Pressure transient response with random distributed fracture networks using a semi-analytical method for fractured horizontal wells in a rectangular closed reservoir

Abstract

The focus of this paper is to establish a general model, which is capable of dynamic simulation of discrete fractures at any position and arbitrary distribution in rectangular closed reservoir. In this article, a semi-analytical model for fractured horizontal wells with random distributed fracture networks is proposed to facilitate pressure transient response using a double node method. A rectangular closed reservoir model and fracture network flow model are established respectively, and then coupled at the fracture wall. In order to deal with the flow distribution at the fracture intersection, a simple adaptive material balance method is proposed in this paper, which successfully solves the flow distribution at the intersection. Using advanced mathematical means, the model is successfully solved in Laplace space, and then the pressure response solution in real space is obtained by Stehfest numerical inversion method. The obtained solutions are verified and compared with the numerical simulation results. The calculation results show that the flow characteristics of the orthogonal fracture network can be roughly divided into six stages, namely, bi-linear flow, first linear flow, first radial flow, second linear flow, second radial flow and boundary dominated flow. However, these flow characteristics will deviate or even be missing, depending on the complexity of the fracture network. Finally, the effects of some important parameters (such as dimensionless fracture network conductivity, main fracture length, fracture network density, reservoir area and eccentric position) on pressure response and pressure field distribution are discussed in detail.