Oil rigs are really only for drilling, not for getting the oil out of the ground and into whatever container there is. So that means they move around all the time. Like every couple of weeks.
What you're thinking of is called a jack up rig. They go in water up to a few hundred feet deep. Nothing over 1000 feet for sure. That's because the entire truss has to come out of the water when the barge is being moved from one location to the other.
