beaslbob water change question of the day

[beaslbob]

ref: https://www.reef2reef.com/forums/reef-chemistry-randy-holmes-farley/182022-reef-chemistry-question-day-68-water-changes-sump-size.html

That reef question of the day reminded me of my old waterchange analysis. So in the form of a question of the day assume:
1 you have an aquarium
2 nitrates are increasing at a constant 1ppm/day
3 You conduct regular water changes as some fraction of the total volume.
4 The size of the water changes are tied to the frequency of changes such that 10% every 10 days, 20% every 20 days, etc etc etc.
5 Nothing changes in the tank as a direct result of the concentration of nitrates.
6 the replacement water has 30ppm nitrates in it.
7. Water changes have been done until you can no longer measure differences in nitrates just before a water change. (steady state has been reached)

Question what is the level of nitrates just before any of the various water change schedules?


Possible answers:

a. Cannot determine—it varies with water changeschedule
b. Cannot determine—Not enough information given like what was the initial nitrates in the tank among other things.
c. Cannot determine—need to know the size of theaquarium
d. 65.34-125.49ppm depending on the water change schedule
e. 25ppm
f. 75ppm
g. 100ppm
h. 130ppm
i. 150ppm
j. Beaslbob doesn’t know.
(if you guys remember this-- let other answer to help the learning experience. Like mine for instance)

 

[Randy Holmes-Farley]

Just curious, why would you use replacmeent water with 30 ppm nitrate in it?

 

[beaslbob]

Just curious, why would you use replacmeent water with 30 ppm nitrate in it?

Because it's another parameter in the equation.

But bottom line here is dr randy holmes-farley does the good questions of the day.

At least ones that get answers and generate discussions.

 

[beaslbob]

Well I guess I should leave the question of the day to Dr. Randy Holmes-Farley. :xd:

This question is where the aquarium winds up. At that point the amount of nitrates removedby the water change equals the nitrate build up between water changes. By equation:
Build up between changes=nitratesbefore change(fraction removed)
Nitrates before change=(buildup between changes)/(fraction removed)
For example, if you are changing out 20% of the water (1/5) and nitrates have increased 10ppm between changes, the nitrates before the water change=10ppm/(1/5)=50ppm
And the amount of nitrates in the replacement water is where any existing initial conditions are finally diluted to.
Being as everything is linear you can just add the two effects together and arrive at the final equation:

Nitrates before change=(buildup between changes)/(fraction changed)+nitrates in replacement water.

The nitrate build up is 1ppm/day and the fraction ofwater changes is (1/100)/day so the buildup in any case is 1ppm* n days. And the size of the water change is (1/100)*n days

Therefore:

Nitrates before change=(1ppm*ndays)/(ndays*1/100)+amount in replacement water

The n days cancel out and the amount before any water change under any schedule is
Nitrates before change=100ppm+amount in replacement water.
In this case 130ppm. So the correct answer is h 130ppm.
(it would be 100 with nitrate free replacement water.)
In Dr Holmes-Farley’s doubling of the sump we found nitrates within 20% of the original value after a year, and the final value to be unchanged. So me what is important is changing the rate of change of nitrates. That way nitrates will remain a 0ppm regardless of the water changes being conducted. Which is why we have to dose calcium/alk/magnesium. Which cannot be maintained through water changes alone.