Coupled Drillstring Dynamics Modeling Using 3D Field-Consistent Corotational Beam Elements

Drilling is essential to extract subsurface hydrocarbons and geothermal energy, or store waste fluids/gases underground. Drilling efficiency directly affects the economics of well construction, and is to a large extent determined by the non-productive time (NPT) associated with downhole tool failure, bit wear/damage, unexpected drillstring vibrations, and insufficient surface-to-bottom energy transfer. Various models have been developed since the 1960s to understand and mitigate undesired drilling system oscillations to ensure efficient drilling operations and help optimize the well design. Significant recent advancements in drilling engineering technology, sensor development, and data science make it possible to develop and apply a faster and more comprehensive drilling system dynamic model that can be used for real-time drilling optimization and automation. In this study, a novel control-oriented physic-based drillstring dynamic modeling framework is developed using 3D field-consistent corotational beam elements with an updated Lagrangian formulation. The structure and element kinematics are firstly derived in global and local coordinate systems respectively, based on which the system dynamics are formulated by integrating the element stiffness, damping, and mass matrices. Different drilling boundary conditions and forms of external loads, including bit-rock interaction, wellbore-drillstring contact, stabilizers, bottom hole assembly (BHA) eccentricities, and gravity/buoyancy are defined within the modeling framework. The numerical accuracy of the model with linear/quintic beam elements is discussed and verified in four different static/dynamic loading cases, which are typically used for beam analysis. Simulations of different drilling scenarios, including dynamics during the pipe connection process, bit on/off bottom process, and pipe rocking during slide drilling, are conducted for an actual L-shape well configuration with comparison to field data. The simulated drillstring tri-axial vibrations exhibit diverse characteristics and patterns in terms of oscillation amplitudes, frequencies, and modes at varying depths, generating valuable understanding of potential drilling dysfunctions and insights for real-time drilling optimization and automation.