Daily Water Changes and the Mathematics

[d2mini]

No, this is not a new punk rock band.

I was having a conversation with someone about how daily changes computes into a total monthly water change volume. I know Randy Holmes-Farley touched on this but I can no longer find his water change article. I'm wondering if there is a formula where you can input how many days per month you are doing water changes, how many times each day and the volume of water changed out each time in order to come up with a number that represents the total volume changed out over the course of a specified amount time (like a month) that would be equal to doing one single large water change.

In other words, if I change out 3% per day, I don't believe that is the same as changing out 90% (3x30 days) over the course of a month. Or is it? We have to take dilution into consideration.

But I'm horrible at math so I'm looking for help. I know this topic has been discussed before but I'm having trouble finding the answer.

The only thing I've been able to find is this quote from Randy's article...
"These changes are slightly less efficient than single batch water changes of the same total volume. A continuous water change of 30% exactly matches one batch 26% water change. "

TIA!

 

[medic155]

They way it would work out, I believe, is that if you change out 3%, you would have 97% old water left. The next day, you would have 94.09% old water left, 2.91% of the day before's water, and 3% new water. The next day, you would have 91.2673% old water, 2.8227% 1st day, 2.91% 2nd day, and 3% new water. It would continue on down the line. Taken like this, after one week you would have ~85.73% original water doing 3% daily changes, versus a one-time 20% water change leaving only 80% original water. Does that make sense?

 

[d2mini]

Yup! I think we are on the exact same wavelength here.

Now what is really beyond anything my admittedly pea-sized brain can understand... is there a mathematical formula that could be put together to do these calculations for us? So someone could just input the amount of water and the frequency to come up with the "adjusted" total over the course of a given time period?

 

[Eud]

It's like an amortization calculation

Water changed = total volume x (1 - ( 1 - (daily removed/total volume))^days)

So in your tank assuming 3% water change per day in a week you'd get

Changed = 325 x (1-(1-(0.03))^7) = 62.4 gallons of new water in a week.

Where doing a 21% wc once a week would give you 325x.21 = 68.25 gallons

 

[medic155]

That, my friend, is beyond my ability lol. I'm sure there is a way to do it, but seeing as I never took calculus, I am at a loss.

 

[d2mini]

That, my friend, is beyond my ability lol. I'm sure there is a way to do it, but seeing as I never took calculus, I am at a loss.

LOLOLOL!!!!! Me too!!!
But I will pass along Eud's info (thank you, Eud!!!) to my friend and see what he can come up with.

 

[5pacey]

I don't believe its that simple actually... because this assumes that if you change 3% today... that 3% stays clean until tomorrow, when you change the next 3% and so on. In effect meaning that all the new water being progressively added into the system (after the old water is taken out) stays clean for the duration of the period of measurement (for example a month). This is clearly false, since the water changed today is a) going to dilute the current 97% of old water, and b) it, itself will be polluted by the system output produced between today and tomorrow. IOW, it will not be as clean tomorrow as it is today right after the change because the system never stops generating pollution.

Spacey

 

[jkapit]

Here you go. Everything you wanted to know about water changes....

http://reefkeeping.com/issues/2005-10/rhf/index.php

 

[worm5406]

http://www.reefcentral.com/index.php/rodi-calc

 

[wooden_reefer]

For the sake of removing matters, the math favors less frequent but more percentage change.

 

[keithhays]

This is the calculator I use just factoring in water: http://www.hamzasreef.com/Contents/Calculators/EffectiveWaterChange.php

This one will factor in a substance in decline such as nitrate starting 100ppm and accumulating at .5ppm, etc.
http://www.hamzasreef.com/Contents/Calculators/EffectOfWaterChanges.php

 

[keithhays]

The cool thing about the second calculator is that it will let you know given a specific water change amount everyday where you will stop i.e. most of the time you will never end up with zero ppt of any accumulate in the water.

 

[Charlene]

This is the calculator I use just factoring in water: http://www.hamzasreef.com/Contents/Calculators/EffectiveWaterChange.php

This one will factor in a substance in decline such as nitrate starting 100ppm and accumulating at .5ppm, etc.
http://www.hamzasreef.com/Contents/Calculators/EffectOfWaterChanges.php

Ok. I've read all the links. I studied the calculator and this is what I conclude. Please correct me if I am wrong in my thinking....

Randy Holmes-Farley recommends (for larger tanks) changing between 15%-30% per month but doing so with smaller more frequent (even continuous) water changes. While this method won't eliminate the necessity to supplement calcium, alk, and mg (plus trace elements) it will be sufficient to both remove toxins and keep tank parameters in check.

While very small or continuous changes result in less "pure" seawater over time, the small or continuous change method results in a more stable system (fewer swings in tank chemistry). Tank water levels, salinity, and temp are more constant than by doing weekly or monthly changes. This means less stress to fish or corals.

 

[keithhays]

Ok. I've read all the links. I studied the calculator and this is what I conclude. Please correct me if I am wrong in my thinking....

Randy Holmes-Farley recommends (for larger tanks) changing between 15%-30% per month but doing so with smaller more frequent (even continuous) water changes. While this method won't eliminate the necessity to supplement calcium, alk, and mg (plus trace elements) it will be sufficient to both remove toxins and keep tank parameters in check.

While very small or continuous changes result in less "pure" seawater over time, the small or continuous change method results in a more stable system (fewer swings in tank chemistry). Tank water levels, salinity, and temp are more constant than by doing weekly or monthly changes. This means less stress to fish or corals.

I think I would have to agree with this, I do continuous water changes that the calculators tell me equates to about 50% per month new water which is probably excessive. I don't know that the results are less pure seawater over time for this reason: once you automate something, it is generally going to happen whether you feel like doing it or not. This does equate to a much more stable system, all things being equal.

 

[Josh40996]

Futuredoc on TRT has a daily water change experiment doing 1% water changes each day. So far the results have been nothing but positive! He has found his system to be a lot more stable and has a huge decrease in algae growth. He missed a few days of daily water changes and the algae took off just as it was before the experiment. He also says that the daily water changes are far more easier than larger changes since all that is required is a scoop out and a scoop in.


Sent from my iPod Touch using Tapatalk

 

[MIASDADDY]

I'm not a scientist,or mathmetition,and obviously not a great speller,but I will weight in and say,I generally change 10% weekly,and years back,for a period of time,I changed on an opprox 70g system,1gl a day instead of the 7 a week,and didn't notice anything good or bad from doing it that way.I think the 10% weekly is way more efficient though,and am now back to that method.