APPENDIX 2:  Relief Valve Sizing for Cryogenic Systems

 1.0    Introduction

Within a cryogenic system, adequate relief valves must be installed for all vacuum and cryogenic vessels, and also for any cryogenic lines that have the potential to trap cryogenic fluids.

Relief valves must be sized so that under worst-case failure conditions, the maximum pressure reached in any vessel is below the maximum safe working pressure (MSWP) for the vessel.  No fixed prescription can be given to determine valve sizing for all, or even most cases.  Each system must be analyzed in detail to properly determine worst-case failure modes and the required relief valve sizing.

Such analysis should proceed through several steps, which are discussed in general terms below.  It should be noted that the following discussion is intended as a brief introductory guide, and in no way should be considered a comprehensive or complete treatment.

2.0    Vessel Pressure Ratings

The MSWP must be determined and documented for each vessel and piping element of the system.  This includes both vacuum and cryogenic vessels, and also, both cryogenic piping and vacuum housing for any vacuum-insulated transfer lines.

In addition, for any vessel serving as a cryogenic storage vessel, DOE Order 6430.1A requires the vessel to be designed in accordance with Section VIII of the ASME Pressure Vessel Code.

The following are some possible methods of determining the MSWP:

A.        Documented manufacturer’s pressure rating.  One could use either MSWP, if provided, or 25% of the minimum yield or burst pressure.

B.    Results of a pressure test, preferably hydrostatic, performed and documented by persons competent to perform pressure vessel tests in accordance with laboratory safety requirements, and in accordance with the requirements of Section VIII of the ASME Pressure Vessel Code.

         C.     Results of a detailed and documented stress analysis of all elements of a vessel, using a maximum allowable stress of 25% of the yield stress of the materials employed.  Such a stress analysis might be a result of a numerical finite-element approximation or of a conservative application of the various formulas detailed in ref. [4] (references are contained in Section 2.3 Technical References for Cryogenic Technology).

3.0    Determining Worst-Case Failure Modes

For each volume requiring a relief valve, a credible worst-case failure mode must be determined.  Generally, one should consider for a given failure mode only a single initiating failure (of either a procedure or a component), together with any subsequent failure or chair of failures that would naturally result from the initial failure.  The following are examples of failure modes that should be considered:

A.     An operator improperly opening or closing any given valve.  This might result, for instance, in liquid nitrogen then being trapped in a section of transfer line, or in air being introduced into a cryogenic insulating vacuum.

B.     Failure of a cryogenic vacuum vessel to air.

C.     Failure of a vessel containing cryogenic liquid into the insulating vacuum vessel.

D.     Failure of the inner, cryogenic tube of a transfer line.

         E.   Failure of the outer, vacuum housing of a transfer line.

In case A, above, the effects of opening valves to or from any connecting systems, such as gas storage or refrigerator, should also be considered.

For relief valve sizing, the worst-case failure mode is that failure mode resulting in the most rapid boil off of cryogenic fluid.  With the exception of failure modes that cause the injection of cryogenic fluid from an outside system, the boil off will be determined by the heat-leak caused by the given failure mode.

3.1    Some Heat Transfer Processes

Determination of the heat leak due to a given failure requires detailed analysis of the particular system.  The general methods for several cases are outlined below.

3.11  Condensation of Air on Vessels Containing Liquid Helium

For a bare (not wrapped in superinsulation) cryogenic vessel containing liquid helium, the worst-case failure mode is likely to be failure of the insulating vacuum to air.  All the constituent gases of air will condense directly on the surface of the helium containing vessel; from reference [1], p. 270, such condensation produces a heat input of 1 to 6 watts/cm².  For the ATLAS cryostats, an experiment was performed to determine the precise number, which turned out to be 1.4 watts/cm².  In the absence of such experimental data, the most pessimistic value, 6 watts/cm² should be assumed.  The heat leak due to air condensation for vessels which are wrapped in superinsulation is also detailed in reference [1].

3.12  Convective and Conductive Heat Transfer

In many cases the worst-case failure mode will be failure of an insulating vacuum to air, nitrogen, or helium with the heat transfer mechanism then being convection, or in the case of substantial amounts of superinsulation or other filler conduction, from the outer vacuum wall of the vessel to the inner vessel or piping containing the cryogenic fluid.  The thermal conductivity of several gases is described in Reference [6].

Convective heat transfer is described in reference [3].  Appendix 2a to this gives estimates of the convective heat transfer values for several gases and temperatures.

4.0    Determining Boiloff Rates

Once the heat input to the cryogenic substance is known, the maximum rate of efflux must be determined.

In many cases the efflux results from simple boiling of a cryogenic fluid, and the rate can be simply estimated from the heat of vaporization of the cryogenic liquid.

In general, the efflux must be calculated by equating the enthalpy released by venting a portion of the cryogen (at the relief pressure) to the worst-case heat input.  This may or may not be a simple matter, depending on the conditions that apply.  Reference [1] contains a thorough discussion of such calculations for helium

5.0    Determining Pressure Drop from Venting Vessel to Atmosphere

For most vent lines and valves, the pressure drop will be dominated by the so-called minor loss term, which is approximately

                                                                                                                       (1)

where G is the mass flow per unit cross-sectional area in grams/ (sec ^* cm²), and ρ is the gas density at the exit of the element considered.  Each bend or orifice in the flow path that causes substantial turbulence will add a term roughly given by expression (1) to the total pressure drop.  Reference [8] details the pressure drops expected for various geometries of bends and orifices.

Expression (1) shows that for a given pressure drop, the flow through any system, such as a relief value, will scale as G²/ρ.  Since manufacturer’s specifications usually give capacity for air at room temperature, this scaling relationship provides a means of estimating capacity of a given valve for various gases at cryogenic temperatures, such as nitrogen at 77 K or helium at 5 K.

Appendix 2b shows some examples of pressure drop estimates.