I have a 2001 Volvo s80 twin turbo and just a few days ago the coolant tank stopped retaining any fluid whatsoever. It drains so fast that I can't fill it up. What should I look for?

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No. As with any vehicle, maintain clean transmission fluid, and the car will serve you well. However, the 2002 S80 does have a high frequency of instrument cluster failure.

Sounds like a bad throttle body.

If the recovery tank and the radiator are full, it could be a faulty sensor.

is this a t6? if so yes. turbocharged engines have more horsepower than naturally asprirated engines, a turbo charger works like a supercharger by forcing more air into the intake, while a super charger is usually belt driven a turbocharger is exhaust driven, it will be located in the exhaust pipe or exhaust manifold and is turned by exhaust gases passing thu with the opposite side connected to the air intake pipeing, some have the intake air piped thru a intercooler which is mounted in front of the radiator(cooler air is more horsepower)
type 2002 s80 volvo in your search bar and you can find a ton of info

Your problem is something like either a hose clip loose /biting into a hose and split it/a metal hose rusted and has a pin hole or a welsh plug (core plug) leaking. or a water plate gasket IE W/Pump/Manifold etc
Because it drips of the centre of engine dosenot mean it coming from the bottom of engine...

The fuel pump which is located in the fuel tank beneath the back seat has gotten bad. Consider replacing it.

Cheers and rate this solution.

go to any good parts store for cars and buy a can of BARS LEAK brand radiator sealant/stop leak, if the leak isn't to bad that will seal it up.
I show that the radiator for your car is around $295.00 new, source rockauto.com
PROLIANCE Part # 432545
A/T * Non-stock item--shipping delayed up to 2 business days $295.89 $0.00 $295.89

First, Is there actually coolant in the over flow tank?

If the bottle is full the coolant level sensor may be bad. The sensor pulls out the bottom of the overflow reservior.

If the bottle gets low overnight there is a leak. Check the radiator side tanks for leaks. You need to look from underneath the car at the joint where the radiator meets the black tanks on the left and right sides.

You also need to look from underneath for most of the other hoses on the car, the car is turbo most likely and there are hoses that go to and from the turbos, into the cabin, and to and from the engine.
Leaks are hard to find from just looking from the top of the engine.

Hope this helps.

You want to go to the dealership or a mechanic WITH THE VOLVO VIDA and DICE tools to properly read the car. It will generally tell you everything you need to know about what's wrong.

If I had to guess at your problem, I would think it's the electronic throttle module that is bad.