Mathematical modeling of hydrate formation in a reservoir saturated with snow by cold gas injection

Abstract

This paper considers the problem of injection of cold gas into the reservoir saturated in the initial state with snow and gas, which is accompanied by hydrate formation. The proposed mathematical model assumes that, depending on the initial state of the system “snow + gas” and the intensity of gas injection, different characteristic zones may be observed in the filtering zone “gas + hydrate”, “gas + hydrate + snow”, “gas + snow”. In order to identify the characteristics of hydrate formation in the equilibrium mode, the initial parameters reflecting the reservoir and gas conditions are chosen on the line of phase equilibrium of the system “gas + snow + hydrate”. A diffusivity equation is obtained in self-coordinates, and its solution is reduced to the solution of two ordinary differential equations of the first order. Numerical implementation is carried out using the fourth-order Runge-Kutta method and the shooting method. Similarity solutions describing the distribution of basic parameters (pressure and temperature fields, saturation of phases) in the reservoir are constructed. The condition for minimum heating of a “gas + snow + hydrate” system that provides a complete transition of snow to the hydration state is derived. It is shown that the complete hydrate formation and partial hydrate formation (depending on the initial state of the reservoir and the parameters determining gas injection) modes are possible in the volume region and on the front surface. It is also established that the greater is the initial saturation of the reservoir with snow, the more intensive is the process of hydrate formation and the smaller is the length of the heated zone. Simulations yield a characteristic value for the initial saturation of the reservoir with snow at which, depending on the value of heating the system “gas + hydrate + snow”, there may take place a zone saturated with a hydrate only.