Boundary Element Analysis of the Stress Distribution Around Multiple Fractures: Implications for the Spacing of Perforation Clusters of Hydraulically Fractured Horizontal Wells

Abstract

Abstract For multi-stage hydraulic fracturing of horizontal wells with casing hole completion, multiple cluster perforations are typically used to create multiple fractures in any single stage. How to place these perforations is a critical issue because the number of perforation clusters to be used and the space between them significantly impact how effective the fractures can be created in the formation. To optimize the spacing of perforation clusters, stress distributions and fracture mechanics need to be well understood. In this study, the displacement discontinuity method is used to construct a boundary element model, which is able to analyze the stress distributions around multiple transverse fractures and the geometries of these fractures. With the boundary element model, multiple cases are investigated for different number of fractures and fracture spacing. Changes of both minimum and maximum stresses, as well as shear stress around these fractures are first illustrated. It is found that for the cases with more than two parallel fractures, there is a strong stress concentration around the center fractures. The calculated displacements indicate that the created fractures are no longer elliptic-like, and the widths of the center fractures are significantly reduced compared with that of a single fracture. For the case of two parallel fractures, the stress concentration between two fractures also results in the asymmetrical shape of fractures, but the fracture widths are not reduced significantly. The study indicates that the number and spacing of the fractures need to be carefully selected in order to create effective fractures with appropriate fracture geometries. The boundary element model provides a useful tool to relate rock geomechanic properties to stress distribution and fracture geometries for multiple fractures in hydraulic fracturing of horizontal wells, which can be served as a guidance to space the perforation clusters. Introduction Hydraulically fractured horizontal wells have been increasingly used to produce ultralow permeability reservoirs, such as tight gas sands and gas shales (Economides and Martin 2007; Waters, et al. 2009). The fractures which are typically vertical can be either transverse or longitudinal (Wei and Economides 2005). Transverse fractures are perpendicular to the horizontal wellbore while a longitudinal fracture is aligned with the horizontal wellbore (Fig. 1). To create multiple transverse fractures, the horizontal wellbore is placed along the direction of the minimum principle horizontal stress because the created fractures follow with the direction of the maximum principle horizontal stress. Multiple transverse fractures are created with multi-stage fracturing treatments (either open hole completion or cemented/perforated casing hole completion). For casing hole completion, multiple cluster perforations are typically used in any single stage to initiate multiple transverse fractures. It is important to place as many fractures as necessary to effectively deplete the reservoirs (Soliman, Hunt and Azari 1999; Ozkan, et al. 2009). This is particularly true for gas shales because given typical shale reservoir in-situ permeability of 200~400 nd (Boyer, et al. 2006; Waters, et al. 2009), it is critical to place multiple closely spaced fractures in order to establish commercial production rate. The effectiveness of the created fracture depends on many factors. How to place the perforation clusters is of the most importance because the number of perforation clusters to be used and the space between them significantly impact how effective the fractures can be created in the formation. To optimize the spacing of perforation clusters, stress distributions and fracture mechanics need to be well understood.