We proposed a modified Green element method based on edge-based element concept. Unknowns and matrix dimension are reduced. Then, a local grid refinement method is proposed based on the improved Green element, which ensures precision in early flow regimes for fractured horizontal wells with complex fractured networks. Solution of a degradation model solved with the method is compared with solutions obtained with a semianalytical model and numerical simulation. It verifies accuracy and efficiency of the improved Green element method based on local grid refinement. Finally, effects of model parameters on transient behavior is analyzed. It shows that the Green element method is a high precision dynamic simulation method, which improves computational efficiency of dynamic simulation of fractured horizontal well by setting node on edge of grid. In addition, local grid refinement method applied to the modified Green element method is based on superposition principle, in which interpolation approximation is not needed. The method is of high accuracy. Under same grid systems, local grid refinement based on improved Green element method is better than using finite difference. On the other hand, conductivity of complex fracture, permeability and size of stimulated reservoir volume have great influence on transient behavior of fractured horizontal wells. These effects should be taken into consideration and interpreted in transient behavior analysis.

As ultra-low permeability reservoir is developed by water flooding,it always presents characteristics of non-Darcy flow and permeability anisotropy. We derived water breakthrough time formula of five-spot well pattern,inverted nine-spot well pattern and rhombic nine-spot well pattern with basic non-Darcy flow formula and streamline integral method. Breakthrough time of one actual well pattern in Ordos Basin was calculated. Calculation results accorded with production data well. Effects of threshold pressure gradient, permeability anisotropy and viscosity difference between oil and water were analyzed. It shows that the greater the viscosity ratio of oil and water,the earlier the water breakthrough time; Corner well of rhombic nine-spot well pattern can realize uniform displacement both in x direction and y direction as ratio of well spacing in x direction and y direction equals to permeability anisotropy degree; The grenter the threshold pressure gradient,the latter the water breakthrough time. Effect of threshold pressure gradient became more apparent as well spacing is larger.

With Green function and Laplace transformation, one-dimensional element is established considering effect of permeability tensor of anisotropic reservoir. Inflow of fracture is obtained by linear interpolation of endpoints and flow in fracture is treated with linear integral of flow rate. Coupling flow in formation and fractures, calculating method for bottom-hole pressure is formed semi-analytically. It shows that there are three flow regimes including fracturing linear flow, formation linear flow and system radial flow. The more the fractures, the less the dimensionless pressure and number of factures has significant impact on flow rate. With increase of fractures increasing rate is dropping in the same time. Fracture length and conductivity have similar characteristics. Flow rate is improving as angle between fracture and wellbore is increasing. Flow rate reaches maximum as fracture is perpendicular to wellbore, and vice versa. Angle between maximum permeability and fracture has similar impact on production. In summary, production rate reach maximum as fracture is perpendicular to wellbore and direction of maximum permeability.

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.