Is the following information on the diffusion of hydrogen in air accurate? The diffusion velocity is proportional to the diffusion coefficient and varies with temperature according to T^n with n in the range of 1.72-1.8. Diffusion in multi-component mixtures is usually described by the Stefan-Maxwell equation. Corresponding diffusion rates of hydrogen in air are larger by about a factor of 4 compared to those of air in air. The rising velocity under the influence of (positively) buoyant forces cannot be determined directly since they are dependent on the density difference between hydrogen and air as well as on drag and friction forces. Also, shape and size of the rising gas volume as well as atmospheric turbulence have an influence on the final velocity of the rising gas. Both diffusion and buoyancy determine the rate at which the gas mixes with the ambient air. The rapid mixing of hydrogen with the air is a safety concern, since it leads quickly to flammable mixtures, which on the other hand for the same reason also will quickly dilute to the non-flammable range.
The information provided is not only outdated in terminology, but also misleading in quantifying the dispersion of hydrogen in terms of comparison of diffusion of air in air. Hydrogen diffuses 4X faster than air, and the rate of mixing has many variables, so there isn’t just one answer. However, it’s generically safe to say that an initial hydrogen gas cloud outdoors and unconfined will dissipate below the flammable range very quickly, likely in just a few seconds once H2 flow is stopped. The factor of 4 mentioned in the question refers to a molecular (laminar) diffusivity, but almost all practical dispersion scenarios are governed by turbulent diffusivities. The turbulence can either be atmospheric (ambient) turbulence or the turbulence associated with the hydrogen release itself, i.e., jet turbulence or vessel failure induced turbulence. Regarding the rise time of hydrogen clouds, these can be calculated from equations in the SFPE Handbook for the two cases of an instantaneous release and a steady-state release. The cloud liftoff time, tl, for an instantaneous release is given by the following simple empirical equation from Beyler’s chapter Fire Hazard Calculations for Large Open Hydrocarbon Fires because it is just based on buoyant rise observations: tl = 1.1m1/6, where m is in kilograms. Therefore, a 10 kg release would lift off the ground in (1.1)(10)0.167 = 1.6 seconds. The initial rise velocity of the buoyant cloud is proportional to "gD(28.8 2)/28.8"1/2, where g is gravitational acceleration, D is the cloud initial diameter, and the 28.8 and 2 are molecular weights of air and hydrogen, neglecting any initial entrainment of air into the cloud at cloud formation. Thus, a 10 ft diameter cloud would begin rising at a velocity on the order of 17 ft/s, and a 20 ft diameter cloud would have an initial rise velocity of about 25 ft/s. In the case of continuous releases, the rise time, tR, of a buoyant plume front from a suddenly initiated release can be calculated from a combination of equations 61, 62, and 16 in Heskestad’s chapter Fire Plumes, Flame Height, and Air Entrainment, where z is the rise elevation of interest, u is the hydrogen release velocity, b is the initial plume (cloud) diameter, and the densities are 2 and 28.8 as above. A consistent set of units is needed for z, u, g, and b to do calculations with this equation, which is based on a combination of theory and experiment.