You are mixing up two different, though related concepts -- reaction rates and chemical equilibrium -- and also mixing up the reaction rate of release of chlorine from CYA with the reaction rate of chlorine killing algae. Let me describe this in more detail to hopefully clarify it. I'll use the primary chemical reaction ignoring other paths.
HClCY
- + H
2O <<<---> H
2CY
- + HOCl
"Chlorine Bound to CYA" + Water <<<---> "CYA Ion" + Hypochlorous Acid
At 77ºF, the forward reaction rate constant (ignoring ionic strength effects), k
for, (from
this paper) is 0.17 sec
-1 (t
1/2 = ln(2)/0.17 = 4.08 seconds but there is another pathway I don't show that has a faster half-life of 0.25 seconds) while the reverse reaction rate constant, k
rev, is 7.4x10
4 M
-1sec
-1. The equilibrium constant is the ratio of forward to reverse reaction rate constants so K = k
for/k
rev = 0.17/7.4x10
4 = 2.4x10
-6 (with rounding -- the equilibrium constant was the most accurately determined of these numbers). The formulas are the following (where "M" is concentration in moles/liter):
Rate of Forward Reaction (M/sec) = k
for*[HClCY
-]
Rate of Reverse Reaction (M/sec) = k
rev*[H
2CY
-]*[HOCl]
A reaction is at equilibrium when the forward and reverse reaction rates are equal which means there is no net change in product or reactant concentrations. Setting the above two equal to each other results in the following definition for the equilibrium constant (both in general in terms of reaction rate constants and specifically for this reaction in terms of reactant and product concentrations).
Equilibrium Constant (K) = k
for/k
rev = ([H
2CY
-]*[HOCl])/[HClCY
-]
Note that none of the above has to do with the rate of killing algae. That is a completely separate sort of reaction (actually, many different reactions) that I over-simplify as follows:
HOCl + "living algae" ---> "dead algae" + other products (combined chlorine or oxidized organics including nitrogen and carbon dioxide gasses)
There is also another reaction (of sorts) in terms of algae growth that I generically write as follows:
"living algae" + "nutrients" ---> "twice as much living algae"
For bacteria, the time it takes to double in population under ideal conditions is around 15 to 60 minutes. For algae, it's around 3 to 8 hours. So the key factor to killing bacteria or algae is for the rate of killing to be faster than the rate of growth. Specifically, killing more than half of the bacteria or algae in the time that it takes bacteria or algae to double in population. Notice that the rate of killing algae from the above equation (the one starting with HOCl) is dependent on the hypochlorous acid concentration and in practice it's pretty much proportional to that concentration. This is why the amount of chlorine in reserve is irrelevant except to ensure that you don't run out of chlorine during the killing process. The amount in reserve has nothing to do with the rate of killing algae -- only the concentration of hypochlorous acid matters for that. This concentration is roughly proportional to the FC/CYA ratio. Remember the soldier analogy -- it doesn't matter if I've got millions of soldiers in reserve if I've only got a handful on the front lines doing the actual killing. Even if these front-line soldiers were instantly replaced when they got used up killing the enemy, the enemy can increase in size (as bacteria and algae do by growing) faster than they are killed -- the amount of soldiers in reserve does nothing to help in this case. Fighting a war with nearly all of the soldiers in reserve rather than on the front-lines is a prescription for failure.
So the key is to have an FC/CYA ratio that kills algae faster than it can grow; preferably quite a bit faster to have some margin/cushion for all kinds of factors such as imperfect circulation. The minimum FC for each CYA level, which is pretty much a minimum FC/CYA ratio, ensures that chlorine will kill algae faster than it can grow in almost all conditions -- that is, in spite of having plenty of nutrients. Though the equation above (the one with "nutrients") would seem to imply that increasing the amount of nutrients will have the algae grow faster and faster, this only works up until one reaches some limiting factor for some nutrient and there is ALWAYS such a factor since the amount of sunlight is fixed, for example, and the rate of cell division is also ultimately limited by temperature due to physical processes such as alignment of organelles and DNA in cells. This is why pools even with high phosphates and nitrates can still have algae completely controlled using chlorine alone, though such pools are no question very reactive if you let the chlorine get too low such that algae grows faster than the chlorine kills it. Very reactive is still on the order of 3 hour doubling times, however, so it's not like it's in seconds or anything like that. For bacteria, it's still 15 minutes or so, but can be more noticeable since one bacteria can become 4 billion in 8 hours if there is a doubling every 15 minutes. For algae, even with 3 hour doubling, one algal cell can become 256 after one day. This is why algae growth almost always starts out as being an invisible increased chlorine demand and then only later becomes visible often as dull water, then cloudy, and then green (some algae go pretty much straight to green as even small amounts make their chlorophyll visible).
So a shocking event increases the FC relative to CYA so that the FC/CYA ratio is higher and that means more of the FC will exist as hypochlorous acid which is the killing agent for bacteria and algae. You can't really say that it forces more of a release of chlorine bound to CYA since normally the chlorine you add for shocking is already unbound -- that is, it's unstabilized chlorine. It would be more accurate to say that adding unstabilized chlorine results in less of it getting bound with more of it remaining unbound, but again the net result is dependent on that FC/CYA ratio and by shocking you are increasing FC without changing CYA.
If you have higher levels of chlorine with higher levels of CYA, such that the FC/CYA ratio remains constant, then this has roughly the same amount of hypochlorous acid so the same rate of killing power against bacteria and algae. I think what you meant was that increasing levels of CYA without proportionally increasing levels of FC will result in slower killing power possibly to the point of algae growing faster than chlorine can kill it. This is because adding more CYA, say from stabilized chlorine (Trichlor or Dichlor) without raising the FC target results in a lower FC/CYA ratio so lower hypochlorous acid concentration.
The concern is not about the FC getting to zero, but rather getting too low such that the FC/CYA ratio gets too low thereby allowing algae to grow faster than chlorine can kill it. The amount of chlorine in reserve isn't usually of concern since there is usually plenty of it available. It's the instantaneous hypochlorous acid concentration that is of greater concern and that is roughly proportional to the FC/CYA ratio (at a pH of 7.5, it's roughly half that ratio). The concern for running out of chlorine comes up more frequently when one isn't using any CYA at all since pools may have low FC levels in that case. The German DIN 19643 standard specifies 0.3 to 0.6 ppm FC (or 0.2 to 0.5 ppm if ozone is used) with no CYA and such low levels of chlorine may get used up locally by bather load events though that doesn't seem to be a concern by those using such a system in commercial/public pools in Europe. That system, however uses activated carbon in the filtration system to strip out all chloramines and chlorine itself which then needs to be re-injected after further coagulation/filtration removes organic precursors. This system is supposed to reduce the amount of disinfection by-products and it does seem to help in that regard, though not as much as one might think because the hypochlorous acid concentration is still higher than in most pools that use CYA. In practice, the pools usually don't target much below 0.5 ppm in order to have at least some reasonable amount of chlorine for local bather load. If one instead used 4 ppm FC with 20 ppm CYA, then one could have the equivalent of 0.2 ppm FC with no CYA while still having plenty of reserve, but that isn't practical if you're going to be removing all chlorine in every turnover of water.
Richard
. 