A New Analytical Solution of the Productivity Equation for a Vertical Fractured Well in 3D Anisotropic Oil Reservoirs

摘要

The authors present a new productivity equation for vertical fractured well in 3D anisotropic reservoirs. By considering the coupling of natural fracture and artificial fracture, we first establish the permeability tensor model with using tensor theory. Then they transform the 3D anisotropic reservoir into an equivalent isotropic reservoir by applying coordinate transformation. Finally, the authors set up the complete mathematical models in polar coordinate system and give the analytical solution of pressure distribution and production rate. Analysis shows fracturing radius and fracture conductivity are the mainly factors that influence the production rate of fractured well. The new solution obtained in this study considers the effect of fractures closure after hydraulic fracturing, so it is more accurate and can be applied to field calculation and productivity predication.