Accurate well-path planning is the prerequisite for operators to drill directional or horizontal wells successfully. During directional drilling operations, bit walk objectively exists along an actual drilled well trajectory. Drilling experience shows that it is an effective measure to control a well trajectory by taking the physical bit walk into account if the rate of bit walk can be accurately estimated. As the planned results of bit-walk path can evidently reduce the frequency of azimuth correction and drilling-string trips, and lessen the difficulty and workload of trajectory control, it will undoubtedly improve the rate of penetration and the quality of well trajectory, and cut down the cost of drilling.

The author has published some related methods to plan 3D bit-walk paths, in which the bit-walk rate must maintain constant over each well-path section (build-up, hold-up or drop-off). In some cases, the bit-walk rates are given on the basis of rock characteristics. In addition, it is also an effective measure to determine an appropriate wellhead location, if there is no limitation of surface condition, for the desired profile of a horizontal well. This paper makes further researches on the mathematical model of bit-walk path and gives more concise formulas, analyzes the compositive relation of inclination units and azimuth units, and yields a method to divide them into shorter intervals for calculation. The author discusses the characteristics of planning bit-walk paths and presents the constraint equations and solutions for directional wells. For the desired profile of a horizontal well, this paper also describes the idea and techniques to accurately determine the surface location and a key parameter of the profile, such as KOP, accounting for bit-walk effects. The model and methods provided employs exact mathematical solution and results, and the planned paths are smooth from the wellhead to the given target.

The methods proposed represent significant improvements over the traditional well-path planning techniques, and were programmed into computer software. Several examples are given, and the results proved satisfactory for various directional and horizontal wells.


Bit walk is the natural tendency of the drill bit to drift in a lateral direction during drilling and occurs in every operation. Operators planning and designing wellbore trajectories, therefore, must consider planning 3D paths, especially in areas where the amount of bit walk is considerable. Bit walk occurs in drilling operations as well trajectories are drilled, generally occurring as right-hand drift but also occasionally as left-handed drift.

Drilling deviation is the result of rock removal under the complex action of the bit. To predict and control the deviation tendencies of a drill bit, the "rock-bit interaction" model is the kernel of the theoretical analysis on the fundamental problems. Lubinski and woods (1953) made the pioneering work in this respect, and Williamson and Lubinski (1987) further discussed the model. The Lubinski's and Williamson's models include two elements: a 2D analysis program using a semi-analytic method to predict the side force on the bit in slick assemblies, and a formation anisotropy effect model to account for the commonly experienced up-dip tendency in directional drilling. They defined a rock anisotropy index to account for the different drill abilities parallel and perpendicular to the formation bedding plane. This model assumes bits to be isotropic, which was later disputed by Ho (1987). Nevertheless, since its inception in 1953, the Lubinski's model has stood for a long time as the only rationally derived rock-bit interaction model.

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