In a reciprocating compressor, a failure of the packing material around the rod can allow high pressure gases from the cylinder to enter into the distance piece that separates the cylinder housing from the compressor frame (see API Standard 618 for more information on the physical structures).  API Standard 521, 6th Edition, §4.4.9.4 indicates that the distance pieces of reciprocating compressors should be protected from these rod packing failures¹:

Reciprocating compressors should be protected from rod packing failures in the distance piece by an adequately sized vent line or PRD. Options to size the PRD or vent line can include the following:
a) determine the annular gap between the compressor rod and packing gland and calculate flow using an equivalent square edge orifice area, or
b) provide a PRD with inlet size equal to the nominal pipe size (NPS) of the vent piping.

Note it is common for the distance piece to be vented to atmosphere; however, there are cases where piping directly vented to a containment system (similar to some pump seals), or even a pressure relief device, is desired.

Equivalent orifice option.  The recommendation for the use of an equivalent orifice area suggests one ‘calculate flow using an equivalent square edge orifice area’.  Typically, the packing case has substantial length, so a thin orifice would provide a higher (conservative) estimate for flow through the annular space.  The cross-sectional area (A_x) of the annular space would be calculated as follows:

Where D_o is the outer diameter of the annulus (inner diameter of the packing rings) and D_i is the inner diameter of the annulus (outer diameter of the rod itself).  Using fluid properties at the discharge conditions from the compressor, one can then determine a flow across the orifice.

When using this methodology, we have found cases where even an open vent does not provide adequate overpressure protection for the flow rate calculated.  For ‘sharpening the pencil’ exercises, we use an annular pipe flow method where an equivalent hydraulic diameter (D_eq) is used in the pipe flow calculations.^2,3,4

To deal with a potential range of packing case lengths, we employ Hooper’s methodology whereby a length to diameter ratio greater than 5 is treated like piping having a square reduction, pipe flow over the length, and a square expansion (ignored if choking occurs).  A length to diameter ratio less than 5 is treated like a thick orifice (essentially a fit of the equivalent velocity head factor between pipe flow and thin orifice flow).⁵

This calculation method is useful for obtaining a flow rate for the design basis of not only pressure relief devices but also piping from the vent, if that is used.

Inlet size option.  Selecting a pressure relief device based on the size of the available vent (for example, a ¾”), while convenient, seems questionable.  The distance pieces we’ve encountered are not designed to handle much pressure, and according to compressor vendors we’ve talked to, the vent was sized to pass a nominal leakage rate directly to atmosphere.  For a given inlet size, there may be many relief orifice sizes, almost all of which are smaller than the inlet area, at least for pressure relief valves.  This introduces a reduction in area for the flow to pass, thus requiring a higher pressure than compared to the open vent.  We’re not aware of any incidents involving the use of this option, so this issue may just be a theoretical question rather than a practical concern.