New analytical solutions have been derived for the isobaric evaporation of a pure
liquid cryogen. In particular, expressions have been provided for the liquid volume,
evaporation rate, Boil-off-Gas (BOG) rate, vapour temperature and vapour to liquid heat
transfer rate as a function of time. Both equilibrium and non-equilibrium scenarios have
been considered. In the former, the vapour and liquid cryogen are assumed to be in
thermal equilibrium, while in the latter the vapour is treated as superheated with respect
to the liquid and acts as an additional heat source.
The derived solutions for two scenarios were validated against the numerical
results for the evaporation of liquid methane and of liquid nitrogen in small, medium
sized and large storage tanks that are used in industry. For the equilibrium model, the
analytical solutions are exact. For the non-equilibrium model, the analytical solutions are
valid for the whole duration of evaporation, except for a short transient period at the
beginning of the evaporation. For physical quantities of industrial interest, they provide
accurate estimates of liquid volume, BOG rate and BOG temperature, with the
maximum deviations not exceeding 1%, 2% and 4.5%, respectively. The vapour to
liquid heat transfer rate is also well predicted to within a maximum deviation of 5%.