COMPARISON OF FULL-SCALE MEASUREMENTS WITH CALCULATED MOTION CHARACTERISTICS OF A WEST OF AFRICA FPSO

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1 Proceedings of OMAE3 ND International Conference on Offshore Mechanics and Arctic Engineering June 8 3, 3, Cancun, Mexico OMAE3-378 COMPARISON OF FULL-SCALE MEASUREMENTS WITH CALCULATED MOTION CHARACTERISTICS OF A WEST OF AFRICA FPSO Radboud R.T. van Dijk MARIN Wageningen, the Netherlands r.r.t.van.dijk@marin.nl Valérie Quiniou-Ramus TotalFinaElf S.A. Paris, France Guillaume Le-Marechal TotalFinaElf S.A. Paris, France ABSTRACT Full-scale measurements of the motions of the Girassol FPSO are available over a one-year period. During this same period also vessel draft, wave height and wave direction have been recorded. This allows the calculation of motion transfer functions as function of the FPSO loading condition. A comparison has been made between the measured motion transfer functions and the calculated motion transfer functions based on diffraction theory, taking into account the measured wave spreading. Viscous roll damping has been added in the calculation to obtain maximum agreement between measured and calculated RAO s. The results show that wave spreading is a very important factor on how the vessel behaves and should be taken into account when evaluating measured full-scale motion RAO s. This paper addresses the full-scale monitoring campaign in some detail and the related issues. Furthermore it describes the technique how measured wave spreading is taken into account in the calculation of theoretical motion RAO s. It is shown that the agreement between calculated and measured RAO s is greatly improved by the use of measured wave spreading in the calculation. The levels of viscous roll damping found in this tuning process can be described as function of loading condition and sea state. The viscous roll damping found in this process also shows good agreement to model test results performed earlier on this same FPSO. INTRODUCTION Even for floating structures in mild environments such as West of Africa the motion response is a dominant aspect in the design of the structure. Accurate information about the motions is important for the evaluation of the risers and topsides, both with respect to extreme loads and fatigue. It is common practice to derive these motions based on linear diffraction analysis [], validated and tuned by model tests. The validation with model tests is necessary because linear diffraction analysis does not take into account viscous effects. It is, however, important to check the results derived with this combined methodology with the motions of the structure in reality. Scale effects at model scale could for instance affect the accuracy of the results. In the present study a comparison is made between measured full-scale response and the combination of diffraction analysis and model tests. Wave frequency motions in 6 degrees of freedom and the heading have been measured on board of the Girassol FPSO, located West of Africa. The monitoring campaign also included wave measurements by means of a directional wave rider buoy, as well as the drafts, trim and heel. To compare the results of the theoretical analysis in longcrested waves with the measurements offshore in short-crested waves, a new methodology is presented in this paper. FULL-SCALE MONITORING CAMPAIGN The motions of the FPSO have been measured since the departure of the FPSO from the yard. For this purpose a motion sensor box was placed in the topsides near the aft perpendicular. This motion sensor uses the same principles as a directional wave rider buoy. The sensor measures accelerations and based on these measurements the translations and rotations are derived. Vessel heading is derived by means of a magnetic compass. A first analysis of the measurements revealed that the Copyright 3 by ASME

2 measured yaw could not be used due to problems with this magnetic compass in the motion sensor. Since the installation of the FPSO on-site West of Africa, the waves have been measured using a directional wave rider buoy located some distance from the FPSO. This sensor produces a time trace of the measured wave height as function of time. Based on the buoy motions, the wave spectrum is calculated as well as the mean wave direction and the standard deviation of wave direction for each frequency component. Each measurement consists of 3 minutes data. A typical measured wave spectrum and the associated wave spreading is shown in Fig. below. wave spectral density [m s] wave direction [deg].. Wave spectrum, Hs =.9 m, Tz = 5.6 s, Tp = 3.3 s µ ζ = 9 σ µ = 3 Geometric wave direction mean wave direction µ ζ stdev wave direction σ µ.5.5 Figure : measured wave spectrum and spreading In this example the measured wave direction at the peak period is 9. It is worth noting that the measured peak- and zero-upcrossing period are very different. The wave spectrum does not resemble a Pierson-Moskowitz wave spectrum. Although the FPSO drafts are measured since the departure of the FPSO from the yard, reliable draft measurements are only available over the last eight months of the period considered. CALCULATION METHOD Based on the measured motions of the FPSO and the encountered waves at the FPSO location RAO s for all six degrees of freedom can be derived. The RAO s are derived using Eq. (): H X ( ω) = SX ( ω) S ( ω) ζ Where S X (ω) is the response spectrum for mode x and S ζ (ω) is the wave spectrum. Normally the RAO s are evaluated in the centre of gravity of a vessel. However, due to the problems with the measured yaw motions, the FPSO motions could not be accurately () calculated at CoG. Therefore, the comparison between measured and calculated RAO s has been done at the motion sensor box location. As a result the RAO for sway is coupled with roll and yaw and the RAO for heave is coupled with roll and pitch. For long-crested waves a direct comparison can be made between measured and calculated RAO s. In reality wave spreading is often present and the waves are short-crested. Due to this wave spreading the measured motion RAO s can not be directly compared to the calculated RAO s. Therefore the following approach is used (see also []): A theoretical wave spreading function D is defined based on a cosine s model. The standard deviation of this wave spreading function is chosen to be equal to the standard deviation of the actual measured wave direction (σ µ ). The area below the spreading function is by definition one. This cos s wave spreading function is defined by Eq. (): spreading function D(µ) [ ] D( µ ) = C cos s µ µ with C chosen such that µ ) δµ = 8 D( 8 The standard deviation of this spreading function can be calculated by Eq. (4): 8 σµ = D ( µ ) µ δµ (4) 8 The resulting wave spreading function is shown in Fig cos s wave spreading function D(µ) around mean wave direction µ with σ µ = wave direction µ [deg] Figure : cosine -s wave spreading model Based on the measured waves, for each wave frequency a standard deviation is calculated. Therefore the wave spreading function varies with wave frequency. This results in a spreading function D(ω,µ), i.e. D as function of wave frequency ω and wave direction µ. Based on the measured spreading parameters µ ζ and σ µ from the example above, a surface plot can be generated of the spreading function D(ω,µ). This two-dimensional wave spreading function is shown in Fig. 3. () (3) Copyright 3 by ASME

3 Wave spreading function D(ω,µ) H(ω,µ) *D(ω,µ) Figure 3: wave spreading function Figure 5: Pitch RAO, including wave spreading Using the above wave spreading function D(ω,µ) the theoretical motion transfer function including the effect of wave spreading can be calculated by Eq. 5: The last step is to sum over all wave direction to obtain one equivalent transfer function for the measured wave spectrum, including the effect of wave spreading. As an example the RAO s for roll and pitch are shown in Figures 6 and 7 below. The main wave direction is near head seas (9 ). 36 ò H X (ω, µ) D(ω, µ)δµ H X (ω) = (5) RAOφ (roll) with/without wave spreading.5 with wave spreading without wave spreading where HX(ω,µ) is the motion RAO for mode x as function of wave frequency ω and ship-fixed wave direction µ. RAO (ro l).5 φ It should be noted that the measured wave direction is the geometric (earth-fixed) wave direction. In order to perform the calculation correctly, the wave spreading function should be transformed to reflect ship-fixed wave directions. The calculation procedure to obtain H(ω) including the effect of wave spreading is shown in the figures below. In this example the RAO for pitch is considered..5.5 RAO H(ω,µ).5 Figure 6: roll RAO, including wave spreading RAO (pitch) with/without wave spreading.7 with wave spreading without wave spreading RAO (pitch) Figure 4 shows the calculated RAO based on diffraction analysis as function of both wave frequency and wave direction. Figure 3 shows the applied wave spreading function D(ω,µ), measured by a wave buoy. Figure 5 shows the resulting RAO for pitch taking into account the measured wave spreading prior to integration over all directions..5.5 Figure 4: Pitch RAO based on diffraction analysis Figure 7: pitch RAO, including wave spreading The solid line shows the calculated motion RAO s including the effect of wave spreading. The dash-dot line shows the RAO s for long-crested seas (i.e. without taking wave spreading into account). From the above example it is clear that wave spreading has a profound influence on the resulting motion behaviour of the vessel. In this example the FPSO will exhibit significant roll 3 Copyright 3 by ASME

4 motions in almost head waves due to the wave spreading. Without wave spreading the predicted roll motions would be much lower. The effect on pitch RAO is smaller but still very noticeable. ROLL DAMPING AND TUNING THE RAO S Diffraction calculations account only for potential damping, i.e. damping due to radiated waves. For roll motions of large floaters this is typically a very low value due to the long roll periods. Viscous roll damping plays a dominant role in the overall roll behaviour and must be taken into account. At present it is not possible to accurately predict the amount of viscous roll damping. Therefore the level of viscous roll damping is tuned to obtain maximum agreement between measured and calculated RAO s. The RAO s based on diffraction analysis are recomputed for different levels of added viscous roll damping. Each of these RAO s is then compared to the measured RAO s. The calculated RAO with the best fit to the measured RAO indicates what level of viscous damping was present in that particular condition. The amount of damping can be expressed in the so-called relative damping β, which is a percentage of the critical damping. Bφ = β M g GM (k M + I ) (6) viscous viscous critical T Bφ = β Bφ (7) Note that in this case the potential roll damping amounts to only approximately.5% of the critical damping. Figure 8 in Appendix I shows an example of this tuning process. The top row shows the RAO s for roll, the bottom row the RAO s for sway. The solid line (blue) is the measured RAO. The dash-dot line (red) is the calculated RAO for different levels of roll damping. The strong coupling of sway due to roll at the position of the motion sensor box is clearly visible. RAO φ.5 xx measured RAO s versus calculated RAO s with different levels of added viscous damping β = % β = % β = 3 % β = 4 % β = 5 %.5.5 φφ.5.5 other degrees of freedom are not sensitive to the amount of added viscous roll damping. This tuning process has been done for a number of sea states over a one-year period with varying loading condition, wave height, wave period and wave direction. For each tuning process an appropriate loading condition was used in the diffraction analysis, close to the actual loading condition present during the full-scale measurements. The figures below show a comparison between the actual measured RAO s and the tuned RAO s from diffraction calculation, taking into account the measured wave spreading. Note that the RAO for yaw is not analysed due to problems with the yaw measurements. RAO X RAO Y RAO Z RAO φ RAO measured RAO s versus calculated RAO s tuned with added viscous damping Hs = m, β = 7% Hs = m, β = 3% Hs =.3 m, β = 3% Hs = 3 m, β = % measured tuned Figure 9: tuned RAO s for various sea states.5 The relative viscous roll damping found in this way can be plotted as function of sea state and loading condition. Model tests have been performed on the FPSO in 998. At that time the viscous damping levels have been established for two loading conditions and a number of sea states. Plotting both the data from the tuned RAO s to full-scale data and the model test data in the same figure results in Figure. Relative viscous roll damping based on model tests and full scale measurements Calm water damping Loaded model tests Ballast model tests LC BAL Full scale LC 5% Full scale LC 5% Full scale RAO Y Figure 8: effect of varying viscous roll damping Relative viscous damping β [ %] Based on Fig. 8 a viscous roll damping level of 3% is selected for this particular loading condition and sea state. For this damping level good agreement is found between measured and calculated RAO s for both roll and sway. The RAO s for Sea state (Hs) Figure : relative damping as function of sea state 4 Copyright 3 by ASME

5 OBSERVATIONS When the measured wave spreading is taken into account, the agreement between measured and calculated RAO s is very good for all degrees of freedom. The available full-scale data mainly consists of waves that are more or less on the stern of the (spread-moored) FPSO. In long-crested seas this would lead to hardly any roll motions, but due to the short-crested nature of the waves, significant roll motions occur. The tuned RAO s cover a one-year period. In this period most of the sea states measured are stern seas with relatively low wave heights. This means that the roll response of the FPSO has been fairly low. A higher roll response is expected in stern quartering and beam seas with higher wave heights. The accuracy of the tuned RAO s can be further improved by analysing the measured motion response if these sea states occur. The agreement between full-scale measured data and model test data is good. When plotting the viscous damping levels versus sea state and loading condition, the model test data shows a clear linear trend of increasing damping levels with increasing sea states and a distinct difference between the loaded and the ballasted condition. The data from the tuning process to the full-scale RAO s shows more scatter, especially for low sea states. This is mainly due to the very small roll motions in these sea states. For higher sea states the same linear trend is observed as in the model test data, although the distinction between the different loading conditions can not be made so clearly. This study shows that the motion behaviour of a vessel can be accurately predicted using motion transfer functions obtained from linear diffraction analysis. The only unknown is the amount of viscous roll damping that needs to be added to obtain a reliable roll response. ACKNOWLEDGMENTS The authors would like to express their thanks to Sonangol and TotalFinaElf E&P Angola for their permission to publish this paper. REFERENCES [] Oortmerssen, G. van: 976, The Motions of a Moored Ship in Waves, PhD thesis, Delft University of Technology, MARIN publication No. 5. [] Waals, O.J., Aalbers, A.B, Pinkster, J.A,, Maximum Likelihood Method as a Means to Estimate the Directional Wave Spectrum and the Mean Wave Drift Force on a Dynamically Positioned Vessel, OMAE-856. CONCLUSIONS A method has been developed to incorporate wave spreading into calculated motion transfer functions. This allows a direct comparison between the actual full-scale measured RAO s and the calculated motion transfer functions. Using this comparison between measured full-scale data and calculations the viscous roll damping levels of the FPSO can be determined. Accurate information about the motion response of an FPSO in the design stage is important for the evaluation of the riser and topsides, both for extreme loads as well as fatigue. In the design stage of an FPSO there is normally no full-scale data available on the motion transfer functions and associated viscous damping. For floaters like the FPSO considered in this paper there are no reliable analytical methods to predict the amount of viscous roll damping. The results of this study show that in such case model tests are a good method to obtain reliable viscous damping values in a very early stage of the FPSO design. 5 Copyright 3 by ASME