Sizing of Pressure Safety Valves in the Supercritical Region
Pressure safety valves (PSVs) on vessels containing liquid hydrocarbon may relieve a supercritical fluid during a fire, if the relieving pressure is higher than the critical point. The typical method for sizing an orifice area for supercritical fluids is presented in API 521, Section 4.4.13.2.4.3 (ref1). As stated in the API text, this method is based on the physical properties of air, the ideal-gas law, no change in fluid temperature, and an uninsulated vessel with no mass. This standard cautions the reader to review these assumptions to ensure that they are appropriate for any particular case.
Supercritical fluids exhibit characteristics of both liquids and vapours and their physical properties can be strong functions of pressure and temperature and may deviate appreciably from ideal-gas behaviour. These deviations from both ideal-gas law and incompressible fluid behaviour present challenges for relief valve sizing. Furthermore, the compressibility factor and the fluid temperature are not constant while the vessel is relieving. The API-recommended method with ideal-gas behaviour simplification is conservative and may lead to improperly sized valves with larger orifice areas than required (Ref2, Ref3). Two main problems with over-sized valves are destructive chattering and cost.
The relieving condition depends on the relation between the critical pressure of the fluid and the relieving pressure. In fire case scenario, for example, if the relieving pressure is less than the critical pressure, the liquid will boil when the valve opens and the relieving will continue until all liquid is vaporized. If the fluid is multi-component the temperature will vary during the relieving process. On the other side, if the relieving pressure is greater than the critical pressure, the liquid will not boil. The fluid becomes supercritical and to be heated until the pressure reaches the valve relieving pressure and the valve opens.
The path taken by the fluid from the initial condition (below the critical conditions) to the relieving condition is shown in Figure 1 (Ref2). The pressure follows the bubble point curve up to the critical point. The temperature and pressure will continue to increase along the path of constant specific volume from the critical point to the relieving pressure. The fluid remains at constant volume because both the mass of fluid and the vessel volume remain constant before the relieving process. After reaching the relieving pressure, the pressure remains constant and the temperature and relieving load will vary during the relieving process.
Figure 1- Path of Fluid from Initial Conditions into the Supercritical Conditions on Pressure-Enthalpy Diagram (Fire Case Scenario)
A rigorous procedure (Ref2, Ref3) is used by Process Ecology for sizing PSVs in supercritical service for a fire case situation. The method is based on the thermodynamic principles instead of ideal-gas law and the sonic flow through the PSV orifice is taken into account. A dynamic model may be required to account for the rising temperature resulting in increasing the relief load and orifice area. This procedure represents a dynamic model controlled by the increase in temperature of the vessel content. The relief rate is first calculated using small increments of temperature, then the valve is sized by modelling mass flux through an isentropic orifice flow. For each temperature, the relieve rate is calculated based on the fluid physical properties obtained from Aspen HYSYS simulator and the heat input.
The choke pressure at the orifice is calculated at each point. Comparing the choke pressure with the back pressure, the velocity and mass flux calculations are performed for the sonic or subsonic flow. As the maximum required orifice area may not occur at the maximum mass relief rate or the maximum volumetric relief rate, the orifice area is calculated for each temperature to verify the location of the condition requiring the largest PSV orifice. The maximum orifice area is selected for the design and is then corrected using PSV discharge coefficient, PSV back pressure factor, and PSV combination factor.
Conclusion
Design engineers must be aware that the API-recommended method for sizing a PSV at supercritical conditions is derived based on the ideal-gas and incompressible fluid behaviour simplifications and it may not be appropriate for specific cases and may lead to conservatively large orifice areas. The rigorous approach used by Process Ecology for the orifice sizing is based on thermodynamic principles where the supercritical fluid physical properties are calculated using an equation of state. Computer simulations is very valuable for property calculations. Orifices sized using this method can be smaller than the ones sized by API method, resulting in cost savings.
References:
1- American Petroleum Institute, Pressure-relieving and Depressuring Systems, API Standard 521, Sixth Edition, January 2014.
2- R.C. Done, Hydrocarbon Processing, January 2010, 63-67.
3- R. Ouderkirk, Chemical Engineering Progress Magazine, August 2002, 34
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