** **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/cm^{2}. For the ATLAS cryostats, an experiment was
performed to determine the precise number, which turned out to be 1.4 watts/cm^{2}.
In the absence of such experimental data, the most pessimistic value, 6
watts/cm^{2} 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 ^{*} cm^{2}), 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 G^{2}/*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.