Mathematical Model of the Process of Gas Displacement in Multilayer Systems

A mathematical framework is proposed for studying the process of gas displacement in multilayer systems within a gas reservoir, and a model problem is solved. In the considered problem, the boundaries of the section are unknown, and the boundary conditions are rather general; therefore, it is not possible to directly apply all the previously published methods discussed in the article. Since it is impossible to simultaneously capture both boundaries at a network node, the coefficient-smoothing method is applied. Numerical simulations have shown that the most efficient gas extraction occurs when the initial boundaries of the section are equidistant from the production well. A computational experiment has also demonstrated that, with increasing flow rate, the influence of differences in layer permeability becomes more pronounced. Furthermore, when the boundaries of the section are equidistant from the production well, the residual gas content after water breakthrough is higher compared to cases with unequal initial interface positions.

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