There are a number of methods available for estimating the capacity of a pressure relief valve for a two-phase relief fluid.^1,2  One primary distinction among these methods is the means for representing fluid property behavior, which may exhibit any degree of thermodynamic and/or mechanical equilibrium.  In order to solve the nozzle mass flux integration (at least the vdP expression of it), one needs a relationship of the specific volume of the fluid with respect to pressure and the relative velocities of the two phases with respect to pressure.

There are two categories of approaches for obtaining the fluid properties³:

1. Determine correlating parameters that are based on fluid properties at limited states (sometimes with a specification of how to obtain those fluid properties, such as thermodynamic constraints on flashes).  This approach allows one to only have limited physical property data, and typically allows one to solve the nozzle mass flux integration analytically (since the specific volume – pressure relationship is expressed as a function of the correlating parameters)
2. Evaluate the nozzle flux integration numerically, determining the required fluid properties based on multiple successive flashes at each point required by the integration step size, with an appropriate constraint based on the expected behavior of the fluid (so for homogeneous fluid, this would ideally be an isentropic thermodynamic constraint).  This approach is deemed more rigorous (although there is still the unknown associated with the expected behavior of the fluid without testing) but requires access to a capable thermodynamic process simulator and appropriate fluid parameters / interaction coefficients.

We were presented with the following compilation of two-phase sizing methods and were asked to describe the differences.  The condensed version is provided in the table below.

Note a: The two-point Omega method is used, see [9] Note b: The Diener-Schmidt method is used, see [7]
Note c: TPHEM is a program “Two-Phase Homogeneous Equilibrium Method” included with the CCPS Guidelines. A variety of empirical fitting equations are used, see [3]
Note d: Under certain conditions, the omega correlating parameter can be estimated using fluid properties from a single point (usually at relief conditions)

For information on selection of the discharge coefficient for two-phase flow, see our blog Relief Device Discharge Coefficient for Non-ideal Flow