# Paradox of the partial water change…do you ever get it all?

I rolled my sleeves up tonight and did a water change. While I was elbow deep in tank-water I found myself wondering if it was possible to calculate exactly what the perfect water change frequency was. To keep things simple, I will just focus on a single parameter–nitrates. I know that we all do water changes for more reasons than just nitrate removal, but it seems like a reasonable place to start. My fish brain told me…that if I could figure out what my nitrate accumulation rate was…I could calculate the ideal water change schedule. What I found out was that it was harder than I had thought.

Let’s assume, my tank accumulates, 5 ppm of nitrates that doesn’t get skimmed out each week and that I do the old textbook 10% water change weekly and I never miss a water change (hopefully my fish aren’t reading this article…or at least haven’t figured out how to use the comments section).

After 1 week, my nitrates should be 4.5 ppm (5 accumulated, removed .5) After week 2, the nitrates would be at 8.55 ppm (4.5 + 5 -0.95). After week 3, the nitrates would be at 12.2 ppm. So clearly the 10% partial water change isn’t enough to keep up with things. Nitrate is building up and getting out of control.

So, my fish brain said, do a bigger partial water change… ok fish brain…let’s double it to 20%. Now the theoretical results are:
week 1- 4.0
week 2- 7.2
week 3-  9.8

The problem isn’t as bad…but it’s still clearly a problem. Now in all honesty, my fish brain started to catch on, and I imagine you are too–but just to make a point, let’s assume my fish brain told me to go even farther–assuming 50% water changes weekly.

Even in this extreme situation, the theoretical results would be as follows:
week 1- 2.5
week 2- 3.75
week 3- 4.375

The math goes on and on like that and gets stuck just below 5 ppm.But let’s face it, THAT is a lot of water to change every week. Who has the time, energy or money to do that? And I was intrigued by the fact that the concentration got stuck at 5ppm. So I went back to my earlier calculations–and if I hypothetically did a 10% water change–my nitrates would steadily rise until they got to a whopping 45 ppm and then basically stop. So then, exhausted by the math, I did one final ‘in between’ value–at weekly 25% water changes, the nitrates would plateau at 15 ppm.

Now my wacky math needs a lot of disclaimers. For one, I arbitrarily picked 5ppm as the accumulation rate. If the accumulation rate was just 2 ppm, my nitrates would plateau at 2, 6 and 18 ppm with either 50%, 25% or 10% weekly water changes.

The reason I bring you through all this math is for the following simple message…don’t just take an old rule of thumb like…do a 10% weekly water change…as gospel. If you can figure out your accumulation rate, you can do a calculation to see where your own tank is going to get stuck. If you’re trying to figure it out for yourself…don’t deal with all the math I did, just take this shortcut:

• If you do 50% water changes forever, your water parameters get stuck at exactly 1 x’s the accumulation rate.
• If you do 25% water changes, your water gets stuck at 3 x’s the accumulation rate.
• Finally, if you do 10% water changes, your water gets stuck at 9 x’s the accumulation rate.

For me, the other take home message is that I’m going to do a major water change–with purpose–on a periodic basis to help remove whatever is building up in the tank that I don’t even know about…

So what do you think…am I crazy for doing all this math?

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