Way back in the day, they used to teach bag breathing as a potential emergency ascent technique. The idea was that an OOA diver could exhale that last breath into the BC and then breathe from the BC for several breaths on the way up.
CO2 levels would come up, but you wouldn't be on the system long, and it was arguably better than having nothing to breathe at all, as the CO2 levels with just the gas in your lungs would spike even faster. It fell out of favor very quickly, in part due to the need to keep the inside of the BC sanitized like rebreather divers do now with their counter lungs. The average recreational diver sucked at that, and lung infections were a real possibility in training and if practicing the technique.
What you're proposing is basically the same thing, but with a counter lung that dumped half the gas from the loop with every breath, and relying on that alone, or perhaps with some scrubbing to keep the CO2 levels in check.
The RB80 rebreather does something very similar, although it dumps only 1/8th of the total gas in the loop with each breath and uses a scrubber to keep CO2 levels low - but it's the same basic idea.
A significant advantage of the system is that if the gas feed to the loop fails, the loop volume continually decreases, and the lack of a full breath is the cue for the diver to bail out to OC. You'd have that same advantage in spades with a SCR that dumped half the loop volume with every breath.
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The problem with the Drager rebreathers like the Dolphin, Ray and Atlantis, is that the lower the O2 content of the gas used, the larger the orifice that has to be installed and the faster you use up the limited gas supply.
For example, with a Dolphin using the 32% orifice, a 27 cu ft tank of 32% Nitrox lasted about 45 minutes. If you used a higher oxygen percentage gas mix you could install a smaller orifice, with a lower flow rate, and get longer bottom times.
But that design limitation really limited the Drager rebreathers for deeper dives, and you either had to add larger tanks on the sides, or you had to modify it with another orifice to add O2 to the loop, and then add some form of loop monitoring to convert it to a fairly simplistic manual CCR rebreather - one without much redundancy.
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With any SCR, the PPO2 in the loop is lower than the PPO2 of the drive gas itself, as the divers uses some of the O2 from the gas in the loop. The average divers uses about 4% of the O2 available in each breath so if you're diving 32%, you're exhaling gas around 28% O2, and if you breathed it again, you' be exhaling 24%. If you were exhaling it into the loop, and half the loop were dumped each breath, with that volume being replaced with 32%, you'd be breathing gas around 30% oxygen.
The question is whether a 2X gas extension is sufficient to warrant the counter lung and the greater complexity, and CO2 levels might be a problem. Most current SCRs extend the gas about 3x but elevated CO2 levels come into the picture and you need a scrubber.
