Abstract:

An accurate analysis of the three-dimensional (3D) deformed configuration of a bottom-hole assembly (BHA) is critical for predicting and controlling well paths in directional drilling. Among the various numerical approaches, the weighted residual method exhibits superior performance owing to its semi-analytical nature, enabling high accuracy in handling diverse boundary conditions. In previous studies, the weighted residual method has been coupled with a dual optimization process to determine the 3D deformation and tangency point of the BHA. However, its applicability is limited by the conventional treatment of contact interactions between the BHA and wellbore wall. Specifically, stabilizer-wellbore contacts are regarded as predefined boundary conditions, rather than solving these contact positions as unknown variables consistent with actual downhole conditions. This limitation reduces modeling fidelity in complex downhole environments. To address this limitation, this study enhances the optimization-based weighted residual method by introducing ant colony optimization (ACO) to solve the 3D contact problem. In the proposed framework, the bending energy of the deformed BHA is conceptualized as “food”, while the contact positions and orientations of stabilizers are assigned a measure of “taste”. Through this metaphor, the ACO algorithm employs artificial “ants” to explore the optimal stabilizer locations and orientations that minimize the BHA bending energy, thereby refining the computed 3D deformation. The simulation results demonstrate that integrating ACO into the previously established dual optimization framework enables the effective determination of the contact configuration between the BHA and wellbore wall. As a result, the overall accuracy of the 3D BHA deformation analysis is significantly improved. In one representative case study, the bending energy of the BHA is reduced by 55.6% compared with that obtained from the original dual-optimization method.

Key words: weighted residual method, directional drilling, bottom-hole assembly (BHA), artificial intelligence (AI)-driven triple optimization, ant colony optimization (ACO)