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It is a challenge to accurately predict the height of hydraulic fractures in stratified reservoirs. This paper presents a semi-analytical model that predicts fracture height growth based on equilibrium height theory. It considers the effects of pressure drop within the fracture and the plastic zone at the fracture tip. The study investigated the effect of in-situ stress, fracture toughness, fluid density, and perforation location influence fracture height growth. This was achieved by iteratively solving a non-linear system of Eqs to plot the fracture height profile at static equilibrium. Sensitivity analysis of the model revealed that: (1) Fracture height exhibited three characteristic growth modes: jumping, stepping, and fluctuating. The stress barrier inhibited fracture growth, necessitating a higher induced stress for fracture propagation. (2) The impact of fracture toughness as a barrier on fracture height growth was found to be less significant compared to the stress barrier. (3) An increase in fluid density led to a higher net pressure difference between the top and bottom of the fracture, resulting in a reduction of fracture growth height at static equilibrium. (4) Modifying the perforation location to control fracture growth essentially entailed adjusting the height of fracture growth through managing stress differences between the layers.
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