This paper presents a mathematical study of stress changes in principal horizontal and vertical stresses around the fracture due to an existing fracture using the Sneddon and Illiott model. The study shows that significant stress changes only occur in a localized near-fracture region, and far-field stresses have been minor influenced. Wellbore pressures to initiate a fracture at different potential locations and orientations are analyzed, too. The analysis shows the potential location of fracture opening/propagation is reopening of or branching from the old fracture away from wellbore. Wagon-wheel multi-fracture disposal domain is mathematically confirmed as impractical by computational investigation on stresses increase or fracture width around the wellbore for two types of assumed wagon-wheel (uniform strain and uniform width) multi-fractures. Creation of wagon-wheel multi-fractures would either require an impractical wellbore pressure to overcome the extreme stress due to existing fractures or the fracture width would vanish at the wellbore. This paper also reanalyzes the data from large-scale Mounds experiments of a series of cuttings reinjection and identifies that vertical fracture growth and branching from old fractures away from the wellbore occur more possibly according to the most microseismic events and tiltmeter patterns. This also confirms the above theoretical analysis and conclusions.
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