OpenSpecEngineering

Finds how much gas a compressed-gas cylinder holds, as moles, mass and free-gas volume, and how much of it you can use before the regulator drops out. It then gives the run time at your delivery flow. Labs, welders and purge crews use it to plan cylinder changes.

Equations

n = P·V/(Z·R·T)
m = n·M
V_free = n·R·T₀/P₀
V_use = V_free·(P − P_reg)/P
t = V_use/Q

n is the amount of gas in mol and m its mass. P is the absolute cylinder pressure, the gauge reading plus 1.01325 bar. V is the cylinder’s water volume and T the gas temperature in kelvin. Z is the compressibility factor, R = 8.314 J/(mol·K) and M the molecular weight [2], [3]. V_free is the volume the gas would fill at the reference state T₀ = 15 °C and P₀ = 1 atm. P_reg is the regulator dropout pressure (absolute) and Q the delivery flow at the same reference state. t is the run time.

Inputs

• Cylinder Water Volume is the internal volume stamped on the cylinder, not the free-gas volume on the label.
• Gas fills the molecular weight. Only gases that stay gaseous in the cylinder are listed. Liquefied gases such as CO₂, N₂O, propane, butane and ammonia are filled and measured by weight [1]. Their pressure stays at the vapor pressure until the liquid is gone, so it says nothing about how much is left.
• Compressibility Factor (Z) corrects for real-gas behavior. Use 1 for a rough estimate. Near 200 bar and room temperature, Z for nitrogen, hydrogen and helium is above 1 and for argon, oxygen and methane below 1. Take it from a compressibility chart or table [2].

Limits and common mistakes

• Entering gauge pressure where absolute is wanted, or the reverse. The cylinder field is gauge; the regulator field is absolute.
• The usable fraction assumes the same Z at the dropout pressure as in the full cylinder. Where Z is far from 1, treat the run time as an estimate.
• Flow meters read in different reference states. Convert the flow to 1 atm and 15 °C first.

Worked example

A lab purges a glove box with nitrogen at 15 L/min from a 50 L cylinder that reads 200 bar at 20 °C. How long will one cylinder last?

1. Enter Cylinder Water Volume 50 L, Cylinder Gauge Pressure 200 bar and Gas Temperature 20 °C.
2. Choose Gas Nitrogen (N₂). The molecular weight fills in 28.013 g/mol.
3. Leave Compressibility Factor (Z) at 1 and Regulator Dropout / Delivery Pressure at 2 bar abs. Enter Delivery Flow Rate 15 L/min.
4. Press Solve. The Solution shows: Absolute cylinder pressure: 201.013 bar
   Moles of gas: 412.354 mol
   Mass of gas: 11.5513 kg
   Free gas volume (15 °C, 1 atm): 9,750.05 L
   Usable volume to regulator dropout: 9,653.04 L
   Run time at delivery flow: 643.536 min
   Run time at delivery flow: 10.7256 hr

Check by hand: the free volume is about 50 × 201.01/1.01325 × 288.15/293.15 = 9,750 L. Then 9,653/15 = 644 min. Real nitrogen at 200 bar has Z a few percent above 1, so it holds a few percent less, and a 10-hour plan is the safe figure.