Simulation of the gas flow in a channel containing ice and accompanied by its thermal destruction

Study of new, not previously observed, processes of formation of axisymmetric regularly shaped craters in permafrost zones requires the creation of models to explain the occurrence of such anomalous phenomena. In this paper, the problem of thermal destruction of the vertical channel (a well) mainly composed of ice and gas-liquid flow is considered. In the developed mathematical model it is assumed that a hot gas is supplied to the channel inlet. When the hot gas moves through the channel, part of its energy is transferred to channel walls, causing thus their thermal destruction. The high-pressure decomposition products of the channel (water and rock) are carried by the flow to the surface. A system of first-order ordinary differential equations is constructed to identify the main parameters of the system “channel-gas flow”: pressure, temperature and flow rate, as well as mass flow and its components (water and rock). Numerical implementation of the upward flow in a vertical borehole consists of two phases. In the first stage, we solve the resulting system of ordinary differential equations using the Runge-Kutta fourth-order method, where the initial values of flow velocity are determined via the method of shooting. With this method, the inlet velocity is taken so that the maximum outlet velocity does not exceed the sound speed at a given local pressure, and the pressure at the end of the channel remains almost the same as the atmospheric one. The parameters of the system of ordinary differential equations are calculated in this case for a fixed radius of the well and its thermal effect. In the second stage, the destruction of channel walls is described. For a given distribution of flow parameters, the time step is performed, and the problem of determining the radii of the borehole and thermal effects is solved. The solution was built using the equation in quasistationary approximation. Simulations give the critical well radius, at which the flow regimes change. The dynamics of parameter changes in the well during its thermal destruction is demonstrated. It has been found that with increasing channel radius the intensity of the channel destruction increases.