Residencia no longer exists and hasn't done for some years.

You need to visit the town hall and register on the 'padron' - this is the 'Enpadronamiento' which registers you as living here and not in another country. It registers you for voting rights etc.

Next you need to obtain a certificate 'Certificado de registro de ciudadano de la union' which you can obtain in Tortosa, the office is near the river in the 'El Temple' área of Tortosa, near the Millenium bridge (the 'new' bridge). It's a long time since I went there but other members can probably advise as it has a reputation for queues.

As always, wherever you go take EVERYTHING, Escritura, Nota Simple (documnets for your house) or rental contract, NIE, Passport, birth certificate, bank book and any other document you can think of as the one thing you don't have is the one thing you'll need to produce.

Good luck!