Three-dimensional numerical modelling of drilling-induced tensile wall fractures

Drilling-induced tensile fractures (DITFs) form due to stress concentrations around a wellbore and are in vertical wells typically parallel to the largest horizontal far-field stress and normal to the least horizontal far-field stress. The peak pressure in the wellbore exerted by the drilling mud that the wall rock can sustain is given by the so-called Hubbert-Willis (H-W) criterion, which predicts that wall rock failure takes place when the circumferential effective stress at the borehole wall reaches the tensile strength of the wall rock. However, even though the H-W criterion is a valuable fracture-initiation criterion, it cannot predict if and how an initiated fracture propagates. Linear elastic fracture mechanics (LEFM) can provide a solution to these questions under simple loading conditions, e.g. a vertical borehole in a rock mass that is under an Andersonian stress state. Predicting the initiation and propagation of DITFs in more complex settings, such as inclined boreholes or wellbores in mechanically layered sequences, however, necessitates three-dimensional numerical modelling.

Here we present results of three-dimensional numerical Rigid Body Spring Network (RBSN) lattice modelling. The model comprises so-called rigid blocks (tetrahedra in the present study), that interact with each other and can be bonded at their contacts; these bonds fail when the effective normal stress exceeds the bonds tensile strength, which corresponds to micro-fracture of the wall rock. Coalescence of these micro-cracks leads to the formation of macroscopic fractures. Wellbore failure is modelled by means of a hollow cylinder discretised by these bonded rigid blocks. The remote (tectonic) stress is applied to the hollow cylinder’s outer surface whilst the pressure exerted by the drilling mud is applied to its inner surface. Fractures connected to the wellbore receive the same internal pressure as the wellbore and quasi-static fracture propagation is achieved by gradually increasing the pressure on the borehole wall.

Validation of the numerical model under simple loading conditions illustrates that fracture lengths and associated aperture profiles as a function of wellbore pressure correspond well with LEFM predictions. Numerical models of moderately inclined boreholes exhibit stepping DITFs, where fracture stepping is most pronounced when the wellbore is inclined towards the least horizontal stress direction and no fracture stepping occurs when the wellbore is inclined towards the greatest horizontal stress direction. In mechanically layered sequences comprised of layers with different Young’s modulus, DITFs first nucleate in the stiff beds. Complex fracture geometries emerge in mechanically layered sequences, such as fracture stepping within individual beds or at layer boundaries. The detailed evolution of these more complex DITFs depends on several factors, such as the orientation of the remote principal stresses and layering relative to the wellbore axis. Our numerical modelling approach permits to systematically investigate the effects of these different factors on the geometry of DITFs and therefore offers a new tool that can assist in construing the mechanical genesis of fractures imaged in borehole logs and the current stress in the Earth’s crust.