A semi-analytical model for characterizing transient flow behavior of reoriented refractures

In order to improve the field productivity, the industries can create new fractured wells to reduce the interval between the initial fractures (initial fracture indicates a fracture that is induced during the initial fracturing treatment). Production from the initial fractured wells can induce stress reorientation in the vicinity of the fractures. As such, a refracturing treatment in the stress reorientation region can lead to a reoriented refracture which has a certain azimuth with respect to the initial fractures. This azimuth can even be 90° if the stress reorientation is sufficiently large. In addition to the conventional parameters (including refracture's length, refracture's conductivity, and the in-situ conditions), there are two more factors, the reorientation azimuth and the interference from the initial fracture, which can exert significant influence on the transient flow behavior of the reoriented refractures. In such case, the conventional analytical/semi-analytical models neglecting these two factors are no longer applicable to characterize the transient flow behavior from such a refracture. In this work, we develop a novel semi-analytical model to characterize the transient flow behavior of a reoriented refracture considering the interference from the initial fractures. In this model, the fractures are explicitly represented with discretized segments. We apply finite difference approximation to the initial fractures and refractures, respectively, to simulate the transient flow in the fracture system. In addition, the fluid flow in the matrix system can be characterized by Green function and Newman product method. Based on the continuity of flux and pressure, we couple the fracture flow equations with the matrix flow equations to construct a semi-analytical model. With the aid of the proposed model, we conduct a thorough investigation of the transient flow behavior of reoriented refractures. It is observed that, at the early production period, two fracture pseudo-steady-state flows can appear due to the interference from the initial fractures. The formation linear flow and bilinear flow can also be observed during the production period of a refractured well. In an anisotropic-permeability reservoir, the refracture's azimuth and position can exert a significant impact on the productivity of the fractures. There is a region in the vicinity of the initial fractures, within which an orthogonal refracture can lead to the highest field productivity.