[cwl1979]

Is there a certain type of tape that should be used for this?

That's tricky to answer, If you can see copper anywhere then no tape should never be used to "repair". If you cant see copper then tape can be used to reenforce the original jacket material. I would recommend a tape like this 

https://www.amazon.com/3M-Professional-S...43-1035250 

The best option for worn power cables is always to replace them though. I know that before i leave Alaska im replacing mine with 6/4SEOOW  at roughly 10 bucks a foot. totally worth it for peace of mind.