Abstract: Complex propagation system of multi-branched，non-planar fractures in naturally fractured formations commonly
occurs due to the effect of natural fractures，which greatly differs from bi-wing，symmetric and planar fracture generated in the
homogeneous formations. Therefore，the conventional hydraulic fracture extending model is no longer adaptable，and there’s an
urgent need to develop a new model to simulate the propagation pattern and geometry of induced fracture in naturally fractured
formations when hydraulic fracture extends along natural fractures. Based on the equivalent planar fracture of propagation
pathway of hydraulic fracture re-orientating along natural fractures，this paper established the mathematical model of hydraulic
fracture non-planar re-orientation propagation and provided corresponding numerical solution. The calculation results show
that the induced fracture width at re-orientation propagation section reduces apparently and the treating pressure increases when
hydraulic fracture extends along natural fractures. Analysis of influence factors shows that the larger differential horizontal stress
and approaching angles are，the more the fracture width at re-orientation propagation section reduces；the higher volumetric
rate and fracturing fluid viscosity are，the larger the whole extension fracture width including re-orientation propagation section
is. It is clear that differential horizontal stress and approaching angles are negative factors but volumetric rate and fracturing
fluid viscosity are positive factors for that proppant transports along hydraulic induced fracture. For this purpose，raising
volumetric rate and fracturing fluid viscosity can reduce fracturing risk in naturally fractured formations. This research in this
paper realizes non-planar extending features of hydraulic fracture and offers a theoretical basis for fracturing design in naturally
fractured formations. Therefore，it has importantly theoretical value and practical significance.

Key words: naturally fractured formations, hydraulic fracture, non-planar propagation, natural fractures, differential horizontalstress, approaching angles