Tc 67/sc 4 n date: 2005-03-9 iso/wd XXXXXX ISO tc 67/sc 4/wg 6 Secretariat: Design of dynamic risers for offshore production systems Élément introductif — Élément central — Élément complémentaire Warning
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- Discretized equation of motion
- Mass modeling
- Buoyancy and pressure forces
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where Ai(z) = Internal area, m = Distributed mass, c = Viscous damping coefficient, r = Density of internal fluid.. This model is adequate for many riser analyses. Moreover, the description of this model can be used to introduce most of the fundamental concepts. Extensions required to cover more sophisticated modeling requirements are dealt with in subsequent sections. In applying Equation 36 to riser analysis, the tension to be taken into account in analyzing an immersed, fluid filled tube is known as effective tension, Te. Effective tension applies to the global analysis of: all types of riser (metal, flexible, drilling, production, and catenary); risers consisting of a single tube, multibore, or tube within tube (e.g. tieback risers); risers of any cross-section, not necessarily circular (e.g. oval); risers with internal fluids of any density characteristics (not necessarily constant density); risers of any materials (not necessarily elastic), with plane sections not necessarily plane (e.g. flexibles); risers with tensioned guidelines threaded through multiple guides. Effective tension can be formulated most clearly as:  ...(37)
for a riser comprising n distinct tubulars, where: Tn = axial tensions in a structural element (pipe wall), PiAi = axial “tension” in an internal fluid column  i = internal sectional area, Pi = internal pressure),
PoAo = axial “tension” in a displaced fluid column  = external or displaced cross-sectional area,  = external pressure).
Lateral force at any cross section of a riser is equal to shear plus the effective tension times the slope. This calculation is valid only because it is equivalent to integrating pressure around the tube circumference and adding shear and the lateral component of tension. It must be stressed however that effective tension only applies to the global analysis of risers. When calculating other effects of tension and pressure on tubes, such as axial strains and the load combinations that lead to failure, the complete stress field in the wall of a riser’s tube must be taken into account. Practical riser analysis requires numerical approximations to the riser differential equation to generate a system of coupled algebraic equations, which can then be solved by standard numerical solution techniques. Starting with Equation 36 and applying the finite element method71 results in the following statement of lateral equilibrium for an individual element:  ...(38)
where [m], [c], and [k] are element mass, damping and stiffness matrices, respectively. Vectors {r} and {q} represent applied element loads and element boundary forces. [k] is defined as:  ...(39)
[kg] is the geometric stiffness matrix and is a function of element length and effective tension. [kf] is the flexural stiffness matrix An equation similar to Equation 38 can be developed for the axial direction, the primary difference being the form of the flexural stiffness terms (i.e. AE/L versus EI). Solution of the axial equations yields axial force in the riser, which is required for the lateral equilibrium equation. Thus, the two equations are coupled through the tension term and are typically solved by iteration. More discussion of tension coupling is given in 6.4.3.4. The keys to building an accurate stiffness model of the riser system is to properly estimate the lateral bending stiffness term, EI(z) and to accurately determine the effective tension distribution in the riser system. The former requires reasonable approximations for auxiliary lines, large appurtenances and changes in wall thickness. The latter requires approximating riser weight and buoyancy.
Mass modelingProper modeling of the riser mass distribution is required for an accurate solution to the dynamic equilibrium equation. Riser mass is usually taken as a mass per unit length, distributed over regions of roughly equal properties. In finite element models, this distributed mass can be used either to develop a consistent mass matrix by the same methods used for developing the flexural stiffness matrix or a simple lumped mass matrix. The riser tube, couplings, coatings, auxiliary lines, anodes, buoyancy modules, appurtenances, and internal contents all contribute mass that must be accounted for in the dynamic model. In addition, the hydrodynamic added mass, as described in 6.3.3.1, must be included. Each component of mass in the riser model contributes a gravity force at the location where the mass is attached to the riser, and all gravity forces contribute, along with buoyancy and pressure forces, to the axial tension in a riser. Riser contents exert a pressure force on internal diameter changes in the riser, as described in the following section. Buoyancy and pressure forcesBuoyancy forces arise from the vertical component of pressure integrated over the submerged area and arise only for exposed horizontal surface. In the case of a completely submerged body, buoyancy force can be shown to equal the weight of the displaced fluid. For most metal riser analyses, the top surface of the riser is above the water surface, and therefore the most significant buoyancy force experienced directly by the riser is at the lower end and then only if not connected to the seafloor (e.g. during riser deployment operations). Significant buoyancy forces occur on buoyancy modules, which are attached to riser joints for that purpose. Buoyancy modules have exposed horizontal surfaces and generate a buoyancy force greater than their gravitational force because their mass density is less than seawater. Data on buoyancy modules is typically given in terms of “net lift”, which is the difference between buoyancy and weight (gravitational force). Buoyancy forces also act on all other submerged material that is attached to the outside of the riser, including nonstructural appurtenances, riser connectors and coatings. It is often assumed that the nominal riser pipe is the only material which is continuous along a riser, therefore all other items attached to the riser are assumed to have horizontal surfaces on which buoyancy forces act. The total buoyancy force on any length of riser can then be taken to equal the difference between the weight of water displaced by the riser and that displaced by the nominal riser tube, which is equal to the weight of water displaced by all attached items. Finally, changes in riser diameter result in horizontal surfaces upon which pressure forces can act. Changes in outside diameter can generate a buoyancy force from external pressure, and changes in inside diameter give rise to a buoyancy force from internal pressure. In fact, proper consideration of diameter change handles the case where the riser terminates above the seafloor, exposing it to pressure force. Pressure of seawater is applied to the entire end (sealed or unsealed), and the pressure of contents, acting in the opposite direction, is applied to the inside area. If the contained fluid is seawater at the same pressure as the external fluid, as it would be for an unsealed end, the net force resultant is simply the product of hydrostatic pressure and riser tube section area. If the riser is empty and at ambient air pressure, as it would be for a sealed end with no contained fluid, the net vertical force is the product of hydrostatic pressure and cross-sectional area of the sealed tube. Directory: standards standards -> Request for proposal contract form for the transit industry standards -> Indiana Academic Standards Resource Guide Grade 8 United States History – Growth and Development (to 1877) Updated April 2016 standards -> Us history Dictionary Based on the sc state Standards standards -> Integrating Standards Education into the Business School Curriculum standards -> Use of Sprint U301 3G/4g mobile Broadband usb device Installation standards -> International organisation for standardisation organisation internationale de normalisation standards -> Standards of Excellence standards -> Common Core State Standards for Mathematics (ccssm) Download 2.34 Mb. Share with your friends:
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