On the theory of formation of gas hydrate in partially water-saturated porous medium when injecting methane

We present a planar one-dimensional theoretical model and numerical solutions for the process of the formation of methane gas hydrate by injecting gas into a porous reservoir partially saturated with water. The case where the intensity of formation of the gas hydrate is limited by the diffusion of gas through a hydrate layer formed between water and gas in the pore channel core is considered. Within this process, the kinetics of hydrate formation is determined by empirical parameter $D$, having the dimension of a diffusion coefficient (m$^2$/s). The effect of the value of this parameter on the characteristics of the hydrate formation process is studied depending on the parameters that determine the initial state of the porous reservoir and its porosity and permeability characteristics. The equilibrium mechanism of hydrate formation is considered, which is a limit adopted by the diffusion pattern that corresponds to the case of $D \to \infty$.