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.

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