Various fracture patterns may develop through hydraulic fracture propagation and interaction with natural fractures which may substantially enhance connectivity and connected fracture surface area in low-permeability formations. Key factors controlling this behavior are analyzed using the continuum simulator TOUGHREACT-FLAC3D that couples the evolution of stress and deformation (FLAC3D) with reactive fluid flow (TOUGHREACT) in fractured rock. The three potential interaction scenarios are accommodated - for the hydraulic fracture to directly cross, stay arrested by, or reinitiate from the intersected natural fracture. The results show that the combined effects of approach-angle and differential stress affect the normal closure response acting on fractures. Also, larger approach-angles, greater stress differences, and higher fracture shear strength favor direct crossing, with tensile stresses more readily transferred to the far-side of the approached natural fracture. Higher injection rates accelerate buildup of wellbore and fracture pressures which lead to more rapid propagation of the hydraulic fracture. Higher injection rates also increase the wellbore pressure and pressure gradient when injection rate exceeds leak-off rate of fractures arrested by the natural fracture. The presence of only single natural fractures results in faster hydraulic fracture propagation and greater propagation length driven by higher developed wellbore pressures than where dual natural fractures are present. The presence of dual parallel natural fractures hinders the propagation of the hydraulic fracture along its preferred original path as a result of greater and redistributed leak-off and diminution of pressure through the natural fractures. Increased natural fracture permeability slows hydraulic fracture propagation by increasing fluid flow and resulting pressure dissipation by the natural fractures. Combined, these factors influence mechanisms of fracture propagation and interaction, and evolution of flow paths, which are essential in design of hydraulic fracturing treatments, hydro-mechanical characterization and prediction of the response of stimulated fracture networks.