A generalized framework model for simulating transient response of a well with complex fracture network by use of source and Green's function

Abstract

The focus of this paper is a generalized model to account for various complex-geometrical fractures with different particularities (conductivity, azimuth, length and connectivity etc.). In this study, a semi-analytical approach was established to facilitate transient response analysis in a 2D infinite reservoir containing a complex fracture network. In this model, according to superposition principle, the flow behavior in reservoir is modeled by using the classical instantaneous Green's function, and each fracture is explicitly represented by using continuous source solution. For the treatment of complex interplay of flow caused by interconnected fractures, a novel approach using mass balance equation is incorporated by restraining the vector sum of sources to determine flow redistribution of fracture segments neighboring interconnection. Furthermore, a set of case studies, from simple planar symmetry fracture to complex fracture network, were performed to demonstrate the accuracy of the generalized model by verifying with existing reliable solutions and alternative numerical simulators. In addition, the representative flow regimes were investigated to capture the physics of the transient response for complex fracture network. Finally, a real-field example was presented to illustrate the potential of our model in practical application. This work can provide a critical compromise in filling the gap between mesh-free solution and mesh-relying numerical methods in petroleum engineering.