Equivalent cloud methods used for explosion risk and consequence studies

The reactivity of a flammable gas mixture depends strongly on the concentration. Explosions can only take place between the flammability limits LFL and UFL (5%–14% for methane), with by far the strongest explosions occurring near stoichiometry. When performing explosion studies to evaluate or minimize risk, optimizing design or ways to mitigate, many different approaches exist. Worst-case approaches assuming stoichiometric gas clouds filling the entire facility are often much too conservative and may lead to very expensive solutions. More refined approaches studying release scenarios leading to flammable clouds can give a more precise description of the risk (probabilistic approach) or worst-case consequences (realistic worst-case study).One main challenge with such approaches is that there can be thousands of potential release scenarios to study, e.g. variations of release location, direction, rate-profile, wind direction and strength. For each resulting gas cloud there can further be thousands of explosion scenarios as the transient non-homogeneous gas cloud can be ignited at a number of different locations and times. To reduce the number of explosion scenarios, in early 1990s GexCon developed a concept called Equivalent Stoichiometric Clouds (ESC, initially called Erfac, later modified to Q5 and Q9) to linearize the expected hazards from arbitrary non-homogeneous, dispersed flammable gas clouds. The idea is that the potential explosion consequences from any non-homogeneous gas cloud can be approximated by exploding a smaller gas cloud at stoichiometric concentration.These concepts are in extensive use in explosion risk and consequence assessments. For probabilistic assessments all transient dispersion scenarios modeled may for each time step be given an ignition probability and an equivalent cloud size. For realistic worst-case assessments, the dispersed gas clouds may be ignited at the time when the estimated equivalent gas cloud has its maximum. Compared to alternative simplifications, e.g. applying faster and less accurate consequence models, the equivalent cloud method simplifications keep much of the precision required in an explosion study. Despite the wide acceptance and use of these methods, they have also been criticized for not being conservative enough or for being inaccurate, and some groups prefer a much more conservative approach substituting any predicted flammable gas cloud volume with the most reactive concentration. It is well known that explosion consequences may vary strongly when changing ignition location and other parameters, and one can therefore not expect that an equivalent cloud method will accurately reproduce any ignited gas cloud scenario (which has never been the goal), but rather provide a reasonable estimate of expected explosion consequences when used according to GexCon developed guidance. The currently recommended Q9 method works well for a range of scenarios, and for certain more confined or high reactivity scenarios a more conservative approach is recommended (Q8). For some scenarios the current approach has weaknesses, e.g. aerosols. This paper will describe different equivalent cloud methods, show examples of use and evaluate performance, and discuss weaknesses and potential improvements.

► Motivation for and development of equivalent stoichiometric cloud concept is described.
► Weaknesses and pitfalls when using equivalent stoichiometric clouds are discussed.
► Evaluation studies, including the modeling of large scale experiments, are described.
► Guidance is given for optimal uses of the concept.