Multi-objective optimization design and control of deviation-correction trajectory with undetermined target

• A new mathematical formulation is presented for deviation-correction trajectory design.
• The multi-objective optimization model is established for deviation-correction trajectory.
• The presented model can guarantee all of the proposed objectives simultaneously.
• The multi-objective control method is proposed in different situation.

In the horizontal drilling process, when the actual trajectory deviates from the planned trajectory, it is necessary to take corrective action. The target point is difficult to determine explicitly; however, it is assumed to be in a certain interval of the planned trajectory. This paper presents a mathematical formulation for deviation-correction trajectory design in the case of an undetermined target point, and an optimum design model is established that considers two cases of planned trajectory. The criteria to evaluate the deviation-correction trajectory are summarized as the total trajectory length, the coincidence rate and the well profile energy. The optimum trajectory based on multi-objective optimization is discussed in terms of comprehensive criteria and different weight factors, and a novel heuristic algorithm to solve the established optimization model is presented. The results demonstrate that the maximum value of curvature results in a trajectory with a minimum total length and maximum coincidence rate yet a maximum well profile energy, whereas the maximum horizontal displacement leads to a trajectory with minimum well profile energy. Additionally, the multi-objective optimization model can guarantee a smaller trajectory length, high coincidence rate and low well profile energy. Finally, the multi-objective control method is proposed to obtain an optimization trajectory in different situations.