The purpose of the model is to simulate aquacultural farming of Tilapia. The basic assumption as, that Tilapia respire in the same manner as goldfish. Thus this model is based on Fry and Hart, 1948.
Most chemical reactions, such as respiration, are catalyzed by enzymes. The rate of enzymatic reactions can be described by Michaelis-Menten kinetics:
V = V(max)*C/(C+Km)
V is the reaction rate, V(max) is the maximum reaction rate, C is the concentration of the substrate, and Km is a constant expressed as the substrate koncentration (C) at half V(max). In this model the substrate is oxygen, and the reaction using the substrate is respiration performed by Tilapia in a tank.
Temp: Temperature is in deg. C, and is held constant at 15 deg C throughout the model. The parameter "Temp" affects "Oxygen solubility" and "Weight specific respiration" directly. The parameter indirectly affects the stock "Oxygen in tank" and the flow "Respiration.
Oxygen solubility: The converter "Oxygen solubility" is based on data from Unisense (link on Blackboard) and is linked to the stock "Oxygen in tank". It expresses the amount of oxygen dissolved in the water at a given temp. The unit is μmol/L.
Weight specific respiration: Describes the respiration performed by the Tilapia in the tank. From the data published by Fry and Hart a fitted polynomial equation is found. This equation represent the parameter "Weight specific respiration". The variable in the equation is the temperature. Therefore the temperature indirectly affects the respiration, and thus the oxygen concentration in the tank. The unit for "Weight specific respiration" isμmol O2/kg*hr.
Flowrate: The parameter "Flowrate" determines the flow in and out of the tank. The unit is L/hr and the flowrate is set 100 L/hr, which 10% of the tank volume.
Volume: The tank volume is controlled by the parameter "Volume" as default 1 L.
Oxygen in tank: The stock "Oxygen in tank" is defined as "Oxygen solubility" / "Volume". As long as the volume of the tank is 1 L, this definition equals the concentration of oxygen in the tank. The unit is μmol/L.
Oxygen concentration: The parameter "Oxygen concentration" redirects the concentration of oxygen in the to the flow "Respiration". Thus the parameter is the concentration in the equation for the respiration performed by Tilapia. The unit is μmol/L.
Km: The parameter "Km" is a constant found by qualified guessing and comparison with the data from Fry and Hart. A given Km was chosen to run the model. The concentration-of-oxygen-in-the-tank-data from the given simulation was compared with the oxygen-concentration-data from fig. 3 in Fry and Hart. This was continued until the best fit was found. In this case the best Km fit was 3,5. The unit for Km is μmol.
Respiration: The flow "Respiration" is described as V = Vmax*C/(C+Km). Four parameter affects the respiration directly: "Fish mass", "Oxygen concentration", "Km" and "Weight specific respiration". These four parameters is combined to an equation that fits the Michaelis-Menten kinetics. Thus "Respiration"="Fish mass"*"Weight specific respiration"*"Oxygen concentration"/("Oxygen concentration"+"Km"). The unit is kg/hr.
Growth rate: The flow "Growth rate" determines how much weight the fishes puts on per hour.
Fish biomass: The startout weight of fish is 5 kg, thus the stock "Fish biomass" is set to 5. The unit is kg.
To find the initial equilibration of
the oxygen concentration in the tank. The model was simulated for four hours. The initial equilibrium was 0,3178 μmol/L. This oxygen is used as an default oxygen concentration.
The model is now simulated for half a year (4380 hr).