1 Copyright © 2012 by ASME

Proceedings of the ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering OMAE2012

June 10-15, 2012, Rio de Janeiro, Brazil

OMAE2012-84121

INVESTIGATION ON THE USE OF DIFFERENT APPROACHES TO MOORING ANALYSIS AND APPROPRIATE SAFETY FACTORS

Sojan Vasudevan InterMoor Marine Services Ltd.

Aberdeen, UK

Paul Westlake InterMoor Marine Services Ltd.

Aberdeen, UK

ABSTRACT This paper presents the results of the analyses of a twelve

line catenary mooring system using a quasi-static method in the frequency domain, and uncoupled and coupled dynamic methods in the time domain. The latter is found to produce significantly higher tensions. The reasons for these differences are investigated.

The minimum line tension safety factors required by design codes do not distinguish between uncoupled and coupled dynamic analyses and some codes use the same factors even for quasi-static analyses. Consequently, the present mooring system passes the acceptance criteria based on quasi-static frequency domain and uncoupled dynamic time domain analyses but does not meet the same criteria when a coupled dynamic time domain analysis is employed.

It is understood that because the coupled time domain analysis determines the vessel motions using all forces the accuracy of mooring line tension estimation will be improved over other methods. Hence the application of less conservative safety factors is proposed.

INTRODUCTION The analysis of a mooring system is performed to predict

responses such as line tensions, anchor loads and vessel offsets under the design environment. The predicted responses are compared against design code criteria to ensure the integrity of the system.

Maritime regulatory authorities permit mooring systems to be designed by quasi-static or dynamic techniques. Either method may be implemented in the frequency domain or in the time domain.

Furthermore, dynamic analyses may be 'uncoupled' or 'coupled'. In an uncoupled analysis environmental forces and motions associated with the vessel are prescribed and are independent of the mooring line tensions. In a coupled analysis all inertial, hydrodynamic and mechanical (mooring lines) forces acting on the vessel are used to determine its subsequent motions.

Various studies are found in the literature on different analyses types, their numerical modelling, and their merits and deficiencies. Kwan et al [1] discusses the modelling of frequency domain and time domain mooring analysis procedures, their applications and limitations, and compares them with quasi-static analysis. Garrett [2] presents computational procedures for fully coupled time and frequency domain analysis of floating production systems, and concludes that the frequency domain approach is computationally more efficient with little loss of accuracy. Mavrakos et al [3] compare numerical predictions from both time and frequency domain analyses against experimental results for deep water mooring systems, and conclude that the time domain simulation shows better correlation with experimental results.

The present study compares the characteristic tensions obtained from the three basic analysis types for a typical mooring system, i.e. a quasi-static analysis in the frequency domain, an uncoupled dynamic analysis in the time domain and a coupled dynamic analysis in the time domain. The effect of cross bracings is also investigated.

METHODOLOGY A twelve line symmetric mooring system is designed for a

modified Sedco 700 series semi-submersible. The following approach is used.

1. The mooring system is designed using a quasi-static frequency domain approach using Romeo [4], which is a riser and mooring system analysis tool developed by Noble Denton.

2. The derived mooring system is then analysed in the time domain using Orcaflex [5], which is a finite element software tool with extensive capabilities for modelling marine and offshore structures. The following variations are considered:

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a. Uncoupled analysis, without cross bracings b. Uncoupled analysis, including cross bracings c. Coupled analysis, without cross bracings d. Coupled analysis, including cross bracings

The cross bracings are modelled as Morison elements generating both inertia and damping forces.

The uncoupled analysis makes use of “displacement RAOs” (frequency and heading dependent displacement per unit wave amplitude matrices). In this case, the equation of motion is solved without considering the forces exerted by the mooring lines. The motions specified by the displacement RAOs are then applied at the top of the mooring lines in order to calculate line tensions.

The coupled analysis makes use of “load RAOs”, which provide the loads (forces and moments) due to the incident wave system acting on the vessel. These loads are used in conjunction with all other loads (such as those from mooring lines, thrusters, wind and current) to determine the vessel’s response from the equations of motion.

The free-floating displacement and load RAOs, and other hydrodynamic data, have been generated using AQWA [6]. The time domain simulations are completed in Orcaflex. Equations of motion are therefore solved in AQWA for the uncoupled analysis and Orcaflex for the coupled analysis.

The results are based on three-hour simulations. The characteristic line tensions are defined as the three hour most probable extreme wire tensions at the fairleads assuming a Rayleigh distribution.

The basis for compliance is Lloyds Rules [7].

MOORING SYSTEM The mooring spread for a Northwesterly heading in a water

depth of 165 metres is shown in Figure 1. The mooring lines are composed of 250 metres of 83mm wire rope and 690 metres of 76mm studlink ground chain. Five ten tonne clumpweights are distributed on the ground chain near the wire/chain connection. With an anchor range of 900 metres and a pre-tension of 75 tonnes the mooring line grounds just after the wire/chain connection.

The Minimum Breaking Load (MBL) of the wire is 457 tonnes and the MBL of the chain is 613 tonnes. The normal added mass and damping coefficients associated with the wire are Ca=1.0 and Cdd=1.8. The normal added mass and damping coefficients associated with the chain are Ca=1.6 and Cdd=2.6.

Figure 1: Mooring spread.

Table 1 provides the one hundred year return period

environmental data used for the analysis. A JONSWAP wave spectrum and an NPD wind gust spectrum are used. The variation of current speed with water depth is taken into account.

Env Direction

(from)

One hour mean wind speed [m/s]

Significant wave height Hs [m]

Peak period Tp [s]

Zero-crossing period Tz [s]

Surface current

[m/s]

N 40.5 16.4 17.0 12.6 12.6

NE 32.8 10.2 13.4 9.9 9.9

E 30.6 9.5 13.0 9.6 9.6

SE 39.9 14.2 15.9 11.7 11.7

S 40.5 16.4 17.0 12.6 12.6

SW 38.9 16.4 17.0 12.6 12.6

W 40.5 16.4 17.0 12.6 12.6

NW 40.5 16.4 17.0 12.6 12.6

Table 1: Directional environmental data.

RESULTS Figure 2 illustrates the characteristic line tensions obtained

from the three analyses. The minimum permissible safety factor as per the Rules [7] is 1.67 in the intact condition.

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Figure 2: Comparison of worst line tensions [t] from various

analyses.

All time domain results follow the same trend with the lowest characteristic tensions associated with weather originating from the East and a maximum for weather from the South West. However the highest characteristic tension provided by the quasi-static analysis is associated with weather from the West.

The difference between the characteristic tensions obtained from the uncoupled and coupled analyses is striking and therefore the component parts of the total tension are examined. This has been done in two ways.

1. The effect of each contributory factor (such as wind, current etc) is estimated as the increase in line tension over the static line tension when that factor alone is applied.

2. The effect of each contributory factor is estimated as the decrease from the maximum dynamic line tension when that factor alone is removed (and all other factors are applied).

The average from these two methods can be taken as the tension contribution of each component part.

In general the sum of the tension contributions from all factors will not exactly match the total characteristic tension when all factors are applied. This is because when multiple environmental loads are applied simultaneously, their effects on

the catenary is not directly related to applying them individually, i.e., the forces interact with one another.

Figure 3 illustrates a typical breakdown of tension components. The interaction effects mentioned above are indicated by the “Combined effects” entry in the figure.

Figure 3: Tension components from uncoupled (Disp RAO) and

coupled (Load RAO) analyses. Wind contribution - constant wind versus gust spectrum

In an uncoupled analysis wind forces are only applied during the initial static equilibrium phase and are omitted from the subsequent time domain simulation. Therefore the wind induced component of line tension is identical for a constant wind speed or a gust spectrum.

In a coupled analysis the gust spectrum is applied in the time domain and results in increased line tensions. Wave contribution

The contribution from first order waves is high compared to the second order waves. Both first and second order wave components of line tension are higher for the coupled analysis. The frequency response of the coupled model differs from that of the uncoupled model because the effects of the mooring lines are included in the equations of motion. This may explain the differences in wave contribution from the two models.

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NE

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Romeo Quasi‐Static

Orcaflex Uncoupled w/o cross bracings

Orcaflex Uncoupled with cross bracings

Orcaflex Coupled w/o cross bracings

Orcaflex Coupled with cross bracings

Maximum Permissible

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Disp RAO Load RAO

Tension [t]

Pre‐tensionWind contributionFirst order wave contributionSecond order wave contributionCurrent contibutionMooring line dynamics contributionCombined effects

4 Copyright © 2012 by ASME

Current contribution The contribution of current to the total line tension is small

and the values are similar for both coupled and uncoupled analyses.

Mooring line dynamics contribution

The contribution of mooring line dynamics to the total line tension is small. Examples show that the hydrodynamic forces on the mooring lines contribute to a 2-3% increase in line tension. Slack mooring lines and snap loads

Figure 4 illustrates the most heavily loaded line tension obtained at 10%, 25%, 50% and 75% of the one hundred year return period environment. All five analyses produce similar results up to about 50%. At 75% the tensions obtained from the coupled analyses begin to deviate from the tensions obtained from the other models. At 100% the tensions from the coupled analyses are significantly higher.

Examination of the line tension time histories indicates that at 50% none of the mooring lines become slack. At 75% the minimum tension in some of the mooring lines becomes zero over a short length indicating that lines are starting to go slack. At 100% the extent of zero tension extends over large lengths of most lines, including the most heavily loaded lines.

Figure 4: Effect of the variation in environment on the

characteristic tension.

A tension spike occurs when the lines re-tension. Both uncoupled and coupled methods model this behaviour; however only in a coupled analysis will the impulsive loads affect vessel motions which will in turn modify subsequent tension time histories.

Figure 5 illustrates a typical tension time history from a coupled analysis. It is evident that when the tension approaches zero a tension spike is subsequently observed.

Figure 5: Slack line instances in line 10 from a coupled analysis.

However not all tension spikes are preceded by a slack line. Figure 6 illustrates a tension spike from the same time history not preceded by a slack line. This is the largest tension observed in the entire simulation (5600kN at 10350s).

Figure 6: Maximum tension occurrence in line 10 from a coupled

analysis.

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0% 20% 40% 60% 80% 100%

Worst lin

e tension [t]

% 100‐yr Return Period Weather (from SW)

ROMEO ‐ quasistatic

Orcaflex Uncoupled w/o cross bracings

Orcaflex Uncoupled with cross bracings

Orcaflex Coupled w/o cross bracings

Orcaflex Coupled with cross bracings

Time (s)40003900380037003600350034003300320031003000

Line

10 E

nd F

orce

(kN

) at

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Time (s)108001070010600105001040010300102001010010000

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10 E

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orce

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End

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5 Copyright © 2012 by ASME

Further examination of the results shows that immediately before this tension spike the rig is at a large horizontal offset caused by a large wave. The arrival of a second large wave causes further offset resulting in the grounded length reducing to zero, thereby causing anchor uplift and the tension spike.

In the case of the tension spikes caused by the slack line instances the grounded length remains positive.

ACCEPTANCE CRITERIA Design codes state acceptance criteria for various parameters such as:

- line tension - permissible vessel offset - anchor loads

The maximum line tension in the intact condition is cited here as an example. In practice all criteria need to be addressed for both the intact and the single line failure conditions.

As per Lloyds Rules [7], the line tension safety factor, defined as the ratio of the MBL to the maximum line tension, should be 1.67 for the intact condition. No distinction is made on the type of analysis (quasi-static/dynamic, frequency domain/time domain, coupled/uncoupled). According to this, the present mooring system passes the acceptance criteria based on quasi-static and uncoupled analyses, but fails based on coupled analyses (Table 2).

Maximum

characteristic tension [t]

Safety factor [-]

Pass / Fail

Quasi-static 230 1.99 Pass Uncoupled, without cross-bracings

200 2.29 Pass

Uncoupled, with cross-bracings

231 1.98 Pass

Coupled, without cross-bracings

320 1.43 Fail

Coupled, with cross-bracings

388 1.18 Fail

Table 2: Line tension safety factors Other commonly used rules such as API [8] and DNV [9]

give different line tension safety factors for quasi-static and dynamic analysis. However, no distinction is made between frequency domain/time domain and coupled/uncoupled analyses.

From the results reported in this paper, the coupled analyses produce larger line tensions compared to the uncoupled analyses. Since all forces on the moored vessel are included in the equations of motion in the case of the coupled analyses (as opposed to excluding the mooring line tensions in the uncoupled analyses), the possibility of lower line tension safety factors for coupled analyses is proposed. The use of the conventional safety factors in the present study results in an unacceptable mooring system if analysed with a coupled method, whereas it passes with a large safety margin if an uncoupled analysis is utilised.

CONCLUSIONS The findings from the study are summarised as follows:

1. The load RAO model can be used for a coupled time domain analysis incorporating the effects of mooring lines on the motions of the vessel and account for loads created by the cross bracings. In the present case, the coupled analyses yield significantly higher line tensions compared to the frequency domain analyses and the uncoupled analyses.

2. For the present mooring design, the quasi-static analyses pass the acceptance criteria (considering intact line tensions only) with safety margins above the permissible limits specified in the rules.

The uncoupled time domain analyses using displacement RAOs (both with and without cross bracings) produce tensions which are comparable with the quasi-static analyses. In this case the mooring system passes the acceptance criteria.

The coupled analyses provide significantly higher line tensions. Applying the same safety factors, the mooring system design would not be acceptable.

3. This study demonstrates that a mooring system designed following a frequency domain approach is not guaranteed to pass the acceptance criteria when re-analysed in time domain.

4. For the present mooring system subjected to a one hundred year return period environment some of the mooring lines, including the most heavily loaded lines, become slack during the simulation. A tension spike occurs when the lines re-tension. Both uncoupled and coupled methods model this behaviour, however only in a coupled analysis will the impulsive loads affect vessel motions which will in turn modify subsequent tension time histories. This feedback mechanism may explain the large differences in tension among the different analysis methods.

5. The tension spikes may also be caused by the grounded length reducing to zero causing anchor uplift.

6. In the coupled time domain model, all forces on the vessel are included in the equations of motion as opposed to excluding the mooring line tensions in the uncoupled model. Hence the coupled model is a mechanically correct representation of the dynamics of the moored vessel when compared to the uncoupled model. However, line tension safety factors recommended by maritime regulatory authorities make no distinction between a dynamic frequency domain analysis, an uncoupled time domain analysis and a coupled time domain analysis. The present mooring system passes acceptance criteria based on quasi-static frequency domain analyses and uncoupled time domain analyses. It does not pass the criteria based on coupled time domain analyses.

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7. Since the conclusions of this investigation are based on a single mooring system, further investigations are proposed in order to generalise the trends indicated in this study.

REFERENCES [1] Kwan C.T., Bruen F.J., “Mooring Line Dynamics:

Comparison of Time Domain, Frequency Domain, and Quasi-Static Analyses”, Offshore Technology Conference 1991

[2] Garrett D., “Coupled Analysis of Floating Production Systems”, Ocean Engineering Vol.32 Issue 7, 2005

[3] Mavrakos S.A., Papazoglou V.J., Triantafyllou, M.S., “An Investigation into the Feasibility of Deep Water Anchoring Systems”, Proceedings of the 8th International Conference on Offshore Mechanics and Arctic Engineering, 1989

[4] Noble Denton, “ROMEO” Mooring and Riser Analysis Package, version 1.5.4

[5] Orcina Ltd, “Orcaflex” version 9.4b, http://www.orcina.com/

[6] ANSYS, “AQWA” version 12.1, http://www.ansys.com/Products/Other+Products/ ANSYS+AQWA

[7] Lloyds Register, “Rules and Regulations for the Classification of a Floating Offshore Installation at a Fixed Location, Part 3 - Functional Unit Types and Special Features”, April 2008, Chapter 10

[8] American Petroleum Institute, “API-RP-2SK Design and Analysis of Stationkeeping Systems for Floating Structures”, 3rd Edition, October 2005

[9] Det Norske Veritas, “DNV-OS-E301 Position Mooring”, October 2008