Estimative Index

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AlexAlbert

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Estimative Index

It's just a simple log curve.Can you please show an equation used to produce graphs and final values..:eek:
 
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Tom Barr

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Tom Barr

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AlexAlbert;26833 said:
It's just a simple log curve.Can you please show an equation used to produce graphs and final values..:eek:

Albert, the equations are simple infinite series.

This is taken from theKrib.com
the link can be found at :
Practical PMDD Information

Figuring the cumulative change in aquarium concentration of Fe (or any element) in PPM after long term daily PMDD use with periodic water changes:


The tricky part about this is knowing depletion rates. I can figure out how water changes will deplete an element, but I don't know how much plants will. Well, since my intent is to avoid overdosing Fe, I'll look at the worst case: one where no Fe is used by the plants (sure, a rotten assumption since the whole point is to provide Fe, but it does yield an upper bound or maximum possible concentration).

In EI, I used 0%, uptake by plants, 25% and 50% and 75% as examples.
Those are the 4 plots you see on the graphs.
This way you can see what your assumptions might be with low, med and high light, with or without a typical fish load etc.

Obviously if you have 100% then the nutrients would end up the same every week(10ppm of NO3 in the EI example). No need to see that:cool:

Turns out concentration buildup given periodic water changes is one of those Geometric Series things.

Say "D" is the total concentration increase after multiple PMDD doses preceding a water change (figured in mG/ltr per part 1). Say "R" is the portion of pre-change concentration that remains after the water change (ie a 25% water change leaves 75% of concentration).

Well, after 6 weeks, you'd have a cumulative concentration of:

(((((D*R)+D)*R+D)*R+D)*R+D)*R+D or
D*R^5+D*R^4+D*R^3+D*R^2+D*R+D or
SUM n=0 to 5 of (R^n+D)

Now, over many many weeks you'd have a cumulative concentration of;

SUM n=0 to infinity of (R^n+D) or
D/(1+R) Simple result, aye?

So, using this secret formula D/(1+R) and putting it in terms of daily doses, days till water change, and % water change (note: % water change = (1+R)):

Long Term Cumulative Increase in Concentration =
(daily increase from dose)*(doses till change)/(% water change)
in mG/ltr or PPM in days in decimal
only valid if water volume
change >> dose volume

Carrying over the example from part 1): 1.66 ml PMDD dose daily, but with 25% weekly water changes;

(0.0144 mG/ltr Fe)*(7)/(0.25) =

_0.4mG/ltr Fe_ final aquarium concentration

Uh-oh, 4 times too high! That's why I ended up leveling off at a lower PMDD dose, about 1/2 ml a day, for my 45 gallon tank.

Again, this all assumes no depletion, a lousy assumption, so I'd measure Fe as you go. As I said, this calculation is only good for an "upper bound".

If you chose 50% weekly, then instead of 4X, you only have 2X(I think? Too lazy right now to make sure but seems about right) the max dose build up.

So if you added 10 ppm per week of NO3, the highest max possible will be 20ppm. Add 20ppm per week, and the max is 40ppm.
In most planted tanks with a fair amount of light and good CO2, dosing etc, 10-20ppm is a normal uptake. So instead of 40ppm, you end up with a range of about 10-15 to about 30ppm. If you worry that 40ppm is too high, simply do a larger water change once a month to flush any excess out and this will drop it down to 30ppm or less. Or run lean for a few days before the next water change etc. I typically run things really rich the day before, because I know I'm going to re set the tank the following day anyhow.

Note, EI is entirely derived from PMDD, as are most every water column dosing routine on the web today. Some acknowledge this, some do not. All I did was add PO4 to the dosing routine and added more to account for the difference in higher light set ups requiring more nutrients, the excess amounts in lower light tanks caused no issues, so the upper bound would target all aquariums with non limiting nutrients.

Most of the general approach to adding ferts was already well in place before I did anything. I do not pretend I came with all this on my own without any help or resources. They where all there. I just challeneged some assumptiosn and modifed a few things is all.

PMDD intimidates/d many folks initially when the first see/saw it. Seemed really complicated.

I was no different. I made simple mistakes. I mixed K2SO4 and KNO3 up more than once. I came back later and thought simply using teaspoons was easier to explain, the 50% water change took test kits out of the issue and the poor accuracy.

That seemed pretty easy, a few simple steps
Then light and CO2 are all that are left.
This can rule things out with much less work and monitoring and see what does and does not cause algae.

Regards,
Tom Barr
 
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