A theoretical model of formation force which derives from 3D rock-bit interaction model and weight on bit (WOB) is presented. Except for considering drilling trajectory changes and formation anisotropy, the model accounts for the effects of bit anisotropy and bit tilt angle which did not study in models published before. The effect of bit anisotropy and bit tilt angle on formation forces is discussed in detail. The analysis allows us to calculate formation forces more accurate in the trajectory controlling. The model is used to estimate the anisotropic drilling characteristics of the formation in Kelasu conformation which has high stratigraphic dip in Tarim Basin in western China. The result reveals that it can properly reflect the strata drifting characteristic of the formation being evaluated.
Estimation of the forces between the drill string and the formation is vital for planning drilling trajectory in directional well and for preventing deviation in straight hole. Many models for calculating formation force have been published [1–11]. Among these, models presented in literature [1–9] assume the bit equilibrium under constant inclination and azimuth angles. They do not consider the effect of bit anisotropy and bit tilt angle. However, in the drilling process, borehole inclination and azimuth may continuously change, and drilling bits are not isotropy. Models suggested by Yan and Yan et al [10, 11] can be used in the condition of inclination and azimuth changes. But they also do not consider the effect of bit anisotropy and bit tilt angle. Because of its anisotropy and tilt angle, a bit can not move on the direction of mechanical resultant force even if it penetrates an isotropy formation, which indicates that bit anisotropy and bit tilt angle have an effect on formation forces.
Thus existing models can not predict formation forces with required accuracy. In this paper, a new model for calculating formation forces is presented. The presented model takes into account the effects of bit anisotropy, bit tilt angle and drilling trajectory changes on formation forces. The effects of bit anisotropy and bit tilt angle on formation forces are discussed.
Anisotropy of the formation can be expressed by the formation anisotropy index. If an isotropic bit drills a hole in the orthogonal anisotropy formation, formation anisotropy index can be defined as [9]:
Equations (available in full paper)
Bit anisotropy expressed by bit anisotropy index is the ratio of drillability in lateral and axial direction of a bit. If an anisotropic bit makes footage in an isotropic formation, anisotropy index of the bit can be expressed by [9]:
Equations (available in full paper)
A Cartesian system of coordinates is selected with Zd axis opposite to the drilling direction (Fig.1). Then the side force at the bit can be obtained from the following equation:
Equations (available in full paper)
