Expensive deviation-correction drilling trajectory planning: A constrained multi-objective Bayesian optimization with feasibility-oriented bi-objective acquisition function

Abstract

While conducting large-depth vertical drilling, correcting well trajectory deviations is a critical and challenging task. Designing a feasible deviation-correction trajectory becomes an expensive constrained multi-objective optimization problem due to the need for refined modeling of large-depth wellbore stability analysis. There is a pressing need for advanced drilling trajectory planning methods designed to handle robust constraints and to consider refined geological formation modeling, as current surrogate model-assisted optimization algorithms lack efficiency and balance among feasibility, convergence, and diversity. A Gaussian process-assisted Bayesian Multi-Objective Evolutionary Algorithm (MOEA) based on the reference point-based Non-dominated Sorting Genetic Algorithm (NSGA-III) is developed to manage the expensive wellbore stability objective. While surrogate models can effectively mitigate the computational expense, they may not adequately satisfy the stringent trajectory planning constraints. To enhance the constraint handling ability, an intricately devised infill criterion, Feasibility-oriented Bi-objective Acquisition Function (FBAF), tends to select promising feasible solutions to infill into the next generation. The deviation-correction trajectory planning simulation experiment was carried out under limited evaluations with real vertical well data. The results of empirical attainment function analysis demonstrate that the proposed FB-NSGA-III reduces the number of evaluations and exhibits superior performance compared to 11 other traditional surrogate-assisted MOEAs, particularly in terms of feasibility. FB-NSGA-III successfully prevents the back-hook by avoiding constraint violations and maintaining curvature within the specified safety and directional drilling tool build-up range.