Two phase flow through a nozzle, as in relief devices, has been reasonably well studied in recent years, although the methods are not perfect and disagree with one another somewhat, we are certainly much further forward in this area than 20 years ago. What is clear is that calculating an area for the gases, and an area for the liquid and adding the two together, as used to be done before the 1980's, is no longer considered to be sound practice, as it nearly always results in a relief size that is too small.
The DIERS institute (Design Institute for Emergency Relief Systems) has been involved in a lot of work to address this issue, and to develop new methods for sizing 2 phase relief valves. These include the HEM model (Homogeneous Equilibrium Model) and the HNE (Homogeneous Nonequilibrium model).
Some useful published articles on this issue include:
"Select the Best Two-phase model for two-phase relief sizing", Darby, Meiller and Stockton, Chemical Engineering Progress, May 2001. (
)
"Easily size relief devices and piping for two-phase flow", J.C. Leung, Chemical Engineering Progress, December 1996.
and "Properly size pressure-relief valves for two-phase flow", Darby, Self and Edwards, Chemical Engineering, June 2002 (
).
If you have used one of the methods described here for your calcs, your answer is almost certainly better than the suppliers answer, if they are using the addition method as you describe.