An evaluation method of hydraulic fracture propagation behavior in rock containing natural fractures based on fractal dimension

Abstract

This study presents a novel method for quantifying the propagation of hydraulic fractures and their interaction with natural fractures under varying fracturing conditions. We examine the impact of approach angle, fracture aperture, borehole distance, differential stress, and injection rate on hydraulic fracture behaviour using the Particle Flow Code 2D (PFC^2D) model. The results reveal two main fracture extension modes: crossing and retained. The approach angle significantly affects the fractal dimension of hydraulic fractures, with peak values of 1.12 at intermediate angles (30°–60°) and lower values (0.96–0.98) at extreme angles (0° and 90°). Increasing fracture aperture accelerates propagation by 13.7 %, while a higher injection rate raises the fractal dimension by 22.6 %. Borehole distance introduces variability, and as differential stress increases, the fractal dimension increases from 0.98 to 1.17, accompanied by a 43.4 % increase in breakdown pressure. To model temporal variations in fractal dimensions, The Logistic method adjusts the fractal dimension amplitude with parameter $A_2$ and controls the growth rate during the acceleration phase with $p_1$. The BiDoseResp method, by contrast, modulates amplitude using $A_3$ and $A_4$, and regulates the entry and exit stages through ${\mathrm{LoGt}}_1$ and ${\mathrm{LoGt}}_2$. Parameters $h_1$, $h_2$, and $p_2$ govern amplitude and growth during the retention and acceleration phases. These models provide a framework for optimising hydraulic fracturing in geothermal development, enhancing fracture dynamics understanding and improving resource extraction efficiency.