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When people are enclosed in an air-tight space, the levels of carbon dioxide will rise to lethal levels (hypercapnia) long before the oxygen is exhausted (hypoxia). For example, the astronauts of Apollo 13 were in danger because the carbon dioxide scrubbers in the lunar module were inadequate. They never "ran out of oxygen", even though the oxygen tank of their service module exploded.

What would be the benefit to supplying such persons with tanks of additional oxygen? It seems to be a futile gesture to me.

The reason I ask is a news story ongoing for several weeks. Twelve children and one adult have been trapped by water in a cave for several weeks. At the time this question was written, four boys were already rescued. Officials have repeatedly expressed concerns that the "oxygen is running out" and are placing oxygen tanks in the cave. Is there any benefit to this, or are officials simply ignorant of human physiology?

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    $\begingroup$ The quantity of CO2 is less important than concentration. By increasing the quantities of O2, you decrease the concentration of CO2, thus reducing hypercapnia. $\endgroup$ – Astrolamb Jul 8 '18 at 19:15
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    $\begingroup$ @DrSheldon, alas yet obviously, nothing in existence today lasts eternally $\endgroup$ – AliceD Jul 8 '18 at 20:06
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    $\begingroup$ CO2 scrubbers are very costly compared to the relative ease by which oxygen is generated. Additionally, they are far more efficient when scrubbing high concentrations of CO2, such as exhaust gases, than the lower concentrations of ambient CO2. $\endgroup$ – Astrolamb Jul 8 '18 at 20:23
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    $\begingroup$ The big issue in the case of the cave is that it is a temporary thing. O2 only needs to be supplied until the trapped people are rescued, and scrubbers are too expensive relative to O2 costs to be used for such a temporary situation. This is hugely different from, say, the ISS, which is intended for long-term occupation. For the ISS, using scrubbers is much more practical. $\endgroup$ – Astrolamb Jul 8 '18 at 20:32
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    $\begingroup$ "...or are officials simply ignorant of human physiology?" You assume much. $\endgroup$ – anongoodnurse Jul 9 '18 at 2:52
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There are a couple of ways to answer your question. If we assume the cave is an air-tight chamber, we've entered the domain of a very specialized field in medicine, so I can't speak as authoritatively as I'd like there, but lets start, with the fact that the cave is not air tight.

It's a cave

A cave is not a submarine or a lunar module. It is not air-tight, but in a large environment with various types of gas exchange. The cave may already have it's own $CO_2$ scrubber of a sort, since common minerals reversibly bind $CO_2$. I expect there is a whole science around $CO_2$ cycles in, e.g., limestone caves, but the point here is there is likely a sink of some sort for the $CO_2$ produced by the boys. For example, I think we could reasonably speculate that the following equilibrium in a limestone cave would be driven to the right with additional $CO_2$:

$CaCO_3 + H_2O + CO_2 \rightleftharpoons Ca(HCO_3)_2$

Why would you give oxygen?

Here I can speak authoritatively. I'd refer you to both of West's excellent texts (Respiratory Physiology and Pulmonary Pathophysiology) for further reference.

Lets clear up a misconception in the comments. It is correct that we're concerned about the concentration (typically expressed as partial pressure) of gas, not the amount. It is not correct that $O_2$ eliminates $CO_2$ from the body. This can be confusing, but it is a misapplication of Dalton's law to human physiology, based on a misunderstanding about where and how the gas is exchanged. By Dalton's law, you can reduce the concentration of $CO_2$ in a container by increasing the concentration of some other gas (e.g., $O_2$). If $CO_2$ is accumulating in the cave (rather than being taken up by the environment), then delivering compressed gas with no $CO_2$ would decrease the concentration of $CO_2$ in inspired air. Inspired air, however, is not the same as alveolar air or arterial or venous gas, and the human body is not well modeled as a container full of various gases.

While it is true that when $CO_2$ is retained in respiratory acidosis, arterial $P_{O2}$ must go down by whatever amount arterial $P_{CO2}$ goes up, it doesn't work the other way around. Delivering a higher $F_{iO2}$, or fraction of inspired $O_2$ does not cause an inverse change in arterial $CO_2$. This ends up being fairly complicated, and a full discussion is beyond the scope of this question. Let me just emphasize that supplemental $O_2$ specifically treats low $O_2$ (or, in a very specific case, $CO$, carbonmonoxide, poisoning). High $CO_2$ is treated by increasing ventilation. In fact, there are a few special cases where supplemental $O_2$ actually increases a patient's $CO_2$ levels, two of which involve hypercapnic respiratory failure. We do give $O_2$ for hypercapnic respiratory failure, but it is given to treat the associated hypoxia, not the hypercapnea. The only way to decrease $CO_2$ is to increase ventilation. This is a very important concept in critical care and respiratory medicine. I'd refer you to West Pulmonary Pathophysiology, Chapter 10, or any critical care textbook.

So, back to the reason you might want to give oxygen...

CNN reports that oxygen levels in the cave have reached 15%. If the atmospheric pressure of the cave is 760mm Hg, then the $P_{O2}$ in inspired air is about 107mm Hg, ((760 - 47 for water vapor) * 0.15, see West Respiratory Physiology, or any physiology text). At 600mm Hg (equivalent to an elevation of ~2000 meters) $P_{O2}$ in inspired air is 83mm Hg. This is low, and could start to be a problem (leading to hypoxemia and hypoxia), depending on the ability of the boys to compensate (again, see West, either respiratory physiology or pulmonary pathophysiology). If the $O_2$ levels in the cave continued to drop, or if the boys weren't compensating well, then it would be reasonable to give supplemental oxygen to treat their hypoxia, regardless of what the $CO_2$ levels were.

But if $O_2$ was low, wouldn't they also have to have high $CO_2$?

I'm not an expert in cave ecology, but it doesn't seem that strange to me that the rate of $O_2$ consumption by the boys could exceed the environment's capacity to produce or release $O_2$ from organic sources, dissolved sources, or ventilation, without their rate of $CO_2$ production overwhelming the environment's $CO_2$ sink. I have no good evidence one way or the other for this speculation.

What if it is an air-tight container?

Atmospheric $CO_2$ is on the order of 400ppm, or 0.04%. Normal levels in the body are 5% (40mm Hg / 760). We rely on this gradient to dump the $CO_2$ produced by cellular respiration using ventilation, but can still operate, with difficulty, with 5% $F_{iCO2}$. Serious problems (same reference) occur at higher levels. Again, in this particular case we're beyond my personal expertise (Dammit, Jim, I'm a doctor, not an aerospace or submarine doctor!), but in an air-tight container without a $CO_2$ sink, if $CO_2$ levels were higher than 5% and rising, I'd expect you would need to directly address $CO_2$. If it's a small container, adding other gases from pressurized canisters, or pumping gases in would decrease the $F_{iCO2}$ by Dalton's law, provided you could overcome the rate of $CO_2$ production by the boys. If $CO_2$ had accumulated in the boys blood (hypercapnea), they would (need to) increase their ventilation as well, adding more $CO_2$ to the chamber.

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