Drain & Fill Question

[chem geek]

Carl,

If you use a sheet to separate the fresh water that has no CYA from the pool water you are diluting that has CYA, then you are right, it doesn't matter how much drain or refill you do in what combination because there is no mixing of these two waters until you are finished adding and removing the total amount.

However, if you do not use a sheet and allow the water you are adding to mix with the existing pool water (say, by draining from one end of the pool while simultaneously filling from the other end, all while the pump is running), then it will take more water to achieve the same dilution compared to the sheet method.

A simple example will demonstrate this. Let's use your numbers of a pool with 20,000 gallons and 100 ppm CYA and you have fresh water you can add that has no CYA in it. If you want to get 50 ppm CYA then using a sheet to separate the fresh water from the pool water, you only need 10,000 gallons for dilution. However, let's do the dilution allowing the water to mix and let's do it in two steps with 5,000 gallons each. So, do the following:

1) Start with 20,000 gallons at 100 ppm CYA
2) Drain 5,000 gallons so you have 15,000 gallons at 100 ppm CYA (remember "ppm" is a concentration so draining doesn't change this, though evaporation would)
3) Add 5,000 gallons of fresh water. This gives you (5,000*0 + 15,000*100)/20,000 = 75 ppm CYA in 20,000 gallons
4) Drain 5,000 gallons again so you have 15,000 gallons at 75 ppm CYA
5) Add 5,000 gallons of fresh water. This gives you (5,000*0 + 15,000*75)/20,000 = 56.25 ppm CYA

Notice that replacing 10,000 gallons of water in two drain/refill steps only gets you to 56.25 ppm CYA and not 50 ppm CYA as you would get in one 10,000 gallon drain/refill step. If you replace less water each time and have more replacements, then you will get even less dilution. Notice that the formula is really

( (20,000 - 10,000/N) / 20,000 )^N * 100

where "N" is the number of water replacements. So doing only 100 gallons at a time would be 10,000/100 = 100 water replacements

( (20,000 - 10,000/100) / 20,000)^100 * 100 = 60.577 ppm CYA

"e" is defined as the limit of (1 + 1/N)^N as N goes to infinity so you can see the similarity of this with the above formula since the above formula in the limit as N goes to infinity (i.e. continuous dilution) is just e^(-0.5) * 100 = 60.653 ppm CYA which you can see is quite close to what happens with 100 water replacements.

The natural logarithm in the formula in my earlier post comes about because we are solving for how much fill water is needed as opposed to starting with a certain amount of fill water and solving for the dilution result.

Richard

[CarlD]

Richard:
I'm aware that if you drain off 200 gallons, then refill, your concentration of CYA changes. The next 200 gallons you drain will have a lower concentration so the refill will give you less "bang for the buck".

I deliberately decided to ignore that problem as it soon becomes an exercise in differential calculus--which I never use for fun or hobbies! I deliberately kept it SIMPLE for clarity.

I wanted to get to the REAL point: with excessively high CYA you cannot try to drain a little, then add a little to be effective.

Sometimes, trying to be very, very accurate causes you to obscure the REAL message and the real answer, so you have to watch for a "forest and the trees" situation: With excessively high CYA, if you want to lower it you must do a large drain and refill. Period.

The object is to give NJPool an effective option.

[chem geek]

I wanted to get to the REAL point: with excessively high CYA you cannot try to drain a little, then add a little to be effective.

OK, I got it. The main takeaway point I wanted to make was that if you want to do significant dilution, especially more than 50% (if you have very high CYA over 100, for example), then using a sheet or silage tube uses much less water and is much more efficient (for water usage, though obviously takes more effort). I just thought the 100 gallons 100 times (to get 10,000 gallons) would be misleading and let people think they didn't need to use the sheet method to be efficient. However, for just a 50% dilution, doing it continuously is certainly a reasonable option and is "close enough" to help get the CYA lowered (going from 100 to 61 isn't that far off from the goal of 50). If the goal was to go from 100 ppm to 25 ppm, then a continuous drain and refill of 75% of the pool water only gets you to 47 ppm. I'm sorry I was so picky.

Personally in my own pool, I dilute it each winter with winter rains filling in and overflowing (to a sewer drain) and that's a continuous method, but since I'm not paying for the water I don't care that it's not efficient (our water is very expensive where I live and is sometimes under restriction). I do this to continually refresh the water each season. I do need to add some more calcium, bicarbonate, and CYA when I open up in the spring. Now that I'm not using extra chemicals (non-chlorine shock, clarifier, polyquat algicide, de-foamers, etc.), this refreshing of the water probably isn't necessary.

Richard