Model
Model of a system from Fry and Hart (2007) with an aquarium containing goldfish and a water flow.
When determining the km value the variables were kept specific values, as described below. Afterwards the water temperature and other variables were changes to values more resembling North Africa. These setting are described below, but can also be adjusted using the sliders below the info box.
The model contains factors such as fish growth, temperature, Km, water flow and aquarium size. The weight-specific fish respiration is determined by water temperature and Km value.
As indicated by the name, 'Growth on/off', the slider turns fish growth on and off. A value of 0 turns off the growth and 1 turns on the growth.
Determining Km value
The Km was determined from trail and error to fit figure 3 in Fry and Hart (2007). The variables were set as following:
- Temp.: 25 degrees celcius
- Aquarium volume: 4 liters
- Fish stock: 0.076 kg (20 x 3.8 g)
- Run time: 4 hrs
- Flow: 0 L/hr (off)
- Fish growth: 0 (off)
When looking at the oxygen concentration (µmol/L) as a function og time (hrs), the Km value was estimated to 40 µmol.
Fish growth
Wet fish biomass consists of 45% carbon, 10% nitrogen, 1.5% phosphor, 1.5% minerals and 43% water. As one mole of carbon weighs 12 grams, is is associated with 26.7 grams of fish biomass. This means that for every one mole of carbon the fish stock assimilate, 26.7 grams biomass is gained.
For determining the growth rate it is assumed that for every mole of oxygen is respired, one mole of carbon is assimilated. Thus the growth is:
Growth in kg = [Fish respiration] * 2.64*10^(-8)
The initial fish stock was 0.076 kg corresponding to 20 goldfish with an average mass of 3.8 grams as described in Fry and Hart (2007).
Results
The factors was set values similar to those expected in North African aquaculture.
- Temp.: 28 degrees celcius
- Km: 40 µmol
- Aquarium volume: 1000 liters (1 cubicmeter)
- Fish stock: 0.576 kg (corresponding to 24 tilapia cichlids with an average mass of 24 grams)
- Run time: 4380 hrs
- Flow: 500 L/hr (on)
- Fish growth: 1 (off)
Oxygen concentration & cichlid respiration
The initial oxygen concentration in the aquarium were ~245.5 µmol/L, but drops to about 238 µmol/L within five hours. From 5 hrs to the end of the experiment there is a slight drop to 230.5 µmol/L.
The initial fish stock respiration were 3693 µmol/hr and increased to 7645 µmol/hr after six months.
A flow rate of 500 L/hr seems appropriate for a runtime of six months as the small decrease in oxygen concentration most likely won't affect the fish.
Fish stock
The initial fish stock were 0.576 kg, corresponding to 24 tilapia cichlids of 24 g. After six months the fish stock is at 1.201 kg, which is an increase of 208.5%. However, I would recommend that a company should more and larger tanks, as 1.201 kg of fish after six months of work does not seem profitable.