The simplification of a real flammable gas cloud is a pragmatic approach to a complex problem. This approach is as old as explosion modelling in safety analysis.
2.1. An Historic Perspective
Following a major explosion accident in a chemical factory near Flixborough in the UK in 1974, a version of an equivalent explosion cloud was developed; this is in the form of the TNT equivalent method. This was to assist in the enquiry of the accident [4
] and for the assessment of explosion hazards in onshore facilities. This method assumes that the size of a flammable vapour cloud involved in an explosion is represented by the chemical energy of the total mass of flammable material released. This was later refined to the mass of flashed vapour [5
This marked the beginning of the application of the concept of ESC, though the term ESC was coined later.
The TNT equivalent method was later further refined to the volume or mass of cloud within the congested volume in the multi-energy model developed by the TNO Prins Maurits Laboratory in the Netherland [7
]. As knowledge improved, the simple multi-energy model evolved to more complex methods, such as GAMES [8
] which incorporates effects of equipment density and layout into the multi-energy model. There are other models developed along similar line to the multi-energy concept. It is beyond this scope of this paper to name them all.
This approach continues to be applied to date to onshore facilities for the assessment of consequence and offsite risks at a distance from the location of the explosion.
A different type of explosion model is required for offshore facilities. Owing to limited footprint and close proximity of gas explosion hazards to equipment, protective structures and people, the assessment of explosion loading within and very close to the exploding cloud is needed for assessment of impact on them. Phenomenological and CFD models were developed for these “near-field” applications. With advances in computers, CFD explosion models are widely used. With time, they are used to simulate progressively more and more complicated scenarios.
The underlying development path of ESC models for offshore mirrored that for onshore, namely, to refine the simple representation of a flammable cloud, progressively removing perceived conservatism with time.
Prior to the large-scale gas explosion JIP (JIP—Joint Industry Project called the Blast and Fire for Topside Structure Phase 2 JIP (BFTSS Phase 2)) in the 1990s, a typical assessment of explosion loading would have included a range of sizes of cuboids, the gas cloud containing uniform mixtures of stoichiometric flammable gas and air. An example of this is in the Piper Alpha enquiry conducted by Lord Cullen [9
] in which the Christian Michelsen Institute (CMI) submitted explosion loading results from FLACS simulations based on a number of uniformly mixed stoichiometric cuboid volume clouds. The largest cuboid filled the entire volume of the module on the platform. This 100% area filled scenario is called the theoretical worst-case scenario.
If the inventory was not sufficient to fill the entire area, maximum cloud sizes were typically determined by volumes of flammable inventories within isolatable sections and assuming these inventories formed stoichiometric flammable mixtures with air. These smaller cloud sizes, shaped in cuboids, are called specific theoretical worst cases; an example of this application is shown in the design of the Andrew platform in the North Sea [10
To distinguish this approach from later ones, we will call this “inventory-based ESC volumes”.
The results of BFTSS JIP Phase 2 showed that all gas explosion models grossly underpredicted experimental results, some by two or three orders of magnitude [11
]. This was the case even for advanced CFD models (including FLACS) which incorporated the state-of-the-art representation of the underlying physics at the time. The theoretical and virtually all the specific worst cases would produce explosion overpressure many times higher than previously estimated, some much higher than the capacities of structures of installed facilities and those being designed at the time.
2.2. Evolution and Type of ESC Volume Methodology
The objective of BFTSS Phase 2 was to provide data at a realistically large scale to validate gas explosion models for application to offshore facilities. Additionally, a subsidiary objective was to evaluate explosion models commonly used at the time. This JIP identified gaps in the industry; the items relevant to our discussion here are:
Accuracies of predictive models: Phase 2 spurred further research in both data generation and analysis, e.g., [12
], and development of predictive models and tools (e.g., a many-year extension to the Gas Safety Programme at the Christian Michelsen Research (GexCon is a spinoff from it)).
Procedures of assessment: while the high overpressure observed caused concern, there was a common acknowledgement that the theoretical worst-case scenarios used in Phase 2 to test the explosion model is not representative of real-life situations in accidents.
There was a concerted move towards defining an ESC model which better reflects the formation of flammable gas clouds in real accident situations where (the perception was that) significant portions of inventories released do not take part in explosions, or release their energy at a slower rate than at the optimal stoichiometric concentration—“realistic scenarios”.
Application of realistic scenarios required the development of a methodology for dispersion-based ESC volumes (henceforth simply referred to as ESC volumes).
Unlike the inventory-based ESC volumes, the dispersion-based ESC volumes would need to account for release conditions (e.g., hole sizes, pressure, direction, etc.), environmental conditions (e.g., platform layout, wind velocities, etc.), non-uniform distributions of gas concentration and flow fields characteristics generated by ambient wind and pressurised releases which interact with equipment and platform layout.
Though the process may appear complex, conceptually it is simple. Instead of inventories released, the ESC volumes are calculated using results from dispersion models; this requires an additional calculation step. Dispersion models can range from simple (e.g., the zonal model, workbook [14
], etc.) to complex (e.g., CFD).
With a CFD model, it is possible, in principle, to use the results from a CFD dispersion model directly as input. In practice, this is impractical for risk assessment due to the large number of scenarios considered, high resources required and long calculation time.
Hence, the approach adopted is to simplify the complex cloud into a simple representation of it. There are many ways to reduce the complexity of a dispersing flammable gas cloud to a simple uniform cuboid representation.
As there were no data for this type of scenario, research was carried out to gather data of flammable cloud volumes and explosion overpressures from pressurised gas releases. During this period, a number of ESC models were developed.
GexCon developed ESC models based on flame speed and expansion ratio; starting off with the simplest ERFAC, then Q5, Q8 and Q9 (see Figure 2
), progressively increasing the effect of the gas concentration and expansion ratio in the model that defines ESC volumes. These names may appear esoteric; they are taken from variable names used in the Flacs engine. Flacs refers to the numerical explosion simulator. The whole modelling package including pre and post processors is called FLACS. The logic behind this is that it is known that the severity of a gas explosion depends on flame speed which varies with gas concentration.
There are simpler ESC models, such as “>LFL” (volume bounded by LFL) and “∆FL” (volume bounded by the upper flammability limit (UFL) and lower flammability limit (LFL)). They were used by BP following their analysis of large-scale experimental data. Definitions of these ESC models are given in Figure 2
Presently, Q9 is used widely, other models (e.g., “∆FL”) have only a few users. While there are slightly more complicated methods for flammable volumes which can be transformed into ESC volumes (e.g., a workbook approach [14
]), they are hardly used.