Nitrates Calculation (Take 2)

[Lbrewer34]

So I was thinking, just how many water changes does it take to remove nitrates in a tank and the answer was MUCH more complicated than I thought. Here is how I approached the problem:
I assumed that I had a 100-gallon tank with 100ppm NO[SUB]3[/SUB]. I wanted to find how many water changes it would take to lower the nitrates to below 1ppm NO[SUB]3[/SUB]. Originally I wanted to figure for zero NO3 but realized this wasn't feasible. I also assumed that I would do 10% water changes.
Here is the shortcut formula I came up with:

[SUP](N[SUP]c[/SUP]/V[SUP](c-1)[/SUP])
[/SUP]Where:
N=(Total NO[SUB]3[/SUB]) – (NO[SUB]3[/SUB] removed based on % of water change)
V=Total Volume of Tank
c=Number of Water Changes

So to solve for how much NO[SUB]3[/SUB] is removed in a certain number of water changes is pretty easy, just plug in the numbers. So let’s say we did five 10% water changes in the tank from the example we get:

(N[SUP]c[/SUP]/V[SUP](c-1)[/SUP])
where:
N= (100ppm NO[SUB]3[/SUB]) -(10ppm NO[SUB]3 [/SUB])
V= 100 gallons

we get

(90[SUP]5[/SUP]/100[SUP](5-1)[/SUP])=59.049ppm NO3

Here is where it gets complicated. If I want to know how many water changes it takes to get the NO[SUB]3[/SUB] to a specific number. For this example, let’s just say we want to get to 25ppm NO[SUB]3[/SUB] but do 25% water changes instead what we have is this:

(N[SUP]c[/SUP]/V[SUP](c-1)[/SUP])= 25ppm NO3
where:
N=(100 ppm NO[SUB]3[/SUB]) -(25 ppm NO[SUB]3 [/SUB])
V= 100 gallons
c= Variable to solve for

so we get
(75[SUP]c[/SUP]/100[SUP](c-1)[/SUP])=25ppm NO3
=100(0.75)[SUP]c[/SUP] = 25
=0.75[SUP]c [/SUP]= (25/100)

To solve for the exponent “c” we have to take a function built into a calculator called “natural logarithm”, or “ln” on a calculator:
0.75[SUP]c [/SUP]= (25/100)
=c ln(0.75) = ln (25/100)

c ln(0.75) = ln(0.25)

c= [ln(0.25)/ln(0.75)]

c=4.82 (rounded)

Round it up to 5 water changes.

For this formula, you should be able to type your parameters in and solve. If your nitrates are high, you can use this formula to see the difference a 10%water change makes compared to a 30% water change, as well as how many water changes you need to get to below 1ppm based on the percent of water you change.




For the math enthusiasts who are curious how I came up with the formula here is what I did based on the example given at the beginning:

C[SUB]0[/SUB]=100ppm NO[SUB]3[/SUB]

C[SUB]1[/SUB]=
[(90(100ppm NO[SUB]3[/SUB])]/(100gal) = 90ppm NO[SUB]3[/SUB] remaining after 10% water change


C[SUB]2[/SUB]=
[90(90ppm NO[SUB]3[/SUB])]/(100gal) = 81ppm NO[SUB]3[/SUB] remaining after second 10% water change


C[SUB]3[/SUB]=
[90(81ppm NO[SUB]3[/SUB])]/(100gal)
=(90)[(90[SUP]2[/SUP]/100)/(100)]

=(90[SUP]3[/SUP])/(100[SUP]2[/SUP])


From this pattern I get:

(Nc/V(c-1))where:
N=(Total NO[SUB]3[/SUB]) – (NO[SUB]3[/SUB] removed based on % of water change)
V=Total Volume of Tank
c=Number of Water Changes

For those graphically inclined, I have attached a graph to the post. From the graph, the NO[SUB]3[/SUB] never really reaches zero, it just gets closer and closer (an asymptote). Of course eventually the remaining NO[SUB]3[/SUB] although present, won’t be testable.
These are just my results and thoughts, if anyone can improve on them or sees anything wrong let me know. Hopefully my math annotation is correct, it looks a lot better in word where I can insert the fractions. I can’t take full credit for all the work, when I got stuck I ran what I had by my calculus teacher for a little help.


I'm not sure if all the formula images and the graph will show, so if anyone wants the word doc just send me a pm
Lee

 

[NC2WA]

ahhh..better formatting...

 

[Lbrewer34]

Thanks for the help and advice!

 

[NC2WA]

you're welcome

 

[Krish]

Great post and great formula!! That's a lot of calculations!!

With that said, un-fortunately even though water changes will dilute nitrate levels in the water column (which is where most tests are taken from) it doesn't necessarily mean it will solve a nitrate problem or will be long lived. If it were so, people would just do a 100% water change and be nitrate free.

Take for instance your sandbed is the fuel of your nitrate issues loaded with rotting and decaying matter, ( eg detritus, un-eaten fish food, fish poop...All that good stuff) or maybe it's that sponge that is never cleaned or even it could be the end product of your wet/dry filter you are running. If nothing is done to say remove these nasties out of your sandbed or done to eliminate the use of your wet/dry system, your big water change will be short lived as your nitrate levels will climb again due to the issue not being dealt with. A water change will basically only dilute your problem as a temporary fix unless you address the problem or in some cases, maybe just allow your tank to mature and find it's balance.

I've done many water changes in the past trying to drop my nitrates from just 10ppm to zero to find that the following day, I was back to square one. A 10-15% water change a week to be exact and it took 9 months to lower my nitrates down to zero. The dilution method to lower nitrates of a water change was short lived because the nitrate problem still existed. Sometimes it's not even a nitrate problem a person has per say, but rather its all in just the tank trying to find it's balance which unfortunately water changes can't do much to help. It's through building up the necessary bacterial colonies that is sometimes all that is needed that will help maintain next to zero nitrates in your system.

To be honest, I wish it only took just a water change to get rid of nitrates. That would be the greatest thing ever and would have saved me tons of headaches


Edit: Btw, I posted a link to this thread from your first one and closed it for you seeing you guys got it all worked out here.

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[Lbrewer34]

Thanks for linking the first post and for the comments. Nitrates have always been a pain for me, actually until recently I haven't been able to get my levels below 20ppm. When I cut back on my water changes, supplementing fewer large water changes for more frequent small water changes I really began to see the spike in NO3. I used this formula to compare which method works better for NO3 removal, and figured if I get a big spike again, I can use it to calculate how much water I need to change to make a dent a high NO3 tank. I figured that the formula wouldn't have much applicable value but it was fun figuring it all out. One of the biggest lessons I have learned in this hobby is problems are all about their sources. Find the source, fix the problem.

 

[NC2WA]

One of the biggest lessons I have learned in this hobby is problems are all about their sources. Find the source, fix the problem.

YES !!! this is music to my ear and brings a tear to me eyes...

 

[Krish]

Yes, finding the source is key and then on the otherhand, depending on your system's age/maturity, it could be just a matter of your tank's biological system finding it's balance to where the bacteria in your tank is able to convert nitrates efficiently enough to keep them next to non existent via your test results. This was all my tank needed. I did weekly water changes, had a very small bio-load, never over fed, had great flow to where no waste really settled, good skimming, but still had 10 ppm of nitrates that took time to work off. I had no real "source" from where my nitrates were coming from, but rather my biological system (bacterial colonies) just wasn't up to standards yet to find that balance.


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[josh88]

Wish I could read it. Font color is dark even for my phone brightness all the way up

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[Krish]

Wish I could read it. Font color is dark even for my phone brightness all the way up

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Get an iPhone!


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[Lbrewer34]

pm me your email and I can send you the word doc

 

[josh88]

Oh that's actually pretty good. I like the explanation you have at the end to explain your answers. Honestly the only thing I understood as far as formulas. And equations go I've seen on this site. Kodos to you man. And thanks. @ Krish I get what your saying about natural time. But how much time is to much waiting for your tank to balance out. And what do you do when water changes, And beneficial bacteria aren't getting the job done

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[Krish]

@ Krish I get what your saying about natural time. But how much time is to much waiting for your tank to balance out.

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It all depends on a number of factors as every tank is different. One example is a person who adds new fish/livestock to the tank every few weeks. With each addition you make, the bacterial colonies have to shift/make adjustments to accommodate the increased bioload. Another example is the condition of your liverock and just how "live" it is in terms of teaming with beneficial bacteria. You need both aerobic and anaerobic bacteria with anaerobic being the ones responsible for dealing with nitrates. These have to be in balance to where you have the right amount to keep things stable. Not enough food for the bacteria to feed on and some die off. Too much food (waste) in the tank for the current bacteria to handle and they have to increase in numbers so it's hard to put a time frame on it or say just how long it takes for a tank to balance out.

And what do you do when water changes, And beneficial bacteria aren't getting the job done

Depends what the source of your problem is. Could be in-sufficient tank husbandry. Some tanks can't be left to run on their own as waste/detritus etc can accumulate and break down degrading water quality. They require you to get in there, vacuum the substrate, change or clean your sponges/filter socks etc every few days etc. Then there is overstocking a tank where your tank physically does not have enough capacity to biologically filter it. Bacteria grows on and in your liverock and sandbed as well as on the surfaces of things. The sad thing is, not much beneficial bacteria found free floating in the water column which is why you can do a 100% water change on a tank and not shock its biological system. So, not enough surface area for bacteria to grow, then it becomes a problem. Therefore, when your bacteria can't handle the excess nutrients in the water column then it makes room for algae to come in and take advantage of the available food source. As a result, you will find some people set up refugiums for this simple fact. Allow an algae to grow in their fuge (rather than overtake their tank) to use up the excess nutrients in the water (ie nitrates, phosphates etc) which helps keep the levels in the tank down.

In all cases, you have to pay special attention to keeping your bioload within reason, your feedings within reason and do your part in aiding in performing tank maintenance that will help keep high nitrate levels down.

Just a few quick thoughts to give you an idea.


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[Krish]

Another thing to add Josh on the time frame just think of how long it takes a tank to cycle. With so many factors involved with condition of the liverock you are using as an example, its really hard to put a time frame on anything in this hobby which is why patience is the key ingredient here.


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[Lbrewer34]

In your opinion Krish, since the balance of aerobic and anaerobic bacteria is important to tank balance, could NO3 levels be indirectly related to the O2 concentration of the water? For the anaerobes, lack of O2 isn't an issue, but if bacterial colonies are vital to NO3 balance O2 is necessary for aerobic bacteria right?

 

[Krish]

In your opinion Krish, since the balance of aerobic and anaerobic bacteria is important to tank balance, could NO3 levels be indirectly related to the O2 concentration of the water? For the anaerobes, lack of O2 isn't an issue, but if bacterial colonies are vital to NO3 balance O2 is necessary for aerobic bacteria right?

Sounds like a question for Boomer or Mojo lol. It's been one of those days and that question just went right over my head . I'll see if I can get one of them in here to respond.


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[mojoreef]

In your opinion Krish, since the balance of aerobic and anaerobic bacteria is important to tank balance, could NO3 levels be indirectly related to the O2 concentration of the water? For the anaerobes, lack of O2 isn't an issue, but if bacterial colonies are vital to NO3 balance O2 is necessary for aerobic bacteria right?

With that you are kind of assuming that CO2 is the only reason water would go anaerobic?? SO its kind of a long explaination so bear with me I will try to make it short.

Bacteria dont just jump onto a product and reduce it, they use enzymes, acids and a variety of other neat little things. What all these products end up doing is creating an environment, we call this bio-film. So now regardless of where it sits (in highly oxygenated water) it can go anaerobic because with in the biofilm it can be void of oxygen. So that is a little thing to keep in mind with bacteria are capable.

Now as per balance. So it is always important to have the various bacteria with in "Hands Reach" of it. An example is the use of bio balls, great for nitrification but to much to build up an anaerobic bacterial population. So now an example of Hand reach would be LR or LS, the bacteria that perform nitrifcation pass their end product down to the bacteria that perform denitrification. They do this by creating channels with in the biofilm to pass these products down, and it doesnt stop their the bacterial process goes alot deeper.

Ok so then you also have to mix in a little bit of what else the bacteria can do, bacteria can be factulative, as in they will use oxygen when it is present in their reduction process, but when the oxygen runs out they can convert to Nitrogen (nitrates).

Now somethings about Nitrate issues. Yes as mentioned above one always have to control what they put in, so easy on the food and try to clean up after it (maintenance). The use of bacteria (with in LR and LS) is very ineffecient, it takes a long time and we can never have the scale that would be required to keep up with the average tank. SO dont rely on it for anything more then polishing the water. Instead look to remove it and ease the pressure you are putting on it. So good flow that keep detritus and left over food in the water column and make it available for corals and similar and also will get it out to your sump where you can deal with it. Also remember that your rockwork will collect detritus and even shed it, so give it a good blow with a power head once a week or so, so that it doesnt collect because if it does you can have the cleanest nitrate free water and you will still feed algae like no other. ANother thing I like to see folks do if they have sand it to syphon the top 3/4 inches of the sand bed to take the waste and detritus that has collected their. This will reduce the pressure put onto the bacteria and also help keep it oxygenated.

Anyway that the short and scattered version, hope it helps

Mojo

 

[Krish]

Thanks Mojo.


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[Lbrewer34]

Mojo,
Are the bacteria using NO3 as the nitrogen source for nitrogen fixation? This would make sense, but I'm not sure if the bacteria can separate the nitrogen from the oxygen. If the NO3 is the nitrogen source for the bacteria, is the remaining oxygen used in aerobic respiration as well? Thanks for the clarification with the biofilms. I thought the biofilms were mainly used to attach bacteria to a medium, I didn't realize that they also use this as a way to control the oxygen in their environment.

 

[josh88]

Ok that make sense Mojo. So I've bought a syphon, and also a clean up crew. A few snails and 5 hermit crab. They are doing a pretty good job turning the sand over. And I understand that one in, one out concept. So I'll keep up on the tank. ? Should I still perform a 15% water change every week. Without it sending coral that I place in The tank into shock. I'm going to buy one more 5 gallon bucket, I have my power head to mix the water And I'll get another thermometer. But if my sg drops does that mean I need to add salt to the mix?.

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