Chemistry:Maximum operating depth

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Short description: Depth below which the partial pressure of oxygen (pO2) of the gas mix exceeds an acceptable limit

In underwater diving activities such as saturation diving, technical diving and nitrox diving, the maximum operating depth (MOD) of a breathing gas is the depth below which the partial pressure of oxygen (pO2) of the gas mix exceeds an acceptable limit. This limit is based on risk of central nervous system oxygen toxicity, and is somewhat arbitrary, and varies depending on the diver training agency or Code of Practice, the level of underwater exertion expected and the planned duration of the dive, but is normally in the range of 1.2 to 1.6 bar.[1]

The MOD is significant when planning dives using gases such as heliox, nitrox and trimix because the proportion of oxygen in the mix determines a maximum depth for breathing that gas at an acceptable risk. There is a risk of acute oxygen toxicity if the MOD is exceeded.[1] The tables below show MODs for a selection of oxygen mixes. Atmospheric air contains approximately 21% oxygen, and has an MOD calculated by the same method.

Safe limit of partial pressure of oxygen

Acute, or central nervous system oxygen toxicity is a time variable response to the partial pressure exposure history of the diver and is both complex and not fully understood.

Central nervous system oxygen toxicity manifests as symptoms such as visual changes (especially tunnel vision), ringing in the ears (tinnitus), nausea, twitching (especially of the face), behavioural changes (irritability, anxiety, confusion), and dizziness. This may be followed by a tonic–clonic seizure consisting of two phases: intense muscle contraction occurs for several seconds (tonic phase); followed by rapid spasms of alternate muscle relaxation and contraction producing convulsive jerking (clonic phase). The seizure ends with a period of unconsciousness (the postictal state).[2][3] The onset of seizure depends upon the partial pressure of oxygen in the breathing gas and exposure duration. However, exposure time before onset is unpredictable, as tests have shown a wide variation, both amongst individuals, and in the same individual from day to day.[2][4][5] In addition, many external factors, such as underwater immersion, exposure to cold, and exercise will decrease the time to onset of central nervous system symptoms.[6] Decrease of tolerance is closely linked to retention of carbon dioxide.[7][8][9] Other factors, such as darkness and caffeine, increase tolerance in test animals, but these effects have not been proven in humans.[10][11]

The maximum single exposure limits recommended in the NOAA Diving Manual are 45 minutes at 1.6 bar, 120 minutes at 1.5 bar, 150 minutes at 1.4 bar, 180 minutes at 1.3 bar and 210 minutes at 1.2 bar.[1]

Formula

The formula simply divides the absolute partial pressure of oxygen which can be tolerated (expressed in atm or bar) by the fraction of oxygen in the breathing gas, to calculate the absolute pressure at which the mix can be breathed. (for example, 50% nitrox can be breathed at twice the pressure of 100% oxygen, so divide by 0.5, etc.). Of this total pressure which can be tolerated by the diver, 1 atmosphere is due to surface pressure of the Earth's air, and the rest is due to the depth in water. So the 1 atmosphere or bar contributed by the air is subtracted to give the pressure due to the depth of water. The pressure produced by depth in water, is converted to pressure in feet sea water (fsw) or metres sea water (msw) by multiplying with the appropriate conversion factor, 33 fsw per atm, or 10 msw per bar.

In feet

[math]\displaystyle{ MOD (fsw) = 33\mathrm{~fsw/atm} \times \left [\left ({pO_2\mathrm{~ata}\over FO_2} \right ) - 1\right ] }[/math]

In which pO2 is the chosen maximum partial pressure of oxygen in atmospheres absolute and the FO2 is the fraction of oxygen in the mixture. For example, if a gas contains 36% oxygen (FO2 = 0.36) and the limiting maximum pO2 is chosen at 1.4 atmospheres absolute, the MOD in feet of seawater (fsw)[Notes 1] is 33 fsw/atm x [(1.4 ata / 0.36) − 1] = 95.3 fsw.[12]

In metres

[math]\displaystyle{ MOD (msw) =10\mathrm{~ msw/bar} \times \left [\left ({pO_2\mathrm{~ bar}\over FO_2} \right ) - 1\right ] }[/math]

In which pO2 is the chosen maximum partial pressure in oxygen in bar and the FO2 is the fraction of oxygen in the mixture. For example, if a gas contains 36% oxygen and the maximum pO2 is 1.4 bar, the MOD (msw) is 10 msw/bar x [(1.4 bar / 0.36) − 1] = 28.9 msw.

Tables

Maximum Operating Depth (MOD) in feet sea water (fsw) for pO2 1.2 to 1.6
MOD (fsw) % oxygen
4 8 12 16 20 21 24 28 32 36 40 50 60 70 80 90 100
Maximum pO2 (bar) 1.6 1287 627 407 297 231 218 187 156 132 114 99 73 55 42 33 26 20
1.5 1205 586 380 276 215 203 173 144 122 105 91 66 50 38 29 22 17
1.4 1122 545 352 256 198 187 160 132 111 95 83 59 44 33 25 18 13
1.3 1040 503 325 235 182 171 146 120 101 86 74 53 39 28 21 15 10
1.2 957 462 297 215 165 156 132 108 91 77 66 46 33 24 17 11 7

These depths are rounded to the nearest foot.

Maximum Operating Depth (MOD) in metres sea water (msw) for pO2 1.2 to 1.6
MOD (msw) % oxygen
4 8 12 16 20 21 24 28 32 36 40 50 60 70 80 90 100
Maximum pO2 (bar) 1.6 390 190 123 90 70 66 57 47 40 34 30 22 17 13 10 8 6
1.5 365 178 115 84 65 61 53 44 37 32 28 20 15 11 9 7 5
1.4 340 165 107 78 60 57 48 40 34 29 25 18 13 10 8 6 4
1.3 315 153 98 71 55 52 44 36 31 26 23 16 12 9 6 4 3
1.2 290 140 90 65 50 47 40 33 28 23 20 14 10 7 5 3 2

These depths are rounded to the nearest metre.

See also

Notes

  1. ↑ Feet sea water (fsw) is a unit of pressure. One fsw is equal to the hydrostatic pressure exerted by a standard sea water column of 1 foot height at normal Earth gravity. 33 fsw is approximately equal to one standard atmosphere (atm). A pressure indicated in fsw is gauge pressure (relative to surface pressure) unless specified.

References

  1. ↑ 1.0 1.1 1.2 Lang, M.A. (2001). DAN Nitrox Workshop Proceedings. Durham, NC: Divers Alert Network. p. 52. http://archive.rubicon-foundation.org/4855. Retrieved 21 November 2012. 
  2. ↑ 2.0 2.1 Clark & Thom 2003, p. 376.
  3. ↑ U.S. Navy Diving Manual 2011, p. 44, vol. 1, ch. 3.
  4. ↑ U.S. Navy Diving Manual 2011, p. 22, vol. 4, ch. 18.
  5. ↑ Bitterman, N (2004). "CNS oxygen toxicity". Undersea and Hyperbaric Medicine 31 (1): 63–72. PMID 15233161. http://archive.rubicon-foundation.org/3991. Retrieved 29 April 2008. 
  6. ↑ Donald, Part I 1947.
  7. ↑ Lang 2001, p. 82.
  8. ↑ Richardson, Drew; Menduno, Michael; Shreeves, Karl, eds (1996). "Proceedings of rebreather forum 2.0". Diving Science and Technology Workshop: 286. http://archive.rubicon-foundation.org/7555. Retrieved 20 September 2008. 
  9. ↑ Richardson, Drew; Shreeves, Karl (1996). "The PADI enriched air diver course and DSAT oxygen exposure limits". South Pacific Underwater Medicine Society Journal 26 (3). ISSN 0813-1988. OCLC 16986801. http://archive.rubicon-foundation.org/6310. Retrieved 2 May 2008. 
  10. ↑ Bitterman, N; Melamed, Y; Perlman, I (1986). "CNS oxygen toxicity in the rat: role of ambient illumination". Undersea Biomedical Research 13 (1): 19–25. PMID 3705247. http://archive.rubicon-foundation.org/3044. Retrieved 20 September 2008. 
  11. ↑ Bitterman, N; Schaal, S (1995). "Caffeine attenuates CNS oxygen toxicity in rats". Brain Research 696 (1–2): 250–3. doi:10.1016/0006-8993(95)00820-G. PMID 8574677. 
  12. ↑ "Physics of Diving". NOAA Diving Manual. National Oceanic and Atmospheric Administration. http://ehs.ucsb.edu/units/diving/dsp/forms/articles/physics.pdf. 

Sources

  • Clark, James M; Thom, Stephen R (2003). "Oxygen under pressure". in Brubakk, Alf O; Neuman, Tom S. Bennett and Elliott's physiology and medicine of diving (5th ed.). United States: Saunders. pp. 358–418. ISBN 978-0-7020-2571-6. OCLC 51607923. 



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