Abstract: Considering artificial fracture,inclined wellbore and formation coupling flow,flow to directional well is divided into three parts： Flow from reservoir to fracture,flow in fracutre and variable mass flow in production pipe. Principles of potential superposition and mirror reflection as well as the concept of infinitesimal line congruence are used to model flow from reservoir to fracture and potential distribution in reservoir. By discreting fracuture to 2D grid,boundary theory is used to couple flow dynamics in fracture with variable mass flow in inclined pipe. A comprehensive coupling model for finite-conductivity fractured directional well is shown.Iteration method is used to solve the model. A practical case shows that for vertical fracutre result of coupling model agrees with that of Prats method. Fracture conductivity and inclined angle have great effects on productivity and pressure.

Key words: fractured directional well, finite-conductivity fracutre flow, coupling flow model, discreted grid, productivity