(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
Carbonate reservoir is one of the important reservoirs in the world. Because of the characteristics of carbonate reservoirs, horizontal well and acid fracturing have become a key technology for efficiently developing carbonate reservoir. Establishing corresponding mathematical models and analyzing transient pressure behaviors of this type of well-reservoir configuration can provide a better understanding of fluid flow patterns in formation as well as estimations of important parameters. A mathematical model for an oil-water two-phase flow fractured horizontal well in triple media carbonate reservoir by conceptualizing vugs as spherical shapes is presented in this article. A semi-analytical solution is obtained in the Laplace domain by using source function theory, Laplace transformation and superposition principle. Analysis of transient pressure responses indicates that nine characteristic flow periods of fractured horizontal wells in triple media carbonate reservoir can be identified. Parametric analysis shows that water saturation of matrix, vug and fracture system and fracture half-length, fracture number and fracture spacing can significantly influence the transient pressure responses of fractured horizontal wells in triple media carbonate reservoir. The model presented in this article can be applied to obtain important parameters pertinent to reservoir or fracture by type curve matching and it can also provide useful information for optimizing fracture parameters.