Finite element with embedded discontinuities analysis of well production decline due to fracture closure in naturally fr

Abstract

In naturally fractured reservoirs, the fractures may represent the main pathway for fluid flow. Therefore, the magnitude of fracture permeability plays a fundamental role in the productivity of such type of reservoir. In reservoirs sensitive to the stress state, the depletion due to production can lead to the closure of the fractures, as a function of the increase of effective confining stress, promoting a significant decrease in the overall permeability of the reservoir. Thus, understanding the hydraulic characteristics of the fracture network as a function of the effective confining stress is fundamental for the design of reservoir development, besides the predictability of its behavior. In this paper, a strong discontinuity approach to embed discontinuities into finite elements was adopted to represent the behavior of fractures in rock formations. To properly derive embedded discontinuity finite element formulations, fundamental aspects regarding to the kinematics and statics of the discontinuity must be considered. The kinematic enrichment must correctly reflect the position of the interface in the element as well as the relative displacement (opening and sliding) between the two opposite faces of the interface. Furthermore, the traction continuity condition must be properly imposed to ensure a correct relationship between the tractions in the internal interface and the stresses in the surrounding continuum portion. The simulation of the problem of closing natural fractures by reservoir depletion was carried out. A numerical tool was used to embed the natural fracture network into the finite element mesh, with respect to the geological mapping of these fractures. To model the mechanical behavior of material, it was adopted a hyperbolic model of fracture closure proposed by Barton & Bandis. It was possible to observe a decrease in the rate of production due to the collapse of the existing fractures that decreased the permeability around the production wells.