Calculating SCUBA Cylinder Capacities

[DiveGearExpress]

all based on Van der Waals equation - Wikipedia

Actually, the method in the article is not based on his equation, although he was the first to recognize the relationship between compressibility and pressure/temperature. The Z Factors in the article and table are simple ratios of the molar volume of the specific gas to the molar volume of an ideal gas at the same temperature and pressure. The values are based on experimental observations taken from a database maintained by NIST, so hopefully they are a little bit more "real world", not that it's going to matter to sport divers. As you point out, round off the last digit or two and it would be good enough but the table just follows the conventional practice of how they are written in engineering handbooks, etc.

For SCUBA gas blending, we like Ashcroft although in a 0-5000 psi o2 clean version it can be difficult to source through distribution and we wind up having to special order a pretty large quantity to get them cost effectively.

 

[Kevrumbo]

To account for compressibility compensation at high pressure in home blending mixes, try a simple practical "fudge" factor like, for example, starting with 10% less the ideal gas calculation for the amount of pure O2 a particular blend calls for (refer bottom p.35 of Vance Harlow's Oxygen Hacker's Companion as it applies to adding O2 first in mixing a Trimix Blend and topping-off with Air) and see what you get when you top off with clean compatible Air through your local dive shop's boosted fill station. Adjust fudge factor as needed via trial & error for your particular cylinder(s) as you gain blending experience over subsequent fills.

So for 3442psi/230bar in a 12L/HP100 cylinder for example, the partial pressure ideal gas recipe for Nitrox32 requires 13.92 psi or 13.92 bar of Oxygen for every 100 psi or 100 bar of Nitrox32: subtract 10% to yield 12.52 psi or 12.52 bar of O2 for every 100 psi or 100 bar.

Hence for every 100 psi X 34.42 = 3442psi full fill, you need 12.52 psi X 34.42 = 430psi of O2, with the remainder a top off of hyperfiltered oxygen compatible clean air; or 100 bar X 2.30 = 230bar full fill, you need 12.52 bar X 2.30 = 29 bar of O2, with the remainder a top off of hyperfiltered oxygen compatible clean air.

My LDS here is Pacific Wilderness, and they fill & maintain all the working HP100 single tanks for the Port Police, County Sheriff and Fire Department dive teams of the Port of Los Angeles and Long Beach. They've been filling with 420psi of Oxygen and then topping off to get a final full fill analyzed blend of 31.8% for Nitrox32.

@Kevrumbo had a really good post somewhere on the superiority of metric units regarding scuba diving. Fact is, the imperial way of measuring tank capacities is pretty silly when it comes to ease of use and functionality in situ.

It's easier to fundamentally explain and conceptualize the rated volume and service pressure of a scuba cylinder based on the European/Asian surface atmosphere reference convention of 1 bar: The common AL80 tank has a metric cylinder rating factor of 11 liters/bar, or in other words, at the surface of 1 bar, if you pour water into the cylinder, the measured volume it can contain is 11 liters. (It's easier to work with Metric Cylinder Ratings like 11L/bar, rather than cf/psi like 0.025 cf/psi at 14.7psi surface pressure Imperial reference for the AL80 tank).

However when pressurized with breathing gas to any value up to its recommended Service Rating (207 bar for the 11L per bar Alu cylinder in this example ), a cylinder carries an equivalent volume of free gas much greater than its water capacity, because the gas is compressed to several hundred times the standard surface atmospheric pressure of 1 bar (as opposed to water which is incompressible). So if you have a gas pressure reading of 200 bar in your AL80 tank, you have a total available free gas volume of 200 bar multiplied-by 11 liters/bar or 2200 liters.

 

[DiveGearExpress]

I would like to correct the impression anyone might have that the article is in any way about gas blending. It is not, and you don't need to know anything about blending to appreciate the article content. The content is about making precise determinations of cylinder free gas capacities for technical divers, and to a lesser extent providing a convenient list of common cylinders and their true capacities. It explains why an AL80 holds 77 cubic feet of air, and an LP85 holds 81 cubic feet of air, why a set of double HP117's holds just 216 cubic feet of trimix and a set of double AL80's holds just 140 cubic feet of air when ice diving. The article also explains, in detail, why the "conventional wisdom" of making determination of cylinder capacity using the method of multiplying water volume in liters by cylinder pressure in bar is somewhat flawed. A "10 litre" bottle at 232 bar can be not 2320 free litres of air, even using ideal gas law.

It could be argued these inaccuracies are not significant, and that's true for sport diving. Sport diving doesn't require calculation of capacity because sport divers don't rely on capacity calculations and it is not generally taught in sport diving. Gas pre-planning in sport diving is rarely more complex than if bottom time of previous dives is being limited by the gas capacity rather than the NDL's, just take a bigger tank next dive. In contrast, technical dive gas pre-planning does require careful calculation of free gas capacity and so accuracy and precision (or the lack thereof) can have consequences for diver safety. The article provides an easy way for any diver, using nothing more than simple multiplication and division, to very precisely determine gas capacity of their cylinders should they have a need for genuine gas pre-planning. As always, once you are in the water the plan often undergoes unplanned transformations.

 

[Kevrumbo]

I would like to correct the impression anyone might have that the article is in any way about gas blending. It is not, and you don't need to know anything about blending to appreciate the article content. The content is about making precise determinations of cylinder free gas capacities for technical divers, and to a lesser extent providing a convenient list of common cylinders and their true capacities. It explains why an AL80 holds 77 cubic feet of air, and an LP85 holds 81 cubic feet of air, why a set of double HP117's holds just 216 cubic feet of trimix and a set of double AL80's holds just 140 cubic feet of air when ice diving. The article also explains, in detail, why the "conventional wisdom" of making determination of cylinder capacity using the method of dividing water volume in liters by cylinder pressure in bar is somewhat flawed. A "10 litre" bottle at 232 bar can be not 2320 free litres of air, even using ideal gas law.

It could be argued these inaccuracies are not significant, and that's true for sport diving. Sport diving doesn't require calculation of capacity because sport divers don't rely on capacity calculations and it is not generally taught in sport diving. Gas planning in sport diving is rarely more complex than when the SPG shows a third or a quarter (depending on the paranoia level of the diver or dive operator) of the service pressure of the hopefully full cylinder is remaining, begin ascent to the surface and be "back on the boat" with whatever SPG reading has been mandated by the operator (in the US typically 300 or 500 psi). If bottom time is being limited by the gas capacity rather than the NDL's, just take a bigger tank next dive. In contrast, technical diving does require careful calculation of free gas capacity and so accuracy and precision (or the lack thereof) can have consequences for diver safety. The article provides an easy way for any diver, using nothing more than simple multiplication and division, to very precisely determine gas capacity of their cylinders should they have a need for genuine gas planning.

It's true that gas compressibility, discussed in the article, is a partial explanation to why gas blending seemingly doesn't obey the math... i.e. blending 12/65 by the ideal math yields 10/70. There are actually several more factors along with van der Waals. In our experience at Dive Gear Express, our customers tell us today's technical diving is more demanding of accuracy and precision in blending. No longer do technical divers have to adjust the dive plan to fit the gas analysis results. Advent of modern blending tools, as close at hand as a smartphone, eliminate the errors and corrections of ideal gas laws versus real world results. Any properly trained blender with modern tools can hit a target mix at well within the accuracy of the gas analyzer itself on the first try, no "fudge" required. Thus modern gas blending is no longer an "art" gained from experience. Today gas blending for SCUBA is much more a science with the skills development no longer about arcane math and focused more on learning safe handling techniques and how to manage the tools.

Ultimately, it's whatever the SPG indicates real time at a planned turn or minimum reserve pressure, and other vital macroscopic factors such as -for example- physical exertion, breathing consumption rate of teammates, and environmental conditions (i.g. Current; Flow; Visibility etc), which are more the more important margins significantly overwhelming and "swamping-out" any of the esoteric FYI minutiae in the OP articles above regarding the "precise" or "accurate" volumetric free gas capacities of various cylinders vis-à-vis ideal versus real gas thermodynamics. A potential 11% variance in an initial twinset fill is at most an annoyance and an issue to correct on subsequent fills; a 30% or greater depth consumption rate than expected at my first time interval SPG check is objectively a more "genuine", meaningful and critical red flag indicator to abort the dive.

And you what you fundamentally learn and understand "properly" by rote, trial & error, and practice equally applies to gas blending -whether using a first world convenience of a "smartphone app" working in a Florida local dive store bank fill station; or performing the "art" of partial pressure mixing using a portable gas compressor, manual calculator arithmetic with applied Dalton's Law gas recipe formulas, and an O2 analyzer -in a sweltering east coast Sri Lanka shed on Expedition:

Album Archive - HMS Hermes, Sri Lanka - Technical Wreck Dive - April 2010 - Full Album