Mathematical modeling of the equilibrium complete replacement of methane by carbon dioxide in a gas hydrate reservoir at negative temperatures

Abstract

Gas hydrates, which contain the largest amount of methane on our planet, are a promising source of natural gas after the depletion of traditional gas fields, the reserves of which are estimated to last about 50 years. Therefore, it is necessary to study the methods for extracting gas from gas hydrates in order to select the best of them and make reasoned technological and engineering decisions in the future. One of these methods is the replacement of methane in its hydrate with carbon dioxide. This work studies the construction of a mathematical model to observe this method. The following process is considered in this article: on one side of a porous reservoir, initially saturated with methane and its hydrate, carbon dioxide is injected; on the opposite side of this reservoir, methane and/or carbon dioxide are extracted. In this case, both the decomposition of methane hydrate and the formation of carbon dioxide hydrate can occur. This problem is stated in a one-dimensional linear formulation for the case of negative temperatures and gaseous carbon dioxide, which means that methane, carbon dioxide, ice, methane, and carbon dioxide hydrates may be present in the reservoir. A mathematical model is built based on the following: the laws of conservation of masses of methane, carbon dioxide, and ice; Darcy’s law for the gas phase motion; equation of state of real gas; energy equation taking into account thermal conductivity, convection, adiabatic cooling, the Joule — Thomson effect, and the release or absorption of latent heat of hydrate formation. The modelling assumes that phase transitions occur in an equilibrium mode and that methane can be completely replaced by carbon dioxide. The results of numerical experiments are presented.