The critical mass for the unconfined vapour cloud explosion of compressed and liquid hydrogen

The (unconfined) vapour cloud explosion (VCE) is a dramatic phenomenon that generates a severe pressure wave with a high potential to damage assets and produce injuries in the far field. This definition applies also to hydrogen. Nevertheless, no clear tools and methodology have been so far developed and tested for this highly reactive gas, and even advanced numerical simulations lack validation and suffer from large uncertainties. In this view, the comprehension of the physic which subtends this dramatic phenomenon for the specific case of hydrogen is still a central issue. This paper revises some of the most adopted theories on VCE based on classical acoustic theory and models for pressure wave propagation and provides a consequence-based, threshold (minimum) value for the critical mass of hydrogen m(f)(crit) (4:0 kg) which is needed-at a stoichiometric concentration in air-for a vapour cloud to behave as a VCE. To this regard, any non-stoichiometric hydrogen concentration in air or lower amount of hydrogen would decrease either the flame Mach number M-f or the total energy, thus resulting in negligible overpressure. In this sense, the effects of buoyancy, diffusivity, and weather conditions on the dispersion of hydrogen should be taken into account. The results are valid either for compressed or cryogenic liquid tanks and can be adopted for the sake of distinction between hydrogen flash fire and VCE; for the hazard analysis of hydrogen production and storage; and more in general for the risk assessment of hydrogen systems.