Abstract
In designing a floating offshore production system to operate in a region with risk of impacts from icebergs, the effectiveness of management and avoidance of detected icebergs may be considered when determining design ice loads. Management can include deflection of encroaching icebergs through towing or use of water cannon. Avoidance would typically consist of disconnecting the floater and moving off site for cases when an iceberg cannot be managed, but could also include moving off site for periods with high numbers of icebergs. There may be grounds for remaining on site in certain cases (e.g., small icebergs in low sea states) if it can be clearly demonstrated that there are no serious risks. This paper discusses issues involved when determining guidelines for remaining on site, including relevant standards and limits states, tradeoffs between ice strengthening and operational requirements, and considerations when presented with a threat by a specific iceberg and set of environmental conditions. A probabilistic approach is presented for establishing operational criteria for disconnection that will still ensure target reliabilities with respect to iceberg impact loads are achieved.
Introduction
The environmental conditions off Newfoundland’s east coast are relatively harsh and include high sea states, icebergs and sea ice (Fig. 1).
Several oil fields are presently in production on the Grand Banks, using both fixed and floating production systems. Floating systems can offer advantages in terms of capital cost, time to first production, and implementation in deep water. Ice strengthened, shipshaped Floating Production Storage and Offloading systems (FPSOs) have been successfully used for the development of two fields. The Terra Nova FPSO, in 95 m water depth, has been in operation since 2002 for development of the Terra Nova field (Fig. 2). The SeaRose FPSO, in 120 m water depth, has been in operation since 2005 for development of the White Rose field (Fig. 3).
To reduce downtime and probability of impact, operators will attempt physical management of icebergs; typically using single rope tows, net tows or water cannon. Single rope tows can be successfully applied for icebergs that are stable enough that they do not roll and where the shape is such that rope slippage does not occur. For small, smooth and/or unstable icebergs, nets or water cannon may be more efficient. Water cannon can also have advantages for diverting smaller icebergs in sea ice, where ropes and nets could be entangled. Towing efficiency is reduced in higher seas and with the presence of sea ice. Efficiency increases with time available. For larger icebergs, additional power (larger or multiple tow vessels) will reduce the time to deflect the iceberg and increase speed along a desired course (Stuckey et al. 2016).
Both the Terra Nova and SeaRose FPSOs have disconnectable turret mooring systems that allow the vessels to remain on site in most conditions, but quickly disconnect if an approaching iceberg cannot be diverted. The Terra Nova has thrusters that can be used to orient the vessel so that icebergs hit the bow rather than the side of the vessel, which has less strength. Similarly, the SeaRose may use its dual propellers to initiate heading control.
The Terra Nova and SeaRose FPSOs have successfully been operated with ice management for a combined total of 31 years without an iceberg impact. Given the areal density and sizes of icebergs in the region, the expected annual impact rate by icebergs with waterline length of 5 m and greater, without ice management and disconnect capability, would have been around 0.16 per year (i.e., 1 impact in six years). This corresponds to a 99% chance that there would be one or more impacts in 31 operational years. Assuming, for example, ice management efficiency of 75% and 99% disconnect reliability, the expected annual impact rate would be around 4 × 10^{−4} per year (1 in 2500 years or a 0.012 probability in 31 years). Both vessels have ice strengthening for iceberg impacts.
In the future, disconnectable FPSOs will likely be used to develop discoveries to the north and east of the Grand Banks. Disconnectable FPSOs could also be used in the Barents Sea north of Norway and Russia, where icebergs also occur (Liferov et al. 2011). To be able to optimally design FPSOs for more challenging ice environments (higher iceberg areal densities, higher drift velocities and greater water depths), it is advantageous to continue to improve our knowledge and modelling capabilities regarding iceberg impact loads. New technical innovations should be encouraged and utilized; for example, improvements in thruster control could potentially allow the use of side tracking in deeper water to avoid encroaching icebergs (King 2018).
An FPSO will likely be custom designed for a new field, though it could be brought from another development that is no longer producing. During the design (or modification) phase, the level of ice strengthening can be determined to meet safety requirements and minimize ice related downtime during operations. Given that the benefit of icemanagement and disconnection capabilities may be taken into account when determining icestrengthening requirements (ISO 19906), the operations planning should done in parallel with the design phase. Later in the field life, it is possible that the operations plan will be adjusted given better information on ice and environmental conditions; changes in regulations or technology; or part of a strategic decision to further reduce downtime (Fig. 4).
In this work, consideration is given to the possibility of remaining on site when confronted with an approaching iceberg, and the selection of appropriate ‘disconnect criteria’ that operators can use to decide when to remain on site. If it can be clearly demonstrated that there are no serious risks posed by a specific encroaching iceberg in a given sea state (e.g., small icebergs in lower sea states), then there are grounds for the operator to remain on site. The criteria used should be clear and straightforward and there should be a negligible chance of ice actions exceeding the abnormal level (AL) values used for relevant abnormal limit state (ALS) design checks. In addition, the probability of deformation of the outer hull or supporting structure to an extent requiring repairs should be minimized.
When considering disconnect criteria, the mainfocus is on impacts by smaller icebergs. As shown later in this paper, if impact energies are small enough, the inertial response of the FPSO will be limited, and so the vessel may be treated as fixed (or as moving solely due to wave forces). For impacts with larger kinetic energy, the inertial response of the vessel (primarily in surge, sway and yaw) may need to be considered. Developed tension in the mooring system will only have a significant influence for more severe impacts assuming minimal environmental preloading.
When designing FPSOs for iceberg impacts, as opposed to interactions with sea ice, the ice belt will be extended upwards and downwards to cover the larger region where iceberg contact would be expected (including the bilge). There will generally be fewer impacts on the side than on the bow, and these will typically be glancing impacts, such that less strengthening is required.
It is challenging to estimate the probability that an iceberg will impact the side of an FPSO as opposed to the bow. Ideally, one would consider the combinations of winds, waves and currents, the iceberg size and shape, the wave induced motions of the FPSO and hydrodynamic interaction effects. FPSOs typically have heading control using thrusters, allowing the operators to point the bow towards oncoming icebergs.
Consideration should be given to the possibility of repeat impacts. These can be a result of waveinduced motions of the iceberg and FPSO. In addition, there can be rotation of then iceberg following initial impact, with subsequent impact on another part of the iceberg. During more severe impacts, global motions of the FPSO may also play a role. Larger icebergs hitting the bow off centre in some cases can cause the FPSO to rotate in a direction that increases the likelihood of further impacts. At the same time, the operators may be able to limit the chance of further impacts using thrusters, and some icebergs could break up following the initial impact.
Estimating the impact loads and effects is challenging given random seas, highly varied sizes and shapes of icebergs and complex ice failure processes. A probabilistic approach is appropriate when determining design values associated with small probabilities of exceedance. There is a tradeoff between implementation of complex models that consider the different processes in detail versus use of simpler models that can be run efficiently within a MonteCarlo framework. Using a mixture of complementary modelling techniques is appropriate.
The objective in this paper is to present related issues and challenges, show available modelling techniques that can be used, and highlight gaps that should be addressed when considering potential disconnect criteria. The results are for demonstration and not specific to any development.
Relevant standards and limits states
The CanadaNewfoundland and Labrador Offshore Petroleum Board (CNLOPB) is responsible to verify that all statutory and regulatory requirements are fulfilled prior to the issuance of an approval or authorization for offshore of petroleum exploration and development projects in the CanadaNewfoundland and Labrador Offshore Area. Their mandate includes ensuring the health and safety of workers and environmental protection. ISO Standard 19,906 provides guidance on designing for ice actions. In Norway, offshore petroleum activities are governed by the Petroleum Safety Authority (PSA) and relevant standards include NORSOK and ISO.
ISO 19906 (2019) references methodologies for estimating both global and local ice actions. It requires that vessel designs be confirmed based on ultimate (ULS) and abnormal (ALS) limit state design checks. For ULS, iceberg actions with an annual probability of exceedance (APE) not greater than 10^{−2} should be considered. An action factor of 1.35 or 1.1 is applied depending on whether the structure is L1 (manned) or L2 (manned but evacuated for larger icebergs). For ALS, iceberg actions with APE not greater than 10^{−4} or 10^{−3} should be considered depending on whether the structure is L1 or L2. For ALS, an action factor of 1.0 is used. The standard allows consideration of the effectiveness of ice management and disconnect systems in reducing impact rates and loads when determining design EL and AL actions; this requires a defendable estimate of icemanagement success rates. In the case of iceberg impacts on FPSOs, when ice management and disconnect are both applied, the annual impact rate may be less than 10^{−2} in which case ULS does not apply. For ULS, design procedures shall be based primarily on linear elastic methods of structural analysis; though some localized inelastic behaviour of the structure and its components is acceptable. For ALS, the structure should be able to sustain large actions and other action effects in the inelastic region without complete loss of integrity. For an FPSO, it is also necessary to ensure that the vessel does not capsize or leak oil. Following impact, the vessel should be able to withstand subsequent wave and wind loads until any required repairs can be carried out.
ISO 19906 also provide guidance on serviceability limit states (SLS). These limit states correspond to criteria governing functional use such as deformations that affect efficient use of structural components. Exceedance of SLS can result in the loss of capability of a structure to perform adequately under normal functional use. Unless the owner has specified otherwise, the representative value of the serviceabilitylevel ice action used for SLS shall be determined based on an APE not greater than 10^{−1}. ISO 19900 (General Requirements for Offshore Structures) indicates that principal actions for SLS checks are usually operational actions with accompanying daytoday environmental actions or, if defined by the operator with respect to particular activities or operations, environmental actions more probable than extreme actions.
Defining disconnect criteria, in terms of those icebergs and environment conditions for which one can remain on site, is similar to defining a SLS in that the ability of the platform to perform adequately should not be affected if an impact happens. The criteria differs in that it is based on an operational decision that essentially allows an increase in the number of impacts (though only those meeting criteria similar to those for a serviceability limit state).
It is first necessary to show that the probability of any denting or local buckling that could require repairs will be very small. Second, given the large variation in iceberg shapes and environmental conditions, it is also critical to verify that AL actions have not been affected.
Note that, if in future one moves into regions with greater numbers of icebergs, then AL actions and required hull strengthening will be increased. The increased strengthening will allow the vessel to withstand larger impacts without serviceabilitylevel damage, so less restrictive disconnect criteria could be used, mitigating increases in downtime because of more icebergs.
Iceberg impacts with an FPSO involve localized ice failure loads with the hull. It is instructive to consider standards that consider ship impacts with fixed and floating platforms.
ISO 19902 (Fixed Steel Offshore Structures) differentiates ship impacts with a structure depending on whether the impact involves low or high kinetic energy. Low energy impacts are considered to represent minor bumps during normal vessel maneuvers and are defined in terms of impact velocity of 0.5 m/s and vessel mass representative of the specific location. Different added masses are considered depending on the vessel size and orientation at impact. ISO 19902 indicates that the owner can treat low energy impacts based on a serviceability limit state and set requirements based on practical and economic considerations. The treatment of low energy impacts as a serviceability limit state is analogous to impact of an FPSO by smaller icebergs in low sea states.
NORSOK N003 (NORSOK 2017) also provides guidance on vessel collisions with a platform. The standard considers impact by passing ships, supply and intervention vessels and shuttle tankers. For passing ships, impact energies for ALS design values should be determined based on traffic in the area. For supply and intervention vessels, for ALS design values, an impact energy of 50 MJ should be considered unless further evaluations are performed. In the latter case, impact velocity should be based on a drifting or erroneously operated ship. Even if velocity limitations are in place, the possibility of a faulty DP system needs to be considered. If there are no operating restrictions, the vessel size should not be less than 10,000 t. Head on speeds of 0.5 and 3 m/s respectively should be considered for ULS and ALS design checks. Added masses of 40% for side impacts and 10% for bow impacts should be used. For shuttle tankers with tandem offloading, an impact energy of 100 MJ should be considered. The impact locations and geometries should be based on the specific structure and vessels. Secondary impacts should also be considered. NORSOK N003 references NORSOK N004 and DNVGLRPC204 for loaddisplacement curves for the impacting vessel and indicates that the energies absorbed by both the structure and impacting vessel should be considered. While ALS and ULS design checks are required, there is no mention of SLS checks. For ALS actions, it would be of interest to compare iceberg impact kinetic energies and load displacement curves with those from ship impacts.
Environmental parameters
Iceberg drift and waveinduced velocities are a function of iceberg size and shape, and the current, wind and wave conditions. Detection of icebergs is largely a function of wind and wave conditions. Iceberg management is strongly dependent on waveconditions. The ability to disconnect the FPSO could also be affected if waves are extremely high.
CCORE uses significant wave height, H_{S}, as a general indicator of the severity of metocean conditions. The models used for iceberg detection, iceberg management, disconnection success rate, iceberg drift velocity and iceberg and FPSO waveinduced velocity are all formulated in terms of H_{S}. Variations due to other environmental parameters are considered, either explicitly or implicitly, as additional randomness.
For probabilistic analyses, the H_{S} distribution representative of the iceberg season is of interest. Seasonal variations in both iceberg frequency and significant wave height (Fig. 5) are captured by combining monthly significant wave height distributions weighted by the number icebergs present to generate a distribution representative of the iceberg season (Fig. 6).
When considering waveinduced motions of an iceberg or FPSO, the sea state needs to be characterized. For the analyses here, a wind generated JONSWAP sea spectra with spectral peak period.
is assumed where the relationship between H_{S} and T_{P} is based on Seaconsult (1988).
Iceberg areal density, sizes, shapes and drift and waveinduced velocity
The required iceberg parameters are areal density and size and shape parameters. The size parameter most commonly available is iceberg waterline length as this parameter is easiest to measure, so there is a relatively large amount of data. Iceberg mass would be a better directly measured parameter for estimating impact kinetic energies, though fewer data points are available and iceberg mass is not always readily available in operational situations. Additional shape parameters are required for modelling the influence of rotation of an iceberg on impact and the influence of the bluntness of the impacting face of the iceberg on global and local loads.
Iceberg areal density is defined as the expected number of icebergs per unit area at any random instant in time. Areal density is used in determining how often the platform will be impacted. The area density may vary by month and year, but for design, the longterm average is typically of interest.
Habib et al. (2016) compare estimates of areal density on the Grand Banks based on available International Ice Patrol (IIP) ice charts versus overflight data. IIP charts are available back as far as 1960, however, only charts from 1984 to present are used when calculating areal density values (the IIP introduced Side Looking Airborne Radar in 1983, which led to a greater degree of confidence in the numbers being reported). Overflight data are available from 1998 to present. For the Jeanne d’Arc Basin, the difference is substantial with the respective areal density estimates being 1.25 × 10^{−4} and 0.53 × 10^{−4} per km^{2}. When including bergy bits, the areal density values increase by a factor of approximately two. There are differences in the years covered, with IIP charts going back as far as 1984. In addition, densities derived from the charts are known to be conservative given that the purpose of producing the charts was to warn shipping of the most southerly extent of iceberg occurrence. For the flight data, it is necessary to normalize the iceberg count by the area of coverage. For this study, the estimate based on overflight data has been used.
Iceberg waterline length, L, is defined as the maximum waterline dimension. The waterline length distribution used is a combination of two exponential distributions representing larger icebergs advected into the region and smaller locally calved icebergs (Crocker 1993; Crocker and Cammaert 1994). The probability distribution function for waterline lengths between 5 m and 400 m is expressed as:
Using this distribution, the mean iceberg waterline length is approximately 44 m. When considering the distribution of lengths of icebergs impacting the structure, Bayesian updating is applied to account for the increased probability of impact by larger icebergs (ISO 2019). In addition, the shape of the distribution will be influenced by ice management as small and very large icebergs are generally more difficult to manage.
Iceberg profile data are required for accurate characterization of global and local shapes of icebergs. Profile data, which were utilized, include the following.
Dobrocky Seatech Ltd. (Mobil Hibernia Development Studies 1984) obtained 23 below water profiles. Four to eight vertical profiles per iceberg were obtained.
Oceans (2003, 2004) obtained profiles for 12 icebergs. Eight vertical underwater profiles were obtained around each iceberg and combined with above water profiles interpreted from scaled photographs collected at the same time.
Ice Engineering Ltd. (Mobil Hibernia Development Studies, 1981, 1982, 1983a, b, 1984 and 1985) obtained 149 below water profiles. Four vertical profiles per iceberg were obtained. Abovewater profiles were determined using stereo photos and Polaroid pictures taken at each of the four target faces. Two orthogonal sections were constructed for each iceberg using above and below water profiles. CCORE fit a series of horizontal ellipses through the two sections at different elevations to create a 3D shape.
Younan et al. (2016) describe the analysis of 28 detailed profiles obtained by Hibernia Management and Development Company (HMDC) in 2012. Abovewater iceberg shape data was collected using photogrammetry and belowwater shape data was collected using multibeam sonar. The resulting combined raw point cloud data was processed to generate iceberg profiles defined in terms of a series of horizontal sections at 0.5 m spacing, as well as STL files.
McGuire et al. (2016) have demonstrated use of a rapid iceberg profiling system and to date have collected about 40 3D highresolution iceberg profiles that could also be used.
Utilization of the above data for iceberg shape characterization of modelling impacts is described in Stuckey et al. (2016). The growth of global ice contact area A with penetration δ of the iceberg into a flat wall (side of an FPSO), is expressed in terms of a power law expression of the form.
The coefficients C_{A} and D_{A} were calibrated by performing an areapenetration analysis for each iceberg and combining the results to formulate random relationships. Contact areas, based on a flat wall interaction, were evaluated at equally spaced orientation angles for each iceberg. Different numbers of orientations were used depending on the resolution of the data for the given data source. Nominal areas A were determined for penetrations δ at increments of 0.25 m up to a maximum of 10 m. The penetration and area data were transformed to log space and regressed to determine a bestfit line through the data. The coefficient C_{A} is best fit using a lognormal distribution (μ=107 and σ=205) with a modified tail to using a lognormal distribution. The coefficient D_{A} is modelled as a function of C_{A}using the linear function.
where e is a normally distributed random variable characterizing the scatter in the data.
For modelling the influence of rotation of the iceberg during an impact with a flat wall, a single parameter G can be used if there is small rotation and relatively small effects due to friction and hydrostatic restoring forces (Matskevitch 1997). The parameter G is determined from the eccentricity of impact and the moments of inertia around the three principal axes (see Stuckey et al. 2016).
A power law equation giving mass as a function of iceberg water line length was developed by Stuckey et al. (2016) using the profile data referenced above, and additional estimates of mass determined solely from abovewater profiles and estimates of the density of iceberg ice, mostly from the Mobil Hibernia Development Studies (1981 through 1984). The mass data set used contained 806 measurement pairs in total. Iceberg mass M is modelled as a function of waterline length using a power law relationship:
where the power law coefficients a = 1.11 and b = 2.67 are the power law coefficients and e is a normally distributed random variable characterizing the scatter in the data with respect to the bestfit curve. The mean and standard deviation for the error term e were determined as quadratic functions of iceberg water line length. The bestfit and model P10 and P90 curves (10 and 90% exceedance level values) are shown with the data in Fig. 7.
Iceberg drift speed is modelled using an empirical model developed by Stuckey (2008). The model is based on data from the Canadian Offshore Oil and Gas Environmental Data archive published by the Marine Environmental Data Service (MEDS 1997) and from iceberg sightings data collected by PAL during the 2004 through to the 2015 iceberg seasons. Regression analyses were conducted to determine mean iceberg drift speed as a function of iceberg length L and significant wave height, H_{S}. The analysis was repeated for the standard deviation of iceberg drift speed. Random drift speeds are then sampled assuming a gamma distribution with mean and standard deviation determined for the specific L and H_{S} combination. Integrating over all L and H_{S} values, weighted by the joint probability of each L and H_{S} combination, gives an averageiceberg drift speed of 0.31 m/s.
Icebergs experience waveinduced motions with magnitude dependent on the size of the iceberg relative to the wave period. Icebergs with small lengths will experience motions approaching that of wave particles. As iceberg size increases, the waveinduced motions generally decrease. There may be peak values in the heave component at the iceberg resonance frequency. The motion characteristics are often expressed in terms of response amplitude operators (RAOs) which give the ratio of amplitude of iceberg response in each of six degrees of freedom to wave height for different regular wave periods. Relative phases are also provided.
An approach for determining random surge impact velocities for different iceberg shapes was developed by Lever et al. (1989), based on work in Lever and Attwood (1988) and Lever et al. (1988). Basin tests were used to obtain RAO’s for a number of iceberg shapes in regular waves. An approach was then developed for obtaining dimensionless irregular significant RAO’s in random JONSWAP type sea states. Figure 8 shows the dimensionless irregular significant surge velocity RAO (V_{S}/(πH_{S}/T_{P})) developed for spherical icebergs. Finally, a method for using Bayesian updating to account for the increased probability of impact when an iceberg is moving forward at higher velocities was developed. Fuglem (1997) further adapted the approach to account for Bayesian updating given combined drift and waveinduced velocities.
Operational considerations
Iceberg impacts are avoided by detecting icebergs, then diverting them or, as a last resort, disconnecting from the mooring system and moving offsite.
Ice management plans are generally proprietary to individual operators and can vary. Typically ice management zones are defined in terms of hours required to carry out required management and shutdown operations. Actions are then initiated once an iceberg enters a zone and has an estimated closest point of approach (CPA) meeting specified ice management criteria.
Figure 9 shows a simplified ice management system for illustration. In this case, icebergs monitored in Zone 1 and subsequently entering Zone 2 will be towed. If towing operations are unsuccessful, and the iceberg enters Zone 3 (Icebergs B and C), suspension of operations and flushing of lines will be initiated. These operations can be reversed if subsequently ice management succeeds or the iceberg turns away from or passes Zone 4 (Iceberg B). If an iceberg reaches the Zone 4 boundary (Iceberg C), the vessel will disconnect. The typical size of Zone 4 (the Exclusion Zone) is around 500 m in radius.
Factoring the efficiency of ice management and disconnect capability to mitigate the effect of ice actions (i.e., reduce exposure) into the design of offshore production facilities is recognized in ISO 19906. It is reasonable with reduced exposure to reduce icestrengthening requirements.
Consider an iceberg at range R directly approaching the platform at a constant velocity, v_{D}. The time to impact is then t = R/v_{D}. Given a probability P_{det}(t H_{S}, L) of detection at range v_{D}t and a probability P_{tow}(t H_{S}, L) of a successful tow given remaining time t, the probability of impact is.
This assumes that H_{S} does not change and one has a good initial estimate of L.
One could integrate the probability of detection and management success over time as the iceberg approaches the platform; but this would require consideration of autocorrelation in detection probabilities at different ranges for a specific iceberg and set of environmental conditions. The following conservative approach from McKenna et al. (2003) is applied, as it is much simpler. The overall probability P_{impact}(H_{S}, L) of impact is taken as the minimum P_{impact}(t H_{S}, L) over time as it approaches the platform, i.e.
On the Grand Banks, icebergs are detected and monitored from many different sources; e.g., upstream satellite detection, midstream aerial reconnaissance flights, and nearstream tactical measures including detection from support vessels and the facility based marine radar (with scan averaging optimized for detecting icebergs). An iceberg detection model based solely on the facility marine radar is considered for this paper and is considered conservative. A performance model for iceberg detection was developed by Sigma Engineering (Johnson and Ryan 1991; Sigma Engineering 1994). Data from this model were used to derive the detection probabilities for various combinations of iceberg size, sea state conditions and range from the platform (Stuckey et al. 2016).
A model for the probability of successfully managing an iceberg, given the iceberg waterline length, significant wave height, and time available was developed based on data in the PERD Comprehensive Iceberg Management Database (CIMD) (PERD 2015).
Each iceberg tow record in the PERD CIMD was compared with information contained in the PAL ice season reports. Many of the icebergs required multiple tow attempts before the planned objective was achieved. Some of the attempts occurred consecutively, while others may have occurred days apart. A tow was considered successful if the tow was categorized in the CIMD as planned objective achieved, iceberg towed past the closest point of approach (CPA), suitable outcome, or the recorded deflection angle was greater than or equal to 5 degrees. Average rates of success were determined by L and H_{S} bin; these are shown graphically in Figure 10.
The relationship giving the probability of physical management success shown in Figure 10 was developed based on the available data. The tow success quantities are influenced by the time available for the towing operations. Based on a review of the data and judgment, the probabilities in Figure 10 are considered to represent an available timeperiod of 8 h. A model outlined in Randell et al. (2009) for the influence of available times different from 8 h is applied. With more time available, the probability of success increases (more attempts can be initiated as well as alternative approaches). With less time available, the probability of success decreases. A minimum of around one hour is generally required for any towing attempt.
The reliability of the disconnect system can have a significant influence on ice loads, for example the difference between a 98% and 99% disconnect reliability is a factor of approximately two on the rate of impacts expected. The operator’s ability to disconnect successfully could also be reduced in very high seas. For this study, the influence of different disconnect reliabilities and limit sea states is investigated.
New build FPSOs will most likely have good heading control using thrusters. This will allow operators to face an oncoming iceberg and ensure that any impact is taken on the bow as opposed to the side where there is less ice strengthening. It is difficult to estimate the effectiveness of heading control systems in higher sea states. For this study, the influence of having different orientations relative to the direction of travel of the iceberg are considered as a sensitivity analysis.
The operators will require criteria regarding disconnection should an iceberg reach the exclusion zone. The decision criteria should be based on the resistance of the FPSO hull, the extent of knowledge regarding the iceberg size and shape, and the range of ice pressures that could be imparted to the FPSO in the event of an impact. The ability to estimate global impact load distributions is a function of the available information on the iceberg (waterline length, iceberg mass or complete profile), as described in Stuckey et al. (2018). For this study, it is assumed that only the iceberg waterline length is known.
A serviceability criterion defined in terms of iceberg waterline length, L, and significant wave height, H_{S}, has been adopted, following the approach by Jordaan et al. (2006). They suggested that a simplified format for the disconnect criterion (such as illustrated in Figure 11) would be preferred for operational use. In developing the disconnect criteria, two serviceability criteria were considered with respect to the structure; first, that the depth of shell plate denting shall not exceed half of the specified plate thickness and second, that localized plastic strain shall not exceed 5%. A MonteCarlo simulation was run to determine local pressures on the FPSO for different structural areas of interest given a specific iceberg and sea state, and finite element analysis (FEA) was conducted to determine the structural response. The basis for the disconnect criteria was that for the given L, H_{S} pair, the serviceability condition should be met with a 90% confidence level. The possibility that an iceberg reaching the exclusion zone could still miss the platform was (conservatively) not taken into account.
Decisions regarding initiation of shutdown versus disconnect also needs to be considered. If an iceberg is clearly below the disconnect criteria, then it may be sensible to not initiate shutdown. If the iceberg is just below the disconnect criteria and there is uncertainty regarding the iceberg size or the sea state forecast, then it may make sense to initiate shutdown until better information is available.
For this paper, combinations of L and H_{S} are determined such that the probability of exceeding specified structural resistance, defined in terms of critical pressure over a defined area, is less than 10%, assuming an impact occurs. In the following, the structural resistance values are referred to as serviceabilitylevel resistance values. Several critical pressures (2.5, 4.0 and 5.5 MPa) have been considered for the purpose of sensitivity analysis; these are not associated with any particular ship structure. The critical pressure would normally be selected based on a specified ship structure to ensure that excessive denting of plate and local buckling of supporting structure does not occur. The local area that is most critical will be a function of how local ice pressure scales with local area versus how the serviceabilitylevel resistance of the ship structure changes with area.
Impact dynamics
Modelling the dynamics of an iceberg colliding with a moored FPSO is challenging given the variety of possible iceberg shapes, random wave fields, and hydrodynamic interaction of two bodies at proximity in waves and crushing and potential fracturing of ice. TwelveDOF simulations in calm water conditions show that there can be multiple impacts due to the iceberg shape coupled with iceberg rotation with a moored SPAR system (Fuglem and Younan 2016), the model has also been applied for FPSOs. Multiple collisions may also occur because of waveactions.
For impacts by smaller icebergs, it may be possible to ignore the motion response of the FPSO to impacts given its relatively high displacement. Waveinduced motions of the FPSO in higher sea states could still be important. Even if the FPSO does respond to the initial impacts by smaller icebergs, the iceberg will impart its momentum to the FPSO before the FPSO displacement is large enough that the mooring system responds (assuming no environmental preloading).
The Ice Load Software (ILS) (Stuckey et al. 2016) uses a simple analytical solution to determine iceberg impact loads. A first order approach is used to account for the rotation of the iceberg around the contact point with the implicit assumption the total rotation of the iceberg is small. Random local shapes of icebergs at the point of impact are modelled using a power law relationship with random distributions for the coefficients fit based on actual iceberg shape data. The initial equation was determined assuming impacts with a flat wall, but corrections can be made for impacts with curved surfaces and corners. It is assumed that friction is small enough that it can be ignored, given that the ice is crushing during the contact. Random surge velocities of the iceberg are sampled based on the iceberg open water RAO and an assumed JONSWAP sea state, accounting for Bayesian updating. Random velocities of the FPSO based on open water RAOs can be included. Added mass effects are modelled by specifying added mass factors for the iceberg and FPSO.
1D and 2D time domain models have been developed that extend the capability of the ILS but are slower to run. Both account for the motion of FPSO and the response of the mooring system. Further work is ongoing with the 2D model to account for the changing contact geometry as the iceberg rotates as well as the removal of crushed ice and the motion of vessel in waves.
Further model development is required to better handle hydrodynamic effects and remove conservatisms. Diffraction analysis programs (e.g., Sesam/Wadam from DNV GL; Aqwa from ANSYS) can be used to model the motions of two floating bodies in a random wave field. For example, Talimi et al. (2016) investigated the motions of icebergs near fixed and floating spar platforms using the MAPS diffraction analysis program (Qiu 2019) for the motions in waves and computational fluid dynamics (CFD) for estimating iceberg deflection in a uniform current. DNV GL (2018) consider interactions between a semisubmersible and bergy bits and growlers using the Sesam HydroD diffraction programs Wadam and Wasim.
Diffraction analysis programs are based on an inviscid flow assumption, though some viscous effects can be approximated. There are some limitations regarding the ability to handle complex geometries near the water surface, green water, and interactions in very close proximity, including impacts.
Potential alternatives to diffraction analysis include the CFD and smooth particle hydrodynamics (SPH) and related methods. CFD can accurately model complex geometries in both still water and waves and can be coupled to finite element analysis (FEA structural models (e.g. Star CCM+ and ABAQUS) to model impacts but take time to set up and are very slow to run, especially if a large domain is use in order to minimize reflections from the boundaries. SPH/MPH solutions look promising; for example, Mintu and Molyneux (2018) simulate vessel movement through pack ice in a wave field.
Ice failure is a complex process and improvements in models for global and local pressures, including effects of spalling and removal of crushed ice are still needed.
FEA models of global ice strength are difficult given crushing and spalling of ice. No FEA models have been developed to date that can adequately capture observed behavior of ice such as development of highpressure zones, recrystallization, spalling and extrusion of crushed ice. Considerable success has been achieved in modelling and better understanding the behavior of single high pressure zones (HPZ’s) (see for example, Jordaan 2001; Jordaan et al. 2016). Statistical models for local pressure have been developed based on observation data from pressure panels on ships transiting multiyear ice conditions (Jordaan 2001, ISO 19906) and also the Terry Fox icebreaker ramming bergy bits (Ritch et al. 2008). Ralph (2016) shows that the statistic local pressure model can be well represented by MonteCarlo simulation of HPZ’s as a Poisson process. One weakness of present approaches outlined in ISO 19906 is that global and local pressure models are independent, the approach outlined by Ralph shows promise as a basis for a combined globallocal pressure model; work in this area is ongoing. In order to approximate global loads while accounting for the changing in contact area associated with crushing,
It is common to use MonteCarlo methods to determine ice design loads, as this method can handle complex and discontinuous functions. To determine AL ice events and 90 percentile ice actions for given L and H_{S} pairs, it is necessary to consider large numbers of impacts. The more detailed simulation techniques tend to be too slow for practical use within a MonteCarlo framework. There are several ways to incorporate more detailed simulation techniques including regression analysis and using simpler models to identify potential design cases, then running the detailed models for these limited cases.
A 1D analytic model is considered for illustration. Consider a direct impact of an iceberg with mass \( {\overset{\sim }{m}}_{IB} \), including added mass effect, and velocity v_{I} with an FPSO having mass including added mass effect \( {\overset{\sim }{m}}_{FPSO} \) at rest with no environmental preloading of the mooring system. For the 1D solution, it is assumed that there is no rotation of the iceberg and FPSO. If the mass of the iceberg is relatively small, then the FPSO will only move a short distance before the FPSO and iceberg achieve equal velocity, so the mooring response force will be small. Conservation of momentum then applies for the initial impact: i.e.
Some amount of energy E_{C} will go into crushing. Conservation of energy the for the remainder of the impact is expressed as.
Combining Eqs. (8 and (9 gives
which can be reduced to
Note that for smaller impacts, the crushing energy does not depend on the shapes and strengths of the two bodies. If the FPSO is much larger than the iceberg, then
If the mooring stiffness can be approximated as a simple spring with constant k_{M} (reasonable for small offsets), the energy imparted into the mooring system will be
which becomes
Figure 12 shows example results for a simplified case. Mass is shown in the upper left based on the mean mass relationship from Figure 7. An initial velocity of 0.31 m/s is assumed. The final velocity based on Eq. (8 is shown in the upper right. The bottom left figure shows different calculations of crushing energy. The dashed line is the initial kinetic energy, which equals the crushing energy if the FPSO is held fixed. The solid line is the crushing energy from Eq. (11. The dotted line is the crushing energy based on a time domain solution of the 1D equations of motion, which does not assume transfer of momentum before significant response of the mooring system. The bottom right figure shows the maximum mooring response based on Eq. (13 and as determined solving the 1D equations of motion.
Figure 13 shows a schematic of the approximate iceberg movement and FPSO response using the 2D impact model. For larger icebergs and off centre bow impacts, the FPSO can be rotated such that iceberg subsequently moves along the side of the vessel. Once it passes the CG of the vessel, it will start rotating the FPSO away again. The mooring system will also play a role if there is preloading or the offset becomes large enough.
Global and local ice loads
Crushing type failure of iceberg and sea ice can involve a number of mechanisms, as ice is a brittle material that is near its melting point and contains numerous variations in crystal structure as well as flaws. Jordaan (2001) gives an overview of the different processes involved. When estimating design ice loads, modelling the different processes is not practical. Because of modelling uncertainty, it is important wherever possible to use methods based largely on fullscale field observations. Two critical aspects of ice failure processes are the significant degree of randomness and the scale effect, where the failure strength of ice, on average, reduces with the contact area. Randomness in nominal or mean global ice strength is a result of different mechanisms such as spalling, development of HPZs that vary randomly in time, location and magnitude and extrusion events (Figure 14). The scale effect is largely a function of the increased likelihood of encountering flaws in the ice as the area (or volume) of ice involved increases, plus the development of alternative pathways or mechanisms for failure. In interpreting field data, it is important to consider these factors and to consider the methods used for measuring ice strength and any associated limitations.
Global ice strength is defined as the global force divided by nominal contact area (Fig. 15), where the nominal contact area is determined from the projected position of the original profile of the ice feature as the interaction progresses. Actual contact areas are smaller than the nominal area due to spalling of ice but are typically not measured as complete instrumentation of large contact faces is expensive. The relationship between global ice pressure and contact areas is complex. Iceberg shape is random, and during an interaction event, different processes such as spalling of large pieces, extrusion of crushed ice and different damage mechanisms can occur.
A random pressurearea model for ice crushing failure, based on data for ship rams with multiyear ice, is described in ISO 19906, Section A.8.2.4.3.5. The equation is based on a study by the Canadian Coast Guard for design of icebreakers as described in Carter et al. (1995). The model is probabilistic and has no restriction regarding aspect ratio (typically the ratio of structure width to ice thickness as used for sea ice rather than iceberg interactions). The pressurearea relationship is useful for modelling the variation in pressure through an impact as contact area changes (generally increases). The relationship (ISO 19906, Equation A.8–24), i.e.
defines the global pressure P_{G} as a power law function of nominal global contact area A_{N} with random coefficients C_{P} and D_{P} calibrated based on the analysis of a large database of ship rams with multiyear ice. The main calibration used data from three vessels covering a range of displacements: the Canmar Kigoriak, M.V. Arctic, and Manhattan. The preferred distributions for C_{P} and D_{P} based on the calibration were a lognormal distribution with a mean of 3.0 and standard deviation of 1.5 and a normal distribution with a mean of −0.4 and standard deviation of 0.2 respectively.
The last paragraph of ISO Section A.8.2.4.3.5 states that the relationship “can yield unrealistically low pressures for the instantaneous ice pressure.” when extrapolated to large contact areas and that a lower pressure cutoff should be considered in such cases. An explicit definition for “large contact areas” is not provided, but it is stated that guidance can be obtained from the ISO model for high aspect ratio interactions (refer to ISO 19906, Section A.8.2.4.3.3). A possible conservative approach for addressing the lack of data for larger contact areas (if larger areas are found to contribute for iceberg impacts with the floater) is as follows. The ship ramming data on which the probabilistic random pressurearea model was calibrated involved contact areas up to approximately 50 m^{2}. It is suggested to apply a cutoff such that if C_{P} and D_{P} result in an impact where a nominal contact area exceeds 50 m^{2}, then for areas greater than 50 m^{2}, a constant conservative pressure \( {P}_G={C}_P{50}^{D_P} \) can be used.
The above model was developed to capture observed global pressures in interactions with limited kinetic energy and increasing contact area with penetration, and to capture the observed variance in load traces. It has been recognized that the model can give conservative design loads for interactions involving larger contact areas.
As given in ISO 19906, assuming the number of interactions can be modelled using a Poisson process, the cumulative probability distribution local pressure p (MPa) acting on a local area A (m^{2}) is formulated as
where:
 B_{P}:
is an empirical coefficient representing ice strength in MPa (1.25 from the Kigoriak ramming trials but varies depending on specific ice regime as show in Fig. 16), and
 x_{0}:
is a constant representing the position of the design distribution (MPa)
 v:
represents the expected annual number of events,
 r:
represents the probability of hitting a panel given an event (0.5 in Kigoriak analysis), and
 t:
is the interaction time (seconds)
The constant 0.7 is a normalizing constant representing the average duration of Kigoriak rams
The equivalent number of impact events μ is a function of the expected annual number of events ν and the ratio of the expected ram duration t in seconds divided by a reference duration of 0.7 s for the Kigoriak rams. An assumption is made that longer duration interactions associated with larger ships and higher impact velocities correspond to greater volumes of ice crushing, increasing the probability of developing larger pressures.
To estimate design pressures, Eq. (15 is rewritten as
For design, x_{0} is typically taken as zero but a designer may choose alternative values based on analysis of appropriate regional local pressure data when available.
ISO 19906 provides that designers with an approach to consider background pressure, i.e., the pressure on structure outside of the local area being considered. It is suggested that the background pressure be determined such that the local force and background force sum up to the global force. A following note is provided “The use of an EL value for the local ice pressure, p_{L}, with an EL value for the surrounding (or global) ice pressure, p_{0}, can potentially lead to an overlyconservative design” and in fact the background pressure may typically be closer to an average global pressure. The design also needs to consider the specific grillage structure when determining local and background areas to consider.
Note that in reality, global and maximum local pressures will be likely be correlated. For example, ice strength for specific icebergs could depend on ice temperature as well as other parameters and one might expect both global and local strength to change in a similar manner. If the ISO models for global and local ice pressures are used, these correlations are not considered. Impacts with weak global ice strength could result in larger than average contact areas and impact durations that might imply large local pressures; this is counterintuitive and not correct.
An approach that that resolves such issues is to simulate actual contact areas and random highpressure zones (HPZs) within the actual contact areas. This approach has been shown to provide a good match to the probabilistic local pressure model outlined in ISO 19906 (Ralph 2016). In the model, HPZs are assumed to form at random locations within the contact area, distributed in space as a Poisson process. The force associated with different HPZs is exponentially distributed, and the HPZ area is assumed proportional to the force. In initial work, the force for each HPZs is held constant over its lifespan; though the force for a given HPZ could vary with time. The values and distributions for the different parameters have been determined based on local pressure data as measured on load panels mounted on ships transiting through different multiyear level and ridged ice conditions.
The model has been successfully implemented within an iceberg impact model, with the assumption of constant percentage loss of nominal global area to spalling. A simple stochastic spalling model has also been considered. The advantage of this approach is that global and local pressures are correlated. In addition, issues of overly conservative global design pressures at large contact areas, and overly conservative local pressures associated with weak global strength are avoided. Development of the model is ongoing including improving simulation time. Note that for the illustrations in this paper, the ISO global and local strength models were used.
When considering local pressures on the forebody or side of a ship, or for interpreting measured data from ship panels, the tangential movement of the iceberg relative to the ship plating, as illustrated in Figure 17 should be considered.
Capacity of FPSO hull structure
When considering disconnect criteria, emphasis is on situations (small icebergs in low or moderate sea states) that will generally result in smaller impact kinetic energies. The global loads and contact areas will also be relatively small.
The capacity of the FPSO hull to withstand ice loading will depend on the grades of steel used, plate thickness and supporting grillage (main frames, stringers and web frames). In higher sea states, there could be additional stress associated with hogging and sagging that could influence the behaviour of the plating, web frames and stringers at midship.
Plating can deform plastically under relatively large pressures resulting in permanent set without loss of function. Stiffeners (on plate and frames) can be used to reduce deformations under small loads, though their effectiveness changes if they trip. Loads at the centers of panels will be shared between supporting structure, whereas loads directly on web frames or stringers could potentially cause local buckling.
Because peak local ice pressures are greater over smaller areas than large areas (i.e. scale effects in ice mechanics), it is necessary to consider the resistance of the hull over different loading areas. Loads on larger areas would tend to be shared over multiple frames or stringers. For side paneling, the distances between adjacent frames or stringers can be relatively large; potentially resulting in panel areas of 20 m^{2} or more, and the possibility of lower strength associated with local buckling should be considered. For local areas with areas less than a panel, the structure can generally withstand greater pressures over small areas than over larger areas, and different loaded areas will be analyzed to determine which governs. FEA will generally be carried out to determine structural resistance for critical areas on the hull by accounting for complex load sharing mechanisms. Guidance on characterizing the structural capacity of the hull, or any steel structure, using finite element methods can be found in DNVGLRPC208 (DNV GL 2016).
As the emphasis in this paper is not on determining the resistance of specific hull structures, the hull serviceabilitylevel resistance with respect to different loaded areas is treated as a sensitivity parameter. A serviceabilitylevel resistance of 4.0 MPa over 1 m^{2} is considered for the base case analyses. As a sensitivity analysis, resistances of 2.5 MPa and 5.5 MPa over 1 m^{2}.were also considered. As a further sensitivity analysis regarding local areas considered, resistances of 1.3 MPa over 5 m^{2} and 0.8 MPa over 10 m^{2} were considered. Note that for the different local areas, A, the serviceabilitylevel resistance was assumed to scale for a given structure as A^{−0.7} based on judgment; note that this is the same power as for local pressure and further evaluation of the variation in structural resistance with local area is warranted. The influence of background pressure should also be investigated further.
Probabilistic approach to evaluate disconnect criteria
MonteCarlo methods have been used to estimate the probability of exceeding AL ice actions. For example, Figure 18 shows a flow chart of the approach used to determine design ice actions (the AL ice action is the 10^{−4} APE case). Details on the approach can be found in Stuckey et al. (2008, 2016).
When determining decision criteria for disconnect, the MonteCarlo simulation is run for a specified L and H_{S} combination, the encounter rate is set to 1 (i.e. an iceberg of size L has reached the exclusion zone) and the pressure associated with a 1in10 probability of exceedance is determined for different hull locations and local areas. This is repeated for all L and H_{S} pairs. It can then be argued that the FPSO can remain on site if, for the given L and H_{S} combination, the 1in10 local pressure is less than the associated serviceabilitylevel resistance for relevant local areas. Consideration of probability of different impact locations and relative movements of contact location is required.
Analysis cases and results
To demonstrate the methodology, a base case analysis has been conducted using the parameters outlined in Table 1. Parameter values used for sensitivity analyses are also shown. A number of simplifications have been adopted to make the analysis tractable, given that the analysis is for demonstration only.
The FPSO is assumed to have a length of 275 m and a width of 50 m.
The base case and sensitivity distributions of FPSO heading relative to the iceberg movement are notional. Appropriate distributions will be required for a real application, considering possible environmental conditions plus the operator’s ability to control the vessel heading.
The FPSO is treated as fixed. In a real application, the response of the vessel to impacts and the waveinduced motions of the FPSO should be considered.
Only impacts on the side of the vessel are considered and notional values of serviceabilitylevel resistance for different local areas have been selected. In a real application, the specific hull grillage and the probability of exceeding the serviceabilitylevel resistance anywhere on the vessel (forward and aft along the side or on the bow, and at different vertical positions) should be considered.
The value selected for disconnect reliability is notional.
A single impact per interaction is assumed. In a real application, the number of impacts will depend on the impact dynamics and on the ability of the operators to control the vessel heading and position following an initial impact.
For the downtime analysis, it is assumed that downtime will be initiated when an iceberg reaches a Ttime of 6 h. In a real application, the operators usually will also consider the drift forecast for the iceberg and its closest point of approach in making decisions.
Note that for the examples and sensitivity analyses presented here, a simple circle model was used in determining shutdown initiation and disconnect completion time; in real operations, the drift forecast for the iceberg and its closed point of approach will also be considered in making decisions.
For the base case analysis, a 6h Ttime is assumed for initiation of shutdown given an approaching iceberg. Given the mean drift speed of 0.31 m/s, this represents a 6.7 km radius circle. Without iceberg management, on average 8.0 downtime events will be initiated each year due to icebergs encroaching the Ttime circle. Accounting for iceberg management, the average number of downtime events is reduced to 3.1 per year.
Of these icebergs entering the Ttime circle, 68% percent fall below the disconnect criteria. If the disconnect criteria could be used to justify not initiating shutdown initiation, 2.1 shutdown initiations per year would be avoided.
When disconnecting for all icebergs and without iceberg management, 0.56 icebergs/year will reach the exclusion zone (1 every 1.8 years). Accounting for iceberg management, 0.22 icebergs will reach the exclusion zone (1 in 4.6 years), requiring complete disconnection if no disconnect criteria is applied. Note that 98% disconnect reliability implies that the FPSO could fail to disconnect due to some mechanical issue for up to 2% of incursions.
A disconnect decision will be made when an iceberg reaches the 500 m radius exclusion zone. For the base case analysis, a disconnect criterion based on a structure serviceabilitylevel resistance of 4.0 MPa for a 1 m^{2} local area is applied. A contour plot of local pressures over 1 m^{2} at the 1in10 exceedance level, as determined using MonteCarlo simulation, is shown in Figure 19. The base case disconnect criteria (based solely on midship impacts) corresponds to the 4.0 MPa contour (shown as thick red line in Figure 19). The influence of H_{S} is diminished for high sea states and small icebergs, this is a consequence of a limit on the proportion of an iceberg that will crush before breaking up as assumed in the ILS.
An iceberg is defined as ‘threatening’ and requires disconnect if the estimated P90 local pressure over a specified local area exceeds the corresponding serviceabilitylevel resistance. For example, for the base case analysis shown in Figure 19, the FPSO should be disconnected if the combination of sea state H_{S} and iceberg waterline length L is above the red line.
Note that in developing practical rules for operations, simpler conservative criteria could be considered such as shown in Figure 11. There is a reduction in the number of disconnect completions from 0.22 per year when disconnecting for all icebergs to 0.03 per year when disconnecting for threatening icebergs (i.e., only need to disconnect for 14% of cases without criteria).
Structure serviceabilitylevel resistance will vary for different FPSO designs, resulting in different disconnect criteria curves. For example, if resistance was 2.5 MPa for 1 m^{2}, then the disconnect criteria would be based on the 2.5 MPa contour. Similarly, a resistance of 5.5 MPa on 1 m^{2} would lead to a disconnect criteria based on the 5.5 MPa contour. This range of possible disconnect criteria is indicated by the red shaded region in Figure 19.
A series of sensitivity analyses were performed based on Table 1; the annual frequencies for initiating shutdown and completing disconnection are provided in Table 2 for all icebergs and for threatening icebergs. The first sensitivity case (different serviceabilitylevel resistance values) was discussed above in reference to the red shaded region in Figure 19.
In the second sensitivity case, the serviceabilitylevel resistance with respect to local areas was varied. For the 5 m^{2} local area case, a 4 MPa resistance for 1 m^{2} scales to 1.3 MPa. A contour plot of local pressures over 5 m^{2}, at the 1in10 exceedance level, was determined and the 1.3 MPa contour identified. Similarly, a contour plot of local pressures over 10 m^{2}, at the 1in10 exceedance level, was determined and the 0.8 MPa contour identified. The three disconnect criteria are shown in Figure 20. The three curves are close for higher significant wave heights, but vary somewhat for lower sea states. The difference in the curves is largely a result of the larger exposure for smaller areas.
The size of the exclusion zone influences the number of disconnect completions. Decreasing the exclusion zone radius from 500 m to 400 m results in a 20% decrease in the number of disconnections for all icebergs (from 0.44 to 0.35 per year) and a 20% increase in the number of disconnections for threatening icebergs (from 0.07 to 0.05).
In some situations, a single iceberg may impact the FPSO in multiple locations along the side of the vessel as it drifts past. A sensitivity analysis was performed in which each iceberg was assumed to impact the FPSO a total of four times. The first impact included iceberg drift and waveinduced components. For the subsequent impacts, it was assumed the drift component was dampened and the impacts were due to waves. This assumption increased the disconnect criteria, resulting in a 46% increase in the annual number of downtime events (0.88 to 1.28) and a 43% increase in the annual number of disconnections for threatening icebergs (from 0.07 to 0.09).
Differences in global ice strength will influence the probability of developing larger local pressures and ultimately change the distribution of local pressures. Two sensitivity cases were investigated. First, a constant global ice pressure of 0.5 MPa was assumed. The softer ice (lower global pressure) led to an increase in the 1in10 local pressures, resulting in a 35% increase in the number of downtime events and the number of disconnections c for threatening icebergs. For the second case, the coefficients in Eq. (13 were set to the mean values of 3.0 and − 0.4 respectively. For this case, the number of downtime events and the number of disconnections decreased by 34%.
The effect of FPSO heading control was investigated. FPSO heading control will affect the number of impacts occurring on the side of the FPSO and determines the normal component of the impact velocity required for calculating global forces. Two additional cases were analyzed: the vessel is oriented 5° for 10% of the time and oriented 25° for 10% of the time. There was a negligible change in the number of downtime events and disconnections when comparing the 5° case and the base case of 15° offset. Increasing the FPSO heading to 25° for 10% resulted in a 2% increase in the number of downtime events and disconnections for threatening icebergs.
The ability to disconnect the FPSO could also be affected if waves are extremely high. A sensitivity analysis was performed in which the maximum significant wave height during which the FPSO can disconnect was set to 8 m. Imposing the disconnect limit increase the number of disconnect completions 3% for all icebergs and 8% for threatening icebergs.
The size of the Ttime circle dictates the number of downtime events with larger Ttime circles resulting in a larger number of downtime events. A 4h Ttime circle results in 33% fewer downtime initiations for all icebergs and for threatening icebergs. For an 8h Ttime circle, there are 35% more downtime initiations for all icebergs and for only threatening icebergs.
General applicability
An approach is outlined for determining disconnect criteria given icebergs approaching a floating production system. The emphasis in this paper is on the overall probabilistic framework and modeling of icebergs and iceberg actions. Gaps that should be addressed in order to reduce uncertainties and conservatisms are highlighted.
It is of note that disconnect criteria for icebergs are not specifically addressed in ISO 19906. The criteria are similar to SLS but are operational.
Conclusions
This paper provides an overview of a general approach, and specific models developed to define disconnect criteria, in terms of iceberg size and environmental conditions. Areas where improvements can be made to reduce uncertainties and conservatisms are identified.
A probabilistic approach is applied that accounts for the large observed variations in sea states, iceberg sizes and shapes, and ice failure strength. The example analyses conducted show how the disconnect criteria vary depending on the serviceabilitylevel resistance for specific hulls.
The example disconnect criteria have been defined in terms of L and H_{S}. Additional information, such as iceberg mass, iceberg profile and observed drift velocity should be utilized if available, as this will allow decisions that are more effective.
For an actual design, the specific vessel and mooring characteristics, plate thickness and support structure, steel grades, ice management plan, disconnect reliability and FPSO response in waves should be considered. FEA is required for determining structural resistance to loads for the specific vessel. The probabilities of impacting and exceeding structural resistance on different locations on vessel needs to be estimated and combined. ALS design checks should be carried out to ensure smaller icebergs cannot exceed AL actions. For simplicity, the distance of icebergs from the FPSO in any direction was used for defining when ice management actions would be initiated. In actual ice management, the forecast trajectory of an iceberg and estimated closest point of approach (CPA) will be considered.
As operators move into regions with greater numbers of icebergs, additional ice strengthening will be required and as a result, the serviceabilitylevel resistance of the vessel should improve. This should help mitigate increases in downtime associated with greater numbers of icebergs.
Recommendations
Identified areas where improvements can be made are outlined below.
Probabilistic approach

A P90 criterion on exceeding the serviceabilitylevel resistance was chosen. Further evaluation of this criterion, in conjunction with the criteria for the level of allowable structural deformation, would be beneficial.

For this demonstration, it was conservatively assumed that any iceberg reaching the exclusion zone will impact the FPSO hull at its weakest point (assuming that the FPSO does not disconnect). The risk that any iceberg reaching the exclusion zone would actually impact the FPSO is small; a risk further reduced as the operators have control of the FPSO heading and position. Fuller consideration of these factors will result in more reasonable criteria.
Impact dynamics

The FPSO was treated as fixed. Consideration of the FPSO translation and rotation will generally result in reduced load estimates.

A simplified model for iceberg global shape was applied. The influence of full 3D shape and its effect both on the initial impact, and on the number and magnitude of subsequent impacts, should be explored.
Iceberg characterization

A number of recently acquired iceberg profiles (McGuire et al. 2016) could be incorporated.
Hydrodynamics

Simplified models reflecting the influence of hydrodynamic effects in reducing impact rates and impact velocities are required to reduce conservatisms in design load estimates. Improved modelling of the role of waves on the velocities of the two bodies in proximity, including the possibility of secondary impacts, is required.
Global and local ice strength

The power law probabilistic model for global ice strength outlined in ISO 19906 is conservative for larger contact areas and development of alternative formulations for global ice strength would be beneficial.

A constant 20% reduction in global contact area due to spalling was assumed based on judgment. Further evaluation of spalling during impacts and the relationship to global and local strength would be beneficial.

The probabilistic local pressure model applied has been calibrated against a number of data sources including Terry Fox bergybit impacts and rams with multiyear ice. There are significant differences in local pressures from different trials, with the pressures for the Terry Fox somewhat smaller than for some trials involving multiyear ice. The reasons for the differences should be further investigated.
Structural response

In looking at the influence of local area, it was assumed that the serviceabilitylevel resistance was proportional to A^{−0.7}. The relationship should be determined based on specific hull structures. Also, the specific location of the load relative to the plate and framing, and the movement of the ice contact during an impact, could be important.

Further review of hull deformation from iceberg impacts such as that by Westmar (2001) could be beneficial to better characterize limit states corresponding to EL and AL designs. For example, should ALS designs be limited to a rather small level of permanent set in the plate, or more extensive deformation, but no reduction in safety or hull integrity, nor loss of containment.
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Acknowledgements
The authors would like to acknowledge seminal work related to this topic by Dr. Ian Jordaan.
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Fuglem, M., Stuckey, P., Huang, Y. et al. Iceberg disconnect criteria for floating production systems. Saf. Extreme Environ. 2, 15–36 (2020). https://doi.org/10.1007/s42797019000074
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Keywords
 Icebergs
 FPSO
 Loads
 Disconnect criteria
 Serviceability