Marcel G
Member
Stable, safe, cheap & non-overdosable CO2 dosing method
The principle of this method
Calculation of the container size
To be continued ...
This is [in my opinion] one of the best, unrivalled stable, cheapest and easiest to implement methods of CO2 dosing, where carbon dioxide is virtually impossible to overdose.
Note: As far as I know, the principle of this method was first formulated and published under the German name Paffrathsche Rinne (Paffrath's channel) or Paffrathschale (Paffrath's dish), named after the German developer Kurt Paffrath, in the German book Bestimmung und Pflege von Aquarienpflanzen (1978). See References at the end of the article for additional sources of information on this method.
The principle of this method
An inverted container (in my case I used a glass beaker) is placed below the water level in the aquarium and fixed to the side of the aquarium, for example with suction cups. Carbon dioxide is fed into this vessel [from a cylinder or fermentation vessel] and accumulates there, forming a so-called gas pocket (a giant CO2 bubble). The carbon dioxide spontaneously passes (diffuses) into the aquarium water at the contact surface [of the formed CO2 bubble] with the aquarium water. So [logically] the larger the contact area, the more carbon dioxide will transfer into the water (i.e. the higher the resulting CO2 concentration in the aquarium water). Since excess carbon dioxide constantly tends to escape through the water surface into the atmosphere, its resulting amount in the water is determined not only by the size of the container [from which it diffuses into the water], but also by the size of the water surface [from which it diffuses into the atmosphere]. The size of the container must therefore be adapted to the size of the water surface. The dissolution efficiency can be significantly increased if the contact surface of the vessel is subjected to a strong flow (e.g. through the outlet of a filter or water pump). The velocity of the water flow at the contact surface [of the gas bubble] is therefore another factor that influences the resulting CO2 concentration.
Calculation of the container size
Initial assumption
Current CO2 concentration in air and its equilibrium concentration in water:
- 425 ppm CO2(air) (= 0.0425%) = 0.616 ppm CO2(aq)
Logic behind this calculation
If the air above the aquarium contains 0.0425% CO2, its equilibrium concentration in the water will be 0.616 ppm CO2. How much does the concentration of CO2 above the surface have to rise for its concentration in the water to increase to, for example, 30 ppm?
Calculating the required CO2(air) concentration
So, if we want to have 30 ppm CO2 in the aquarium water, we need to have 2.07% (= 20,700 ppm) CO2 in the air above the aquarium. How to achieve this higher CO2 concentration [above the aquarium]?
Problem
The problem with this option is that such a high CO2 concentration (= 20,700 ppm) in the air [above the aquarium] would not only be difficult to ensure (and maintain) in the long term, but would also be toxic to humans (i.e., could poison us). Fortunately, there is a workaround to this problem:
Solution
We can move this much more CO2-concentrated atmosphere underwater. And not only that, we can increase this concentration to the maximum (i.e. 100%).
The logic behind this solution is as follows:
- If there were 100% CO2 above the entire aquarium, then the CO2 concentration in the aqurium water would rise to 1,450 ppm (100 * 0.616 / 0.0425). But, as we only want to achieve a concentration of ~30 ppm CO2, then the contact area of the container with that 100% CO2 needs to be only 2.07% of the water surface area (30 * 100 / 1,450).
- Given our aquarium has a water surface area of say 30 * 25 cm = 750 cm2, then the underwater container with 100% CO2 only needs to have a surface area of ~15.5 cm2 (2.07% of 750 cm2 or 750 * 30 / 1,450).
Thus, a contact area of 15.5 cm2 is [theoretically] required to achieve the target concentration of 30 ppm CO2(aq).
In other words, to achieve a concentration of 30 ppm CO2 we need a CO2 container with a contact area of 15.5 cm2.
Consideration of other factors
However, as the above calculation does not take into account some factors (which will reduce the efficiency of CO2 diffusion), it is advisable to increase the contact area by a certain coefficient.
Factors negatively affecting CO2 diffusion in water:
- The air inside the diffuser won't be 100% CO2 for long, other gasses dissolved in the water will enter the diffuser.
- Yugang attempts to solve this problem by using what is called an "overflow" → a small cutout in the bottom edge of the container, through which the excess gas escapes from the container in the form of small bubbles. He assumes that these escaping bubbles contain "old" gas (i.e. other gases besides CO2 that diffuse into the container from the water over time => e.g. N2, O2), and that their removal has a self-cleaning function => thanks to their removal the gas in the container remains 100% pure and concentrated.
- The problem I see with this assumption is that other gases that diffuse from the surrounding water into the container are lighter than CO2 (molar mass of CO2 is 44 g/mol while the molar mass of O2 is 32 g/mol and that of N2 is 28 g/mol), and therefore will accumulate in the upper part of the container, not in the lower part where the excess gas escapes as bubbles. The bubbles that escape from the bottom part of the container will therefore contain nothing but pure CO2.
- In order to solve this problem, some sort of gas venting would have to be done at the top (and not at the bottom) of the vessel as e.g. Kurt Paffrath had in his original design →
Entlüftung = deaeration (air removal)
- This can be a problem especially with low (shallow) containers. If a taller container (e.g. a beaker) is used, in my experience no significant accumulation of foreign gases will occur (at least not within a few months). Still, it may be a good idea to manually empty the container from time to time (i.e. every few months) and fill it completely with fresh carbon dioxide.
- There is a difference in speed between CO2 dissolving from the diffuser into the water, and from the water in to the air at the rest of the surface. This can also be influenced by water movement, etc.
- The water in an aquarium is not 100% pure, it contains small amounts of salts that have a negative effect on the solubility of CO2.
- Consumption/production of CO2 by plants, bacteria and fish is not accounted for.
Calculating contact area
Based on the above factors and practical measurements, it seems appropriate to increase the diffuser contact area by about 1/3 = 33%
PS: Using Yugang's alternative method of calculation, it comes out to 37%.
Thus, the calculated [theoretical] value of the diffuser contact area (= 15.5 cm2) should [in reality] be approximately 20.6 cm2 (15.5 * 1.33).
Calculating container size
- Round container (diameter)
- Ø = 2 * √ ( surface-size / π )
- Ø = 2 * √ ( 20.6 / 3.14 ) = 5.1 cm
- Square container (width x length)
- Dimensions = √ ( surface-size )
- Dimensions = √ 20.6 = 4.5 x 4.5 cm
Yugang's alternative method of calculation:
S = water-surface / ( cA * cB )
- water surface = the surface area of our aquarium (in cm2)
- length and width of my aquarium (height is not important here): 30 x 25 cm
- water surface area = 30 * 25 cm = 750 cm2
- cA (coefficient A) = 17.7
- determined experimentally
- cB (coefficient B)
- for a pH drop of 1.5 (~60 ppm CO2) = 1
- for a pH drop of 1.2 (~30 ppm CO2) = 2
- for a pH drop of 0.9 (~15 ppm CO2) = 4
- container surface
- for 15 ppm CO2: 750 / (17.7 * 4) = 10.6 cm2
- for 30 ppm CO2: 750 / (17.7 * 2) = 21.2 cm2
- for 60 ppm CO2: 750 / (17.7 * 1) = 42.4 cm2
- conversion to square or circle
- round container (diameter): 2 * √ ( S / π )
- for 15 ppm CO2: 2 * √ ( 10.6 / 3.14 ) = 3.7 cm
- for 30 ppm CO2: 2 * √ ( 21.2 / 3.14 ) = 5.2 cm
- for 60 ppm CO2: 2 * √ ( 42.4 / 3.14 ) = 7.35 cm
- square container (size): √ S
- for 15 ppm CO2: √ 10.6 = 3.3 x 3.3 cm
- for 30 ppm CO2: √ 21.2 = 4.6 x 4.6 cm
- for 60 ppm CO2: √ 42.4 = 6.5 x 6.5 cm
- round container (diameter): 2 * √ ( S / π )
