Numerical Simulation of Hydrate Formation on Injection of Cold Gas in a Snow Massif

Abstract

The problem on hydrate formation in a snow massif initially saturated with gas with the injection of the same gas is solved. The constructed mathematical model is based on the equations of continuum mechanics. For the axisymmetric formulation with an elongated region of the phase transitions, self-similar solutions are constructed that describe the temperature and pressure fields, as well as the saturation of snow, hydrate, and gas in the massif. The numerical solution of the problem is implemented with the shooting method. It is shown that, depending on the initial thermobaric state of the gas–ice system and on the intensity of gas injection determined by its mass flow rate, three characteristic zones can be distinguished in the filtration area that are different by their structure and elongation: (i) the near zone, in which the snow has completely passed into the hydrate, and, therefore, only the hydrate and gas phases are present; (ii) the intermediate zone, in which the hydrate is formed from gas and ice, and (iii) the distant zone, which is saturated with the gas and ice phases. The effect the mass flow rate of the injected gas, the initial snow saturation, and the initial temperature of the massif have on the elongation of the hydrate volume formation zone under negative temperature conditions and on the temperature and hydration saturation at the boundary separating the near and intermediate zones is studied.