For overpressure protection systems involving only rupture disks (that is, not a rupture disk in combination with a pressure relief valve), the frictional losses throughout the piping system is typically used as a means for evaluating the capacity of the relief system, in accordance with API Standard 520 §5.11.1.3.¹  Of course, equivalent velocity head factors and roughness factors are needed for the analysis, and we provide discussions regarding these inputs in other Fireside Chats.^2,3

For the rupture disks themselves, the manufacturer tests a rupture disk assembly to determine its equivalent velocity head factor, which is commonly specified as a constant value (turbulent flow) and is associated with the pipe diameter of the inlet piping.⁴  This equivalent velocity head factor is currently reported as the Resistance Factor, K_r, in the ASME National Board Pressure Relief Device Certifications NB-18.⁵

One should note that there can be different resistance factors reported depending on the fluid phase being relieved: K_rg for gases, K_rl for liquids, and K_rlg for either phase.  Even for the same rupture disk make and model, these values can be different; therefore, it is important to select the appropriate factor based on the fluid phase being initially relieved.  One factor contributing to the difference is how the compressibility of the fluid affects the opening of the rupture disk itself, with compressible fluids like gases imparting some of their energy of expansion to the opening of the disk, resulting in a more open profile and thus, commonly, lower resistance factors.

This effect has two important implications.  The first is that the initial fluid phase that is responsible for bursting the disk can have an effect on the resistance factor.  This is evidenced by the K_rl test procedure itself (ASME PTC-25 §4-10⁶), in which the rupture disk is first burst using water, then the resistance factor is determined using air.  For this reason, if we encounter cases where the rupture disk is normally in liquid service, we recommend selecting the liquid resistance factor, even if the relieving scenario is gas.

The second implication is for the selection of resistance factors for two-phase flow.  Since there is no testing for two-phase flow, there is no resistance factor specified.  In the absence of a manufacturer’s specific recommendation, we will use the resistance factor most appropriate to the compressibility of the two-phase fluid.  The two-phase omega factor is a convenient basis for this determination, with omega factors less than 1 being associated with incompressible flow and greater than 1 with compressible flow.⁷

Finally, after calculation of the theoretical capacity of the piping system, this capacity must be multiplied by a factor of 0.9 “to allow for uncertainties inherent with this method”¹ to determine the reported relieving capacity.  This relieving capacity is then compared to the required relief rate to determine the adequacy of the ‘sizing’ of the system.