Estimation of the Response, Power Spectra, and Whirling Patterns Generated From Mud Circulating Along the Annulus During Drilling Procedures: An Alternative Mathematical Representation via Finite Element Modelling

In this study, an alternative mathematical representation of a drill-string is proposed to provide an alternative assessment on BHA dynamic alterations. Lateral vibrations remain the focal point of drill-string breakdowns given their high frequency characterization and ability to deviate perforation trajectories from the subsurface target. In this paper, the proposed model consists of an anisotropic rotor subjected to distinct RPMs, an axial force, and a bidirectional harmonic excitation with specified amplitude and assorted duration to simulate annulus motion generated from the mud fluid. In this regard, Euler-Bernoulli beam theory was adopted to establish a complete MDOF mathematical expression and thus model an exclusive section of the BHA. Parameter identification implied incorporating a finite elements methodology, where the flexibility of the drill-string and elastic characteristics of the well-bore were accounted for. Particularly, a two-node element containing two displacements and two rotations per node was adopted to describe the rotor as a uniform, elastic beam. Thus, it is concluded from the proposed mathematical model that the harmonic excitation imposed along the annulus is introducing subharmonic frequencies and a potential (unmodeled) nonlinearity into the system.