Breather Tube

Hi deepdiver Purpose is to carry crankcase gases passed thru the breather valve assembly out to the air intake so the gases can be reintroduced to the intake via the air filter plate/ or box. If your breather tube is blowing oil, remove and clean the breather assembly bolted to side of engine. Clean the tube of oil also. The breather is somewhat fragile, so do not push on the disc inside it. There should be a very small amount of play in the crankcase breather assembly disc (or valve). Yes, the breather assemblies can go bad with gunk and neglect.

not sure what you mean by breather assembly. this is model 31D777. type 0233E1, 18hp. would you have a part number? thanks

DeepDiver The smaller Briggs OHV engines have this breather assembly. I know you have seen them before bolted to the side of Briggs engines.

http://www.ereplacementparts.com/breather-assembly-p-251335.html

Your engine has a BREATHER TUBE, BREATHER COVER, and REED VALVE . The cover and valve act together as the breather assembly on YOUR engine. The reed valve acts as the disc in the smaller breather assembly does, basically a one-way valve. Lets crankcase gases out, but nothing back in. I have a 17.5HP like yours. I have not had the oil blow-by problem though. Those parts are in DIAGRAM D

http://www.ereplacementparts.com/briggs-and-stratton-31d7770233e1-engine-parts-c-16758_17347_17438_217751.html

The bottom of the breather tube most likely plugs into the back of the air filter housing on your model.
If your carb has leaked some gas into the crankcase of the engine, the resulting excessive pressure could push oil out past the reed valve; through the breather tube into the air filter housing on your engine. Check your oil level for overfill and gas smell.