The brief
Mr Su brought his BMW in for a service and mentioned a lot of white smoke coming out of the back. Smoke from the exhaust is the engine telling you something is being burnt that shouldn't be, so it gets chased down rather than ignored. Two jobs in one visit, then: the service, and the smoke. The oil separator is part of the crankcase ventilation system. The engine breathes out a mist of oil and gases from the crankcase, and the separator catches the oil and returns it to the sump while letting the gases go back into the intake to be burnt cleanly. When the separator fails, that oil mist goes straight into the intake instead of being caught, so the engine burns oil and you get white or blue smoke out the back. A failed oil separator doesn't recover, so it gets replaced.
The diagnosis
The smoke pointed at oil getting into the intake, and the check narrowed it down: the oil separator had failed, pulling oil mist into the engine to burn, which is the white smoke. The undercarriage inspection that's part of the service also turned up the rear brakes: the rear pads were worn and the rear discs scored, due as a set. The rest of the car was sound. So it was an oil separator replacement plus rear pads and discs, the smoke fixed at the source and the rear brakes brought back to spec.
The work
The failed oil separator was removed and a new genuine BMW-spec separator fitted, the crankcase ventilation hoses checked while it was apart. At the rear, the worn pads and scored discs were removed, the calipers cleaned and the slides freed, and new genuine BMW-spec discs and pads fitted, torqued to the manual figures and bedded in. The service items were done alongside. A road test confirmed no exhaust smoke, smooth running, no warning lights, and the rear brakes pulling up firm and even.
The outcome
No white smoke from the exhaust, smooth running, no warning lights, the rear brakes firm and quiet on fresh pads and discs, and the service done. Mr Su got the car back with the smoke fixed and the rear brakes sorted. A failed oil separator only burns more oil the longer it runs, so replacing it dealt with the smoke for good, and the service inspection caught the rear brakes in the same visit.