# How to calculate gas volume released from vessel at drop of press

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#### Mani15

Hello Technocrats !!!

I have puzzled with some calculation of volume calculation of oxygen and nitrogen gas . In our unit we have three vessels each capacity is 50kL of water, designed press is 36kg. For oxygen storage the two vessels are connected with common header and for nitrogen the single line is connected to the pressure reducing system.
We want to calculate the gas volume released form the vessel. Initially I calculated with with PV=nRT and from another formula but both are not matching.

For example suppose at one instance the total press was 26.5kg/cm2 and after some time it press dropped to 25.5 kg/cm2 then how much volume of gas release. The calculation is as follows-

 Oxygen Gas Change in Mole (P1-P2)*(V/RT) T Temp in Deg C 40 Deg C T Temp in K 313 Kelvin P1 Press in Kg/Cm2 26.5 kg/cm2 P1 Press in Kpa 2598.76225 kpa P1 Press in N/m2 2598762.25 N/m2 P2 Press in Kg/Cm2 25.5 kg/cm2 P2 Press in Kpa 2500.69575 kpa P2 Press in N/m2 2500695.75 N/m2 P1-P2 Press Drop 98066.5 N/m2 R Univeral Gas constant 8.314 Nm/K Mol For Oxygen Gas 0.2598 kJ/kg K Molar Mass of Oxygen 31.99 g/Mol For Nitrogen Gas 0.2968 kJ/kg K Molar Mass of Nitrogen 28.02 g/Mol V Vessel Volume 100 m3 RT 2602.282 Nm/Mol V/RT 0.038427811 Mol -m2/N Diff In Mol (P1-P2)*V/RT 3768.480895 Mol 1 Mol 22.4 Liter Change in Volume (Liter ) Mol X liter 84413.97204 Liter 1 cubic Meter 1000 Liter Change in Volume (M3) 84.41397204 M3

Another calculation-
 Since the volume capacity of the vessel is 50kL at 36 kg/cm2 Then gas volume when press was 26.5 kg/cm2 press = 50 x1000x26.5/1000 V1= 1325​ m3 Then gas volume when press was 25.5 kg/cm2 press = 50x1000x25.5/1000 V2= 1275​ m3 Gas Volume released =V1-V2 50 m3 Since both vessels are joint with common header hence the total volume releases = 2x (V1-V2) =100 m3

I want to know which calculation is correct

#### PhilCorso

Mani15...

Your approach seems rather hectic, so, let's start with basics:

Step 1) Before you consider any change of condition(s), what are the total moles of each gas at the temperature and pressure conditions you cited?

Step 2) Will be given once you have presented the answer to Step 1 !

Regards, Phil Corso

#### PhilCorso

Mani15....
Your "Ideal Gas Law" Formula is incorrectly applied !
For a simpler approach I suggest you search this Forum's Archives for Gi.Fi.E.S. pronounced "Jiffys".

Thread Starter

#### Mani15

Mani15...

Your approach seems rather hectic, so, let's start with basics:

Step 1) Before you consider any change of condition(s), what are the total moles of each gas at the temperature and pressure conditions you cited?

Step 2) Will be given once you have presented the answer to Step 1 !

Regards, Phil Corso
Ok Sir
Can you please correct me .

I want to calculate the gas volume released from the vessel with help of press drop.

My volume capacity of the tank is 50kL of water and the max allowed press is 36kg/cm2 . Normally we fill the gas (N2) up to 32 kg/cm2 . Now we utilized the gas for our process after some time the press dropped to 28Kg/cm2 after 1hr 36 min. them how much valve of nitrogen gas we utilised.
The vessel is under open air environment and the ambient temp is max 40 degree in side gas temp is 35 degree.
No filling is going on during the utilization of the gas.

Thanks in advance

#### PhilCorso

Mani...
If you prefer we can work it out off-forum and provide conclusion to the forum later.
Contact me at [email protected]

#### PhilCorso

Mani15...
For your 1st calculation... the "Ideal Gas Law" calculation:
a) You used the wrong units for "P" and "V".
b) The two O2 tanks should be treated as one tank.
c) "N" should be "n",
d) The equation should have been PV = nRT.
e) "N" is used in the equation PV = NkT.
f) Time of pressure decrease had nothing to do with problem, just added confusion.
g) Finally, you paid no attention to "rounding-up" the final answers.
Had you done the simple equation I asked you to do, your error would have become clear !

Phil Corso

• Mani15
Thread Starter