Pilot reported after takeoff at about 1;500 feet; ECAM VENT SKIN VALVE FAULT occurred. Flight crew returned to departure airport and landed.

Narrative

After takeoff at about 1500 ft.; ECAM VENT SKIN VALVE FAULT occurred. We waited until the after takeoff checklist was complete to look at the problem. We realized it was a pressurization problem; so we asked ATC for a level at 10;000 ft. and vectors away to handle it. The ECAM called for Blower and Extract fans to override; which we did; then it says 'if unsuccessful...' to stay below 10;000 ft. and manually control the outflow valve. After going to override; the cabin altitude seemed to stabilize; be we did not know what a normal climb pressurization schedule looked like anyway. We questioned what successful or unsuccessful was. So; we SATCOM dispatch along with Maintence. After a discussion; we agreed that if the cabin altitude looked stable; then continue; monitoring the cabin altitude in the climb. I did notice the inlet valve was closed; the outlet valve was amber Xs and the outflow valve was completely closed. We continued on our flight plan and got a climb to FL230. Passing FL180; the cabin altitude; which climbs to a delta P of 8.0 psi; stagnated at around 4.5 psi and the cabin altitude started to climb. We realized we were not going to properly pressurize and started working with ATC. By the time we got a level off; then a turn so we could descend and then a descent; the cabin had continued to climb. At 10;000 cabin altitude; the First Officer and I donned 02 masks. The max cabin altitude reached was 10;900 ft. for about 4 minutes. After we descended to 10;000 ft. and got vectors back to ZZZ. Dispatch; Operations and Local Operations were all advised. No [request for priority handling] was made because we got down quickly and Center accommodated us for the return. Back at the Gate; it was found the outlet valve had failed in an open position and was replaced. Two crew members; the F2 and F3; and several customers experienced altitude sickness. They were seen by local fire/ EMT and eventually recovered.