The acid addition is non-linear with pH. To lower the pH by 0.2 from 7.6 to 7.4 when the TA is at 400 (and for 13,400 gallons) takes 37 fluid ounces of Muriatic Acid. The 11 ounces is what it would be IF the TA were at or near 100. With the much higher TA it takes more acid to lower the pH by the same amount. It is true that you can do the aeration method by bouncing between 7.2 and 7.4 pH and that this is safer, but the TA will get lowered faster (the aeration will be more effective) if you bounce between 7.0 and 7.2. Of course, that assumes you have a pH test kit that measures to at least 6.8 since you have to know for sure that you are at 7.0 and not below that.
Though it takes 89 ounces of acid to go from 7.6 to 7.2 and the TA will go from 400 to 374, it takes another 72 ounces of acid to go from 7.2 to 7.0 and the TA will go from 374 to 353. This is what I mean by the amount of acid being non-linear with respect to pH. It is harder to make the pH go lower at lower pH -- sort of like pushing or pulling on a spring. This is due to the carbonate buffer that becomes "stronger" in resistance to pH change at the lower pH.
For MikeInTN, I calculate that going from a TA of 100 ppm to 60 ppm (assuming a CYA of 30 ppm) in the same volume of water takes a total of 137 fluid ounces or 1.1 gallons -- about what he said it took. Mike, did you start at a TA of around 100? I'd like to validate the calculations with more real-world results.
As for the acid addition method, I believe JasonLion summed it up best. There IS some effect by concentrated acid addition, but when I calculate even the best case of completely removing the carbonate from a volume that gets to high acidity, it just doesn't contribute very much. By the time the acid disperses into enough volume to make a difference in terms of the amount of potential carbonate that can be removed, the acid is then diluted enough to not have as much effect on pH (so not as much effect on driving out carbon dioxide). Also, I wouldn't do this in a vinyl pool since concentrated acidity (low pH) isn't good for the vinyl liner though it is for a short time. Generally speaking, adding concentrated pool chemicals to the pool very slowly over a return (at the deep end) so that it gets readily dispersed is safer.
Of course, experiment trumps theory so if you find the acid ball method to be measurably better, then at least for plaster/gunite pools (where the method would be safer) it might be worth it. If you can quantify the difference in the two methods (next time you or anyone needs to lower the TA in their pools) that would be helpful info. Basically what is needed is a measurement of the TA drop after adding acid quickly with the pump off (of course, the measurement would have to be made after the pump was turned back on so as to mix the pool water for the measurement) vs. after adding acid slowly with the pump running (waiting 30 minutes or so for mixing).
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As a simple example starting with standard starting numbers of pH 7.5, TA 100, CYA 30 in a 10,000 gallon pool, then adding 2 cups (16 fluid ounces) of Muriatic Acid if fully mixed would result in a pH of 7.19, TA 93.7 while if the acid mixed with only 10% of the pool water than that 10% would have a pH of 6.0 and a TA of 37.4 with an outgassing rate about 13 times higher than normal. Even if this resulted in a complete loss of all carbonate in that 10% water volume, this would result after dilution of the acid in the rest of the pool water in a pH of 7.72 and a TA 93.7 or with further acid addition is equivalent to a pH 7.5, TA 91. So it is theoretically possible for the "slug" or "acid ball" method to have an effect, but it is highly unlikely that very much of the carbonate is actually driven out of the water into the air (as carbon dioxide) since it only does so at the surface (unless there is aeration) and the concentration of acid in a part of the pool water is not static (i.e. will not last very long, even with the pump not running).
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