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Something about half times May 5, 2009

Posted by Chris Sullivan in Technical Diving.
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Decompression models use theoretical body tissue compartments as models for gas absorbtion and assume that the rate of absorbtion is proportional to the pressure gradient (difference between the pressure in the tissue and the ambient pressure). This is all well although not rigorously explained in the Encylopedia of Recreational Diving which every PADI Divemaster Candidate must study.

In one of the papers I read on the subject, called Understanding M-Values by Erik Baker, I noticed that the tissue half times were much shorter for Helium (He) than for Nitrogen (N2). Just recently I read another paper by Baker, called Introductory Deco Lessons (which for most people, I suspect, are not introductory at all), which mentioned that the rate of absorbtion is proportional to the square root of the ratio of the molecular weights of the gases. Referring to my handy Periodic Table of the Elements, the molecular weight of Nitrogen Gas (N2) is 28.02, while Helium Gas (He) is 4.003. So I looked at the Buhlmann compartment half-times published in Understanding M-Values to see how well it matched. Turns out it matches pretty well.

Comp # N2 H/T He Calc He Act H2 Calc
1 4 1.51 1.51 1.07
1b 5 1.89 1.88 1.34
2 8 3.02 3.02 2.15
3 12.5 4.72 4.72 3.35
4 18.5 6.99 6.99 4.96
5 27 10.21 10.21 7.24
6 38.3 14.48 14.48 10.27
7 54.3 20.52 20.53 14.57
8 77 29.10 29.11 20.65
9 109 41.20 41.20 29.24
10 146 55.18 55.19 39.16
11 187 70.68 70.69 50.16
12 239 90.34 90.34 64.11
13 305 115.28 115.29 81.81
14 390 147.41 148.42 104.61
15 498 188.23 188.24 133.58
16 635 240.01 240.03 170.33

The first column is the compartment number. There are two versions of compartment #1, and I’ve listed them both below. Implementations of the model use one or the other, usually the 1b version. The second column is the Nitrogen half times in minutes, while the second is the calculated half time for Helium. It is consistently within 1/100 of a minute with the published values, which are in column 3. Just for fun, I calculated the half times for Hydrogen Gas (H2) which has a molecular weight of 2.016. The 1b compartment is a mere 90 seconds with Hydrogen, not that it is much longer with Helium, and not very useful as it would clear with all but the most extreme ascent rates.

Hydrogen has been used experimentally for very deep diving as it is both cheaper and less dense than Helium. It has the unfortunate property of being explosive in the presence of more than about 4% Oxygen which limits its usefulness in most diving applications.

So what’s this all mean? For me, merely that I understand decompression theory a little better now. Knowing that the ratio of absorbtion is proportional to the molecular weights is another piece of the puzzle.

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Comments»

1. Half-times and parallel compartments « Chronicle of an older diver - May 12, 2009

[…] Diving, tissue compartment, Trimix trackback I realized a couple of days after writing my last post about half times what the whole point of Bühlmann method of having the same compartment numbers for Helium and […]

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