Seems too tight in any case. Assuming you're on time at say 13:40, you need to go up to the main hall, purchase a ticket (in the ATMs! the booths are far slower), and then find the right track to the airport (there are 16+ tracks). There's a train every 30', say you have to wait 15' (50%) of those minutes for the next train, then the ride to the airport is around 30' more.... it's reasonable to say you'd be at the door of the terminal at 2:30ish... but that's to me a very (very!) optimistic assumption... everything would have to be very smooth.
Then you need to find your checking desk, line up to check in... and checking in closes 40' before departure (more for some international flights)..., then go thru the custom and immigration area... and finally you have to walk to your finger gate (if in Terminal 1 pray your gate is not a high number or else you'll be walking forever to find it!).
In short, I find it a "thrilling" challenge :))
Taxi from Sants to the airport can buy you say 15' (plus those 15' that I estimated as average wait for the airport train), but it's not that much either... still "frenzy heart-pumping", lol!