Assessment of expected production of a deep‐sea mining system: An integrated model‐based systems engineering and discrete event simulation approach

In this paper, model‐based systems engineering (MBSE) and discrete event simulation (DES) are combined to assess the performance of an offshore production system at an early stage. Various systems engineering tools are applied to an industrial case concerning the retrieval of deep‐sea minerals, and a simulation engine is developed to calculate the annual production output. A mean production of 1 Million tonnes of ore per year is estimated for an operation in the Norwegian Sea using Monte Carlo simulation. Depending on the limiting design wave height of the marine operations, the estimated production output ranges from 280,000 tonnes to 1.8 Million tonnes per year. The constrained parameter of the production system is particularly the wave height operational limit of the ship‐to‐ship transfer operation. We present the learning outcome from applying MBSE and DES to this case and discuss important aspects for improved performance.

This article aims to understand and assess the annual expected production of a virtual industrial deep-sea mining system.The approach combines model-based systems engineering (MBSE) and discrete event simulation (DES).MBSE is applied to understand the behavior of the system and its requirements, while DES is conducted to understand how well these requirements are met.To examine the effect of uncertainty, Monte Carlo simulation is performed -a common method to assess the behavior and value of systems. 35][6][7] The chosen location is the Norwegian extended continental shelf, where the Norwegian Government has initiated a regional environmental impact assessment as part of an opening process for potential exploration and mining activities. 8

METHODOLOGY
The economic performance of a deep-sea mining system is linked to its ability to produce continually, which in turn is determined by the capacities of each sub-system, how they relate, and also the negative influence of any downtime. 2The complexity of this topic, along with the limited information, turns the attention to relevant methods for developing models to design offshore production systems and how well they provide insight.Traditional systems design methods, where requirements are decided upon early in the design process, are increasingly regarded as too rigid.According to the editorial of Systems engineering 20th-anniversary special issue 9 : "Systems are no longer just conceived, designed, implemented, and operated in a linear fashion to satisfy stakeholder needs.They are ever-changing, coalescing into systemsof-systems driven by dynamic technological, economic and political forces, and they require us to constantly reassess, upgrade, and evolve them over time".When dealing with complex industrial systems, it is necessary to carefully think through the modeling process. 10Bringing a modeling framework into the engineering process means that the entire engineering problem is considered while keeping an efficient and consistent process from the start. 11dels of technical systems have two distinct purposes: (1) support learning and communication among stakeholders (pragmatic models), and (2) support computer-based simulations and calculate performance indicators (formal models).Both developing pragmatic models and formal models are essential parts of a systems design process. 10e traits of MBSE make it a major advantage when solving systems design problems. 11MBSE supports the development of pragmatic models, while formal models are needed for calculation and simulation.Describing the behavior of a system by means of discrete events is the most suitable mathematical framework due to its appropriate level of abstraction.A discrete event system can be interpreted as a representation of a system which is in a certain state and only changes state when a significant event occurs. 10Change of state is caused by a triggering condition, which may be comprised of one or several circumstances that must take place.If the triggering condition does not take place, the system stays in its current state, and such behaviors might identify weak links or bottlenecks which need further improvement.
For marine systems design applications, DES has been found to be a favorable technique with its low computational cost and flexibility in terms of fidelity level. 12Our two-fold approach starts with the MBSE tool used to support the building of the model, and then the simulation engine used to execute the model.
The model of the Nautilus system has been designed in Sigma language and in the WorldLab Wizard environment.Sigma is an object-oriented modeling language dedicated to system modeling and simulation.It belongs to the S2ML+X family. 10The central idea of languages of this family is that any behavioral modeling language consists of two parts: a mathematical framework in which the behavior of the system under study is described, the X, and a set of constructs to structure the model, S2ML.S2ML stands for Systems Structure Modeling Language. 13It gathers object-oriented and prototype-oriented primitives that make it possible to structure models and to reflect into the model the architecture of systems.Several modeling languages entering the S2ML+X paradigm have been developed, notably S2ML+SBE 14 that aims at providing a unified framework for combinatorial probabilistic safety analyzes, and AltaRica 3.0 which is probably the most widely used modeling language implementing the modelbased approach in reliability engineering. 15At the time we write these lines, the Sigma language and its associated assessment tools are still under development by Systemic Intelligence® as a joint effort between academia and industry.The mathematical framework of Sigma is the notion of activity algebra.The WorldLab Wizard environment embeds a dedicated text editor, a compiler of Sigma model into executable interactive and stochastic simulators as well as some peripherical tools.
It uses also the WIDL (WorldLab Interface Description Language), which is a domain-specific language dedicated to the description of graphical user interfaces.WorldLab Wizard also makes it possible to generate systemic digital twins from Sigma models. 16

Design of model using MBSE
The system architecture framework consists of the following parts 17 : • System sketch: Describes the key features of the system to communicate to stakeholders the general idea of the technical system.• Environment diagram: The environment diagram shows the elements which the technical system interacts with.Some interactions might impact the performance of the system more than others.
• Functional architecture: Description of capacities provided by the system, and functions required to provide these capacities.
• Physical architecture: Description of technical components of the system which are the physical objects that exercise the functions.
• Operation modes: Modes of operation during a system's life cycle are identified to help define what services and functions are needed from external systems in different phases.The triggers that cause the system to switch from one mode to another should also be described.
• Use cases: Scenarios for which the system's functioning is analyzed.

2.2
Executing model using DES The information from the physical architecture, the functional architecture, the operation modes, and rates and capacities are integrated, and simulation is conducted to evaluate how the system meets these requirements.The simulation framework is a step-by-step algorithm describing the processes of the deep-sea mining operation.
During the planning stage of marine operations, the workable weather window is useful to estimate operability.Important earlystage information may be obtained, such as planning of logistics, process optimization, equipment selection, and input to feasibility studies. 18A deep-sea mining operation is affected by downtime due to waiting-on-weather (WoW).Thus, the planning of weather-restricted marine operations means taking weather uncertainty into consideration.The planned duration of a marine operation, T R , can be defined as 19 : T POP represents the scheduled operation period and should be based on a detailed, planned schedule for the marine operation.The weather window must include the estimated contingency time, T C .The weather window, that is, the time period during which it is safe to safely carry out an operation, should be below the maximum or allowable operational criterion, OP WF : The OP LIM represents the design criterion for load effects like vessel motions and accelerations.The alpha factor, , represents the relation between the design criterion and operational criterion, estimated based on the weather uncertainty for the site and the planned length of operation.

System sketch and environment diagram
The system sketch and environment diagram of Nautilus Minerals can be found in Figure 1. 20The system sketch shows the many parts of the system that have to function together in order to produce ore.The environment diagram shows some intersecting factors, for example, waves, benthic fauna of the seabed, and wastewater.The diagram is not exhaustive.

Functional architecture
The functional architecture for Nautilus Minerals is shown in Figure 2.
Ore extraction is the first activity in a steady state production.The type of resource found on the Norwegian extended continental shelf requires cutting, as the resources are lithified (solid rock).With chimney-like formations, it might also be necessary to clear and level out the mine area before bulk production.Finally, it is necessary to collect the stock.The Nautilus Minerals concept had two seafloor-going machines doing the cutting and another machine doing the collecting work.The collecting operation is critical as it requires integration with the submersed pumps.Given sufficient feed from the collector, the ore is lifted as a slurry (water/rock mix).Onboard the mining vessel, the ore is dewatered to get rid of the excess water.These tailings (or wastewater) need to be returned in the water column.Regulations are not yet in place regarding how deep this should take place, but return pipes will be needed.Due to the remoteness of the mineral deposits and offshore sites, ship-to-ship (STS) transfer of ore was chosen by Nautilus Minerals to maximize the operational hours of the mining vessel.

Physical architecture
The physical architecture for Nautilus Minerals is shown in Figure 3.
The seabed production tools are track-mounted cutting tools.The primary purpose of the auxiliary cutter (AC) is to prepare suitable platforms for the bulk cutter (BC) by removing chimneys and sediments as well as cutting benches and stockpile areas. 22The BC serves as the main production unit on the seabed.The auxiliary BC and the main BC deliver fragmented rock to a stockpile simultaneously.The collecting machine (CM) collects from the stockpile and delivers a slurry mix to the subsea slurry lift pump (SSLP).The SSLP, along with the riser and jumper hose, are part of what is referred to as the riser & lift system (RALS).Power and control come from an umbilical cable from the mining vessel.Onboard the mining vessel, the slurry is dewatered, stored, and later transferred to a transportation ship using a conveyor belt.Further, Nautilus Minerals' mining vessel was designed for a maximum storage capacity of 39,000 tonnes.The slurry mix was going to contain 12% solids and 88% seawater.After dewatering, the wastewater is returned close to the seafloor via tubes clamped to the riser (auxiliary pipes). 22The jumper hose is a flexible hose connecting mining vehicles with the riser-based vertical transport system.The launch and recovery system (LARS) was intended to be used to recover seafloor mining tools by using three A-frames mounted on deck.The decomposed physical architecture elements do not match decomposed functional architecture elements one-to-one.The functional and physical architecture mapping is provided in Table 2.

Operation modes
The deep-sea mining operation covers steady state production (useful life period), meaning that mine ramp-up and end-of-life activities, such as levelling chimneys, are not included.The implication of this is that increased failure rates due to undiscovered defects (early phase) and wear-out (late phase) are not accounted for [23].The following operation modes are included: • Mode: {Launching; Operation; Recovery; Maintenance} The duration of the mining operations is determined by each subsystem's mean time between maintenance (MTBM).The recovery and launching are events triggering the maintenance and operation, respectively.If the maintenance or operation cannot start due to weather conditions, they will serve as standby modes -updating the weather forecast every 6 h in this simulation.The standby mode occurs with any sub-system waiting for permission to start its operation.
This could be a sub-system waiting for the previous sub-system to finish its operation, or waiting for the next sub-system to have the required capacity to accept the ore.It may also be linked to waiting for acceptable weather conditions (WoW).
Some systems are assumed to be maintained when they are not operational, and as such, their maintenance does not represent any additional downtime.This includes the conveyor belt and the dewatering system.The conveyor belt is only used sporadically and is usually on standby and operational on demand.The dewatering system is maintained when the plant is not utilized, such as when the CM or RALS are not operating.The RALS is maintained four times a year with a maintenance time of 24 h, where the riser string is raised through the moonpool of mining vessel. 22

Use case
The CM, STS transfer and RALS have previously been identified as particularly sensitive sub-systems regarding yearly ore production. 24 this paper, we describe a use case related to the STS transfer.A challenge for STS transfer is that it must be realized in less time than the mining vessel is being loaded, and preferably significantly less as a practical requirement so that one does not need a vessel always connected.The proximity of vessels during the transfer is challenging, and an acceptable weather window is needed during the transfer.This leads to the use case found in Table 1.
TA B L E 2 Production rates by the various systems.The performance characteristics of systems with an asterisk (*) are not known, but have been estimated based on [22, 25].All outputs, except auxiliary pipes, are stated in the dry ore form.

Functions
The formalized model used for simulations.The systems with boundaries have significant dependencies.

SIMULATION ENGINE
The systems engineering tools were integrated with the output data to form the simulation engine, see Table 2.The variation of the mean production is shown by the standard deviation ().To ensure both randomness in executions and reproducibility in Monte Carlo simulations, the analyst can set up the seed of the random number generator at the beginning of simulations: two simulations starting with the same seed unwind in the exact same way and consequently give identical results.The resulting architecture of the simulator is found in Figure 4.
The surrounding environment is the seabed, waves, and home port for discharging the minerals cargo, while the technical systems are divided into two main elements: mining vessel and bulk vessel.The physical architecture is reorganized accordingly, with the seabed mining tool further decomposed into AC, BC, and CM.
Every action, or event, has a discrete duration triggered by some condition, see Table 3.These events relate to the transportation or consumption of the ore in the production system, see flowchart of material flow in Appendix: Figure A1.The parts of the system that are modeled stochastically are the mining efficiencies, transit times, and the mean time between maintenance.The weather also constitutes a stochastic parameter, but its input to the simulator is deterministic in the form of binary decision variables to start up weather-restricted operations.
The wave modeling is explained in the third subsection of this chapter.

Seabed and home port
The seabed and home port constitute two important interfaces for the technical system: the starting point and end point of the ore stock.The port is assumed to have the capacity to retrieve all ore, any amount at any time.In other words, no limitations in any land-based facilities.
The seabed is assumed to be abundant and available for extraction in a 1-year production cycle.Also, modeling the seabed topography, slope, and other inherent qualities is deemed outside the scope of this paper.
However, these characteristics do affect the production efficiency of the seabed mining tools, and the modeling of this efficiency is explained next.

Deep-sea mining system
The maximum performance production rates of the seabed mining tools are set to 470 tonnes per hour.The productivity of the AC and BC are stated to vary between 30% and 100%, including planned maintenance schemes and bad weather. 22As no further information is given, we have assumed that the uncertainty in the extraction efficiency for the AC is uniformly distributed between 40% and 60%, and for the BC is uniformly distributed between 75% and 100%.Further, the tonnage of cut ore, T cut , is calculated as: where  cut is the individual extraction efficiency of the two individual BCs, r cut is the extraction rate, and t cut is the extraction duration per event.All other sub-systems follow a pattern of calculating the ore stock from the production rate of that system and its duration per event, constrained by their maximum capacities.

TA B L E 3
A comprised list of events, triggering conditions, and duration of the simulator.Limitations of the storage capacity might be an issue, as seen in the use case in Table 1.Storage limitations also apply to the shuttle bulk vessel, which had a storage capacity of 25,000 tons in the Nautilus Minerals case.Therefore, a buffer is desirable, and a capacity utilization factor is added in the code.The mining vessel has a storage capacity of 80% of the real capacity.The bulk vessels have a storage capacity of 90% of the maximum capacity.Two shuttle bulk vessels will be used. 26ey have a speed uniformly distributed between 12 and 14 kn.

Wave modeling
The system is exposed to weather conditions from the Norwegian Sea.Time series for significant wave height of 3 h interval is found in Figure 5.
The limiting wave height of a marine operation is determined by the motions that can be handled.The significant wave height of the specific mine site is the design criterion in this paper, based on Equation (2): There is no available information about the maximum design wave heights of the Nautilus Minerals' equipment, so these are both estimated from literature and scenario-tested.The capability to perform a task depends on the vessel -it could be H s,d = 2.5 m for one vessel and H s,d = 4.0 m for another. 28The duration of the quarterly retrieval of the RALS, including contingency time of T C = 2 ⋅ T POP , has been set to 68 h. 24 There is limited information about the STS transfer operation of Nautilus Minerals.The total duration of this type of operation depends on the amount of dewatered ore to be discharged, the unloading rate, and the duration of additional activities related to the start-up and finalization of the operation.A side-by-side STS transfer operation may start by preparation of equipment (1 h), approach (1-2 h), mooring (1 h), and connecting (1-2 h).In an example of liquid cargo transfer, the transfer operation itself may take 10-12 h.The disconnecting, unmooring, and departure take about 2 h.From this example, it is seen that one can expect about 6-10 h of related activities apart from the transfer itself, which must be accounted for literature 30 .Previous work on preliminary ship design of a mining vessel has identified an unloading rate of 5000 t/h to 8000 t/h for a system producing around 3 Million tonnes per year.This gives a duration of 12-18 h total. 31The amount The launch and recovery time of mining tools is calculated assuming a descent and lift speed of v = 0.5 m/s. 25 For a water depth of 2400 m, 32 the duration becomes 1.33 h.Additional activities are set to take 3 h, we set T POP,SMT = 4.5 h.With a 50% contingency time, we get T R,SMT = 6.8 h.The available wave height data set has intervals of 3 h, so we check for a 3 × 3 h = 9 h window for the launch and recovery of mining vehicles, respectively.
The information about hindcast wave heights, design wave heights, and duration pave the ground for the wave modeling, which is done as follows: The weather window is calculated based on the design wave height for the marine operations with a predefined duration.This is checked towards the wave data set, and a new data set with decision information is made based on the criteria in Equation (4).A binary value tells whether the operation may start or not.Whenever the marine operation is triggered, the simulator calls this data set at the corresponding time of year, and the event may begin if the element has a value 1.A separate data set is made for each design wave for each weather-sensitive event, with the events being the mining tool maintenance, STS transfer, and RALS maintenance.In total, this becomes eight data sets.Examples of the data sets are found in Figure 6 and Figure 7.
A binary value (yes/no) informs whether an operation has permission to start, given the significant wave height (Hs) at the site, the design criteria of the technology, and the duration of the marine operation.If there is a request for start-up of an operation, it will proceed if the value at the specific time of the request is 1.Should, for instance, the launch of the BC take place at 1752 h (= 73 days) into the year, it will not be allowed to start up this operation as there is no available weather windows at that time.Similarly, if the quarterly retrieval of the riser and lift system takes place at 5256 h (= 219 days) into the year, it will have permission to start this operation.It is assumed that the vessels will not operate in extreme weather conditions.This represents a source of downtime which must be accounted for.The simulator checks every 6 h whether the next 48 h fulfil H s ≤ 6 m.If this condition is not A 69 h weather window with H s,OP = 3.8 m for 2021.Generated using Copernicus Climate Data. 27.
fulfilled, the mining vessel will not operate, and in practice, it will have at least 42 h for emergency relocation.Similarly, the bulk vessel will not leave port when this condition is not fulfilled.

SIMULATION RESULTS
The simulations are conducted for one year at a time (8760 h), and we run N = 10, 000 Monte Carlo simulations for each scenario.The annual mean production of the deep-sea mining system given various likely design wave heights is shown in Table 4.The data on the base case is found in Table 2, and in addition we have: H s,d,SMT = 2.5 m, H s,d,STS = 2.5 m, H s,d,RALS = 4.5 m, and MTBM = 240 h for all seabed miners.In this base case, the mean production of the mining system of Nautilus Minerals is just over 1 Million tonnes per year.If there were no weather restrictions on marine operations, the highest theoretical production would be just under 2.5 Mt per year.This shows that deep-sea mining production is, in fact, significantly constrained by waves in the Norwegian Sea.
Case 1 studies the effect of reducing allowable design wave heights.
A reduction in design wave height to 3.5 m for maintenance of the RALS in case 1a did not affect the annual production.When studying cases 1b∕c∕d, it is seen that various combinations of design wave heights of H s,d = 1.5 m (H s,OP = 1.1 m) reduce the mean annual production by up to 74%.This is not surprising since, looking back at Figure 6, there are hardly any weather windows in Q1 of that year.This means that the seabed mining tools cannot be launched or recovered, and STS transfer is delayed for more than 100 days into the year.Similarly, the last day of any 9-h weather window is mid-August, which would only be acceptable if aiming for seasonal production.The variable that points out is the H s,d,STS = 1.5 m, which seems to worsen the production significantly.Cases 2a∕d examine the effect of increased maximum allowable design wave heights of seabed mining tool maintenance and STS transfer.Case 2b shows no effect in increasing the design wave height of mining tools maintenance compared to the base case.However, increasing the design wave height of the STS transfer shows immediate effects in the other cases: Adjustments may increase production by up to 60%.
In cases 3a∕b, we wish to study the effect of low/high combinations of design wave heights closer.In case 3a, the production does not suffer as much even though the design wave height of seabed mining tool maintenance is H s,d,SMT = 1.5 m.This might be explained by the fact that the launch and recovery of seabed mining tools require a relatively short weather window, which allows for a higher number of possible weather windows throughout the year.Case 3b confirms the previous tendencies that the design wave height of the STS transfer is a critical parameter.

DISCUSSION
This paper has presented the modeling and simulation of an offshore system in an early-stage industry.Scenario-testing of allowable design criteria showed how the application context of technologies affects the producibility.Changes in design criteria of one technology can largely affect the entire sequence of operations, and -ultimately -the annual production and profitability.
The allowable wave limit for STS transfer clearly stands out as a critical parameter for the annual production.When the wave limit is low, the bulk vessels have to spend much time waiting for acceptable weather conditions.The use case in Table 1 was found to be relevant in the DES.When the mining vessel storage fills up, and a shuttle bulk vessel is at the site waiting, the STS transfer operation might be postponed.
A backwards cascading effect is that the RALS and CM cannot produce.
On the seabed, the auxiliary BC and BC might still be cutting, but then there is a risk of ore stock piling up.Another effect that was seen is that once the STS transfer operation started, the bulk vessel could not always collect all material onboard the mining vessel due to lower storage capacity.This indicates that the bulk vessels were under-specified.
Since transportation vessels are the cheaper asset, they should have a higher ore storage capacity than the mining vessel to allow a complete emptying of the mining vessel once STS transfer operation is initiated.
The success of STS transfer is not just a question of allowable wave limits but also the operation and vessel arrangements.Nautilus Minerals opted for using a conveyor belt for this purpose.However, it is uncertain whether this is the ideal technology in the Norwegian Sea due to the waves and the risk of losing the valuable cargo during the transfer.Another suggestion that has been put forward is the tandem offloading using a floating hose -favorable due to its similarities with existing practices in the offshore oil and gas industry. 33The pros and cons of side-by-side versus tandem transfer were studied in a liquid cargo transfer setting.There is a good proven track record of side-by-side transfer, but tandem offloading can be used in harsher weather conditions because of the larger distance between vessels and easier disconnection and departure in case of emergency. 30In a deepsea mining setting, the floating hose technology option would require pumping of the slurry mixture from the mining vessel to the bulk vessel.
Again, this requires a dewatering unit onboard the shuttle bulk vessel (or dewatering interface connecting with the bulk vessel) and a watering unit onboard the mining vessel since slurry storage is unlikely.Then water has to be taken from the riser or dewatering plant, and free water must be supplied to the auxiliary pipe.A downside from a commercial standpoint is that an onboard dewatering system requirement means that shuttle bulk vessels would need to be converted, and making them more specialized.This would decrease the vessels' second-hand value in the market.
Another technology choice that can be discussed is the seabed mining tools.A concern in the development of this industry is how to keep the ecologic connectivity intact when humans intervene with industrial systems.It is questionable whether three seabed-going bulldozers is the most gentle approach for the seabed.Others have proposed one miner to cover the three excavation functionalities from Figure 2. 33,34 A wide search for technology options is still needed to ensure that good solutions are found.The use of known or mature technology in a new setting has lead to incidents in the past.Generally, it is necessary to carry out a technology qualification process when introducing new technologies in the offshore oil and gas industry. 35Even if known technologies from the offshore oil and gas industry are used, deep-sea mining is still a new setting requiring technology development efforts.
The real number of available weather windows varies from year to year.The duration of weather windows is a conservative estimate accounting for uncertainties in marine operations.The alpha factor works by reducing the operational limit, while the contingency factor, T C , works as a safety factor by adding buffer time for unexpected events.Another conservative estimate was used: the design wave height of the governing activity during the marine operation, that is, the activity with lowest design wave height, has been used to calculate the weather window.This might result in unnecessary downtime if the activities are non-continuous, that is, can be interrupted.This would not have been done in the actual execution of the marine operation, where forecasts are used and tested towards a sequence of activities requiring different operability limits.
There is limited operational experience with deep-sea mining systems and significant uncertainty in the production output presented.
In addition to the uncertainty in the underlying assumptions presented previously in the paper, there is also uncertainty in the material losses during the different stages of production.How much material that will be lost is not known yet.The excavation process is influenced by particle size distribution.For vertical transportation, there is the extent of damage to particles during transportation, as well as the amount of water involved.During dewatering, the material losses depend on the choice of dewatering system.The free water can be separated easily, but extracting the valuable finer material from this water is more expensive and depends on the economics of the project.Put differently; there is a risk that valuable metals are sent down with the wastewater.
This simulator is intended as a screening tool during the planning of a deep-sea mining operation.If the results from this early-stage screening are satisfactory, further analyses of the operability and response of the vessel would be needed.The allowable limits of sea states need to include not only H s but also the wave period, T p , as it is an essential parameter for floating vessels. 18Other central environmental parameters are wave direction, wind speed, and wind direction.

CONCLUSION
We have shown in this paper that MBSE and DES can be combined to assess the performance of deep-sea mining systems at an early concept design development stage.The benefits of applying MBSE and DES to the case study was that the system could be properly and systematically understood before building a more detailed model for the simulator.By testing various scenarios, we have shown the versatility of the simulator.The expected production of the deep-sea mining system of Nautilus Minerals was assessed given different scenarios, and results show that the design wave height of the STS transfer operation was critical to the overall production.This analysis is based on yearly production, but such an analysis could also be executed for cost scenarios by including CAPEX and OPEX.

F I G U R E 1 21 F I G U R E 2
The system sketch and environment diagram of Nautilus Minerals.The technical system under study is found inside the dashed lines.Functional architecture of the material flow in offshore operations during exploitation.

•
State: {Operation; Standby } • Location: {Port; Transit; Site} TA B L E 1 A use case for ship-to-ship transfer.Description Pre-condition Continuous production; Mining vessel signals need for ship-to-ship transfer Post-condition Collecting machine is forced to stop production Trigger Fully loaded cargo holds on mining vessel Story 1. Cargo holds are filling up at the mining vessel, and it is time for unloading of ore to bulk vessels 2. Bulk vessel arrives at the offshore location, and crew onboard mining vessel prepares for mooring 3. Mooring is delayed due to waiting for acceptable weather conditions 4. Cargo hold onboard the mining vessel has reached the maximum limit 5.The capacity constraint onboard the mining vessel forces the riser & lift system to stop its flow output 6.The collecting machine must stop its flow output to the riser & lift system Since our wave data set has a resolution of 3 h, we test a reference time of T R,RALS = 23 × 3 h = 69 h.The design wave height of this operation is not stated, but similar types of operations have stated a design criterion of H s,d = 3.7 m. 29 In this paper, we test H s,d,RALS = 3.5 m and H s,d,RALS = 4.5 m.F I G U R E 5 Hindcast time series for significant wave height (Hs) in the Norwegian Sea during the year 2021.A 2 m maximum threshold is included for illustration purposes.Generated using Copernicus Climate Data, 27 accessed 2022-08-19.

F I G U R E 6
A 9 h weather window with H s,OP = 1.1 m for 2021.Generated using Copernicus Climate Data, 27 accessed 2022-08-19.to be transferred per operation is constrained by the vessel with lowest capacity, in our case the bulk vessel.We set the unloading rate of 5000 t/h and T POP,STS = 16 h.With a contingency time of 50%, this gives T R,STS = 24 h.
Case 1b shows that the production might suffer less if the design wave height of STS transfer is increased to H s,d,STS = 2.5 m.The results indicate that design wave heights for STS transfer should be H s,d = 2.5 m as a minimum requirement for a continuous all-year operation in the Norwegian Sea.Simulation results for different wave height criteria.A case with no weather restrictions shows the highest theoretical yearly production. is the standard deviation.Abbreviations: RALS, riser and lift system, SMT, seabed mining tools, STS, ship-to-ship.