Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Time Pressure; Troubleshooting; Workload
Aircraft Equipment Problem Critical
Flight Crew Landed in Emergency Condition; Flight Crew Requested ATC Assistance / Clarification; Flight Crew Returned To Departure Airport
Aircraft
During the departure climb the First Officer indicated to me that the right engine oil quantity was decreasing at a moderate rate. After approximately two to three minutes the right oil quantity reached zero. We then received an ECAM Warning for 'ENG 2 OIL LOW PR (in red)'.  We followed SOP and performed the ECAM procedure; which directed us to shut down the right engine.  We [advised ATC]Center and requested a return to our departure airport. I notified Dispatch of our engine shutdown and our diversion. I performed a single engine approach. We landed without further incident. Oil leak in the right engine
A319 pilot reported an oil leak on departure caused them to shut down an engine and return for a landing.