The math of the Partial Water Change... without all the math.
This time I am not aiming for a discussion of water changing over not water changing, although I wasnít aiming for that last time either... I think that has been beaten to death now... as interesting as it is it's a matter of opinion and individual results and let's leave it there.
I did a quick spreadsheet to figure out where the regular water changes fall due to BBob mentioning his ppm equation that tended to lead us to believe that water changes were a futile effort. I recalled an interesting little demonstration in chemistry to show how an equilibrium reaction reaches it's equilibrium when, at first glance, you would expect that one reaction would overtake the other. This is no different.
I only did two water change frequencies.
1) weekly 25% water changes with a contaminant increase of 1 ppm daily
In week one it looks dismal, starting with 1ppm it increases 700%. A 25% change is nothing relative to that and definitely seems futile. In week 14 something interesting happens. The ppm reaches 28 and stays there. I only ran it for 80 weeks but the level never reaches 29 in that period. I am sure that this is a parabolic curve so, in theory, if I ran decimals I would see a steady increase in the levels, I did, and I do, but who needs 10 decimal places?
2) 25% water changes every four days, same contaminant increase
Everything starts out looking very similar but due to the increased frequency the equilibrium point is reached at week 7 and pegs at 16 ppm
Frequency is more important than quantity for a number of reasons.
First, a 7 day schedule with the same contaminant increase rate would take a 45% water change to reach the same equilibrium point as a 25% 4 day schedule, it would reach that point in 10 weeks.
Second, due to the less water needing to be changed, the job is easier and quicker.
Third, the water contaminant level is more stable as weekly swings from 10 to 16ppm and four day swing from 13 to 16ppm (I know, lower levels are better) but I expect that wide swinging levels are worse than stable levels if the maximum is managed.
Both have the same end result BUT neither reduce the contaminant level over time. Larger periodic changes are the only way to do this, I didnít work it out but eventually, with steady contaminant increases, the same equilibrium will be reached every time.
It must be pointed out that these steady numbers are nowhere near what may happen in any given tank as every tank setup and owner are different, it only serves to point out that many small regular water changes are effective at managing contaminant levels in our closed systems.
If you are still here, it takes a 7% daily water change to hit a lower contaminant level (14 ppm) in 6 weeks. in a 40 gallon tank that is 2.8 gallons, about a half a pail. Pretty easy and doesnít mess with the water numbers much.
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