Audi Repair: Something is running after car is shut off, audi a4, turbo quattro

Question
Greg, I like to believe that I have some car knowledge but I am new to my 2001 Audi A4, 1.8 turbo, quattro. When I turn the car off I can hear something running in the engine comp on the passenger side of the car. It runs throughout the night and my battery is dead in the morning. After a boost it charges back up and good to go. Any ideas, thank you in advance

Answer
hello
The is only one thing on the pass/side, secondary air system pump, which is a electric motor. This system is used on cold starts, electric motor pump the air into exhaust to warm up the CAT. Pump is control by the relay . Relay is locate next to ECM  . ECM is in the box right next to wiper motor. We have seen this before,  relay gets stuck ON and makes the pump run untill the battery is dead.
So , I will start with the relay .
good luck              Greg