M.H. Patel

Review of flexible riser modelling and analysis techniques

The past decade has seen significant developments in the use of flexible risers for floating production duties throughout the world. The technological developments in the construction of these pipes have, in parallel, been followed by advances in the analysis of their hydrodynamic and mechanical behaviour. At present, the hydrodynamic analysis is well established with several commercial analysis packages at the disposal of designers. The analysis of flexible pipe mechanical behaviour has produced new analytical and numerical models for the prediction of pipe internal wear and fatigue behaviour. These models are currently being exploited in the optimization of pipe construction and design. New issues of reliability and risk assessment are also entering the scene and are beginning to influence the development of design codes for flexible risers. This paper presents an historical overview of the development of hydrodynamic analysis techniques for flexible risers. It highlights key issues addressed during these developments including the effects of internal and external hydrostatic pressures and of internal flow. The paper also presents an overview of the current status of analysis techniques for flexible riser design and engineering and identifies those uncertainties that remain.

Three-dimensional behaviour of elastic marine cables in sheared currents

Abstract This paper presents the formulation and solution of governing equations that can be used to analyse the three-dimensional (3D) behaviour of either marine cables during installation or the response of segmented elastic mooring line catenaries as used for floating offshore structures when both are subjected to arbitrary sheared currents. The methodology used is an extension of one recently developed for analyses of marine cables when being installed on the seabed or being towed. The formulation describes elastic cable geometry in terms of two angles, elevation and azimuth, which are related to Cartesian co-ordinates by geometric compatibility relations. These relations are combined with the cable equilibrium equations to obtain a system of non-linear differential equations, which are numerically integrated by fourth and fifth order Runga–Kutta methods. The inclusion of cable elasticity and the ability to consider arbitrary stored currents are key features of this analysis. Results for cable tension, angles, geometry and elongation are presented for three example cases—the installation of a fibre optic marine cable, the static analysis of a deep water mooring line and the response of a telecommunications cable to a multi-directional current profile.

Combined axial and lateral responses of tensioned buoyant platform tethers

Abstract This paper presents the results of an investigation into the combined axial and lateral vibrations of the tethers of tensioned buoyant platforms, (TBPs). Wave-induced motions of the TBP excite tether vibrations through lateral forces at the tether top end (called external or forcing excitation in this paper) combined with a time-varying axial force (called parametric excitation here). Although, the forcing and parametric excitations have been considered separately in the research literature, this paper examines their combined effects — particularly with a view to determining tether behaviour for different water depths. The governing partial differential equation of tether lateral motion is reduced to a nonlinear differential equation and solved by a combination of the Romberg method and the fourth-order Runge-Kutta method. Comparisons for tether vibrations when taking both axial and lateral forcing into account and when considering axial and lateral forcing separately are presented. It is shown that the combined excitation gives greater amplitude of vibration with this feature being particularly dominant in even numbers of the instability region of the Mathieu stability chart. The frequency of oscillation of the combined response is also dependent on the relative magnitudes of axial and lateral excitations. The results demonstrate that the above is true for a wide range of water depths.

Analysis of drill strings in vertical and deviated holes using the Galerkin technique

This paper presents an analytical investigation into the use of Galerkins technique for the analysis of oil field drill strings in vertical and deviated holes. The technique is used to present results for drill string dynamic stability in vertical holes and drill string static deflection in curved and straight inclined holes. In the first case, the critical loads and natural frequencies for lateral vibration are calculated assuming that the drill string is hinged at both ends. In the latter case, emphasis is placed on the particular conditions of low weight on bit and large drill string pendulum length for which other solution techniques run into difficulties. Results from Galerkins technique compare well with those from other semi-analytical solutions of the problems and it is shown that the technique offers a simple and easily programmable alternative for the analysis of deviated drill strings.

Finite-element analysis of the marine riser

Abstract A two-dimensional finite-element computational method is presented for determining marine riser displacements and stresses due to self-weight, buoyancy, internal and external pressures, surface vessel motions and environmental forces arising from currents and waves. A dynamic analysis is performed in the frequency domain for regular waves by linearizing the hydrodynamic damping term. A fully nonlinear time step integration of the equations of motion using the Newmark constant acceleration method is also presented. Extensive use is made of a substructuring technique in the dynamicv analysis to reduce the number of degrees of freedom and, therefore, achieve a substantial reduction in computer time and storage without a discernible performance penalty. A number of test cases are presented to compare the linearized and nonlinear dynamic analyses and to highlight the performance of this method in relation to other marine riser analysis techniques. The application of this finite-element method to multitube production risers with complex cross-sections is discussed.

Transient behaviour of towed marine cables in two dimensions

Abstract This paper presents a numerical solution for the transient motion of marine cables being towed from a cable ship which is changing speed. The cable ship is assumed to move rectilinearly, hence the cable configuration is two-dimensional. The solution methodology consists of dividing the cable into n straight elements with equilibrium relationships and geometric compatibility equations satisfied in each element. A system of n non-linear ordinary differential equations is derived from this and then solved by fourth- and fifth-order Runge—Kutta formulations with the dynamic axial tension calculated iteratively because it is itself dependent on the solution. Results are presented for the cable-top tension and element angles as functions of time and for transient cable geometries when the towing velocity is linearly or parabolically increased (or decreased). It is shown that the results from this analysis compare reasonably well with full-scale experimental data from Hopland (Proc. Int. Wire and Cable Symp. , 1993, pp. 734–39).

On the non-linear forces acting on a floating spar platform in ocean waves

Abstract The exploitation of hydrocarbon reservoirs under the seabed in very deep water requires the use of innovative floating platform configurations. The hydrodynamic interaction of such platforms with ocean waves and the understanding and quantification of the non-linear components of these interactions have been a subject of continuing research. This paper examines these non-linear interaction components for a specific very deep draft spar platform type that is increasingly being used in the oceans. It investigates a formulation for two non-linear force components — called the axial divergence force and the centrifugal force. The latter is invariably neglected in conventional analyses but is shown in this paper to actually be of significant importance. Non-linear equations for wave loading and motion are developed and solved, and the results are used to demonstrate the significance of the above terms. A limited comparison with experimental data is also presented.

Conceptual design of a floating support structure for an offshore vertical axis wind turbine: the lessons learnt

The design of floating support structures for wind turbines located offshore is a relatively new field. In contrast, the offshore oil and gas industry has been developing its technologies since the mid 1950s. However, the significantly and subtly different requirements of the offshore wind industry call for new methodologies. An Energy Technologies Institute (ETI) funded project called NOVA (for Novel Vertical Axis wind turbine) examined the feasibility of a large offshore vertical axis wind turbine in the 10–20 MW power range. The development of a case study for the NOVA project required a methodology to be developed to select the best configuration, based on the system dynamics. The design space has been investigated, ranking the possible options using a multi-criteria decision making (MCDM) method called TOPSIS. The best ‘class’ or design solution (based on water plane area stability) has been selected for a more detailed analysis. Two configurations are considered: a barge and a semi-submersible. The iterations to optimise and compare these two options are presented here, taking their dynamics and costs into account. The barge concept evolved to the ‘triple doughnut-Miyagawa’ concept, consisting of an annular cylindrical shape with an inner (to control the damping) and outer (to control added mass) bottom flat plates. The semi-submersible was optimised to obtain the best trade-off between dynamic behaviour and amount of material needed. The main conclusion is that the driving requirement is an acceptable response to wave action, not the ability to float or the ability to counteract the wind turbine overturning moment. A simple cost comparison is presented.

INTERNAL FLOW-INDUCED BEHAVIOUR OF FLEXIBLE RISERS

Abstract It has been found in recent years that the pressure distribution and flow behaviour of fluid inside the bore of a flexible riser has a substantial effect on its static and dynamic behaviour. This paper is concerned with examining the contributions of internal flow to both the governing equations and the dynamic excitation forces applied to a flexible riser. A derivation from first principles of the full governing equations for a flexible riser in two dimensions is presented, together with equations for riser excitation due to slug flow through the riser bore. A frequency-domain numerical solution scheme is also described and its results are compared with model tests for both riser global behaviour due to external disturbances (such as surface vessel motions and waves) and due to internal flow.

Coupled dynamics of tensioned buoyant platforms and mooring tethers

Abstract A mathematical model is presented of the coupled dynamics of a tensioned buoyant surface platform and the lateral dynamics of its taut mooring tethers. A finite element model of the lateral mooring tether dynamics is extended to take account of nonlinear square law fluid damping by a simple global ‘whole tether’ linearization and an alternative computationally more expensive ‘element-by-element’ linearization scheme. The resultant finite element model is combined with the surface platform dynamic analysis and the coupled dynamic model is used to investigate the effects of water depth, surface platform mass and tether mass per unit length on the tether displacements and bending stresses as well as the resultant surface platform displacements. The results show that the bending stresses induced in the tethers due to their dynamic motions are quite small and that the tether dynamics only affect the motion response of the platform appreciably if the tethers are long (∼1500 m or more), have a large mass per unit length and have a relatively low tension; or if the platform mass is relatively small. It was also found that the additional computing time required for the local ‘element-by-element’ equivalent linearization was not matched by the small improvement in accuracy obtained over the global ‘whole tether’ technique.