An Advanced Three-Dimensional Bottom-Hole Assembly Model: Validation and Application
Authors: Zhang H. , Tian K. , Bhaidasna K. 
Published: September 2024

Abstract
Static analysis of the lateral deformation of a bottom-hole assembly (BHA) has been crucial in controlling the deviation of the borehole trajectory in the directional drilling process. Moreover, it is widely accepted that outputs from the static analysis, such as contact points and tangency points, are necessary for calculating the modal characteristics and forced-frequency responses of the BHA lateral vibrations.
In drilling practices, the lateral deformation of a BHA is typically constrained by the surrounding borehole wall. Proper modeling of the BHA's constrained deformation is crucial for evaluating its static response. Mathematically, the contact configuration introduces a set of boundary conditions at the contact points. However, the contact configuration is unknown a priori, as it is subject to a contact law in terms of deflections and contact force, which must be determined separately. As a result, the contact problem introduces nonlinearity, and the BHA-wellbore contact significantly affects the BHA deformation and bit side forces, which are crucial to the propagation of well trajectories in directional drilling. Furthermore, the tangency point, which is closely related to the continuous BHA-wellbore contact, is vital for extracting modal characteristics of the BHA lateral vibrations. Its characterization should also be considered in the BHA-wellbore contact problem.
This paper first proposes a finite element model for static BHA analysis, which accounts for the borehole curvature, axial force, actuating force from a downhole rotary steerable system, and contacts between the BHA and the borehole wall. A novel iterative algorithm is developed to solve the nonlinear contact problems in both two-dimensional and three-dimensional BHA analysis. The static BHA analysis lays the foundation for both the modal analysis of the BHA lateral vibrations and the borehole propagations in directional drilling.
The validity of the proposed BHA model is confirmed by comparison with field data in various scenarios. First, the static BHA model is used to simulate the bending moment-on-bit (BOB) with varying actuating force. The simulation results match well with high-frequency downhole BOB data. Second, the natural frequencies of a BHA deployed in the field were calculated and compared with the peak frequency from the downhole triaxial acceleration data. Their close agreement reveals that the lateral vibration of the BHA is responsible for the failure of the downhole tools. The BHA configuration can thus be optimized to avoid resonant vibrations. Lastly, the BHA model is combined with a bit-rock interaction model to predict the evolution of the borehole trajectory in directional drilling. With the measurements of downhole weight-on-bit (WOB) and actuating force, the prediction from the model agrees well with survey data by tuning a parameter related to the bit side cutting efficiency.
The above validations showcase various applications of the model in the drilling process. The proposed BHA model is versatile and computationally efficient, making it suitable for various application scenarios, including pre-job designs for borehole trajectory control and vibration suppression, real-time analysis to infer and monitor downhole conditions by interpreting downhole measurements with the model, and post-job analysis to diagnose the root causes of different undesirable limiters for optimal drilling performance.