Jan Mathisen

Prediction of Mooring Line Tensions for Hurricane Conditions in the Gulf of Mexico

A probabilistic metocean model for hurricane conditions is briefly described. The model is based on site-specific, hindcast data and defines the time variation of the metocean conditions during the realisation of a hurricane at the site. The annual extreme value distribution of mooring line tension for a large, semi-submersible, mobile drilling unit is computed. Time domain analysis is applied to obtain the short-term, extreme value distribution of line tension, conditional on stationary metocean conditions. A large number of different conditions are considered. A response surface is used to interpolate on the short-term distribution parameters in order to describe the tension response during the varying conditions associated with the passage of a hurricane. The hurricane duration is split into a sequence of 15-minute intervals such that the conditions can be assumed stationary during each such short interval. The tension distribution, conditional on the realisation of a hurricane, is accumulated across the sequence of short intervals. The distribution of hurricanes is taken into account to obtain the tension distribution in a random hurricane. Finally, the frequency of hurricanes is taken into account to give the annual extreme distribution of line tension. The characteristic tension computed using 10-year return conditions and the ISO 19901-7 design standard is found to correspond to a return period of 29 years in the test case. The effects of various assumptions in the design analysis are investigated. Sensitivities to simplifications of the metocean model are considered. The effects of uncertainties in the response calculation and in the distribution of peak significant wave height during hurricanes are quantified and included in the response analysis.Copyright

NorMoor JIP: On Safe Mooring Line Design

DNV is currently running a Joint Industry Project, “NorMoor JIP”, on calibration of safety factors for mooring lines together with several oil companies, engineering companies, rig-owners, manufacturers of mooring line components and Norwegian authorities.Our motivation for initiating a study on mooring line safety factors started out with questions raised with regards to the safety level given by the Norwegian regulations. However, this is equally important for other mooring regulations like ISO, API and class-regulations. What we see is that the mooring standards are interpreted and applied in different ways. The reliability level implied by the regulations is not known, and the present safety factors were set when frequency domain analysis was prevalent while time domain analysis is often applied today.DNV carried out the DeepMoor JIP [9] during 1995–2000 using frequency domain analysis and reliability-based calibration. Now, a decade later, the increase in computing capacity makes it feasible to carry out a similar calibration for time-domain analysis of the mooring systems.The objective of the project work is to investigate and compare the characteristic line tension calculated according to design standards with the annual extreme value distribution of the line tension. Further, to calibrate safety factors for mooring line design for the ultimate limit state (ULS) as a function of the target probability of failure.The original proposal for this JIP included calculations for chain and wire rope moorings on a typical drill rig and a turret moored FPSO at three different water depths at Haltenbanken. However, since this JIP has been very well received in the industry, the scope has been extended to include calculations for a production semisubmersible, for fibre rope systems and for Gulf of Mexico environmental conditions.This paper will focus on the reasons for doing this calibration study, and the importance of seeking to agree on unified calculation recipes and requirements. Preliminary results for characteristic tension and annual extreme value distributions of tension for some designs are presented and discussed. The calibration of safety factors will be carried out later in the project when all designs are finalized.© 2012 ASME

Probabilistic Modelling for Reliability Analysis of Jackets

Experience from recent reliability analyses of jacket platforms is used to discuss selected aspects of probabilistic modelling in more detail. These modelling details can have a significant effect on the computed reliabilities. An overview of basic considerations and failure modes in jacket reliability analysis is included to set the various details into context. Ultimate limit states for jackets in relatively shallow water are emphasised; i.e. quasi-static structural response is applicable. The following topics are considered: (a) Failure modes and some requirements to load and resistance analysis. (b) Directionality in loading and resistance. (c) Random periods of individual extreme waves. (d) Foundations — axial and lateral capacity modelling for multiple piles and model uncertainty for pile capacity.Copyright

A Probabilistic Metocean Model for Mooring Response in Gulf of Mexico Hurricanes

Hindcast data for a specific location is utilised to develop a joint probability function for the metocean variables that are expected to have a significant effect on mooring line tensions for a floating platform moored at that location. The main random variables comprise: peak significant wave height, peak wind speed, peak surface current speed, peak wave direction, peak wind direction and peak current direction, where “peak” indicates the maximum intensity of the metocean effect during a random hurricane. The time lead of peak wind relative to peak waves and the time lag of peak current after peak wind are included as random variables. It is also necessary to describe the time variation around the peak events. Simple models are assumed based on inspection of the time variations during severe hurricanes. Only the part of the hurricane during which the significant wave height exceeds 80% of the peak value is taken into account. The duration of this interval is included. Linear variation is assumed for the directions, hence the rates of change of the 3 directions are included. A linear (triangular) plus parabolic model is assumed for the time variation of the intensities of the 3 metocean effects around their respective peaks. A single parameter is required to define the proportion of linear and parabolic models for each effect and the values of this parameter for each of the 3 metocean effects are also included as random variables.A random hurricane can be drawn from this metocean model, such that the time variation of the metocean actions is deterministic once the values of the random variables have been selected. The overall duration of the hurricane is split into short intervals, each of 15 minutes duration, such that stationary response may be assumed during each short interval. The extreme value distribution of line tension during each short interval is obtained. These distributions are combined to obtain the extreme distribution of line tension during the hurricane. Second order reliability methods are applied to integrate over the distribution of the metocean variables and obtain the distribution of extreme tension during a random hurricane. The annual frequency of hurricanes is used to derive the annual extreme value distribution of line tension.The model is intended for the reliability analysis of the ultimate limit state of mooring lines, but may also be applicable to other response variables. The present paper is primarily concerned with the metocean model, but it is intended to include sample results for the extreme line tension.Copyright

On the Probability Distribution of Mooring Line Tensions in a Directional Environment

A joint probabilistic model of the metocean environment is assembled, taking account of wind, wave and current and their respective heading angles. Mooring line tensions are computed in the time domain, for a large set of short-term stationary conditions, intended to span the domain of metocean conditions that contribute significantly to the probabilities of high tensions. Weibull probability distributions are fitted to local tension maxima extracted from each time series. Long time series of 30 hours duration are used to reduce statistical uncertainty. Short-term, Gumbel extreme value distributions of line tension are derived from the maxima distributions. A response surface is fitted to the distribution parameters for line tension, to allow interpolation between the metocean conditions that have been explicitly analysed. A second order reliability method is applied to integrate the short-term tension distributions over the probability of the metocean conditions and obtain the annual extreme value distribution of line tension. Results are given for the most heavily loaded mooring line in two mooring systems: a mobile drilling unit and a production platform. The effects of different assumptions concerning the distribution of wave heading angles in simplified analysis for mooring line design are quantified by comparison with the detailed calculations.Copyright

Extreme Storm Wave Histories for Cyclic Check of Offshore Structures

Offshore platform resistance to cyclic storm actions is addressed. In order to achieve the best economy of the structure especially when assessing existing structures, the ultimate capacity of the structure is utilized. This means that parts of the structure may be loaded into the non-linear range and consequently the load-carrying resistance of the structure against future load cycles may be reduced. In such cases it is required to carry out a check of the cyclic capacity of the structure. Such checks are required in the ISO 19902 code for Fixed Steel Offshore Structures. The paper presents a proposal for how a load history for cyclic checks can be established. The method is in line with what is included in the NORSOK N-006 standard on “Assessment of structural integrity for existing load-bearing structures”. The load-history for the waves in the design storm may be expressed as ratio of the dimensioning wave. The ratio will be different for check of failure modes where the entire storm will be relevant such as crack growth, compared to failure modes like buckling where only the remaining waves after the dimensioning wave need to be accounted for. Using simple order statistics and simulation, the statistics for the ith (Hi ), i = 1, 2, 3, 4 etc. highest wave in the storm is studied in some detail, assuming that the maximum wave (H1 ) is equal to an extreme wave obtained by a code requirement. Environmental contours for the pair (H1 ,H2 ) are established by Inverse FORM for design conditions. Further, the long term statistics for load effects that are expressed as a function of H1 , .., H4 , i.e. L = f(H1 , .., H4 ), are determined. The R-year value LR for the load effect L is determined by structural reliability techniques, and the most probable combination (design point) (H1 *, .., H4 *) for L = LR is determined. The design point values Hi *, as well as the design point value for the significant wave height, are determined for different load effects, and their characteristics for different types of load effects are discussed. The paper gives advice also on how to establish the magnitude for the remaining waves in the storm.Copyright

Reliability Reassessment of a Jacket Platform With Gas Seepage in the South China Sea

A structural reliability analysis is carried out on a jacket platform in 75 m water depth, in the South China Sea. A platform collapse failure mode is considered, with emphasis on uncertain soil conditions around the pile foundations, due to gas seepage while the platform has been in service. Random environmental conditions due to wind, waves and current are taken into account, based on observed data. Allowance for the short duration of environmental measurements is included and has a marked effect on the results. Two response surfaces are applied in the reliability calculation, to model the loads and the system capacity.Copyright

Consistent Design Codes for Anchors and Mooring Lines

As the water depth of hydrocarbon discoveries becomes deeper, the technological challenges related to the design of mooring systems increases. Changing from steel catenary mooring systems (CMS) to fibre rope taut mooring systems (TMS) has been accompanied by an immense focus on how to qualify and approve fibre rope material for use in a TMS. This involves items related to specifications for manufacturing, handling and testing fibre ropes, as well as calibration of safety factors to use in the design of TMSs. One consequence of moving to a TMS is that the anchors will have to take more uplift load than in a conventional CMS, which makes the anchors a more critical component of the mooring system than before. The types of anchor normally available to the designer of a TMS are pile anchors, suction anchors and various types of plate anchors. Anchors of all types are designed and installed in ever-deeper water, but the safety of the designed mooring systems varies with the design code adopted. There is thus an obvious need for an industry standard, a design code for each anchor type that is calibrated based on structural reliability analysis using the current experience and knowledge in the industry. This paper compares anchor design codes that use total safety factors (TSF) with the DNV design code that uses partial safety factors and failure consequence classes. Examples of design codes for station-keeping systems that adopt the TSF format are API RP2SK and (assumed herein) the ISO code, which is under development. The comparison demonstrates that use of the safety format adopted in the DNV code provides more flexibility and ensures a uniform safety level of all components in a mooring system than the TSF format. If all types of anchor were designed to the same safety level it would be possible to compare anchors without worrying about differences in safety. A typical approach for calibration of a design code is described.Copyright

Wellhead Fatigue Analysis Method: Benefits of a Structural Reliability Analysis Approach

Structural Reliability Analysis (SRA) methods have been applied to marine and offshore structures for decades. SRA has proven useful in life extension exercises and inspection planning of existing offshore structures. It is also a useful tool in code development, where the reliability level provided by the code is calibrated to a target failure probability obtained by SRA. This applies both to extreme load situations and also to a structural system under the influence of a time dependent degradation process such as fatigue.The current analysis methods suggested for service life estimation of subsea wells are deterministic, and these analyses are associated with high sensitivity to variations in input parameters. Thus sensitivity screening is often recommended for certain input parameters, and the worst case is then typically used as a basis for the analysis. The associated level of conservatism embedded in results from a deterministic analysis is not quantified, and it is therefore difficult to know and to justify if unnecessary conservatism can be removed from the calculations.By applying SRA to a wellhead fatigue analysis, the input parameters are accounted for with their associated uncertainty given by probability distributions. Analysis results can be generated by use of Monte-Carlo simulations or FORM/SORM (first/second order reliability methods), accounting for the full scatter of system relations and input variations. The level of conservatism can then be quantified and evaluated versus an acceptable probability of failure.This article presents results from a SRA of a fictitious but still realistic well model, including the main assumptions that were made, and discusses how SRA can be applied to a wellhead fatigue analysis. Global load analyses and local stress calculations were carried out prior to the SRA, and a response surface technique was used to interpolate on these results. This analysis has been limited to two hotspots located in each of the two main load bearing members of the wellhead system.The SRA provides a probability of failure estimate that may be used to give better decision support in the event of life extension of existing subsea wells. In addition, a relative uncertainty ranking of input variables provides insight into the problem and knowledge about where risk reducing efforts should be made to reduce the uncertainty.It should be noted that most attention has been given to the method development, and that more comprehensive analysis work and assessment of specific input is needed in a real case.Copyright

Refinement of Fatigue-Life Estimates by Interpolation on Metocean Conditions

The fatigue life of ships and offshore structures is commonly based on the Miner-Palmgren hypothesis and S-N curves. Fatigue damage rates can be calculated for each short-term sea state, and then combined with the probabilities of the short-term sea states to obtain the long-term damage rate and the estimated fatigue life. Each short-term stress response is usually computed for one point within the corresponding bin of the scatter diagram. In order to minimize uncertainty arising from the choice of a single representative point within a relatively large bin, a refinement procedure is proposed by interpolation on metocean conditions. The proposed procedure is applied to the most heavily utilized girth weld of a TLP tether and discussed.Copyright