Research on tritium and helium-3 content distributions in steel wall of spherical pressure vessel under general boundary condition

In order to understand the changes of mechanical properties of the wall materials and the carrying capacity of vessel which contains high pressure tritium, the spatiotemporal changes of tritium and helium-3 content in the wall should be studied during tritium storage. Taking into consideration the case that the outer surface of the vessel is with general mass transfer boundary condition and the tritium inside the vessel is van der Waals gas, and also taking into account both decay and permeation of tritium inside the vessel and decay and diffusion of tritium in the wall material, the analytical theoretical models of tritium and helium-3 content in the wall are developed and solved, and relevant theoretical formulas are deduced. Through analytical calculations, the curves of tritium and helium-3 content in the wall versus mass transfer coefficient of the outer surface, storage time and the spatial positions are plotted. Through analysis, a law called 21+2/2 time law of helium-3 content is put forward, where 1 and 2 are the coefficients which are related to van der Waals constant of tritium. The law is proposed: helium-3 content in the wall of the spherical high pressure vessel storing tritium which is in an open space rises along the radius from outer to inner, and the content radial gradient increases with storage time. If storage time is long enough, the helium-3 content at any point will approach to its final value, that is, a maximal value at a relevant point. The ratio of the maximum helium-3 content to the related initial tritium content is 21 + 2/2 at the inner surface. The obtained formulas and understandings can be used as a premise of the safety assessment of tritium stored vessel.