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Calibration of Design Conditions Based on Long Term Top Tension for Catenary Risers
Abstract
Response based approaches are not common in riser design. Due to the high computational costs associated to these methodologies, it is usual to replace the calculation of extreme long term responses by the calculation of responses to a few number of artificial sea states, supposed extreme. However, this hypothesis may not always be applicable. The extreme response of a riser is influenced by several factors. For instance, vessel response motions resonance can occur for waves of periods lower than the ones associated to the desired long term period. In this way, this work has two main objectives. The first is to propose a computationally feasible methodology to calculate long term extreme responses; the second is to calibrate loading conditions, based on the long term responses, to be used when designing catenary risers. The parameter selected to represent the response is the centenary (100y) riser top tension. The utilization of the proposed methodology is illustrated by a case study where three possible positions for a turret in a FPSO hull were compared. The obtained results indicate that this methodology can contribute to substantial changes in the way risers are designed, focusing on the response instead of on the occurrence of extreme sea states.
... As described in SOUSA et al. [5], the tension at the top of a given riser can be interpreted as a combination of three main components: ...
... The first two components can be easily evaluated by the catenary equation, including drag forces on the riser by means of Morison's equation [5]; the dynamic tension, however, is much more difficult to obtain at low computational cost. ...
... However, the top tension can be considered a "well behaved" nonlinear parameter (or almost linear), especially for deep waters. Consequently, the proposed RAO concept can be implemented as a reliable approximation in the evaluation of the dynamic tension [5]. ...
Traditionally, fatigue life calculations are very expensive in terms of time and computer resources. They are usually performed during riser design phases, when several lines with similar characteristics need to be analyzed. While operating, when problems are detected, fatigue analyses are also necessary to help to decide if any action is needed. In both situations, end fittings and bendstiffeners are usually the critical regions. Considering the high number of flexible risers installed in Brazil and the structural complexity of this kind of structure, a robust and fast methodology to evaluate the fatigue life of flexible risers becomes attractive. In this way, this paper proposes a analytical/numerical methodology to evaluate the fatigue life at the top region of flexible pipes. Using the top imposed motions and taking into account the properties of all structures in the riser, it is possible to evaluate tension analytically. Combining tension and the rotations imposed at the top of the riser, curvatures are determined, and stresses can be calculated. Finally, SN curves and the Miner’s rule for damage accumulation allow the estimation of fatigue life. The obtained results indicate that the proposed methodology is conservative when compared to traditional ones. Also, it is very fast, allowing the fatigue life estimation in minutes.
... This methodology adopts simplified analytical models to evaluate the short term responses, and then estimate the extreme longterm response. One of its possible applications is the calibration of short-term design conditions whose short-term extreme responses are equivalent to the long-term one and use them for more detailed riser design analyses [1][2][3]. ...
... This choice enables one to quickly evaluate the long-term integral. Then, this procedure is suitable for fast assessment of extreme excursions, as required in the methodology of equivalent design environmental conditions for riser analyses [3]. ...
In this paper, the long-term extreme response of a floating marine structure subjected to first and second order (slow-drift) wave effects is addressed. The proposed formulation is based on the long-term up-crossing rate, which is obtained by integrating the contribution of all short-term sea states. In order to speed up the evaluation of the long-term integral, an analytical expression for the short-term responses up-crossing rates was adopted. This expression is based on Hermite polynomials, and considers the response as a second order Volterra stochastic process. This formulation was applied to evaluate the 1-yr, 10-yr and 100-yr lateral motions of a circular-shaped monocolumn platform, and the non-Gaussian (nonlinear) results are compared with those obtained by assuming the response as a Gaussian process.
... This numerical modeling of risers considers the environmental loads acting as movements imposed by the float, self-weight, buoyancy, and ground contact reactions. It is performed by discretizing the continuous length of these slender structures into finite elements, with a non-linear formulation, using 3-D beam elements [1]. Despite getting highly accurate results, the FEM is not an exact method. ...
Fatigue life calculation of slender marine structures, such as risers and mooring lines, usually requires a high computational cost. This cost comes from using finite element-based numerical models to predict the stress response of such structures under the action of many fatigue-inducing environmental loadings that they will face during their operational life. Lately, alternative methods to reduce the computational cost of these predictions have been proposed. One consists of a hybrid method that combines the FEM (Finite Element Method) with Artificial Neural Networks (ANN). Most of the available hybrid FEM-ANN models are based on shallow neural networks, and the models are trained individually for each fatigue load case. The main goal of this work is to investigate a fatigue analysis methodology based on hybrid FEM-ANN models where the ANN modeling is developed using modern deep learning techniques, such as Long Short-Term Memory (LSTM). Besides, instead of using a case-to-case approach, this work presents a generalized deep learning model, i.e., the trained hybrid FEM-ANN model can make predictions in the top of the riser for various environmental loadings without the need for new training. The model is tested for a flexible lazy-wave riser and a free-hanging flexible riser. Results of the hybrid FEM-ANN model are compared to those from the complete FEM-based numerical analyses to show the former model’s accuracy.
... In addition, the method of contour generation can affect the accuracy of predicted extremes [2]. A response based approach to riser design was conducted by Sousa [3] who found the response method resulted in significant changes to predicted riser top tensions when compared to methods based off of extreme sea state predictions. When direct simulation approach is applied, the RBA extreme value models are required at various scales, including short term (within each stationary interval), storm, and long term (entire storm history) scales. ...
The variability of extreme responses of a flexible riser due to wave frequency motions of weather-vaning FPSO is investigated numerically. The objective of this study is to examine such variability in isolation from that caused by the low frequency (slow drift) vessel motions and vessel offsets.
Investigation of the extreme value distributions of flexible risers provides the statistical foundation for flexible riser Response Based Analysis (RBA) for use in system design; the determination of the statistical properties of extreme flexible riser responses provides a method for the prediction of extreme responses of offshore systems in cyclonic conditions.
A case study conducted in OrcaFlex included an FPSO vessel with a Lazy-S configured riser system. Five riser responses were selected in critical locations including tension, heave, and curvature responses. The environmental cases included two cyclonic storms consisting of multiple half-hour intervals. For each interval, time domain simulations included 40 wave realizations in order to provide a dataset for robust fitting of the extreme value distributions in the Gumbel format.
Once the short term interval distributions were established, response distributions in a storm were generated by multiplying the short term distributions and the most probable maximum (MPM) response in a storm computed. A comparison of maximum interval, storm and 3-hour MPMs is presented, which indicates to what extent the MPM response in a storm exceeds the corresponding maximum interval response. Differences between the tension and heave responses are compared with those observed in the curvature responses.
This study was limited to riser excitation by waves, current and wave frequency motions of a turret moored FPSO and it is expected that further inclusion of low frequency motions would contribute to the response variability. The inclusion of such variability will ultimately enable the storm-based statistical approach to be used for the development of long-term distribution of the riser responses.
The joint probabilistic models (JPM) of the environmental parameters of wave, wind and current are nowadays extremely needed in order to perform reliability analyses of offshore structures. These JPM are also essential steps for the design of offshore structures based on long-term statistics and to perform dynamic response analysis of floating units that are strongly dependent on the directionality of the environmental actions, such as turret-moored FPSOs. Recently, some JPM have been proposed in the literature to represent the joint statistics of a reduced number of environmental parameters. However, it is difficult to find a practical and fully operational model taking into account the complete statistical dependence among all the environmental parameters intensities and their correspondent directions. In this paper, it is presented a straightforward methodology, based on the Nataf transformation, to create a JPM of the environmental parameters taking into account the dependence between the intensity and direction of all variables. The proposed model considers the statistical dependence of ten short-term variables: the significant wave height, peak period and direction of the sea waves, the significant wave height, peak period and direction of the swell waves, the amplitude and direction of the 1-h wind velocity and, finally, the amplitude and direction of the surface current velocity. The statistical dependence between them is evaluated using concepts of linear-linear, linear-circular and circular-circular variables correlation. Some results of the proposed JPM methodology are presented based on simultaneous environmental data gathered in a location offshore Brazil.
A riser or mooring line, when excited dynamically at its upper end, resists the imposed displacement by increasing its tension. Viscous damping in the lateral motion is known to be crucial and the resulting problem is thus intrinsically nonlinear. In this paper, an algebraic expression for the dynamic tension, formerly obtained [Polar Engineers, ISOPE'-93 (1993)], is revised and enlarged, once the variation of the tension along the suspended length is specifically focused here. The obtained expression is systematically compared with results from usual nonlinear time domain programs and with experiments, showing a fair agreement. This algebraic expression is used then, in two accompanying papers, to address relevant problems from a more practical point of view: in the first one, the question of the dynamical compression of risers, with a proper estimative of the related critical load, is analyzed in conjunction with the results here derived; in the second one, the algebraic expression is used to obtain an analytic approximation for the probability density function of the dynamic tension in random waves.
The performance of a combination formula, extensively used in stochastic dynamics for estimating extreme values of linear combination of load effects, is investigated. It is shown that this combination formula is nearly optimal in the case of independent Gaussian load effect components. For non-Gaussian load effects the performance is investigated by studying specific examples, and it is shown that the accuracy deteriorates significantly.