Reef Chemistry Question of the Day #68 Water Changes and Sump Size
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Mike&Terry
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The answers are C & E.
For part one, my calculations are like Mike J's. Essentially, the daily net increase is 0.25ppm (which is a concentration or ratio of NO3 to total water volume - more on this later it is important!) and the daily reduction is 1%. Iterate that 365 times and I arrived at 24.11843 ppm.
For part two, the calculations are very similar. The daily net increase remains the same at 0.25ppm (and since it is a ratio of water volume, I assume that in order for the concentration to remain the same even though the water volume has doubled, then the amount of NO3 producing stuff going into the water has effectively doubled as well). The daily reduction drops to only 0.5% since we still doing the 1g water changes. This method yields 41.76605 ppm.
Now maybe I've made some bad assumptions or my math is flawed. That's entirely possible too!
For part one, my calculations are like Mike J's. Essentially, the daily net increase is 0.25ppm (which is a concentration or ratio of NO3 to total water volume - more on this later it is important!) and the daily reduction is 1%. Iterate that 365 times and I arrived at 24.11843 ppm.
For part two, the calculations are very similar. The daily net increase remains the same at 0.25ppm (and since it is a ratio of water volume, I assume that in order for the concentration to remain the same even though the water volume has doubled, then the amount of NO3 producing stuff going into the water has effectively doubled as well). The daily reduction drops to only 0.5% since we still doing the 1g water changes. This method yields 41.76605 ppm.
Now maybe I've made some bad assumptions or my math is flawed. That's entirely possible too!
Mike J.
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Take a deep breath, man.:frusty:
beaslbob
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How about not enough information given? Depends on what nitrates were at the start of the year. Could have been 2 billion zasillion ppm and has only gone down to a few million ppm. :wink:
In Iowa we have the a huge denitrifying plant that gets activated once the river hits above 10ppm, the EPA level for safe drinking water. It doesn't come on very often, but it is really expensive when it does. Right now they are trying to blend the river with other water sources around here to get it under 10ppm so they don't have to spend the money - 7,000 a day.
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beaslbob
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true but then we wouldn't care about water changes and how effective they are. Which means we'll miss this entire discussion.
beaslbob
2500 Club Member
Can I exhale now?
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And the answer is...C. 24 ppm and G. It is smaller because the nitrate is diluted more with a larger total water volume
This question did generate a lot of interesting discussion. Perfect!
Like gtbarsi, I used a spread sheet to determine the answer. I didn't know the answer in advance
D). More on that later.
beaslbob was the first to point out that one could look at the input vs the output. If the input is 0.25 ppm per day, when the system eventually reaches an equilibrium, the amount removed will have to be the same. So 0.25 ppm in 100 gallons is balanced by something out in 1 gallon. That would have to be 25 ppm in that one gallon to have the same total amount of nitrate as the daily addition.
BUT, there is no reason to assume that you reach equilibrium in a year. In fact, you do not.
So, to the spread sheet method.
In excel you can set up a few column and 365 rows, one for each day. On each day you take the nitrate input (0.25 ppm) and add it to the total from the previous day (the previous row), then multiply the product by 0.99 to account for the water change to get the value for that day.
Run that down 365 rows and you get 24.36 ppm, which rounds to 24 ppm.
If you run that longer and longer, it gets closer and closer to 25 ppm, which is the equilibrium mentioned above.
Now, let's look at a larger sump that doubles the total water volume.
Don't forget that the total nitrate input is the same, so we have only 0.125 ppm per day since the water volume doubled. The multiplying factor in the spread sheet is now 0.995 because you are only changing 0.5%, not 1% of the water volume each day. Eventually this tank must also reach 25 ppm, but it takes a lot longer to get there. At one year you are at 20.97 ppm. Two years you are at 24.33, same as the smaller sump at 1 year.
This question shows two interesting things (at least to me):
1. Larger sumps delay the accumulation of impurities, even with the same water change routine.
2. Excel spreadsheets are a great way to solve problems like these.
Happy Reefing!
This question did generate a lot of interesting discussion. Perfect!
Like gtbarsi, I used a spread sheet to determine the answer. I didn't know the answer in advance
D). More on that later.beaslbob was the first to point out that one could look at the input vs the output. If the input is 0.25 ppm per day, when the system eventually reaches an equilibrium, the amount removed will have to be the same. So 0.25 ppm in 100 gallons is balanced by something out in 1 gallon. That would have to be 25 ppm in that one gallon to have the same total amount of nitrate as the daily addition.
BUT, there is no reason to assume that you reach equilibrium in a year. In fact, you do not.
So, to the spread sheet method.
In excel you can set up a few column and 365 rows, one for each day. On each day you take the nitrate input (0.25 ppm) and add it to the total from the previous day (the previous row), then multiply the product by 0.99 to account for the water change to get the value for that day.
Run that down 365 rows and you get 24.36 ppm, which rounds to 24 ppm.
If you run that longer and longer, it gets closer and closer to 25 ppm, which is the equilibrium mentioned above.
Now, let's look at a larger sump that doubles the total water volume.
Don't forget that the total nitrate input is the same, so we have only 0.125 ppm per day since the water volume doubled. The multiplying factor in the spread sheet is now 0.995 because you are only changing 0.5%, not 1% of the water volume each day. Eventually this tank must also reach 25 ppm, but it takes a lot longer to get there. At one year you are at 20.97 ppm. Two years you are at 24.33, same as the smaller sump at 1 year.
This question shows two interesting things (at least to me):
1. Larger sumps delay the accumulation of impurities, even with the same water change routine.
2. Excel spreadsheets are a great way to solve problems like these.
Happy Reefing!
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Randy Holmes-Farley
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If that's the real question, then my answer is no.
But I like seeing all the rows. It makes the trend clear.
Actually it's very simple to do...
It's essentially a present value problem.
In excel, you can use the PV function to easily calculate it.
Your "rate" is the WC%. So in this problem that is .01 (for the first part)
The nper is the number of days - 365
The "payment" is the amount of nitrates added per day
Stick this in an excel sheet...
=PV(0.01,365, 0.25)
It spits out 24.34
Just have to format it so it's not in currency, and then set it up so that instead of values, you pull from cells so you can easily manipulate the variables.
It's essentially a present value problem.
In excel, you can use the PV function to easily calculate it.
Your "rate" is the WC%. So in this problem that is .01 (for the first part)
The nper is the number of days - 365
The "payment" is the amount of nitrates added per day
Stick this in an excel sheet...
=PV(0.01,365, 0.25)
It spits out 24.34
Just have to format it so it's not in currency, and then set it up so that instead of values, you pull from cells so you can easily manipulate the variables.
Quick screen cap to be more clear...
The numbers in blue are the variables. Enter whatever you want, and it spits out what you end up with.
The formula in cell E8 is =ABS(PV(D4,E4,F4))
I formatted it to be a 2 decimal place number.
So this example says that if you are adding 6ppm of nitrate every month, and you do a 10% WC once a month, at the end of the year you will have 40.88ppm nitrates
Also, Randy, there's very little that excel can't do when it comes to algebraic operations and the like. If there's something you'd like to make as far as an excel sheet goes - complete with graphs, pivot tables, macros, etc - let me know. I'm a total excel nerd and love tooling around with stuff like this.
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Randy Holmes-Farley
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You should extend that offer to everyone. Haha. It seems like half of lab work now is excel or PowerPoint, but for visualization most here, DuPont pioneer, have switched to spotfire, I like it. But talking about excel crosses the line too much for me - don't make reef tanks like work! Lol
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And the answer is...C. 24 ppm and G. It is smaller because the nitrate is diluted more with a larger total water volume
This question did generate a lot of interesting discussion. Perfect!
Like gtbarsi, I used a spread sheet to determine the answer. I didn't know the answer in advance
beaslbob was the first to point out that one could look at the input vs the output. If the input is 0.25 ppm per day, when the system eventually reaches an equilibrium, the amount removed will have to be the same. So 0.25 ppm in 100 gallons is balanced by something out in 1 gallon. That would have to be 25 ppm in that one gallon to have the same total amount of nitrate as the daily addition.
BUT, there is no reason to assume that you reach equilibrium in a year. In fact, you do not.
So, to the spread sheet method.
In excel you can set up a few column and 365 rows, one for each day. On each day you take the nitrate input (0.25 ppm) and add it to the total from the previous day (the previous row), then multiply the product by 0.99 to account for the water change to get the value for that day.
Run that down 365 rows and you get 24.36 ppm, which rounds to 24 ppm.
If you run that longer and longer, it gets closer and closer to 25 ppm, which is the equilibrium mentioned above.
Now, let's look at a larger sump that doubles the total water volume.
Don't forget that the total nitrate input is the same, so we have only 0.125 ppm per day since the water volume doubled. The multiplying factor in the spread sheet is now 0.995 because you are only changing 0.5%, not 1% of the water volume each day. Eventually this tank must also reach 25 ppm, but it takes a lot longer to get there. At one year you are at 20.97 ppm. Two years you are at 24.33, same as the smaller sump at 1 year.
This question shows two interesting things (at least to me):
1. Larger sumps delay the accumulation of impurities, even with the same water change routine.
2. Excel spreadsheets are a great way to solve problems like these.
Happy Reefing!
Awesome, thanks!
I barely remember math in college but maybe you could do a summation (remember that big E in math?) to calculate any point in time, maybe not...
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