A mathematical model was constructed to better characterize and predict the growth of induced hydraulic fracture networks (HFN) in naturally fractured formations such as shale. The model represents the HFN developed during a hydraulic fracturing stimulation treatment by a growing elliptic volume of the stimulated formation. It consists of two perpendicular sets of vertical planar fractures with mechanical interactions among themselves and with injected fluid fully accounted for. The model is further constrained by the amount of fluids pumped into the formation. Based on this mathematical model, a semi-analytical simulator was developed for design and planning of hydraulic fracturing stimulation jobs. It is capable of predicting the growth of HFN (height, length, width)predicting proppant placement (all directions or dominant fracture only) and fracture conductivitysupporting variable pump schedules for fluid and proppantsupporting limited entry for slurry injectionsupporting multiple fluid typessupporting multiple proppant typesdegenerating to bi-wing fracture
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