Study on Rock Mechanical Properties and Wellbore Stability of Fractured Carbonate Formation Based on Fractal Geometry

To mitigate borehole wall instability in fractured carbonate formations in an oilfield, the main factors affecting borehole wall instability were determined by combining the characteristics of underground cores, logging data, and a series of laboratory mechanics experiments. The geometric morphology characteristics of a carbonate rock fracture surface were studied together with an artificial rock fracture surface formed by triaxial mechanics experiments. A relationship between the geometric morphology characteristics of a fracture surface and rock mechanical properties was established based on fractal geometry. Using the Mohr-Coulomb failure and weak plane failure criteria, a rock strength criterion based on the fractal characteristics of a rock fracture surface was established. Finally, the mechanical rock properties characterized by fractal geometry were imported into the established borehole stability evaluation model. The results show that a collapse formation is mainly limestone with relatively developed microfractures, and some fractures are filled with expansive clay. The anisotropy of mechanical properties of bedrocks and microfractured rocks is obvious, whereas drilling-fluid immersion has little effect on the mechanical properties of a rock. 3D scanning experiments of artificial fracture surfaces formed after a triaxial mechanical test of a bedrock and fracture surfaces of a rock with microfractures show that the geometric characteristics of fracture surfaces after bedrock failure were more complex than those of fractured rocks. The geometric characteristics of rock fracture surfaces were numerically expressed through astatistical analysis and fractal geometry. Function relationships among cohesion, an internal friction angle, and fractal dimensions of bedrocks and microfracture rocks were fitted. A numerical simulation of borehole stability based on the fractal model of a carbonate fracture surface shows that different fracture inclinations and borehole trajectories significantly influence the collapse pressure equivalent density of a borehole wall. On drilling a horizontal well along the inclination of a fracture, the collapse pressure equivalent density of the borehole wall is relatively low when the fracture inclination is along the direction of the minimum horizontal principal stress. Unlike that from a conventional borehole stability model, the collapse pressure equivalent density calculated from the fractal model will increase by 0.1-0.2 g/cm³. The study results provide a theoretical basis for safe and efficient drilling in fractured carbonate formations.