A nonlinear PDE formulation for offshore vessel pipeline installation

In this paper a nonlinear dynamic PDE formulation for a pipe string suspended from a pipelay vessel to the seabed in a pipelay operation is developed. This model extends a three-dimensional beam model capable of undergoing finite extension, shearing, twist and bending, to apply for marine applications by adding the effects of restoring forces, hydrodynamic drag and seabed interaction. The model is validated against the natural catenary equation and the FEM code RIFLEX. The model is extended to include the pipelay vessel dynamics by applying a potential theory formulation of a surface vessel, suited for dynamic positioning and low speed maneuvering, as a boundary condition for the PDE. This system is found to be input–output passive and stable. Pipeline installation applications where the presented model is suited are e.g., analysis and simulation of the installation operation, operability analysis, hardware-in-the-loop (HIL) testing for vessel control systems, and automation of the pipelay operation.