Stopping time

Luca Pivano and Øyvind Smogeli, Marine Cybernetics, examine the use of dynamic capability analysis by time-domain simulations to develop improved designs and safer operations.

With steady growth in the number of dynamically positioned (DP) vessels, technology advances with more complex designs, along with a decline in number of experienced and trained operators, operational risk management tools have become key elements for supporting incident free and efficient DP operations, according to DP operation guidance.

Figure 1:Example of heading and position acceptance limits.

One of the key aspects, also addressed in the recent MTS Guidelines, is the importance of the vessel’s station keeping capability. Many operations and facilities such as deepwater drilling, diving, subsea construction and maintenance, pipe-laying, shuttle offloading, platform supply and flotels rely heavily on the vessel’s capability to maintain position and heading within defined acceptance criteria. Operational planning should take into account not only prevailing environmental conditions but also the ability to abort the mission in a controlled manner after a failure – including the post-failure transients. For these operations, where the consequences of a loss of position are high regarding cost, safety and impact on environment, it is essential that the vessel operators can rely on credible and realistic estimates of the vessel’s DP capability to determine the weather operational window. This is particularly important when not all the equipment is available after the worst-case single failure (WCSF), as decisions made on wrong assumptions may compromise the safety of the operation with undesired outcomes.

Figure 2: Thruster layout.

The current industrial standards for DP capability analyses are described in IMCA M140 specification and DNV ERN standard, with the objective of enabling a direct comparison of individual vessel’s performance and provide an indication of station keeping capability in a common and understandable format. However, these standards, which are based on static balance of the maximum obtainable thruster force against a resultant mean environmental force while considering the vessel at rest, may be limited in their ability to provide other relevant and desired information. This means that the vessel footprint is not evaluated and therefore it is not possible to consider any operation-specific positioning acceptance criteria. These methods, assuming the vessel pinned to a fixed position, may produce capability results which are representative for calm and moderate weather, where the vessel motion is little, but not for limiting weather condition.

The current standards present also shortcomings with respect to the vessel model requirements. The IMCA M140 specification allows the analysis to be computed with environmental forces from non-vessel-specific coefficients, thruster forces from generic rules-of-thumb and without including specifications on DP control system and thrust allocation. It is possible to extend the analysis with more realistic assumptions and models but such extensions are not standardised. Due to the lack of precise requirements, capability plots computed from different suppliers may differ significantly when computed for the same vessel.

The DNV ERN standard on the other hand presents a prescriptive method, which does not give much space for the use of different thruster and environmental force models. The drawback of this standard is the simplicity of the mathematical models to be used; for example, the thrust loss factor is fixed to 10% of the nominal thrust regardless of thruster position and type. In real life this can vary significantly due to propeller aeration, thruster-thruster and thruster-hull interactions. Also this method considers only environmental directions from the vessel side. These are among the reasons that led DNV GL to establish the project ‘DP Capability Assessment’ which aims to establish a new standard for computing the DP capability.

Figure 3: Wind envelopes after the loss of Switchboard A.

All these considerations led to the development of DynCap, which main purpose is to calculate the station-keeping capability of a vessel based on systematic time-domain simulations. This is obtained by employing a complete 6° of freedom vessel model, including dynamic wind and current loads, 1st and 2nd order wave loads including slowly-varying wave drift, a complete propulsion system including thrust losses, a power system, sensors, and a DP control system with observer, DP controller, and thrust allocation. This will provide better understanding of the vessel performance, because the simulated motion corresponds to the total vessel motion where full interaction between the different degrees of freedom is considered (i.e. surge, sway, heave, roll, pitch and yaw).

The DynCap analysis, compared to a traditional analysis, computes the limiting environment by applying a set of operational specific acceptance criteria. The position and heading excursion limits can be set to allow a wide or narrow footprint, or the acceptance criteria can be based on other vessel performance characteristics such as sea keeping, motion of a crane tip or other critical point, dynamic power load or the stroke of a gangway for personnel transfer. In this way, the acceptance criteria can be tailored to the requirements for each vessel and operation. An example of position and heading acceptance criteria is shown in Figure 1. In this case, the station-keeping capability is attained by searching for the maximum wind speed (and correspondent wave height) in which the vessel footprint stays within the predefined position and heading limits.

The station-keeping capability is usually presented in a form of polar plots termed wind envelopes, where the maximum wind speed at which the vessel can maintain position and heading is plotted for each angle of attack. An example of wind envelopes computed for a diving vessel is presented in Figures 3 and 4, where results from both the traditional analysis based on the IMCA M140 specification (defined as DPCap) and DynCap are provided.

Figure 4: Wind envelopes after the loss of Switchboard B.

The vessel, 80 m long and with a mass around 6000 t, is equipped with three tunnels in the bow and one tunnel in the stern (Figure 2). In addition, there are two main propellers with high lift rudders at the stern. The main propellers are directly driven by prime movers, and therefore not affected by failures in the switchboards. The power plant is composed of two switchboards (A and B). Switchboard A is connected to the far most forward tunnel and the stern tunnel while switchboard B is connected to the remaining bow tunnel thrusters. The vessel’s main particulars are given in Table 1.

The DPCap analysis includes all static thrust losses: Coanda, inline, thruster interaction and transverse losses and 15% dynamic allowance. The dynamic allowance is the reserved amount of thrust assumed to be used to counteract dynamic forces; in this case, the thruster will be used only up to 85% of maximum thrust in the quasi-static force balance. DynCap is performed by considering the acceptance criteria for positioning and heading at 5 m and 5° and with high control gains.

The higher the gain, the faster is the response of the control system upon position and heading deviations. During operations, the DP control gains are normally chosen based on the vessel characteristics, the weather conditions and the required positioning accuracy. High control gains would normally be used for harsh weather and for high positioning accuracy. Low gains are typically employed to reduce wear-and-tear on the propulsion and power system, reduce fuel consumption and with low required position accuracy. Medium gains would be a trade-off between the two. Three gain levels are available in most of the industrial DP systems. However, depending on the DP manufacturer, there may be other levels of DP control gains and DP control settings influencing the vessel position accuracy and responsiveness of the control system upon position and heading deviations.

Figure 5:Loss of switchboard A- time series for headsets.

Figure 3 shows results for the WCSF condition, defined as loss of Switchboard A, for the DPCap (blue) and DynCap (black) analyses. The DynCap wind envelope presents a limiting wind of about 25 m/s for head seas, much smaller compared to DPCap. For head and following seas, the DP capability is mainly limited by two factors: the thruster pitch angle rate limit and the bow tunnel thrust loss due to aeration.1 This was deducted by observing the time domain series from the DynCap analysis. An example is given in Figure 5, which was obtained from simulation for wind direction 10° off the bow.

If the vessel is positioned against the mean environmental forces (head sea), the vessel heading will swing from port to starboard due to wave direction dynamics.

This is a phenomenon that is very familiar to shiphandlers. To control the heading, the bow thruster has to invert often the thrust direction (i.e. reverse the pitch angle). As this cannot be done immediately due to the pitch angle dynamics, a significant delay can occur between the commanded and the actual thrust. The other limitation is the tunnel thrust loss due to aeration caused by large vessel pitch motion. This can cause a sudden drop in the propeller thrust, as shown in Figure 5 around 2380 s where the pitch motion is over 5° and the actual thrust from thruster 2 drops significantly with respect to the nominal thrust.Compared to DPCap, the DynCap wind envelope presents reduced capability also for quartering seas, where the limiting wind speed is about 15 m/s. In this condition, since thruster 4 is disabled, one main propeller with the corresponding rudder produces side force while the other main propeller balances the surge force by thrusting in the negative surge direction (push-pull configuration). In this case the push-pull dynamics are key for achieving good station-keeping, the performance of which is limited by the amount of available sway force due to the use of only the rudder and limited surge force to counteract the environmental loads in the surge direction.

When comparing DynCap results with the traditional DPCap analysis, the wind limits from the quasi-static method appear unrealistic for head and following seas. For beam seas, where the tunnel thrusters push mainly in the same direction all the time and the heading motion is smaller than for head seas, the relative difference between the DPCap and DynCap results is smaller. It is important to notice that the differences between DynCap and DPCap wind envelopes may change significantly when employing different position and heading acceptance limits. For larger acceptance criteria, the wind envelope results typically in larger wind speed limits.

The wind envelope computed from DynCap after the loss of switchboard B is shown in Figure 4. While the results show that the maximum wind speed at head sea (0°) is comparable with the case where switchboard A is lost, from wind directions of around 20° to 140°, loss of switchboard B will have a reduced station-keeping capability. With only one tunnel thruster left at the bow the amount of sideway force that can be used for controlling the heading motion is limited.

Another feature of DynCap, compared to the quasi-static DPCap analysis, is the ability to consider the transient conditions during a failure and recovery after a failure. Even if the capability plots show that the vessel can maintain position and heading both in intact condition and after a single failure, nothing can be gleaned about the motion of the vessel from the time the failure occurs until the desired position and heading has been regained. Especially after a worst-case single failure for a DP2 or DP3 vessel, where as much as half of the thrust capacity may be lost, re-allocation of thrust can take considerable time due to limitations in rise time for propellers as well as rudder and azimuth angle rates. For a safety-critical DP operation such as diving or vessel-to-vessel replenishment or personnel transfer, the allowance for such transient motion can be very limited. With DynCap, by considering the complete vessel dynamics, it is also possible to identify temporary position and/or heading excursions due to dynamic and transient effects.

Table 2 shows the results from a transient study which aims to investigate if the vessel may go temporary out of position during the transient after the worst-case single failure, i.e. loss of switchboard A. Since waves are modelled by a stationary, random process with certain statistical properties (the significant wave height does not change), the time instant when the failure is triggered will have impact on the result of the simulations. For this reason, the analysis is performed by running multiple simulations (32 in this case) where the failure is triggered at random intervals.

The results presented in Table 3 consider three wind speeds, which are inside the post-failure DynCap wind envelope computed with high control gains:

For a wind speed of 25.2 m/s at 10°, after the failure, the vessel went temporarily out of the position acceptance limits 63% of the time. Even with a smaller wind speed (23.7 m/s at 10°) the probability of an excursion outside the position limits was quite high (44%). Considering environmental forces attacking from 90° off the bow, with wind speed of 13.6 m/s, which is well inside the post-failure dynamic capability, the failure caused the vessel to go temporarily out of the position acceptance limits 38% of the time. The magnitude of the wind speeds (23.7 m/s at 10° direction and 13.6 m/s for beam seas) were suggested by an experienced operator of such a vessel as the maximum probable wind speed at which he would operate.

The results obtained from the DynCap analysis demonstrated that there are various operational aspects to be considered when choosing a vessel and planning for an operation. Concerning the operational risk, the post-failure dynamic capability appears to be the most important vessel performance characteristics to consider. For the vessel analysed in this paper, the worst-case single failure, as reported from the Failure Mode and Effect Analysis (FMEA), is the loss of switchboard A. However, for most of the weather directions, the loss of switchboard B resulted in worse vessel station-keeping capability. This shows that not only the worst-case single failure should be analysed but also different power and thruster configurations.

The analysis should be performed by employing operational specific acceptance criteria for positioning, as the wind envelopes can differ quite significantly when employing tight or relaxed acceptance criteria. This is one the advantages of running time-domain analysis contra the quasi-static approach, where the acceptance criteria is not accounted for. Operation location-specific weather statistics and data should be employed in order to obtain relevant results for the actual operation.

Another important aspect to consider is the vessel motion transient after a failure. The results presented above showed that, even with environmental conditions well inside the DynCap (and DPCap) post-failure capability, there is a significant risk that the vessel may experience temporary excursion outside the positioning acceptance criteria when the worst-case single failure is triggered. Looking only at the wind envelopes would not have identified this. These results have to be considered in relationship to the operational specific positioning accuracy. For some operations, temporary vessel excursions over the limits may not be a problem, but for others – such as diving - this may not be acceptable.

Last, but not least, the results from the DynCap analysis demonstrated the limitation of the single stern thruster configuration for the industrial mission being contemplated. This was revealed by the transient analysis. The information gleaned from the analysis can then be used to aid decision-making and a better understanding of operational risk and its management.

Reference

_1. Propeller aeration (or ventilation) is due to the propeller being closed to (or piercing) the water surface and is the result of air or exhaust gases being pulled into the propeller blades.

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