Would this work as a chiller?

You can go as scientific as you want. Several years ago I had very similar systems on a few of my tanks. With my chlorinated water source, I was able to drip 10% chlorinated water into the tank per day with no ill effects. This was no where near enough to chill the tank, nor change the temperature at any noticeable level. If you had an inline filter that removed chlorine, and did a 100% water change daily, you may actually come close to chilling the tank, maybe. A much better approach would be a dorm fridge with heat exchangers inside the fridge, and in the tank. Ideally filled with RV antifreeze and put the exchanger(copper coils in the freezer compartment of the fridge, and run them directly into a heat exchanger in the tank. You would have to decide if 1/4 inch copper tubing coiled inside the tank itself would be problematic as far as leaching copper into the tank itself. I would not expect this to cool a large tank.

I started on the math and the steady state, accumulation = 0, is in fact the equilibrium point in the 'limit' we are interested in. Assuming no Cl2 loss other than the overflow this limiting equilibrium point puts the aquarium Cl2 concentration effectively equal to the tap water Cl2 concentration. What we are after is enough reduction/evaporative Cl2 losses to put this equilibrium point at a sufficiently small percentage of the tap water concentrations of Cl2. So instead of trying to calculate the actual Cl2 consumption rate, from chemistry and gas laws, it might be better to simply define the theoretical Cl2 consumption rate needed to reach a target percentage of tap water Cl2 concentrations. From there it is trivial to scale it (scales linearly) to the flow rate of the tap water. Hence doubling the tap water flow rate doubles the required consumption rate needed to hit the target percentage of tap water Cl2 concentration. This bypasses the very difficult calculation of consumption rates and requires only that the system meets some set consumption rate in practice. Which can be experimentally determined as described below.

In fact the formula gets quiet simple when stated in terms of targets rather than actual consumption rates. By way of the tap, stated in terms of time rather than volume, you are inputing (X mg/s). Time as opposed to volume is because we are after some percentage of tap water levels of Cl2 rather than some absolute value.
Input rate from tap: (X Cl2 mg/s)
Consumption rate: (Y Cl2 mg/s)
Tap Cl2 concentration is: (Z)
Hence the resulting equilibrium Cl2 concentration is:
X/Y * Z = mg/L expected in the aquarium at equilibrium.
Thus, if we want a target Cl2 concentration of 1/10th the tap water Cl2 concentration the system consumption rate must be (0.9X mg/s). So doubling the flow rate from the tap doubles the consumption rate needed, with caveats stated below.

If you have a Cl2 tester you can easily determine the consumption rate of any given system by setting a known flow rate from the tap, with no water initially in the tank and allowing time for the first fill to be completely replaced, and measuring the Cl2 concentration difference between the input and overflow. From there you should be able to predict Cl2 concentrations, as a percentage of tap concentrations, at any flow specific rate given the above linear relation with one caveat. That is the variation in Cl2 consumption rate as a result of variations in Cl2 concentrations. However, with a graph of this Cl2 concentration dependent variance in consumption it is trivial to simply rescale the otherwise linear relation once solved. When this is known for any specified flow rate in any specific system you can then easily calculate the maximum flow rate allowed while keeping the Cl2 concentrations below some maximum.

I solved it. I gave up on trying to calculate surface area's effect on evaporation and just went with a partial pressure of 0.5 atmospheres. It's probably not too far off the actual value.

Volume of tap water inside the tank at and above which the concentration inside the tank will equal the value in the X1 column:

 chlorine data table.png   11.76KB   0 downloads
http://gallery.nanfa... table.png.html

Below these values of F, the concentration of chlorine inside the tank will be less than X1.
Example interpretation: It would take 3.51 L of 1.25 mg/L tap water inside the 55 gallon (208 L) tank to get the concentration of chlorine up to 0.04 mg/L.

Data and formula:
 chlorine values.png   6.06KB   0 downloads
http://gallery.nanfa...values.png.html

 chlorine volume water inside tank.png   18.38KB   0 downloads
http://gallery.nanfa...e tank.png.html

I think that's right. I hope I've interpreted the time-independent flow rate correctly as the volume inside the tank. I'm not sure that's the right wording. Either way, I'm satisfied that my fish would be in no danger of chlorine toxicity from an automatic water changer. This makes sense to me, because people who have automatic water changers don't complain of chlorine toxicity killing their fish.

And if I needed a chiller I could vary those equations using Microsoft Excel to simply plug in my desired temperature and solve for my flow rate, and then set my flow rate to that value. There would also be heat contamination coming in to the tank from the room and the lights to account for, depending on individual setup.

I still have no idea if any of this is right or really any idea of what I'm doing, but I think I'm done with it until I get some good data / explanations of how this works.

Edited by EricaWieser, 08 April 2011 - 11:21 PM.

If you want to set up an explanatory model for this system you may have to use logistic regression, which you could set up in Excel but is much easier to solve in a dedicated software package like SPSS. The chemistry of atmospheres is always an interesting 3D problem-type to solve.

I am having a hard time following. I do not get how a flow rate can be defined as time independent without missing something, unless you are talking about the limit or the equilibrium at some flow rate. But then the surface area effects are required. For instance when I do a simple water substitution replacing 9 liters of a 208 liter tank with chlorinated water at 0.5 mg/L Cl2 I get a chlorine content of 0.0226 mg/L Cl2. The same volumes at 2 mg/L Cl2 tap water I get a chlorine content of 0.09 mg/L Cl2. This is without any evaporation. On the green 0.5 mg/L line in your graph for instance, I am not seeing how 8.5 liters of chlorinated water in a 208 liter tank corresponds to a 0 mg/L Cl2 concentration.

Trying to work through it from the previous page the use of the ideal gas law looks funny. Admittedly I view it from a kinetic perspective and likely missing something in the chemistry. But the way it was used here seems more applicable to internal chemical reactions within a gas as a result of interaction rates occurring during collisions. In the case of Cl2 concentrations, internally the medium is mostly chemically neutral, like when in the water pipes during transport, requiring contact with the external atmosphere to evaporate into and provide agent to react with.

So I am confused.

I am having a hard time following. I do not get how a flow rate can be defined as time independent without missing something

If you assume that the period of time is one minute/hour/whatever your unit is, then time cancels out across all terms since every one of them is per time.

Ex:
This is a per time basis: 60 miles per hour = 50 miles per hour + 10 miles per hour
If you go for one hour then you went: 50 miles + 10 miles = 60 miles.

The miles in the example above are the equivalent of the volume in my solution to the flow rate. Volume per time = flow rate. Volume is in Liters, flow rate is in Liters per time unit.

Edited by EricaWieser, 09 April 2011 - 10:41 AM.

Trying to work through it from the previous page the use of the ideal gas law looks funny.

Pressure * Volume = number of moles * the R constant * Temperature
P V = n R T
If you substitute partial pressure for total pressure, then n becomes moles of that chemical species instead of total moles.
Partial pressure of chlorine * Volume = moles of chlorine * the R constant * Temperature
Volume = (moles of chlorine * the R constant * Temperature) / (Partial pressure of chlorine)
And the same is true for a per time basis.
Volume per unit time = (moles of chlorine per unit time * the R constant * Temperature) / (Partial pressure of chlorine)

Edited by EricaWieser, 09 April 2011 - 10:44 AM.

My conclusion is that the water exchanger would not raise chlorine concentration high enough to poison the fish, even if the flow rate was fairly high and used to cool the tank.

I used the assumption that none of the chlorine was becoming chloramine, though, because chloramine does not evaporate nearly as much as chlorine gas does. No chloramine is a good assumption only if there is 0 ppm ammonia in the water. If you get an ammonia spike, some of the chlorine will convert to chloramine, which has a different partial pressure than chlorine and a different evaporation rate. Ammonia would be 0 mg/L in a fully cycled tank, so that shouldn't be a problem.

And again, as an aside, I am a lowly chemical engineering bachelor's student, and all of this was done in less than a day. I'm no expert, and you can feel free to pick aside my math and help if you want.

Edited by EricaWieser, 09 April 2011 - 10:56 AM.

Here is a fit line (that applies to the narrow region shown on the graph. It's a 4th degree polynomial, so it'll dip somewhere. Don't extend the concentration out to 1000 mg/L and expect this to still fit).

If the inlet flow rate was 2 mg/L, then the increase in concentration in the tank would be as follows with increasing flow rate:
 fit line to chlorine concentration trend.png   10.71KB   0 downloads
http://gallery.nanfa... trend.png.html

I just wanted to do that to see that my trend was right. It was hard to see, using the previous plot, that increasing the volume term increased the chlorine concentration. *nods* Okay, so far it's still right.
That line represent the max flow rate you can have in the tank, the first time the chlorine concentration reaches the concentration on the X axis. Above that flow rate, concentration is below that X value. Below that flow, concentration is below the X value. So it's a maximum, a cap, for the flow rate.

And the way to interpret that is that yes, you can use this equation. F = Par Press * (V / (R T (X-X1))) Not that that line applies to your tank, because it only applies to 55 gallon tanks.

Edited by EricaWieser, 09 April 2011 - 11:10 AM.

Many municipalities now use chloramine rather than chlorine as disinfectant, because it's a more stable molecule and keeps the chlorine in the water bound to an amine group rather than in free form. As amine groups go into solution with time they can tweak the pH, and thus probably the solubility of chlorine. I'd guess all of that would push the mass balance away from being easily described by ideal gas laws.

Many municipalities now use chloramine rather than chlorine as disinfectant, because it's a more stable molecule and keeps the chlorine in the water bound to an amine group rather than in free form.

Cleveland city water is Chlorine gas, so that's what I worked with. If you plug in the partial pressure of chloramine, the mass balance equation F = Par Press * (V / (R T (X-X1))) would give you data for it.

I'm still trying to understand the meaning of F, the volume in Liters. If anyone knows anything about the time scale values of chlorine evaporation, please let me know.

it might also work as a chiller

Looks like the answer is "no".

You grazed a legit cooling solution in your deep dive into calculation, but seemed to be more concerned with chemical concentrations.

Evaporation...

Evaporating one gallon of water requires roughly 8500btus. So, simplest idea, set a big fan to blow on your (open top) tank, and top off the water with treated replacement water. You'll be surprised how well it cools the tank.

Going into DIY mode, I guess you could fashion a "cooling sump", a big wide container, with big fans and lots of surface area, or get a swamp cooler mat and make a mini nuclear power plant type cooling tower. Then run filter return water through a bunch of stainless tubing coiled up in the sump as a heat exchanger. You wouldn't have to worry about treating the replacement/top-off sump water, as the sump water is separate from the aquarium water. Might be fun to build, might even drop the temp a couple more degrees over just a fan + open top on a 55g, depending on the relative humidity where you live...

Dorm fridge cooling could work for a couple degrees drop on a >5g nano, but a dorm fridge is only good for 100 or so btu, max, and then you'll burn out the compressor.

Peltier coolers (like a CPU liquid cooler) work pretty well for smaller (20g) tanks, though a ready made aquarium peltier cooler would probably be cheaper ($150) than DIY, once everything was said and done.

For your 55g - forget about coldwater fish until you can scratch up enough to buy a commercial chiller.
Properly designed compressed coolant chillers are pretty darned efficient (starting at about 1000btu for a 1/15th hp unit, and then waaaay up). You'd be -very- hard pressed to find a compact, cost effective DIY alternative with similar results for a tank over 30g.

Rick (party pooper)

I am still working out how to interpret this but I do understand partial pressures. Even from a kinetic perspective the interpretation is effectively the same. Your general trend also appears correct under relative changes in flow rate. However, I do not know how this applies to any real world flow rate as metered from a tap water source.

In particular your starting point is defined by:
Accumulation = In - Out + Generation - Consumption
0= (1.25 mg/L)*(X L/min) - (0.04 mg/L)*(X L/min) + 0 - Evaporation rate
Evaporation rate = (1.25 mg/L)*(X L/min) - (0.04 mg/L)*(X L/min)

In the first line "Accumulation = 0" is assumed. Here is how I am picturing "accumulation". I will initially assume a 0 evaporation rate. I will get to that and the time units shortly. You have a 208 L tank with 0 mg/L Cl2. If you drain 1 L of tank water and replace it with 1 L of 1.25 mg/L Hence you have "accumulated" 1.25 mg of Cl2 in 208 L, or 0.006 mg/L of Cl2. If you repeat this again then the 1 L drained will also drained ~0.006 mg of Cl2, while the liter added will add 1.25 mg of Cl2, or 1.244 mg of Cl2. Thus, discounting evaporation, each you repeat this you accumulate Cl2 slower as the Cl2 concentration in the tank approaches 1.25 mg/L. Hence you have a Cl2 accumulation that asymptotically approaches, or a summation of, 1.25 mg/L. Once you account for some presently unknown evaporation rate then the summation of this limit will only come to some percentage of 1.25 mg/L.

Now if we assume these limits as initial conditions the accumulation rate is indeed 0. But with an unknown evaporation rate we have no idea what initial conditions to begin with. This is why I suggested defining evaporation rates in terms of the target evaporation rates required at different flow rates rather than actual values. This way if you know the Cl2 concentration in the tap, and in the tank, and know the flow rate from the tap, you can calculate how high you can turn the tap flow rate without driving the tank Cl2 concentration above some maximum.

Now time units:
Again, for simplicity, we will start by considering the canceled out time units just for "in" and "out", i.e., "(1.25 mg/L)*(X L/min) - (0.04 mg/L)*(X L/min)". I am not sure where the 0.04 mg/L came from but consider the same summation done above, replacing 1 L of tank water with tap water at a time (time independent). Recall that in the first L 0 Cl2 was drained "out" while 1.25 mg was added "in". The second L drained 0.006 mg Cl2 "out" while another 1.25 mg was added "in", for the balance of an additional 1.244 mg of Cl2. Hence, after many repeats, "out" increases to an asymptotic limit of 1.25 mg/L as accumulation tends to 0, and "in" remains constant at 1.25 mg/L. Therefore the presumption that "out" is defined by (0.04 mg/L) must a priori assume (0.04 mg/L) as the limiting value. This is doable if consumption or evaporation is zero or known a priori, but a priori assuming a value that is needed to derive that same value ends up only justifying whatever presumed value it was assumed to be.

Getting back to the consumption part of the equation I temporarily ignored, if "consumption" is 0 then the limiting value of "out" is 1.25. If consumption or evaporation is unknown then the limiting value of "out" becomes unknown. So if (0.04 mg/L) is a limiting value it cannot be stated a priori, and if it defines initial conditions, when the tap is turned on, it is not a constant value in dimensionless units or time as provided. This also means that the X in "(1.25 mg/L)*(X L/min)" is not equal to the X in "(0.04 mg/L)*(X L/min)" in terms of Cl2 content. If X is in terms of total flow rate then the cancellation entails the presumption that the consumption rate scales at some set percentage of flow rate. This becomes even more problematic when the evaporation rate, "(1.25 mg/L)*(X L/min) - (0.04 mg/L)*(X L/min)" is given exactly the same signature as the "in"/"out" flow rate.

This does not mean you are wrong, as I could easily be interpreting the intended meaning in ways it was not meant to be defined, and/or missing something basic about chemical dynamics. But, even if I arbitrarily limit the problem to known values that are solvable, I have yet to find such an interpretation that does not have problems, whether interpreted in terms of limiting values or summations providing those limits.

I went through again and you did give (0.04 mg/L) as the target maximum Cl2 concentration. So basically "(1.25 mg/L)*(X L/min) - (0.04 mg/L)*(X L/min)" is the required evaporation rate needed. If you increase X in "(1.25 mg/L)*(X L/min)" you are not necessarily increasing X in "(0.04 mg/L)*(X L/min)". Turning up the tap flow rate in not going to linearly increase the consumption rate. So, rather than canceling, the required consumption rate should be written:
((1.25 mg/L) - (0.04 mg/L)) * (X L/min)
Or:
(1.21 mg/L) * (X L/min)

This means that for every liter of flow per time unit you need a consumption rate of 1.21 mg. A flow rate of 2 L/min then requires a consumption rate of 2 * (1.21 mg/min) to have a (0.04 mg/L) Cl2 concentration at equilibrium. This does look like a good interpretation where the values are defined in the limit, or at equilibrium. Though I still do not know how to interpret it with the rate terms canceled, but it makes no difference what unit of time is used so long as the same unit is used for flow rate and required consumption rate.

Deriving the actual consumption rate is a messy problem mathematically. To derive this we need the PH, turbulence, temperature, air flow, Cl2 concentration, etc. Since we are after an equilibrium state with a maximum Cl2 of (0.04 mg/L) we can assume that as the effective Cl2 concentration. You have specified Cl2 gas used to treat the water, which disassociates in the water to produce HOCl and HCL. It is a two way reaction with an equilibrium state given by (with environmental variables taken as constants):
k(eq) = HOCL(aquatic) * HCl(aquatic) / Cl2(gas)

However, the actual value of k(eq) depends on temperature, PH, etc., even when in an enclosed system. Since HOCL and HCl are acidic their levels also effect the equilibrium state k(eq). So as the Cl2 gas is allowed to evaporate HOCL and HCl combine to produce more Cl2 gas to reestablish equilibrium, which then itself evaporates. This mathematically goes way over my head with way too many variables that must be guestimated. Even then if the maximum is exceeded you can merely add surface area, turbulence, bubbles, pumps, etc., until it falls under that maximum.

That is why I prefer a simple real world experiment with which to bypass all these variables required to calculate real world evaporation rates. Much like previously described where any setup of choice is given a tap water source with a known flow rate and a known Cl2 concentration. The real world measured difference between Cl2 concentrations between the input and output can then be used to calculate the maximum flow allowed while maintaining a Cl2 concentration below 0.04 mg/L, all without requiring all these variables to be accounted for. Of course the derived maximum flow rate is only valid for the system the input/output test was done on, but that is fine as the maximum flow formula itself would still be valid for any system the input/output difference was provided from.

(Note the "chiller" thread has become a "chlorine / mathematics" thread. Not that there's anything wrong with that.)

Or ... for under $40 you can get an inline water filter (GE "undercounter") at your local home improvement store and plumb into the water supply to your fishroom. The cheap disposable filters just remove sediments, but the better ones also remove all chlorine. I think they're rated for 15,000 gallons. I have 2 on the my whole-house line that I change every three months, but if I wanted to mess with testing for chlorine I could make them last MUCH longer.(*)

Put one of those in, and you can go straight city-water-tap-to-tank, as long as you pay a little attention to water temperature. (And bear in mind that city water may have low oxygen levels going out of the tap.)

AND ... you're not risking your fish based on any unfounded SWAG about how sensitive this or that species is to chlorine concentrations.


(* For the cheapest long term operation, install two filter units in series, with a faucet in between. On a weekly basis, sample water from the between-filters faucet and test for chlorine. If any is detected, the water-supply side filter is used up, so toss it, move the house-side cartridge to the water-supply side, and put a new filter cartridge in the (backup) house-side unit.)

One of the perquisites to get a an automatic water changer from tap to act as as chiller is to insure the Cl2 consumption rate is high enough for the flow rate to actually chill it effectively without driving the Cl2 levels too high. The two conditions can work against each other. In particular the bubble driven pump I described likely lacks the water pumping capacity needed to chill the water. Though by setting the water level slightly above drain while still requiring the water to pass through a length of pipe with bubbles would not depend on the bubbles for water flow. Yet the bubbles would still be restricted to contact with the water actually draining into the fish tank. A float valve would not even be absolutely required that way.

I very much like the general idea Erica proposed.