Use of Different Mooring Models on Global Response Analysis of an Innovative Deep Draft Platform

QIAO Dongsheng, LI Binbin, and OU Jinping

1) Deepwater Engineering Research Center, Dalian University of Technology, Dalian 116024, P. R. China

2) Regional Oil & Gas Offshore Center, Bureau Veritas, Singapore

Use of Different Mooring Models on Global Response Analysis of an Innovative Deep Draft Platform

QIAO Dongsheng1),*, LI Binbin2), and OU Jinping1)

1) Deepwater Engineering Research Center, Dalian University of Technology, Dalian 116024, P. R. China

2) Regional Oil & Gas Offshore Center, Bureau Veritas, Singapore

The global responses of an innovative deep draft platform are investigated using catenary, semi-taut, and taut mooring models, respectively. The three mooring systems have the same arrangements and similar static restoring force characteristics. The dynamic coupling effects between the platform and the mooring systems are calculated in the time domain. Free-decay and 3-h simulations are conducted under 1-year and 100-year return period environmental conditions in the South China Sea. The mooring damping contributions, the response characteristics, and the mooring line tensions are investigated.

spar; mooring system; coupled analysis; response; tension

1 Introduction

The oil industry is currently concentrating its exploration efforts and activities on deep water. Accordingly, suitable floating platforms such as semi-submersible platform, tension leg platform (TLP), and spar platform are increasingly being applied to practical projects. A TLP adopts vertical tension legs to moor the upper floating platform, whereas others adopt an outspread mooring system, such as the traditional catenary mooring system as well as the recently developed semi-taut and taut mooring systems (Fig.1). Currently, floating platforms can go beyond 2000 m water depth and future designs will target 3000 m water depth range, so the need for an efficient station mooring system increases.

Since the conceptual design of the spar platform was first proposed by Edward E. Horton in 1987 (Vatdeman et al., 1997), a variety of the spar platform have been developed ranging from the Classic Spar to the Truss Spar and the Cell Spar (Young et al., 1999; Bangs et al., 1999; Lamey et al., 2005). Different approaches, ranging from a quasi-static approach (Cao and Zhang, 1997) to a fully coupled dynamic approach (Ran et al., 1999; Astrup et al., 2001; Li et al., 2010), have also been developed to predict different types of spar platform motions. Today, new spar platform designs are still being proposed (Zhang et al., 2007; Yu and Huang, 2010; Sun and Huang, 2012). Despite the development, only a few scholars have used mooring models to investigate floating platform motions. Chen et al. (2001) used a quasi-static method and a coupled dynamic method to calculate the motions of a spar and its mooring lines in three water depths. Tong et al. (2009) compared the dynamic effect of a semi-submerged platform with catenary and taut mooring systems, respectively. Sun and Wang (2010) studied the motion performance of a deepwater spar platform using an equally distributed mooring method and a grouped mooring method.

The present work is based on an innovative deep draft multi-spar (DDMS) platform. Global response of the spar platform is calculated and analyzed using catenary, semitaut, and taut mooring systems in a 1500 m water depth. The three types of mooring systems have the same arrangements and similar static restoring force characteristics. The environmental conditions are considered with 1-year and 100-year return periods in the South China Sea.

Fig.1 Mooring line configurations.

2 DDMS Platform and Environmental Conditions

2.1 DDMS Platform and Mooring System Configurations

The DDMS platform concept (Fig.2) combines the advantages and design features of the truss spar and SEMI platforms. The DDMS appears like a semi-submersible platform; however, its hydrodynamics more resembles that of a spar platform. Table 1 summarizes the mass and dimension information of the DDMS platform. For more information, refer to Li and Ou (2009).

Fig.2 DDMS platform.

Table 1 Details of the DDMS platform

The mooring system consists of four (4×4) groups as shown in Fig.3. Between two neighbouring groups is a 90-degree angle. There are four mooring lines in each group and each mooring line has three segments: upper chain, middle wire and bottom chain, and it is separated by a 5-degree angle. Three types of mooring systems, catenary, semi-taut and taut, are designed and calculated for the spar platform.

Fig.3 Mooring system layout.

The pre-tension of mooring system is primarily set to resist the steady environmental forces, such as wind, current, and waves. Aiming to keep the similar static restoring force characteristics, the pre-tensions for the three mooring systems only slightly differ. Considering the gravity, tension and mooring line extension, the piecewise extrapolating method is used for the static analysis of the multicomponent mooring line (Qiao and Ou, 2009). Finally, based on the design optimization of the three types of mooring systems, the mooring system configurations are showed in Table 2 and the mooring line properties in Table 3.

The tension–horizontal displacement characteristic curve of a single mooring line (#1) is plotted in Fig.4. The total horizontal force–horizontal displacement is plotted in Fig.5. As shown in Fig.3, the total horizontal restoring forces should be symmetric about the x-axis because the arrangement of mooring lines is symmetric about the y-axis. The positive direction of the offset in Figs.4 and 5 is the 0° direction, and therefore, Fig.5 only shows the total horizontal restoring force along the 0° direction.From Figs.4 and 5, a few differences among the three mooring systems are observed, but the overall trend is consistent, and the static restoring force characteristics are in agreement with each other under the possible maximum horizontal offset of the semi-submersible platform (shown in Tables 7 and 8).

Table 2 Mooring system configurations

Table 3 Mooring line properties

Fig.4 Tension–horizontal displacement curve of a single mooring line (#1).

Fig.5 Horizontal restoring force–horizontal displacement curve of the mooring system.

2.2 Environmental Conditions

The environmental conditions considered have the 1-year and 100-year return periods in South China Sea as listed in Table 4. The mean wind speed, JONSWAP wave spectrum, and uniform current distribution are used in the numerical simulations. The wind, waves, and current are assumed collinear. The environmental heading is assumed to be from the x-axis (Fig.3).

Table 4 Environmental conditions

3 Hydrodynamics and Full Coupled Numerical Method

The numerical methods used in this paper are from the previous research work by Li et al. (2010), and described below.

3.1 Hull Hydrodynamics

The AQWA hydrodynamic software is used to calculate the hydrodynamic wave loads, including the first-order wave exciting force, steady wave drift force, frequencydependent added mass, and radiation damping. The panel elements are used to model the hard tank and ballast tank of DDMS, and the potential flow theory is adopted to calculate the wave hydrodynamics. The hull panel model is shown in Fig.6.

Fig. 6 Coupled model.

The first-order hydrodynamic problem of a floating body can be divided into two components, i.e., the forces and moments on the body due to incident regular waves and the forces and moments on the body related to the structure oscillation with the wave excitation frequency. The first-order wave exciting forces and moments are acquired by integrating the pressure over the wetted surface of the body as

where ρ, ω, Iφ, Dφ, njand SBrepresent the water density, wave frequency, incident wave potential, diffraction wave potential, generalized surface normal in the jth direction, and wetted body of the structure in a calm water, respectively. Therefore, the forces related to the structure oscillation with the wave excitation frequency can be expressed as a summation of the real and imaginary parts of the complex number,

Eq. (2) can be further simplified as

Neglecting the insignificant second-order sumfrequency forces, the second-order wave slow drift forces are calculated using the full quadratic transfer function (QTF) matrix. Generally, the second-order wave slow drift force can be written as follows

Besides the hard tank and ballast tank, the hydrodynamics of which is predicted by applying the potential theory, the middle section, composed of columns, is simulated as the Morison type element. The drag, inertial force, and added mass force are considered due to the small diameter of the section relative to wave length. The Morison force for each element is expressed as follows

where D, l, Ca, CI=Ca+1 and Cdare the diameter, length, added mass, inertial force, and drag coefficients of the Morison element, respectively; u, u˙, x˙, and x˙˙ denote the flow velocity, flow acceleration, element velocity, and element acceleration, respectively.

For the heave plate, due to its extraordinarily small thickness, some special disc elements with zero thickness and mass are used to represent the added mass and drag force:

where FP, r and y express the hydrodynamic force for the heave plate, disc radius, and relative vertical displacement, respectively. The viscous damping induced by the hard tank, significantly limiting the surge response near the natural period in the low frequency range, is estimated by employing the Morison drag term.

3.2 Mooring Coupling

The equation of motion for mooring line dynamics is as follows

where Mm, Mma, and Amexpress the structural mass, added mass, and acceleration, respectively; Fg, Fb, Fdand Fsdenote the gravity force, buoyancy force, drag force, and sea bed reaction vector, respectively. In fact, this equation has six degrees of freedom for two nodes of an element, and each node has three degrees of freedom, including one inline and two normal ones. The friction between the mooring line and seabed is ignored in the calculation.

For the time domain simulation, the motion solutions for the hull and mooring are fully coupled during a certain period of time, e.g., the period when the tension for the mooring line and the hull motion are considered to be jointly interactive, in which the mooring line affects the hull motion. In the present test, each mooring line is divided into 50 elements to ensure adequately precise calculations.

4 Numerical Simulation Results

4.1 Natural Periods

The natural periods for the three types of mooring systems are obtained from free-decay tests in 1500 m deep water according to the first six cycles. The initial amplitudes for surge, heave, and pitch are 10 m, 2 m, and 10 degrees, respectively. The natural periods from the freedecay simulations are summarized in Table 5. Fig.7 shows the free-decay test results of surge, heave, and pitch.

Based on Table 5, the natural period of surge of the taut mooring system is longer than those of the semi-taut and catenary mooring systems and the catenary mooring system has the smallest period because of the smallest horizontal stiffness of the taut mooring system (Fig.5). The natural periods of heave and pitch have no significant differences for the three systems, indicating that the vertical stiffness of the three is almost the same.

Table 5 Natural periods

4.2 Natural Damping Ratios

Fig.7 shows the natural damping ratios derived from the free-decay simulations, which are summarized in Table 6. The natural damping ratio of surge for the catenary mooring system is about 10% and 20% larger than those for the semi-taut and the taut mooring system, respectively. The longest catenary mooring line results in the largest drag force. Therefore, the catenary mooring system encounters the largest damping. The damping ratio of pitch of the three systems has slight differences. The taut mooring system has the largest damping ratio of heave, and the catenary mooring system the smallest. In the vertical direction, the total mooring line length of the taut mooring system is larger than the efficient mooring line length of the semi-taut and catenary mooring systems due to the designed angle between the mooring line and the seabed. Therefore, the drag force in the taut mooring line is the largest, followed by that in a semi-taut.

Fig.7 The free-decay test results of surge, heave, and pitch.

Table 6 Natural damping ratios

4.3 Motion Responses of the DDMS Platform

The 3h simulations were conducted under the environmental conditions with 1-year and 100-year return periods in South China Sea using the catenary, semi-taut and taut mooring systems, respectively. The motion statistics (surge, heave, and pitch) are summarized in Tables 7 and 8. The motion time series and their spectra for the 1-year return period are plotted in Figs.8–13, and the ones under the 100-year return period environmental conditions are omitted for brevity.

Based on the surge motion results, the magnitudes of the averages, standard deviations, and maximum surge motion of the three mooring systems rank in the following order from smallest to largest: catenary, semi-taut, and taut, which are similar to the case with natural damping ratios. In the low frequency (LF) range, the changes in the standard deviations of surge motion are the same as those in the average surge motion, indicating that the LF motion dominates the total surge response. The effect ofmooring damping is the main reason for the LF dominance. Based on the calculations by Qiao and Ou (2011), the mooring damping is mainly affected by the efficient mooring line length with the same mooring line material. The catenary mooring system has the longest efficient mooring line, and the taut mooring system the shortest. Therefore, the catenary mooring system has the largest mooring damping contribution and the taut mooring system the smallest to the DDMS platform motion. In the wave frequency (WF) range, the standard deviations of surge motion show insignificant changes for all three systems. Because the inertia forces are dominant in this frequency range where the natural frequencies of the platform are far lower, the mooring-induced damping does not have significant contributions to the DDMS platform motion.

Table 7 Motion statistics of the DDMS platform under the environmental conditions with 1-year return period

Table 8 Motion statistics of the DDMS platform under the environmental conditions with 100-year return period

Based on the heave motion results, the magnitudes of the average and maximum heave motion of the three mooring systems rank in the following order from largest to smallest: catenary, semi-taut, and taut. Because the total heave motion is dominated by the WF motion, the main influencing factor of heave motion is the inertial force rather than mooring damping. Therefore, the the catenary mooring system, which has the longest mooring line and the largest inertial force, corresponds to the strongest heave motion.

Based on the pitch motion results, the magnitudes of the averages, standard deviations, and maximum pitch motion of the three mooring systems rank in the following order from smallest to largest: catenary, semi-taut, and taut. In the LF and WF ranges, the changes in the standard deviations of pitch motion are the same as those in the surge motion because the mooring damping dominates the LF pitch motion and the inertial force dominates the WF pitch motion.

Fig.8 Time series of surge motion.

Fig.9 Surge motion spectra.

Fig.10 Time series of heave motion.

Fig.11 Heave motion spectra.

Fig.12 Time series of pitch motion.

Fig.13 Pitch motion spectra.

4.4 Mooring Line Tensions

Two mooring lines are analyzed: #1 is the most unloaded mooring line in downstream and #8 is the most loaded mooring line in upstream. The statistics of the two mooring line tensions of the three mooring systems are summarized in Tables 9 and 10, respectively. The time series of mooring line tensions and the corresponding spectra under the 1-year return period environmental conditions are plotted in Figs.14–16, and those under the 100-year return period environmental conditions are omitted for brevity.

For #1, the dynamic mooring line tension is calculated by subtracting the initial pre-tension from the average mooring line tension. The magnitudes of the average dynamic mooring line tension of the three mooring systems rank in the order from largest to smallest: catenary, semi-taut, and taut, and the magnitudes of the standard deviations in the LF and WF ranges rank in the same order. This phenomenon may cause more severe fatigue problems for the catenary mooring system. The changes under the 100-year return period environmental conditions are more apparent.

For #8, the change trend in the average and standard deviations are opposite to that for #1, which is most apparent under the 100-year return period conditions.

Table 9 Mooring line tension statistics under the environmental conditions with the 1-year return period

Table 10 Mooring line tension statistics under the environmental conditions with the 100-year return period

The different trends between #1 and #8 are due to the much larger average tension of #8 and the corresponding mooring damping changes. Based on the investigation on the effects of pre-tension on mooring damping, Webster (1995) pointed out that the mooring damping increases with the amplitude of motion if the pre-tension is smaller than the peak value and decreases if the pre-tension is larger than the peak value. The average tension of #1 is smaller than the peak value, but the average tension of #8 is larger than the peak value. Meanwhile, the taut mooring system has the largest motion response of DDMS. So, the different change laws between #1 and #8 are reasonable.

Fig.14 Time series of mooring line tension.

Fig.15 Mooring line tension spectra of #1.

Fig.16 Mooring line tension spectra of #8.

5 Conclusions

A fully coupled hull and mooring model is developed based on an innovative DDMS platform. The global response analyses are conducted in the 1500 m deep water in the South China Sea using the catenary, semi-taut and taut mooring systems, respectively. Based on the 3h freedecay simulations, the preliminary findings are list as follows:

The different mooring models have significant effects on the global responses of the DDMS platform, and it is imperative to couple the hull and mooring system in a numerical model.

The mooring line length, pre-tension, and configuration affect mooring damping and thus the global responses of the platform.

The mooring damping is the major factor affecting the natural damping ratios, platform motion, and mooring line tension.

In general, the model results indicate that the selection of a mooring system is an important step in the preliminary design.

Acknowledgements

This paper is funded by the National Basic Research Program of China (Grant Nos. 2011CB013702 and 2011 CB013703), the National Natural Science Foundation of China (Grant Nos. 51209037 and 51221961), and the China Postdoctoral Science Foundation Project (Grant No. 2013T60287).

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(Edited by Xie Jun)

(Received April 17, 2012; revised October 17, 2012; accepted October 28, 2013)

© Ocean University of China, Science Press and Springer-Verlag Berlin Heidelberg 2014

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