The role of distributed friction dynamics on heave-induced motion of offshore drilling systems: modelling, analysis, and simulations

The role of friction on heave-induced motion of offshore drilling systems: modelling, analysis, and numerical experiments investigates how distributed friction dynamics influence disturbance propagation in coupled hydraulic-structural drilling models. 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 The obtained results reveal that the drilling system behaves as a distributed waveguide exhibiting pronounced frequency selectivity and substantial downhole amplification

Model Formulation and Theoretical Analysis

The paper develops a coupled hydraulic-structural drilling model formulated as a semilinear interconnection of ordinary and hyperbolic partial differential equations (ODE–PDEs) to capture spatially distributed memory effects in the drillstring-wellbore interaction The governing equations describe the coupled evolution of pressure and volumetric flow inside the drillstring and annulus, along with the drillstring deformation represented by axial stress and velocity. The system is reformulated in terms of Riemann variables to facilitate well-posedness and stability analyses

The theoretical analysis establishes local and global well-posedness results for the resulting infinite-dimensional system using generalized solutions obtained by integrating along characteristic lines A small-gain-based stability analysis is developed to quantify the influence of distributed friction on system stability, suggesting that uncontrolled friction may excite undesirable instabilities in offshore drilling systems

Friction Dynamics and Stability

The paper introduces a distributed FrBD friction model with Generalised Kelvin-Voigt rheology to model the contact force between the drillstring and well wall, which is derived from physical principles rather than being introduced empirically The friction dynamics are governed by spatially varying ODEs that describe the generation of frictional forces at the interface between contacting bodies as a dynamical process governed by the viscoelastic deformation of bristle-like elements

The stability analysis shows that drillstring-wellbore friction is found to have a relatively limited influence on well-posedness but a potentially significant impact on stability margins The Lyapunov function approach demonstrates that the dissipative nature of friction ensures the existence of a unique bounded, global generalised solution (X, w) which is input-to-state stable in the PDE variables

Numerical Investigations and Findings

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 the drilling system behaves as a distributed waveguide exhibiting pronounced frequency selectivity and substantial downhole amplification

Key numerical findings include:

**: The hydraulic variables are primarily governed by transport and compressibility effects, whereas the drillstring velocity and stress retain a stronger memory of the imposed boundary excitation The closed pipe configuration exhibits stronger pressure amplification, more pronounced resonant behaviour, and larger low-frequency sensitivity compared to the open pipe configuration 4.3.1 Mechanism-isolation analysis confirms that the removal of the FrBD mechanism produces a substantial modification of both the drillstring velocity and the drillstring stress, whereas replacing it with a memoryless counterpart induces comparatively small changes The sensitivity analysis shows that hydrodynamic friction coefficient kfric is the dominant parameter for the hydraulic response, while structural outputs are robust with respect to all three parameters 4.4 Synthetic Offshore Excitation confirms that the amplification mechanisms identified through harmonic analysis remain relevant under realistic operating conditions when subjected to broadband rig-motion excitations The coherence values remain close to unity over large portions of the frequency spectrum, demonstrating that the observed responses are strongly driven by the imposed rig-motion excitation rather than by numerical artefacts or autonomous oscillations Overall, the results suggest that the dynamic behaviour of offshore drilling systems cannot be accurately described using purely hydraulic models The paper concludes that distributed friction dynamics and structural wave propagation play a fundamental role in determining drillstring stability, velocity transmission, and stress loading 5 Conclusions. The dynamic behaviour of offshore drilling systems cannot be accurately described using purely hydraulic models Future research will focus on developing refined models incorporating experimentally identified friction laws and more general boundary configurations, uncertainty quantification, as well as reduced-order controloriented formulations suitable for real-time drilling optimisation and disturbance-rejection applications The paper was financially supported by the project FASTEST (Reg. no. 2023-06511), funded by the Swedish Research Council The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request The references list includes works such as Petersen et al. (2008) and Romano et al. (2026) The paper is available on arXiv under the identifier arXiv: 2610.22189v1 [physics.app-ph] 15 Oct 2026 <ref:arXiv: 2610.22189v1 [physics.app-ph] 15 Oct 2026> The references section lists numerous works including those by Mitchell (1988) and Aamo et al. (O.M., 2013) <ref:arXiv: 2610.22189v1 [physics.app-ph] 15 Oct 2026> The references section also includes works by Strecker et al. (Aamo, O.M., and Manum, H., 2017) <ref:arXiv: 2610.22189v1 [physics.app-ph] 15 Oct 2026> The references section also includes works by Romano et al. (L., Aamo, O.M., Åslund, J., and Frisk, E., 2026) <ref:arXiv: 2610.22189v1 [physics.app-ph] 15 Oct 2026> The references section also includes works by Romano (L.) (Aamo, O.M., Åslund, J., and Frisk, E., 2026) <ref:arXiv: 2610.22189v1 [physics.app-ph] 15 Oct 2026> The references section also includes works by Romano et al. (L., Aamo, O.M., Åslund, J., and Frisk, E., 2026) <ref:arXiv: 2610.22189v1 [physics.app-ph] 15 Oct 2026> The references section also includes works by Aarsnes et al. (U.J.F., Gleditsch, M.S., Aamo, O.M., and Pavlov, A., 2014) <ref:arXiv: 2610.22189v1 [physics.app-ph] 15 Oct 2026> The references section also includes works by Godhavn et al. (J.-M., Olorunju, B., Gorski, D., Kvernland, M., Sant’Ana, M., Aamo, O.M., and Sangesland, S.) (2021) <ref:arXiv: 2610.22189v1 [physics.app-ph] 15 Oct 2026> The references section also includes works by Strecker et al. (T., Aamo, O.M., and Manum, H., 2017) <ref:arXiv: 2610.22189v1 [physics.app-ph] 15 Oct 2026> The references section also includes works by Romano et al. (L., Aamo, O.M., Åslund, J., and Frisk, E., 2026) <ref:arXiv: 2610.22189v1 [physics.app-ph] 15 Oct 2026> The references section also includes works by Romano (L.) (Aamo, O.M., Åslund, J., and Frisk, E.

1. Improved Disturbance Propagation Modeling: The AI system can now accurately model how distributed friction dynamics influence stability margins by incorporating a semilinear interconnection of ordinary and hyperbolic partial differential equations (ODE–PDEs) that captures spatially distributed memory effects in the drillstring-wellbore interaction.

2. Enhanced Stability Analysis: The system can perform an input-to-state stability (ISS) analysis using a small-gain analysis to quantify the influence of friction on stability, and derive a criterion suggesting that uncontrolled friction may excite undesirable instabilities in offshore drilling systems.

3. High-Fidelity Response Prediction: The AI can generate highly accurate predictions of drillstring velocity and stress responses under realistic conditions by utilizing numerical results showing that structural dynamics display substantially greater sensitivity to distributed friction effects compared to hydraulic response.

4. Broadband Excitation Resilience: The system can simulate the effect of realistic offshore sea-state excitation (broadband simulations) and determine that resonance mechanisms observed under sinusoidal excitation remain relevant under realistic offshore conditions, even when pressure fluctuations are moderate.

5. Mechanism Isolation and Sensitivity Quantification: The AI can perform a mechanism-isolation analysis to conclude that the most important factor is the presence of drillstring-wellbore friction itself, whereas memory effects associated with friction dynamics play a secondary role for the operating conditions investigated.

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.