"Blowdown" of an air-filled pressure vessel, assuming compressible, supersonic- or subsonic-flow, or incompressible subsonic flow, are elementary problems. I've even modelled the free-molecular flow regime for this type of problem, and found excellent agreement to test results (pump-down of a vacuum vessel).
This type of problem is typically dealt with in the examples in most fluid mechanics flow texts. The basic assumption is that the outlet flow area is much smaller than the tank cross section. Calculate the flow rate through the outlet area as a function of upstream pressures, construct differential equation of tank conditions (P, T) use known starting volume/pressure/temp. of vessel to provide an initial condition. Integrate, numerically or classically, to find time when tank pressure drops to ambient.