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Proceedings of the ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering OMAE2011 June 19-24, 2011, Rotterdam, The Netherlands

OMAE2011-49580

EQUIVALENT DESIGN WAVE APPROACH FOR CALCULATING SITE-SPECIFIC ENVIRONMENTAL LOADS ON AN FPSO

Resmi Sarala Naval Architect Mohammad Hajiarab Floating Structures Team Leader Lloyd's Register - Aberdeen, UK ABSTRACT This paper demonstrates the method used by Lloyd's Register (LR) to derive an equivalent design wave from a response based analysis (RBA) to represent extreme loads on a weather-vaning FPSO [1] and proceeds to compare the results with that of the industry practice of the response amplitude operator (RAO) based approach. The responses investigated include roll, pitch, vertical wave bending moments, vertical wave shear forces and vertical acceleration. The RBA is based on 3 hourly hindcast metocean data and uses the results of the heading analysis directly, considering the combined effect of wind, wind-sea, current and swell. An equivalent design wave is then derived based on the spectral characteristics of each response instead of the common practice for ship design [2] which uses only the characteristics of the RAOs. For each response the design wave for the RBA and RAO approaches is compared. Deriving equivalent design waves using only the RAO characteristics is found to give some non-conservative and unrealistic equivalent design waves in some cases. INTRODUCTION In a harsh environment a turret mooring system is often utilised to take advantage of its passive weather-vaning characteristics. The instantaneous equilibrium position is reached through the combined effects of varying environmental loads due to wind, wave (wind-sea and swell components), and current. Accurate modeling of the FPSO responses is important for predicting the loads on the structure and the operational envelope. This requires a good understanding of the vessel response characteristics and the site-specific environmental conditions. The relative importance of the environmental parameters depends upon the response being investigated. To use the extreme responses (e.g. vertical wave bending moment) for structural design it is necessary to also derive the associated responses (e.g. vertical acceleration) which occur at the same instant as the extreme, accounting for the phase differences between the responses. Note that the environmental conditions associated with the extremes are usually different for each response (e.g. the sea states resulting in large vertical wave bending moments do not necessarily also result in extreme roll responses). The RBA equivalent design wave method as described in Section 4 of the LR ShipRight-FOI procedure [1] is used to derive dynamic load combinations associated with the extreme (100 year return period) values of the following responses at amidships for an Aframax FPSO operating in a harsh environment: ? ? ? ? ? ? Vertical Wave Bending Moment Vertical Wave Shear Force Vertical Acceleration Transverse Acceleration Roll Pitch Richard Bamford FOI Global Technology Leader

The RBA equivalent design waves are compared with RAO based equivalent design waves for each response. The design waves are used to derive dynamic load combination factors (DLCFs) as would be used for structural design calculations [4]. NOMENCLATURE Vertical Acceleration at Port Side tank av-PS at-PS Transverse Acceleration at Port Side tank FOI Floating Offshore Installation Hs Significant wave height Mwv Vertical Wave Bending Moment Qwv Vertical Wave Shear Force Peak spectral period Tp γ Non-dimensional peak shape parameter [5] σa Numeric spectral parameter [5] σb Numeric spectral parameter [5]

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BACKGROUND The purpose of the load response analysis is to provide environmental loads for use in the assessment of the strength, hull girder ultimate strength, local scantlings, and sloshing assessment. The CSR [2] derivation of characteristic design wave loads is based on a long term statistical approach which includes representation of the wave environment (North Atlantic scatter diagram), probability of ship/wave heading and probability of load value exceedence based on IACS Recommendation 34. Non-linear effects (due to vessel geometry and wave profile) are considered for the expected lifetime maximum loads. In deriving the simultaneously occurring loads, one particular load component is maximised or minimised and the relative magnitude of all simultaneously occurring dynamic load components is specified by the application of dynamic load combination factors (DLCF) based on the envelope load value. These dynamic load combination factors based on the equivalent representative design waves are tabulated in the CSR [2]. It is not sufficient simply to replace the individual tanker loads given in the CSR Section 7/3 [2] with FPSO loads unless the load combination factors given in the CSR Section 7/6 [2] are also replaced. This is because the heading probabilities, environmental load characteristics and hence response characteristics of an FOI differ from those of a trading tanker. Furthermore the values of fβ in CSR [2] which account for the probabilities of head seas and beam seas are not necessarily applicable to an FOI. LR RBA Method The LR RBA method makes use of the following for calculating extreme responses and associated DLCF using the design wave approach: ? A site specific directional scatter diagram or hindcast/measured data series; ? Linear hydrodynamic theory with the hull modeled using 3D-diffraction elements; and ? Heading probabilities determined from a heading analysis. Figure 1 shows a flow chart of the complete hydrodynamic analysis to calculate required loads for determining the local scantlings for the hull structure.

3D Diffraction Model

Metocean database

Hydrodynamic database

Heading analysis

Wind and current coefficients

Heading database

Response Analysis

Dynamic Load combination factors

RulesCalc Scantling calculations

Figure 1: Flowchart of the analysis The 100 year return period values for each response is determined based on spectral analysis methods for each loading pattern as follows: ? The Response Amplitude Operators (RAOs) of the response under investigation for each loading condition and vessel heading is produced. ? The short term response is calculated for each sea-state by adding the wind sea response spectra and swell sea response spectra for the response under investigation. The mean heading for each sea-state determined by the heading analysis is used. ? The long term distribution of the response under investigation is determined by combining the statistics of the Rayleigh distributions for each sea-state. From the long term distribution, the extreme value for the required (100 year) response is calculated. This procedure assumes the response to be narrow banded. Where the response is not narrow banded, a bandwidth correction may be applied. Idealised quasi-static load cases are required for the response variable defined in each loading condition in the strength analysis. The idealised quasi-static load cases that induce the 100 year return period value for each response variable are derived using the concept of an equivalent design wave. These design waves yield the information required to replace the CSR DLCF values. There are numerous possible design waves and

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using one design wave for each response is a significant simplification irrespective of the selection method. The LR method employs the results of the extreme response analysis rather than only the characteristics of the response RAOs. The steps in the method are as follows: 1. The relative heading 'H' which produces the greatest contribution to the 100 year response of interest is identified. The relative heading 'H' is the dominant relative heading from cumulative response spectrum (See Annex A). 2. For relative heading 'H', the frequency 'F' is identified which produces the greatest contribution to the 100 year response of interest. The frequency 'F' is the frequency at the peak of the cumulative response spectrum for relative heading 'H'. 3. For relative heading 'H', the phase angle 'P' is found which generates the amplitude of the RAO for frequency 'F'. 4. The amplitude 'A' of a regular wave is calculated with relative heading 'H', frequency 'F' and phase angle 'P' so that it produces the 100 year response value. At this step the design wave can be identified by it's four parameters, i.e. heading, frequency, phase and amplitude. 5. For relative heading 'H', frequency 'F' and amplitude 'A' all response components for phase 'P' and phase 'P+180 degrees' are calculated. This will give the positive and negative loads. RAO based method In the RAO based approach the RAOs for a given parameter are calculated for each heading. The design wave heading is then taken to correspond to the heading of the largest RAO from the calculated set of RAOs. Thereafter the method is the same as the RBA approach. DESCRIPTION OF THE MODEL Preparation of the hydrodynamic model and hydrodynamic analysis was performed using the AQWA software package from ANSYS. The AQWA model for the analysis is presented in Figure 2.

z z y

The hull is modeled with 3D-diffraction elements. The effects of current drag loads and wind loads on the hull were represented by the current force and wind force coefficients. The mooring lines are modeled as composite catenary lines consisting of chains and wire rope components. The main characteristics of the vessel used for the analysis in the ballast condition are presented in Table 1 below: Table 1: Main characteristics of the vessel Vessel Characteristics (approximately) LBP (m) Breadth (m) Draught (m) Displacement (t) GM (m) LCG from AP (m) VCG from keel (m) Tran. radius of gyration (m) Vert. radius of gyration (m) Long. radius of gyration(m) 230 45 12 110,000 4.5 110 16 20 65 65

ENVIRONMENTAL DATA The environmental data includes a total of approximately 30,000 continuous three hourly hindcast sea states which represents more than 10 years of data. Definition of this data is in accordance to requirements of Section 2.8 of ShipRight FOI Procedure [1] and no spreading is assumed in the wave data. The environmental data includes: ? Wind wave JONSWAP spectrum parameters (i.e. Hs, Tp, γ, σa and σb) and direction ? Swell wave JONSWAP spectrum parameters (i.e. Hs, Tp, γ, σa and σb) and direction ? Wind mean speed and direction ? Current mean speed and direction RBA PROCEDURE Analysis was performed as indicated in Figure 1 based on the following procedure: 1. A 3-D diffraction model of the vessel's hull was generated in AQWA-LINE based on the characteristics defined in Table 1. 2. The calculated linearised roll damping is verified against field measurements and included in the hydrodynamic model. 3. A hydrodynamic database containing amplitude and phase of the RAOs for design parameters stated in Table 2 was prepared for frequency range of 0.1 rad/s to 1.5 rad/s with 0.05 rad/s increments and heading range of -180° to 180° with 5° increments.

-900

00

cog

x

900

1800

Figure 2: The Hydrodynamic model and Reference System

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4. The mooring arrangements were added to the AQWALINE model to create the AQWA-LIBRIUM model. 5. Wind and current coefficients from wind tunnel tests were added to the AQWA-LIBRIUM to include the wind drag and the current drag forces for the specified loading condition of the vessel and the headings relative to wind and current directions. 6. The three hourly environmental data, which contained sets of wind-sea, swell, wind and current data with their associated directions were included in the hydrodynamic model. 7. Using the AQWA-LIBRIUM software, the stable equilibrium positions for each three hourly sea state was calculated individually. 8. The vessel headings were post-processed to find the relative vessel heading to wind seas and swell seas at each three hourly sea state. 9. Using RAOs calculated in step 3 above and the relative vessel headings calculated in step 8 above, an extreme response analysis was performed in accordance with [1] to calculate the 100 year return period for the parameters listed in Table 2. 10. The outcome of the response analysis from step 9 is post processed to define individual design waves associated to each response. In this process for each sea state the relative headings of the wind seas and swell seas are rounded to nearest 5°. The response spectra for wind seas and swell seas with the same rounded headings are added together and are presented in the form of a histogram. The total area on the starboard side (i.e. from 0° to 180°) and port side (i.e. from -180° to 0°) are calculated and the biggest area is considered as the "Governing Side". The dominant heading is chosen from the Governing Side of the histogram (See Figures 9 to 14 in Annex A). 11. The calculated design waves are used to determine the associated values in phase with each 100 year return period responses from the hydrodynamic database calculated in step 3. Table 2: Presented FPSO responses FPSO Response Roll Pitch Mwv Qwv av-PS at-PS Approx. Position (m) At center of gravity At center of gravity At 0.5L from AP (x=115 from AP) At the trans BHD with max.combined seagoing permissible SWSF and VWSF in the midship region, (x=130 from AP) At COG of the mid tank – Port Side (x=120 from AP, y=9 from CL, z=9 from BL) At COG of the mid tank – Port Side (x=120 from AP, y=9 from CL, z=9 from BL)

RESULTS The calculated 100 year return period values from the Response Based Analysis (RBA) and their design wave characteristics for the specified responses stated in Table 2, are presented in Table 3. Using the design waves in Table 3 and the RAO database of the responses, associated loads in phase with each 100 year return period response can be calculated. The calculated design parameters associated with each design wave are presented in Table 4. For each design wave (i.e. each column in Table 4), the 100 year return period is highlighted for further clarity. For example, at the time of the 100 year return period vertical wave bending moment (i.e. Mwv=5.8E9 N.m), the associated vertical wave shear force, vertical acceleration, transverse acceleration, roll and pitch are -2.7E7 N, 0.50 ms-2, 0.00 ms-2, 0.00 deg. and 2.46 deg., respectively. Table 3: The RBA 100 year return period values and design waves Response 100 Yr. R.P. Value Design Wave Characteristics A F H P (m) (rad/s) (deg.) (deg.)

Mwv 5.8E9 11.87 0.50 180 167 (N.m) Qwv 4.3E7 12.06 0.55 -180 37 (N) av-PS 1.70 16.13 0.60 180 54 (ms-2) at-PS 5.83 8.66 0.35 150 -133 (ms-2) Roll 22.93 8.54 0.35 150 -175 (deg.) Pitch 9.46 13.66 0.50 180 94 (deg.) Note: A: Amplitude, F: Frequency, H: Heading, P: Phase Table 4: The RBA associated design parameters for each design wave Resp. Mwv (N.m) Qwv (N) Design Wave av-PS at-PS (ms-2) (ms-2) Roll (deg.) Pitch (deg.)

Mwv 5.8E9 -2.6E9 3.71E8 1.25E9 1.8E9 1.99E9 (N.m) Qwv -2.7E7 4.3E7 5.15E7 -9.92E6 -1.1E7 2.72E7 (N) av-PS 0.50 0.64 1.70 0.20 0.41 0.688 (ms-2) at-PS 0.00 0.00 0.00 5.83 4.23 0.00 (ms-2) Roll 0.00 0.00 0.00 17.11 22.93 0.00 (deg.) Pitch (deg.) 2.46 3.34 4.05 -3.60 -0.40 9.46

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The relation between 100 year return period design parameter and other associated design parameters for each design wave is normalized in Table 5. This demonstrates the dynamic load combination factor (DLCF) for each design wave. Table 5: The RBA normalised associated design parameters for each design wave Design Wave Resp. Mwv (N.m) Qwv (N) av-PS (ms-2) at-PS (ms-2) Roll (deg.) Pitch (deg.) Mwv (N.m) 1.00 -0.63 0.30 0.00 0.00 0.26 Qwv (N) -0.46 1.00 0.38 0.00 0.00 0.35 av-PS (ms-2) 0.06 1.18 1.00 0.00 0.00 0.43 at-PS (ms-2) 0.21 -0.23 0.12 1.00 0.75 -0.38 Roll (deg.) 0.32 -0.25 0.24 0.73 1.00 -0.04 Pitch (deg.) 0.35 0.62 0.41 0.00 0.00 1.00

Table 7: The RAO based associated design parameters for each design wave Design Wave Resp. Mwv (N.m) Mwv (N.m) Qwv (N) av-PS (ms-2) at-PS (ms-2) Roll (deg.) Pitch (deg.)

5.8E9 -2.97E9 3.47E7

-5.6E7 -9.06E7 1.86E9 9.7E4 -0.07 5.83 17.60 -0.01 1.61E5 -4.28E6 -0.02 -0.02 22.93 -0.02 0.59 -0.26 -0.46 9.46

Qwv -2.73E7 4.3E7 -8.99E5 (N) av-PS 0.51 -0.08 1.70 (ms-2) at-PS 0.51 0.00 0.37 (ms-2) Roll (deg.) Pitch (deg.) 0.00 2.47 0.00 3.57 0.74 0.00

Table 8: The RAO based normalised associated design parameters for each design wave Resp. Mwv (N.m) 1.00 -0.63 0.30 0.09 0.00 0.26 Qwv (N) -0.51 1.00 -0.05 0.00 0.00 0.38 Design Wave av-PS at-PS (ms-2) (ms-2) 0.01 -0.02 1.00 0.06 0.03 0.00 -0.01 0.00 -0.04 1.00 0.77 0.00 Roll (deg.) 0.02 0.00 0.01 0.00 1.00 0.00 Pitch (deg.) 0.32 -0.10 0.35 -0.04 -0.02 1.00

The RAO based design wave characteristics of each response are presented in Table 6. The associated responses to each 100 year response, using the RAO based design waves are shown in Table 7 and the same values are normalized in Table 8 for further discussion. Table 6: The RAO based 100 year return period values and design waves Response Mwv (N.m) Qwv (N) av-PS (ms-2) at-PS (ms-2) Roll (deg.) Pitch (deg.) 100 Yr. R.P. Value 5.8E9 4.3E7 1.70 5.83 22.93 9.46 Design Wave Characteristics A F H P (m) (rad/s) (deg.) (deg.) 11.87 8.62 3.25 3.16 3.28 9.46 0.50 0.55 0.65 0.35 0.35 0.60 180 0 90 90 90 120 167 -57 -131 -128 -169 112

Mwv (N.m) Qwv (N) av-PS (ms-2) at-PS (ms-2) Roll (deg.) Pitch (deg.)

Note: A: Amplitude, F: Frequency, H: Heading, P: Phase

DISCUSSIONS For each design wave the RBA and RAO based response parameters are tabulated in Table 3 to Table 8. It can be seen from Table 5 that at the time of the 100 year return period av-PS , the associated Qwv is about 18% more than the calculated 100 year return period Qwv. This is because the response of the vessel due to two separate wave spectra (i.e. wind wave and swell) is approximated by only one regular design wave. In order to eliminate such discrepancies when calculating local scantlings it is usual to truncate any associated value exceeding the calculated 100 year value to the corresponding 100 year value [4]. However when applying the design wave directly for FE analysis using a full ship FE model such truncation is not practical.

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Among the approximately 30,000 seastates analysed in this study, the sea states which contribute the most to the responses under investigation are shown in Figures 3 to 7.

Figure 3: The sea state contributing most to extreme Mwv

Figure 4: The sea state contributing most to extreme Qwv

Figure 5: The sea state contributing most to extreme av-PS

By comparing Table 5 with Table 8 it can be concluded that the DLCFs presented in Table 5 are more representative of reality than the values in Table 8. This phenomenon is most significant in transverse responses. For example, by applying the RAO based design wave approach (i.e. Table 8), at the time of the 100 year return period at-PS , the corresponding Mwv, Qwv and av-PS are calculated to be negligible. However using the RBA based design waves, associated Mwv, Qwv and av-PS at the time of the 100 year return period at-PS are demonstrated to be 21%, 23% and 12% of their 100 year return period values. This is due to the fact that the heading and frequency of the RBA design wave correspond to the peak of the energy concentration in the response, not the peak of the RAO. Therefore the RBA design wave is considered to be more realistic. Furthermore, in order to compare the RBA design wave approach with the commonly used RAO based design wave approach, the roll and pitch response are chosen as representative of transverse and longitudinal responses respectively. As presented in Table 3, the heading of the roll using the RBA approach is calculated to be 150 degrees. From the RAO based approach it can be seen that in this case the design wave heading of the roll response will be 90 degrees, since the peak of the RAO occurs in this heading. As it is demonstrated in Figure 8, by choosing the design wave heading of 90 degrees for roll response, the minimum amount of contribution from pitch will be considered in the design load case. However by choosing the heading of 150 degrees, not only is the 100 year return period roll response recovered, but a considerable pitch response in phase with the 100 year roll response will be considered as well.

Max. Roll and Max. Pitch RAO Amplitudes

1.2 8

1

Max. Pitch Ampl. Max. Roll Ampl.

7 6

Max. Pitch ampl. (deg/m)

0.8 5 0.6 4 3 0.4 2 0.2 1 0 95 100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 0

Figure 6: The sea state contributing most to extreme at-PS and Roll

Heading (deg.)

Figure 8: Maximum roll and pitch RAO amplitudes It should be noted that the response based methods are based on linear frequency domain analysis which assumes infinitesimally small wave amplitudes. When applying the design waves for structural design it is usual to make corrections for the finite wave height by making assumptions about the pressure distribution above the waterline [4]. Figure 7: The sea state contributing most to extreme Pitch CONCLUSIONS From the preceding discussions, it is concluded that the RBA design wave approach adopted by Lloyd's Register

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180

5 10

15

20

25 30

35

40

45 50

55

60 65

70

75

80 85

90

0

Max. Roll ampl. (deg/m)

provides more realistic responses compared to the more commonly used RAO based method. As a result of more accurate estimation of the site specific responses, a better optimized hull scantling design can be achieved. Furthermore the topside process machinery can be designed for more realistic motion and acceleration operating limits. ACKNOWLEDGMENTS The authors wish to thank Lloyd's Register Group Services, especially Dr. Graham Stewart, for his support of this work. The opinions expressed in this paper are those of the authors and are not necessarily those of Lloyd's Register. REFERENCES [1] Lloyd's Register, 2011, "ShipRight-FOI Design, Construction and Operation; Floating Offshore Installations Assessment of Structures, Ship Units, Guidance on Calculation". [2] IACS, 2008, "Common Structural Rules for Double Hull Oil Tankers". [3] Lloyd, A.R.J.M., 1998,"Seakeeping: Ship behavior in rough weather". [4] Lloyd's Register, 2011, "Rules and Regulation for the Classification of a Floating Offshore Installation at a Fixed Location," Part 4A. [5] BS EN ISO 19901-1:2005, "Petroleum and Natural Gas industries – Specific requirements for offshore structures, Part 1: Metocean design and operating considerations".

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ANNEX A

Figure 9: Histogram of the energy distrubution for Mwv response

Figure 10: Histogram of the energy distrubution for Qwv response

Figure 11: Histogram of the energy distrubution for av-PS response

Figure 12: Histogram of the energy distrubution for at-PS response

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Figure 13: Histogram of the energy distrubution for Roll response

Figure 14: Histogram of the energy distrubution for Pitch response

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