Z factor and true capacity formula

[YuchenEasonJiang]

I'm researching the calculation of the true gas capacity based on the Z factor and ideal volume (water capacity). I noticed that some calculate the true capacity as:
True_Capacity ≈ Ideal_Capacity ÷ Z_Factor(gas & pressure@temperature) - Dive Gear Express and Teach me to dive

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But according to the formula PV=ZnrT, true capacity should equal to ideal capacity times Z factor, rather than divided by.
So, I have a question: How do you calculate the true capacity? Multiply divided by Z factor?

 

[rjack321]

Z factors increase as pressure increases.
Ideal divided by Z to equal a smaller actual or true is correct. DGX's formula is correct.

The Vs in these are in PVideal=nrT or PVactual=ZnrT. Moving things around you get...

V/Z = nrtT/P. If n, r, T, and P are all held constant then Videal/Z = Vtrue

 

[inquis]

True Capacity = Ideal Capacity / Z is correct
Z is typically > 1 for gasses & pressures we care about. For example, Z(air, 3000 psi) = 1.032 from the DGX link.

It may help to know that Z is *defined* as Z=PV/(nRT), where P and n are both the actual or measured quantities. V is always actual, since it's a rigid vessel.

At 3000 psi, the molecules don't compress as well, so fewer are required (n is smaller than in the ideal case) to yield a given pressure when in a given volume container.

ETA: I failed to connect the dots previously: Ideal Capacity = PV. True capacity is defined as the volume that non-ideal gas would occupy at 1 atm pressure. Conveniently, air behaves as an ideal gas at 1 atm(^), therefore PV (after expanding to 1 atm) = 1 * Real Capacity = nRT. From the above definition of Z, we see that

Z = Ideal Capacity / Real Capacity or equivalently​

Real Capacity = Ideal Capacity / Z​

(^) for our purposes, find Z(air, 1 atm) in a table and observe the value 1.0.

 

[J-Vo]

Info - Real gas - the real deal

Hello, I posted this article about real gas models (GERG-2004 among others) for nitrox and trimix blending and associated open source code on thedecostop forum back in 2007. Reposting it here so it doesn't get lost, since both thedecostop and rebreatherworld seem dead. .

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