15 weeks with a low placenta.?

Has anyone been told they had a low placenta early on and then had it move as they got bigger? My OB says that the placenta could move up as I get bigger, I have had an abrasion, meaning part of the placenta has pulled away from the uterus, the baby is fine and the dr. isn't too worred, I'm just wondering if anyone has experience with this. Has anyone had a placenta not move and still have it over your cervix when you were due? What did the dr.'s do?