Numerical analysis of an over-boarding operation for a subsea template

Lin Li ,,Adhm M.Amer ,Xinying Zhu

a Department of Mechanical and Structural Engineering and Materials Science,University of Stavanger,Norway

b Ocean Installer AS,Stavanger,Norway

Abstract Subsea templates are normally transported to the installation site on the deck of a crane vessel.After being lifted off from the deck,the template is 1) over-boarded from the initial location to the target position by the side of the vessel;2) lowered through the splash zone;3)further lowered down to the seabed and 4) finally positioned and landed.All the mentioned phases should be evaluated.Usually,the splash zone crossing phase is taken as the critical phase and analyzed to define the installation weather criterion.The over-boarding phase has not been the focus of analysis due to a large involvement of human actions and little involvement of hydrodynamic effects.During offshore operations,the offshore manager may decide to decrease the defined installation weather criterion if the risk of the personnel safety on deck during over-boarding phase is considered high.Thus,it is of great need to quantify the operational criterion for such operation.The objective of this paper is to perform numerical analyses and define the allowable sea states for a safe over-boarding operation.The numerical analyses using time-domain simulations have been performed in various sea states.Tugger lines have been modelled to control the motions of the template during the operation.The pendulum motions of the subsea template are considered as the critical responses for the assessment of the allowable sea states.

Keywords: Over-boarding;Subsea template installation;Tugger lines;Allowable sea states;Pendulum motion.

1.Introduction

Safe and efficient installation of subsea structures and equipment is an essential part of the development of offshore fields.Many installation activities involve lifting operations by floating crane vessels.Lifting operations are often classified as weather restricted operations,and operational limits need to be assessed during the planning phase [1].For operations dominated by waves,operational limits are normally expressed in terms of sea state parameters,such as significant wave height (Hs) and spectral peak period (Tp).They are also defined as allowable sea states [2].To quantitatively assess the allowable sea states,detailed numerical analysis is required to evaluate the critical responses and compare them with their allowable limits [2].For complicated systems with nonlinearities,dynamic analysis using time-domain simulations are usually applied.Examples of assessment of operational limits for various lifting operations have been studied in the literature,such as lifting operations of foundations,spool pieces,and suction anchors [3-6].Moreover,various sources of uncertainties,such as weather forecasts and wave spectral shape have also been evaluated to provide safety margins to the operational limits 7,8].

Subsea templates are commonly used as bases for various subsea structures,for instance,wells and subsea trees and manifolds.The traditional way to install the subsea template is to transport the structure either on the deck of a crane vessel or a barge,depending on the size and the shape of the structure.For both cases,the structure is then lifted off from the deck and over-boarded to the target location,from where the structure is further lowered down through the splash zone.The over-boarding phase is a critical phase of the operation in which there is imminent danger of large dynamic loads and collision between the structure and the deck equipment due to relative motions.During the lowering phase through the splash zone,the slamming forces on the structure may occur.Hence,these potential hazards constrain the operational limits for the whole installation activity of a subsea template.

Many studies have been carried out to focus on the installation phase when the subsea structures are crossing the splash zone 5,9,10].Numerical simulations of the crane vessel and the structure were established,and time-domain simulations were performed to predict the crane loads and performance of the installation system.Due to the complexity of the loading in the splash zone,many researchers also focused on predicting the slamming loads using advanced numerical approaches11,12].These studies can improve the prediction of the nonlinear wave loads on the structure in the splash zone,and thus can increase the accuracy for the estimated operational limits.

Despite the over-boarding phase does not involve complicated hydrodynamic loading on the structure,it is also a critical operation phase for which a safe deck handling needs to be ensured.In particular,the pendulum motions of the template in air need to be well controlled.Arranging tugger lines connected with controlled winches are normally used for this purpose.The vessel roll and pitch motions,in this case,affect the performance of the lifting system,significantly.Both tugger lines arrangement and the crew working onboard help in limiting the motions of the lifted object during the operation.The human involvement during the horizontal transition controls the winches to ensure a safe and smooth engaging and disengaging tension forces on the tugger lines as the template reaches the lowering position.The sudden activation and release of the tugger lines may cause transient motions of the lifted objects.The excessive horizontal motions of the template are hazardous to the working individuals and may also damage the assets onboard.

Therefore,numerical studies on over-boarding operation are necessary in the planning phase to reduce the associated risks.The focus of this paper is to assess the operational limits for the over-boarding phase of a subsea template by performing dynamic analysis of the installation system.The performance of the system under various sea states with different tugger line arrangements is compared.Due to the involvement of different tugger lines,the over-boarding phase is dominated by non-linear responses.To simulate the operation for such study,two simulation approaches are normally used 3,13]: 1) a steady-state approach which is based on finding the most critical position for the template during over-boarding phase and running the simulations at this position under various wave conditions;2) a transient approach which is based on repetitive simulation of the whole transient over-boarding phase with different irregular wave realizations.Both approaches are used in this study to assess the allowable sea states for the over-boarding process.

This paper is organized as follows: the installation system and the numerical model are firstly presented.Then,the dynamic responses from the time-domain simulations using different methods are presented and discussed.The allowable seas states using steady-state and transient methods are also compared.Finally,conclusions are drawn from this study.

Fig.1.Top view and side view of the template model in SIMA-SIMO.

2.Description of the installation system

The installation system includes the construction vessel and the subsea template.A typical offshore construction vessel is employed for the operation [5].The overall length and breadth are 156.7 m and 27 m,respectively.The displacement is 1.70E4 ton at the maximum draft of 8.5 m.The construction vessel is equipped with a crane with a maximum lift capacity of 400 ton.The radius of this crane is between 10 m and 40 m.

A typical subsea template is to be installed on the seabed.Fig.1 presents the side and top views of the subsea template in the numerical model,where the position of the center of gravity (CoG) is highlighted.The total length of the subsea template is 20.8 m and the width is 17.4 m.The overall height of the template,from the bottom of the suction anchors to the top of the guideposts,is 12.9 m.The template body mainly consists of four hollow suction anchors,four hollow washout sleeves,and eight guideposts attached to the top of the template.The symmetrical distribution of the template mass facilitates the required slings arrangements for lifting and handling the template in air during the operation.The total mass of the template is 263 ton.The dimensions of the main tubular members of the template are listed in Table1.

The hoisting system for the template lifting operation includes the crane lift wire,slings and the winch.The slings connect the template to the hook of the crane block,and the lift wire is between the crane block and the crane tip.Because of the large dimension of the template structure,four slings on top of the four suction anchors are arranged to distribute the loads on the template.

Fig.2.Overview of the numerical model of the installation system.

Table1 Subsea template specification.

3.Numerical model

The numerical model is established using SIMA-SIMO program [14].SIMA-SIMO is a time-domain analysis software developed by the research institution SINTEF Ocean.The software was developed to perform analyses of marine operations,and most of the force effects that present in a marine operation can be properly modeled.The program was well-validated for a wide range of marine operations.The current model includes the construction vessel,the subsea template,and the hook.The construction vessel and the template each have six degrees of freedom (DOFs),while the hook only includes three DOFs.The global coordinate system is a right-handed coordinate system.The origin of the global coordinate system is located on the still water surface,and in the mid-ship section of the construction vessel.The X axis points towards the bow of the construction vessel,the Y axis points towards the port side,and the Z axis points upwards.The crane tip position is -50.4 m,0 m,54.2 m]in the global coordinate when the operation starts,and the working radius of the crane is 18 m.The overview of the numerical model of the operation system is shown in Fig.2.

3.1.Modelling of the vessel

The hydrodynamic properties of the construction vessel have been calculated in WADAM [15]based on the panel method in the frequency domain.The hydrodynamic properties include the potential added mass and damping coefficients,the hydrostatic stiffness,the first order wave forces and mean drift forces.Fig.3 presents the response amplitude operators (RAO) of the vessel in heave and roll for three wave directions.As observed,the natural periods of the vessel in heave and roll are around 8 s and 13 s,respectively.The properties of the vessel are imported into SIMA-SIMO to be applied in the time-domain simulations.

The vessel is equipped with dynamic positioning system to keep its position during the operation.However,since the horizontal motions have minor influence on the critical responses for the lifting system,the dynamic positioning system is simplified by four non-linear springs in the numerical model.Equivalent stiffness and damping coefficients are used for the non-linear springs to provide restoring to the vessel motions in the horizontal plane.

3.2.Wire couplings

The wire couplings,including four slings and the lift wire are modeled as linear springs.The effective axial stiffness can be expressed as:

whereEis the modulus of elasticity;Ais the cross-sectional area of the wire;1/kois the connection flexibility;lis the total length of the wire.For the lift wire,lincreases as the winch runs during the lowering operation.The main parameters for the lift wire and slings are chosen based on the practical operations,and they are shown in Table2.In this study,the critical responses considered are the pendulum motions of the template,and using different properties of the lifting wire,sling and fender has a minor influence on these responses.Thus,the same wire properties are used for all numerical simulations.

Fig.3.RAOs of the construction vessel in heave and roll.

Table2 Properties of the lift wire and slings.

Table3 Fender coupling properties.

3.3.Fender couplings

Four fenders are modeled to support the template on the deck of the vessel in the initial condition.A fender is defined as a contact element between the supported object and the vessel.The fender coupling can provide compression force normal to the sliding plane (the deck of the vessel) and a friction force along the sliding plane.In the model,the fenders provide normal force acting upwards to support the weight of the template.The friction coefficients are chosen based on steel-to-steel friction [16].The main properties of the fender couplings used in the numerical model are summarized in Table3.

3.4.Modelling of the tugger lines

Tugger lines are often used in the over-boarding operation to constrain the horizontal motions of the template [17].Usually,the constant tension mode of the tugger winches can be used,where the winches automatically pay out and pay in to compensate the relative motions and aim to keep a stable tension in the lines during the operation.For over-boarding operations of large structures,both crane and deck tugger lines are necessary to control the motions of the structures during the operations.The crane tugger lines connect the structure with the crane winch,while the deck tugger lines connect the structure with the deck winches at different locations on the deck.

In this study,two crane tugger lines are always applied.In addition,four deck tugger lines are also includedto study their influences on the responses.Among these four deck tugger lines,some are activated during the whole operations,while the others are only activated for a limited time,depending on the locations of the deck winches and the operation requirement.The arrangement of all the tugger lines are illustrated in Fig.4,and their identities in the numerical models are given.Three of the deck tugger lines are designed to operate only at certain periods of the operation,and one tugger line,SternR is engaging during the whole operation to support the main crane tugger lines and to minimize the motions of the template when the other three tugger lines are disengaged.The operating sequence of the deck tugger lines are summarized as below (the simulation starts at 0 s and lift-off starts at 100 s):

1) SternL tugger line is engaged at the start of the lift-off at 100 s and disengage at around 200 s when the lift-off is finished.

2) Starb tugger line is activating around 200 s (when overboarding starts) until 370 s (halfway through the overboarding phase).

3) Finally,Bow tugger line takes over at the last phase of the over-boarding process until the end of the simulation.

Fig.4.Crane model and arrangement of tugger lines in the numerical model.

Table4 The engaging and disengaging distances for deck tugger lines in the numerical model.

All these tugger lines should contribute in controlling the horizontal motions of the template induced by the vessel motions in order to improve the operational limits,especially at higher sea states.In the numerical model,the tugger lines are engaged and disengaged by specifying the range of the relative distances between the deck winches and the connecting points on the structure.Based on the installation procedure,the engaging and disengaging distances of the tugger lines are calculated and presented in Table4.The defined distance ensures that each tugger line operates at its intended period and disengages right after to make sure that the tugger line does not interfere in other sequential operations.Moreover,gradual buildup and decay of the tensions in the tugger lines are also implemented when engaging and disengaging the tugger lines.This is to minimize the transient effects on the motions of the template due to the shift of tugger lines.

In the numerical models,constant tension modes are applied to both crane and deck tugger lines.However,the line tensions still oscillate greatly around the target values during the operation due to the strong dynamics of the system.The maximum tensions of the tugger lines depend on the capacity of the winches.In this study,a comparative study on the arrangement of the tugger lines is performed by using different tugger lines with different target constant tensions.The purpose is to compare the influences of the tugger line arrangement on the performance of the lifting system.Therefore,three different tugger line arrangements (TLA) are defined below and will be studied in detail in the time-domain simulations:

1) Only the main crane tugger lines with predefined constant tension of 5 tons (TLA1).

2) Main crane tugger lines of 5 tons tension together with all deck winches with tensions of 2 tons (TLA2).

3) Main crane tugger lines of 5 tons tension together with all deck winches with tensions of 5 tons (TLA3).

3.5.Modeling of the crane and the hoisting system

The starting position of the template on the vessel and the direction of the over-boarding operation is shown in Fig.2.The operation initiates from lift-off,where the crane winch pays in the wire to lift the template off from the deck.During over-boarding phase,the crane will rotate to bring the template from the middle of the vessel towards the port side of the vessel.Thus,a prescribed motion of the crane is required.In the numerical program,‘articulated structure’ is applied to model the crane into two components,the crane bottom and the inclined crane boom (see Fig.4).The two components are rigid members and can have relative motions between each other and the vessel.To realize the over-boarding process,the prescribed rotations are set to the crane bottom.From the initial position to the target location where the template will be deployed,the rotation angle for the crane bottom is 136.25 °.Based on the crane specifications,the rotational speed of the crane base is chosen as 0.4 deg/s and the whole over-boarding duration is 341 s.

3.6.Modeling of the ballast system

During over-boarding,the center position of the template moves from the middle of the vessel to the port side,creating heeling angles to the vessel.To maintain the stability of the vessel during the operation,the heeling angle should be balanced using ballast system.In the numerical model,ballast tanks are modeled to pump in and out water to keep the vessel stable and level during over-boarding.The flow rate is calculated based on the rotational speed of the crane.Fig.5 shows the roll angle of the vessel with and without using ballast system.It can be observed that the mean roll angle when the template reaches the lowering position will be around 11°without the ballast system.This will affect the vessel performance during the heavy lift operation.The time history of the flow rate of the ballast system is also shown in Fig.5.The flow rate is within the capacity of the ballast system of the construction vessel,with a maximum flow rate of 2.1 m3/s.

Fig.5.Comparison the vessel roll motions with and without using ballast system (Tp=8 s,Hs=1.8 m).

4.Eigenvalue analysis

The eigenvalues of the system are first obtained from the static analysis in SIMA-SIMO to assess the natural periods of the system before evaluating the time-domain simulation results.Eigenvalue analysis is conducted in the frequency domain,without including any external forces or damping effect.The natural periods can be obtained by solving the following equation:

whereωis the natural frequency;MandMaare the mass and added mass matrices of the system;Kis the stiffness matrix,andxis the motion vector.The eigenvalue analysis is based on a linearized model of the system,which is solved by a standard Jacobian solver [14].The mass matrix is built from the virtual mass matrix,including both structural and hydrodynamic added mass.The asymptotic values of the added mass for the construction vessel at infinite frequency is used in the analysis.The secant stiffness for different modes is calculated at the initial position to establish the stiffness matrix.The stiffness matrix is symmetric.For each natural period,the eigen vectors express the relative contribution from each mode.

In this study,eigenvalue analysis has been carried out for three cases,i.e.,the vessel alone,and the coupled system with vessel and template at two over-boarding positions.The critical modes and natural periods are identified for each case.

4.1.Eigenvalue analysis for the installation vessel

Table5 shows the natural periods of the installation vessel alone,in which the dominated rigid motions are emphasized.Only three modes are within the typical wave peak periods range,i.e.,modes 1,2 and 3.These modes are dominated by the vessel pitch,heave and roll motions,respectively.

4.2.Eigenvalue analysis for the coupled system

For simplicity and an easier identification of the modes,the hook is neglected when calculating the eigenvalues for the coupled system of the vessel and the template.Thus,the coupled system has 12 DOFs corresponding to 12 modes in total.The eigenvalues are obtained from static analysis with the vessel and the template as well as the corresponding tugger lines included in the system.The two most critical positions for the template during the operation are chosen based on the dynamic response in the time-domain simulation,which will be discussed later.The first location is at the end of the one third over-boarding process,and the second location is at the end of the over-boarding.Thus,the eigenvalues of the coupled system are obtained and evaluated when the template reaches these locations.The results are presented in Tables 6 and 7,and the dominated rigid motions are emphasized.

From Tables 6 and 7,among the 12 modes for each case,the natural periods for modes 4-8 are considered critical and they are within the operational wave period range.As can be seen,the modes are coupled with contributions from the vessel,as well as template rotational and translational motions.

In Table6 when the template is located at the one third of the over-boarding process,the pendulum modes are observed in modes 6-7 where the natural periods are close to 8 s.In mode 6,the template pitch motion is dominating and with a relatively large contribution from the surge motion.The natural period increases to 8 s in mode 8 and the pendulum response appears from the dominating roll combined with sway motion.The coupling between the vessel and the template can be clearly seen in mode 7,where the vessel roll motions induce the rotations of the template.Modes 9-12 are dominated by yaw motions of the template and the natural periods are outside the operational wave period range.

Compared to Table6,the critical natural periods in Table7 show minor differences when the template is located at the end of the over-boarding process.However,the dominating modes are different compared to the previous location.The natural periods of the modes dominated by the template pendulum motions increase to over 8 s when the crane tip is at the final position.Moreover,at the end of over-boarding,the coupling mode 6 is dominated by the vessel roll and heave motions with less contribution from the template pendulum motion compared to the corresponding mode in the previous location.The differences in the contributions of different motions at the two positions are due to the change of the crane tip position,as well as the change of the deck tugger line engagement.In general,the eigenvalue analysis indicates that the pendulum motions of the template will be easily excited at both locations when the wave period is close to 8 s.

5.Time-Domain simulation

In this section,the simulation settings and the environmental conditions for the numerical simulations are discussed.The chosen statistical model to evaluate the extreme responses is also explained.

Table5 Eigenmodes and eigenperiods for the installation vessel.

Table6 Eigenmodes and eigenperiods for the coupled system at the one third of the over-boarding.

Table7 Eigenmodes and eigenperiods for the coupled system at the end of the over-boarding.

5.1.Simulation settings

Two time-domain simulation approaches are considered in this study,i.e.,the transient and the steady-state approaches.In both approaches,step-by-step integration methods are applied to solve the coupled equations of motion using an iterative routine.The equations of motion are solved by Newmark-beta numerical integration with a time-step of 0.02 s.The wave excitation forces on the construction vessel are pre-generated from the transfer functions obtained from the frequency-domain analysis at their mean positions using Fast Fourier Transformation (FFT).The radiation effects on frequency dependent added mass and damping forces are included in terms of coupled retardation functions in the time domain.The coupling forces are directly calculated for each time step based on the relative motions between the bodies.

5.2.Environmental conditions

The selected environmental conditions are listed in Table8.Hs is the significant wave height,and Tp is the spectral wave peak period.For selected Tp,Hs will vary to search for the allowable sea states.For each combination of Hs and Tp,the irregular waves are modelled by JONSWAP spectrum with a peak enhancement factor of 3.3 [18].In principle,lifting operations are sensitive to wave directions,and numerical analysis for various directions should be analyzed.However,the installation vessel has dynamic positioning system and it can keep the vessel heading to the most favorable direction relative to the waves.Thus,we limit the numerical analysis by considering one main wave direction of 180 ° with directional spreading waves.The directional spreading of wave energy is considered using short-crested waves characterized by the wave spectrum S(ω) and the directional spreading function D(θ) [18]:

Table8 Environmental conditions for time-domain simulations.

whereθ0is the main wave direction about which the angular distribution is centered.The parameternis a spreading index describing the degree of wave short-crestedness withn→ ∞representing a long-crested wave field.C(n) is a normalizing constant as follow:

whereΓdenotes the Gamma function.Consideration should be taken to reflect an accurate correlation between the actual sea state and the indexn.In this study,a constantn=2 is used in the spreading function,which is reasonable to represent wind-generated seas [17].

5.3.Statistical model

To account for the variability of stochastic waves,25 realizations of irregular waves are generated for each wave condition using different seeds.A statistical method is applied to estimate the extreme responses when assessing the allowable sea states.In this study,the critical responses include the pendulum motions of the template during over-boarding.The Gumbel extreme value distribution has been chosen as the model for the extreme values,and it is widely used in predicting extreme responses for offshore structures [19].

wherexis the variable,andλandκare the location and shape parameters,respectively.The parameters can be estimated based on the maximum likelihood method using the maximum values from each seed of the time.With the fitted Gumbel distribution,the extreme values can be calculated for a target probability of non-exceedance.The extreme values are sensitive to the selection of the target probability of nonexceedance.Often,a value between 0.9 to 0.99 is used based on the associated risks of the operation.A high probability of non-exceedance may introduce high uncertainties in the extreme values when the sample size (seed number) is small.Sensitivity study on the seed number of one lifting operation can refer to Ref.[5].In this study,25 wave seeds are used for each sea state.A target probability of non-exceedance of 0.9 is considered to provide a reliable prediction of the extremes,and thus is used in the assessment of the allowable sea states.

6.Operational criteria and evaluation approach

For the over-boarding process,the horizontal motions of the template are considered as critical responses.The operational criterion is to ensure that the extreme horizontal displacement of the template during over-boarding is within a limiting value.The limiting value is often decided based on the deck arrangement to avoid collisions with other equipment onboard.For the current lifting system,a limiting value of 3 m is used.Thus,the criterion to assess the allowable sea states is to limit the extreme pendulum motion of the template within 3 m.The extreme pendulum motion corresponds to the target probability of non-exceedance of 0.9 in the statistical model.This operational criterion is applied for both transient and steady-state approaches.

6.1.Transient time-domain simulation approach

In the transient approach,the winch starts at 100 s with a constant speed of 0.03 m/s for lift-off and stops at 200 s.Then,the crane bottom starts to rotate at 200 s.The whole simulation length is 1000s,and the over-boarding takes place between 200 and 541 s.During the over-boarding process,the mean X and Y displacements of the template go through large changes due to the changing positions of the crane tip.In order to evaluate the dynamic pendulum motions,the mean values of the X and Y displacements need to be subtracted from the total motions.Fig.6 illustrates the mean and the total displacements of the template in X and Y directions during the over-boarding phase.The coordinate system refers to the global coordinate system in Fig.2.The mean motions in the figure are calculated based on the crane tip positions in still water with prescribed rotations.

The equivalent dynamic pendulum motion is then calculated from the combined X and Y displacement by subtracting their mean values.Thus,the pendulum motion at one suction anchor location is formulated as follows:

Where,Ais the equivalent dynamic pendulum motion for a given suction anchor location.AxandAyare the total pendulum motions in X and Y.andare the mean motions for the given anchor in X and Y.When using the transient approach,25 seeds are applied for each irregular wave condition.The maximum dynamic pendulum motion can be obtained for each seed,and the extreme pendulum motions are calculated from the fitted Gumbel distribution.

Fig.6.Comparison of crane tip motions in still water and under the sea state of Tp=8 s and Hs=1.2 m during the whole time-domain simulation.

It can be seen from Fig.6 that the motions of the crane tip in still water deviate from the actual mean motions from the dynamic time histories.As a result,the calculated equivalent pendulum motion from Eq.(7) will be higher than the true dynamic pendulum motions due to these differences.These differences are caused by the tensions from the deck tugger lines as well as the transient effects from the engaging and disengaging of these tugger lines.In the real operation,the winch operator onboard controls the deck winches manually to reduce the dynamic effects and it is challenging to implement this manual interference in the transient approach.Therefore,to compare with the transient approach,the steady-state analysis is also used for the allowable sea states assessment to reduce the effect of the excessive motion of the system during the transient time-domain simulations.

6.2.Steady-state time-domain simulation approach

Steady-state approach is considered for the most critical crane tip positions based on the dynamic responses in the transient time-domain simulation.The first critical location is at the one third over-boarding process,and the second critical location is at the end of the over-boarding.The crane tip location is set at each critical position with no rotations to neutralize the dynamic effects of the crane rotation and to minimize the effects due to the engaging and disengaging of the deck tugger lines.In this study,two different set up of simulation lengths are applied for each sea state when using the steady-state approach:

1) Assume the system can stay at the defined critical positions for the whole over-boarding process (around 400 s) and carry out the simulation for each sea state with a duration of 25 repetitive processes.(SS1)

Fig.7.Time history of the total and dynamic motions in X and Y using steady-state approach at the end of the over-boarding (Tp=8 s and Hs=1.2 m).

2) Assume the system can stay at the defined critical positions for a shorter period (150 s) compared to the whole over-boarding process and carry out the simulation for each wave condition with a duration of 25 repetitive processes of 150 s.(SS2)

In the first approach,the maximum pendulum motion value is extracted every 400 s to obtain a total of 25 maximum values to fit the Gumbel extreme distribution.However,this approach is in principle over-conservative since the template will not maintain at the same critical position for such long period during the real operation.The second approach is less conservative,but more practical.It assumes that the template will remain at the critical position for about 1/3 duration of the whole process.Since the first critical position is at the 1/3 of the over-boarding process,using 1/3 of the duration(150 s) is considered reasonable.

Fig.8.Time histories of the vessel roll motion using transient approach for Tp=12 s and 6 s (Hs=1.2 m).

Different from the transient process with changing of tugger lines,the required deck tugger lines are continuously engaged at the given template position during the steadystate simulations.The dynamic oscillations time history at the given crane tip location is obtained by subtracting the mean values from the dynamic motions in X and Y.Fig.7 presents the total and subtracted motions in both X and Y when the crane tip is set at the end of the over-boarding.The instantaneous dynamic X and Y motions are fitted into Gaussian distribution,and the probability density functions (PDF) are also plotted.From the standard deviation values of the fitted PDF,the pendulum oscillations in X is almost twice as high as those in Y at this condition.This is because the crane tugger lines mainly control the motions of the template in Y,while the motions in X are not controlled efficiently.The equivalent pendulum motions for assessment of the sea states are then obtained following Eq.(7).Compared to the motions obtained using the transient approach (Fig.6),the responses using the steady-state approach are closer to stationary processes.The unrealistic dynamic effects from the engagement of the tugger lines are thus avoided using this approach.

7.Results and discussions

In this section,the dynamic responses from both transient and steady-state approaches are discussed.The allowable sea states are assessed based on the chosen operational criterion.

7.1.Dynamic responses using the transient approach

Two peak periods,6 s and 12 s are chosen to compare the response of the vessel roll motion for the same Hs,see Fig.8.From the figure,the induced roll motion at 12 s peak period is clearly higher compared to 6 s because 12 s is closer to the natural period of the vessel roll motion.The mean roll motions for both cases are close to zero due to the use of ballast system.By fitting the instantaneous roll motion into Gaussian distribution,the standard deviations of the vessel role motion are 0.46 and 0.25 deg at 12 s and 6 s,respectively.

Fig.9.Time history of the pendulum motion for Tp=12 s and 6 s at(Hs=1.2 m).

Fig.10.Deck tugger lines tension force profile at Tp=8 s and Hs=1.2 m using TLA3.

The template equivalent pendulum motions for different wave peak periods are evaluated in Fig.9.The result shows high dependency on the chosen peak period at the same Hs.The pendulum motions for both peak periods are fitted with Rayleigh distribution in Fig.9.The shape parameter is 0.44 and the standard deviation is 0.29 m at Tp=6 s.However,as the peak period increases to 12 s,the shape parameter and the standard deviation increases significantly to reach 0.71 and 0.45 m,respectively.The pendulum motion tends to be more centered around its mean value for low peak periods at the same Hs.

Fig.9 also shows that high pendulum motions occur close to the end of the one third of the over-boarding (250 s) and at the final location of the template during the operation (540 s).Similar trends are also observed for various sea states.These two positions are therefore chosen as the critical positions for the steady-state analysis as well as the previously discussed eigenvalues analysis.

Fig.11.Time histories of the pendulum motions using steady-state approach(Tp=8 s,Hs=1.2 m).

Fig.12.Time history of the tensions in the deck tugger lines with TLA3 using steady-state approach (Tp=8 s,Hs=1.2 m).

During the transient analysis,the deck tugger lines operate according to the pre-defined sequence in Table4.Fig.10 presents the time histories of the tensions in different deck tugger lines during the over-boarding process using TLA3.As mentioned,the buildup and decay phases are added to avoid the sudden change of the tension during engaging and disengaging instants.It can be seen from Fig.10 that all tugger lines operate at the pre-defined phase and the mean tensions are 5 tons.However,larger fluctuations of the tensions are observed.The fluctuations in the tension forces for both Bow and Starb tugger lines are much higher than those for SternL and SternR.These fluctuations are caused by the increased template motions during the over-boarding process.

7.2.Dynamic responses using the steady-state approach

Fig.11 presents the dynamic pendulum motions of the template at the two critical positions using steady-state simulations.The maximum response of the pendulum motions for the given sea state at both positions does not reach the limiting value 3 m.The comparison also shows a slightly higher responses when the template is at the end of the over-boarding process.The pendulum motions are fitted into Rayleigh distribution in Fig.11,and the fitted distribution agree well with the original simulation data.The uncertainty in the fitting of the pendulum motions (in Fig.11) reduces greatly in the steady state compared to that in the transient phase,as shown in Fig.9.This is because the system conditions are stable in the steady state without changes in the mean positions and the disturbances from the engagement of different tugger lines.

The time histories of the tension in the deck tugger lines when the template is located at the end of the over-boarding position are shown in Fig.12.Only SternR and Bow tugger lines are continuously engaged at this position.The instantaneous tension forces are fitted into Gaussian distribution.The fittings show that the distributions of the tension at thetwo locations are similar,the evenly distributed forces over the two tugger lines help to keep the template stable before being deployed through the sea surface.

Table9 Allowable Hs values for different TLA using transient time-domain approach.

7.3.Allowable sea states based on the transient approach

The extreme values of the pendulum motions from different wave seeds are fitted into Gumbel distribution to compare with the operational criterion.Fig.13 (a) shows an example of a fitted extreme values of pendulum motion into a Gumbel distribution probability paper.Although uncertainties do exist in the tails,the fitting shows that the sample in general follow the Gumbel distribution well.For the presented condition,the extreme pendulum motion corresponds to the non-exceedance probability of 0.9 is around 2.80 m.By evaluating the extreme values for different sea states and comparing with the limiting criterion,the allowable sea states can be found.

Fig.13.Fitting the extreme values of the pendulum motion into Gumbel probability paper using 25 seeds (TLA3,Tp=8 s and Hs=1.2 m).

Table9 presents the allowable sea states using different tugger line arrangements (TLA) as discussed in the modelling section.The operational limits are significantly low at the higher peak periods compared to 6 s peak period.These results are consistent with the eigenvalues of the coupled system in the static analysis.The static modeling and the dynamic responses of the template and the vessel show that the 6 s peak period will most likely have less induced pendulum motion,as most of the critical natural periods are around 8 s.However,adding the deck winches with an increased tugger line tension helps to achieve higher allowable sea states for the operation.The improvement is more obvious in the sea states with 6 s peak period,while the higher peak periods show slightly less improvement.Despite the small differences,it is concluded that TLA3,i.e.,crane and deck tugger lines with 5 tons tension,provides the highest sea states compared to other tugger line arrangements.

It should be noted that all the dynamic responses in this study are based on numerical simulations which apply linear wave theory for waves.The allowable Hs values at 6 s presented in Table9 exceed the application range for linear wave theory [17].In addition,the Hs values with Tp of 6 sare normally lower than 4 m in the real sea.Thus,the results indicate the operations can be operated at any Hs when Tp is 6 s.

Table10 Allowable Hs values for different TLA using steady-state SS1 approach(400 s for each seed).

Table11 Allowable Hs values for different TLA using steady-state SS2 approach(150 s for each seed).

7.4.Allowable sea states based on the steady-state approach

In the steady-state approach,the maximum pendulum motion values are extracted using both SS1 and SS2 corresponding to a simulation duration of 400 s and 150 s,respectively for each wave seed.A total of 25 maximum values are fitted into Gumbel probability paper with the same method followed in transient time-domain simulation.Fig.13 (b) present the fittings of the extreme values under the same sea state using the two steady-steady approaches.Compared to Fig.13 (a),the uncertainties in the Gumbel fittings seem to be reduced when using the SS1&SS2 steady-state methods.For the same nonexceedance probability of 0.9,the extreme pendulum motions decrease significantly from 2.80 m using transient method to 2.35 m using SS1 and 2.07 m using SS2.This is because the motions using the transient method are over-estimated due to the influence of changing tugger lines in the whole process.Moreover,using SS2 provides lower extreme values due to the shorter simulation time compared to SS1.By evaluating various Hs values for the target Tp,the allowable sea states are determined based on the results at the most critical suction anchor position.

Tables 10 and 11 show the allowable sea states using SS1 and SS2 approaches for three TLAs.It is obvious that the sea states have been improved significantly for longer Tp using the steady-state approach than the transient approach.When the simulation time for each seed is 150 s (SS2) instead of 400 s (SS1),the sea states increase again.This provides more realistic sea states and the allowable Hs values can reach over 2 m with Tp of 12 s.

Fig.14.Allowable sea states using different time-domain approaches with tugger line arrangement TLA3.

Similarly,as observed from the transient approach,tugger lines arrangement TLA3 leads to the highest sea states.This again proves the importance of deck handling operations during the over-boarding operation.For a better comparison,the sea states from the different approaches using tugger line arrangement TLA3 are summarized in Fig.14.As mentioned earlier,because the sea states are unrealistically high at 6 s,they are not included in the figure.The comparison shows clearly that different approaches applied in the time-domain simulation influence the sea states greatly.The results from this figure can be used further together with the sea states obtained for the splash zone crossing phase in order to plan for the whole deployment operation of the template.

8.Conclusions

This paper focuses on numerical study on the overboarding operation of a subsea template.The fully coupled numerical model has been established in SIMA-SIMO including the installation bodies,the lifting system as well as the tugger lines.Eigenvalue analysis and dynamic simulations are performed to study the performance of the installation system in both frequency and time domains.Three different tugger line arrangements are modeled and applied in the analysis to compare the influences of the tugger lines on horizontal motions of the template.Due to the complicity of the overboarding process with nonlinearities from the tugger line engagement,both transient and the steady-state approaches are employed to assess the allowable sea states.The pendulum motion of the template is considered as the critical response,and the statistical method is applied to estimate the extreme pendulum motions from various wave seeds when assessing the allowable sea states.

The study shows that the allowable significant wave height highly depends on the peak periods.When Tp is 6 s,the operations are considered safe under all possible wave heights.With increasing Tp,the sea states drop significantly compared to Tp of 6 s,and the allowable Hs are around 2 m for Tp from 8 s to 12 s with the best tugger line arrangements.By comparing different tugger line arrangements,it is found that the involvement of the deck tugger lines can help to increase the allowable sea states of the over-boarding operation.The higher tensions in the tugger lines can provide a better control on the pendulum motions.However,the application of the tugger lines in the operation highly depends on the deck arrangement as well as the capacities of the deck winches.Moreover,the real operations rely on human interactions to control the engagement of the tugger lines,and it is very challenging to model these interactions due to the limitations of the numerical tool.It is observed that the engagement and disengagement of different tugger lines in the numerical model introduce extra disturbances in the transient simulations,which lower the allowable sea states.Therefore,the steady-state approach is found to be more realistic to assess the allowable sea states for this operation.In general,higher sea states are obtained using the steadystate approach for the over-boarding operations.Future improvement in modelling the tugger line engagement may improve the allowable sea states obtained from the transient approach.