(I should preface this by saying that, unlike you, I have no real water disinfection expertise, so I may be overlooking significant fundamentals in what follows.)

Those costs sound reasonable for niche uses (though I do think they would prevent it from "revolutionizing water disinfection technologies" as they claim in the Conclusions), and being able to operate in practical terms at a very small scale seems to me like an advantage rather than a disadvantage. It clearly is more expensive than conventional water treatment and would have difficulty scaling to replace it for reasons of material availability. Other alternative very-small-scale disinfection approaches are probably cheaper than their process in its current form; they mention ozonation, UV irradiation with germicidal lamps, photocatalytic disinfection, and the Fenton process in the paper and supplement.

I don't see how the square-cube law plays into it; the reason they're supporting the catalyst on rutile (anatase?) instead of just using solid bars of metal alloy is precisely to ensure neat linear scaling, and the reason it's 1% metal instead of 0.1% or 0.001% is that the rutile is in the form of 1–100 nm particles. (See p. 8/12 in the article and Fig. 4 on p. 7/12). The only square-cube thing that occurs to me is that a large ice bath requires much less ice input than a small ice bath, but that favors scaling the process up, not down.

A couple of other points:

⓪ Your calculations seem to be correct.

① People's drinking water needs are lower than you suggest by a factor of about 65, although conventional surface-water treatment plants cannot take advantage of this.

② You're not taking into account the supply-chain issues that plague smaller-scale treatment facilities.

③ The cost of consumables that this process would eliminate would still be lower than the cost of the catalyst.

④ There are plausible ways the process might be improved that could make it economic.

Thanks to mkr-hn I found the paper at https://www.researchgate.net/publication/352882305_A_residue... the canonical paper link (unforgivably missing from the original press release) is https://www.nature.com/articles/s41929-021-00642-w, and the supplementary material is at https://static-content.springer.com/esm/art%3A10.1038%2Fs419....

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⓪ Scaling calculations.

Here are the calculations in more detail, since I misread yours badly at least twice.

You say 0.5 MGD is 6.5 million times higher than the 0.2 mℓ/min (3.3 μℓ/s) in the experiment. 0.5 MGD is 21.9 ℓ/s, which is 6.6 million times higher than 3.3 μℓ/s.

I think you are reading it correctly; they do say their catalyst is 0.5% Au and 0.5% Pd on a TiO₂ support: 0.6 mg of gold and 0.6 mg of palladium to process 0.2 mℓ/min of water. The supplementary material has a plot of different catalyst mixes they tried (Sup. Fig. 14, p. 12, 13/32).

If we normalize that amount of catalyst metal to SI units, that's 180 gram seconds per liter (g·s/ℓ) each of gold and palladium. Your 0.5 MGD (22 ℓ/s) for 5000 people is 4.4 mℓ/s per person, which works out to 790 mg per person each of gold and palladium. Palladium at US$2800 per troy ounce (https://www.kitco.com/charts/livepalladium.html — that is per troy ounce, isn't it?) is US$90/g. Gold at US$1800 per troy ounce is US$58/g. Multiplying it out, that's US$71 of palladium per person and US$46 of gold per person, for a total of US$117 of catalyst metals per person. This seems likely to be the dominant cost of the whole shebang at anything larger than laboratory scale; the actual preparation of the catalyst with these metals by the process they reported in the paper might be even more expensive, but presumably cheaper methods are possible.

The 5000-person 0.5 mgd plant you cite as an example would need 3.9 kg of gold (US$230k) and of palladium (US$350k) for its catalysts, a total of US$580k, which is the number you gave for "our small plant".

790 mg of gold per person, times 7.7 billion people, would be about 6100 tonnes, about 3% of all the 200 000 tonnes of gold that has been mined so far. However, the corresponding 6100 tonnes of palladium would vastly exceed the above-ground stocks of palladium, estimated at 4.5 "moz", which I think means "million troy ounces", or 140 tonnes.

However, they also tried 1% gold without any palladium, and although this produced lower H₂O₂ concentrations, they were still high enough to be somewhat effective (≈80 ppm rather than 220 ppm, resulting in a 1.6 log₁₀ reduction rather than the 8.1 they were so satisfied with). So in the face of resource limits you could trade off a larger amount of gold and a longer residence time against scarce palladium.

① Potable water needs are 5.7 ℓ/day/person, not 380.

Your figure of 4.4 mℓ/s/person is 380 liters per day per person (100 gallons per day per person), but Burning Man recommends 1.5 gallons per day per person (5.7 liters/day/person, 0.066 mℓ/s/person), which includes water for showers, for cooking, and for drinking in a very dry environment with extensive physical exertion, though not for bidets. My experience at Burning Man is that you can get by on less.

That's 67 times less water than your figure.

Maybe your waterworks is supplying not only drinking water but also toilet-flushing water and lawn-irrigating water? Those don't normally need antibacterial treatment. Even the 0.2 mℓ/min benchtop catalyst they used in the paper (containing 5.4¢ of palladium and 3.5¢ of gold) would supply 0.29 liters per day; it would only need to be scaled up by a factor of 20 (to 12 mg gold (US$0.69) 12 mg palladium (US$1.10), 2.4 g rutile) to supply the requisite 5.7 liters per day per person.

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