Absolute pressure control equates to absolute temperature control for cryogens

Absolute pressure control enables direction of cryogen pressure and ensures precise temperature

Cryogens are loosely defined as substances which liquefy at or below 120 K under standard pressure (760 Torr). Cryogens are used for applications including cryopreservation, rocket propulsion, and medical imaging – all of which require liquefied substances at extremely cold temperatures. Absolute pressure control leads to tight control of absolute temperature. Mass flow and pressure controllers and meters therefore play critical roles in cryogenic temperature control, including:

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

The effect of absolute pressure control on absolute temperature

Liquid nitrogen and helium are perhaps the most well-known cryogens. Liquid nitrogen is commonly used for cold storage and flash freezing in lab settings, and is near the upper end of the cryogen temperature spectrum. Helium is particularly notable for its proximity to Absolute Zero (0 K): it is typically at 3-4 K, with variations depending on the specific isotope and the ambient pressures. Table 1 indicates boiling points for common cryogens, including several isotopes of helium.

Cryogen Boiling Point (K) Boiling Point (°C) Boiling Point (°F)
Helium-3 3.19 -269.96 -453.93
Helium-4 4.214 -268.94 -452.08
Hydrogen 20.27 -252.88 -423.18
Neon 27.09 -246.06 -410.91
Nitrogen 77.09 -196.06 -320.91
Air 78.80 -194.35 -317.83
Argon 87.15 -185.90 -302.80
Oxygen 90.18 -182.97 -297.35

Table 1: Reference table for common cryogens, with temperature conversions between Kelvin, Celsius, and Fahrenheit.

 

Cryogen behavior is highly dependent on the interplay of ambient temperature and pressure. Table 2 indicates equilibrium temperatures at low medium, and high pressures for common cryogens. Figure 1 shows the interdependence of those pressures with fluctuations in temperature, with the graph on the right showing an expanded view focusing on lower pressure scenarios.

Pressure: 100 Torr 760 Torr 1,000 Torr 10,000 Torr
Helium-4 2.64 K 4.21 K 4.53 K
Hydrogen 14.99 K 20.27 K 21.23 K
Neon 27.10 K 28.04 K 39.36 K
Nitrogen 63.49 K 77.36 K 79.76 K 108.39 K
Argon 87.30 K 89.98 K 121.73 K
Oxygen 74.45 K 90.19 K 92.90 K 124.76 K
Methane 91.72 K 111.67 K 115.11 K 155.69 K

Table 2: Equilibrium temperatures for common cryogens at various pressures

 

Graphs at various pressures showing that absolute pressure control can equate to absolute temperature control

Figure 1: Interdependence of temperature and pressure for common cryogens. Overview (left) and at lower pressures (right).

 

Back pressure control in cryogenic dewars

In systems with cryopreservation as the goal, researchers must focus on maintaining the volume of the cryogen as evaporation inevitably occurs. However, fluctuations in atmospheric pressure may also be driving source of pressure changes in dewars, which are typically not fully-closed systems. In an extreme example, pressure fluctuations in propellant storage tanks at NASA’s John F. Kennedy space center resulted in boiloff of 650 kg of liquid hydrogen each day – estimated in 2001 to cost $625,000 each year.

Here, we analyze a more common volume: a 100 L dewar of liquid helium.

Back pressure controller used for headspace control in a cryogen dewar

Figure 2: Back pressure controller used to control headspace pressure in a cryogen dewar and minimize helium loss.

Atmospheric pressure often fluctuates by as much as ±25 Torr. For our 100 L dewar of liquid helium, a 25 Torr decrease in pressure will result in the vaporization of 0.874 liquid liters generating 25 standard cubic feet (or ~700 standard liters) of helium gas. This is approximately $25 worth of liquid helium.

As there is currently a supply shortage of helium, it’s unlikely that the price will decrease in the future. Over a period of years, the helium vaporization may quickly amount to thousands of dollars in unnecessary loss.

Alternatively, absolute pressure controllers can be used to maintain a constant absolute pressure in the head space of the dewar, which will ensure minimal cryogen loss. Alicat pressure controllers are multivariate, allowing the pressure controller to double as a mass flow meter. A single instrument can therefore measure any lost gas while controlling the headspace pressure. Further, the totalizer functionality can be used to directly measure the mass escaping over time. This technique allows the researcher to infer the amount of cryogen remaining in the vessel.

When the helium recovery system is utilized, the exhaust port of a back pressure controller should be connected directly to the recovery manifold, rather than venting to atmosphere (shown in Figure 2). This system configuration simple and low-cost, while allowing for precise back pressure control of cryogens.

Active headspace pressure control in cryogenic dewars

Using the technique described above, the only source of positive pressure in the system is boiloff due to heating of the cryogen itself. Therefore, any attempt to control the absolute temperature of the system using pressure changes is dependent on the time it takes to boil off a certain amount of the cryogen (generally a slow process). Some people use a pressure building coil to speed up the pressure increase and subsequent warming: the coils expose more of the liquid cryogen’s surface area, which results in faster gas formation and pressure buildup.

However, faster and more flexible control of cryogen pressures and temperatures can be achieved using an active headspace pressure control scheme.

Dual-valve pressure controller used for active headspace control in a cryogen dewar

Figure 3: A dual valve pressure controller used to actively control pressure in the headspace of a cryogen dewar

Attaching a both a positive pressure source of a warm gas and a vacuum system to a dual valve pressure controller will give you greater speed and better control of the cryogen pressure and temperature. This configuration (Figure 2) allows you to rapidly introduce the warm gas, which increases the system pressure. This effect is greater increased by the increased rate of boiloff as the cryogen shifts its equilibrium conditions. 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.

In this way, the cryogen temperature rapidly increases or decreases while you are maintaining precise control. Because the vapor pressure of any liquid is a function of temperature, the temperature of a liquid in thermal equilibrium with its saturated vapor is a function of its absolute pressure.

Device recommendations for control of absolute pressure and temperature

The techniques discussed here utilize an Alicat mass flow or pressure controller’s multi-parameter measurement features.  These instruments simultaneously measure mass flow, volumetric flow, absolute pressure, and temperature 100 times each second. As indicated in the diagrams above, we also 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, absolute pressure control is achievable and accuracy is not compromised.

Author:

Neil Hartmann, CTO