Oil and gas productivity prediction model and semi-analytical method for fractured horizontal wells in fractured reservoirs

Naturally fractured reservoirs develop natural fractures, and after hydraulic fracturing in horizontal wells, the distribution of reservoir fractures becomes more complex. To address the challenge of predicting multiphase productivity in multiple flow regions involving hydraulic fractures, natural fractures, and the matrix, this paper proposes a productivity prediction model based on equivalent fracture elements and dynamic drainage distance, which is solved rapidly using a semi-analytical method. First, equivalent fracture elements are introduced based on fracture occurrence, and a characterization formula for equivalent permeability that considers multiple physical parameters such as fracture aperture, density, and stress sensitivity is derived, achieving an equivalent representation of the flow characteristics in complex fracture systems. Furthermore, a three-region three-phase flow mathematical model that accounts for complex fracture occurrence is developed. This model couples multiphase flow between hydraulic fractures, natural fractures, and the matrix using the principle of material balance and enables efficient solution based on dynamic drainage distance. The model incorporates the occurrence of hydraulic and natural fractures as well as stress sensitivity, enabling productivity prediction across multiple regions and phases. The model is applied to a production well in a fractured reservoir, and comparison with actual field production data demonstrates its high prediction accuracy and strong engineering applicability. The research results indicate that hydraulic fracture half-length, natural fracture orientation, and stress sensitivity are key factors influencing ultimate recovery, while natural fracture aperture and density affect early-stage oil and gas productivity and decline rates. This study provides theoretical support for multiphase productivity prediction and production optimization in complex fractured reservoirs.