Effect of mooring line layout on the loads of ship-shaped offshore installations
Introduction
Ship-shaped offshore installations such as floating production storage and offloading (FPSO) units operate in deep and ultra-deep water regions to extract oil and gas in the remote locations. The mooring system of such structures has the function of keeping the floater in position, comprising mooring lines and anchors (Montes-Iturrizaga et al., 2012).
At the early design stage of mooring systems, one of the challenges is defining the design variables (DVs) such as materials, anchor positions, line diameter, and line length. Like other marine structures, moored floating systems must be able to withstand the harsh environmental loads coming from waves, wind, and current. However, the life-cycle costs must be kept low, considering initial costs, operational costs, and future costs arising from the mooring system failure. Therefore, setting a mooring layout by taking into account uncertainty and consequences is essential to reduce costs without jeopardising safety. In this paper, the former is addressed.
Scholars have developed various techniques for assessing the safety of offshore mooring systems. To mention a few early studies, Sengupta and Ahmad (1996) used Monte Carlo simulation (MCS) and Newmark-beta method in the nonlinear dynamic analysis of a tension leg platform (TLP) to assess the structural reliability of the mooring system and also to predict the service life. Later, Mathisen and Larsen (2004) developed an algorithm for optimising mooring inspection planning by introducing random variables into a crack growth model while considering inspection costs. Vazquez-Hernandez et al. (2006) performed a benchmark study of Level I reliability analyses considering extreme sea states with associated return period, worst sea state from contour lines, and analysis based on response statistics; they concluded that the response-based approach, although more computationally expensive, results in accurate calculation of the reliability index.
Recently, one of the most employed approaches is the use of genetic algorithms for solving multi-objective optimisation problems. Concerning spread mooring systems, early studies where a genetic algorithm for optimisation of a mooring system can be attributed to Yu and Tan (2005) and Shafieefar and Rezvani (2007). Later, Yan et al. (2018) employed a genetic algorithm to optimise a spread mooring system with submerged buoys for a semi-submersible platform; accordingly, they found the optimum design parameters, including buoys’ sizes and positions. Tang et al. (2020) analysed the positioning mooring system to install a jack-up platform during towing and positioning operations; the system was optimised in order to derive an appropriate tension and length of the lines.
With the advent of offshore renewable energy projects, advanced methodologies have been developed for the analysis and design of mooring systems. Pillai et al. (2019) coupled a random forest model with a genetic algorithm to minimise the cost and fatigue damage of a spread mooring system for a semi-submersible floating offshore wind turbine (OWT). Ringsberg et al. (2020a) defined two optimum mooring layouts for a floating point-absorbing wave energy converter (WEC) by proposing 22 conceptual layouts and reducing the number of candidates employing the Pugh and Kesselring matrices procedure. Extensive research can be found on the validation of the numerical analysis for the motions of a taut-moored WEC and the forces on the lines employing full-scale measurements (Ringsberg et al., 2020b) and wave basin experiments (Yang et al., 2018, 2020).
Focusing on single point mooring (SPM) systems (in which all mooring lines are attached to a single point at the floater), Ryu et al. (2016) used the gradient-free harmony algorithm to optimise the initial costs associated with the SPM for FPSOs. Similarly, Schut and Dam (2016) employed the harmony algorithm to minimise the load on the turret chain table for an FPSO in deep water and harsh environment. Cabrera-Miranda et al. (2018) developed a probabilistic approach for estimating the loads on disconnectable mooring systems for FPSOs; they defined a disconnection criterion by minimising life-cycle costs. Li et al. (2019) used a Kriging model with a gradient-based algorithm for minimising the material weight of a mooring system; they applied the methodology for determining line section lengths, diameters, and anchor position of an SPM system for a vessel-shaped offshore fish farm.
Despite the growing body of literature on optimisation of mooring layouts, a qualitative approach for assessing how the DVs influence the loads on the floating system is still lacking. Existing studies have focused on robust design methods that systematically find the combination of DVs that result in the best performance of a mooring system, minimising costs and maximising safety. Nevertheless, the effects of the input variables and their interactions on the loads and other output variables have often been left out of the discussion.
This paper presents a novel framework for assessing the influence of the DVs defining a mooring layout on the loads of floating systems. We propose the use of response charts and response divergence charts to describe the nonlinear behaviour of loads as a function of several input variables. Next, we conduct Sobol's sensitivity analysis, to calculate variance-base indexes in order to rank the input variables according to their importance for the loads. Furthermore, we use metamodels, namely artificial neural network (ANN) models and Kriging models, to accurately predict the loads while alleviating the computational cost. Since the proposed methodology is rare in the analysis of offshore systems, it is expected that this work will generate fresh insight into the aforementioned area of research.
In the applied example, the target structure of this study is a ship-shaped FPSO installed in ultra-deep water. FPSOs are floating offshore installations that store oil in tanks located in their hulls and periodically offload the petroleum to shuttle tankers, and for construction speed, they are based on converted tankers (Ozguc, 2020; Paik and Thayamballi, 2007). Furthermore, in our application of interest: (1) the mooring system consists of the SPM type with taut mooring lines organised in clusters, (2) the loads are a function of DVs that define the mooring layout and (3) uncertainty from the sea environment are taken into account. Said uncertainties are taken into account in the short-term and long-term by means of the Moment-based Translation model (Ding and Xinzhong, 2016; Hao and Yang, 2020) and probabilistic scenario sampling techniques, respectively. Motivated by the results of previous studies (Cabrera-Miranda et al., 2018; Noble Denton Europe Ltd, 2001), we investigate the loads for the ultimate limit state (ULS) and fatigue limit state (FLS) for the mooring lines, and the ULS for the FPSO's hull.
Even though the present work deals with ship-shaped offshore floating structures, the proposed procedure is general, and thus, it can be applied in probabilistic-based analyses of other offshore and onshore structures.
The remainder of this paper is organised as follows. Section 2 presents the proposed framework and a detailed description of the procedure followed in this investigation. Section 3 introduces an applied example and gives details on the computation of numerical analyses and metamodels to predict the loads. In Section 4, results for numerical analysis are presented in the form of response and response divergence charts, and the sensitivity analysis to rank the importance of the input variables for the loads. Conclusions are finally given in Section 5.
Section snippets
Methodology
We propose the procedure presented in Fig. 1 to investigate the influence of the design parameters.
Target floating structure
The selection of production floating units and their mooring system is based on a number of factors such as environmental conditions of the specific sites and functional requirements. In this study, to demonstrate the applicability and effectiveness of the developed framework, we consider a hypothetical tanker-based FPSO that operates in the ultra-deep water regions of the Gulf of Mexico. The mooring system consists of the SPM type with a regular disconnection function made of 12 lines. FPSO
Probabilistic selection of mooring layouts
To predict the effect of different mooring layouts on the loads, we generated six layouts using LHS. Table 3 summarises the fixed values of DVs, where represents the turret position normalised with respect to the length between perpendiculars.
A 3-D illustration of selected six layouts (denoted by A, B, C, D, E, and F) is shown in Fig. 7, and their qualitative description is as follows:
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Layout A: midsize layout radius, external turret, anchors grouped in a tight position within the clusters,
Conclusions
This work investigated the loads on ship-shaped offshore installations for hull ULS, mooring lines ULS and mooring lines FLS. It aims to find how the parameters that define the mooring layout, such as layout radius, number of clusters and diameter, influence the said loads. For this purpose, a DASE procedure has been followed. It starts by sampling credible scenarios by LHS, which are then analysed in the time-domain to obtain the moored floater loads. With the generated data, metamodels are
Funding
This work was supported by a 2-Year Research Grant of Pusan National University.
CRediT authorship contribution statement
M.P. Mujeeb-Ahmed: Methodology, Software, Formal analysis, Investigation, Data curation, Writing – review & editing. José Cabrera: Conceptualization, Methodology, Software, Resources, Data curation, Writing – original draft. Hyeong Jin Kim: Software, Formal analysis, Writing – review & editing. Jeom Kee Paik: Validation, Resources, Writing – review & editing, Supervision.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
We are indebted to Prof Wilson Guachamin-Acero at Escuela Politécnica Nacional (EPN) for his in-depth discussion on the time-domain hydrodynamic analysis of floating structures. Furthermore, we are grateful to all the researchers cited in this paper.
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