A Semianalytical Model for Pressure-Transient Analysis of Fractured Wells in Unconventional Plays With Arbitrarily Distributed Discrete Fractures

Abstract

Summary In this paper, we present an efficient semianalytical model for pressure-transient analysis in fractured wells by considering arbitrarily distributed fracture networks. The semianalytical model included three domains: matrix, hydraulic-fracture networks, and discrete natural fractures. Using the line-source function, we developed the diffusivity equation for fluid flow in matrix. By applying the vertex-analysis technique, we eliminated the flow interplay at fracture intersections and established the diffusivity equations for fluid flow in hydraulic-fracture networks and isolated natural fractures. The pressure-transient solution of these diffusivity equations was obtained using Laplace transforms and the Stehfest numerical inversion. Results showed that with the discrete natural fractures, a “V-shaped” pressure derivative (the classical dual-porosity feature of naturally fractured reservoirs) emerged. With the hydraulic-fracture networks, the reservoir system would exhibit pressure behaviors such as “pseudoboundary-dominated flow,” “fracture-interference flow,” and “fluid-feed flow.” All these pressure characteristics were dependent on the properties and geometries of natural/hydraulic fractures. In addition, through synthetic field application, we found that different (natural/hydraulic) fracture distributions and geometries had distinct behaviors of pressure derivatives, which may provide an effective tool to identify the properties of randomly distributed natural fractures as well as complex hydraulic fractures in unconventional plays.