(615g) A Systematic Algorithm to Compute Hazardous Area Extent for Two-Phase Releases Based on an Improved Low-Dimensional (simple) Dispersion Model

This contribution aims at systematically determining the extent of classified areas in two-phase releases of pure components. To this end, a novel algorithm is proposed to ensure all proper steps are taken towards accurately computing the required properties of the resulting cloud. The intended framework is based on a refined one-dimensional dispersion model that accommodates (i) the influence of the vapor component on the energy balance of the two-phase jet model, (ii) new decay constants to calculate velocity, concentration, and temperature profiles, (iii) a new normalization ratio to compute the temperature along the centerline, and (iv) a new correlation for the entrainment coefficient in the two-phase region. Altogether, these modifications produced results that are in very good agreement with (scarce) experimental data available in the literature. The hope is that this simple algorithm can predict within reasonable precision the reach of the hazardous cloud in open field situations.

Understanding the mechanism of cloud dispersion is fundamental as it defines the properties needed for the determination of the hazardous area extent. In some situations, the material released to the environment can only partially vaporizes, giving rise to a two-phase flow system where the liquid breaks up into fine droplets producing an aerosol cloud, whose behavior in the atmosphere affects dispersion distances. This complex system is the result of such phenomena as expansion of the material released to ambient pressure, liquid atomization to form the aerosol cloud, and (possibly) rainout of liquid droplets. The use of rigorous mathematical models capable of describing these processes appears as a reliable alternative to empirical criteria described in specific standards (Lacome et al., 2021). In fact, the use of standardized diagrams, such as those found in the IEC 60079-10-1 (IEC, 2015) and in the API RP 505 (API, 2018) standards, can produce dubious results due to the oversizing of the classified areas, increasing the cost of the project and sometimes creating a false impression of safety.

Suppose that a liquefied gas contained in a control volume is discharged through a small diameter orifice and that it partially evaporates, giving rise to a two-phase jet, as illustrated in Figure 1. The escaping liquid is subjected to a sudden decrease in pressure resulting in the formation of a jet of vapor laden with droplets. Previous studies (Calay & Holdo, 2008; Fauske & Epstein, 1988; Fthenakis, 1993; Johnson & Diener, 1991; Polanco Piñerez, 2008) showed that the configuration of this release basically depends on the conditions of the jet at the orifice outlet (plane “e”), at the end of the expansion region (plane “f”), and after the total evaporation of the droplets (plane “j”).

The proposed systematic algorithm designed to compute the extent of hazardous areas for two-phase releases as per Figure 1 above is better depicted as the flowchart of Figure 2. Application of the algorithm to important experimental test cases available in the open literature produced the following results shown in Figure 3, considering the models without and with the important modification mentioned above. The isopleth, i.e., the line connecting points of equal concentration around the cloud boundary (Crowl & Louvar, 2019) are depicted in Figure 4 along with the volumes at different measures of the LFL (lower flammability limit). As seen from the above results, those improvements resulted in a simple model that fitted well to measured temperature profiles. It is therefore believed that the algorithm can compute hazardous extent, volume, and shape of the resulting dispersions with satisfactory accuracy.

References

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