Calculating optimal water changes

[jzmckay]

For those inclined to do a little math, I figured out a simple equation to calculate approximate nitrate levels, based on the size and frequency of water changes. The following is based on simple math and assumptions. Everyone's tank is different, so be sure to measure things on a regular basis if changing your maintenance routine.

Nitrates are usually the main indicator used by freshwater aquarium keepers to determine waste buildup in tanks, but these calculations should also give a rough idea of the accumulation of waste products in your tank in general.

Thus, you can use these calculations to determine the approximate impact of alterations in your water changing regime -- for example, what impact will more or less frequent changes have, or what if I start doing larger or smaller water changes?

If you play around with numbers here, you'll find some potentially interesting results. For example, NO3 levels will stabilize so that maximum NO3 levels will be lower with a 50% water change every two weeks than with a 25% water change every week. More frequent is not always better, though it depends on the relative amounts. Of course, a 50% water change will shock your fish more, so I wouldn't recommend this particular regime. But, using these equations can allow you to figure out whether there is a better way to do things. I entered them into a spreadsheet and found it to be an illuminating exercise. (For example, to get the equivalent nitrate levels for a 50% water change every two weeks, you'd need to do about a 30% change every week. That 5% can actually make a pretty big difference over time, depending on nitrate production.)

Average NO3 level
= w + {N * t * [(100 / p) - 0.5]}

Maximum NO3
= w + [N * t * (100 / p)]

Minimum NO3
= w + {N * t * [(100 / p) - 1]}

where,
w = NO3 level in replacement Water
N = Nitrate production per week (net)
t = Time between changes (in weeks)
p = Percentage of water changed each time

For example, let's say you do weekly 25% water changes, and your tank gains an average of 10 parts per million (ppm) of nitrates per week from fish waste, uneaten food, etc. minus the amount absorbed by plants, etc. Let's also say the tap water you use for doing water changes measures 5 ppm for nitrate levels.

Average NO3 level
= w + {N * t * [(100 / p) - 0.5]}
= 5 + {10 * 1 * [(100 / 25) - 0.5]}
= 40 ppm

Maximum NO3 (before water change)
= w + [N * t * (100 / p)]
= 5 + [10 * 1 * (100 / 25)]
= 45 ppm

Minimum NO3 (after water change)
= w + {N * t * [(100 / p) - 1]}
= 5 + {10 * 1 * [(100 / 25) - 1]}
= 35 ppm

There are important assumptions made here for these equations:
(1) Water changes are performed on a regular schedule, so the time between changes is always about the same.
(2) Water changes are the same size. If you do different size water changes on a schedule, you're on your own with the calculations.
(3) Net nitrate production is relatively constant. This isn't true, of course, particularly for extreme values. If you wait a long time between water changes, generally plant, algae, bacteria growth, etc. will change the rate nitrates are produced and absorbed in the tank. But if nitrates are kept relatively low and water changes are performed on a regular basis, these equations should give good estimates.

Net nitrate production is also hard to measure. More fish and excess food will cause it to rise, while more plants and such to absorb it will cause it to slow. You can estimate an upper bound for it by weighing the food you add to the tank each week and dividing it by the approximate weight of the water in the tank. Because some of that food (and waste from it) will always be absorbed, that's just the highest amount that nitrates should rise per week. (With a well-planted tank, it will usually be a LOT less.)

Another way to estimate the net nitrate production is to measure the nitrates just before a water change (maxNO3), and then solve the MAX nitrates equation above for N:

N (net nitrates per week)
= (maxNO3 - w) / [t * (100 / p )]

Once you have a rough estimate of this number, the equations can help to explain if you are unhappy with your average nitrate values and want to improve things.

These equations seem to give reasonable estimates for my tank. If you try using them and discover that they work for you (or don't), it would be good to hear about it.

I recently posted this information in a saltwater discussion about water changes, but I thought it might also be relevant to give a summary in this forum. For the original thread, see here:

http://www.fishtankforums.com/6-salt...ange-myth.html

[jzmckay]

By the way, one other CRITICAL assumption I forgot to mention -- all of these equations assume a well-established tank with a functioning biological filter where ammonia and nitrites are essentially zero.

The calculation of ammonia, nitrite, and nitrate levels during tank cycling is a much more complicated process and depends a lot on what is in the tank. Also, massive water changes and/or major filter maintenance (replacement of a lot of filter media, etc.) can cause minor cycling in a tank where nitrate production gets disrupted.

So, don't try to use these equations in cycling tanks. With excess ammonia and nitrites floating around, you have bigger problems to worry about than nitrate accumulation.

[peanutbowl]

nitrate and waste removal are not the only reasons to change water. water changes replenish trace nutrients as well. this is a good thing. and i don't believe that 50 percent water changes stress the fish any more than a 10 to 25 percent change. and really, it's about the same amount of work either way, unless you are talking about a very large tank. there are many ways to simplify the process. in my humble opinion, fish will enjoy more fresh water in the tank at any given time. i can appreciate the thought, however, given the amount of variables that can effect your equation, you have greatly confused the issue.

[Jay]

Of course, a 50% water change will shock your fish more, so I wouldn't recommend this particular regime.

I change out all of my tanks 50% per week, sometimes 50% twice a week. Have been for years. I could see it if a tank has been terribly neglected, poor husbandry practices etc. Then there is the real possibility of osmotic shock.

Perhaps you could elaborate.

My well planted 75 with a big bio load, eats NO3 somewhere in the range of 10 ppm every 24 hours. My problem is adding enough NO3 to keep it from bottoming out.

I agree with peanutbowl and IMO and IME the bigger the water change the better to replenish GH and trace minerals. Even with the large changes I still have to supplement Mg and trace minerals eaten by the plants between water changes.

I would be hard pressed to fit into a formula the amount of Nutrients to add to my tank as the plant mass is constantly changing. A few quick tests, once in a while, gets me in the ballpark.

Please do not take what I am saying as an argument over the math or your great illustrative formulas. I have often used the basic math to explain to newcomers why their Nitrates or DOC are not declining even though they are doing 5 - 10% water changes religiously.

Jay

[jzmckay]

First, in reply to Jay, I did not intend to downplay 50% changes.

In fact, you'll note that the equations argue that 50% changes less frequently will result in a lower average waste accumulation than smaller changes on a more frequent basis. That is an important conclusion, but how frequently or how much larger you have to be to get a significant difference... well, that's what I wanted to find out.

I was afraid that if I put up equations that seemed to argue for less frequent, greater changes, some people might object to that. That's why I put in your quoted comment about 50% changes. I certainly didn't intend to offend the other side.

I personally like to stick to 25-30% changes myself because the water I add can't be guaranteed to be exactly what I have in my tank, and therefore I want to avoid changing things too quickly. But I'm not strongly committed to that regime, and larger changes are certainly better if you can match water parameters rather closely.

As for plant mass changing, etc., yes I agree that that's a further difficulty. You could certainly model something like that mathematically, but I just wanted to keep things simple for people trying to decide roughly whether small variations in their routine might cause significant changes. As you noted, they can also show why people who try to do 5-10% water changes very frequently often don't have a lot of good results.

Trace nutrients are critical too; see below for more thoughts on that. Also, the equations will break down for people whose tanks eat nitrates up quickly, though I think that's the minority among freshwater aquarium keepers, and these are more concerned with the waste buildup issue that plagues many people.

Anyhow, thanks for your comment!

Originally Posted by peanutbowl

nitrate and waste removal are not the only reasons to change water. water changes replenish trace nutrients as well. this is a good thing. and i don't believe that 50 percent water changes stress the fish any more than a 10 to 25 percent change. and really, it's about the same amount of work either way, unless you are talking about a very large tank. there are many ways to simplify the process. in my humble opinion, fish will enjoy more fresh water in the tank at any given time. i can appreciate the thought, however, given the amount of variables that can effect your equation, you have greatly confused the issue.

Thanks for your perspective, though I feel your tone is a bit condescending for no apparent reason. I'm a relatively new contributor to these forums; I've used them and found them helpful for a while, and I don't exactly appreciate that my first attempt at a contribution is disparaged so much.

A few comments in response:

(1) I am well aware that water changes replace trace minerals, etc. However, particularly for beginners, I think the greatest worry is to get on a regular regime to avoid build-up of wastes. Do a Google search for water changes, and see what the primary concern of most commentary on the web is -- it's about making sure to clean out tanks and prevent waste build-up. That was the issue I was trying to address, but you are of course right that providing regular water changes also restores some important minerals. If you have a measurement kit for those trace nutrients, you could use similar equations to determine how that might impact water changes. Most people don't. But most people do have a NO3 kit, so they can use these equations to think about how water changes impact those levels. That was my main point.

(2) I shouldn't have implied that 50% water changes are inferior. I have done them myself many times. In fact, I would say that my equations actually argue FOR such larger changes rather than more frequent, much smaller changes. That was actually one of my primary reasons to put this information out there, and I'm sorry it didn't come across clearly. If you read carefully again, you'll see that I in fact point out that a weekly 25% water change will be INFERIOR to a biweekly 50% change in terms of waste accumulation.

That in itself is something to note, and in fact is an argument in favor of larger changes. I personally tend to avoid large changes, but that opinion has nothing to do with my equations. I only included that sentence because I was afraid that those people who tend to argue for smaller, more frequent changes would jump down my throat when I pointed out that the equations show that a less frequent large change would be better than a more frequent small change. Instead, it appears that I offended the opposite crowd. Apologies. If you use the equations, you'll see that the numbers are actually in YOUR camp.

(3) Finally, I really don't appreciate the statement that because there are many variables, I have "greatly confused the issue" just because I attempted to model one important aspect of it. Mathematical modeling is an abstraction that can never account for all elements in a real system, but that's how science works. Biological systems are often even more difficult that physical ones in that respect. But unless we attempt to measure things and then model them, we can't make any useful predictions or progress in figuring things out other than guesswork.

If you have a better way to model or other things you'd like to take into account, by all means, I'm interested in hearing how to improve things. And as I clearly point out in my disclaimers, the equations won't work for extreme cases or for massive swings in water quality.

What I was merely trying to do was provide a way to compare and evaluate the potential results of small variations in water change procedure. For example, is it better to do a 25% water change every week or a 50% change every two weeks? Is it better to do a 10% water change every few days, or a 30% one every few weeks?

At least according to most of the things I've read online, no one can answer these questions outside of educated guesswork. Everyone has their own opinions about it. I was just attempting to build a very simple model that should be able to roughly predict the effect of these sorts of small variations in water change regime, at least in terms of waste buildup (though you could easily modify the equations only slightly to calculate the effect of water changes on restoration of depleted resources).

I would simply ask that you play around with the equations and see what sorts of things happen (and perhaps suggest improvements to the model) before you dismiss them out of hand as "greatly confus[ing] the issue."

[peanutbowl]

please allow me to apologize. it was not my intent to condescend you or to dismiss your formulas as incorrect. i am sorry for the misunderstanding. my response was merely short and to the point.

i do stand by my opinion that "optimal water changes" are characterized as being larger and more frequent. this is clearly corroborated by your formulas. the only part of the original post that i disagree with was the statement that suggested 50 percent water changes are more stressfull to the fish. in my experience, this is just not true. my fish swim around playfully in the bubbles and spray from the returning replacement water. i truely believe that they like it.

allow me to conclude by offering this suggestion. weekly nitrate accumulation can be calculated more simply by taking readings of your water parameters just before and after water changes and then making note of the difference. the only assumption here is consistancy. (i.e. bio-load, w/c percentage) do this several times on a constistant schedule and you will begin to notice a trend. all things considered, the results will be specific to your tank. i would tend to believe these actual readings over more complex algebra based on estimates.