Mathematical modeling of synthesis of gas hydrate during its injection into a snow massif saturated with the same gas

Abstract

A mathematical model of the formation of gas hydrate in a snow massif, in the initial state saturated with gas, at injection of the same gas is proposed. For the axisymmetric problem with the lengthy zone of gas hydrate formation, the self-similar solutions describing temperature and pressure fields, saturation of snow, hydrate and gas in the massif are constructed. It is shown that, depending on the mass flow rate of gas and the initial state of the «snow-gas» system, three characteristic zones can be distinguished in the filtration region: the near zone, where hydrate is not formed, and therefore it is saturated with gas and snow; the intermediate zone, in which the conditions correspond to hydrate formation, i.e. phases of snow, gas and hydrate are concurrently present; the distant zone saturated with gas and snow. Accordingly, two frontal surfaces are introduced: one - between the distant and intermediate zones, where the transition of snow into the hydrate begins, and the other - between the near and intermediate zones, where the hydrate formation process finishes. The influence of the mass flow rate of the injected gas, the initial snow saturation and the initial temperature of the massif on the length of the volume zone of hydrate formation, as well as on the value of hydrate saturation at the boundary separating the near and intermediate zones, is studied. It is established that an increase in the mass flow rate of the injected gas leads to an increase in the length of the volume zone of phase transitions, and with an increase in the initial snow saturation the sizes of the volumetric zone of hydrate formation and the near zone, where phase transitions do not occur, decrease. Lowering the initial temperature of the snow massif leads to an increase in the hydrate formation zone, with an increase in the fraction of hydrate at the near boundary.