Fatigue Analysis of Deepwater Hybrid Mooring Line Under Corrosion Effect

Abstract In the deepwater exploitation of oil and gas, replacing the polyester rope by a wire in the chain-wire-chain mooring line is proved to be fairly economic, but this may provoke some corresponding problems. Te aim of this paper is to compare the fatigue damage of two mooring system types, taking into account corrosion effects. Using a semi-submersible platform as the research object, two types of mooring systems of the similar static restoring stiffness were employed. Te mooring lines had the chain-wire-chain and chain-polyester-chain structure, respectively. Firstly, the numerical simulation model between the semi-submersible platform and its mooring system was built. Te time series of mooring line tension generated by each short-term sea state of South China Sea S4 area were calculated. Secondly, the rain flow counting method was employed to obtain the fatigue load spectrum. Thirdly, the Miner linear cumulative law model was used to compare the fatigue damage of the two mooring system types in long-term sea state. Finally, the corrosion effects from zero to twenty years were considered, and the comparison between the fatigue damage of the two mooring system types was recalculated.


INTRODUCTION
Floating platforms and their mooring systems need to resist various ocean environmental conditions. Changes in wind, current, and wave loads provoke variable motion and stress in the mooring system. Gradual accumulation of the variable stress can lead to cumulative fatigue damage. In recent years, many fatigue damages of the mooring line in the practical projects have been recorded [1]. Therefore the investigation of fatigue damage is still necessary, and the problem is discussed by many scholars.
A traditional catenary mooring system is still widely used in practical projects nowadays [2][3]. It usually has the chain-wirechain structure. With increasing water depth, the weight of the chain and the wire become very large, and the cost becomes uneconomic. Recently, the results of successful development of synthetic fibres have been applied to deepwater mooring system, for instance in the form of the polyester mooring system to FPSO-2 project conducted by Brazil Petroleum Company [4]. Some problems concerning the use of a new type of mooring system can be named, including the fatigue problem discussed in this paper.
At present, the commonly used calculation method of fatigue damage is the Miner linear cumulative law model which is based on the S-N curve, and this method is suggested by many criterions [5][6][7]. Another calculation method is the fracture mechanics approach, which is not very mature and still needs to develop [8][9]. That is why the S-N curve was used to calculate the fatigue damage in this paper.
Mathisen et al. [10] applied the S-N curve to calculate the fatigue damage of the mooring system in the DEEPMOOR project, and indicated that the wave responses could provoke more fatigue damage than the drift responses. Omar et al. [11] applied the Dirlik method, the rain flow counting method, the narrowband spectra analysis method, and the broadband spectra revised method to count the mooring line tension, and used the S-N curve to calculate the fatigue damage. Gao and Moan [12] investigated a catenary mooring system for a semi-submersible platform, and calculated the fatigue damage under wave loads and drift loads. Han et al. [13] investigated the influences of different mooring layouts to the fatigue damage of a mooring line. Qiao and Ou [14] calculated the fatigue damage of the polyester mooring line based on the S-N curve. Huang et al. [15] used the Ariane software to calculate the fatigue damage of a taut mooring system in the South China Sea.
The influence of corrosion effects to the fatigue damage is a separate problem. Gao et al. [16] introduced the reliability calculation to the corrosion fatigue damage analysis. Lardier et al. [17] applied the S-N curve and the fracture mechanics method to calculate the fatigue reliability of catenary mooring lines under corrosion effect.
In those research activities, the scholars mainly applied the S-N curve to calculate the fatigue damage of a certain mooring system. This paper aims at comparing the fatigue damage between the chain-wire-chain and chain-polyester-chain mooring systems, taking into account the corrosion effects.
A semi-submersible platform was selected as the research object, along with two mooring system types of similar static restoring stiffness. The Miner linear cumulative law model was used to compare the fatigue damage, and the corrosion effects from zero to twenty years were considered in the calculation.

FATIGUE ANALYSIS The S-N curve
According to American Petroleum Institute (API) Recommended Practice 2SK [6], the S-N curve presents the number of cycles to failure for a specific mooring component as a function of a constant normalized tension range, based on the results of experiments. For mooring systems, the T -K approach which only considers the tension fatigue and ignores the bending fatigue is normally used. The formula (1) presents the T -K curve.
where N is the number of cycles, R is the ratio of tension range to reference breaking strength, and M and K are material parameters in the T -K curve.
According to Miner's linear cumulative damage rule, the annual cumulative fatigue damage D can be summed up from the fatigue damage D i arising in a set of short-term sea states. (2) The fatigue damage D i in the i-th short-term sea state: where n i is the number of tension cycles encountered in this short-term sea state, R i is the ratio of the tension range to the referential breaking strength, E[R i M] is the expected value of the normalized tension range R i raised to the power M.
In the calculations, the values of M = 9.0 and K = 316 for chain, and M = 5.05 and K = 10 (3.25 -3.42 Lm) for wire, were chosen from the T -N curve of wire recommended by API RECOMMENDED PRACTICE 2SK [6]. L m is the ratio of the mean load to the referential breaking strength for wire. M = 9.0 and K = 7.5 and were chosen from the curve of polyester recommended by API RECOMMENDED PRACTICE 2SM [18].

Corrosion effect
The corrosion effect has many influence parameters, such as salinity, humidity, current velocity, water depth, etc. Melchers et al. [19] investigated the corrosion on fully submerged chains, and indicated that the mean value of the corrosion rate is slightly smaller than that given in DNV OS-E301 [7]. So, the corrosion rate of the chain used in this paper was assumed according to the DNV OS-E301. Besides, in practical applications a galvanized or plastic jacket is usually added to the wire or the polyester mooring component to protect against the corrosion effect [6], so only the corrosion effect of the chain was taken into account in this paper.
According to DNV OS-E301, the corrosion rate of a chain is divided into three parts. The corrosion rate in the splash zone is 0.8 mm/year, while the corrosion rates in the catenary and bottom zones are both 0.2 mm/year.
The influence of the corrosion effect to the fatigue damage is mainly represented in two ways. Firstly, the material parameters and in the curve are changed. Secondly, the stress in the mooring line is changed due to the reduction of the chain diameter provoked by the corrosion.

Semi-submersible platform
The main structure of the semi-submersible platform model consisted of two pontoons, four columns, a deck, and a derrick. The main characteristic parameters are listed in Table 1. Centre of gravity from water surface (m) 8.9 Roll gyration radius (m) 32.4 Pitch gyration radius (m) 32.1 Yaw gyration radius (m) 34.4 Initial air gap (m) 14 Diameter of brace (m) 1.8

Mooring system
The mooring system consisted of four (4×4) groups, as shown in Figure 1. Two mooring system types, which are chain-wirechain and chain-polyester-chain, were used respectively during the calculation in combination with the semi-submersible platform. The mooring line properties are listed in Table 2. The static characteristics of the two mooring types are compared in Fig. 2   According to Fig. 2 ÷ 3, the static characteristics of the two mooring system types are similar. Then the two mooring system types were added to the semi-submersible platform.

Environmental conditions
Motion responses of the semi-submersible platform were calculated under the combination of wind, current, and wave loads. The sea state condition was selected from the South China Sea S4 area, along with the angle of incidence with respect to the X-axis. The long-term sea state usually consists of a number of short-term sea states. According to the wave scatter diagram of South China Sea S4 [15] in one year, the chosen sea states are listed in Table 3 and the JONSWAP spectra with the peak value γ = 2.0 were used. H s is the significant wave height, T s is the zero up-crossing period. V s is the wind speed. In the calculations the API wind spectrum was used. is the mean current speed. "p" is the occurrence probability of each sea state.

NUMERICAL SIMULATION Coupled model between the semi-submersible platform and its mooring system
To calculate the coupled motion, the Cummins's method [21] was applied in this study. The wave forces on the semisubmersible platform were calculated using the boundary element method based on the diffraction theory and the commercially available program AQWA [22]. The panel model is shown in Figure 5. The model for the coupled analysis of the semi-submersible platform and its mooring lines is shown in Figure 6. A coupled model of the semi-submersible platform and its mooring system is known from the literature [23]. It was also established by the authors of this paper.

Fatigue load spectra
In the comparative analysis of fatigue damage, the fatigue load spectra of the mooring line need to be obtained firstly. In this study, the rain float counting method [24] was employed to count the mooring line tension. A histogram of the tension range can be obtained from this counting, in the form of fatigue load spectra of the mooring line.
A time series of the mooring line tension at point A (shown in Fig. 4) between the two mooring system types under sea states No. 16, 36, 56 are plotted in Figure 7, and the corresponding fatigue load spectra are plotted in Figures 8 ÷ 9  The statistic analysis of the fatigue load spectra in all short-term sea states reveals that they don't satisfy the normal theory probability distribution. Therefore the histograms were employed to reflect the short-term distribution of tension range under all short-term sea states, and the rain flow counting results were used to calculate the fatigue damage directly in the later study.

FATIGUE ANALYSIS
Based on the abovementioned fatigue damage calculation method, the fatigue damages of the two mooring system types were calculated. The fatigue damages of Point A, B, and C, which represent the upper end point of three segments in the mooring line (shown in Fig. 4), were compared without the corrosion effect. Then, the corrosion effect after 5 years, 10 years, 15 years, and 20 years was taken into account. The fatigue damages of Point A, B, and C under each shot-term sea state were recalculated under the effect of the corrosion rate.

Fatigue damage without corrosion
The fatigue damages of the two mooring system types under each short-term sea state are plotted in Fig. 10 ÷ 11, and the comparisons of point A, B, and C are plotted in Fig. 12 ÷ 14. The vertical-axis is the logarithm of fatigue damage. According to Fig. 10 ÷ 11, in both cases of the two examined mooring system types the main fatigue damage occurred in the chain segment, independently of the fact whether the mooring line has the chain-wire-chain or the chain-polyester-chain structure. At the same time, the fatigue damage in the wire or polyester segment is relatively much smaller. In the chain-wire-chain mooring line, the fatigue damage in the upper chain is obvious larger than in the bottom chain, while for the chain-polyester-chain mooring line the fatigue damage in the upper chain is almost the same as in the bottom chain. This phenomenon should need additional attention in the practical project. When using the chain-polyester-chain mooring system, the most possible fatigue damage zone includes not only the upper chain in the splash zone, but also the bottom chain.
According to Fig. 12 ÷ 14, the fatigue damage of point B in the steel mooring line is larger than the one in the polyester mooring line, but the fatigue damages of point A and C in the steel mooring line are smaller than those in the polyester mooring line. In other words, replacement of the polyester rope for the wire in the chain-wire-chain mooring line resulted in a much smaller fatigue damage than that observed for the wire, but also provoked fatigue damages of the upper and bottom chains which are larger than those recorded for the chain-wire-chain mooring line. This interesting phenomenon still needs additional attention in the practical project. The replacement of the polyester rope for the wire in the chainwire-chain mooring line means immolating the fatigue life of the chain to improve the fatigue life of middle segment.       Fig. 18 ÷ 20, the difference in the scale of the fatigue damage between the two mooring system types is getting bigger with the increasing corrosion years. Under the 20-year corrosion effect, the difference between the fatigue damage of the two mooring system types at point A, B, and C is much larger than the ones without corrosion. In other words, the corrosion effect increases the difference between the fatigue damages of the two mooring system types.

CONCLUSIONS
The fatigue damages between the chain-wire-chain and chain-polyester-chain mooring systems applied for a semisubmersible platform were compared. The two types of mooring systems had a similar static restoring stiffness. The analysis took into account the corrosion effect. The following preliminary findings can be formulated: • The fatigue load spectra of the mooring line don't satisfy the normal theory probability distribution and the rain flow counting results needs to be used directly in calculating the fatigue damage.

•
The main fatigue damage occurred in the chain segment, and the fatigue damage in the wire or polyester segment is relative much small. In the chain-wire-chain mooring line, the fatigue damage in the upper chain is obvious larger than in the bottom chain, while in the chain-polyesterchain mooring line the fatigue damage in the upper chain is almost the same as in the bottom chain.

•
The replacement of polyester rope for the wire in chain-wire-chain mooring line provokes the fatigue damage which is much smaller for the polyester than for the wire, but simultaneously the fatigue damages of the upper and bottom chains in the chain-polyester -chain mooring line are larger than those in the chain-wire-chain mooring line.

•
The nature of fatigue damage changes under corrosion effect is similar to that without corrosion. With the increasing corrosion years, the fatigue damage under each short-term sea state also increases.

•
Under the corrosion effect, the increase of the fatigue damage of point A under long-term sea state is much larger than the one of point B and C. The corrosion effect increases the difference between the fatigue damage of the two mooring system types.