'The Design Institute of Emergency Relief Systems (DIERS) was formed in 1976 as a consortium of 29 companies to develop methods for designing for the design of emergency relief systems to handle runaway reactions.  DIERS spent 1.6 million to investigate the two-phase vapor-liquid onset/disengagement dynamics and the hydrodynamics of emergency relief systems.  Of particular interest to DIERS were the prediction of two-phase flow venting and the applicability of various sizing methods for two-phase vapor-liquid flashing flow".  DIERS Website

In general, the most stringent relief requirement is due to all-liquid venting.  Since this venting mode is unlikely for a top venting ERS design, the homogeneous -vessel behavior offers the next most stringent requirement and is therefore the recommended design approach for this configuration.  Sizing based on all-vapor venting is both unrealistic and unsafe.  J.C. Leung  Fauske and Associates, Inc. AIChE Journal October 1986

Before taking a serious look at the DIERS case study below that employs several of the DIERS methodologies that have been developed over the years it is a good idea to read the article, "Size Safety-Relief Valves for Any Condition", by Ron Darby, Texas A&M University.  In this article Darby gives an overview and explanation of many of the  DIERS methods and models, and he provides an understanding of the advantages and limitation of each of the DIERS sizing models that are being used today.  The article briefly discusses the single-phase design model, and for two-phase he discusses, the one-point Omega method, the two-point Omega method employed by API 521, the TPHEM model from CCPS, the Homogeneous Non-Equilibrium model (HNE), the equilibrium rate model (ERM), and the more rigorous, Homogeneous Direct Integration model (HDI) that is employed by the Mach II CDS System.  He also discusses phase slippage and when to apply Slip, or when to design for non-equilibruim.  For flow regime models he identifies several models but only discusses homogeneous since it is typically used to provide the most conservative design.

DIERS Case Study:

Problem Definition:

In this example we first take a typical fire case scenario and design for single-phase to determine if the existing orifice size, and inlet and outlet piping configuration is adequate for the single-phase fire case scenario.  Download the Mach II CDS, Single-phase Design and Training Manuel. Download   If you are using the Mach II CDS, PSM Network System to follow this example you can download the User Guide.  Download

We then run a two-phase test to determine the likelihood of two-phase flow.  If two-phase flow is likely, we then run the homogeneous two-phase fire case model to determine the two-phase relief capacity.

We then determine the fluid maximum flux rate (Gmax) to size for the two-phase orifice based on the equation, A = W/Gmax, where "A" is the two-phase required orifice size,  "W" is the two-phase relief capacity, and "Gmax" is the maximum fluid flux.

After we have determined the required orifice size we will select a standard orifice and perform the necessary inlet and outlet pressure drop calculations to determine the proper piping design.  We can then compare our existing relief design against the single-phase and two-phase design to determine if the existing relief design is adequate for both single-phase and two-phase venting.

Finally we will explore different methods that can be used to reduced the single and two-phase relief capacities, or move the two-phase venting into the single-phase region utilizing the (alpha)  α vs. Ψ ( Psi) curve.  One method of reducing the two-phase relief rate is by using the coupling equation to find the mass fraction of vapor entering the nozzle for bubbly or churn-turbulent flow regimes.  These flow regimes are less conservative than the homogeneous flow regime because they assume more vapor-liquid disengagement between the vessel and the nozzle thus creating more vapor space and less liquid flowing through the relief nozzle.