In cable lay analysis the response of offshore power cables to a vessel exposed to waves and currents is investigated. We’ve already touched upon this subject in a previous blog, stating that cables are delicate and easily damaged. Especially the motions of the vessel have a strong influence on what tensions (positive or negative) and bending a cable will experience. We will use some terms that are visualized in the figure below. The cable leaves the chute with a certain departure angle to end up on the sea bed with a layback distance from the vessel. We identify the following relevant cable limits: maximum compression, maximum tension and minimum bending radius (MBR). The cable should not be installed exceeding this limits.
So what does MO4 have to do with all this? We can relate the motions of the vessel in a very straight-forward way to what happens in the cable. We’ve observed in many cable lay projects executed by Mocean Offshore that the cable response shows a strong correlation to the vertical chute motions. To show this, we’ve conducted a study, where we perform forced oscillations of the chute for various periods and amplitudes. The analysis is performed in OrcaFlex (as the purists have already noticed from the figure above). We’ve post-processed the minimum bending radius for all these cases and plotted it to the chute vertical motions. From the results we can conclude that the best correlation for the minimum bend radius is the velocity of the chute, this because there is the least spreading in the allowable minimum bend radius. Similar results are obtained for the maximum tension and compression.
Vertical chute displacement (left), velocity (middle) and acceleration (right) versus cable bend radius:
Of course, reality is always more complex, with wave kinematics and additional relevant vessel motions (surge, pitch, etc.). However, the influence of these effects is limited and the correlation holds well.
In conventional cable lay analysis the cable response is investigated for various laybacks, water depths, current velocities and directions, wave heights, periods and directions. It is common to have more than one cable type. The results from these batches are then post-process into a range of Hs-allowable tables.
There are a few issues with this approach, for which we need to dive into statistics. First, it is uncommon to perform a so-called seed study. A seed is a realization of an irregular wave spectrum. If you perform an operation in the same sea state a hundred times, you will see different maximum events each time. In a seed study this is investigated and a statistical maximum value is identified. In order to ensure the cable stays in one piece, this maximum value should be multiplied with a safety factor. The resulting value should always be lower than the allowable limit obtained from the cable manufacturer. We have often seen that the maximum value from one simulation is used. In essence this is just a random draw from an extreme value distribution that remains unknown. I’ve visualized this with three example extreme value distributions, shown in the figure below. These three distribution vary greatly. But we could end up with the same value if we only perform a single simulation. Especially the situation with the third distribution would be problematic. We’ve greatly underestimated the response. The message here is that it is important to understand the underlying statistics.
Secondly, often the maximum wave height is searched for in one seed and around that moment a simulation is performed. However, it is not the moment where wave height is maximal that leads to the extreme cable response. It is the moment where the chute motions are maximum that leads to governing responses. Lastly, the Hs-allowable tables obtained often show huge steps with 1s peak period or 30degree heading changes. A workability table from a old cable lay study is shown below, where we can see those large steps, for instance at a peak period of 7s a difference of 1.5m is seen between relative wave headings 30 and 60 degrees.
We believe that with MO4 it is possible to get a better grip on cable integrity during installation. We have performed a small seed study for one sea state and heading, where we run 100 seeds. On the left side the histograms of the extreme chute velocity (a Rayleigh distribution) and the extreme bend radius. The latter probability density function is unknown and not studied. It can be seen that it is very wide. In the same sea state we can expect bend radii from 2 to 7m. If no seed study is performed, one single case will provide barely any information. On the right side we see the bend radii plotted to the chute velocity. A very good correlation is found. If for the sake of argument allowable bend radius was 3m, then a chute velocity limit of -1.4m/s would be selected. In the conventional method this case could be allowed or not, dependent on an arbitrary seed choice.
We believe that working with motion limits has the potential to improve cable lay operations. It provides clarity as measurements can be used to trace back cable response, it takes away a lot of assumptions related to the wave spectra, loading conditions, and other unknowns during engineering. it also simplifies a large number of tables into a couple of heave limits, making it easier to work with.