When deviated from the planned wellbore path, it is imperative for a system to take correction actions. A new trajectory control model is developed based on minimum well profile energy criterion to achieve smooth well paths. In this model, the returning path from a deviated position (Xn-2, Yn-2, Zn-2, αn-2, φn-2) to the planned trajectory position (Xn, Yn, Zn, αn, φn is divided into two sections, each of which has its own length ΔD1, inclination change rate καi, and azimuth change rate κφi, i=n, n-1. The incremental well profile energy of the correction path can be computed as a function of section lengths, curvatures, and torsions. From the constant section build/drop rate settings and geometric relationships, five equations can be established corresponding to the changes of three-dimensional (3D) space coordinates and orientation angles (ΔX, ΔY, ΔZ, Δα, and Δϕ). By applying minimum well profile energy criterion, a unique solution set of deviation correction parameters (ΔDi, καi, and κϕi, i=n, n-1) can be obtained.

Different trajectory calculation algorithms are employed to solve the aforementioned deviation correction parameters. The results are consistent from the simple balanced tangential method, the industry standard minimum curvature method, and the more accurate natural curve method. The model is tested using wellbore trajectory simulations of different two-dimensional (2D) and 3D well paths. The simulation results show that the new trajectory control model, in comparison with proportional- integral-derivative (PID) control and fuzzy control methods, yields much smoother wellbore trajectories. Consequently, the new model is promising to reduce torque, drag, and friction of the drilling string.

Unlike PID and fuzzy control methods, which usually require subjective inputs of several controller parameters, the new trajectory control model offers deterministic solutions based on objective minimum-energy criterion. This is a significant advantage for the limited computation power of downhole tools. In addition, the settings of constant inclination/azimuth change rate in each correction section also provide benefits such as less frequent steering required; hence, less electric power consumption and less abrasion failure of downhole tools.

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