In addition to using Trichlor pucks (which are highly acidic AND highly concentrated in chlorine) for getting rid of black algae, the other takeaway is a confirmation of what we've said all along about SWG systems. The superchlorination that appears to allow for lower Free Chlorine (FC) levels in keeping away free-floating green algae does not apply to algae stuck in biofilms on pool surfaces, such as black algae. So keeping the minimum chlorine level in Ben's Best Guess CYA chart is important. At 20 ppm CYA and 2 ppm FC that's at the minimum in Ben's chart, but at 40 ppm, you would need to have the FC at a minimum of 3, but probably closer to 4 ppm. This is the tradeoff between higher CYA protecting chlorine from sunlight vs. needing a higher FC level to keep away algae.
As for shocking, perhaps it needs an even higher level than that for green algae. There isn't a lot of experience with black algae on this forum -- mostly green algae and some yellow/mustard algae. Trichlor is the fastest way (and has been discussed as a definitive way to determine if a stain is organic or algae vs. a metal stain), but others have shocked and scraped with success so it's probably a matter of the degree of shocking. At any rate, you had success using Trichlor and that's what is most important. Now, at the 40 ppm CYA level you need to target an FC level of 4 ppm to keep away this algae.
Richard
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