Modeling Oil-Water Two-Phase Flow Behavior of a Fractured Vertical Well with a Finite-Conductivity Fracture in Triple Media Carbonate Reservoir (Advances in Applied Mathematics and Mechanics, 2018)
Because of the characteristics of carbonate reservoir, vertical well and acid fracturing have become a key technology for efficiently developing carbonate reservoir. A mathematical model for an oil-water two-phase flow fractured vertical 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 seven characteristic flow periods of fractured vertical wells in triple media carbonate reservoir can be identified. Parametric analysis shows that water saturation of matrix, vug, fracture system and acid fracture, acid fracture half-length and acid fracture conductivity can significantly influence the transient pressure responses of fractured vertical 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.