(27c) Properly Size Two-Phase PRV - Easier Than API 520 HDI Method

API 520 Part I (9^th edition) selected three (3) methods to size two-phase PRV. One of them is the HDI (Homogeneous Direct Integration) method described in section C.2.1. HDI method involves generating multiple data points over an isentropic range of pressure from the inlet to the discharge. These data are used to evaluate the mass flux integral by direct numerical integration.

The HDI method requires intensive effort depending on how close engineers desire the result, comparing to the actual integration. Therefore, an easier HD (Homogeneous Direct) method without integration, yet producing identical mass flux, is needed and proposed.

The new easier HD (Homogeneous Direct) method compares the velocity of fluid and the velocity of sound along the isentropic expansion path. The choke point is determined when the velocity of fluid equals the velocity of sound. The mass flux is then simply calculated by multiplying mass density and the velocity of fluid at the choke point. A detailed example will be given in the presentation.

The HD method is compared against the established data in “Benchmarking of two-phase flow through safety relief valves and pipes” by Shawn Adair and Harold Fisher. The mass flow rate through a 4P6 relief valve by HD method is well within the reasonable range, among other established methods. The new easier HD method is also validated against API examples for gas, liquid, two-phase and supercritical relief.