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**To**:**Aquatic-Plants at actwin_com****Subject**:**Re: CO2 rates (continued)****From**:**"Roger S. Miller" <rgrmill at rt66_com>**- Date: Mon, 19 Jan 1998 21:59:01 -0700 (MST)
- In-Reply-To: <199801192048.PAA03997 at acme_actwin.com>

Hark back to Jeff Kropp's letter... > > I have tank conditions > > (steady co2 injected, dKH 6) resulting in a pH change of .4 for each light > > cycle but have very slow growth to show for it. Could this be symptomatic > > of a particular nutrient deficiency? > > > To which I "duh'd"... > Don't know. I'll give it some thought. First, I had a maybe similar case in one of my tanks last year. I had lots of photosynthesis evidenced by active bubbling every afternoon, but not much growth to show for it. I never identified a nutrient deficiency that I was confident caused the problem. The growth problem and a couple other symptoms disappeared after I switched to lights with a stronger true red spectrum. I never did figure out what might be happening to the CO2 that I thought was being fixed. On to the problem of photosynthesis rates (carbon fixation rates) from pH swings. This is going to get a little hairy. Sorry. I gave it some thought and came up with a simple model that suffers all the usual ills of simple models. The model might also be useful for the alternate problem (constant pH, varying injection rate) that George Booth posed a few days ago. A CO2-injected tank has two sources of CO2 - respiration in the tank and the CO2 injection. Let's call the CO2 input "I" for input. For simplicity, I'm going to assume the part of "I" due to respiration is negligible, or at least constant. Some of the CO2 diffuses out to the atmosphere. The rate of escape depends on a lot of factors, including temperature, water turbulance, CO2 concentration, surface area and probably a few other things. In most of out tanks, temperature is regulated within small limits. Turbulance and surface area are constant. For simplicity, I'm going to assert that the loss rate could be approximated as D*(C-0.43), where C is the CO2 concentration in the tank, the constant 0.43 is the CO2 concentration in water at equilibrium with the atmosphere and D is a coefficient that varies from tank to tank, but is contant for any one tank. Further, for CO2 concentrations much higher than 0.43, the constant can be ignored so the diffusive loss rate is approximately D*C. While the lights are on some CO2 is also taken from the water by photosynthesising plants and algae. Lets call that rate "F" for fixation. The CO2 concentration "C" (or, in a pH-regulated tank, the injection rate "I") starts to change after the lights are turned on, but after some time the values should stabilize. Under stable conditions, the rates of CO2 input, loss and output just balance. That is: I = F + D*C Similarly, the CO2 concentration (or in a pH-regulated tank, the injection rate) starts to change after the lights are turned off, but should eventually stabilize. Without carbon fixation going on, the equation is just I = D*C Concider Jeff's case where the input rate is constant. I'll use C(light) for the stable CO2 concentration with the lights on, and C(dark) for the stable CO2 concentration with the lights off. I = F + D*C(light) and I = D*C(dark) I can combine these equations and rearrange to get rid of D. F/I = 1 - C(light)/C(dark) The ratio F/I gives the part of the total CO2 input that is fixed by plants and algae. We have formulas that relate pH and alkalinity to C, and those can be inserted here. I won't go through the details. Using pH(light) and KH(light) for the pH and alkalinity measured under stable lit conditions and pH(dark) and KH(dark) for values measured under stable dark conditions, the formula becomes: F/I = 1 - (KH(light)/KH(dark))*10^-(pH(light)-pH(dark)) If the KH is pretty much constant then it drops out of the formula, which becomes: F/I = 1-10^-(pH(light)-pH(dark)) Jeff had a day-to-night pH swing of 0.4. Assuming the KH is constant, F/I in his tank is about 0.6. That is, with lights on 60% of the CO2 that Jeff injects is getting fixed by his plants. That's probably a pretty good number. Anybody want to compare their's? The case of a pH-regulated tank is simpler. If pH and alkalinity are constant, then so is the CO2 concentration. If alkalinity doesn't change then regulating the pH also regulates the CO2 concentration. I'll assume alkalinity stays constant. The basic equations can be combined and the "D" value eliminated. Using I(light) for the injection rate measured under stable lit conditions, and I(dark) for the injection rate measured under stable dark conditions: F = I(light) - I(dark) These equations indicate that alkalinity may not be a factor when you use pH swings to estimate the F/I ratio, or injection rates to estimate the growth rate. I find that a little hard to swallow. "I" as used in these equations is the rate that CO2 is dissolving into the water. If your system allows some CO2 to bubble out of the water, then "I" isn't the same thing as the rate you bubble CO2 into the tank. But in the pH-regulated case the "bubble count" rate can be used as the inflow rate as long as the efficiency of the injection system (amount dissolved/amount injected) doesn't change from night to day. Incidentally, I've got some interesting calc's on what happens inside a CO2 bubble after it's released under water. Maybe some other time. Roger Miller In Albuquerque, where it's dark out.

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