Using hypochlorite dilution to measure pool volume

I'm not sure this is the right place for this post, so please feel free to move it.

I have a free-form, plaster & concrete pool, shaped like an ameba, with varying depths in different parts of the pool and a curved bottom. As a result it has proven difficult to accurately estimate the pool’s volume using conventional algorithms.

The estimate of pool volume has been a source of considerable disagreement with my (former) pool company, since I believed their calculations were too high and tended to amplify the amount of chemicals that got dumped into my pool! When I decided to look after the pool myself I felt it was essential to get a better estimate to minimize chemical additions.

When I obtained Ben’s testing kit and read the various posts about using regular bleach as a source of hypochlorite , I realized that it should be possible to back calculate the volume of my pool using proportions. Knowing the volume of bleach used, its concentration and measuring the peak concentration after dilution in the pool should provide an estimate of the volume of my pool.

The question I ask myself and now ask the experts from the forum is what are the sources of error and therefore how reliable is the result?

Data and calculation - I have performed this experiment a couple of times and come to approximately the same answer. I provide data for one experiment.

PoolVol= (Bleach Concentration * Bleach Vol *1,000,000) /FC change
PoolVol= 0.06*5.4375*1000000/11.5 = 28300 gallons

Pool data: pH 7.5, FC 3.5, CC 0,Alk 100, Cal 160, CYA 50, Temp 76F
Sampled from different parts of the pool after sunset.
1. 15 minutes after addition pH 7.8+, FC 14
2. 30 mins pH 7.8+, FC 16
3. 45 mins pH 7.5, FC 15 (pH corrected with muriatic acid)

Assumptions and sources of error
Chlorine consumption – assumed neither sun nor organics (CC=0) significant at this time
Dilution – Appears to occur within 30-45 minutes with liquid bleach. (Hayward 2 HP superpump turns over pool approx every 6 hours)
Measurements – 1230 gallons +/- per 0.5 ppm FC (i.e. per drop of FAS-DPD#2 solution at 10mls pool water)….in hindsight probably 25 mls would be more accurate
- 220 gallons +/- per oz bleach (not measured but assumed to have vol on label)
- 283 gallons +/- per 1% bleach (anyone know how often is store bought bleach is 6% exactly?)
Conclusion My pool company guestimated 40K gallons and I, using dimensional estimation, calculated about 35 K. The dilution method gives about 30K gallons.

Anything big I have missed? 30K seems about right, but I would value some thoughts from the forum.
:) Thanks

Welcome to the forum!

What I am about to say is still controversial, but here are some things to consider. This linked thread has some more details of what I summarize below.

First, with regard to the concentration of chlorine in bleach, the Material Safety Data Sheet (MSDS) for Clorox Regular Bleach says 6.15% while Ultra Clorox Regular Bleach says 6-7.35%. Such concentrations in an MSDS refer to the weight percentage (i.e. percent of the weight of the ingredient out of the total weight). The density is listed as approximately 1.1 (g/ml) as compared to your pool water which has a density closer to 1.0 (g/ml).

Second, the ppm of chlorine in pool water is for the disinfecting form of chlorine, namely HOCl, which has a molecular weight of 52.46 g/mole. However, the molecular weight of sodium hypochlorite is 74.4424 g/mole. This means that a weight of 74 units of sodium hypochlorite results in a weight of 52 units of chlorine in the pool.

So, in my opinion, the proper formula for calculating ppm from a volume of liquid chlorine is as follows:

(PoolVol) = (Bleach Frac. Conc.) * (Bleach Vol) * (Density in g/ml = kg/liter) * (1,000,000 mg/kg) * (52.46 g/mole HOCl) / (ppm = mg/liter) / (74.4424 g/mole NaOCl)

Using some of your numbers I get the following:

PoolVol = 0.0615 * 5.4375 * 1.1 * 1,000,000 * 52.46 / 11.5 / 74.4424 = 22,541 gallons.

If I use 7.35% for the high-end of Ultra Clorox Bleach then I get 26,939 gallons.

Since this is quite a ways off from your dimensional estimation then either something is wrong with my analysis or with the measurements or assumptions (concentration). I have a very accurate estimate of my pool volume since I measured all the dimensions when the pool had not yet filled with water so I should try a similar experiment to what you have done and see what happens. One problem is that I use the more concentrated 12.5% chlorinating liquid (from my local pool store) and it might be less accurate in its concentration measurement than Clorox Regular bleach.

[EDIT] It may be that the convention for ppm of Chlorine in a pool uses the "standard" of 100% being the amount of chlorine from chlorine gas (Cl2) in which case the molecular weight is 70.9064 g/mole for Cl2 and that is pretty close to 74.4424. If we use that instead, then for the 6.15% we get closer to what you got or namely 30,467 gallons. I will continue to investigate this, but if your measurements and estimates are correct, then this would imply that the ppm Chlorine number indeed refers to the chlorine gas as the "reference". [END-EDIT] [SECOND-EDIT] I found a source that says that indeed the ppm FC is indeed measured relative to Cl2 so the 30,467 gallon number is the right one and your calculations are quite close to the "accurate" way of doing it. The density and molecular weight ratio somewhat cancel each other out which makes your calculation and mine very similar. [END-EDIT]

Richard

Richard,

Thank you for your thoughtful analysis. You confirm my impression that this approach is also fraught with potential inaccuracies.

Of course the pragmatic answer is not to worry about the pool volume, but rather empirically build a data set by direct observation (which I have done), on the effect of adding different amounts of different chemicals . However I confess to now being entertained by the challenge of finding a better estimate of my pool volume for its own sake!

A few further thoughts and comments for your consideration:

As you suggest, it certainly makes sense when using proportions to represent ‘before’ and “after’ in the same units and also measure the concentartion ‘before’ and “after’ with the same test. The bleach I used was a supermarket's own brand (Shoprite), which is probably from the makers of Chlorox anyway, but presumably your point about it not being 6% still applies. At least for bleach it should be possible and probably be worth the effort to accurately measure the amount of bleach, and its strength with the FAS-DPD before it is added. I imagine this will involve taking a sample with insulin syringes and dilution etc.

I wonder if using another dilutional agent might provide more data to help triangulate this elusive pool volume estimate? Using calcium hypochlorite would seem to be a better choice than other possible compounds which are readily available, apprpriate to add to the pool and easily measurable, such as sodium bicarbonate, cyanuric acid, muriatic acid etc. What do you think?

I don’t know the selectivity and accuracy of Ben’s test for Ca but in theory it could offer more data....or more uncertainty!(assuming I could get Ca shock fully dissolved quickly). I’m also not sure how close the amounts of calcium hypochlorite represented on the package are to what is actually inside. Confirming this with measurment might be much harder with Ca shock before addition.

It looks like I need to go back and do a better estimte with dimensional analysis. Unfortunately i don't have the original architechural drawings of the pool to get an accurate surface area, but I think I could get a better idea using google earth to generate an accurate shape.

Finally I would be fascinated to see the results of your experiments with your own pool.

Thanks again for the stimulating response:)

[Ben, feel free to move this thread to The China Shop if it's too technical, though the point of just using rough measurements at some point is valid for all.]

With all of the "roughness" and inaccuracies of the testing methods and percentage of chlorine in chlorine sources, the estimate of "about 30,000 gallons" for you pool will be fine for figuring dosing amounts. At this point, if I were you I would just use the 30,000 number and then note if there seems to be a consistent undershoot or overshoot when you add chemicals to your pool. However, the only chemical you will be adding consistently to your pool will be chlorine (in whatever form).

Calcium Hypochlorite in most sources for pool use is 65-75% while sources for scientific (and some commercial) use it's 100%. It is true that it is less likely for solid calcium hypochlorite to breakdown and if you can find a source that has an MSDS (or labeling) that is accurate, then this would give you a more accurate chlorine concentration value. Then you would have to adjust for the molecular weight of Ca(OCl)2 which is 142.98366 vs. Cl2 gas of 70.906, but then also have a factor of 2 since there are two OCl in each Ca(OCl)2. Lo and behold -- 70.906 * 2 / 142.98366 = 0.992 so you can pretty much just treat the "weight" of calcium hypochlorite as equivalent to the ppm "weight" of FC. Just convert the weight to milligrams and divide by the volume of your pool in liters to get ppm (mg/l).

As for sodium bicarbonate, the conversion of it into alkalinity is not straightforward since this is dependent on the pH of your pool. Only the bicarbonate that remains HCO3- directly contributes one-to-one to TA. At a pH of 7.5, about 5% of the sodium bicarbonate (NaHCO3) that you add (molar percentage) is converted to H2CO3 which does not contribute to TA (and a very small amount is coverted to CO3(2-) which contributes double its amount to TA). At a pH of 7.0, about 15% of the sodium bicarbonate you add (molar percentage) is converted to H2CO3 and is not counted towards TA. Converting from sodium bicarbonate to TA also requires the conversion factor of (100.0892 g/mole CaCO3) / (84.0069 g/mole NaHCO3) / (2 CaCO3 TA / NaHCO3 TA) = 0.596 since TA is measured in units of ppm of Calcium Carbonate (which has twice the TA molecule for molecule as NaHCO3 due to CO3(2-) being able to take two hydrogen).

The Cyanuric Acid (CYA) appears to be 100% pure, but the turbidity test is not very accurate.

Muriatic Acid (31.45% HCl) and possibly Borax would be accurate sources, but their effect on pH in pool water is dependent on the TA (and CYA since CYA also acts as a pH buffer) and the pH test is not very accurate (+/- 0.1 or possibly 0.05 if you are really good) unless you were willing to force your pool to have rather large pH swings.

I hope I have impressed upon you the hopelessness of trying to get an "accurate" answer for the volume in your pool just by using chemicals added to your pool. And this is coming from someone who just loves being accurate!:D

Richard

Interesting discussion. I kept track of the water meter during the first fill.

Since Chlorine % is based at the time of manufacture and decreases during shipment/storage, I don't think it is a good starting point from which to determine your pool volume.

If your pH drifts considerable, you could wait until it gets to one extreme, and see how much Muriatic Acid it requires to get to the opposite extreme. Or similiar with CYA.

If you have an SWG, do the same with ppm of salt.

If at next years opening significant adjustments are required, you may get better results.

Also don't forget that depending you your test kit, the measurements themselves are not exact values.

Don't know if your pool is a constant depth, or is sloped so please bear with me. Why not take a water meter reading (and make sure no water is being used in the house) and then measure the level in the pool - now add exactly 2" of water to the pool, then go read the water meter. (2" is an arbitrary number - you pick what you want to do.) This information will tell you how many gallons per inch to your pool. If the bottom is sloped you can use basic trig to figure its realative size. I think this method will be far more accurate than using titration results with reagents that are not of exact concentrations.

For instance I know that my pool is almost exactly 500 gallons to the inch.

Framcus, welcome to the forum! Your and Richard's discussion went a little over my head, but I'll try to offer some practical advice :D
Since the shape of the pool (and it's bottom) precludes a 'plug and chug' number, do what we pool dudes have been doing since the first pool was built - guestimate. Run the numbers with your best guess as to depths and areas and get a good approximation of the gallonage, then use 'trial and error' to make chem adjustments (and follow the first rule of pool dosing: "add less than what you think you need" - you can always add more to get where you want). Also, please keep in mind that there is a fairly forgiving range of 'acceptable (optimal) levels' for the various parameters of pool chemistry - use your guestimate as a starting point and, through keeping a journal, adjust the suspected gallonage accordingly.
While it would be more satisfying to KNOW the exact gallonage of the pool, sometimes you just need to be satisfied in knowing that 5 lbs of baking soda will raise your total alk 10 ppm. Don't loose track of the fact that the end result; having water that is clear, sanitary, not gonna hurt the pool nor equipment and a swimmable, hastle-free pool, is what's really important!!
Again, welcome to the forum - I suspect that you'll be a great source of knowledge, though I shudder to think about the headache I'll get if you, Richard, Evan, Steven, Pat, Michael & the rest all post on one thread :eek: