Rapid Design Exploration to Determine Feasible FPSO

8/6/2019 Rapid Design Exploration to Determine Feasible FPSO

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Altair Engineering 2007 11-1

Rapid Design Exploration to Determine Feasible FPSO and Spar

SystemsJohn ShanksRiserTec

Arnhall Business Center, Arnhall Business Park, Westhill, Aberdeenshire, AB23 [email protected]

Abstract

The riser design process is well established and uses verified simulation tools to predict response toenvironmental loading. Design optimization is an established technology which has been widely used in otherindustry sectors including aerospace and automotive. Riser systems show inherently non-linear sensitivity toapplied loading and parametric changes. For this reason response surface methods are required foroptimization. The paper discusses two example riser configuration design problems and describes integration ofAltair HyperWorks design optimization technology with the existing design process. The optimization proved tobe efficient and repeatable. The designs produced for each configuration proved to be strong improvementsover the baseline starting points and the wealth of information on sensitivity provided deeper understanding ofthe factors influencing design performance.

Keywords: Riser Design, Optimization, Flexcom, Orcaflex, HyperWorks

1.0 IntroductionComputer aided engineering (CAE) has for a long time been part of the Riser design process. The use ofadvanced simulation tools for capturing response in the offshore environment has enabled efficient derivation ofhigh-quality designs. Automating the CAE driven design process using optimization technology is the next stepand this paper describes two example applications: a spar riser system and a FPSO steep wave riser system.

The benefits of design optimization are well known and have demonstrated capability to increase theperformance of engineering systems, reduce time to market and provide deeper understanding of the factorsinfluencing performance. Response surface technology [1] is used as the basis for the optimization examples inthis paper and provides a method for optimizing highly non-linear systems. When used with the correct samplingmethods, these processes can provide a very efficient means of fully exploring the design space, helping withidentification of general system characteristics and assessing reliability.

A typical riser design process is shown (Figure 1). The design process is complex and the ultimate solutionmust meet a diverse range of often conflicting requirements. Optimization can play a part early in the designprocess and help to speed up development of initial concepts. The details of the process and implementationare provided for each example.

The spar riser system is commonly used with a floating platform which contains tensioning equipment to keepthe riser in the correct configuration. In common with the Steep wave Riser the system has to be able towithstand environmental wave loading, and in the case we will look at a specific wave loading event known tocause damage to such systems.


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Altair Engineering 2007 Rapid Design Exploration to Determine Feasible FPSO and Spar Systems 11-2

Figure 1: Overview of a Typical Riser Design Process

The steep wave riser system design example is a typical FPSO System (Figure 2) and must be shown to becapable of withstanding enveloping environmental wave loading. The system must be constrained to meetclearance requirements as well as attachment loading limits.

The application of the optimization technology to both examples demonstrates a high level of efficiency inevolving designs from initial concepts. The final solutions have strong scientific basis providing justification for allof the design parameters. A by-product of application of the process is the wealth of information availableregarding sensitivity of the performance to all of the controllable design characteristics.

Figure 2: Typical Spar and Steep Wave Riser Systems

2.0Design Optimization Process for Riser Design2.1 Introduction

The design optimization problem is defined using a standard approach which is general for a range ofengineering design challenges. A baseline model is developed, which is correlated against known response.

A set of design variables are defined which may be geometric (pipe lengths, section geometries), material

characteristics (Youngs modulus, yield stress) or constraint conditions which can be used to allow analysis ofmultiple configurations and therefore assess the most suitable for purpose. A set of experiments are thendefined, which select a number of settings for each of these variables to provide a broad and evenly distributed


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mix of design options. Responses from the simulations (e.g. pipe loads and stresses) are extracted and plottedagainst design variable ranges. The data is then fitted and verified using advanced multi-dimensional surfacefitting technology. Once this data fit is available and verified, optimization algorithms can be deployed to find theoptimum solution.

2.1 Definition of Baseline Model

For the examples in this paper, the baseline design refers to the nominal design produced using the traditional

design approach. This design is modelled using OrcaFlex or FlexCom, and a set of design load cases definedand analysed. The results from this model are compared with expected response providing confidence in theanalysis procedure.

2.2 Design Variable Definitions

Design variables are defined as parametric changes to the baseline model. These are generally geometricchanges such as changes in pipe length or cross section or changes in material properties. These changes aredefined and combined to explore a controlled set of design variations. In the optimization process, the variationsare applied to the model automatically based on carefully chosen weightings defined in a test plan. The designvariables are chosen to fully explore the available options and are selected from a larger set of variables byfiltering those to which the required responses show greatest sensitivity.

2.3 Test Plan Definition

The selection of a good test plan which samples a broad range of designs evenly distributed between thebounds of the design variables is important to provide sufficient data for initial surface fitting. To populate thedesign space, the Extended Uniform Latin HyperCube space filling algorithm is generally used which usesgenetic algorithms to iterate towards the required distribution of samples. Each design sample pointcorresponds to a design iteration which includes a specific set of design variable combinations.

2.4 Submission of Simulations and Response Extractions

Once a test plan has been defined, a single analysis process is performed for each design sample usingHyperStudy and the interface with Orcaflex or FlexCom. Post processing of each analysis run is then performedto extract the responses required for sensitivity assessment and design optimization. These are typically loads

and stresses in the pipe, but may also include relative displacements and clearances between vessel and pipe.The analyses can be run in parallel to take advantage of multi-processor computing systems

2.5 Surface Fitting and Verification

Surface fitting is performed to provide a means of estimating the response continuously across the designspace. The quality of the fit will depend on the gradients of the surface and the concentration of sample points.Since the gradients are not known before starting the design of experiments, the best strategy is to evenly fill thedesign space and check the quality of the fit. A new set of samples are then defined in zones where the fit ispoor and a subset of responses generated before revising the surface fit. This loop is repeated until the fit iswithin acceptable bounds across the design space. Advanced surface fitting techniques are used to give therequired quality of fit to the data, in general the only technique found to give such a quality of fit is the MovingLeast square Method (MLSM).

2.6 Design Optimization

The typical design optimization problem is set up to minimize a cost function (often related to mass, installationor assembly costs), or some physical requirement such as maximum curvature found in the pipe. Constraintsare defined on the remaining responses to limit other component loads in the pipe and displacements.

3.0 Spar Riser Design Optimization

3.1 IntroductionThe spar riser design problem documented in this section is typical of this type of configuration. The riser runsfrom the seabed through a guide structure which is attached to the spar buoy. There is a small clearance


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between guide and riser. Under dynamic loads, this gap opens and closes and gives rise to high local bendingand contact stresses.

3.2 FlexCom Model Development and Baseline Analysis

The spar model (Figure 3) was developed in Flexcom [2] to include a detailed riser model with 9 different riserline segments, the spar buoy and guide to riser contact. Motions were defined for the buoy as time history datameasured offshore.

Figure 3: Spar Model

Figure 4: Maximum Von Mises Stress Envelope vs Riser Height

A dynamic simulation of the spar was performed using the implicit solver in Flexcom. Results for Von Mises

stress along the riser close to the contact zone were extracted using a HyperStudy interface with Flexcom(Figure 4).

3.3 Parameterisation and Design of Experiments

The parameterisation of the model was defined as pipe section variations for each of the 9 sections. A total of 9design variables were defined, each with 19 discrete levels. The chosen values for the sections (Figure 5) wereordered in increasing stiffness to avoid stiffness discontinuities as the design variables a varied throughout theirrespective ranges.

The design of experiments was defined using an Extended Uniform Latin Hypercube, generating 202 analysisruns. We used 202 runs because some of our original runs failed. This occurred in regions where the designvariable combinations werent physically possible, or the models became numerically unstable for other

reasons. HyperStudy allows us to deal with this in the Response Surface Generation phase withoutcompromising the result quality. Of course care has to be taken that there are not too many failed runs withinthe explored space. If this is the case we have to re-evaluate the bounds of the design space we explore. The


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HyperStudy-Flexcom interface was used to generate the models and execute the analysis automatically at eachsample point. Stress results and the overall mass of the riser were extracted and stored as responses for eachrun.

Figure 5: Parameterisation of Riser

3.4 Optimization

A moving least squares approximation was developed for each response and tuned to provide a good fit to thedata. This was an iterative process which involved adjustment of the closeness of fit parameter and review ofthe errors for each point of the matrix. Error reduction in this process has to be balanced against getting a goodquality curvature in the response surface otherwise step changes may occur which mitigate against optimisation(Figure 6). A validation matrix was then constructed and a further set of runs performed. The adequacy of theapproximation fit (Figure 7) to the new results was then assessed and further points added where the fit wasfound to be poor.

Figure 6: Surface Fitting Process


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Figure 7: Example Response Surface

Main effects plots were then generated to assess the sensitivity of the two responses to each of the design

variables (Figure 8). It should be noted that there is a difference in the sensitivity of the mass response to eachof the design variables because each section length is not of equal size. The stress response shows a highlynon-linear relationship with each design variable and is a result of the complex interaction between thevariations of the sections of the line. The main effects plots help to determine which design variables may beremoved from the optimization. Since all design variables had a significant effect on each response, all weremaintained for this example.

Figure 8a: Main Effects Plots for Riser Design Parameters

Figure 8b: Anova Plots for Riser Design Parameters

The optimization was performed with mass reduction as the objective and stress as the constraint. The SQPalgorithm was used to perform the optimization. A further validation GA optimization was performed. As we arenow working on the Response Surface to calculate our results each iteration can be performed in a few secondswhich means we can try different optimisation technologies, and formulate different Optimisation problems veryquickly to explore different hypotheses. The optimal point was verified by performing a final solve in Flexcomwith design variables set at the optimum values (Figure 9).


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Figure 9: Final Optimized Design Parameters and Stress Response

3.5 Discussion of Results

The optimum solution confirmed that the maximum stress was lower than the allowable and that all sections

were highly utilised.

4.0 FPSO Steep Wave Riser Design Optimization4.1 IntroductionThe FPSO example is a typical steep wave riser system provided by Risertec (Figure 10). A steep wave riserformation has support provided at about midwater by distributed buoyancy modules and has a near verticalconnection at the seabed. 'Steep' means that the riser centreline is near vertical at the lowest end while 'Wave'describes the line shape as a result of the buoyancy modules.

Some of the key design requirements for a system of this configuration include:

i) Limiting maximum and minimum tension

ii) Limiting maximum curvature

iii) Controlling of the pipe clearance from the seabed and vessel during dynamic excitation

These design requirements form the basis of a set of responses for the design optimization process. The designvariables for this system are lengths of the various pipe sections. The overall objective for the design is tominimize the pipe curvature.


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Figure 10: Riser Configuration Examples

4.2 OrcaFlex Model DevelopmentThe Orcaflex model was developed based on good practice for a starting point steep wave riser design. Threesections of pipe were defined, with the central section defined as buoyant. Three configurations were chosen tocover the main design conditions:

i) Static datum position

ii) Near Condition (Figure 11)

iii) Far Condition (Figure 11)

A single water depth was selected for each configuration.

Figure 11: Steep Wave Riser Example Showing Datum, Near and Far Configurations

A single pipe section was used for the model with properties as summarised in Table 1.

Section PropertiesLine Identifier Length

OD ID Mass/Unit Length

Riser

Buoyant Riser

Riser

137

70

32

0.354

0.630 (buoyant)

0.354

0.254

0.254

0.254

0.15

0.15

0.15

Table 1: Summary of Line Parameters


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4.3 Baseline AnalysisThe baseline analysis provides verification that the analysis setup is specified correctly and that the responsescan be extracted using the interface between HyperStudy and OrcaFlex. Baseline analysis was performed inthree stages:

i) Static Analysis of DATUM position to define Azimuth and Declination angles

ii) Dynamic Analysis of Near Condition using the DATUM angles (100 year wave)

iii) Dynamic Analysis of Far Condition using the DATUM anlges (100 year wave)

Results were extracted for logging in HyperStudy for items ii and iii for ship clearances, peak tensions andmaximum curvature.

Snap shots of the dynamic response for the Far and Near positions and the variation of curvature along the pipelength are provided (Figure 12).

X

Z30 m

OrcaFlex 9.0a:NEAR.dat( modified 12:20 on 30/03/2007 by OrcaFlex 8.3a) (azimuth=270;eleva tion=0)

Replay Time:-3.20s

X

Z30 m

OrcaFlex 9.0a:NEAR.dat( modified 12:20 on 30/03/2007 by OrcaFlex 8.3a) (azimuth=270;elevation=0)

Replay Time:1.80s

X

Z30 m

OrcaFlex 9.0a:NEAR.dat(modified 12:20 on 30/03/2007 by OrcaFlex 8.3a) (azimuth=270;elevation=0)

Replay Time:7.70s

Figure 12: Dynamic Response to Wave Loading for Baseline Design

The dynamic response of the line in the far and near conditions is as expected and clearances from the vesseland seabed are within acceptable limits for both cases. No compression was detected in the line throughout thesimulations.

4.4 Parameterisation and Design of ExperimentsThree design variables were defined for the optimization, namely the lengths for the three line segments. Table1 provides a summary of how the lengths were varied for each line. The parameters were varied automatically

using HyperStudy and the interface with OrcaFlex.To populate the design space fully, an Extended Uniform Latin Hypercube space filling approach was used. Onehundred and twenty designs were defined to provide the resolution required for surface fitting (Figure 13). Thisprovided a thorough examination of the design options within the practical limits of the system. The number ofsamples was relatively high for three design variables, but could be run very efficiently thanks to the implicitsolution technique.

Figure 13: Design of Experiments Sample Points Shown for 3 design Variables

A suite of solves similar to the baseline analysis was performed for each sample point. Responses wereextracted automatically for each analysis and stored in HyperStudy.


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4.5 Surface Fitting and Design OptimizationThe optimization process commences with generation of a fit to the response data generated in the DoE stage.A separate data fit was implemented for each response. The data fitting technique was MLSM, as for the sparexample. It was not necessary to run a further validation matrix for this example since the sample point densitywas large for the number of design variables. Parameters for the MLSM fit were chosen carefully to achieve agood trade-off between fit accuracy and smoothness of the response surface (Figure 14). This was performedin an iterative loop, starting with adjustment to the closeness of fit parameter followed by examination of the

errors for each point in the matrix (Figure 15).

Figure 14: Approximation Build Panel

Figure 15: Residual Evaluation Plot

The design optimization problem was defined as:

Objective: Minimise Max Curvature

Constraints:

Ship Clearance >= 2.5m

Seabed Clearance >= 2.5m

Minimum Tension >= 1kN

Maximum Tension


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optimum where other techniques may fall into local optima. Restarting SQP from the GA optima allows us to findthe real optimum point that the GA has indicated for us. Finally, a validation run was performed using Orcaflexwith the optimum design variable settings to produce a final set of responses (Table 2).

Objective Constraints Design Variables

DescriptionCurvature(Minimise)

PercentImprove.

ShipClear.

(>=2.5m)

SeabedClear.

(>=2.5m)

MinTens.

(>=1kN)

Max Tens.(


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5.0 Conclusions

The examples have demonstrated that an existing design optimization process can be applied successfully toriser design without any further enhancements. The solution is implemented in Altair HyperStudy and interfaceswith widely used riser design software systems. There is no need for any fundamental research to broaden thereach of the technology. There is a need to explore a wider range of riser design problems and to address somemore of the design issues and practical constraints. Vessel offset positions, fatigue load cases and different riserconfigurations are all areas where further focused study is required.

The benefits of using the response surface approach have been identified through application of the process.Design sensitivity information is automatically produced by the process, which can be assimilated with theresponse surface visualisations to provide a much greater depth of understanding of the design problem. Theaspects of the design which have the greatest influence on key responses can be identified through thesensitivities. The shape of the response surfaces, bounded by the variable ranges, can help to identify whetherthe general configuration can be made robust (smoother surfaces) or if it is inherently unstable (highly non-linearsurfaces). Once a verified data fit has been defined, a range of assessments can be made including designoptimization and robustness assessment. The sampling strategy for definition of the DoE provides a practicalmanageable number of analyses, making the technology suitable for commercial use.

Two design optimization examples have been documented. The spar example provided a minimum mass

solution which would meet peak stress requirements with a practical manufacturable solution. In the secondexample a steep wave riser example was optimized to minimize curvature subject to constraints on seabed andvessel clearances. A 10% reduction in maximum curvature was achieved even though the response surfacewas highly non-linear.

6.0 References

[1] HyperWorks Version 8.0, Altair Computing Inc., 2006.

[2] FlexCom v7.1, MCS, 2006

[3] Orcaflex v9.0, Orcina Ltd, 2006

Documents

Rapid Design Exploration to Determine Feasible FPSO