As I noted in the post Certified Pool Operator (CPO) training -- What is not taught, the 2009 "CPO® Handbook, National Swimming Pool Foundation®" with front cover title "Pool & Spa Operator™ Handbook" indicates that at higher levels of TA, the pH is usually higher than ideal and becomes very difficult to change, but does not indicate that TA itself is a source of rising pH due to carbon dioxide outgassing. In the Spa & Therapy Operations section, when discussing pH, there is a discussion of aeration and carbon dioxide outgassing causing the pH to rise (and it says the TA decreases which is incorrect; the TA only drops when acid is added as acid lowers both pH and TA). However, even in this discussion it is not made clear that this effect can be reduced by lowering the TA level (nor how to do that efficiently) and supplementing pH buffering with a different non-carbonate pH buffer such as borates.
So there are bits and pieces of the correct chemistry, but not the definitive procedure as Ben describes in Lowering Swimming Pool Alkalinity -- A Step By Step Guide. Unfortunately, the industry still too often touts the "slug" or "acid column" method which is dangerous and inefficient as described in this paper, a shorter version of which may be found in this paper and this link. The fact is that 25-1/2 fluid ounces of full-strength Muriatic Acid (31.45% Hydrochloric Acid) in 10,000 gallons will lower the Total Alkalnity (TA) by 10 ppm no matter how you add it. The only thing you can affect is how quickly you can bring the pH back up without changing the TA, and that is accelerated by increasing the amount of aeration and having the pH be lower (at least near the water surface). This chart shows how over-carbonated the water is with respect to being in equilibrium with the air. The rate of outgassing increases with how far you are out-of-equilibrium, though the effect with TA is non-linear and appears to vary as the square of the TA (this effect is not shown in the table).
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