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.