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Re: CO2 rates (continued)

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

	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 

	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.