The dynamic analysis of a vertical riser in the deep sea

Abstract

Offshore technologies are used for exploration and production of oil, gas and mining and for the research and production of hydrothermal energy. Beside the conventional flexible risers, there are compliant production risers and the hybrid production risers as well.The lower end of the riser is connected to the top of the blow out preventer with a ball joint. The upper end of the riser is connected with a small pipe extended from the tensioner device. The vertical balance of riser is provided by the tensional force. The riser is forced by the waves, current and the motion of floating platform or a vessel. Development of the mathematical model, evaluation of hydrodynamic forces and application of a solution technique are the steps of the analysis. For the mathematical formulation; the material is assumed to be homogenous, isotropic and linear elastic. Considering Euler beam-column theory, the shear strength effect is neglected. The equations of motion are obtained using a variational method. The statements for flexural and torsional curvatures of deformed beam are expressed in terms of elastic displacements. The strain energy of the system is also obtained in terms of these curvatures. The nonlinear, coupled equations of motion are derived using Hamilton’s principle. The effect of internal and external static fluid pressures is included into the model by using the concept of effective tension and weight. It is assumed that flow characteristics don’t change in the direction of the flow due to the riser. This means that the incident wave kinematics remains same in the vicinity of the wave. As the riser is assumed as a hydrodynamically permeable structure, the hydrodynamic forces due to waves and currents are assessed using a modified form of the Morison equation. This equation is empiric, however, it is reliable in the estimation of wave forces on the slender structures as risers and widely used in the design of hydrodynamically permeable offshore structures. In Morison equation, the in-line forces are given as the sum of inertia and drag forces. Airy wave theory is used in the water particle kinematics. The static or dynamic problem can be solved in two forms: analytical and numerical. Using the numerical method directly, the fourth order governing partial differential equation is solved either by numerical approaches or by finite element procedures. The finite difference method and numerical integration processes are examples of numerical approaches. Numerical methods are more generic in studying risers with variable geometry such as added buoyancy modules. The forced dynamic problem is generally solved in two categories, deterministic or nondeterministic (stochastic) and the calculations are made in frequency and time domain. The frequency analysis is more appropriate for fatigue analysis, but for a solution the drag term is required to be linearized. Time domain methods are based on a simulation in time domain of hydrodynamic loads. Nonlinearity of drag forces is preserved in these methods. Therefore, they require more computing time.In the static and dynamic analyses of long risers, the governing equation of motion is transformed into a Bessel differential equation. The critical effective longitudinal force and the position of this force are also calculated. In dynamic analysis, the drag and inertia forces are ignored, because the effects of hydrodynamic forces are disappeared after half a wave-length depth. Instead of these forces, the amplitude of the surge motion is used at the surface in the upper boundary condition. The accuracy of computer programs made for static and dynamic analysis is shown with the results calculated by sample data. Then, the conventional riser in depth of 1500 ft (457.2 m) in the bulletin of American Petroleum Institute (API) is examined. This riser is called API 1500-0-1 and API 1500-20-1-D in static and dynamic analysis, respectively. The data for the given riser are used separately both in static and dynamic analysis. The results are compared with the mean of nine results which were presented for testing by API. Although the calculated results show some numerical differences from the API results in the location where is closer to the lower end of riser, the results by present method are in good agreement with those of API. One of the possible reasons of this is that the effects of current are ignored in this study.

Özet

Bu çalışmada, rayserin yatay hareketi incelenmektedir. Rayser, platform veya teknede bulunan gerdirici aygıtı ile gerilmekte olan düşey asılı duran bir kiriştir. Bu kiriş; dalgalar, akıntı ve yüzen platform veya tekne hareketi ile zorlanmaktadır. Dördüncü mertebeden kısmi türevli hareket denklemi, Euler kiriş-kolon teorisi gözönüne alınarak, varyasyonel bir yöntem kullanılarak elde edilmiştir. Hidrodinamik kuvvetler, Morison Denklemi'nin düzeltilmiş bir şekli kullanılarak değerlendirilmektedir. Bu denklem ampirik olmasına rağmen, rayser gibi hidrodinamik geçirgen açık deniz yapılarının dizaynında yaygın bir şekilde kullanılmaktadır. Lineer dalga teorisi, su parçacığının kinematiğinde kullanılmaktadır. Daha sonra, uzun rayserin statik ve dinamik analizi yapılmaktadır. Her iki analizde de, yönetici hareket denklemi Bessel diferansiyel denklemine dönüştürülerek çözüm aranmaktadır. Statik analizde kritik efektif boyuna kuvvet ve bu kuvvetin yeri de hesaplanmaktadır. Derin su analizinde, hidrodinamik kuvvetler dalga boyunun yarısı kadar bir derinlikten itibaren kayboldukları için, dalganın direnç ve atalet kuvvetleri gözönüne alınmamış, onun yerine yüzeyde dalgadan kaynaklanan surge hareketinin genliği sınır şartı olarak kullanılmıştır. Hazırlanan bilgisayar programlarının doğruluğu, statik ve dinamik analizler için kullanılan örnek veriler işlenerek karşılaştırmalı olarak gösterilmektedir. Daha sonra, Amerikan Petrol Enstitüsü’nün bültenindeki 1500 ft (457.2 m) su derinlikli konvansiyonel rayser incelenmiştir. Statik analizde API 1500-0-1, dinamik analizde API 1500-20-1-D olarak adlandırılan bu rayserin verileri kullanılarak bulunan sonuçlar, enstitünün test için sunduğu, dokuz bağımsız araştırmacı tarafından elde edilmiş birleşik sonuçların ortalaması ile karşılaştırılmıştır. Bulunan sonuçların bu sonuçlar ile uyumlu oldukları görülmektedir.