The role of friction on heave-induced motion of offshore drilling systems: modelling, analysis, and numerical experiments

This paper investigates the influence of friction dynamics on heave-induced disturbance propagation using a coupled hydraulic-structural drilling model formulated as a semilinear interconnection of ordinary and hyperbolic partial differential equations (ODE-PDEs), and capturing spatially distributed memory effects in the drillstring-wellbore interaction. First, local and global existence and uniqueness results are established, and sufficient conditions for boundedness and input-to-state stability are deduced via a small-gain analysis. Subsequently, extensive numerical investigations are carried out, including harmonic excitation studies, nonlinear distortion analysis, spatial amplification investigations, mechanism-isolation experiments, parameter sensitivity analysis, and broadband simulations under realistic offshore sea-state excitation. The simulation results indicate that, whilst the hydraulic response is governed primarily by wave propagation phenomena, compressibility, and boundary reflections, the structural dynamics display substantially greater sensitivity to distributed friction effects. Furthermore, drillstring-wellbore friction is shown to have a relatively limited influence on well-posedness but a potentially significant impact on stability margins. These findings highlight the importance of accounting for coupled hydraulic-structural dynamics and distributed friction mechanisms when analysing, monitoring, and controlling offshore drilling systems.