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I will assume you want to do the same water change routine every week. How much water should I change to keep the Nitrates below a certain value?

Figure your tank generates N nitrates per day.

In a week you get 7N Nitrates in your tank.

You do a P percent water change at the end of a week. Assume 0 Nitrates in the incoming water.

You have 7N (1-P) of the Nitrates left after the water change.

Next week 7N nitrates generated again added to the previous left over:

7N + 7N (1-P)

You do a water change and are left with:

(7N + 7N (1-P))(1-P) = 7N (1-P) + 7N (1-P)(1-P)

Next week you get before the water change you end up with

7N + 7N (1-P) + 7N (1-P)(1-P)

Well, it looks like we have a geometric series of the form:

a + ar + ar^2 + ar^3 + ar^4 = ...

If r is less than 1 (and for us it is) the convergence for a series of this form will be:

a / (1 -r)

and,

a = 7N

r = (1 -P)

so,

(7N)/(1 - (1-P)) = 7N/P

For Maximum Steady state Nitrate levels then it is simply:

**(Nitrate Increase per time period / Percentage Waterchange per time period) = Nitrates in your tank just before your next water change.**

21ppm Nitrate Increase per week / 75% waterchange = 28ppm Nitrates Max before next water change

21ppm Increase in Nitrates per week / 30% water change = 70ppm Nitrates Max before next water change

21ppm Increase in Nitrates per week / 10% water change = 210ppm Nitrates Max before next water change

Makes too much sense that the steady state you will be removing what is added each week as in 10% of 210ppm is 21ppm - which matches the water change.

These values are for final steady state - so if your nitrates are going up you are not removing as much with your water changes as is being created by the tank each week.

This calculation shows where the stopping point will be.

Hope this helps someone.