Cryogenic Refrigeration - Part I -Introduction

Why does a cryogenic process require refrigeration?
Processes that separate some mixtures of gases or which cool and liquefy pure gases for storage and transport, need to operate at a temperature well below ambient. Despite good insulation, heat leaks in from the warmer surroundings and this needs to be offset by a supply of refrigeration. This becomes increasingly important in the cryogenic the temperature range -100 to -269 degrees celsius.

For processes that deliver a liquid product, significantly more refrigeration is needed than for a separation process. We look at some refrigeration methods used in the cryogenic industries.

Before  proceeding it may be helpful to introduce the terms enthalpy and mol or kmol. The ‘Specific enthalpy’ is energy per unit quantity of fluid and typically has units of kJ/kg or kJ/kmol. The prefix ‘k’ means 1000, so 1 kmol = 1000 gram mols.

A kmol is a quantity of substance with its the molecular mass expressed in kg.  It is useful because 1 kmol of different substances always contains the same number of actual molecules, so it’s a true measure of the molecular quantity. 

Knowing their molecular weights, it should become clear that the mass of ‘substance’ in 1 kmol of H2 is 2 kg whereas the mass of 1 kmol of N2 is 28 kg.

Enthalpy or energy content of an amount of fluid (gas or liquid) is roughly proportional to its temperature. The constant of proportionality being the specific heat at constant pressure, Cp for that substance.

Note that Cp this is not actually constant except for a perfect or ideal gas.  A corresponding specific heat where a fluid is heated but is kept at constant volume i.e. is prevented from expanding is the specific heat at constant volume or Cv.

Units for both specific heats are kJ/kg-K.  Their dimensionless ratio (Cp/Cv) is often denoted k or γ and appears in compressor and turbine calculations.

Review of main methods of refrigeration

Near to ambient temperature say down to - 40 degrees Celsius, refrigeration can be provided by a single stage vapour compression cycle for example to liquefy carbon dioxide using a refrigerant such as R32, Ammonia or propane / propylene. CO2 can itself be used as an auto-refrigerant or an auxiliary refrigerant, subject to staying above its triple point pressure of 5.2 bar, below which it forms solid CO2 or dry ice.

The stages in a vapour compression cycle are conveniently shown on a thermodynamic diagram of Pressure (Y-axis) and Enthalpy (X-axis) – namely a P-H chart.  A generic chart is shown below.

These charts are convenient to visualise vapour compression refrigeration processes but can sometimes be hard to read.  This is because the isotherm lines are curved, but near vertical close to the x-axis (enthalpy) and the constant entropy lines (isentropes) are also curved.  Constant density lines or isochores are also sometimes provided, but add more complexity and are not shown on the generic example below. Point ‘c’ at the top of the 2-phase dome is the critical point. The values are omitted for clarity and are substance-specific, but the shape of the chart is quite similar for most substances.

Typical Pressure – Enthalpy or  P-H Chart.

P-H Charts with numerical values of the variables for all common substances are found in most engineering and thermodynamic textbooks e.g. GPSA Engineering data book.

The flow schematic below shows the steps in a vapour compression cycle.

Vapour compression cycle - showing energy flows.

The path 1->2 is an ideal isentropic compression, and 1->3 is an actual compression where the temperature rise, and the enthalpy input  (h3-h1) are greater.  The HP gas is then cooled from T3 to the vapour phase boundary T2.  It is then condensed typically against air or cooling water.  In the basic cycle the liquid is then expanded 3->4 (at constant enthalpy) to the low pressure P1, when its temperature drops to T1, and a portion of the liquid ‘flashes off’ i.e. vapourises instantly. 

A generic vapour compression refrigeration cycle shown on P-H chart

The balance of the cold liquid is vaporised in the evaporator to provide the refrigeration. The vapour returns to the compressor inlet which is the starting point of the cycle.

The fraction of flash vapour is readily found by the ‘lever rule’ as the ratio of enthalpy differences (h4 – h-sat. liquid)/ (h-sat. vapour – h-sat. liquid).

The amount of flash vapour can be reduced if there is a means of subcooling the HP saturated liquid at point 3 before expanding.

A key feature of most vapour compression cycles is the ability to condense the refrigerant stream at near the ambient temperature using atmospheric air or cooling water and at a reasonable pressure.

We have looked a a single-stage vapour compression cycle, but to reach lower temperatures, two or more vapour compression cycles employing different refrigerants can be connected in a cascade.  The top cycle will always reject the nett heat removed to the environment.

It can be shown that as the temperature at which refrigeration is required becomes lower, the mechanical vapour compression cycle efficiency starts to lose out to alternative refrigeration techniques.  See part II.