Pool Water Chemistry (Warning: Can Get Technical)

[chem geek]

This thread presents my findings so far on pool water chemistry including the following:

1. More Accurate Calcite Saturation Index (CSI) to replace Langelier Saturation Index (LSI)
2. Calculation of ppm HOCl (disinfecting chlorine) at various levels of Total Free Chlorine (FC) and Cyanuric Acid (CYA)
3. Determination of pH and Alkalinity changes when adding chemicals to the pool
4. Various reaction rates including chlorine breakdown by UV

Disinfecting Chlorine (HOCl) vs. Total Free Chlorine (FC) and Cyanuric Acid (CYA)

The most important finding was how little disinfecting chlorine (HOCl) is left after chlorine combines with Cyanuric Acid (CYA) to get "stored" as chlorinated cyanurates (aka cloramides). The chart at the following link shows this relationship. (I recently discovered that all forms of chlorine are measured as ppm equivalents of chlorine gas, so all charts, graphs and the spreadsheet have now been updated to reflect this.)

HOCl Chart

Note that the red in the linked chart above represents a cutoff of 0.011 ppm HOCl which roughly corresponds to the 650 mV ORP level that the U.S. and WHO set as the minimum required for disinfection. The green color is a guess at 0.05 ppm HOCl of the minimum level of chlorine needed to prevent algae. The actual number may be quite different, from 0.02 or less to 0.1 or more, but based on Ben's "Best Guess CYA Chart" which is based on real-world experience, I suspect the actual number will be somewhere in this range. So, red means bacterial growth while green means possible algae growth. Blue is the safe area.

The following shows this same data in graphical form with lines showing the same two (probably correct) "bacteria" and (totally a guess) "algae" levels.



The following is an approximate formula you can use so long as your CYA ppm is at least 5 times your FC (the formula really falls apart terribly below a ratio of CYA/FC of 3).

(HOCl as ppm Cl2) = (FC as ppm Cl2) / ( 2.7*(ppm CYA) - 6.6*(FC as ppm Cl2) + 6 )

and if you are interested in the FC for a given HOCl (to construct the equivalent of Ben's table, for example), you can use the following which just solves for ppm FC from the above.

(FC as ppm Cl2) = ( 2.7*(ppm CYA) + 6 ) / ( 6.6 + 1/(ppm HOCl) )

The constants in the above formulas are for a pH of 7.5 (which is the only parameter that significantly affects these constants). With the spreadsheet I can easily calculate the constants for other pH, but remember that the above formulas are approximate. For example, with FC of 3 and CYA of 15 the formula gives HOCl as 0.112 when the correct answer is 0.095. That's not terrible (about an 18% error). However, with FC of 5 and CYA of 15 the formula gives HOCl as 0.370 while the correct answer is 0.199 (about an 86% error) which isn't very good.

A rough rule of thumb that applies at a pH of 7.5 is that the effective chlorine level is reduced by a factor about equal to the ppm of the CYA. So, a CYA of 30 ppm reduces the disinfecting chlorine (HOCl) level to about 1/30th of what it would be with no CYA.

The inverse of the above chart may be seen at this link:

FC Chart

The chart columns from 0.02 to 0.1 ppm HOCl roughly correspond to "Ben's Best Guess CYA Chart". Ben's chart converted to show HOCl may be found here where you can see that the rough Min FC corresponds to 0.03 ppm, the rough Max FC corresponds to 0.07 ppm (implying an ideal target of 0.05 ppm) and the shock table is not consistent, but probably implies a minimum of 0.3 ppm, at least for green algae. User experience indicates that hard-to-kill yellow or mustard algae (and maybe black algae) may need 1.0 ppm HOCl for shock. User experience with black algae indicates that keeping active black algae from growing requires around 0.07 ppm HOCl.

A comparison of the "traditional" HOCl/OCl- graph with the same graph in the presence of CYA may be found at this post. This also shows how CYA is a "chlorine (specifically HOCl) buffer" that makes HOCl concentration about half as sensitive to changes in pH.

The original source for the equilibrium constants was done in 1973 (and published in 1974) where the recommended maximum CYA level was 25 ppm:

J. O'Brien, J. Morris and J. Butler, “Equilibria in Aqueous Solutions of Chlorinated Isocyanurate”, Chapter 14 in A. Rubin, ed.,
Chemistry of Water Supply, Treatment and Distribution, 1973 Symposium, (published 1974), Ann Arbor Science, Ann Arbor, MI, pp.
333-358.

[EDIT] See document here. [END-EDIT]



A Little CYA Goes A Long Way

NOTE: The mechanism of protection of chlorine from sunlight by CYA is currently under review in this thread. Higher CYA levels may protect even proportionately higher levels of chlorine more, especially in deeper pools.

The following is a graph showing that a large amount of the benefit of CYA protection of chlorine from UV (sunlight) is already there at around 20 ppm. This data is approximate, not only because it is dependent on the amount of sun exposure, but because the rate constants themselves change with FC level (because there is a mix of two different rates of destruction -- one from HOCl and the other from the chlorinated cyanurates which are more stable, but still breakdown from sunlight). The limiting half-life for HOCl/OCl- is 35 minutes which is consistent with pool studies, but some experimental studies give 11.6 minutes. The limiting half-life of the chlorinated cyanurates is 8.4 hours though some other data shows it could be 6 hours.



The following graph combines the two concepts of needing more chlorine at higher CYA vs. the greater protection of chlorine by CYA. The graph shows the total chlorine (FC) loss rate in ppm/hour vs. CYA at different HOCl levels. Remember that this rate of loss will slow down as chlorine gets used up. Nevertheless, the absolute loss of chlorine is greater at higher CYA levels (keeping HOCl constant) and is the downside to a "high CYA & high Chlorine" approach. However, the primary reason to have higher CYA and Chlorine is to have a sufficient buffer of chlorine to prevent it from dropping to dangerous levels. There is obviously a tradeoff here. Though using no CYA results in the least amount of chlorine loss, the fact is that you simply can't maintain a pool with only 0.05 ppm chlorine everywhere in it -- hence a minimum level is needed as a buffer.



Salt Water chlorine Generation (SWG) pools seem to require a higher level of CYA, about 70-80 ppm, to operate efficiently. The theory is that the CYA is slow to "store" the chlorine as it is being generated so without enough CYA there is a build-up of chlorine that degrades the performance of the salt cell. I would prefer that the SWG manufacturers offer a larger lower-power (per length) cell that would work efficiently at lower CYA concentrations.

pH Rising

If you find that your pH wants to keep rising, this may be due to your pool outgassing CO2 to the air. The rate of outgassing increases with lower pH, higher alkalinity, and aeration of water (splashing, water fountains or slides, high wind, jets pointed up, etc.). The aeration of pool water is a physical process that will vary greatly from pool to pool, but the following chart shows the relative outgassing rate as a function of pH and Total Alkalinity. It is possible that the hydrogen gas bubble production from SWG systems contributes to significant aeration and is a source of rising pH in such SWG pools. The rate is actually a function of Carbonate Alkalinity so this chart is for a CYA of 30, but the variation with different amounts of CYA is not large. Note that there is a large variation with pH (the Y-axis is logarithmic). I have drawn a somewhat arbitrary "Limit" line at a relative rate of 15 that I have found is roughly the tolerance limit where many people start complaining about rising pH, but again aeration is a factor I cannot predict.

CO2 Chart



Spreadsheet For Detailed Calculations

The link to the spreadsheet (in a ZIP file) that calculates all of the above data is PoolEquations.zip and was last updated 29-Jul-2010. It also does some of the things that BleachCalc does, but is not for novice users.

Also see Equations for Chlorine Chemistry.

Also see Oxidation-Reduction Potential (ORP) vs. HOCl

(I will continue to edit this post to add more detail and discussion.)

[stualden]

These are great - personally I find I need to stare at them quite a while to grasp them (I guess it's because you're dealing with 3 variables on two-dimensional graphs) but they convey more than words can.

Just a couple comments / question for clarification:

--What are the numerical values corresponding to "algae" and "bacteria" on your first graph? Do they correspond to the colors of the numbers in the table (i.e., red is below bact, green is above algae, black is in between)? Do these levels of HOCl correspond to particular levels of "oxidizing power" or "disinfecting power" that we commonly see quoted?

--Taking that algae line as a given, I read (roughly) the following minimum chlorine PPM for various CY PPM:

CYA..........Chlorine
5...........1
10..........2
20..........3
30..........4
50..........6

(Could you do another graph or chart which transforms the data into this format?) Unfortunately, these look even a bit higher than Ben's chart - discouraging!

--On the second graph, would you say the "take-away" is really that most of the chlorine-retention benefit of CYA is *already there* by 20 ppm, rather than "starts at" 20 ppm?

--The "no CYA" and "infinite CYA" entries are really points, right, not horizontal lines? (Hard to show clearly on this graph, though, I'll agree.)

--You talk about the "half-life" of chlorine, which gets at a concept you mentioned in that other post and I asked about there. I'm assuming that half-life here means the time in which the free chlorine ppm drops to 50% of what it was before. Perhaps you could also recast this graph to illustrate your point that "with twice as much chlorine, you lose it twice as fast." To me, this emphasizes the "double gotcha" with CYA - it forces you to bring your chlorine levels higher, which in turn means that your chlorine loss each day will be higher.

Thanks.

[chem geek]

These are great - personally I find I need to stare at them quite a while to grasp them (I guess it's because you're dealing with 3 variables on two-dimensional graphs) but they convey more than words can.

Just a couple comments / question for clarification:

--What are the numerical values corresponding to "algae" and "bacteria" on your first graph? Do they correspond to the colors of the numbers in the table (i.e., red is below bact, green is above algae, black is in between)? Do these levels of HOCl correspond to particular levels of "oxidizing power" or "disinfecting power" that we commonly see quoted?
Yes, below the "bacteria" line are red numbers in the chart and above the "algae" line are green numbers in the chart. The "bacteria" line corresponds to 0.011 ppm HOCl which appears to be about 650 mV ORP which is the minimum standard for disinfection in the U.S. and by WHO (though Germany has higher standards). I will add more data to my post to support this assertion, based on the Oregon Commercial Spas Study. However, the "algae" level is a guess since I cannot find good data to determine the level of chlorine needed to inhibit all algae, so I set an agressive level of 0.05 ppm HOCl. The real number could be 0.03 or less, or 0.1 or more, but given that Ben's table is based on reality, the real number is probably somewhere between 0.02 and 0.1 which correspond to the ranges in Ben's table (for the most part -- the shock section is the most inconsistent). I have been in communication with Ben on this and eventually he'll update his tables, but we want to get more real-world experiences from users first -- I plan to start another thread (non-technical) to get such data.

--Taking that algae line as a given, I read (roughly) the following minimum chlorine PPM for various CY PPM:

CYA..........Chlorine
5...........1
10..........2
20..........3
30..........4
50..........6

(Could you do another graph or chart which transforms the data into this format?) Unfortunately, these look even a bit higher than Ben's chart - discouraging!
See my response above. The 0.05 ppm HOCl level I set for "algae" is a guess so don't be distressed by it. Ben's table has low to high ranges that are roughly 0.02 ppm HOCl to 0.10 if you take combinations of "high chlorine & low CYA" to "low chlorine & high CYA". Please do not change any dosing behavior away from Ben's chart unless you are willing to take risks. Though I believe you will be fine from a disinfection point of view, we simply do not know enough about the algae prevention level to make a determination. You also don't want to "run out" of chlorine at any time, so Ben's approach of having a sufficient "buffer" of chlorine (stored in chlorinated cyanurates) is both conservative AND prudent.

--On the second graph, would you say the "take-away" is really that most of the chlorine-retention benefit of CYA is *already there* by 20 ppm, rather than "starts at" 20 ppm?
Yes, that is better phrasing and I will edit my post accordingly. Thank you.

--The "no CYA" and "infinite CYA" entries are really points, right, not horizontal lines? (Hard to show clearly on this graph, though, I'll agree.)
Yes, this is also true. Perhaps I can "truncate" the lines and/or dash them so that they look more like asymptotes which is what they represent.

--You talk about the "half-life" of chlorine, which gets at a concept you mentioned in that other post and I asked about there. I'm assuming that half-life here means the time in which the free chlorine ppm drops to 50% of what it was before. Perhaps you could also recast this graph to illustrate your point that "with twice as much chlorine, you lose it twice as fast." To me, this emphasizes the "double gotcha" with CYA - it forces you to bring your chlorine levels higher, which in turn means that your chlorine loss each day will be higher.
This is true, though I'm not sure how to graph this combination. Perhaps I can target a fixed ppm HOCl level and then the graph will show the relationship between FC and CYA that produce that HOCl level. On the same graph I can show the half-life of FC as a function of CYA (so CYA will be the X-axis and FC and half-life will be Y-axes). I'll try something and you (and others) can give me feedback/suggestions.

Thanks.

Thanks a million for you comments, questions, and suggestions. I have only just started this post and will add more and hopefully make things clearer. Right now I'm going to add a link to the spreadsheet that is sure to scare the bejesus out of most people! I'll also explain how the HOCl table and graph are only for a pH of 7.5 and will also post approximate formulas for calculating HOCl or FC given CYA levels.

[haze_1956]

If I understand the first chart correctly.

Red numbers denote - Level to low to kill bacteria or algae

Black numbers denotes - no bacteria but algae possible

Green numbers denotes - algae also killed.


If this is the case, perhaps you should switch the Black and Green colors.
A small point I know, but most people will associate the color green with algae growth. And it should help a layman to comprehend the chart.

[chem geek]

If I understand the first chart correctly.

Red numbers denote - Level to low to kill bacteria or algae

Black numbers denotes - no bacteria but algae possible

Green numbers denotes - algae also killed.


If this is the case, perhaps you should switch the Black and Green colors.
A small point I know, but most people will associate the color green with algae growth. And it should help a layman to comprehend the chart.

Yes, you understand the chart correctly. I was thinking of red being "bad" and green being "good", but I see your point that green, in the context of pools, probably means algae to most people. I'll change the colors in the table when I make some other changes I'm working on.

[haze_1956]

in the context of pools, probably means algae to most people

I personally made the "green means algae" association so I mentioned it.

But now you have me thinking completely in context of pools. How about these for full visual association?

Red = Germs
Green = Algae
Blue = Clean water

.

[jereece]

This data is very interesting. Thank you for doing this research.

I downloaded the Excel spreadsheet and began playing with it. Only problem is when I click on the "Calculate pH/TA" button, I get an error message "Compile Error - Can't find project or library". When I click OK, it takes me to the debugger. It highlights "SolverReset" in the "Sub Calculate_pH_TA_FC_CYA()" section of Module1. Any idea what the problem is on my end?

Thanks,
Jim

[chem geek]

This data is very interesting. Thank you for doing this research.

I downloaded the Excel spreadsheet and began playing with it. Only problem is when I click on the "Calculate pH/TA" button, I get an error message "Compile Error - Can't find project or library". When I click OK, it takes me to the debugger. It highlights "SolverReset" in the "Sub Calculate_pH_TA_FC_CYA()" section of Module1. Any idea what the problem is on my end?

Thanks,
Jim

Jim,

You might have downloaded the spreadsheet before I edited my post to give the following instruction:

The “Pool Equations” spreadsheet uses macros to compute the reverse computations (calculating pH and alkalinity when you add chemicals) so to get this to work on a PC using an older version of Excel you will need to go into your “Tools – Add-Ins...” menu in Excel and check the box for “Solver Add-In”.

The error you are getting sounds like the Solver toolpak is not installed so try adding it in as I describe above and let me know what happens.

Richard

[jereece]

I am using Office 2003, the latest version. I have all the addins turned on, including "Solver Add-In" and still get this error.

[chem geek]

I am using Office 2003, the latest version. I have all the addins turned on, including "Solver Add-In" and still get this error.

I'm sorry you are having trouble getting it to work. I created it on a Mac in Microsoft Excel 2004 for Mac Version 11.2.5 (060620) and I also tried it on a PC that has Microsoft Excel 2000 (9.0.6926 SP-3) running Windows 2000 Professional. It worked for me on the PC though I had to add the Solver Add-In and I also had to change the security level to Medium and accept the warning about macros running.

[EDIT]I have been very frustrated with trying to get Solver to work consistently when running from a macro on the PC. So, I'm going to delete my later posts that tried to explain workarounds since they are a pain and may not work. Instead, I'm going to try to rewrite the macro to do the Solver function myself. I've only got two "goals" with two "variables" so that shouldn't be too hard to do with a 2-variable partial differentiation (Newton-Raphson) approach. I hope that doesn't end up being as hard as it sounds![END-EDIT]

[SECOND-EDIT] Since around 8/23/06 (see later posts) Solver is no longer used. [END-EDIT]

Richard