**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)

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