Lauro Massao Yamada da Silveira

An Investigation on the Effect of Tension Variation on VIV of Risers

This paper aims at investigating the effect of vertical motion (or equivalently the effect of variable tensioning) of the floating unit on the vortex-induced vibrations of vertical risers. This is done using a numerical procedure, based on modeling assumptions, which, though simple, succeeded in describing some expected dynamic behaviors. The model simulates the riser dynamics using a finite element model coupled to a wake-oscillator model, of the van der Pol type, used to emulate the fluid dynamics. Vertical motion (or dynamic tension) is directly imposed to the top. The transverse amplitudes at each section feed the wake-oscillator, which responds with a transverse force that is applied to the riser. The rigidity matrix is updated at each time integration step. The analysis is also carried out with a commercial simulation code dedicated to riser analysis, with a similar wake-oscillator VIV module. Amplitude envelopes are extracted from the time series, showing response mode jumps. The application of the Hilbert-Huang spectral analysis technique helps distinguishing mode jumps by tracking frequency responses in time. The results of the two different dynamic models are compared with very good agreement.Copyright

Bending Stiffener Design Through Structural Optimization

Bending stiffeners are very important ancillary equipments of umbilicals or flexible risers, since they protect the lines from overbending. Their design however is a complex task, since many load cases must be taken into account; the structure itself has a section that is variable with curvilinear coordinate. To aid the designer in this task, optimization algorithms can be used to automate the search for the best design. In this work an optimization algorithm is applied to the design of the bending stiffener. First, a bending stiffener model is created, which is capable of simulating different load case conditions and provide, as output, results of interest such as maximum curvature, deformation along the stiffener, shear forces and so on. Then, a bending stiffener design procedure is written as an optimization problem and, for that, objective function, restrictions and design variables defined. Study cases were performed, comparing a regular design with its optimized counterpart, under varying conditions.Copyright

A Numerical Method to Solve the Static Problem of a Catenary Riser

The static configuration of a catenary riser can be obtained, with a good approximation, by a perfectly flexible cable model. However, such a model cannot deal with all the boundary conditions, as for an ideal cable there is no continuity of curvature at the touchdown point, at the top and at the points where there is change in the submerged weight. At the touchdown region, for instance, the cable model overestimates the maximum curvature. For real risers, the bending stiffness effect is relevant only at small boundary layers around the points where the cable model cannot represent well the curvature continuity. This represents a big problem in the numerical integration of the differential equation of the riser, as the leading order term is very small. One approach that can be adopted is to use firstly a perfect cable model and correct later the results with analytical expressions obtained from a boundary layer method. For a two-dimensional formulation it was already shown that this approach is very good. For a three-dimensional formulation, however, such expressions are very difficult to derive and the problem must be solved numerically. This work presents a numerical method to solve the differential equation of a catenary riser, including the bending stiffness. The results obtained are compared to analytical boundary layer solutions, for a two-dimensional case, and to a full nonlinear well-known commercial computer code.Copyright

Structural Behavior of Umbilicals: Part I—Mathematical Modeling

Umbilicals for offshore application are very complex, since they combine elements of different mechanical behavior, such as steel tubes, thermoplastic hoses and power cores in a single structure, not to mention helically laid-up armouring layers and polymeric sheathes. This motivates continuous research on their mechanical modeling. This paper presents research undertaken in the structural behavior of umbilicals and focus on the mathematical modeling of the elements, which are gathered into concentric layers. Interaction between layers is included as well as helical lay-up of elements. The model here presented will be compared to a set of experimental results in a separate paper (Part II). An analytical model was developed combining equilibrium equations, geometric compatibility and constitutive relations to obtain a set of equations that describe the umbilical behavior under external loads. This set of equations is numerically solved to obtain contact pressures (or gaps) among layers, radial variations and strains in the elements (used to calculate the stresses). The model was built to be general in order to be able to cope with complex cross-sections designs often encountered. It was then implemented in a tailor made local analysis software, called UTILFLEX®. Both modeling and software resulted from a development program partnership between Prysmian Cables & Systems and University of Sao Paulo. The paper will present modeling hypotheses and structural models that were used for steel tubes, hoses (thermoplastic and reinforced) and power cables and how the interaction among them has been treated.Copyright

A Numerical Method to Solve the Three-Dimensional Static Problem of a Riser With Bending Stiffness

Numerical integration of the governing differential equations of three-dimensional riser statics may experiment large stability problems due to the inclusion of bending stiffness, as the leading order term becomes usually very small. These numerical problems may be avoided by working with a perfectly flexible cable model. However, such a model cannot deal with all the boundary conditions, as for an ideal cable there is no continuity of curvature at the touchdown point, at the top and at the points where there is change in the submerged weight. At the touchdown region, for instance, the perfectly flexible cable model overestimates the maximum curvature. To overcome these difficulties, one approach that can be adopted is to use firstly a perfectly flexible cable model and correct later the results with analytical expressions obtained from a boundary layer method. This approach is based on the fact that bending stiffness is relevant only at small boundary layers around the points where the perfectly flexible cable model cannot represent the curvature continuity. For a two-dimensional formulation it was already shown that this approach is very good. For a three-dimensional formulation, however, the analytical expressions become too cumbersome, the authors could not so far find an exact analytical solution and, therefore, the problem must be solved numerically. Another possible approach is to use finite elements method, as many full nonlinear commercial softwares do. However, it is not difficult to face convergence problems. This work presents a numerical method to solve the set of differential equations of the three-dimensional riser statics, including the bending stiffness. The results obtained are compared to a full nonlinear well-known commercial computer code.Copyright

Structural Behavior of Umbilicals: Part II—Model-Experimental Comparisons

A set of tests was performed in a non-armored Steel Tube Umbilical (STU), including pure pressure loading, constant and variable tension loads and combinations of constant and cyclic bending moment and tension. Tests were made for pressurized and non pressurized conditions. Strains were measured with strain gages attached to the external surface of selected tubes. Instrumentation was performed in four windows that were opened on the umbilical outer sheath to provide access to the tubes. Besides the strains, tension, internal pressure and imposed angle were measured. Comparisons with results obtained using the model presented in Part I, [1], are presented for different load conditions.Copyright

RiserView: An Open Source, Multiplatform Post-Processing Tool for the Visualization and Analysis of Riser Dynamics

Offshore oil exploitation, given its importance, is the target of intense research throughout the world. Much of this research generates large amounts of raw data of difficult interpretation. This paper presents RiserView, a free, open-source and multiplatform post-processing tool that merges virtual reality and scientific visualization techniques to allow a three-dimensional interactive visualization of these data for the specific domain of riser dynamics. This tool, its use, the results of performance tests and how the tool may aid in the analysis of riser dynamics, in view of the visualization tools in commercial riser analysis software, are discussed.Copyright