2001 3.0 Diesel white smoke from exhaust video

[X5Sport]

What's your oil consumption like? Should be no more than 1 litre/1600km. Did the repairer put the right grade in - if it's too thin you may get an issue perhaps?

I know you said you replaced the turbo, but was it with a new one? It's possible the centre bearing has a problem and is leaking oil into the exhaust stream. This is potentially more serious if you get oil into the inlet stream as the engine can run on oil and will rev until it destroys itself. A very rare event but it can happen - especially given oil is just a thicker diesel!!

Everything you describe sounds like oil burning, but I have seen coolant failures laying down a cloud of short lives steam (though not for very long as the engine tends to overheat very quickly). I also would not expect steam to linger long in your climate either. One of either your coolant or oil levels will show which system is the likely culprit.

I suppose it's just possible you may have bad fuel on board - have you used different fuels to eliminate that remote possibility (has someone refuelled your vehicle and put a small amount of petrol in it by accident and kept quiet?). How is your fuel consumption under normal driving?