On the probabilistic distribution of loads on a marine riser
Introduction
Risers constitute a key component for offshore facilities. In drilling activities, risers allow communication between wellheads and the drilling rigs. Fig. 1(a) illustrates a riser that interacts with a mobile offshore drilling unit and a blowout preventer. Risers are also used in production activities for either carrying oil and gas from the seabed to a production platform, or by sending water and gas to injection wells. Fig. 1(b) illustrates a riser system and subsea umbilicals that link a subsea production system with a floating production and storage (FPSO) unit which in turn serves as host of an offshore oil field.
While in service, risers are exposed to a variety of loads. They are subjected to axial tension and bending moments arising from the motions of the floater in association with waves, winds, and currents; and to internal and external pressure loads caused by internal flows and external seawater pressure.
Several studies dealing with floater-riser interaction loads have been reported in the literature. Model tests in wave basins, like those conducted by Mao et al. (2016) and Wei et al. (2012), are the preferred method since the observations allow to validate numerical models and to study the feasibility of new riser concepts. Floater vertical and horizontal motions may demand for large riser deformations, affecting riser's ultimate strength and fatigue life. Li and Low (2014) demonstrated that low-frequency vessel motions shift the touchdown point of steel catenary risers and thus spread the fatigue loads along their length. Katifeoglou and Chatjigeorgiou, 2015, Katifeoglou and Chatjigeorgiou, 2012 found that soil reaction force at the touchdown point has paramount influence in bending moment-induced fatigue, and proposed the use of nonlinear finite element method to analyze the detailed distribution of dynamic stresses on risers by means of shell-like tubular segments. Dong et al. (2013) emphasized the importance of the global riser motion in the design of bend stiffeners at the floater-riser connection and proposed a mathematical model that considers geometrical and material nonlinearities of such components.
Planar governing differential equations that describe the riser response under the action of floater motion and external fluid loading are often used to investigate loads on the risers. Wang et al. (2014) combined large and small deformation beam equations and utilized the finite difference method to analyze the static configuration of steel lazy-wave risers, which is greatly influenced by the vessel position and pipe-soil interaction. Wang et al. (2015b) derived the riser equation of motion in one plane with the aim to estimate bending moments and shear loads. Kuiper et al. (2008) identified the mechanisms in which the heave motion of a floater can destabilize a top-tensioned riser, causing large compressive loads. Yang et al., 2016, Yang et al., 2013 and Yang and Xiao (2014) found that parametric instability of top-tensioned risers in irregular waves can be enhanced by vortex shedding, and they recommended to pay attention to such instabilities since they are source of fatigue loads.
Risers’ installation loads have a different spatial distribution than the in-service loads. Wang et al. (2015aWang et al., 2014a, Wang et al., 2014b studied the static and dynamic response of marine drilling risers during installation which induces a spatial distribution of loads that is different to operating condition. Wang et al., 2015a, Wang et al., 2015b) investigated the large deformation of steel lazy-wave risers during installation which can induce large bending moments. Bai et al. (2014) analyzed the response of drill pipe during subsea manifold installation and found that the top portion can be exposed to dangerous bending moment and axial tension.
Accidental and maintenance loads on risers are also investigated in the literature. Liu et al. (2013) analyzed grounding loads of a drilling riser in disconnected mode, based on an actual accident, and found that the riser was subjected large deformation and stresses specially in its lower portion. Chen et al., 2016, Chen et al., 2014 performed experiments that explain how a pipeline inspection gauge (PIG) tied to a coiled tubing transfers its load to the inner wall of the riser.
The literature about probabilistic distribution of loads on risers is scarce. Farnes and Moan (1993) proposed a method to derive long-term loads on flexible risers by fitting a Weibull distribution to the load maxima of and smoothing the parameters to maintain accuracy with reduced number of sea state blocks.
Besides, several authors have studied reliability of risers without discussing the probabilistic distribution of the loads. Nazir et al. (2008) studied the fatigue reliability by using log-normal distribution of the random variables to obtain a close form solution of the probability of failure. Li and Low (2012) studied the fatigue reliability of steel catenary risers with the use of metamodels and the first-order reliability method. Shi et al. (2014) studied the probabilistic distribution of fatigue loads and probability of failure with update by field measurements. Xiao and Yang (2014) investigated the probability of instability of top-tensioned risers in irregular waves by considering the uncertainties in environmental conditions, geometric and material properties. Gao and Low (2016) developed an efficient procedure to derive sea states for fatigue analysis of risers by simulating some sea states and deriving the remaining ones by altering the importance sampling waiting function. Mousavi et al. (2016) proposed a simplified method to calculate the ultimate strength and fatigue reliability of steel catenary risers, and implemented an integrity-based optimal design criterion to achieve a target annual probability of failure. Low and Srinil (2016) investigated the riser reliability associated to vortex-induced vibration by considering as random variables the parameters of a van der Pol-type oscillator which results in large variability of the riser fatigue loads.
This paper focuses on the probabilistic distribution of loads on risers. Risers and other offshore structures are traditionally designed based on environmental conditions with low probability of exceedance; nevertheless a load statistics-based design would lead towards a more rational approach. In this manner, design loads can be selected with specific probability of exceedance or return period, from the respective probabilistic distribution. Moreover, in today's industry practice, reliability analyses are generally accepted to evaluate the integrity of risers, and the probabilistic distributions of loads and strengths are necessitated, but not that of the environment. In this regard, the quantification of loads in a probabilistic manner is essential.
In this article, we introduce two methodologies for determining the probabilistic distribution of loads on marine risers which comprise the distribution of effective tension, bending moment, and internal overpressure. First, we propose a dynamic analysis-based method in which the load distribution is estimated from the selection of relatively few scenarios; a previous paper in which loads were estimated for another type of marine structure (Paik et al., 2015) is used as reference. In order to improve the upper tail of the obtained distribution, we use a second approach so called metamodel-based method that has already been applied to approximate loads on risers (Farnes and Moan, 1993, Yang and Zheng, 2011). The novel aspect of this study is that we account for the load reduction during riser disconnection mode in a non-permanent riser system. Furthermore, the probabilistic distribution of loads on marine drilling risers is discussed, as not previously done in the literature.
The remainder of this paper is organized as follows. In Section 2, we propose the two methods for determining the probabilistic distribution of riser loads. In Section 3, we solve an applied example of a riser that operates in a harsh, ultra-deep water environment. In Section 4, we compare the results of the two methods, and explore the role of the most influential input parameter. Finally, in Section 5 we offer concluding remarks on the proposed methods.
Section snippets
Methods for quantifying the probabilistic distribution of loads on a marine riser
Two methods for quantifying the probabilistic distribution of loads on a marine riser are considered here. The first one is based on dynamic riser analysis of selected scenarios, and the second one is based on developing approximate functions or metamodels.
Numerical example
In this section, we use an example to illustrate the aforementioned methods. We analyze a marine drilling riser system that is operated from a semi-submersible drilling vessel in a harsh environment at a water of 3000 m depth, as sketched in Fig. 3.
A riser made of X-80-grade steel with a 21-in. main conductor outer diameter is considered, with the properties being extracted from Permana (2012), as listed in Table 1. A hypothetical semi-submersible platform is employed in the dynamic analyses to
Results and discussion
In this section, we discuss the derived probabilistic distribution of the riser loads. The influence of the PDF of internal fluid density is also addressed.
Conclusions
The aim of the present study is to derive the probabilistic characteristics of loads on marine risers. Two methods are proposed herein. The first uses an efficient sampling technique to obtain scenarios, and then performs time-domain dynamic analysis and statistical analysis to fit a probabilistic distribution to the loads. The second one requires load prediction of the first one, then constructs a metamodel and uses MCS. A numerical example is presented to illustrate the application of both
Acknowledgements
This study was undertaken at the Lloyd's Register Foundation Research Centre of Excellence at Pusan National University, Busan, Korea. The first author would like to acknowledge the partial financial support from CONACYT (the Mexican National Council for Science and Technology). The authors are grateful to Mujeeb Ahmed M.P. who served in the proof reading of the manuscript.
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