Recent technologies developed for drilling, completion, and fracturing in horizontal wells have allowed the oil and gas industry to effectively use multistage fracturing stimulation treatments to help improve production in tight and unconventional gas and oil reservoirs. The fracturing process usually involves placing multiple perforation clusters exposed to the injected fluid in each treatment's stage. It has been shown that very strong interactions occur between the fractures propagating from the clusters, which further influence the effectiveness of production following a fracturing treatment. This paper presents a computational methodology to simulate and analyze the major physics associated with the interactions between multiple injections using a tightly coupled fluid-structure interaction (FSI) numerical model for hydraulic fracturing. This approach uses the finite element method (FEM) to computationally evaluate the stresses and deformation of elastic rock blocks. Nonpenetration contact conditions between adjacent solids, coupled with tensile and shear failure models, are developed to describe fracture evolution and its interaction with the rock blocks. The fluid flow in opened fractures is modeled using the cubic law formulation. The proposed coupling computational method leads to an integrative algebraic system for a set of variables that fully describes this multiphysics phenomenon, including rock block corner displacements and Lagrange multipliers for cases where the blocks are in contact, along with the fluid's pressure at junctions of the opened fracture network. The suggested algorithm solves all of the unknowns simultaneously and in a tightly coupled manner. This algorithm is not limited to the specific study of the interactions between hydraulically induced fractures from different perforation clusters, but it can also be used to properly describe the interactions between hydraulically induced fractures and natural fractures. Yet, because of the existence of natural fractures, the interactions between multiple injections become more complicated than the interactions between only hydraulically induced fractures. In these cases, the natural fractures between multiple injections provide a stronger interaction and pathways for injected fracturing fluid between multiple injections. The spacing of injection clusters is studied for its effect on fracture length and the width of fractures for each injection cluster.

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