BMW Repair Questions? Ask a Mechanic for Answers ASAP
It is quite normal on vehicle to hear various things running after the engine and the ignition have been turned off.
On most vehicles with Electronic Modules it takes approimately 3 minutes for all of these modules to enter thier sleep mode. During this time they are used to check various components after shut down for fault diagnosis purposes and to ensure the vehilce is in a state ready to start again.
On most modern vehicles some of the things you may continue to hear are the following:
I think your vehilce is too early for AdBlue so I suspect what you are hearing is the Leak Detection Pump which is usually located at the rear of the vehicle. This is normally out of sight under one of the Wheel Arch Liners close to the Fuel Tank Filler Pipes.
It could just be that the Leak Detectiion Pump if that is the noise could be worn and requires replacement. It is in effect a motor which contains bearings that the motor runs in.
You would have to gain access to the pump and check it when you turn the vehicle off and see if that is the fault. I believe it is behind the Arch Lining near the Fuel Filler Pipe.