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Optimization Procedure of Steel Lazy Wave Riser Configuration for Spread Moored FPSOs in Deepwater Offshore Brazil Edmundo Queiroz de Andrade, Ludimar Lima de Aguiar, Stael Ferreira Senra, Elizabeth Frauches Netto Siqueira, Ana Lucia Fernandes Lima Torres, Marcio Martins Mourelle/ Petrobras S.A

Copyright 2010, Offshore Technology Conference This paper was prepared for presentation at the 2010 Offshore Technology Conference held in Houston, Texas, USA, 36 May 2010. This paper was selected for presentation by an OTC program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Offshore Technology Conference and are subject to correction by the author(s). The material does not necessarily reflect any position of the Offshore Technology Conference, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Offshore Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of OTC copyright.

Abstract

The interest in the application of a SCR connected to a FPSO for exploration and production in deep water, has motivated the need to carefully study this concept due to the high offsets and vertical motions imposed by the vessel at the top of the riser. Petrobras has developed through its Research Center the study of different steel riser configurations. For bow turret-moored and spread-moored FPSOs based on VLCC converted hulls, the steel lazy-wave riser (SLWR) has been considered as an adequate solution due to its structural dynamic behavior and costs when compared to other configurations. Although the SLWR furnishes acceptable results for fatigue and extreme environmental conditions, the search for the best configuration is very demanding as any changes to a geometric parameter affect its whole structural dynamic behaviour. The search for configurations that meet all the code criteria for the riser project required meticulous detail that has not always lead to the best results because the number of variables involved is quite significant. Another important aspect is the installation procedure that can also influence the final configuration. In order to reduce the engineering time in generating and analyzing several configurations, optimization tools were studied and used in association with Petrobras in-house software to help define a model that could achieve all design verification phases more easily. This paper presents the experience with the use of an optimization procedure applied to facilitate the design of a SLWR connected to a FPSO unit offshore Brazil. The process of optimization begins with a set of preliminary geometric variables and constraints that are associated with multiple objectives related to economic, construction and safety factors. The result of the optimization process is a set of feasible configurations from which, through careful selection, the "one of the best" configuration is chosen. Introduction At the end of the nineties, Petrobras became interested in the application of steel catenary risers connected to a FPSO for exploration and production in deep water which in turn has motivated the careful investigation of this concept. The Campos Basin environmental characteristics and the dynamic behavior of a FPSO based on VLCC converted hulls led to high offsets and vertical motions imposed by the vessel at the top of the riser. For a free-hanging configuration these motions cause high stress range levels leading to high fatigue damage, mainly in the touch down zone (TDZ). Flexibilization elements, such as buoyancy modules, allow a reduction of motions arriving at the TDP making the use of the steel catenary riser feasible. The studies concluded that the lazy-wave configuration was adequate and attractive due to its structural dynamic behavior and costs when compared to other configurations [1] [2] [3] [4] [5]. The project of a steel lazy wave riser (SLWR) needs to meet the same design criteria used for the free-hanging configuration design. Basically, the DNV-OS-F201 code [6] was used in this work. All the verification tasks carried out demanded a huge amount of computer analysis. The main tasks are the Extreme Load Riser Strength Analysis, Fatigue Analysis, Interference Analysis and Installation Analysis. The search for the best riser configuration characteristics that match all task design criteria, based on a trial and error procedure, demands a huge effort and is time consuming. This is because of the significant number of variables involved and the model is sensitive to any variation in the parameters such as top angle, length, thickness, buoyancy modules characteristics and extension, fairings or strakes, etc,

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affecting the whole configuration. Moreover, the optimum configuration for the Extreme Load Analysis may not meet the Fatigue criteria and vice-versa. Another important aspect in the lazy-wave definition is the installation phase, when the riser assumes configurations different from those in-situ. During the installation, and considering the riser empty, the presence of the buoyancy modules influences load distribution and geometry so that even if all the code criteria have been accomplished for the other verification tasks, the riser may not be able to be installed [7]. These particular SLWR characteristics led to an iterative procedure to define the feasible configuration. Therefore, in order to reduce the effort in generating and analyzing several configurations, optimization tools have been studied to facilitate the definition of a model that could accomplish all design verification phases more easily [8]. Among them, the ModeFrontier software [9] was adopted due to the optimization algorithms available and its pre and post processing facilities. Besides, the successful previous experience in Petrobras of ModeFrontier in offshore platform sizing optimization also motivated its adoption [10]. In this work the optimization of the SLWR configuration was based on the Extreme Load Analysis, more specifically, on the most critical load case, since this design criterion had been identified as critical to the project. This is justified by the following facts: deep water scenario with SWL beyond 2000m, severe extreme environmental conditions, connection to FPSO vessels, high-pressure and corrosive fluid production. The process of optimization begins with a set of geometric variables and constraints which are associated with multiple objectives related to economic, construction and safety factors. The result of the optimization process is a set of feasible configurations from which, through careful selection, the "one of the best" configuration is chosen.

Load Case and Riser Position: Selection of those most critical

Extreme Load Analysis conditions were defined based on the combination of wave curves (represented by pairs of Hs x

Tp) with the associated current profile, for each direction and each return period (1yr, 10yr and 100yr), according to the Santos Basin Meteocean Data Report [11]. Based on the eight main directions provided for the wave direction, a linear interpolation between Hs neighboring directions was adopted, creating 8 intermediate directions, leading to a number of approximately 2500 loading cases.

In accordance with the naval architecture team, a standard FPSO based on a VLCC hull was chosen which provided the worst condition in terms of motions to be imposed on the top of the risers. A study was established in order to find the FPSOs most favorable heading for the riser design. This study concluded that a heading range between 180 and 210 should be used, as shown in Figure 1.

YG

XGEW

NW

SE

NE

SW

SSESSW

NWW

SEE

SWW

NEE

NNE

210

NNNW

180

S

H

YL

XL

YG

XGEW

NW

SE

NE

SW

SSESSW

NWW

SEE

SWW

NEE

NNE

210

NNNW

180

S

HHH

YL

XL

Figure 1 - Range of headings required for the riser design

In preliminary studies, before applying the optimization process, several SLWR models were generated for different

functions and azimuths positions, according to the subsea layout available, as shown in Figure 2. The configurations were generated by using the trial an error procedure that revealed unsuccessful models or ones that were very close to the limit of design criterion.

To overcome some of these difficulties, the sensitivity of the model response to the drag coefficient was studied and the use of fairings instead of strakes as a vibration suppressing device was adopted, although being more expensive and having limitations for some regions of the riser.

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Figure 2 - Subsea layout for rigid risers

Still before using the optimization process, a vessel maximum motion criterion was generated for the FPSO hull design that

would operate in the intended location, so as to enable a feasible riser design. Based on previous experience, it was known that the vertical motion magnitude had an important influence on the SCR dynamic response and had to be minimized. In this case, as the floating unit was a spread moored FPSO, a roll motion limitation was also included in the criterion. Maximum displacement and acceleration values were established for vertical and roll motions to be obeyed along a certain length around the midship, both towards the bow and stern where the SLWR could be connected.

Following extensive Extreme Load Analysis of all the rigid risers of the subsea layout available and all the involved loading cases, it was possible to identify the most critical riser position (the farthest from the midship towards the stern) and the most critical environmental load associated with this critical riser.

Thereafter, the optimization process was started varying the parameters of the riser configuration, as subsequently described in this work.

Aspects of VIV analysis

At the TDP (touchdown point), the fatigue damage due to VIV can be more critical than that due to wave and imposed top

motions. So, it is very important to evaluate this criterion immediately following the optimization process, in order to verify a suitable position for the vibration suppressing devices.

The VIV analyses were performed with SHEAR7 software [12] with a set of representative sea current profiles defined in the Santos Basin Meteocean Data Report [11].

A bi-dimensional methodology was used, i.e., all the current profiles have been considered as acting in-plane or out-of-plane of the riser. The directions of the whole current profile were modified to act just in-plane or out-of-plane. The out-of-plane currents turned out to be the worst cases in the VIV analyses. This methodology is available in ANFLEX (Petrobras in-house software) [13] that automatically generate files, for each current profile, that are the SHEAR7 input.

The VIV fatigue damage for the in-plane and out-of-plane cases have been calculated using the same stress concentration factors and S-N curves employed in the wave fatigue analysis. The natural frequencies and the corresponding mode shapes and curvatures have been obtained by means of ANFLEX.

The VIV fatigue damage in some critical points tended to be higher than in the rest of the riser, because of the high curvature at these points (TDP, SAG and HOG). SHEAR7 is a frequency-domain mode-superposition program and, consequently, the TDP position does not change during the dynamic analysis. Another point to be considered is that all the VIV analyses were performed without taking into account the platform offset due to the current action. These two aspects impose the fatigue damage concentration at a single point in the touchdown zone (TDP).

A post process graphical interface to SHEAR7 was developed to visualize the main results, making it easier to identify the power-in regions, where it could be necessary to install VIV suppressors. This procedure is illustrated in Figure 3.

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Figure 3 - Illustration of the graphic interface for evaluation of SHEAR7 results

Aspects of Installation Analysis Release

Following the optimization process, an important step is to verify the feasibility of the chosen configuration for the

installation vessel critical positions in relation to the FPSO. The Installation Analysis was performed focusing on identifying the maximum tension forces, maximum stresses and

verification of compression during the riser installation procedure. The analyses were performed considering the riser empty. Some installation vessel positions were analyzed trying to

reproduce different buoyancy modules position. For each position, a length of installed riser was chosen in order to minimize stresses, maintaining top angles at acceptable levels, so, different riser configurations were analyzed, as shown in Figure 4.

buoyancy

strakes

pipe

pipe

Platform Vessel installationVessel installation Vessel installation Vessel installationVessel installation

Riser configurationwith oil

Other configurations: Riser empty

buoyancystrakes

pipe

buoyancy

strakes

pipe

pipe

Platform Vessel installationVessel installation Vessel installation Vessel installationVessel installation

Riser configurationwith oil

Other configurations: Riser empty

buoyancystrakes

pipebuoyancystrakes

pipe

Figure 4 - Some of the riser configurations for Installation Analysis

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For some of the above configurations, the impact of buoyancy modules position and dynamic amplification due to installation vessel motions could lead to very critical stresses results.

The consideration of the riser full of water would ease the high stress level problems close to the buoyancy modules region, but would also increase the forces to be supported by the installation vessel in a very deep water location. That was the reason why the empty riser condition has been set as a requirement for the riser design.

Project steps

In this work, the adopted analysis steps and sequence for a riser design using an optimization process is schematically shown in the following flow chart:

Anflex Model

Identification of the CriticalCase (Extreme)

OptimizationOptimization

Wave Fatigue Analysis

Heuristic Selection

VIV Fatigue Analysis

Instalation Analysis

Extreme Loads Analysis

ReviewOptimizationParameter

Review Model

Anflex Model

Identification of the CriticalCase (Extreme)

OptimizationOptimization

Wave Fatigue Analysis

Heuristic Selection

VIV Fatigue Analysis

Instalation Analysis

Extreme Loads Analysis

ReviewOptimizationParameter

Review Model

Figure 5 Steps of the analyses involved in the optimization process

Optimization procedure

The tool used to carry out the optimization process was the program ModeFrontier from ESTECO, which had been previously successfully used by Petrobras to optimize offshore platform motions [10]. This program enables the user to set up the analyses or workflow sequence and it also verifies if the riser configurations generated during the optimization process satisfy the constraints and objectives.

The optimization process was performed with a SLWR configuration in the worst position and submitted to the most critical loading case, named seed. The seed was modeled by ANFLEX and represented the base case for the generation of all population during the optimization process.

Special care was taken to choose a seed that would converge on a viable and optimal configuration at the end of the optimization process.

Figure 6 illustrates an overview of the analyses sequence set up in the ModeFrontier software.

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InputData

OutputData

AnflexAnalyses Testof

differentSpecific Weight

FeasibleConfigurations

Testof theGeometricLimits

InputData

OutputData

AnflexAnalyses Testof

differentSpecific Weight

FeasibleConfigurations

Testof theGeometricLimits

Figure 6 Workflow in ModeFrontier

In this work the NSGA-II Non-dominated Sorting Genetic Algorithm II of prof. K. Deb et all [14] has been used. Genetic

algorithms are a particular class of evolutionary algorithms that make use of natural principles of selection and evolution to explore design space in the search of an optimal configuration. The algorithm starts with a set of designs, called initial population, which can be randomly generated. In this study the initial population had 50 designs (or riser configurations). Each individual is evaluated and classified according to its efficiency and feasibility, and a new population is formed based on the evolution of existing designs. The principle of natural selection indicates that the best designs have a better chance to be selected during the evolution operations (cross-over and mutation).

Input Variables

The optimization process begins with the variables of the problem definition. Figure 7 schematically shows some of the

variables that are used to set up a lazy-wave configuration. The main geometrical parameters are the length of segments, L1, L2 and L3 and the top angle of the line ().

Figure 7 Geometrical parameters used in optimization process

Other important parameters used on the workflow are the diameter of the floaters (HDf), the length of the floaters (Lf) and the spacing between them (Spac), as shown in Figure 8.

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L f Spac Spac L f

Hdf Hdr

L f Spac Spac L f

Hdf Hdr

Figure 8 Floaters parameters used in the optimization process All the variables described above are supplied to the seed configuration file and can vary within a range of pre-established values. Output Variables

For each configuration, several variables are posted to the output data such as: maximum total horizontal projection, suspended length projection, distance between the TDP and the PLET/anchor point, suspended length and riser length, the number of floaters and the floaters buoyancy force.

All these variables will also support the engineer to choose a specific configuration as one of the best.

Constraints Test of the geometric limits

In the first phase of the optimization process the configurations generated were tested to verify if they were within a geometric feasible range. The parameters that control this test are the maximum and minimum heights of the lazy-wave hog and sag regions as shown in Figure 9 (Zmin and Zmax). The Zmax limit is imposed to avoid interference problems with neighboring lines as the high current velocities in the mid depth region can cause large displacements when acting on the riser buoyancy modules segment. The Zmin value is to avoid the sag segment touching the seabed when full of water. The shape of the floaters is also controlled to keep a defined aspect ratio.

Figure 9 Sag and Hog regions of a Lazy-wave

The horizontal distance between the top connection point and the seabed connection (PLET) was given as a constraint, and

came as a subsea layout requirement. A minimum distance between the maximum TDP position obtained in the dynamic analysis and the PLET was also given in order to avoid the occurrence of high values of axial loads at the anchor point of the riser.

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ANFLEX analyses The acceptable configurations are then submitted to static and dynamic analyses using the ANFLEX software. The results

were verified according to the DNV Offshore Standard [6]. After the analyses, all the configurations that fulfilled DNV criterion were considered as feasible configurations. Objectives

A great number of feasible configurations were generated. The choice among all the viable solutions was made taking into account 3 main objectives: the minimization of the floaters volume, the tension force at the riser top and the code criterion.

The minimization of the floaters volume is important for the installation process as the number of floaters has to be minimized to reduce the installation time and cost. It is also important to maintain the load levels within an acceptable range during the installation procedure.

The minimization of top tension force is considered critical for large diameter risers. Other different variables may be used as objectives, depending on the riser function or application.

Test of different specific weight

The previously described procedure was performed considering the fluid mean specific weight. As schematically shown in Figure 6 the feasible configurations were also tested by the minimum and maximum values of the operational fluid specific weight. Each configuration considered viable after these tests, was stored in the general database of feasible designs.

Finding the best solution - Merit functions

Some variables, herein referred to as merit functions, are very important to be analyzed and will indicate the best

configuration. These merit functions can be plotted on graphs as shown in Figure 10. This graph relates the values of the utilization factor, the volume of the floaters and the values of the buoyancy force in the legend for each configuration.

A maximum value of buoyancy force per length was used in order to mitigate high stress occurrence during the installation phase. This value had already been set in a previous Installation Analysis.

In the graph it is possible to refine the search for configurations around a specific value. The dark blue bubbles near the graph origin correspond to the best solutions.

Search region of interest.

DNV Utilization Factor

Search region of interest.

DNV Utilization Factor

Figure 10 - Bubble 4D Results

Finding the best solution - Feasible configurations The ultimate goal is to reach a set of feasible configurations. In this work, a large number of analyses were carried out

reaching a set of solutions. Figure 11 shows the distribution of results between feasible and unfeasible configurations after the optimization process.

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FeasibleConfigurations (14932analysis)

Configurationsthat Break theConstraints of the Project(1713analysis)

Configurationsthat Breakthe Geometric Limits (5791analysis)

22436 analysis with ModeFrontier

FeasibleConfigurations (14932analysis)

Configurationsthat Break theConstraints of the Project(1713analysis)

Configurationsthat Breakthe Geometric Limits (5791analysis)

FeasibleConfigurations (14932analysis)

Configurationsthat Break theConstraints of the Project(1713analysis)

Configurationsthat Breakthe Geometric Limits (5791analysis)

22436 analysis with ModeFrontier

Figure 11 Design Summary

The most practical way to choose the configuration is to plot several parameters on the same graph, as shown in Figure 12. In this kind of graph it is possible to change the range of values for each parameter. These refinements make it easier to find the best solution.

Figure 12 Parallel Coordinates Results of a Case Study

A 20 inch (0.508 m) nominal diameter gas export riser in 2200m of water depth was studied. The comparison between two lazy wave configurations (the seed one and the chosen optimized one) shows that the stress

level is around 22% lower in the optimized case. As previously stated, the optimization process was performed just for one extreme loading case. The complete Extreme

Load Analysis and other verification analyses such as Installation, Fatigue, etc, were performed outside the optimization process. So, based on a previous experience of the Installation Analysis, it was decided that the net distributed buoyancy in the floaters segment, named a merit function, should receive a higher priority. As a result, an increase of 9.8% in the tension force at the riser top was obtained when compared to the seed configuration.

Additionally a reduction of 3.2% in the total length of the riser and 58% of the floaters volume has been achieved. Table 1 shows some results for other variables that presented an improvement with the optimization process. There was

also a significant change in the top angle from 8.3 to 10.

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Table 1 Difference in values obtained (optimized versus seed configuration) Percentage Differences (%)

Riser Length (m) -3.17 Internal von Mises stress (MPa) -21.59 DNV Utilization factor -24.10 Maximum top tension force (kN) 9.84 Floaters Volume (m3) -9.08 Net Dist. Floater's Buoyancy Force (kN/m) -58.11

The distances between the sea bottom and the extreme points of the lazy wave riser sag and hog segments had their values

significantly changed. Figure 13 shows the change in the shape of the lazy wave, making it smoother than the original configuration.

Figure 13 Seed and Optimized configurations

Conclusions This paper presented a preliminary approach to use optimization techniques as a way of reducing the effort of generating steel lazy wave riser configurations that meet design code criteria. The study performed on a SLWR for a water depth of 2200m demonstrated that optimization tools are very attractive to be used in riser design as they can potentially save a lot of engineering time by reducing the number of design cycles that would be necessary in order to achieve feasible solutions by the traditional means. For other risers also studied, the employment of the optimization procedure has given an important safety margin and a good increase in the riser compliancy, making it possible to accept higher motions from the floating unit. Due to the complexity of the SLWR configuration and its sensitivity to parameter changes, the use of optimization techniques was applied, primarily, to search for configurations that meet the Extreme Load Analysis criteria. Further studies will incorporate other verifications, such as Installation, VIV, Fatigue, Interference, etc, in order to generate more robust designs.

Acknowledgements To the Petrobras PROCAP-3000 coordinator, Mauricio Werneck de Figueiredo, for the support, interest demonstrated in the solution and the incentive to this paper elaboration. To Mr. Roger Wilkinson for the support to the English text revision.

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