A method was recently presented for determining quasi-static and dynamic riser angles using measured data typically found in a riser fatigue monitoring system, specifically acceleration and angular rate data. The riser angles were determined at sensor locations. In this paper quasi-static riser displacement, inclination angle, curvature, and stress are estimated along the entire length of the riser, using only the quasi-static inclinations angles at sparse sensor locations. In addition the distribution of applied forces along the entire riser length is also estimated. A rough representation of the current profile can be calculated using the drag coefficients of riser joints.
The riser deformation (displacement, inclination, curvature) and applied forces are estimated by solving the matrix equation f = K*x, where f is the vector of forces and moments, K is the stiffness matrix and x is the vector of displacements and inclination angles. In the equation, force and displacement vectors are unknown and the stiffness matrix is determined using Finite Element (FE) modeling. Constraints are applied, setting the inclination angle at the sensor locations to the values derived from measured data. The remaining highly-underdetermined problem cannot be solved in a classical sense, as it admits infinite solutions. To get a solution that is consistent with the physics of riser deformation, smoothness of the solution is enforced as a constraint. The smoothest solution is solved using quadratic programming methods.
Following implementation of the method in Matlab®, the procedure was validated using numerical simulations of a riser in applied current. Both connected (to the wellhead) and disconnected cases were simulated. Estimated riser displacements, slopes, curvatures and applied forces are found to match the simulation results closely.
The algorithm was then run using measured data from an emergency disconnect event that occurred on the Chikyu drill ship in November, 2012. The riser displacement, inclination and curvature were determined and found to agree well with results determined using another method.
The additional capabilities presented herein further expand the utility of a riser monitoring system. Quasi-static and dynamic riser angles are derived from acceleration and angular rate sensors using previously published methods. Using the method developed herein, the quasi-static inclination angles at the sensor locations can be used to determine the displacement, inclination, curvature (stress) and even applied force along the entire riser. These results are particularly useful in strength assessment, model verification, clashing and emergency event reconstruction analyses.