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Rigorously Size Relief Valves for Supercritical Fluids
Ryan Ouderkirk, Fluor Corp.

Previously published methods can be tricky to apply, and may lead to improperly sized valves. Here is a stepwise, detailed method that more-accurately determines the orifice area.


ideal-gas behavior. Relief venting of supercritical fluids upercritical fluids exhibit characteristics typihas beenstudied previously, resulting in guidelines for cal of both liquids and vapors. Transport calculating the relief rate (3, 4) and the relief-valve oriproperties, such as viscosity and diffusion fice area (5, 6, 7). However, if one is not careful in readrate, are closer to those of typical vapors, ing these guidelines, he or she may size the relief valve while solvent strength resembles that oftypical liquids. based on ideal-gas simplifications or merely for the Further, the properties can be strong functions of presmaximum mass relief-rate. The reader can inadvertently sure and temperature, allowing the solvent strength to be use the vapor or liquid sizing-equations (for an ideal or easily manipulated. This led to the use of supercritical compressible gas), for example. Also, Ref. 4 tellsthe fluids in industrial processes such as extraction of cafreader how to find the maximum relief rate, as opposed feine from coffee with carbon dioxide, and the Residuto the maximum orifice area. The maximum required um Oil Supercritical Extraction (ROSE) process with either butane or pentane (1). However, these same deviaorifice area may not occur at the maximum mass relief tions from both ideal gasand incompressible fluid berate or the maximum volumetric relief-rate (Figure 1). havior present distinct challenges for relief valve sizing. Here is a step-by-step procedure to rigorously size Here is a rigorous procedure to calculate the relief the relief valve for supercritical fluids. In presenting rate and size the relief valve for supercritical fluids. The relief rate is modeled over time for ablocked-in vessel using small increments of Volumetric Relief Rate temperature. The relief valve is sized by mod100% eling mass flux through an isentropic orifice up to the limit of choked flow. An n-butane fire Orifice Area 80% case will illustrate the procedure using LeeKesler properties (2). The method is suited for 60% Mass Relief Rate other heat-input cases, as well as otherproperty-determination methods. 40% Many relief problems are simplified signifi1.05 1.10 1.15 1.20 1.25 cantly by assuming incompressible-fluid or Reduced Temperature ideal-gas behavior. A fluid at supercritical conditions can be quite compressible, and its physs Figure 1. The maximum required orifice area may not occur when expected ical properties may deviate appreciably from
during relief venting.
% of Maximum Value34


August 2002


s Figure 2. A simplified logic diagram for sizing relief valves for supercritical fluids. Summary of method The case considered here is heat from a fire or other means. The fluid does not boil, since Without boiling, the temperature will continue to rise until the relief pressure is above the fluid’s critical pressure. the heat input is zero. Sincesupercritical fluid properties

this method, we will start by discussing the fluid conditions leading to supercritical relief. Then, the method will be presented in a simplified form, followed by a detailed step-by-step example to guide the user through the process, while highlighting potential problems with abnormal cases. Afterwards, we will cover the basis for the procedure: therequired-relief-rate derivation and the relief-valve orificearea derivation. Also, mention is made of several alternate procedures for sizing the orifice and of the potential for supercritical relief to turn into twophase relief flow. Consider a blocked-in vessel full of liquid with a vessel-relief pressure greater than the fluid’s critical pressure. If heat is added by fire or other means, boiling cannot occur....
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