Analytical solution to the problem of ice ring formation in underground cryogenic gas storage

Abstract

Storage of liquefied gas in an underground cavity created in hard rocks is a promising new technology that can significantly reduce the dimensions of a storage facility. The intense heat transfer between the cryogenic fluid and the surrounding rocks leads to the formation of an ice ring in water-saturated rocks, which acts as a natural protective barrier. In this paper, we provide a general theoretical analysis of the existence and evolution of the freezing ring. The analysis is based on solving the problem of heat transport in heterogeneous domain with two thermal waves initiated inside the domain and propagating into two opposite directions. The analytical solution was obtained by the modified Karman–Pohlhausen integral method. We have developed the extension of this method to a heterogeneous medium, in which the effect of the temperature semi-stabilization occurs.It has been shown that the propagation of the freezing front is non-monotonic and changes direction, so that the lifetime of the ice ring is finite. General analytical formulae have been obtained that describe all process parameters depending on the thickness of the insulating layer, in particular: the maximum thickness of the ice ring, its lifetime, conditions of existence, the critical thickness of the insulation above which the ice ring does not arise, as well as the global evolution of the temperature field. These results enable to select an optimal thickness of the insulation.