Most Brazilian Jiujitsu schools do have children's ranks which automatically get turned into adult ranks when they turn 16. So a children's orange belt will become an adult's blue belt automatically at age 16. A children's green belt will automatically become an adult's purple belt at age 16. This is usually how it's done, but a teacher might decide to award higher or, very rarely, lower adult rank depending on the student's ability, experience, and attitude.
With over 11 years of experience, your son should probably get ranked at least purple belt, maybe higher. I would think so, anyway.
The thing you might want to keep in mind about Brazilian Jiujitsu is that there's fairly good agreement between different schools about what a blue belt should be able to do, what a purple belt should be able to do, and so on. And yet, it's completely normal to find blue belts that are able to win against purple belts, and purple belts that can often win against brown belts and some black belts even. That's normal.
Each school's instructor has a set of criteria they use to judge whether someone should be advanced in rank. A blue belt may be able to tap some brown belts, for example, but maybe that's only because they've become really good at a particular technique they rely on a lot while not developing the other techniques they need to develop in order to get promoted to the next rank. The teacher in that case, might be holding the blue belt back until he can get better at the techniques he's supposed to know before being promoted.
It's not all about winning, in other words.
So if you ever wonder if/why your son is being "held back" in rank, go ask the teacher what your son has to learn in order to be at the rank you think he deserves. Ask respectfully. Don't accuse. Most teachers will not hesitate to tell you what your son still has to do. Your son should know it as well, so he knows what to work on.