You can use API RP-521 conventional method for sizing the PSV in supercritical service but it is conservative, producing larger orifice areas than required. API RP-521 treats all “un-wetted” vessels the same, whether the fluid contained is supercritical, a vapor or a gas. It also does not account for the change in fluid temperature.
Furthermore, an over-sized valve has two potential problems: there is a potential for destructive valve “chatter” and larger PSVs are more expensive. Following reference details a procedure for calculatingt the PSV in supercritical service:
Designing for pressure safety valves in supercritical service
Use this rigorous method to prevent over-sizing
R. C. DOANE, S&B Engineers and Constructors Inc., Houston, Texas