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
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....