How to determine needed FC ppm to cover being out of town or FC loss rate

[3dogowner]

Seems to be a common problem that people have to work and that not all pools or spas have an in house "pool boy" to do daily testing and add chlorine. So if anyone out there is interested, this is what I'm going to experiment with for the next few weeks....based on the calculation to determine compound interest, I think I can estimate how much to bump my chlorine to hold my spa over while I'm gone.

The basic compound interest formula is as follows:
future value = present value multiplied by [(1+interest rate) raised to the nth number of time intervals]

For this purpose, I juggle the equation to give this:
present value = future value divided by [(1+interest rate) raised to the nth number of time intervals]

example:
present value is the goal ppm for the night prior to leaving town
future value: high end of FC range you want to come home to..... for instance, you might pick 4 ppm from the 2-4 ppm range associated with a CYA of 30 or 3 if you have a CYA of 20 (FC range 2-3).
the interest rate in this case is your pool or spa's current baseline 24 hr chlorine loss..... for some spas, that may be as much as 25% and is as good a place to start as any. Because it is a loss and not a gain, the rate is subtracted from 1.
the number of time intervals may be the number of days you will be out of town....for instance, from Sunday to Wednesday night, the time interval is three (3) 24 hr time periods, so that is 3.

So, if tonight is Sunday and I want to come home to a spa with a FC of 4 ppms on Wednesday, and my spa's current rate of loss is ~30% (don't ask, look up my other posts ;-)), then the goal ppm I want to get to tonight is:
goal ppm= 4 / (1-30%) raised to the 3rd
goal ppm = 4 / (0.7x0.7x0.7)
goal ppm = 11.67 or roughly 12 ppm

So, if my current ppm is say 3 ppm, then using PM, for my 390 gallon spa, I would add 5.3 oz of 8.25% bleach to bump to ~12 ppm. Then if my 24 hr chlorine loss holds true to ~30%, when I get home Wednesday night, my FC pre-use should be about 4 ppm.

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Likewise, this formula can also be used to determine your loss rate as follows:
loss rate=1 minus the nth root of (future value divided by present value)
multiple the loss rate by 100 to give your percentile.
nth roots can be calculated here: http://www.calculatorsoup.com/calculators/algebra/radical.php

example:
Sunday aka present night - 6 ppm
Thursday aka future night - 2.5 ppm
number of nights or 24 hr intervals - 4
loss rate = {1- [4th root of (2.5/6)]} x 100
loss rate = {1-[4th root of 0.417]} x 100
loss rate = {1-0.8} x 100
loss rate = 20%

Comments or suggestions welcome.

 

[3dogowner]

If no one is in the pool/spa, is there a problem with each week elevating the FC above the shock level noted for a particular CYA? - I'm not doing a shock, just trying to determine an amount that I can put in to cover at the most 7 days......(see above).

 

[pooladdict]

Interesting post, I know I tried to stretch out my testing on my spa, only to find out my demand changed quite often. Resulting in higher then expected levels x days when I went in spa. The most I could do and consistently have low entry levels was 3 days.

 

[chem geek]

Your analysis and formulas are correct. The formula for FC as a function of time given a daily loss rate percentage is the following:

FC = FC₀ * (1 - DailyLoss%/100)^Days

so as you indicate the needed starting FC₀ is as follows:

FC₀ = FC / (1 - DailyLoss%/100)^Days

and the loss rate percentage is given by:

DailyLoss % = 100 * (1 - (FC/FC₀)^(1/Days))

For one week (7 days) the following table shows the ratio of starting to ending FC for different daily loss rates:

Daily Loss % . FC Ratio
..... 5% ............. 1.43
... 10% ............. 2.09
... 15% ............. 3.12
... 20% ............. 4.77
... 25% ............. 7.49
... 30% ........... 12.14
... 35% ........... 20.40
... 40% ........... 35.72
... 45% ........... 65.68
... 50% ......... 128.00

So if your daily loss is too high, then it is impractical to be able to raise the chlorine level enough to last a week. The pool services that use chlorine gas and/or chlorinating liquid once a week and do not use any Trichlor usually have the CYA level up at 100 ppm or more to minimize loss from sunlight such that the daily loss is around 15%. They raise the FC to 14 ppm and end up with around 4-5 ppm at the end of the week. If a pool is instead losing 25% per day, then if the CYA were 50 ppm so that the minimum FC is 3.75 ppm, then you'd have to raise the FC to 28 ppm so would be starting even higher than normal shock level. However, the daily loss rate is often higher than 25% and is closer to 50% unless the CYA level is higher.

In a spa, one can start one's soak at 1-2 ppm FC so at 25% loss starting with 8-15 ppm FC (with around 30-40 ppm CYA) is plausible, but if one has an ozonator which usually results in 50% or more per day chlorine loss, then one cannot add chlorine only once a week. The rate of loss in a covered spa is a function of the water temperature so letting the water cool off helps. Note that in a spa, the largest demand by far is from bather load so the formula above only works for the background chlorine demand in between uses. You have to add sufficient oxidizer after your soak to handle the bather load. Additional chlorine is then needed to last through to the next soak.

The main downside with large FC swings is that when the FC/CYA ratio is high then the higher active chlorine level is reacting with pool/spa covers and equipment faster. It also ends up using more chlorine than more frequent dosing so it's more expensive.

In my own pool with a mostly opaque cover and warm 88ºF water temperature, the daily loss rate with the pool being used every day for an hour or two is in the 20-25% per day range (around 1 ppm FC per day) while if the pool is not used the loss is closer to 15% per day (around 0.7 ppm FC per day). I'm able to add chlorine twice a week, but I wouldn't add it only once a week since the swing would be much higher having to start with 17 ppm FC to end up with 3 ppm FC (with 40 ppm CYA).

 

[3dogowner]

If you're not going to be there for 7 days, would it not be more appropriate to estimate your starting ppm based on your no-user, covered rate of 15% per day? That would require only a starting level of ~9 ppm, rather than the 17 ppm based on an ~ 22.5% (20-25%).

Your daily loss % - FC ratio chart is the best arquement to date for me to not wait until January to dump my spa and clean the remaining Baqua goop out of those pipes......the Aww-some is sitting here on the desk.
Speaking of which, having converted from Baqua to chlorine, the cost of chlorine is really, really cheap (it's all relative), so I don't think of the extra chlorine as a $$$ issue at all.

Curious - how do you think the effect of my dropping my spa temperature from 98F to say 88F would effect the background chlorine loss, all other things being equal? and my pool from 88F to 79F? Both would be ~10% drops in temperature.

 

[chem geek]

That 15% would only be applicable in a spa at lower water temperatures, not if you were to keep it hit at 95-104ºF. Spas tend to stay warm from the pump, though usually in the 80's. This also assumes no ozonator. With an ozonator, the ozone reacts with chlorine depleting it much more quickly -- often by 50% or more per day.

A 13ºF drop in temperature will roughly cut the chlorine loss rate in half. 98ºF to 88ºF may cut the chlorine loss by 0.5^(10/13) = 41% so a 25% chlorine loss would become 15%. A drop in temp from 88ºF to 79ºF may cut the chlorine loss by 0.5^(9/13) = 38% so a somewhat smaller drop in chlorine loss. The actual formula follows the Arrhenius equation, but for the temperature ranges we are looking at this approximates well to the linear temperature drop leading to a proportional chlorine loss drop. Over a 40ºC range, the error of this approximation is only around 2%.

 

[3dogowner]

Wow, that minor a temperature drop in my spa, 98F down to 88F, might be worthwhile, as it would allow for a smaller FC swing, and would be quickly regained upon returning home. A slightly smaller drop in the pool might be worth considering, but maybe not, as my rinky dinky Gecko Controller In.XE only has a little-itty bitty heater (4.0 Kw)and it would likely take more than a day to regain 10F (esp now that this Artic front is effecting even our corner of the country).