Please Note that in Portugal, LPG is GPL; Propane is Propano; Butane is Butano.
We currently know of no way of getting non-Portuguese Butane bottles re-filled in the Algarve at this time.
Camping Gaz is widely available as an alternative, both here and throughout the Mediterranean, and this is probably the simplest option. Camping Gaz is sold at Sopromar, Sanipina (a garden center situated to the right of the market, just over the marina bridge), larger supermarkets, many hardware stores and I Nova, although prices will vary.
You should be aware that carrying any LPG (GPL) cylinders in an ordinary car is illegal in Portugal, and no taxi will take them as luggage. If you are stopped by the police and your car is searched, you are liable to an on-the-spot fine of c. €120 – and perhaps more serious penalties. While we have never heard of anyone being stopped with an LPG (GPL) cylinder in a car - you should be aware of the risk.
If staying in Portugal for some time, one option would be to change over to a local supplier of Propane, buy the suitable fittings and rent a cylinder. As well as Galp, BP and Repsol are widely available here, and it may help that Repsol is also available in Spain.