Influence of Hydraulic Fracture Fractal Propagation on Fracturing Result

The influence of fracture fractal feature on net propagation pressure and fracture size was studied for better understanding of fracture fractal propagation effect.Based on fractal fracture mechanics,the fractal propagation net pressure model was established through modification of linear propagation net pressure model,and analysis of hydraulic fracture fractal geometry and fractal crack tip stress field features.Then coupled with force equilibrium model and Sneddon maximum crack width model,fracture height ratio model and fracture maximal width ratio model of fractal propagation and linear expansion were built.Analysis results show that net pressure ratio increased from 1.5 times to 6.3 times when the fractal dimension increased from 1.20 to 1.80 under constant fracture length of 50 meters.In addition,fracture height ratio increased from 1.04 times to 1.11 times and fracture maximal width ratio increased from 1.70 times to 2.70 times at given formation mechanical parameters when fractal dimension increased from 1.30 to 1.60 under fracture length of 20 meters.So,fractal propagation influences geometric dimensions of hydraulic fracture significantly and the higher the hydraulic fracture fractal level,the bigger the fracture height increment and maximal width increment.