Analysis of borehole collapse and fracture initiation positions and drilling trajectory optimization

For borehole stability analysis, it is of vital importance to correctly determine the borehole and fracture initiation postions; currently studying their variation rule, most of them are based on borehole stress solutions for plane stress condition, or neglects the influence of shear stresses. This research analyses the failure directions of deviated boreholes in different faulting stress regimes for plane strain condition with the polyaxial strength failure criterion Mogi-Coulomb and develops a new analytical equation of determining the optimum drilling trajectory. The analytical results show that Poisson׳s ratio generally exerts more influence on the angular positions of borehole collapse than fracture initiation positions with the exception of some cases where Poisson׳s ratio has no influence on the angular positions of borehole collapse and the borehole collapse and fracture initiation positions. It is not always correct to neglect the effect of shear stresses on the borehole collapse and fracture initiation positions with respect to particular cases; when drilling orientates along the direction of minimum horizontal in-situ stress in normal faulting stress regime, there is a range of inclinations where the borehole collapse and fracture positions are identical; moreover, the same circumstances will also take place in a direction parallel to the maximum horizontal in-situ stress in the reverse faulting stress regime or the borehole is horizontal with particular drilling orientation in the strike-slip faulting stress regime. The optimum drilling trajectory lies in the critical turning point, which corresponds to the aforementioned three situations, respectively, of angular positions of borehole collapse. Therefore, this study's result can provide a theoretical basis for the optimization design of borehole trajectory and a safe drilling fluid density window.