Hi. ASME has no issue using open bonnet for air service, although the usual/expected observations should be noted (back pressure, spring protection etc).

Per ISO, only the term Safety Valve is used regardless of application or design.

There is NO ASME Requirement for an Open Bonnet PRV on Air, just a lifting Lever. The Bonnet (open or enclosed) houses the spring.

Per ASME Section VIII, Division 1, Paragraph UG-136(a)(3), "Each pressure relief valve on air, water at the valve inlet that exceeds 140°F (60°C), excluding overpressure or relief events, or steam service shall have a substantial lifting device which when activated will release the seating force on the disk when the pressure relief valve is subjected to a pressure of at least 75% of the
set pressure of the valve."

Notice ASME uses the generic term Pressure Relief Valve. In ASME, a Safety Valve is used for compressible fluid, typically steam or air. Typically the Safety Valve has an Open Bonnet with a visible spring. Conversely, a Safety-Relief Valve has a Closed Bonnet so that can be used for compressible or incompressible fluids. Typically, incompressible fluids do NOT have a Lift Lever, unless it is hot water as defined by UG-136(a)(3) as mentioned above. The Relief Valve is primarily for Liquid (incompressible) fluid. I hope this is helpful.

JAC