It is supposed to take 48 hours, provided you've cleared all dues. However, most operators make this process extremely difficult. Some excuses you'll get:
1. Prepaid sims are over. As if this really was a thing.
2. Wait till end of bill cycle. When bill cycle ends, you'll be given reason 1.
3. Your number is a 'special' one that can't be converted.
VF is particularly bad about this. I've had friends try to replace damaged sims only to be told, that the sim would be replaced only if they migrated to postpaid.
Anyway, if you face any of the above, porting out is far more hassle free.