the pure gases compressibility
It is interesting to know that some equations have existed for several decades; for example , a few years ago, I was looking for calculations of Helium at high pressures.
I found that a U.S. Department of the Interior, having the need to correctly calculate the amount of Helium stored after extraction, had commissioned a study to obtain a formula taking into account the compressibility of Helium and even the deformation of the storage cylinder due to thermal expansion and the stretching of steel due to the internal pressure .
Helium was shipped and stored as compressed gas, but the equivalent volume at base conditions of 14,7 psia (1 atm) and 70 °F (21.1 °C) was used for accounting purposes.
It’s amazing that not only were these calculations performed since 1944 in the U.S., but even since the Helium grade was much lower (98.2 % purity produced at that time) than in later years, and since a new different stretch factor of the cylinders steel was adopted, they decided to update the formulas !
In fact, the new better standard Helium was 99,995% pure and this fact has led the U.S. authorities to review the system of calculation, also introducing a more accurate stretch factor of steel !
This equation has been included, just for information, in the program features; it can be found under the menu Tools, Real Gas EOS comparison (EOS stands for "Equation of State" ), by checking the " U.S. Bureau of Mines " and only helium as a gas ( this algorithm is for Helium only).
To calculate the behavior of Oxygen, Helium and Nitrogen as a pure gas is relatively simple today.
There are a number of real gas equations to accurately calculate the behavior of Oxygen, Helium and Nitrogen as a single gas.
All you need is to have the skills to implement them in a blending software integrating them with the mathematics of technical diving interest.
Tech Gas Blender is based on the most accurate single gases:
• Oxygen: Helmholtz Equation of State for Oxygen - Schmidt and Wagner
- uncertainty in density: 0,1%
• Helium: MBWR Equation of State for Helium - McCarty and Arp
- uncertainty in density : 0,1%
• Nitrogen : Helmholtz Equation of State for Nitrogen of Span
- uncertainty in the density : 0.02%
The different compressibility of gases, at the same pressure, temperature and internal volume of the cylinder, causes different amounts of actual content.
This means that, for example, bringing the contents of a cylinder at 200 bar at ambient pressure, where the differences in compressibility are negligible, we obtain volumes very different from each gas:
80 CF (11.1 Liters int.vol.) at 200 bar gauge and 20 °C
free uncompressed gas at 1 Atm and 20 °C
(Liters and cubic feet, including internal cylinder volume)