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