An integrated methodology for the design of mooring systems and risers

Marine Structures 39 (2014) 395e423

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Marine Structures journal homepage: www.elsevier.com/locate/ marstruc

An integrated methodology for the design of mooring systems and risers
n a, 1, Fabrício Nogueira Corre ^a a, Aldo Roberto Cruces Giro b
zquez Herna
ndez , Breno Pinheiro Jacob a, * Alberto Omar Va a

LAMCSO e Laboratory of Computer Methods and Offshore Systems,2 PEC/COPPE/UFRJ e Post-Graduate Institute of the Federal University of Rio de Janeiro, Civil Engineering Dept., Avenida Pedro Calmon, S/N,
ria, Ilha do Funda ~o, Caixa Postal 68.506, 21941-596 Rio de Janeiro, RJ, Brazil Cidade Universita b
zaro Ca
rdenas 152, Gustavo A. Mexican Petroleum Institute,3 Deep Waters Exploitation Dept, Eje Central La Madero 07730, D.F., Mexico

a r t i c l e i n f o

a b s t r a c t

Article history: Received 18 July 2013 Received in revised form 18 March 2014 Accepted 6 October 2014 Available online 30 October 2014

Traditionally, the design of mooring lines and risers of floating production systems (FPS) has been performed separately, by different teams, employing uncoupled analysis tools that do not consider the nonlinear interaction between the platform hull and the mooring lines and risers. Design processes have been focused on fulfilling the design criteria of the respective component (mooring/riser) alone, with few or no consideration to the other component, and little interaction between the design teams. Nowadays the importance of employing analysis tools based on coupled formulations is widely recognized, and analysis strategies have been proposed to consider feedback between mooring lines and risers within their respective design processes. In this context, this work details a proposal of one single and fully integrated design methodology for mooring systems and risers for deep-water FPS. In this methodology, the design stages of both risers and mooring lines are incorporated in a single spiral, allowing the full interaction of different teams; mooring design implicitly considers the riser integrity, and vice-versa, leading to gains in efficiency and cost reduction.

Keywords: Floating production systems Mooring systems Risers Integrated design methodology Coupled analysis

* Corresponding author. Tel./fax: þ55 21 2562 8496.
n), [email protected] (F.N. Corre ^a), [email protected] (A.O. E-mail addresses: [email protected] (A.R. Cruces Giro
ndez), [email protected], [email protected] (B.P. Jacob). V
azquez Herna 1
zaro Ca
rdenas 152, Permanent address: Mexican Petroleum Institute, Deep Waters Exploitation Department, Eje Central La
xico, D.F. Gustavo A. Madero 07730, Me 2 http://www.lamcso.coppe.ufrj.br. 3 http://www.imp.mx/.

http://dx.doi.org/10.1016/j.marstruc.2014.10.005 0951-8339/© 2014 Elsevier Ltd. All rights reserved.

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Different analysis strategies are employed, taking advantage of uncoupled and coupled numerical models. The models generated at the initial/intermediate design stages can be reused in subsequent stages: simpler models are used in the initial stages, and more refined models are gradually introduced, to reach an ideal balance between computational cost and accuracy of results. In the advanced stages, the exchange of information between mooring/ riser also allows the definition of criteria for the selection of governing/critical loading cases to be revised and verified in detail. This leads to the reduction of the original loading case matrix, allowing a feasible use of time-consuming fully coupled analysis. Results of a case study illustrating the application of some of the main processes of the methodology are included. © 2014 Elsevier Ltd. All rights reserved.

1. Introduction Offshore oil production activities have been increasing in recent years, and extending to ultra-deep waters. Such activities are mainly performed by floating production systems (FPS) such as semisubmersibles, SPAR buoys and FPSOs, in which two of the most important components are the risers and the mooring system. Risers convey oil, gas and other fluids that result from the production processes; and the mooring system is responsible for constraining the horizontal motions of the platform, to keep it within a safe operating area. Traditionally, the design of mooring lines and risers has been performed separately, by different teams, employing uncoupled analysis tools that do not consider the nonlinear interaction between platform hull and the mooring lines and risers. Those components have different design requirements, therefore codes or standards are available separately for mooring systems (e.g. Refs. [1e3]), for rigid risers (e.g. Refs. [4,5]), and for flexible risers (e.g. Refs. [6,7]). Design processes have been focused on fulfilling the design criteria of the respective component (mooring/riser) alone, with few or no consideration to the other component, and little interaction between the design teams. More recently it has been acknowledged that, although risers and mooring lines have different functions and design requirements, both (in conjunction with the vessel) constitute an integrated system that jointly responds dynamically to the environmental loadings. Nowadays it is widely recognized that the interaction between the hydrodynamic behaviour of the vessel and the hydrodynamic/structural behaviour of the lines should be taken into account, by using analysis tools based on coupled formulations [8,5]. Subsequently, with the popularization of coupled analysis tools, analysis strategies have been proposed to consider more interaction between mooring lines and risers within their respective design processes, corresponding to varying levels of complexity and design integration [9e11]. In this context, this paper presents a methodology for the design of mooring systems and risers. The main focus is to obtain a more efficient design, with the full integration of the processes and engineering teams associated to the mooring lines and risers. Another aspect of the methodology is the optimal use of different analysis tools (uncoupled, hybrid/simplified, and fully coupled), to reach an ideal balance between computational cost and accuracy of results. The remainder of this paper is organized as follows: Initially, Section 2 presents a historical background of the analysis and design methodologies, beginning with a description of the different analysis formulations (uncoupled, fully coupled, hybrid), and proceeding with the design methodologies that have been considered with the use of such analysis tools. Then, Section 3 presents a brief summary of the integrated design methodology proposed in this work. The stages of this methodology are then described in detail in the following Sections 4e6. Finally, in Section 7 a representative deep water platform is taken as a case study to illustrate and assess the use of some of the procedures incorporated on the methodology; final remarks and conclusions are presented in Section 8.


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2. Review of analysis and design methodologies for FPS 2.1. Analysis methodologies The design of mooring lines and risers of FPS for deep and ultra-deep waters depends on the availability of model tests and numerical simulation tools. Historically the latter has been the issue of several research studies, leading to analysis methodologies that have been categorized as uncoupled, fully coupled or hybrid, as follows: 2.1.1. Uncoupled methodology This was the classical procedure for the analysis of mooring lines and risers, characterized by the use of numerical tools based on uncoupled formulations. In general, this process involves an initial stage of motion analyses, in which mooring lines and risers are represented by simplified models (e.g. as scalar coefficients), obtaining vessel motions in terms of static offsets and of wave frequency (WF) and low frequency (LF) components. In a second stage, structural analyses of the lines modelled by Finite Element (FE) meshes are performed using those offsets and motions as input. Usually such analyses are performed for each single riser. The main advantage of uncoupled methodologies is the low computational cost of each simulation. However they present important, well-known shortcomings that may lead to severe inaccuracies for deep-water scenarios and FPSs with a large number of risers. Such shortcomings were already recognized in 1998 by Ormberg and Larsen [8], who mentioned the following topics: 1) The uncoupled approach normally do not account for mean current loads on moorings and risers, but in those scenarios the interactions between current forces on the underwater elements and the mean offset and LF motions of the floater are pronounced; and 2) Important damping effect from moorings and risers on LF motions has to be included in a simplified way, usually as linear damping forces acting on the floater. Establishing simplified models of this phenomenon is not straightforward because several parameters are involved. The reader is referred to Ref. [8] for a detailed assessment of the inaccuracies of the uncoupled approach. Here it should be noted that different analysis methodologies could be incorporated into this classification of “uncoupled methodologies”. As has been discussed in Ref. [10], two main aspects can characterize a so-called basic or “classic” uncoupled methodology: a) The use of numerical analysis tools based on uncoupled formulations, where the hydrodynamic behaviour of the vessel is not influenced by the nonlinear dynamic behaviour of the lines; b) The consideration, in the analysis procedures, of few or no integration between the moored system and the risers. It is important to distinguish between these two aspects, because, as shown in Ref. [10], some level of integration between mooring lines and risers can be achieved even when only uncoupled programs are available, comprising refinements on that “classic” uncoupled methodology. Such refinements, which have been available for the last 20e30 years or so, consist for instance in employing enhanced procedures for the determination of the scalar coefficients introduced in the vessel equations of motion to represent the behaviour of the lines; for more details please refer to Ref. [10]. However, as extensively discussed in Refs. [10,11], even these refinements still involve several simplifications. They fail to completely represent the non-linear dynamic interaction between vessel and lines (including for instance the nonlinear behaviour of the damping of the lines that influence the LF motions of the vessel). As the water depth increases this interaction becomes more important, and consequently the results can still be inaccurate for these deep-water scenarios. 2.1.2. Fully coupled methodology The most accurate procedure to consider the interaction between the components of an FPS, and accurately predict the individual responses of vessel, risers and mooring lines, consists in using coupled analysis tools. Generally such tools are based on a time-domain solution method and a rigorous representation of the lines by FE models, therefore considering all nonlinearities involved in the dynamic response of the system. Several research works on coupled analysis have been conducted (see for instance [8,12e19]). Recently, Jacob et al. [20,21] described and studied alternative formulations (referred as “weak coupling” WkC and “strong coupling” StC) for the fully coupled analysis of FPS. The WkC formulation is focused on

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the equations of motion of the hull: the coupling between the hydrodynamic model of the hull and the hydrodynamic/structural model of the lines is performed by forces acting on the right-hand side of the hull equations. In the StC formulation, the FE meshes of all mooring lines and risers are assembled together forming a single set of equations, and the hull is considered as a “node” of this model. A “fully coupled methodology” can be characterized by using only coupled analysis tools, which can simultaneously generate the vessel motions and the detailed structural response of the mooring lines and risers. For this purpose, the mooring lines and risers should be modelled by FE meshes refined enough to accurately determine all relevant aspects of their structural response (not only their top tensions, but also, for instance, tensions and moments near the touch-down zone). However, this may lead fully coupled analysis tools to demand high computational costs; in any case the literature (see for instance [8]) indicates the importance of performing fully coupled analyses for at least some selected critical cases, or for particular studies where small-scale tests are not possible due to limited depth in laboratory tanks. 2.1.3. Hybrid methodologies; simplified coupled analyses Although an important line of research consists of devising alternate solution methods and algorithms to minimize the computer costs of coupled analyses (e.g. optimized time-domain methods including adaptive time-step variation [22e25], or frequency-domain methods [26e28]), the goal of obtaining a balance between accuracy and computational efficiency has also been sought by proposing “hybrid” analysis methodologies combining the use of coupled and uncoupled tools. Different procedures may be included into this classification [29,10,11,30,31]. In this work we will consider the “coupled motion analyses” [29,11,31] and the “semi-coupled analyses” [32] that will be described next. Since these hybrid procedures may be characterized by using coupled models that introduce simplifications or approximations, from now on they will also be referred as “simplified coupled analyses”. 2.1.3.1. Coupled motion analysis. This is a two-step analysis procedure. The first step (the “coupled motion analysis” itself) employs a coupled model with the risers represented by FE meshes coarser than those employed on fully coupled analyses. The meshes are designed to adequately represent the global contribution of the risers in terms of its top tensions, mass and damping (therefore considering the non-linear dynamic interaction between vessel and lines). In consequence, they provide more accurate vessel motions than those from uncoupled motion analyses. The accuracy is equivalent to fully coupled analyses, with lower computational costs. However, these relatively coarse FE meshes are not refined enough to provide the detailed structural response of the risers (e.g. tensions and moments near the touch-down zone); therefore, these results are obtained in the second step of the procedure, which consists on prescribing the motions at the top of uncoupled FE models of each individual riser, now modelled with more refined meshes to obtain the detailed structural response. A more detailed description of the approximations and advantages of this procedure can be found in Refs. [29,11,31]. 2.1.3.2. Semi-coupled (S-C) analysis [32]. This is a three-step analysis procedure. The first step employs a coupled model (similar to the described above) for a nonlinear static analysis with the static components of the loadings, resulting in the mean equilibrium position of the system. On the second step, other static analyses are restarted from that static equilibrium configuration, applying small values of prescribed displacements at the centre of gravity (CG) of the platform for each one of the 6 rigid-body DOFs. From the corresponding forces that are obtained, an equivalent 6-DOF global stiffness matrix is determined, representing the global contribution of all mooring lines and risers. This is a tangent stiffness matrix that is linearized around the static equilibrium configuration. Finally, the third step consists in an uncoupled dynamic analysis of the platform, where only the 6-DOF vessel equations of motion are solved, with the equivalent global matrix added to the hydrostatic matrix of the platform. This approach can be considered as quasi-static from the point of view of the lines, therefore providing results not as rigorous as those of a fully coupled analysis; however they are more accurate than those evaluated by a traditional uncoupled formulation (in which the lines are represented by scalar models or catenary equations). The equivalent stiffness matrix for the lines is calculated taking


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into account a full FE model; therefore it can be evaluated for general complex configurations of the lines, taking into account effects usually neglected by traditional quasi-static scalar formulations e for instance, the influence of current loads along the lines, the coupling of two or more lines, and the bending moments when the lines are modelled by beam elements. To improve the accuracy of the platform motions provided by this S-C scheme, the inertial and damping contributions of the lines can be incorporated by computing equivalent global 6-DOF matrix coefficients for its mass and damping. These calculations can be performed with the help of numerical decay tests. If the main purpose of analysis is to obtain reasonably accurate values for the vessel motion, the above procedure is adequate. However, if more accurate results for dynamic line tensions are also required, this scheme can be enhanced by performing additional dynamic simulations with an uncoupled FE model including the mooring lines only, and prescribing the motion time series obtained from the third step of the S-C scheme as described above. This way the inertial forces on the lines are captured, with very low additional computational cost. 2.2. Design methodologies As mentioned before, in classical design methodologies mooring lines and risers have been designed separately, with little interaction between the different teams, and employing uncoupled analysis tools. The design premises of the mooring system considered given target values for the maximum offset (for intact and damaged situations), irrespective of the direction. These target offset values were defined in a somewhat arbitrary manner, based on previous experience. The design of the mooring system involved the first stage of the uncoupled analysis methodology described above, leading to a mooring configuration for which the offsets were calculated in terms of static offsets and of WF/LF components. Subsequently, each individual riser was designed to satisfy its functional requirements under the action of such offsets, and also of the environmental loadings directly acting upon them. The design involved the second stage of the uncoupled analysis procedure, by positioning the top of the riser at distances corresponding to the static offsets previously obtained, and performing dynamic analyses applying the WF/LF components. The analyses were performed under different environmental load combinations (not necessarily the same that were considered for the mooring design), applied on different directions relative to the plane of the riser e referred as the near, far and other cross and transverse positions. It can be seen that, in these separate mooring and riser design methodologies, the main link between both designs is the target offset: both structures have to meet their corresponding design criteria in that condition. Risers should meet their design criteria conditioned and constrained by the mooring system; this may not be the most adequate approach, since it is well known that for deep water systems the risers are far more expensive than the mooring lines. Slowly, with the experience gained over the years and with the availability of coupled analysis tools, these classical design methodologies have shown some improvements. Mooring lines and risers of FPS may still be designed by separate teams, but hybrid analysis methodologies have been used more frequently, thus increasing the feedback between these design stages, and integration on the analysis models. For instance, mooring analyses have been performed with the risers being modelled with different levels of complexity: from simpler models based on restoring curves or catenary equations (comprising the “refinements” on the classic uncoupled methodology that were mentioned on Section 2.1.1), to more complex models such as those considered on the “coupled motion analysis”, one of the hybrid methodologies mentioned on Section 2.1.3. This is how such hybrid methodologies allow more integration between mooring and riser designers: mooring analyses can consider the influence of the risers (in terms of their contribution of stiffness, damping, added mass and hydrodynamic loads) on the platform motions and, on the other hand, riser analyses can use motions that are more accurate than those provided by the uncoupled methodologies. Currently, hybrid methodologies are being included in design codes, for instance DNV-RP-F205 [33] and DNV-OS-F201 [5]. Along the last decade it has been recognized that the integrated design of risers and mooring lines has the potential to bring substantial benefits for deep water FPSs, in terms of overall system response, cost

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and safety. Different analysis strategies that consider some interaction between mooring lines and risers within their respective design processes, corresponding to varying levels of complexity and design integration, have been proposed [9,34,10,11]. For instance, Seymour et al. [35] adopted an integrated design approach for the P-43 and P-48 Petrobras FPSOs: the goal was to design a cost-effective mooring system that allows the use of simple catenary configurations for flexible risers meeting all contractual design criteria, safety requirements and relevant codes and standards. The authors mention that the major design challenge for deep water FPSO mooring and riser systems is to quantify, at an early stage, the constraints imposed by one system over the other. Garret et al. [36] proposed a fully coupled frequency domain method for an integrated design of mooring and risers considering the riser fatigue life. Senra [37] evaluated several hybrid analysis methodologies; the focus was to evaluate and propose
n [38] adequate methods for each phase of the design procedures of mooring lines and risers. Later, Giro studied the application of the concept of “safe operational zone” of risers (SAFOP as originally proposed by Connaire, Kavanagh et al. [9,34]), allowing the inclusion of information from the design of risers into the design of the mooring system. More recently, an integrated analysis procedure of mooring and riser systems for FPSOs in harsh shallow water environments was proposed by Martens et al. [39]; the main issue was to conduct the mooring and riser analyses using a common set of design loading cases. Finally, a first proposal of one single and fully integrated design methodology for mooring systems
n et al. [40], and partial results of its application were and risers for deep water FPS was outlined by Giro evaluated in Ref. [41]. In this methodology, the design stages of both risers and mooring lines are incorporated in a single spiral, allowing full interaction of different teams, and resulting in gains in efficiency and cost. Here, this work presents the consolidation of subsequent studies conducted to evaluate some key processes of the integrated design methodology, resulting in an overall improvement. A detailed description of the design stages is presented, and results of a case study illustrating the application of some of the main processes are included. 3. Summary of the proposed integrated design methodology As with any engineering design methodology, the mooring/riser integrated design methodology described here consists of different stages, from preliminary to advanced. Along each stage the design activities for the mooring system and risers are gradually integrated. Fig. 1 presents a flowchart of the methodology; a brief summary is presented in this section, and a more detailed description will be presented in the following sections. The methodology begins with the specification of the design basis. Design basis documents must contain all necessary information, and follow guidelines provided by design codes and standards. For mooring systems and risers, general guidelines for required design data can be found on codes such as Refs. [2] and [5] respectively. The remaining steps of the methodology are grouped in initial, intermediate and advanced stages. The initial/intermediate stages employ either uncoupled or simplified coupled analyses (as described in Section 2.1). Fully coupled models are employed only in the final, advanced stages. It will be seen that the main innovative contributions of the methodology presented here are concentrated in stages IIb to V. As will be seen along the description of these steps, most of the analyses (with the exception of those employed in the preliminary stages Ia and Ib) consider irregular sea states with waves defined by spectral data. This requires the use of adequate statistical models for the prediction of extreme response values, taking into account non-Gaussian response time histories. Also to obtain adequate levels of statistical confidence in the extreme value predictions, the usual current design practice for the analyses involving coupled LF/WF time series should be followed, i.e., employing large simulation lengths such as 3-h or 10,800 s. 3.1. Initial stages (Ia, Ib, IIa and IIb) Firstly, preliminary design steps are performed separately for risers and mooring employing uncoupled models (stages Ia and Ib respectively, described below in Sections 4.1 and 4.2). These stages are similar to those employed in the classical, separate design methodologies for mooring system and risers as mentioned before in Section 2.2.


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Fig. 1. Flowchart of the integrated design methodology.

Then follows the establishment of the safe operational zone (SAFOP) for the risers (stage IIa, Section 4.3), and the generation of offset diagrams for the mooring system in intact and damaged conditions (stage IIb, Section 4.4). It is interesting to note that, while the former stage still uses uncoupled models for the risers only, and follows a procedure that has evolved from the original proposition of Refs. [9,34], the generation of the offset diagrams already considers the use of simplified coupled models incorporating the risers, and is focused on results that will later (in stage III) allow a joint verification of both mooring system and riser criteria. This verification is further expedited by the fact that the analyses are performed for a reduced subset of the matrix of loading cases, i.e., taking only the load combinations that cause the maximum offsets. 3.2. Intermediate stages (III, IV and V) These stages include the first direct interaction between mooring and riser analysis and design. In stage III (Section 5.1) the riser SAFOP and mooring offset diagrams that resulted from stages IIa and IIb are compared, allowing the assessment of the design criteria for both mooring system and risers. If

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results are not adequate, redesign steps to assure riser integrity should be performed; else, the design proceeds to stage IV (Section 5.2) where the full matrix of loading cases is analyzed (still using simplified coupled models), to provide vessel offsets and mooring line tensions. In stage V (Section 5.3), the combined results of these analyses and those of the SAFOP diagram are assessed, to identify governing cases to be considered in the following advanced stages. Along the description of stages III and V in Sections 5.1 and 5.3 respectively, it will be seen that both corresponds to verification/assessment tasks using the SAFOP diagrams, comprising respectively preliminary and more advanced revision tasks. 3.3. Advanced stages (VI, VII and VIII) In these stages more detailed and specific analyses are performed. Stage VI (Section 6.1) consists of performing analyses with more complex fully coupled models only for the governing cases selected at stage V; the remaining non-governing cases are revised with analyses employing the classical uncoupled analysis methodology that requires much lower computational cost. Stages VII and VIII corresponds respectively to fatigue assessment (using hybrid methodologies), and to analyses of the installation procedures. 4. Preliminary stages (Ia, Ib, IIa, IIb) 4.1. Risers (stage Ia) As usual, preliminary design of risers includes material selection; wall thickness sizing (for rigid risers) or cross section configuration (for flexible risers); definition of global configuration, and specification of ancillary devices such as flexjoints or stressjoints. This stage involves analyses with relatively simpler numerical models, but verifying all relevant design criteria, considering several factors such as temperature, pressure and type of internal fluid. A promising line of research related to the conceptual design of risers consists in employing synthesis and optimization procedures to devise preliminary global configurations of catenary risers [42e44]. 4.1.1. Numerical models and analysis strategies For flexible risers, local analyses may be performed to define cross section configurations. The preliminary global configuration of each individual riser is evaluated with global static analyses under self-weight and buoyancy. Then the structural behaviour under environmental loadings is assessed by dynamic analyses. At this stage these analyses may be simplified, considering regular waves and/or combining the prescribed wave frequency (WF) vessel motions (determined by crossing the vessel response amplitude operators RAO with the selected wave parameters) with the low frequency (LF) motions (that may be represented as an equivalent harmonic sine function, or using more complex representations such as those proposed in Refs. [45e48]). Regarding the FE mesh, the use of 6-DOF frame elements is recommended to better represent the flexural behaviour, even for flexible risers. Sensitivity studies should be performed, to assess the structural response of the risers with the variation of different parameters, such as: top angle; current velocity; wave height and period; weight of internal fluid; vessel draft. 4.1.2. Loading cases Loading cases should be sufficient to evaluate the preliminary configuration of each riser, considering different operational situations (fluid weight, internal pressure or different functions along its service life). The matrix of loading combinations should include current and wave, associated to vessel offsets prescribed at the top of each riser, in different directions relative to the plane of the riser, i.e., near, far, cross, transverse. 4.1.3. Design criteria Risers must comply with appropriate structural criteria (hoop stress, von Mises stress, hydrostatic collapse). Preliminary design of hang-off devices and other ancillaries (bend stiffeners, buoyancy


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modules) should be performed, for later consideration in the global analyses. Adequate safety factors for intact and damaged conditions should be considered [4e7]. Regarding fatigue life, all factors that contribute to modify the lifetime of a riser should be identified and evaluated. For instance, corrosion on rigid risers reduces thickness and decreases its lifetime, motivating the use of clad or lined pipe with corrosive fluid flow. Initial studies on the feasibility of installation procedures for each riser should be performed (e.g. based in experience). Analyses to assess VIV-induced fatigue should be carried out and, if necessary, VIV suppressors such as strakes should be defined; this is an important issue to consider in subsequent riser analyses (e.g. extreme loads, wave fatigue or installation analyses) because strakes increase drag forces. Finally, interference analysis should be performed to evaluate clearances between risers. 4.2. Mooring system (stage Ib) The preliminary design of the mooring system includes material selection, definition of global configuration and mooring layout. This stage involves analyses with relatively simpler numerical models, but considering all relevant design criteria, as described next. 4.2.1. Numerical models and analysis strategies Traditionally, at this initial stage design codes [1] recommended performing quasi-static analyses, neglecting line dynamics. Steady current, wave and wind loads are applied to obtain the vessel static position; wave-induced vessel motions are taken into account by including a representative static offset applied to the top of lines. However, presently with the advances in computer hardware such simplifications are not required, and even in this preliminary design stage more refined models and analysis types may be considered. Time-domain dynamic analyses are feasible, using models where the mooring lines are represented by FE and that already take into account the influence of the risers on the moored system (in terms of global stiffness, damping, mass and current loading), albeit with simplified scalar models such as restoring curves, or other simplified procedures as described in Refs. [9,10]. 4.2.2. Loading cases Again following usual recommendations from design codes (e.g. Refs. [1,2]), the moored system should be analyzed for operational, accidental (e.g. considering failure of a mooring line), and extreme environmental conditions, under loading cases including combinations of current, wave and wind acting on different directions relative to the platform (considering collinear and non-collinear combinations). As with the preliminary riser analyses of stage Ia, here using deterministic regular waves may also be adequate. Load combinations should cover all relevant cases for a preliminary evaluation of mooring system capability, leading the platform to maximum vessel offsets, and maximum/minimum mooring line tensions. 4.2.3. Design criteria Tension limits should be verified and vessel offsets should not exceed an “initial target offset” (normally based in similar FPS design experiences). When defining the mooring layout, restricted zones in seabed must be considered. Furthermore, other factors and design criteria that may hinder the feasibility of a mooring line should be identified and evaluated (e.g., polyester segments may not touch the seabed). Adequate safety factors should be considered for intact and damaged situations [1,2]. 4.3. Safe operational zone for the risers (stage IIa) The safe operational zone or SAFOP [9,34] of risers is a diagram defining the envelope of horizontal excursions within which their top connections must remain, to avoid the violation of any riser design criterion. Fig. 2 illustrates a representative SAFOP diagram considering sixteen directions, with excursions represented as percentages of water depth. The centre of the diagram corresponds to the neutral equilibrium position of the vessel. A pioneer proposal of determining safe operational zone of risers for use in mooring design was made in Ref. [9]. According to Ref. [34], SAFOP diagrams can be used to give a preliminary indication of

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Fig. 2. SAFOP diagram.

the directional compliancy of the risers. In the context of the mooring/riser integrated methodology described here, they will be compared with the offset diagrams for the mooring system, to assess the integrity of the risers (as proposed in Ref. [38]); also, they will provide other important qualitative information such as identifying the most critical risers, the design criteria that are first violated, and the associated environmental loading combination. Different procedures can be established to generate a SAFOP diagram. Roughly speaking, they are generated by taking an FE model of a riser (or group of risers) and performing several sequences of analyses, each one for a given direction of prescribed displacements incrementally applied to the top node of the risers, and also including wave/current loadings. For each direction, the corresponding point of the SAFOP diagram corresponds to the offset where one or more riser design criteria are about to be violated. The following items detail some aspects related to the generation of such diagrams. 4.3.1. Numerical models A SAFOP diagram for the whole array of risers of an FPS can be assembled by computing one diagram for each individual riser, and then superimposing all curves. This procedure also allows obtaining SAFOPs for a specific group of adjacent risers. Alternatively, the full SAFOP diagram can be computed using a single model that includes all risers. In any case, the numerical model of the risers should comprise an FE mesh of frame elements, refined enough to obtain their detailed structural response. Hang-off devices should also be included, e.g. for a steel catenary riser (SCR), flexjoints or stressjoints should be modelled, with a tapered joint and extension up to the first weld, in order to assess the correct stresses along the top region. 4.3.2. Loading cases A representative matrix of current and wave loadings should be selected amongst those that most affect the riser system. A sufficient number of directions of prescribed offsets should be analyzed; the higher the number of directions, the better is the definition of safe operational zone. An important issue to consider here is the relative directionality of the loadings and the prescribed offsets for each direction of the diagram. For example, one should consider applying a southward current while the riser top is displaced northwards. This depends on the probability of occurrence of a combination of environmental loading that can displace the vessel northwards even with the presence of a southward current.


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Therefore, a comprehensive study on the environmental conditions should be undertaken, considering collinear and non-collinear combinations of wave and current for each direction of the diagram. 4.3.3. Design criteria The riser utilization criteria that indicate a failure may be established from riser top angle variation, interference, top and bottom tension, compression, and other criteria depending on the type of riser, such as minimum bending radius (MBR) and torsion for a flexible riser; or von Mises stresses for a steel riser. The violation of any utilization criterion, taking into account the appropriate safety factor, indicates a failure position. Other examples of additional criteria would be, in the case of a lazy wave riser, the contact of the sagbend region with the seabed. 4.3.4. Sequence of analyses For each direction of the diagram, the analysis strategy consists in first performing nonlinear static analyses, under the action of a current profile and prescribed displacements incrementally applied to the top riser connections. This simulation stops when the first riser design criterion is violated, and the corresponding offset is then identified. From the static equilibrium configuration thus obtained, a dynamic analysis is restarted with the offset slightly decreased (assuming that dynamic analysis leads to more severe results and therefore the design criterion probably will be violated for an offset smaller to the identified by the previous static analysis). The dynamic analysis proceeds by adding prescribed first order wave motions, and wave loads. The results of these analyses are time-series of the main parameters of the riser response, which should be processed to determine extreme values using the appropriate distribution model taking into account non-Gaussian response time histories. If the criterion ceases to be violated, the point of the diagram for the considered direction is then identified; otherwise, if the criterion is still violated, the offset is decreased again until the criterion ceases to be violated. After the analyses for all directions have been completed, the points for all directions are connected to generate the diagram that delimits the safe zone. Besides the limit offset values, other important information that must be reported from these analyses are: which design criteria has been violated for each direction, which are the most demanded risers, and for what associated load combination. It is important to mention that the horizontal offsets applied in the initial static analyses that define the SAFOP implicitly include the mean position of the platform and the amplitude of the LF motions. Then, the subsequent dynamic analyses add the WF motions, so the offsets incorporate mean þ WF þ LF. The methodology described up to this point can be directly applied to semi-submersible platforms or other systems where the yaw motions are less significant. However, its applicability to FPSOs or other ship-like platforms requires further considerations. For instance, in the case of FPSOs with a spread-mooring system, and risers arranged along one of the sides of the hull (such as the DICAS system considered in Ref. [11]), there may be important variations in the heading of the platform that will affect the performance of the risers. In such cases, different SAFOP diagrams should be generated, considering different headings of the system (for instance 15 , 0 , þ15 ). Moreover, FPSOs may also operate with different drafts that are also relevant to the performance of the risers; these should also be taken into account in the generation of SAFOPs. 4.4. Offset diagrams (stage IIb) The so-called offset diagrams are comprised by the envelope of maximum vessel excursions. These diagrams are generated by taking a coupled model platform þ lines and performing dynamic analyses under collinear and non-collinear combinations of current, wind and irregular wave loads, for a given number of directions of incidence (at least eight). Therefore, the response of the platform also considers the mean offset and the LF/WF motions. From the result of the analysis for each load combination, time-series of the resultant of the planar motions (surge and sway) can be built. From these series, extreme offset values are determined by statistical procedures (using a properly selected distribution model taking into account non-Gaussian

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response time histories). Finally, a polar offset diagram can be built by connecting the maximum offsets for each direction, as illustrated in Fig. 3. Besides the offset diagram itself, which allows an easy interpretation of the compliancy of the mooring system in all directions, these analyses also allow one more stage of verification of the mooring design criteria, mainly the line tensions. They also provide important qualitative information to evaluate the mooring system capability, i.e., a measure of the compliancy of the mooring system along the different directions, and also the information of what are the most critical environmental loading cases, which lead to higher tension values in the mooring lines. In any case, the focus of this stage is to obtain expedite results that will later (in stage III) allow a joint verification of both mooring system and riser criteria. This task is expedited by the fact that the analyses are performed for a reduced subset of the matrix of loading cases (i.e., taking only the load combinations that cause the maximum offsets), and also by some simplifications on the numerical models, as described next. 4.4.1. Numerical models and analysis strategies Recalling that the previous stages Ia and Ib (preliminary design of the risers and mooring system) employed simpler uncoupled models, this stage IIb is the first where the risers are represented by FE models in a coupled model. However, here we are still in a preliminary stage (where the focus is on the estimation of vessel motions and mooring line tensions, and not on the detailed riser structural response). Therefore, at this point there is no need to perform fully coupled analyses, and we can safely assume the simplifications involved in the hybrid analysis methodologies described in Section 2.1.3, namely the coupled motion analysis and semi-coupled analysis, providing adequate accuracy and dramatically reducing computing costs when compared to fully coupled models. Regarding the “coupled motion analysis”, on the context of this design stage (focused on line tensions and platform motions) only the first step (the coupled motion analysis itself) is required. Analyses corresponding to the second step (prescribing the obtained platform motions at the top of uncoupled FE models of each individual riser) will be employed later on stage VI, for the detailed riser analysis with the full matrix of loading cases, as described on Section 6.1. Regarding the S-C scheme, we recall that it is based on incorporating all non-linear behaviour of the lines as calculated by the static coupled simulation of the first stage. On the dynamic analysis that provides the dynamic motion response of the vessel, the elastic influence of the lines is linearized

Fig. 3. Offset diagram.


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around the mean equilibrium position. Therefore, this scheme is applicable for this stage of the integrated design methodology, where all we need is to calculate vessel motions with acceptable accuracy. 4.4.2. Loading cases At this stage, loading cases should again include different extreme combinations of current, wind and irregular wave following usual recommendations from design codes (e.g. Refs. [1,2]). Only a reduced subset of the matrix of loading cases need be considered; however, all relevant directions of incidence for the environmental loading should be included (at least eight), not only with collinear wave-wind-current, but also some non-collinear combinations (for instance, considering current misaligned at ±30 relative to wave-wind). 4.4.3. Offset diagrams for damaged mooring conditions The procedure described above corresponds to the mooring system in an intact condition. Since design codes (e.g. Ref. [7]) recommend analyzing also damaged conditions, such as the rupture of one or more of the mooring lines, the integrated design methodology must incorporate also the generation of offset diagrams for such damaged conditions. The procedure is similar to the previously described, using numerical models that omit one mooring line. The choice of the line to be omitted is usually associated with the estimation of what situation leads the FPS to more critical situations, in terms of higher line tensions and larger offsets. In current design practices this is commonly done by studying the results of a motion analysis of an intact mooring system under extreme environmental conditions, and choosing amongst the following two alternatives: 1) Omit the second most tensioned line, so that the tensions of the most tensioned line is increased further; 2) Omit the most tensioned line, so that the maximum offset is increased. However, this procedure may not completely assure that all the most critical situations are covered. In actual FPS operation, any line may fail e.g. due to an accident with a tugboat. Therefore, since computational efficiency is ascertained by the simplifications assumed in the analysis strategies presented before, in this integrated design methodology we recommend omitting all mooring lines, one at a time. Considering for instance a mooring system with eight lines, then eight additional offset diagrams should be built. 4.4.4. Design criteria Design criteria are similar to the described in stage Ib (Section 4.2.3). Adequate safety factors should consider intact/damaged conditions and quasi-static/dynamic analysis [1].

5. Intermediate stages (III, IV and V) 5.1. Assessment of SAFOP and offset diagrams (stage III) In this stage, the SAFOP and offset diagrams that result from stages IIa and IIb are compared by plotting both diagrams in the same graph. This allows the visual assessment of the design criteria for both mooring system and risers, by verifying the occurrence of one or both the following situations: a) Directions where the vessel offset point is outside the safe operational zone of the risers. In this case, the integrity of the risers is compromised and redesign steps are mandatory because the mooring system is not able to keep the risers within the safe zone e the mooring system should be modified to reduce the offsets. b) Regions where the offset points are far inside the SAFOP boundary, meaning that the risers are not highly demanded. This could suggest redesign steps leading to more cost-effective solutions, either for the mooring lines (allowing larger offsets), or else for the risers themselves. Of course, if one or more risers are modified then their SAFOP diagram should be established again. Fig. 4 illustrates one comparison of offset and SAFOP diagrams, corresponding to situation a) above, where offsets exceed the SAFOP boundary between N and NE directions. Next, Fig. 5 presents two graphs

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Fig. 4. Comparison of diagrams: offsets violate SAFOP.

illustrating situation b): Fig. 5a corresponds to a case where the preliminary design of mooring and risers lead to vessel offsets close to the SAFOP curve in the North direction, while on other directions (e.g. S, SW, W) the offset points are far inside the SAFOP boundary. In this case the designer may opt to adjust the compliancy of the mooring system, leading to the new offsets presented in Fig. 5b with smaller offsets in the North direction, and higher in the area between west and south. Such comparisons should be performed taking the offset diagrams for intact and all damaged conditions; as mentioned before, several damaged offset diagrams should be available, e.g. one for each broken mooring line. In summary, stage III comprises a first task of joint assessment of results from mooring analyses (in terms of offset diagrams) and from riser analyses (in terms of the SAFOP diagram). This assessment allows designers to make the first decisions that take into account results from both mooring and riser systems. That is, the mooring system can be redesigned to comply with the integrity of the risers;

Fig. 5. Comparison of diagrams: offsets inside SAFOP.


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otherwise, the risers can be redesigned with new analyses modifying the “initial target offsets” (used as premises for analyses on near, far and cross conditions in the preliminary stages), based on the maximum vessel offsets from the offset diagrams. 5.2. Simplified coupled analyses for the full matrix of loading cases (stage IV) Once the preliminary design of the mooring system and risers is consolidated from the results of the previous stage, we now proceed to stage IV that consists in performing analyses for the full matrix of loading cases, for intact and damaged conditions. 5.2.1. Numerical models and analysis strategies Here the focus lies still on obtaining mooring line tensions and vessel offsets are inside the safe zone of risers. Therefore, to maintain the adequate balance between required accuracy and computational costs, here the numerical models and analysis strategy are the same that were employed in stage IIb for the generation of offset diagrams, as described in Section 2.1.3: either coupled motion analysis, or semicoupled analysis. 5.2.2. Loading cases While eight directions with one collinear and one non-collinear combination could be sufficient for the reduced subset of loading cases for the generation of the offset diagrams on stage IIb, here at least 16 directions and more non-collinear combinations should be included. Therefore the number of loading cases can reach hundreds or thousands, again stressing the importance of using fast simulation strategies such as those described in Section 2.1.3. 5.3. Identification of governing cases (stage V) The most critical loading cases (that will be the governing cases in the following advanced stages) are those that lead to the higher values for the parameters of the response of the mooring lines and risers, approaching the corresponding limits defined by the respective design criteria (Sections 4.1.3, 4.2.3 and 4.3.3). Therefore, a critical case may be associated to the mooring system, to the risers, or to both. In addition to classifying each case according to riser and mooring criteria, they should be associated to intact and damaged conditions. Since the number of loading cases/analyses performed in stage IV may be considerably large, we need to establish a procedure to gather all relevant results, and allow an easier visualization and comparison with the corresponding design limits. Initially the extreme offset values obtained from each simulation are plotted as points in the graph of the SAFOP diagram. This is illustrated in Fig. 6, where each point represents the maximum offset corresponding to a given loading case. Such graph allows a visual interpretation of some of the most relevant design criteria for both mooring and riser system: a) Mooring system: The most critical cases correspond to the points with maximum line tensions (which were calculated before in stage IV); b) Risers: The most critical cases correspond to the points that are closer to the SAFOP boundary (indicating that one or several risers are closest to exceed some design criterion). Of course, assembling a graph such as the one illustrated in Fig. 6 is useful for a global visualization of all results, but the actual procedure for selecting the governing loading cases should be based on an automated procedure (such as a spreadsheet) to classify and sort the cases according to riser and mooring criteria as mentioned above. 6. Advanced stages (VI, VII and VIII) 6.1. Detailed analyses (stage VI) Up to now, plenty information regarding the mooring system and the risers was gathered, by analyzing all design cases and verifying all relevant design criteria, leading to decisions/redesign steps to improve the performance of the FPS.

410


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Fig. 6. Offset points and SAFOP diagram.

In the initial and intermediate stages, uncoupled and simplified coupled models were used, contributing with an efficient use of computational resources without compromising the required accuracy. Now, these results will be verified by employing more refined models, according to the classification of the loading cases as governing or non-governing obtained in the previous stage (V), which allows the selection of the numerical model/analysis strategy that will be employed for the detailed analyses in stage (VI). This way, a judicious use of the more expensive coupled models will be provided, contributing to the efficiency of the proposed methodology: only the critical/governing cases will be evaluated in detail by fully coupled models, while for the remaining cases the riser design criteria may be evaluated by uncoupled models. 6.1.1. Governing cases Governing cases will be evaluated by nonlinear time-domain dynamic analyses using fully coupled models, which simultaneously provide accurate values for the vessel motions and the detailed structural response of the lines in one single analysis (see Section 2.1.2). These models can be built by taking the model employed for the “coupled motion analysis” in stage IIb (generation of offset diagrams), and introducing the following modifications in the FE mesh of the risers: a) Replace truss elements by frame elements; b) Refine the mesh in order to allow the accurate representation of the riser structural response. It should be recalled that the main purpose of these fully coupled models is exactly to obtain the accurate detailed structural response of the risers (including for instance tensions and moments near the touch-down zone); we do not expected the accuracy of the floater motions to be significantly improved. In this context, an interesting side-effect of the results of these more accurate analysis is that they can be compared with those obtained by the simpler models employed in the previous stages; this allows the assessment and calibration of those models. 6.1.2. Non-governing cases Non-governing cases may be revised by performing dynamic analyses using uncoupled FE models of the risers, modelled with refined meshes to obtain their detailed structural response. These analyses are equivalent to the second step of the hybrid methodology that included the “coupled motion analyses” as described earlier in Section 2.1.3; here the motions that are prescribed at the top connection of the risers are those obtained in stage IV.


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6.2. Mooring and riser fatigue (stage VII); installation (stage VIII) Up to this point the main focus has been on extreme, operational environmental conditions. The remaining stages of the design methodology are related to the assessment of fatigue behaviour, and to the evaluation of installation method for the risers; however, due to limitations of space, we will leave these important issues to be addressed in future works. 7. Case study This section presents results of a case study, where the application of some of the procedures proposed above are illustrated for a deep water FPS, representative of actual systems installed in Campos basin, offshore Brazil. The main focus is on stages II to VI, which comprise the initial/intermediate and advanced stages of the integrated design methodology, for operational and extreme conditions. It is important to stress that, due to limitations of space, the procedures presented here for this case study are only illustrative of the main aspects and stages of the proposed methodology. They are not intended to encompass the whole set of procedures and analyses that would be needed for its practical application for actual design activities. For example, damaged situations are not considered; also, redesign steps are not included. 7.1. General description The FPS is a semisubmersible platform with two pontoons and four columns, installed at a water depth of 1000 m. The main characteristics are presented in Table 1. The mooring system is comprised of 8 lines with chain and steel wire rope segments, with azimuths and pretensions as indicated in Table 2. For this application, the utilization criterion for the mooring lines is the minimum breaking load (MBL), which is equal to 8730 kN. The riser system includes 22 flexible risers (including umbilicals) and 2 SCRs. Their main characteristics, along with the limits for the corresponding design criteria, are presented in Table 3. An additional utilization criterion not included in Table 3 is interference between risers. The layout of the system is shown in Fig. 7. The in-house SITUA-Prosim program [49] is employed to generate the numerical models and perform all analyses. Fig. 8 presents a 3D view of the coupled numerical model including the platform hull, mooring lines and risers. 7.2. Environmental data The values for the environmental loading parameters should be taken from metocean data for the offshore location: irregular waves (significant height Hs, peak period Tp), current and wind. For this case study, considering that the goal is merely to illustrate the main aspects of the sequence of analyses comprising the proposed integrated design methodology, some simplifications are assumed: current is represented by a triangular profile with a given surface velocity; and wind is represented by a constant velocity. Of course, in the application of the methodology for actual design activities, taking the actual metocean data would be mandatory (for instance, the actual current profile with directions and velocities varying along the depth, and an adequate spectral representation of dynamic wind excitation). Fig. 9 presents a directional comparison of magnitudes of current, wave and wind. The values are expressed as percentages of the respective maximum values for all directions. The higher currents are

Table 1 Hull main characteristics. Length Beam Draft Displacement Azimuth

90 m 65 m 21.7 m 33,200 ton 0


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Table 2 Mooring line azimuths and pretensions. Line

Azimuth (degrees)

Pretension (kN)

L1 L2 L3 L4 L5 L6 L7 L8

330 300 240 210 150 120 50 25

1610 1503 1484 1436 1439 1457 1688 1655

found in the S and SW directions; higher waves in NE and N directions, and higher wind velocities in the E, NE and N directions. Table 4 summarizes the range of values (amongst all directions) for the environmental data corresponding to the extreme 10-year and 100-year return periods. From these data, two extreme environmental combinations are defined: E1 ¼ 10 yr current þ 100 yr wave/wind; E2 ¼ 100 yr current þ 10 yr wave/wind. 7.3. Safe operational zone for the risers (stage IIa) As mentioned in Section 4.3, the SAFOP diagram for the array of risers can be determined from analyses for each individual riser, or groups of risers; the SAFOP curves thus obtained can then be superimposed. However, it is more convenient to perform the analyses with a single model including all risers, thus obtaining directly the SAFOP for the full system. Another advantage is that such model can be reused in later stages, specifically for the detailed analyses of stage VI, where a fully coupled model can be generated by adding the hydrodynamic model of the platform and the FE model of the mooring lines. This approach has been followed here, with the risers modelled by meshes refined enough to obtain their detailed structural response. Table 3 Riser characteristics and utilization limits. Riser

Ø (in)

Sector

Max. von Mises (kN/m2)

Min. bending radius MBR (m)

Top tension (kN)

Seabed connection tension (kN)

1-Flex 2-Flex 3-Flex 4-Flex 5-Flex 6-Flex 7-Flex 8-Flex 9-Flex 10-Flex 11-Flex 12-Flex 13-Flex 14-Flex 15-Flex 16-Flex 17-SCR 18-SCR 19-Flex 20-Flex 21-Flex 22-Flex 23-Flex 24-Flex

2.5 4.0 2.5 2.5 4.5 8.0 3.0 3.0 3.0 3.0 2.5 3.0 3.0 3.0 4.5 3.0 10.0 8.0 3.0 4.5 4.5 2.5 9.0 11.0

Bow (North)

e e e e e e e e e e e e e e e e 276,000 276,000 e e e e e e

10 5 10 10 10 8 5 5 5 5 10 5 5 5 5 5 e e 5 5 5 10 10 5

2400 1000 2400 2400 2000 1000 800 800 800 800 2400 800 800 800 1000 800 e e 800 1000 1000 2400 4000 7000

200 200 200 200 300 500 200 200 200 200 200 200 200 200 200 200 1300 1300 200 200 200 200 350 700

Starboard (east)

Stern (south)

Port (west)


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Fig. 7. Riser and mooring system layout (plan view).

To obtain a well-defined safe operational zone, 16 directions for the prescribed motions were considered. For each direction, the relative wave/current directionality and the corresponding values for the loading parameters are defined according to the following assumptions: a) Considering first order wave forces, the higher wave in a range of ±45 around any given direction is taken; b) Considering surface current velocity: for the eight main directions (NeNEeEeSEeSeSWeWeNW) the corresponding value as designated in the metocean data is taken; for the remaining (intermediate) directions (NNE, etc.), for which there is no metocean data available, the higher value amongst the adjacent currents is taken. For the SSE for instance, S current and S wave is applied (see Fig. 9). Design criteria were selected as indicated in Section 4.3.3, in terms of von Mises stress; Minimum bending radius (MBR); Maximum tension on top connection (TT); Maximum tension on seabed connection (SCT); Interference (Int). The corresponding limit values are presented in Table 3. On actual design activities the top angle variation should also be considered, associated to the modelling of bending stiffeners at the top connection of the flexible risers; however, since the purpose of this case study is to comprise an illustrative example of the methodology, here the top connections were pinned and angle variation was not considered as a utilization criterion. The sequences of static-dynamic analyses that generate the boundary of the SAFOP diagram are performed according to the strategy described on Section 4.3.4.

Fig. 8. Coupled numerical model, 3D view.


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Fig. 9. Directional comparison of magnitudes of environmental loadings.

Fig. 10 illustrates the SAFOP diagram. Besides the boundary curve, the numerical values of the corresponding offsets are indicated for the 16 directions, as well as the utilization criterion that has been violated first. The offset values do not represent the position of any particular riser top connection; rather, they are measured between the original position of the vessel CG at its neutral position, and the position of the CG when the first criterion is violated. More detailed results are presented in Table 5, including the identification of the riser for which the violation was detected. The loading combination leading to the most critical result has been the E2 case (100 yr current þ 10 yr waves). Several important quantitative and qualitative observations can be drawn from Fig. 10 and Table 5: for instance, the most frequently violated utilization criterion is MBR in flexible risers, followed by interference. The bottom tension (SCT) was violated only for the N direction, in riser 17. In general, the boundary of the SAFOP zone varies in a range between 105 m and 180 m. The most restricted zone for riser operation lies between the SE and SW directions; this reflects the facts that the MBR criterion (usually associated to the “near” situation for a given riser) has been in general more critical, while, as can be seen in Fig. 9, the maximum values for the environmental loading parameters are found around these same SE and SW directions. It is also interesting to note that the MBR criterion was violated mostly around the main directions (N, E, S, W). This can be attributed to the particular layout of the riser system, shown on Fig. 7: they are arranged following mostly these main directions, and therefore few risers were offset to their “near” direction as their top connections were moved along the cross directions (NE, SE, SW, NW). 7.4. Offset diagram (stage IIb) The analyses to generate the offset diagram for intact conditions follow the semi-coupled strategy described in Section 4.4.1. A coupled model comprising the hull, mooring lines and risers is built from the data presented in Section 7.1. A simplified set of loading cases is considered taking conditions E1 and E2 defined in Section 7.2, with linear and non-collinear cases with current misaligned by ±30 Table 4 Environmental data.

Current velocity (surface) Wave Hs Wave Tp Wind velocity (10 min)

10-year

100-year

1.2e1.8 m/s 3.6e7.1 m 8.2e14.5 s 36.0e46.0 m/s

1.3e2.0 m/s 4.0e7.7 m 8.6e15.5 s 47.0e60.5 m/s


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Fig. 10. SAFOP diagram indicating failure modes and offset values.

relative to the wave/wind direction. On actual design activities a higher number of loading cases should be selected. Mooring line tensions are verified following the recommendations of API RP 2SK [1], i.e. using 60% of the MBL as the limit value for the tensions in the intact condition. The offset diagram with the maximum offsets from extreme condition E1 and E2 for each direction (about 12% of water depth) is presented in Fig. 11 (already superimposed to the SAFOP diagram). All mooring line tensions remained below the limit (i.e. 60% MBL). Later, Sections 7.6 and 7.7 present some of the most relevant results of line tensions. 7.5. Assessment of SAFOP and offset diagram (stage III) Following the methodology described in Section 5.1, the SAFOP and offset diagrams obtained in Stages IIa and IIb are plotted together in Fig. 11. We can observe a region where the offset curve crosses and

Table 5 SAFOP results. Dir. no.

Dir.

SAFOP limit (m)

Violation

Riser

Sector

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

N NNE NE ENE E ESE SE SSE S SSW SW WSW W WNW NW NNW

130 130 130 130 130 160 160 105 120 110 150 120 140 180 150 125

MBR/SCT MBR Int MBR MBR MBR Int MBR MBR MBR Int MBR MBR Int Int MBR

3, 4, 5, 7/17 8 6 & 7/10 & 11 11 11 13,14 18 & 19 16 16, 19, 20 20 18 & 19 22 22, 23 18 & 19 23 & 24 3, 4

Bow/Stern Bow Bow/starboard Starboard Starboard Starboard Stern Stern Stern Stern Stern Port Port Port Port Bow

416


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Fig. 11. Comparison of SAFOP and offset diagram.

exceeds the SAFOP boundary, between SWeSE directions. This means that, although the results obtained during the generation of the offset diagram in stage IIb indicated that the mooring design criteria were totally fulfilled, now it can be seen that the mooring system does not keep the risers within a safe zone. At this point we should recall that, due to limitations of space, we are assessing only the diagram for intact conditions. In actual applications of the integrated methodology, offset diagrams would also be generated for damaged conditions, which would present more points where the offsets exceed the limits of the SAFOP. This would suggest redesign steps to avoid the offsets to exceed the safe boundary, possibly involving slight changes in the mooring system, leading to the re-generation of the offset diagrams (the SAFOP diagrams could be maintained since they are not affected by changes in the mooring system). Considering that at this point we are still in an intermediate stage of the design methodology, these tasks should not demand much effort; the analyses used to generate the offset diagrams are relatively fast (using either the semi-coupled or the coupled motion approaches), and performed for a relatively reduced set of environmental combinations. However, as we have pointed out at the beginning of this section, in this case study we have opted not to perform redesign steps (also due to limitations of space), and to continue with the following stages of the design procedure. 7.6. Simplified coupled analyses for the full matrix of loading cases (stage IV); identification of governing cases (stage V) As described in Section 5.2, in stage IV the full matrix of loading cases is analyzed to obtain offsets and mooring tensions. On actual design activities, hundreds or thousands cases would be defined. However, recalling again that the goal here is merely to illustrate the application of the representative procedures of the methodology, only 48 load combinations are considered: 16 collinear cases (E1 and E2, eight directions each); and non-collinear cases with a misalignment of ±30 , comprising 32 cases (E1/E2, eight directions, ±30 ), thus reaching a total number of 48 cases. From these cases, a smaller subset of governing cases will be selected. As mentioned in Section 5.2.1, the analysis strategy is the same employed to generate the offset diagram. In Fig. 12 the offset points obtained for all loading cases are plotted together with the SAFOP


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Fig. 12. Offset points vs. SAFOP diagram.

diagram. Also, as described in Section 5.3, to each loading case/offset point is associated the corresponding value of maximum mooring line tension, and the distance to the closest SAFOP boundary. Such associations allow an easy interpretation of the results, to identify the critical or governing cases where mooring lines and/or risers are demanded the most. All mooring line tensions remains below the limit (60% MBL). The offsets are in the range of 7e12% of water depth. The maximum offset is 119 m (11.9% of WD), associated to the E2 case 8 of Fig. 12: noncollinear 10 yr S wave/wind þ 100 yr S-30 current. In general, the offsets for extreme combinations E2 are higher than those calculated for the combinations E1. Table 6 lists nine selected governing cases, numbered as indicated in Fig. 12. Cases 3, 4, 7 and 8 can be considered critical from the point of view of the risers, since they are close to the SAFOP boundary, indicating that one or more riser utilization criteria could be violated. The information of the more critical criterion can be found in Fig. 10: either MBR or interference. From the point of view of mooring lines, the maximum tensions are found in case 3 (non-collinear 10 yr S wave/wind þ 100 yr S þ 30

Table 6 Governing cases. No.

Extreme condition

Direction (going to)

Current misalignment (degrees)

Mooring line tension (%MBL)

Distance to SAFOP (m)a

1 2 3 4 5 6 7 8 9

E2 E1 E2 E1 E1 E2 E1 E2 E2

SW SW S S S S S S SE

þ30 þ30 þ30 þ30 Collinear Collinear 30 30 30

44.6 42.9 51.2 48.0 36.3 34.7 50.4 47.3 43.0

15.6 21.8 0.0 4.1 18.5 22.5 þ0.4 þ4.6 39.4

a

Negative sign means that SAFOP limit was not exceeded.


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current): line L7 with 51.2%MBL, and line L8 with 50.9%MBL. Then follows cases 7 and 4, respectively 50.4%MBL and 48.0%MBL. See Fig. 7 for the mooring layout and line numbering. 7.7. Detailed analyses (stage VI): governing cases Now follows stage VI where detailed analyses are performed for the full matrix of loading cases: as described in Section 6.1, the selected governing cases are verified with more refined analyses using fully coupled models, while for the remaining cases the risers are verified by dynamic analyses using uncoupled FE models. Regarding the governing cases, due to limitations of space we will not present results for all cases identified in Table 6. The procedure can be adequately illustrated by considering three representative cases: 3, 8 and 9. The first two are those closest to the SAFOP boundary; case 9, although far from the SAFOP boundary is also representative from the point of view of the mooring lines, since the associated mooring tension is also relatively high. As mentioned in Section 6.1.1, these analyses with more rigorous fully coupled models allows the assessment of results from previous stages, obtained with simpler models (e.g. uncoupled models for generation of the SAFOP diagram, and semi-coupled analyses to determine the offset diagram). Therefore, firstly we will assess the results of the S-C analysis strategy employed for the offset diagrams (as described in Section 4.4.1). The results are compared in Table 7 in terms of offsets and mooring tensions, and graphically in Fig. 13 as offset points. A reasonable agreement can be observed between the results; in fact, offsets and tensions provided by the semi-coupled strategy are slightly higher than the corresponding values obtained by fully coupled analyses. This confirms that the semi-coupled approach can be safely used in preliminary/intermediate design stages, since they provide a given level of conservatism. Next, we will assess the results for the risers that were obtained using simpler models on stages IIa and IV. We will not compare specific structural results: the number of results is rather huge (in terms of tensions, moments, curvatures, and stress components for any given node of the FE mesh that discretize the risers). Considering that we have 24 risers, discretized with different FE meshes along the different analyses, and submitted to a large number of loading cases, such comparison would not be practical. Therefore, the comparison between the results from the different stages of the design methodology is presented here directly in terms of the verification of the design criteria, which is the most relevant aspect regarding the proposed methodology. However, confirming what have been stated along the text, from the results we have observed that the semi-coupled scheme is indeed not able to provide the accurate detailed structural response of the risers (including for instance tensions and moments near the touch-down zone), because the meshes are not refined enough. This confirms that the difference between the fully-coupled and semi-coupled analyses is notably larger for the riser structural response than for the mooring response. As mentioned in Section 7.3 (and depicted in Fig.10), the most frequently violated criterion has been the MBR on flexible risers, followed by interference. Regarding interference, the results of the analyses of stage VI with the fully coupled model did not indicate any violation. The results in terms of MBR are summarized in Table 8, for all risers whose top connections are displaced approximately in the “near” direction. The results from the fully coupled models confirmed that, in cases 3 and 9, no MBR has been violated.

Table 7 Comparison of mooring results from stages IV and VI (semi-coupled and fully coupled analyses). Case no.

Analysis type

Offset (m)

Mooring line tension (%MBL) L1

L2

L3

L4

L5

L6

L7

L8

3

FC SeC FC SeC FC SeC

112.8 119.1 111.5 114.3 113.7 114.7

32 33 48 50 37 38

19 19 36 38 42 43

13 13 18 19 31 33

13 13 14 15 20 21

15 15 12 13 13 14

19 19 13 13 12 13

50 51 24 25 15 15

50 51 34 36 18 18

8 9


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Fig. 13. Governing cases corresponding to selected offset points.

However, case 8 presents a violation of the MBR on riser 15 (depicted in the bold entries of Table 8). As indicated on Fig. 13, this case corresponds to an offset on the SSE direction; observing the SAFOP results on Table 5, for this direction the violated criterion is also MBR, but there the violation was identified on riser 16. This may be attributed to the simplifications assumed on the uncoupled model employed for the generation of the SAFOP curve: the offsets determined by the coupled analysis are not restricted to any given direction, and even with the application of environmental loadings on the SSE direction the mean vessel planar motions slightly deviated to the SSE direction. Along this direction, riser 15 is the most aligned with its corresponding “near” direction, therefore being more demanded in terms of TDZ bending radius.

Table 8 Assessment of riser criteria: MBR. Riser

9-Flex 10-Flex 11-Flex 12-Flex 13-Flex 14-Flex 15-Flex 16-Flex 19-Flex 20-Flex 21-Flex 22-Flex 23-Flex 24-Flex

MBR (m) Case 3

Case 8

Case 9

e e e e e e 18.8 13.3 20.4 9.8 13.7 64.3 104.3 139.3

59.5 53.3 60.7 50.1 31.8 27.9 4.7 8.7 20.5 24.6 34.7 114.2 151.0 165.3

21.0 16.6 19.1 15.4 7.9 7.5 30.4 41.1 67.4 81.8 93.8 e e e

Limit (m)

Status

5 5 10 5 5 5 5 5 5 5 5 10 10 5

Ok Ok Ok Ok Ok Ok Violation Ok Ok Ok Ok Ok Ok Ok


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Finally, the revision of the other relevant utilization criteria did not indicate any violation. The main results are summarized in Tables 9 and 10, respectively in terms of von Mises stresses, top tension and seabed connection tension. All maximum values of VM stresses occurred on the riser TDZ, with the exception of riser 18 in case 8, where the maximum value occurred at the top zone; in all cases, the maximum values are well below the limit. The values of seabed connection tension are also well below the limit, while the top tension for riser 6 in cases 3 and 8 approached the limit, but stayed about 10% below. 8. Final remarks and conclusions We would like to point out the more relevant characteristics of the proposed mooring/riser design methodology. Firstly, in the initial/intermediate stages simplified simulations are performed; more refined models are gradually introduced. To illustrate the CPU requisites of the different analysis types, in the case study a representative uncoupled (prescribed motion) riser analysis for one 1-h simulation required around 0.25 h (15 min) on a typical Intel Core I7 CPU; an analysis using the semi-coupled strategy (described in Section 2.1.3) required 4.5 h (270 min), while a representative fully coupled dynamic analysis required 73 h (4380 min). This means that the semi-coupled scheme represents approximately 7% of the execution time of a fully coupled analysis. As could be seen in the results presented in Table 7, the semi-coupled strategy represents an attractive procedure to obtain vessel offsets and mooring line tensions in intermediate design stages, due to its low computational costs and adequate accuracy. Another (and perhaps more important) positive characteristic of the proposed methodology is that the design processes related to the mooring lines and risers are gradually integrated along its different stages (preliminary, intermediary, advanced), and are incorporated in a single project spiral, allowing the interaction (or even unification) of the design teams, contributing to gains in efficiency and cost reduction of the final project. The fact that mooring design implicitly considers the riser integrity, and vice-versa, comprises an important advantage over traditional, separate design methodologies. The interaction between mooring/riser analysis models and design criteria begins to be incorporated already in the initial and intermediate stages; the procedure can be automated to provide fast results that ease the decisionmaking processes regarding redesign steps. For instance, the mooring system can be redefined considering criteria related to the integrity of the risers; on the other hand, the risers can be reanalyzed and modified by reducing the “target offsets” (used as premises for analyses on near, far and cross conditions in the preliminary stages), based on the maximum vessel offsets from the offset diagrams. In the advanced design stages, this exchange of information between mooring/riser also allows the definition of criteria for the selection of governing/critical loading cases to be revised and verified in

Table 9 Assessment of riser criteria: von Mises stress. Riser

VM stress external wall (%VM) Case 3

Case 8

Case 9

17-SCR 18-SCR

51.2% 42.9%

52.6% 42.5%

36.2% 37.5%

Table 10 Assessment of riser criteria: top and bottom tensions. Case

% of TT limit

Riser

% of SCT limit

Riser

3 8 9

90% 90% 70%

6-Flex 6-Flex 6-Flex

52% 58% 52%

2-Flex 2-Flex 24-Flex


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detail with more refined numerical models. This leads to the reduction of the original loading case matrix, allowing a feasible use of time-consuming fully coupled analysis. It should also be pointed out that the numerical models generated at the initial/intermediate stages can be reused in subsequent stages; for instance, the uncoupled model for the risers employed to generate the SAFOP diagrams (with the risers discretized by refined FE meshes) can be employed again to perform the analyses for the non-governing cases in stage VI; and can be added to the simplified coupled model employed to generate the offset diagrams, to comprise the fully coupled model employed for the verification of the governing cases. This has a positive effect on the documentation and repeatability of the design process, contributing to control the provenience of the models that were employed to perform the analyses. Although here we did not focus on the stages related to fatigue and installation analysis, the proposed procedures can be extended to the estimation of fatigue life of FPS components. This is normally done using different sets of analyses, performed separately for mooring lines, rigid risers and flexible risers; instead, following the proposed integrated methodology, fatigue on mooring lines and risers can be evaluated from results of single coupled analyses using hybrid methodologies similar to the semicoupled scheme. To conclude, the proposed integrated mooring/riser design methodology presents interesting characteristics for its application in FPS projects in deep and ultra-deep waters. Of course further studies should be performed before completely establishing its use for practical situations, including its full application to case studies on different types of FPSs, and comparing its results to the ones obtained by conventional design methodologies. Such studies are currently underway, including aspects related to the final stages of fatigue and installation procedures. Another issue that is currently being investigated is the association of the SAFOP diagrams for the risers with the offset diagrams for the mooring system, in the context of optimization procedures to obtain an overall cost-effective system. Preliminary results were presented in Ref. [50]; more detailed studies are presently underway, to formulate the appropriate criteria and methodology to be implemented in the optimization tool. Acknowledgements The first author would like to acknowledge Mexican Petroleum Institute (IMP) for allowing the realization of his doctoral studies at PEC/COPPE/UFRJ. Support from the Brazilian and Mexican funding agencies CNPq and Conacyt-Sener-Hidrocarburos is also acknowledged. Finally, the authors would like to acknowledge the active support from Petrobras (the Brazilian state oil company), particularly from Dr. Stael Ferreira Senra of CENPES e Petrobras Research Centre, who had contributed positively with discussions and valuable suggestions. References [1] API RP 2SK. Design and analysis of stationkeeping systems for floating structures. 3rd ed. American Petroleum Institute; October 2005. [2] DNV-OS-E301. Position mooring. Det Norske Veritas; October 2010. [3] ISO 19901-7. Petroleum and natural gas industries e specific requirements for offshore structures e part 7: stationkeeping systems for floating offshore structures and mobile offshore units. 1st ed. International Standard; 2005. [4] API RP 2RD. Design of risers for floating production systems (FPSs) and tension-leg platforms (TLPs). 1st ed. American Petroleum Institute; June 1998. [5] DNV-OS-F201. Dynamic risers. Det Norske Veritas; October 2010. [6] ANSI/API Spec 17J. Specification for unbonded flexible pipe. ISO 13628-2:2006 (identical). 3rd ed. American Petroleum Institute; July 2008. [7] ANSI/API RP 17B. Recommended practice for flexible pipe. ISO 13628-11:2007 (identical). 4th ed. American Petroleum Institute; July 2008. [8] Ormberg H, Larsen K. Coupled analysis of floater motion and mooring dynamics for a turret-moored ship. Appl Ocean Res 1998;20:55e67. [9] Connaire A, Kavanagh K, Ahilan RV, Goodwin P. Integrated mooring & riser design: analysis methodology. OTC-10810. 1999. [10] Senra SF, Correa FN, Jacob BP, Mourelle MM, Masetti IQ. Towards the integration of analysis and design of mooring systems and risers, part I: studies on a semisubmersible platform. In: Procs of the 21st int. conf. on offshore mechanics and Arctic engineering; 2002. Paper OMAE 2002-28046, Oslo, Norway.

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