Conclusions
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1.
The equation of bit rotation in anisotropic rock allows the difference in directions of the bit axis and the borehole axis (the tangent ot the trajectory) to be determined.
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2.
The asymptotic approach here proposed allows the curvature and the normal to the trajectory with a specified direction of the borehole axis at the face to be determined for weakly deviated borehole trajectories. The equations of the borehole trajectory are thus determined.
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3.
Combined numerical calculation of the column equilibrium and the borehole deviation is unnecessary in the new method of describing the characteristics of the drilling-column base; instead, the solution is obtained by taking account of just a few simple parameters of the column base, determined separately by solving the problem of elastic deformation of the base of a heavy drilling column in a distorted inclined shaft.
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4.
The formulas for the curvatures and components of the normal to the borehole trajectory obtained for the case of gyrotropic rock describe the locally independent distortion of the projection of the borehole trajectory in two planes orthogonal to the bed, one of which includes the bit axis.
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O. V. Voinov and V. A. Reutov, “Equations of bit mechanics in drilling anisotropic rock,” Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 2 (1991); Paper 1666 Deposited at VNIIOÉNG [in Russian], Moscow (1991).
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Additional information
Paper 1667 deposited at VNIIOENG, Moscow, 1988.
All-Union Scientific-Research Institute of Petroleum Technology, Moscow. Translated from Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, No. 3, pp. 82–89, May–June, 1991.
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Voinov, O.V., Oganov, G.S. & Reutov, V.A. Model of borehole deviation in anisotropic rock. Soviet Mining Science 27, 244–250 (1991). https://doi.org/10.1007/BF02500904
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DOI: https://doi.org/10.1007/BF02500904