Dear Deep Diving Frog,
I was reading a paper on your web site “Silicone Injection: Better with Pressure” that was discussing fluid pressures that different cable insulations could withstand. The testing was done at Florida Power and Light and showed that XLPE cable could withstand up to 750 PSI before bulging and approximately 650 PSI before a point of inflection was reached where deflection accelerates with further pressure increases. The pressure was increased 50 PSI every 15 minutes. Have any sustained pressure tests been performed on XLPE cables under the pressures that will be used for submarine cables, since the pressure will be sustained for months? Also, I assume that shore ends will be a bigger concern for pressure impacts than deep water sections where the weight of the water will be pushing back on the cable?
Concerned about Creep
Editors note: I had to fight my froggy urge to respond "Dear Creep."
Nearby, I have reproduced Figure 5 from the “Better with Pressure” paper, to which you refer, except I embellished it with my lovely image. I would encourage my other readers to immerse themselves in the entirety of that paper. First, I must make an important correction to your question. The insulation of the cable in Figure 5 was uncrosslinked HMWPE or high molecular weight polyethylene. Cross-linked polyethylene or XLPE has significantly better mechanical properties. In fact, similar sized XLPE cables were injected “on-the-reel” by Hendrix Wire & Cable in the late 1980’s at pressure of 750 to 1000 psig. See Table 1, the accompanying text on page 2, and references  and  of the “Better with Pressure” paper.
The inflection point at 650 psig is labeled as such in the figure. Up to 650 psig the difference in the inside pressure and outside pressure increased the diameter less than about 1.5% – this is less than the diametrical deflection caused by a temperature cycle to the cable’s design temperature. However, once this inflection point is reached, polymer bonds are actually broken and the diameter change is not entirely reversible. That is, the diameter does not return to its original value when the pressure is removed. Of course, this frog would never get close to the inflection point … we stay below this point by a factor of at least three!
We have not done laboratory experiments with multi-month injection periods, but we have something even better – multi-month operational experience. At a meeting of the Insulated Conductors Committee (ICC) on May 19, 2009, my colleague, Glen Bertini, made a presentation titled “Lessons in Submarine Cable Rejuvenation” in the C11 discussion group. Slide 14 of that presentation describes an injection of a 14,432 foot, 1/0 compact, 25kV XLPE cable crossing Desolation Sound in beautiful British Columbia. Desolation Sound is about 1,500 feet deep at that location. The fluid took about 100 days, or over three months, just to reach the other end. The injection pressure was about 300 pisg. Several years later the cable remains in operation.
Polymer creep is the slow plastic flow suffered by polymers when a force is applied to them over a long time period. Cross-linked polymers do not suffer the same level of creep as their uncrosslinked cousins unless the polymer bonds are actually broken by exceeding the yield strength of the material. The concern you express should definitely be considered for HMWPE insulated cables.
To the extent that there is any creep at all, you are correct the greatest pressure differential (ΔP) is at the feed end of the cable. At the other shore end or outlet end, the ΔP is zero. If the cable had no elevation changes, the ΔP would decline in a straight line from the feed pressure on the feed end, to zero at the outlet end. Of course, as you recognize, there are elevation changes inherent in all submarine cable installations. The water on the outside of the cable does reduce the ΔP in the submerged portion of the cable, but not exactly as you imagined. You see gravity pulls upon the fluid too, so the absolute pressure inside the cable goes up as cable plunges into the abyss. Water, in general, and seawater in particular, are denser than the injection fluid so the external pressure increases faster with depth than the internal pressure. If there were going to be an issue it would occur on the shore, right at the feed point. The photograph nearby is the termination at Desolation Sound … still providing reliable service today.
Willing to dive deep, but never creepy,