Eq. A
Semiclosed Rebreather Theory
Some Background Physiology
Semi Closed Rebreather Theory
References
All of
the above has been gracefully contributed by Åke larsson !
What does it all mean ?
Here I
have tried to put the above in laymans and practical terms,
please remember that I am not a
Nuclear Scientist so please value the information accordingly.
In a human body in steady
state work, i.e. during aerobic working conditions, the
relationship between
the minute ventilation, VE (the sum of tidal volumes
over a minute, sometimes denoted RMV), and
oxygen uptake, VO2, is about constant. The ratio of
minute ventilation and oxygen uptake is often called
the extraction ratio, here denoted KE.
Eq. A
The extraction ratio falls in
the range 17 to 25 with a normal value of 20 for healthy humans,
the variations
primarily depends on the diet of the diver and the dead space of
the diver and his equipment.
(For those of you who hate physiology – skip the rest of this paragraph completely!! )
The body of a diver needs
oxygen to perform its work. The breathing in a normal diver
during non-exerting
work (i.e. below the anaerobic threshold) is primarily controlled
to maintain a certain pH, i.e. primarily the
carbon dioxide partial pressure, PCO2. The PCO2
level in the body depends on the alveolar ventilation and
the CO2 production.
The alveolar ventilation is
the minute ventilation minus the wasted dead space ventilation,
the latter is
normally less than 30% of a normal breath.
The ratio between the CO2
production and the oxygen consumption, is called the respiratory
quotient,
is usually assumed to be slightly below 1 but varies between 0.8
(only fat being burned) over
1 (pure carbohydrates) depending of what kind of substrate is
being burned.
During excertion when the
diver starts to produce lactic acid the ventilation will increase
in relation to the
oxygen consumption as seen in the figure below and the effective
respiratory quotient will increase as
will the extraction ratio.
Figure 2. Simplified
graph showing the relation between the oxygen uptake and minute
ventilation for a group of subjects, from [1].
The really interested reader is referred to [2], especially chapter 5 respiration and excertion.
Some Semi Closed Rebreather Theory
In a semi closed rebreather
the oxygen fraction in the breathing circuit, FO2,
depends on the diver's
oxygen uptake, VO2, and the added flow, Qmix,
and composition, Fmix, of the fresh gas as expressed
in the equation below.
Eq. B
(For those of you who hate math – skip the rest of this paragraph completely!! )
For a semi closed rebreather
the general mass balance equation is valid. Using the notation
indicated
in the figure below a differential equation for the change of
oxygen fraction over time can be set up and
solved assuming instantaneous mixing and neglecting breath to
breath variations in gas concentrations.
The oxygen fraction in the breathing circuit will be according to
the equation D below. Note the steady
state term (to the left) and the transient term (to the right).
The time constant in the transient term has
a strong dependency on the volume (in normal liters) of the
breathing circuit.
Note: the time constant
relates to the transients of the oxygen fraction of a SCR only,
the time constant
for fall of PO2 in a CCR is linear and not depth
dependent!
Figure 3. A simplified model of the rebreather.
In the Figure 3 above the:
Fmix is the oxygen fraction of the fresh gas
Qmix is the flow of fresh gas [normal L/min]
VO2 is the oxygen uptake of the diver [normal L/min]
V is the volume of the breathing circuit [in normal liters]
FO2(t) is the oxygen fraction over time in the breathing circuit.
Eq. C
/* The basic differential equation */
Eq. D
/* The solved FO2 equation with steady state and transient term */
Some References and further Reading.
[1] Åstrand P., Rodahl K., Textbook of work physiology, MacGraw Hill, 1977.
[2] Bennet P. Elliot D., The physiology and medicine of diving, ISBN 0-7020-1589-x, 1994.
Before I start I would like to
state firmly:
If you can not
understand the above theory you shall not dive a Rebreather !!
Period. Its that simple. It has to be said.
Ok now lets have look at what
the theory means in practice; As humans, we, depending on certain
conditions,metabolise different amounts of Oxygen O2 over time.
At the same time the Semiclosed
rebreather will continually add a fixed amount of O2 over time.
This means that if we metabolise O2
at diffrent rates then consequentially the O2 (nitrox-mix) level
in the loop will differ. If we metabolise
slowly (at rest, peaceful calm diving conditions) the nitrox
level will be closer to the original mix than
if we metabolise a lot (stressed, working hard, bad conditions)
This means that we will in
practice during the dive have different nitrox mixes in the loop.
We can
both be very close to the Tank mix and at times very much below.
This does not have lifethreatening
consequence as long as we keep the partial pressure of O2 within
survivable limits i.e. 0.16-1.6 PO2.
The partial pressure is as you know a product of the absolute
Atmospheres, Atm, and the Fraction of
Oxygen FO2 in the loop.
Lets make a table and have a closer look at this.
The table above shows PO2 on
the standing axis, and depth in meter on the horisontal.
The differern coloured graphs represent diffents metabolic rates
of the diver.
Lets take the yellow graph;
-At 20 meter this diver who is metabolising 1.0 liter
of O2/min will have a PO2 of 0.8 in the loop.
His buddy, diving on similar
unit but who is fat, unconditioned and metabolises close to 2.0
liters of
O2/min will at the same depth have a PO2 of 0.6 in his loop.
(follow the maroon/brown graph)
This translates to in
"Nitrox values" 27% for the yellow diver and 20% for
the fat one.
These two better not dive on the same computer or plan !!
Another issue is breathing
hard on the loop at the surface. At low mixes like the D (32,5%)
mix and the
relative slow (relative to a civilian rebreather like the Draeger
Dolphin) adiition speed you could actually
by hard work such as swimming against a current back to the boat
breathe down the loop below a PO2
of 0.16 and pass out. That one reason why you always start and
end a dive with a flush.
as you see its very important
to have an idea of your O2 consumption at different levels of
stress, work
load and comfort levels
I regurlarly measure mine using my Buddy inspiration CCR RB and
my consumption sits at around
0,9 to 1,2 depending. So use a graph that is in between the
yellow and blue diver to plan my dives.
I hope this has illustarted a
little of the practicalities of the theory. If you happen to own
a FGT-1/D feel
free to download an excelsheet with the rest of the tables for
the other mixes as well. FTG PO2.xls
Since 00-12-17