Dynamic Analysis of Semi-Submersible Production Platform Under the Failure of Mooring Lines

This paper quantitatively studies the transient dynamic response of a semi-submersible production platform with the loss of one or several positioning mooring lines. A semi-submersible platform, production risers, and positioning mooring lines are all included in the numerical simulation. Increased motion of the semi-submersible platform, tension variation of the remaining mooring lines/risers and the risk of mooring line or riser clashing are all investigated through fully coupled time-domain analysis. Combined environmental loads are selected from irregular waves and the steady current varying from very rough to extreme sea conditions. Three dimension radiation/diffraction theories and Morison’s equation are applied to calculate first-order wave force and second-order mean drift force of floating semi-submersible platform. Nonlinear time-domain finite element methods are employed to analyze the behavior of mooring lines and risers. Results show that the failure of mooring lines seriously reduce the platform’s stability performance. The tension of the rest lines is also increased accordingly. Remaining lines which are closer to the failed lines will have larger tension increase to compensate. Line-Line distance provides practical information for the risk of clashing investigation.


Introduction
The deep-sea area represents the future of marine industry developments due to the presence of abundant oil, gas, and renewable energy resources. Various offshore floating structures like semi-submersible platform, spar platform, tension-leg platform, floating production storage and offloading unit (FPSO) are the main facilities being used for exploitation activities. The floating structure, which is subjected to different environmental loads, such as wave, wind, current and ice, is moored to be kept in position. A passive mooring system consists of freely hanging lines connecting the surface structure through fairlead to anchors and uses steel-linked chain, wire rope, or polyester rope as the main components (Li et al., 2019). The mooring system is closely related to operation efficiency and safety and needs to be carefully designed (Xu et al., 2018).
Moreover, mooring systems are an essential part of floating structures to ensure production system survival capability and stability (Barrera et al., 2019). They constitute an important element in the cost breakdown, typically about 8% of the capital expenditure of a typical marine platform installation (Hassan, 2012), and therefore have a large impact on the cost of energy. For the past 20 years, more than 150 mooring lines have been replaced (due to accidents or preventive action) (D'Souza and Majhi, 2013;Maslin, 2013). There were 21 mooring failure incidents from 2001 to 2011, either causing the mooring system impacted only, or causing production shut down and potential damages to the riser system (Ma et al., 2013). The root causes can be categorized as the follows (Mochet et al., 2014): (1) The chain comes as the first cause of failure, accounting for 50% of the cases; (2) Connectors come second (23% of issues reported); (3) Wire rope represent 19% of issues, making it the third cause of mooring failure; (4) Fiber represents only 8% of failures reported and monitored.
Consequences such as vessel drift, riser rupture, production shutdown, hydrocarbon release usually come after the mooring line failure in addition to the repair cost.
Research has been carried out to investigate the importance of mooring system integrity management. A series of guidance documents and standards about position mooring systems have been published by major associations and class societies, such as API (2005), ABS (2014), DNV (2015). All these guidelines and standards require redundancy to line break during the mooring design stage (Ren et al., 2015). The main failure modes that affect the dynamics of a mooring system are investigated by Gordon et al. (2014). He provides a comprehensive review of the current state-of-the-art in mooring integrity management. Particular focus is given to coverage of the latest information on mooring failures, component degradation processes, monitoring and inspection technology, and mooring integrity management systems.
The impact of mooring system failure on the dynamic response of a floating platform has been studied by various researchers. Li et al. (2018) carried out time-domain simulations to investigate the transient response of a Spar-type floating offshore wind turbine in scenarios with fractured mooring lines. The focus is on the motions of a floating platform, the tensions in the remaining cables as well as the energy harvesting performance with or without the emergency shutdown at the moment of cable fracture. Yu et al. (2019) studied the coupled hydrodynamic response of a TLP platform after a tendon's one-time failure and the progressive failure of several tendons under extreme tropical cyclone environment. Different disconnection positions of tendons are all investigated. The importance of wave drift force is also addressed in their work. Oyejobi et al. (2017) did research on the stochastic response of intact and removed tendon tension leg platform to random wave and current forces. They found out that the percentage increase in all degree of freedoms and tendon tension is <5 % when one tendon was removed compared with intact tendon TLP. Oyejobi et al. (2017) did an investigation on TLP behavior under tendon damage. It is interesting to see that roll and pitch motions are the most important ones that affect tendon tensions of TLP. Tabeshpour et al. (2018) analyzed the transient motion of a Truss-Spar in time domain after one or two mooring lines were damaged. In their simulations, the quasi-static approach was applied to calculate the mooring loads. It is observed from their study that the effect of damaged mooring lines on symmetric and asymmetric configurations was nearly the same. Kim et al. discussed the transient effects of a broken mooring line that were also investigated on FPSO (Ahmed et al., 2016) and Mobile Offshore Drilling Unit (MODU) (Girón et al., 2015;Faltinsen, 1990).
However, one common shortage of the previous work is lack of production riser system in the research. This is different from the engineering reality. The existence of the production riser plays an important role in the system because the risers will influence the platform motions, riser tension could be changed after mooring line failure, and risers may have the risk of being damaged or clashing against the failed mooring lines. So far, few publications take these effects into account. In this paper, all these influences from production risers are taken into full consideration.
This paper aims to numerically investigate the dynamic response of the semi-submersible production platform under the failure of mooring lines. The slender system consists of 12 positioning mooring lines and 22 production risers. Different scenarios including one line failure and several lines failure are all investigated under high sea states of wave and current. Time-domain simulations are carried out to analyze platform motions, tension variation of the remaining lines and risk of lines clashing.

Model description
The numerical model of a semi-submersible production platform system as shown in Fig. 1 is established. The whole system composed of a semi-submersible floating platform, 12 mooring lines and 22 risers. The semi-submersible platform consists of two pontoons to provide buoyancy, and four columns going through the free surface to support topside and two slender bracings connecting the columns to increase the strength of the structure. The main particulars of the semi-submersible platform are given in Table 1. Table 2 presents the major particulars of mooring and riser lines. Material properties along the mooring lines are chain (top segment), steel wire rope (middle segment)  and chain (end segment). Top chain segments of the mooring lines are in connection with the platform through fairlead connectors. Arrangement of positioning mooring lines and production risers exhibits in Fig. 2 (M is shorten for mooring and R for riser). Platform and slender system (including mooring lines and risers) are fully coupled in the time-domain analysis. This means that forces and moments from the slender system will be transformed to platform as external loads through fairlead nodes or riser-hang-off super nodes connection at each time step; at the same time, displacement of the platform will also load onto each slender line through connection node. Lost of mooring lines due to fairlead connection failure are numerically simulated by releasing the fairlead connector's boundary restrains in 6 degrees of freedom. The length of element for the whole slender system is 1 m.

Hydrodynamic analysis of semi-submersible platform
Global coordinate system is chosen for hydrodynamic analysis. Motions of the platform are solved and reported in this system. The global coordinate system is right handed with the origin in the still water level. The Z-axis is normal to the still water level and the positive Z-axis is pointing upwards. Propagation direction of the environmental wave and current loads are applied in this system, as shown in Fig. 3. Hydrodynamic properties regarding platform first order and second order motion and wave load transfer functions are computed by a frequency-domain code Wadam (DNV, 2017). Coupling mechanics between platform and mooring system, including the dynamic effect of mooring line failure are investigated by a time-domain code Sesam Marine (Simo&Riflex) (SINTEF Ocean, 2019a, 2019b).

First order wave force transfer function
Potential flow solution and Morison equation (Faltinsen, 1990) are combined to calculate the hydrodynamic characteristics of the platform. Potential flow solution is used on the large volume pontoon and columns where meshes are distributed. The platform shows double-symmetric geometry, so panels are generated for 1/4 of the wet surface of pontoons and columns. Morison equation is used at two slender bracings to account for the viscous effect. As drag coefficient in Morison equation has to be empirically dependent and is dependent on many parameters like Reynolds number, Kc number, relative current number and surface roughness ratio (Faltinsen, 1990). For most cases, typical drag coefficient is 0.7 for transcritical flow past a smooth circular cylinder. As morison viscous force is much smaller compared with large volume structure potential force in the current model, so the referenced value is adopted in this paper.
First order transfer function of semi-submersible platform is obtained by solving the motion of equation established for rigid body system, as shown in Eq. (1).
ρ where, is the density of water; D is the diameter of the cylinder; C D is the drag coefficient; u is the horizontal undisturbed fluid velocity at the mid-point of the strip.
Regular wave periods for RAO (Response amplitude operator or Transfer function) calculation are selected from 3 s to 60 s with step being 2 s in between. As the semi-submersible platform is double symmetric, only 0−90° wave directions are selected with space being 15° in between.

Mean drift force
Mean drift forces are of equal importance as the linear first-order motions in the design of mooring system for large volume structures (Faltinsen et al., 1980). In this paper, horizontal mean drift forces (surge, sway and yaw) are calculated by far field method; while rotational mean drift forces (heave, roll and pitch) are calculated by direct pressure integration method.
(1) Far field method In head sea condition, mean drift force is calculated by the method proposed by Maruo (1960). This method is based on the far field principle under the assumption that the energy in the radiated waves caused by the wave induced ship motions is equal to the work of mean drift force. Mean drift force is calculated by Eq. (3) (Maruo, 1960).
where A R is the amplitude of reflected waves. This equation shows that mean drift force is connected with structure's ability to generate waves and it will always act in the wave propagation direction. So only horizontal modes in surge, sway and yaw are calculated with the method in this paper. Maruo also derived formulae as Eqs. (4) and (5) for drift force on three-dimensional structure in incident regular waves.
where A( ) is the wave amplitude generated by the body far away; is the wave propagation direction; is defined as the horizontal radial distance from the body.
(2) Direct pressure integration method Another way to compute mean drift force is to use direct pressure integration method which was developed by Pinkster and van Oortmerssen (1977). This method expands the Bernoulli's equation to second order taking instantaneous ship motion and wet hull surface into consideration and integrates the longitudinal component of the oscillating pressure over the wet surface of the hull. Mean drift force can be expressed as: where c is the water line curve; is the relative wave amplitude along the ship; is the encounter frequency; is the first order velocity potential; (i=1, 2…6) is the vessel displacement in six degrees of freedom; S B is the average wet surface of the body; M is the ship mass and Z G is the z-coordinate of the center of gravity of the ship; indicates that the variables should be evaluated on the average position of the wet ship hull; the bar over the expressions indicates time-averaged values. Six degrees of freedom means drift force can all be obtained from this method.

Convergence study
The aim of this section is to verify the numerical model by convergence study of the hull mesh impact. Potential force is dominating for the large-volume columns of the semi-submersible, so panel meshes are generated on these parts with varying numbers and sizes. 5% critical damping is added to heave, roll and pitch modes respectively to compensate for the viscous effect on the columns and pontoons which are not included in the potential flow solution. Four models in Table 3 are created by displaying different meshes in longitudinal and girth-wise directions for the mean wet surface under water. Mesh display for Model 4 is shown in Fig. 4. Figs. 5−10 show platform 6 degrees of freedom first order motion transfer function during wave period 3−60 s. And first order wave force transfer functions are presented in Figs. 11−16. It is good to see that all these first order quantities have a good agreement with each other for all these four models. Mean drift force in surge, sway and yaw from far field method and pressure integration method are displayed in Figs. 17−19. Generally speaking, the four models show a good correspondence with each other in second order mean drift force. However, some deviations are observed for mean drift force in the shortest wave condition from far field method and pressure integration method. The reason is that diffraction force is being well included in far field method; while this part of force is quite mesh dependent in pressure integration method. From the overall evaluation, Model 4 is being chosen for its good accuracy and performance.
Eigen values of Model 4 for its peak response in waves in rotational modes: heave, roll and pitch are listed in Table 4. The horizontal modes of motion like surge, sway and yaw, which lack natural restoring force, are regarded as infinite values. It is clear from Figs. 7−9 that the maximum response is observed with relevant mode of motion while wave period is approaching to structure's eigen period.             Dynamic response of the semi-submersible production platform with mooring line failure is analyzed within ten selected environmental conditions with combined loads from wave and current as shown in Table 5. These ten sea states cover from Grade 3 (slightly) to Grade 9 (Phenomenal) according to sea state code from World Meteorological Organization (WMO, 2020). The water depth where the platform operated is 330 m. Developed sea spectrum Jonswap (DNV, 2014) is selected. Head sea is chosen for all ten conditions, which aims to make sure mooring lines 1−6 and risers 1−20 will always be exposed to incoming head wave directly. Figs. 20a and 20b present the time series of platform surge and sway motion within 3 600 s where single mooring lines 4, 5 and 6 lost connection at fairlead at 250 s in their own each case. It is obvious to see platform start to suffer a transit period at the moment of mooring line failure at 250 s. Surge and sway motion reacted more obviously than other modes of motion. It takes around 150 s and 270 s until platform surge and sway motion come into another stable position. It can be seen that mooring line 4 has a more significant influence than the other two lines regarding horizontal motion control, especially for surge motion under severe sea conditions. Figs. 20c−20f illustrate platform heave, roll, pitch and yaw motions in time series. There is very little change with mean heave and pitch motion. It demonstrates that the semi-submersible platform has good dynamic robustness in heave and pitch motion recovery. Roll and yaw motions experience a quick transient amplification, then gradually converged at a new stable posture. However, the change is not significant. Fig. 21 indicates platform averaged motions with single line failure under all the ten selected environmental conditions. Owing to the mooring line layout properties, the failure of mooring line 4 causes the most surge motions, while the loss of mooring line 6 triggers the most sway drift away motions. With the increasing of sea states, larger surge and sway motions were observed. Heave, roll and yaw motions are still oscillating around the balanced position which seem to be not significantly influenced by different sea states. Pitch angle as shown in Fig. 21e changes from negative (head up) to positive (head down) in high sea states condition 9 and condition 10. The reason is that much larger surge motion is observed in the two conditions, and mooring lines M1−M6 yield much larger positioning force to hold the platform back. So positive pitch angles happen in this scenario.   Figs. 22 and 23 show time series of the platform motion response when two mooring lines are damaged at the same time. Fig. 24 gives the averaged drift surge and sway motions. Here in this paper, three different two-mooring line   CHUANG Zhen-ju et al. China Ocean Eng., 2021, Vol. 35, No. 1, P. 84-95 91 impact. Compared with a single line failure, two lines failure will induce more motion deviations. But it is interesting to see that the transient period is almost the same in the case with one or two mooring lines failure. Zero sway motion is observed in scenarios No.1 and No.3 with failed mooring lines being displayed in the symmetric position. Under such conditions, there is no extra force in Y direction to excite more sway displacement. But large sway motion are observed in all sea conditions in scenario No.2.

Mooring line tension variation
After the target mooring lines are broken, the remaining lines are still working and oscillating with the platform. Redistribution of tension among these remaining lines is studied in this section. Fig. 25 presents time series of tension change of mooring lines 1−6 with mooring line 4 failure in environmental condition 5. The tension of mooring line 4 becomes zero after a loss of connection at 250 s as expected. At the same time, the tension of the remaining lines starts to quickly increase to compensate for the loss until a new balanced position is achieved. Statistical analysis regarding maximum tension, minimum tension, mean values and standard deviation are all listed under Fig. 27. Fig. 26 shows a tension increase of six remaining moor-ing lines in all ten sea conditions. Tension increase percentage is calculated from: (Tension_ after failure −Tension_ no line failure )/ ( Tension_ no line failure ) × 100%.    Mooring line 5 which is closest to mooring line 4 has the largest tension increase; while mooring line 1 which is the furthest one from mooring line 4 has the least change. The same trend has been observed in all the sub figures in Fig. 26. After certain lines failure, the remaining lines which are the closest to the failed line will have the most tension increase to compensate for the loss. Fig. 27 shows the riser tension variation in the time domain and statistical data analysis. It is clear to see that there is no obvious change in the tension of the risers. Here it actually reflects a healthy and stable production system. One reason for this is that the riser tension is generally much smaller than the mooring line tension. The tension of riser 20 is less than half of that on mooring line 4. So most of the compensation force will be covered by the mooring system. Another reason is that the top part of the riser which is in connection with the platform is in a quite vertical configuration. So the tension of the riser will be mostly influenced by platform heave motion, but not surge and sway. As platform heave motion has the minimum change under mooring line failure, riser tension will also stay quite stable with its designed values.

Risk of mooring line and riser clashing
There is always a potential risk of clashing between dropped lines and the remaining mooring lines or risers. One of the most practical methods is to measure the time series minimum distance between two lines. If the minimum distance is always larger than zero, then there is no risk of clashing. Otherwise, clashing happens with a negative distance. In this paper, clashing risks between dropped mooring line 5 and its neighboring mooring line 4 and mooring line 6 are investigated numerically. Distance between every element of two lines is calculated to find out the minimum value. Different sea conditions as shown in Table 6 are selected with wave and current coming from different directions. Fig. 28 shows three representative images of the failure process of mooring line 5. The top of the line lost connection at fairlead position, then gradually dropped down until reached sea bed.   Time series of the minimum distance between mooring line 5 and mooring lines 4 and 6 are plotted in Fig. 29. The minimum distance of two lines start from the distance of two fairlead nodes, then begin to pick up since mooring line 5 lost connection. The maximum value is achieved until the top of mooring line 5 ended in the sea bed. Statistical values are shown in Fig. 29. Then the value is oscillating with small variations due to environmental loads induced motions. Wave amplitude, current speed, and direction are all influential factors for line-line distance investigation. In this paper, the studied case is free of lines clashing risk for all the positive values obtained.

Conclusions
Dynamic response of the semi-submersible production platform under the failure of mooring lines is studied in this paper. A numerical model of the production system includes three parts: a semi-submersible platform, positioning mooring lines, and production risers. Time-domain simulations are carried out to investigate platform transient motions, remaining lines tension variation, and risk of lines clashing under the failure of a single line or two lines at the same time. The coupling effect is taken into account while solving the interactions between platform and mooring lines. Potential solution and Morison equation are adopted together to solve platform first-order wave force and second-order mean drift force. Different sea states are selected with varying wave height, wave direction, current speed, and current direction. Conclusions can be drawn as follows.
(1) Platform will experience more surge and sway motions compared with heave, pitch, roll, and yaw. The heavier the sea states are, the more drifted surge and sway will be. The transient period is much longer for surge and sway compared with the other modes of motion.
(2) Compared with single line failure mode, the plat- form is drifted away much further when two mooring lines are lost at the same time. But transient period is almost the same for these two scenarios.
(3) After certain mooring line failure, the tensions of the remaining lines increase accordingly to compensate for the tension loss. The remaining lines which are closer to the failed mooring line will have the most tension increase. The remaining lines which are further away from the failed lines will have less tension variation.
(4) No change is observed for the tension of risers when the mooring lines are lost. One reason is that the tension of the riser is much smaller compared with that of the mooring line. Most of the lost tension force is being compensated by the rest of the mooring lines. Also, due to vertical connection between the riser top and the platform, riser tension is less impacted by the platform surge and sway motion, but the heave motion which is minimum is changed by the mooring line failure.
(5) A practical method to judge if clashing between two lines will happen or not is to observe the minimum distance between them. Clashing will happen if the negative distance is seen. Wave and current with regarding amplitude and directions play an important role here.
One basic assumption of this paper is using linear hydrodynamic properties on the mean wet surface of the semisubmersible platform. Under such condition, instantaneous wet surface of the platform due to high wave elevation in severe sea states is not taken into account. Research work on the improvements of the non-linear hydrodynamic properties study needs to be done in the future. Another supplementary work is to include wind load which will also influence the drift motion of the platform system.