alicat Mass Flow Controller’s multi-parameter measurement features, also found in Alicat’s unique Bidirectional Mass Flow Controllers.  All Alicat Mass Flow Controllers simultaneously measure mass flow, volumetric flow, absolute pressure and temperature over 1000 times/second. As implied by the diagrams shown, we recommend the use of heat exchangers to maintain the gas temperature at the control valve above 263 °K. Alicat’s very low temperature and pressure span shift means that even with a large temperature difference, accuracy is not compromised (See our paper on this topic for more information)

The vapor pressure of any liquid is a function of temperature.  Conversely, the temperature of a liquid in thermal equilibrium with its saturated vapor is a function of its absolute pressure.  Therefore absolute pressure control = absolute temperature control.

 

To summarize, an Alicat Mass Flow or Pressure Controller or Meter can be used in many scenarios that benefit from cryogenic temperature control:

  • Monitoring of cryogen loss from closed volumes
  • Control of back pressure in cryogenic storage containers
  • Maximizing efficiency of cryogen recovery systems
  • Temperature control of cryogenic experiments via absolute pressure control

 

REFERENCES:

1. Quick reference for common Cryogens with temperature conversions between Kelvin, Celsius and Fahrenheit.

Cryogen Boiling Point (°K)Boiling Point (°C)Boiling Point (°F)
Helium-33.19-269.96-453.93
Helium-44.214-268.94-452.08
Hydrogen20.27-252.88-423.18
Neon27.09-246.06-410.91
Nitrogen77.09-196.06-320.91
Air78.80-194.35-317.83
Argon87.15-185.90-302.80
Oxygen90.18-182.97-297.35

2. “Cryogenics.” Wikipedia, Wikimedia Foundation, 12 Dec. 2019, https://en.wikipedia.org/wiki/Cryogenics#Industrial_applications.

3. Salerno, L. J., et al. “Terrestrial Applications of Zero-Boil-Off Cryogen Storage.” SpringerLink, Springer, Boston, MA, 1 Jan. 1970, link.springer.com/chapter/10.1007/0-306-47112-4_98.

4. “Helium Users Grapple with Supply Crunch.” American Institute of Physics, 9 Apr. 2019, www.aip.org/fyi/2019/helium-users-grapple-supply-crunch.

 

 

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