[iso1337]

There is a well known relationship summarized in the Sherwood plot.

https://www.pnas.org/content/pnas/108/51/20428/F1.large.jpg

related paper: https://www.pnas.org/content/108/51/20428

Your basic intuition is correct in that the more dilute something is, the more costly it is to extract/purify it.

[pfdietz]

A properly engineered DAC system will be much less expensive than the number they found.

https://www.cell.com/joule/fulltext/S2542-4351(18)30225-3

[jandrewrogers]

That paper only looks at the energy/cost balance of the plant, not the chemical feedstock. Production of that feedstock is energy intensive, the recycling is not 100% efficient per the paper (i.e. it will constantly have to be replenished), and the industrial infrastructure to produce those chemicals at the necessary scale to materially reduce atmospheric carbon simply doesn't exist.

Any cost model for large-scale DAC must include the capital and operational costs of new feedstock factories to keep the DAC supplied at scale. It won't be cheap. The pilots can ignore this because they rely on the excess capacity of existing industrial infrastructure.

[pfdietz]

Not at all -- the cost of makeup streams for chemicals are included in the O&M cost (table 2).