How fast will the pressure decrease from a leaking gas tank?

[chrisse]

Hi!

At my plant we have a tank filled with hydrogen gas used for cooling a generator. The tank volume is 360 m^3. We have a constant leakage of 1 m^3/h. The system pressure is about 0,4 MPa. We also have a constant inflow to the system and the ventilation in the room is good so the leakage is normally not a problem. There is a risk however that we might loose the inflow of hydrogen and my question then is at what rate we will loose pressure? For instance how long will it take until we have reached 0,35 MPa?

I'm not sure how to perform this calculation and would really appreciate some help! I guess the ideal gas law would be a good start.

Thanks in advance!
/Christopher

 

[bm0p700f]

PV = nRT is the equation that is relevant hear.

At 293K and 0.4 Mpa you have 59113 moles of gas.
At 293K and 0.35 Mpa you have 51724 moles of gas.

The problem here is the pressure inside the cyclinder is changing. So I will make an approximation that the average pressure is 0.375 MPa so this mean 1 m^3 of gas at this presure contains 153 moles of gas.

Therefore (59113 -51724)/153 \approx 50 hours