I worked the rigs on shore and off shore for many years, and I can tell you that the ones on shore will not have much there, yes you may find a few coins that the crew drops , but when you work on one you do not have much on you . It is just how it is. And as to anything of value from the rigs , there is not much that you would be able to do anything with.
You might find come copper wire. But the main thing is the place will be so trash heavy with everything you can think of and grinding slag and welding slag and nuts and bolts every where.
I am not just trying to get you not to do a search , it's that I know what is around the rigs and what goes on. And after they complete the well they will grade the place off , now you might be able to find some loose money at the fence rows after they are graded . BUt if you give it a try , good luck.
And a word of warning , if they have a reserve pit out off to the side do not go near it. As it will give way with you and you can not get out. Worse than quicksand .