Modeling of the process of gas movement in a channel with the presence of ice, accompanied by its thermal destruction

¹ Birsky Branch of Ufa University of Science and Technology, 10, Internacionalnaya street, Birsk, Republic of Bashkortostan, 452450, Russian Federation
² Institute of Oil and Gas FSBEI of HE "Ufa State Petroleum Technological University", (Branch in the City of Oktyabrsky), 54a, Devonskaya Street, Oktyabrsky, Republic of Bashkortostan, 452607, Russian Federation

^* Corresponding author: bulatbirsk@yandex.ru

Abstract

The study of new, previously unobserved processes of formation of craters of regular axisymmetric shape in permafrost zones requires the creation of models explaining the occurrence of such anomalous phenomena. In this paper, the problem of thermal destruction of a vertical channel (well), mainly consisting of ice, by a gas-liquid flow is considered. When constructing a mathematical model, it is assumed that warm gas is supplied at the entrance to the channel, passing through which it gives part of its energy to the channel walls, while thermal destruction of the walls occurs, and due to high pressure, the decomposition products of the channel (water and inert rock) are carried out by the flow to the surface. A system of first-order ordinary differential equations for the basic system parameters (pressure, temperature, and flow velocity) is obtained. The numerical implementation of the obtained system of ordinary differential equations was carried out using the fourth-order Runge-Kutta method, where the firing method was used to find the initial value of the flow velocity. The use of the firing method was that the inlet velocity was selected so that the maximum outlet velocity of the flow did not exceed the speed of sound at the local pressure value and the pressure at the end of the channel was not lower than atmospheric. The solution of the thermal conductivity equation in the quasi-stationary approximation was used to describe the destruction of the channel walls. Critical values of borehole radii have been obtained, at which flow modes change. The dynamics of changes in the parameters in the well, accompanied by its thermal destruction, is shown. It has been revealed that with increasing channel radius, the intensity of its decomposition increases.