I don't think so that in near future such thing can happen. Bitcoin is a virtual currency and many people still  doesn't believe on this. Bitcoin is not a global currency. It is not accept worldwide. In many country it is ban because of its decentralised nature and association with criminal activities. Because of above reason i don't think so it can replace fiat currency. Another reason is its volatility because of this its increase risk in investment market. Cryptocurrency is runs over a complex algorithm because of this many people still doesn't believe on this. Because of this above reason it cannot replace fiat currency.