TRANSIENT PRESSURE BEHAVIOR OF A FRACTURED VERTICAL WELL WITH A FINITE-CONDUCTIVITY FRACTURE IN TRIPLE MEDIA CARBONATE RESERVOIR

Carbonate reservoir is one of the most important reservoirs in the world. Because of the characteristics of carbonate reservoir, vertical well and acid fracturing have become the 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 coupling mathematical model for a fractured vertical well in triple media carbonate reservoir by conceptualizing vugs as spherical shapes is presented in this paper, in which the finite conductivity of the acid fracture is taken into account. A semi-analytical solution is obtained in the Laplace domain by using source function theory, Laplace transformation, discretization of fracture, and the superposition principle. Analysis of transient pressure responses indicates that several characteristic flow periods of fractured vertical wells in triple media carbonate reservoir can be identified. Parametric analysis shows that fracture conductivity and fracture length can significantly influence the transient pressure responses of fractured vertical wells in triple media carbonate reservoir. The model presented in this paper 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.