I honestly don't think it'll happen, certainly not in 15 years... In 100 years maybe?
I don't think the problem is technology- we already are extremely close to being able to replace the dollar in that matter, due to smartphones[1]. The problem lies with government control of money, and the legal guarantee and security (stability-wise) that it brings. If smartphone technology becomes cheaper, I think we may see countries with unstable dollar value using it more[2].
[1] How does the use of smartphone would make bitcoin replace dollar? Smartphone is owned by almost everyone. Even older people that used to hate technology are loving their iPads nowadays. I don't see any strong relation between bitcoins and smartphones. If anything, it's because smartphones allow you to have a bitcoin wallet. But smartphones have so many uses that one efficient use of it is covered by another depending on the priority of the user.
[2] There are actually really really cheap smartphones on poor countries. Here's a 4 dollar smartphone featured by Unbox Therapy. You can throw it away and not worry about anything. When it goes low battery, you can simply buy a brand new one.
