Proceedings of the ASME th International Conference on Ocean, Offshore and Arctic Engineering OMAE2011

Transcription

1 Proceedings of the ASME 20 30th International Conference on Ocean, Offshore and Arctic Engineering OMAE20 June 9-24, 20, Rotterdam, The Netherlands Proceedings of the 30 th International Conference on Ocean, Offshore and Arctic Engineering OMAE-20 June 9-24, 20, Rotterdam, The Netherlands OMAE OMAE GLOBAL PERFORMANCE OF SYNTHETIC ROPE MOORING SYSTEMS FREQUENCY DOMAIN ANALYSIS Erik Falkenberg DNV Høvik, Norway Vidar Åhjem DNV Høvik, Norway Kjell Larsen Statoil Trondheim, Norway Halvor Lie Marintek Trondheim, Norway Karl Erik Kaasen Marintek Trondheim, Norway ABSTRACT For deep and ultra-deepwater applications, synthetic fibre ropes are considered an enabling technology due to their higher strength-to-weight ratio as compared to steel wire ropes and chains and due to their superior station-keeping performance. The advantages of synthetic fibre rope mooring systems include: A higher floater payload and reduction in structural costs due to lower vertical load from mooring lines. A reduction in vessel offsets and associated riser loads due to taut mooring system. A potential reduction in installation costs due to lighter installation and handling equipment. Superior endurance under cyclic loading compared to steel moorings. Synthetic fibre ropes have visco-elastic stiffness and stretch characteristics. The change-in-length response of a fibre rope is non-linear, load-path dependent (different unload-reload stiffness), and the length varies with the rate and duration of loading (due to elongation and contraction). The commonly accepted analysis approach is a simplification where a lower-bound and an upper-bound stiffness is used. This practice is primarily based on two factors:. The industry at large does not at present have a common, well-defined understanding of fibre-rope change-in-length performance. 2. There is a lack of commercially available mooring analysis programs with the capability to simulate the non-linear change-in-length response of the synthetic fibre rope. Individual designers may however have more advanced analysis procedures, but these are not commonly accepted yet. This paper presents results from the Syrope pilot study, Ref. /5/ and /6/, which has used rope testing to determine the characteristics of the elements in the spring-dashpot model. On this basis a strategy for software implementation in the frequency-domain has been proposed. A case study was performed for a semi-submersible production unit in deep water and harsh environment. The paper focuses on the differences between a commonly accepted, hereafter called traditional analysis approach and the proposed new frequency domain approach. The results show that there are large differences in extreme tensions and offsets as well as fatigue results. Hence, the new approach is considered to represent a significant improvement. INTRODUCTION The objective of the work presented herein was to determine a model for fibre-rope behaviour with respect to axial stiffness and stretch. The work has included: Physical testing of a rope. These tests include tests for parameter identification and tests with irregular tension variation. Investigation of different models to describe rope behaviour based on the spring-dashpot model proposed by Flory, Ref. //. Testing the different models in a simple program that simulates the tension based on time history of motion. Concluding on modelling principle. Copyright 20 by ASME

2 Implementation of rope model in frequency-domain analyses and conducting a case study with this model comparing results against a traditional approach. Implementation of rope model in time-domain and conducting case study with this model. Presentation of these results is not included in the present paper. NOMENCLATURE The following terms are used in the paper: Stretch, L, is the change in rope length caused by applied tension. Strain is the non-dimensional stretch, the ratio of stretch under tension to the original length before applying tension, ε = (L-L 0 )/L 0 = L/L 0. Stiffness, K, is the ratio of change in tension to the amount of stretch that results from that change, K = T/ L. Non-dimensional stiffness is the stiffness multiplied by original length and divided by average strength, AVS. K nondin = T*L/( L*AVS). This work discusses exclusively non-dimensional stiffness so for short, the word stiffness is used throughout this paper. ROPE CHARACTERISTICS time. Much of the focus has been put on obtaining a better understanding of these elastic properties. The words dynamic stiffness and static stiffness are often used when characterizing the properties of a rope. The dynamic stiffness is used to characterize rapid tension variations, and with reference to Figure it can be regarded as if the fast spring only is in effect. Static stiffness is used to characterize slow tension variations, and in this case both the fast spring and the slow spring are contributing. The permanent stretch includes two effects, the creep dashpot and the construction spring with ratchet. The creep dashpot represents polymer strain, which is irreversible and takes place whenever the rope is under tension. Its rate becomes small as time elapses. The construction ratchet arranged in parallel with the construction spring allows that spring to stretch in response to the highest tension applied to the rope, but prevents it from retracting. The construction ratchet is believed to be an effect of burrowing among individual strands and yarns in a sub-rope upon tension. ROPE TESTS A subrope with a diameter of 28 mm and an average strength of 286 kn was tested in The Bristle Worm test machine at DNV s laboratory (Figure ). The subrope had been manufactured by Parker Scanrope. All tests were performed according to a pre-programmed tensioning sequence, and the resulting stretch of the rope was measured. Five different tests were run, including:. Harmonic cycling at different tension levels at periods representative for wave-frequency and low-frequency motions of a floating structure, see Figure Irregular excitation. The rope had previously been tensioned to 35%. The irregular drive file for the testmachine controller had energy in the intervals [0s - 20s] and [05s - 40s], see Figure 3. Figure Spring-dashpot model //. The spring-dashpot model in Figure is presented and discussed in Ref. //. This model does not represent actual components of a polyester rope, such as linear springs and linear damping elements, but it has been found helpful for a qualitative description of complex non-linear rope behaviour. When fibre ropes are used in a mooring line there is usually some length of chain close to the anchor and at the top. Buoys may also be attached to the lines. This will result in some geometric stiffness due to the catenary shape of the line profile, and some drag effects. These effects are not included in the following discussion, but must be considered in a mooring system analysis. The catenary effect in the polyester rope itself will normally be small due to the high tension/weight ratio. The elastic stretch comprises the fast spring, which is tension-level dependent and slightly amplitude dependent, and the slow spring which gives additional change in length over Figure 2 Harmonic cycling test 2 Copyright 20 by ASME

3 Figure 3 Irregular cycling test All five tests performed are presented in the same diagram in Figure 4. Each test is drawn in different colour. The other tests were designed for identifying the characteristics of the different parts of the spring-dashpot model. Figure 4 All tests The main findings from the tests are: Dynamic stiffness follows a predictable behaviour that can easily be modelled. Dynamic stiffness can be considered frequencyindependent within wave-frequency and low-frequency domain for floating large-volume structures. There is repeatability in rope behaviour between different rope samples. The static stiffness is generally smaller than the dynamic stiffness obtained from sustained cycling. Construction stretch is low for the tested rope type. TRADITIONAL APPROACH There exist different strategies for analysis of mooring systems with polyester ropes. For benchmarking of the developed method, analyses with a traditional approach have been performed. The traditional approach was based on DNV- OS-E30, Ref. /2/: Synthetic fibre ropes are made of visco-elastic materials, so their stiffness characteristics are not constant and vary with the duration of load application, the load magnitude and number of cycles. In general, synthetic mooring lines become stiffer after a long service time. The following stiffness models should be applied in the analysis: a) An exhaustive non-linear force elongation model, which fully represents the change-in-length behaviour of the fibre rope. If such exhaustive model for the complete change-in length performance is not available, then the procedure in b), c) and d) should be applied. b) To establish the unit s excursion and demonstrate that it does not exceed the excursion capability of risers or other offset constraints. This analysis is carried out using the postinstallation stiffness in ULS and ALS. c) To establish characteristic line tension in ULS and ALS the dynamic stiffness should be applied. Alternatively, a model consisting of the static stiffness for calculation of characteristic tension due to mean loads and low frequency motions, and a dynamic stiffness for the characteristic tension due to wave frequency motions. Guidance note: In order to avoid potential over conservatism for tensions it is advisable to apply the pristine force vs. elongation curve for new fibre rope. d) The fatigue (FLS) shall be performed using the same procedure as for ULS and ALS in c). The stiffnesses referenced above are defined as follows: Post-installation stiffness: Resulting static stiffness that may be used in analysis for the case where the maximum design storm occurs immediately after installation. Dynamic stiffness: Maximum stiffness of the mooring lines, which applies when the mooring system is subject to the cyclic loading of a maximum design storm. Static stiffness: Ratio of change in force to change in length when tension is either increased or reduced. Based on the test results for the present rope, the following stiffness values for analysis with traditional approach have been selected to be used in the case study, see Figure 4: Post-installation stiffness: EA = 8 AVS Dynamic stiffness: EA = 28 AVS The selection of these values, particularly post-installation stiffness, is subject to judgment since they do not come out from standardized testing. Analysis modes -3 as presented in Table 2 were applied for the traditional approach in the case study. Mode 2 uses dynamic stiffness throughout, and is conservative with respect to calculation of extreme tensions. Mode 3 used postinstallation stiffness throughout, and is conservative with respect to extreme offsets. Mode uses post-installation stiffness for static equilibrium and low-frequency motions (and tensions), and dynamic stiffness for wave-frequency tension. 3 Copyright 20 by ASME

4 Analysis of test results has shown that dynamic stiffness is equal for low-frequency and wave-frequency response. It must therefore be assumed that Mode is conservative with respect to calculation of extreme offsets and non-conservative with respect to extreme tensions. The proposed model consists therefore of non-linear characteristics for mean tension and linear stiffness for wavefrequency and low-frequency motions and tensions. NEW FREQUENCY DOMAIN MODEL In the operational phase of a moored floating structure it will be exposed to changing environmental conditions. For analysis of mooring systems it is common practice to analyse stationary sea states with 3 hours duration. From the tests presented herein it is found that most of the change in length in a polyester line occurs during the first 0 to 20 minutes after a change in tension level. The environmental parameters (significant wave height, wind velocity and current velocity) vary with typical periods of 6 hours and longer. It is therefore assumed to be a good approximation to analyse the mooring lines with the length that they will have at the end of each 3- hour sea state. With this in mind an empirical model of the change-in-length behaviour for a polyester rope is proposed is shown in Figure 5 and presented in the following. The original curve is the force versus elongation that is obtained during the first rapid loading of a new rope, F = f 0 ( ε ) The maximum curve represents the equilibrium working points if the rope is working around its historical maximum tension. This equilibrium is found when the maximum elastic stretch has been imposed on the rope. F = f ε ), ( ε 0 For the tested rope it has been found to be a good approximation to use f ε ε ) = f ( ). ( 0 0 ε After the rope has been on its maximum mean tension, it will retract along a working curve down to a length corresponding to the state after unloading a couple of hours at low tension. This strain depends on the maximum tension. Top of working curve: ε = ε + f F ) max ε 0 ( max = ε 0 + k ( ε max ε 0 Bottom of working curve: ) where k is determined from tests. ε ε k2 Working curve: F = Fmax, where the ε max ε exponent k 2 is determined from tests. The working point will be on the maximum curve if the mean tension in the rope is at its historical maximum. Otherwise, it will be at the working curve corresponding to its historical maximum. The dynamic stiffness is dependent on the mean tension in the line. For the present rope it has been found reasonable to model this by a linear dependency on mean tension: K = a + b. dyn F mean ε Figure 5 Rope model working curves depending on max mean tension CASE STUDY The objective of the case study was to investigate the consequence of using the new approach for analysing fibre-rope mooring systems with regard to calculated offsets and extreme tensions. The selected unit is a semi-submersible production platform in 300 m water depth and harsh environment. The 6- line mooring system is based on long polyester segments with short top and bottom segments of chain. The mooring lines are located in 4 clusters as presented in Figure 6. The analyses cover intact ULS analyses along the 00-year return-period contour, and a long-term simulation using hindcasted time series of environmental conditions as input. No accidental load cases have been analysed and no riser system has been modelled. Fatigue in fibre ropes has been disregarded since it is negligible compared to fatigue in the chain segments. Analyses were performed with MIMOSA 6.3, ref. /3/. The model was implemented through iterations on line lengths in the input file since the new model has not been implemented in the program yet. Input data for the analysis included:. Mooring system definition. 2. Linear diffraction results from WADAM (first-order motion RAOs and mean second-order wave drift forces) 3. Wind force coefficients, current force coefficients and low-frequency damping coefficients. 4 Copyright 20 by ASME

5 Figure 7 00-year return period sea state The following analysis approach was followed: Read vessel data. This includes st order motion transfer functions, wave drift force coefficients, wind force coefficients, current force coefficients, and damping coefficients. Figure 6 Mooring line directions The target safety factor for dynamic analyses is 2.5 for intact ULS analyses with the traditional approach. Top and bottom chain consisted of 4-mm stud-less chain with MBS 2420 kn. For the polyester rope the data in Table have been used. The pretension in the mooring lines is set to 5% of polyester AVS. Table Polyester rope data (assumed data) Diameter 203 mm Minimum breaking strength, MBS Weight in water 0009 kn.054 kn/m The extreme (ULS) analysis has been based on an omnidirectional environment: Sea states with % annual probability of exceedance (00-year return period) are defined by the contour in Figure 7. The top of the contour is characterized with significant waveheight 6.7 m and peak period 8.5 sec. The Torsethaugen double-peaked wave spectrum has been applied, Ref. /8/. Wind with % annual probability of exceedance (00- yr wind), specified as a -hour average wind speed of 34 m/s 0 m above sea level. The ISO (NORSOK) wind spectrum has been applied, Ref. /7/. Current speed with annual probability of exceedance 0. (0-year return period):.43 m/s. Read mooring system data and calculate anchor coordinates based on specified pretension and for the new model also installation tension. Specify environmental condition. Calculate equilibrium position using average environmental forces. Calculate low-frequency and wave-frequency motions about the equilibrium position. Calculate maximum line tensions. With the new approach the mean tension in each line will be on the working curve which depends on the maximum mean tension the line has experienced. Table 2 Analysis modes and stiffness models Mode Static equilibrium Low-frequency motions Wave frequency motions Post-installation Postinstallation Dynamic 2 Dynamic Dynamic Dynamic 4-6 Working curve. Installation tensions 5%, 20% and 25% of polyester segment strength Dynamic tension dependent 3 Post-installation Postinstallation Postinstallation Dynamic tension dependent The installation tension is the maximum tension applied during installation to impose permanent stretch to the rope. The 5 Copyright 20 by ASME

6 analyses for the new model have been performed for different installation tensions, modes 4-6 in Table 2. RESULTS ULS analysis Intact ULS analysis has been performed for sea states along the 00-year return-period contour in combination with 00- year return-period wind and 0-year return-period current. Environment was collinear and approaching at 45 relative to the semi. The purpose of this analysis is to investigate the difference between traditional and new approach in an extreme condition. The new approach is dependent on the initilisation of the lines. The base case was maximum installation tension of 5% AVS. Sensitivities to installation at 20% and 25% were also analysed. If the unit is equipped with mooring winches it will be possible to compensate for low tensioning during installation. This has however not been considered any further in the study. Results from the ULS analyses are presented in Figure 8. for mode 2 where both low-frequency and wave-frequency tensions are calculated using the dynamic stiffness. For the new model (modes 4, 5, and 6) it is seen that the results depend on the installation tension. A low installation tension (mode 4) gives a relatively high safety factor and a high offset, while a high installation tension gives the opposite. It is further seen that mode gives higher safety factors than the new model, since a lower stiffness is used for low-frequency motions and tensions, while the new mode use the same dynamic stiffness for both. It should be noted that the results for the new model are obtained assuming that the extreme sea state is occurring immediately after installation, so that the maximum tension each line has experienced has not increased since installation. In practice, if installation tension was low, the leeward lines would have been stretched in a previous storm from the opposite direction, giving larger offsets and smaller extreme tensions. FLS analysis Long-term analyses were also run for all sea states in the hind-cast database for ½ years, assuming installation in July. The development in significant wave height is presented in Figure 9. Figure 8 ULS analysis results It is seen that the lowest safety factors are obtained for the 8.5 seconds peak period, which corresponds to the largest significant wave height. The offsets also have their maxima at this period except for modes and 3 which have slightly larger offsets at peak period 5.2 seconds corresponding to a significant wave height of 5 m. The highest safety factors were obtained for mode 3 where both low-frequency and wave-frequency tensions are calculated using the post-installation stiffness. This is however a nonconservative approach. The lowest safety factors were obtained Figure 9 Development of significant wave height in long-term analyses The development of maximum mean tension in the different lines is presented in Figure 0 for the 5 % installation tension. The lines experienced increase in maximum tension during the first winter period, and also in some of the lines towards the end of the year. For the intermediate installation tension the maximum tension increased slightly in one of the line groups at the end of the year, while for the highest installation tension no change occurred. 6 Copyright 20 by ASME

7 installation tension in the new approach, and is nearly the double of the conservative estimate using Mode 2 in the traditional approach. Mode 3 in traditional approach is far too non-conservative. Mode Table 3 Main results from case study Installation Max Min SF Min tension offset (m) fatigue life (years) % % % CONCLUSIONS Figure 0 Development of maximum mean tension in different lines Summary of results The results from the case study are summarised in Table 3. For traditional approach it is seen that the lowest safety factor is obtained for mode 2 which uses dynamic stiffness for both lowand wave-frequency tension. Mode 2 is not valid for calculation of maximum offset, as the mean offset and low-frequency motions have been calculated with the dynamic stiffness which is without discussion non-conservative. Modes and 3 give the same extreme offsets, as both use post-installation stiffness for calculation of mean offset and low-frequency motions. For the new method it is seen that the installation tension matters. High installation tension gives lower maximum offsets and lower safety factors. Fatigue in the top chain has been calculated according to ref. /2/ using sea states in the last year of the long-term simulation. The fatigue life prediction vary little due to This paper presents an improved frequency domain method for design of mooring systems with synthetic mooring line segments. Results from the case study show that the improved method gives significantly different line tensions and vessel offsets compared to the traditional design methods: The predicted extreme line tension and offset estimates are in general dependent on the past load history. A pronounced variability is observed for different levels of selected installation tension. The estimated fatigue damage of the connecting chain is insensitive to the selected installation tension, but the fatigue damage is considerably different compared to the use of the traditional design methods. The method is still in its initial stage of development. As a further refinement of the model the following may be considered: The working curve will not only depend on the maximum mean tension but also on minimum tension after the maximum tension. Contraction of the rope can be modelled by decreasing the maximum tension. The amount of test data available is however not sufficient to quantify this characteristics. Both of these refinements will require additional testing to determine the model and its parameters. Both are considered to be minor improvement compared to the effect of implementing the new approach as presented herein as an alternative to a traditional approach. The final analysis method must be accompanied by simple standardized test methods, such as developed in the preceding Joint Industry Project, Ref. /4/. 7 Copyright 20 by ASME

8 REFERENCES ACKNOWLEDGMENTS The content of this paper is based on the Syrope pilot study under contract for Statoil. The work in this project has been based on the findings from the Joint Industry Project Improving Fiber-Mooring Design Practices, Ref. /4/. The spring-dashpot model used as basis for this continued work has been developed by Mr. John Flory, who also has contributed vital understanding to this pilot study. The Bristle Worm subrope test machine shown in Figure was designed and commissioned by Mr. Jonny Nikolaisen at DNV together with MessTek Prüfsysteme GmbH who provided the cylinder and control systems. Also thanks to Jonny for assistance with the testing. The authors wish to express their thanks to Statoil for permission to publish the paper. The views expressed are those of the authors at the time of publication and not necessarily those of Statoil, DNV and MARINTEK. It is further foreseen that details will change as research progresses. // Flory, J.F., Åhjem, V. and Banfield, S.J, A New Method of Testing for Change-in-Length Properties Of Large Fiber Rope Deepwater Mooring Lines, OTC 8770, May /2/ Offshore Standard DNV-OS-E30, Position Mooring, October 200. /3/ MIMOSA User s Documentation, Marintek report, MT55 F05-9, March 2007 (Confidential). /4/ Project Report The 6 Change-in-Length Properties (6CILP) Method For Testing and Analyzing Fiber Ropes for Joint Industry Project Improving Fiber- Mooring Design Practices, December 2009 (Confidential). /5/ Syrope Pilot Study Model selection and Parameter Estimation, DNV report (Confidential) /6/ Syrope Pilot Study Case Study Frequency Domain, DNV report (Confidential) /7/ ISO 990- Petroleum and natural gas industries Specific requirements for offshore structures Part : Metocean design and operating considerations, /8/ Recommended Practice DNV-RP-C205, Environmental Conditions and Environmental Loads, October 200. Figure DNV Test Machine The Bristle Worm 8 Copyright 20 by ASME