A new non-equilibrium model relevant to LNG weathering in large storage tanks under constant pressure has been developed. It treats the heat influx from the surroundings into the vapour and liquid phases separately and allows for heat transfer between the two phases. The main heat transfer mechanisms in the vapour phase are assumed to be advection, due to upward flow of evaporated LNG, and conduction. It has been observed that the vapour temperature increases monotonically as a function of the height, in agreement with recent experimental results. In all the simulations performed the vapour to liquid heat transfer was small, also in line with recent experimental findings, and is estimated to contribute less than 0.3% to boil-off gas rates. The results of this work indicate that the heat transfer by the advective upward flow dominates the energy transfer within the vapour, while the natural convection, in the body of the vapour, can be neglected. The initial liquid filling has a pronounced effect on all the relevant variables, leading to a decrease in vapour temperature and boil-off gas temperature and an increase in boil-off rates. A rule of thumb for estimating the boil-off gas temperature in industrial storage tanks is provided. (C) 2019 Elsevier Ltd. All rights reserved.