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Oxygen - Sizing your Aquaponic Air System

credit to: nwestwood

link: http://www.urbanaquaponics.com/content.php?129-Oxygen-Sizing-your-Aquaponic-Air-System

The success of an aquaponic or aquaculture venture depends on providing as near an optimum environment for the rapid growth of the fish as possible. Of all the environmental factors, water quality and in particular, dissolved oxygen (DO) is the most important and critical. 

Although the air we breathe usually contains about 21% oxygen, oxygen is only slightly soluble in water. As a result, aquatic species must spend a great deal of energy to remove what little dissolved oxygen there is. Temperature, barometric pressure, salinity, and altitude all directly affect oxygen concentrations in both air and water.

In addition, each species has varying tolerances to low levels of dissolved oxygen. Salmonids (trout), as a group, require 6.0 to 8.0 mg/L of dissolved oxygen. For catfish and tilapia allowable minimum levels can be as low as 2.0 or 3.0 mg/L although the recommended levels are 5.0 to 6.0 mg/L.

Cold water will hold more dissolved oxygen than warm water. Likewise, it is easier to reach a level of saturation at lower elevations than at higher elevations.

General Aeration for General Systems - The Easy Answer

Most aquatic suppliers provide data sheets that can help you quickly determine your general air flow needs. For example, AquaticEcos chart for their air diffusers here shows the number of pounds of fish a given diffuser will support. (In the column under the blue AES logo.) The AS15L 6" medium pore diffuser will support 14lbs of fish. This is a general guideline and was calculated for adult Tilapia at sea level and 72-78 degree water temperature with a healthy saftey margin. 

If our system is at sea level and we plan on having 125lbs of fish at harvest time, we would need (125/14=8.928) or 9 diffusers. At the suggested rate, each diffuser needs an input flow of 0.5 cfm of air, so we would need a pump that puts out 4.5 cfm (9 x 0.5) at a 3 depth in our tank. For each 1000 feet of elevation above sea level, the air requirement increases by an additional 4%. For example, if our system is located in Denver, Colorado at 5,000 feet, we would need 20% more air diffusers to get the desired result (8.928 x 1.2 = 10.7 or 11 diffusers). In our experience this general guideline contains a wide safety margin. If you want to more precisely calculate your specific system, read on.

How Big of an Air Pump do I Need?

In designing an aquaponic system we ask ourselves:

1. How big of a fish tank can I afford and fit into the space I have?

2. Which kind of fish will I raise and how many can I safely fit in my tank at harvest size?

3. How many grow beds and/or floating raft tanks do I need to process the bio-load from the fish?

4. How big of a water pump do I need to turn over the fish tank water at least once per hour?

5. Finally, How big of an air pump and how many air stones do I need to maintain safe levels of Oxygen? (generally 6.0 mg/L or above).

Key Aquaculture Oxygen Design Parameters:

1. Oxygen (O2) Consumption by the fish and bacteria(1)

A. 0.025kg of O2 needed per kg of feed fed to the fish for the fish.

B. 0.012kg of 02 needed per kg of feed fed for the nitrifying bacteria.

C. 0.13kg O2 needed per kg of feed fed for the heterotrophic bacteria (can be as high as .5)

Total = 0.5kg of O2 needed per kg of feed fed, or 1/2lb of O2 per pound of feed fed.

The author of Recirculating Aquaculture states: "In a pure recirculating aquaculture system (RAS) the ratio of 1.0 kg of oxygen per 1.0 kg of feed fed is the safe recommended design value"(1). However, in our experience the 0.5kg of O2 per kg of feed is adequate in traditional home aquaponic systems.

Next we look at how aeration transfers the oxygen into the water. In Urban Aquaponics we use air diffusers (air stones). There are many other methods aeration, most are more efficient, but more expensive. We will limit our discussion to 6" air diffusers and you can easily adapt the example to other methods.

2. Oxygen Production and Distribution.

A. There is 21% oxygen in normal air.

B. There is 0.075 lbs of air in a cubic foot.

C. By weight, 23% of a cubic foot of air is oxygen (oxygen is heavier than many of the other gases in air).

D. Standard Oxygen Transfer Efficiency rate (SOTE) or rate at which oxygen will transfer to water under "standard" conditions per 1 foot of depth. For a 6" medium pore diffuser it is .01 lbs per foot of depth.

E. Field Transfer Efficiency (FTE) - The actual tested transfer efficiency based upon the existing oxygen content of the water (the higher it is, the less will transfer), temperature and salinity. We assume the input water is at 68-78 degrees and 4.0-5.0 mg/L DO which gives an FTE of approximately .5 (2)

Note: Oxygen is transferred into water by having a density differential (low oxygen water to high oxygen air), exposing the greatest surface area of oxygen to the water and by keeping the oxygen in contact over time. The smaller the bubbles, the greater the surface area, but small bubbles require higher pressure. Medium pore air diffusers are recommended as the most cost effective. The deeper the diffusers, then the longer the time the air bubbles are exposed to the water, increasing diffusion. 

Plants in the system may also require or produce some oxygen (algae produces during the day, consumes at night). Additionally, in a RAS system, there may be other components that require oxygen. For the purpose of this article we will work the calculations as if there were no other demands. We want to produce enough oxygen to maintain 6.0 mg/L of oxygen in the fish tank if the water pumps were to fail, assuming 0.5lbs of Oxygen per 1lb of feed fed. (Again, in our experience this is more than adequate for a typical aquaponic setup, including the plants and other components.)

Lets work through an example system using this 0.5:1 ratio and see how this all goes together.

Let’s assume we have a fish tank in our system that is 250 gallons (946 liters). And we are raising Rainbow Trout and that final stocking density is 1/4 lb per gallon (25-30grams per liter).

Also assume that the fish consume 2% of their body mass at harvest (species vary) or 1.25lbs (567 g) of feed per day. (250 gallons x 0.25 = 62.5lbs x 0.02 = 1.25lbs of feed per day). 

Figuring at the 1lb of Oxygen to 1lb of feed, that means we need 1.25lbs (567g) of Oxygen every 24 hours or 0.052lbs (24g) per hour. Or, using the 0.5 to 1 oxygen to feed ratio, 0.625lbs (284g)/24 hours, 0.026lbs (12g) per hour.

The formula for oxygen injection is as follows:

CFM (ft3/min) of device X lbs of air/ft3 X lbs of oxygen/lb of air X (SOTE X Depth) X FTE X Time = lbs of O2 per Time transferred.

To break this down:

CFM (ft3/min) of device = 0.5 cfm (Using our 6" medium pore diffusers from Aquaticeco).

Lbs of air/ft3 = 0.075 (The weight of a cubic foot of air)

Lbs of Oxygen per lb/air = 0.23 (The weight of the Oxygen in a pound of air)

SOTE = 0.01 

Depth = 3 (assuming a standard IBC tote or typical circular fish tank).

FTE = 0.5

Time = 60 (minutes per hour to get to O2 per Hour)

or

0.5 x 0.075 x 0.23 x (0.01 x 3) x 0.5 x 60 = lbs of O2 per hour per 6" stone = 0.0077625 lbs of O2/hr

You can calculate 3" air stones or calculate different depths by substituting the correct values.

Then we divide the oxygen needs of the example system by the O2 produced by each air stone to find out how many air stones are needed.

0.02604167 / 0.0077625 = 3.35 air stones at sea level.

Im at 5000 feet so with a 4% loss per thousand feet, I need an extra 20%. I need 3.35 air stones x 1.20 = 4.026 air stones.

If I go with 4 air stones (5 would be safer), and each air stone uses 0.5 cfm, then we need a pump that produces a minimum of 2.0 cfm at 3 depth. (0.5 x 4 = 2.0).

In my own system I have enough fish to reach a density of 1/2lb per gallon (not recommended). I started with an air pump that produced 2.5 CFM at 3 and as the fish grew, the Dissolved Oxygen levels declined to 5.6 mg/L and I had fish that were not eating as well and showing signs of stress and sickness. I added a second air pump (same as the first) and several more air stones (equivalant of 10) and the Dissolved Oxygen level went back up to 6.4 mg/L.

Much higher densities are supported in pure RAS systems through the use of pure oxygen and more efficient aeration methods. These are not generally employed or needed in a properly designed and sized aquaponics system.

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