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.

在硬岩中形成的地下空腔中储存液化气是一种很有前途的新技术，可以显着减小储存设施的尺寸。低温流体与周围岩石之间的强烈热传递导致在水饱和岩石中形成冰环，作为天然保护屏障。在本文中，我们对冻结环的存在和演化进行了一般性的理论分析。该分析基于解决异质域中的热传输问题，其中两个热波在域内启动并传播到两个相反的方向。解析解由改进的 Karman-Pohlhausen 积分法获得。我们已经将这种方法扩展到异构介质，

已经表明，冻结锋的传播是非单调的并改变方向，因此冰环的寿命是有限的。已经获得了描述取决于绝缘层厚度的所有工艺参数的一般分析公式，特别是：冰环的最大厚度、其寿命、存在条件、冰环超过的绝缘临界厚度不出现，以及温度场的全球演变。这些结果能够选择最佳的绝缘厚度。