The CDC link[1] says 20 ppm FC for at least 12.75 hours, but amounts to the same thing (and the chart they show has 10 ppm FC for 25.5 hours similar to your calculation). The problem is that these are CT values WITHOUT CYA. With CYA in the water, it's not practical to get to the very high FC levels needed for equivalent disinfection rates. At 30 ppm CYA, you'd have to raise the FC to 37.5 ppm FC to be equivalent to 10 ppm FC with no CYA (it just works out that way -- at a pH near 7.5 so you'd better lower the pH before adding that much chlorine).
The CDC link[2] talks about this CYA limitation as follows:
Crypto CT values are based on the inactivation of 99.9% of oocysts. Laboratory studies indicate that this level of Crypto inactivation cannot be reached in the presence of 50 ppm chlorine stabilizer,†** even after 24 hours at 40 ppm free chlorine, pH 6.5 at a temperature of about 77°F (25°C).
It is pretty obvious that the CDC is not aware of the chlorine/CYA relationship in detail because a straightforward calculation using my spreadsheet shows that 40 ppm FC with 50 ppm CYA at a pH of 6.5 and temperature of 77F is technically equivalent (in hypochlorous acid concentration which is the disinfecting form of chlorine) to 4.8 ppm FC with no CYA at a pH of 7.5. To be equivalent to 10.625 ppm FC for 24 hours (to get the 15,300 CT), you would need 51 ppm FC with 50 ppm CYA at a pH of 6.5 or 57 ppm FC with 50 ppm CYA at a pH of 7.5. This clearly becomes impractical at high CYA levels and even at lower 30 ppm CYA levels raising the FC to 38.4 ppm FC and holding it there for 24 hours isn't practical.
Generally speaking, I wouldn't worry about Crypto in a residential pool. As for what commercial/public pools can do, they are in a tough position. There currently is no method they can use that will clear the pool of Crypto in any reasonable timeframe.
- UV will kill Crypto, but it takes 4.6 turnovers (with perfect circulation) to have 99% of the water go through the UV system.
- Chlorine Dioxide is at least 10 times as effective as chlorine and does not get reduced in effectiveness by CYA and could potentially be created in the pool by addition of sodium chlorite to produce just 2 ppm over 12 hours for 99.9% inactivation of Crypto, but the EPA won't allow this without studies that would cost $4+ million showing that the chlorate and chlorite byproduct concentrations would be safe (this is part of what I learned talking to people at the NEHA conference in January, 2008).
Effective way to remove Crypto
Just raising the chlorine level to a shock level of 40% of the CYA level is practically useless against Crypto. The equivalent FC with no CYA at this level is only 0.6 ppm so with the 15,300 CT value for Crypto this would be 15300/0.6/60/24 = 17.7 days for a 99.9% inactivation. The CDC recommendation is at least 20 ppm FC with no CYA for 12.75 hours or equivalently 10 ppm FC with no CYA for 25.5 hours. To achieve this latter equivalent with CYA in the water one needs to raise the FC to roughly 10 ppm more than the CYA level. If the CYA level is high, this becomes impractical.[3]
The filtration using a flocculant/coagulant to capture the oocysts in the filter and then backwashing to remove them will probably work to some extent but it's unclear as to the precise level of reduction that would be achieved. Even if there were 100% removal for passing through the filter in this situation, it still takes multiple turnovers since one turnover only filters 63% of the water, two turnovers filters 86%, three turnovers filters 95%, four turnovers filters 98%, five turnovers filters 99%, and it takes almost 7 turnovers to filter 99.9%. And this all assumed perfect mixing and circulation while in reality actual numbers are lower.
Ozone and UV systems are effective at killing Crypto, but have the same issues of needing good circulation and multiple turnovers. Since a relatively small amount of chlorine dioxide will kill Crypto in the bulk pool water overnight, I think that a periodic (weekly?) dosing would at least limit the exposure time if there are undetected fecal accidents and would also be viable after a known fecal accident and for pools that have CYA without resorting to excessive superchlorination. Unfortunately, there doesn't seem to be any manufacturer willing to step up to pay for the studies to get EPA approvals for this nor to do some studies to make sure it doesn't cause more problems than it solves.
There was a 2011 poster paper presented at the World Aquatic Health Conference (WAHC) last year from the CDC on measuring kill times for the more chlorine resistant bacteria Staphylococcus aureus and with the protozoan oocyst Cryptosporidium parvum. There were detailed graphs for the bacteria measurements and I created a model to account for the delay of chlorine oxidizing the thicker cell wall before disinfection/inactivation could occur. I also accounted for disinfectant demand. The model fit the data very well and then I ran into this paper that takes a different modeling approach.
Though the resulting formulas are a bit different, they end up fitting each other almost identically for the range of log reductions and times in the experiment. I also fit the actual inactivation time data at a fixed log reduction to a model where the chlorine bound to CYA had 1/100th the oxidation rate of hypochlorous acid (which I got from this paper a while ago) and the data almost perfectly fit. I sent all of this to the CDC and they thanked me for my interest and for the info, but we'll see if anything comes of it.
In case anyone is interested in the formulas, their paper's formula and the one I came up with have the following forms where PHI is the cumulative distribution function (CDF) of the standard normal distribution and the constants a,b and a',b' (and "k" in the disinfectant demand formula) are fitted to the experimental data:
the paper: log10 reduction = PHI( (a - b*t)/sqrt(b*t) ) mine: log10 reduction = PHI( a’ - b'*ln(t) )
To account for disinfectant demand, the "t" time variable is replaced with -(1/k)*exp(-kt) + (1/k) and though technically this is a C*t formula, the constant "C" gets combined with the other constants implicitly on "t" in the above formulas (i.e. "b" in the paper's formula and "a'" in my formula since ln(x*y) = ln(x) + ln(y)).
