Three-dimensional numerical simulations of hydraulic fracturing processes associated with arbitrarily oriented, perforated wellbores are presented. The objective is to enable the simulation of multiple, non-planar fractures in the near-wellbore region of perforated wellbores. A system that couples the structural response of a fractured rock with the flow of a Newtonian or power-law fluid between the fracture walls is described. Example applications are presented and compared to published solutions to validate the system. 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