The dynamic method is used to measure kLa in a fermentor operated at 30degC. Data for dissolved-oxygen concentration as a function of time during the re-oxygenation step is given (table with time (s) and CAL (% air saturation)). The equilibrium concentration of oxygen in the broth is 7.9*10^-3kgm^-3. Determine kLa.
-> I know the equation for kLa, but I'm not sure what the CAL (%) corresponds to, or the equilibrium concentration of oxygen. what is C*AL? How do I convert DO% to CAL (if that's what the CAL% is)???
In the given context, "CAL (% air saturation)" refers to the percentage of dissolved oxygen (DO) in the fermentor relative to the maximum amount of dissolved oxygen that can be achieved at a given temperature and pressure. It represents the saturation level of dissolved oxygen in the liquid.
To convert the DO% to CAL value, you can use the following formula:
CAL (%) = (DO% / 100) * MaxOxygenSaturation
Where DO% is the dissolved oxygen concentration as a percentage, and MaxOxygenSaturation corresponds to the maximum saturation level of dissolved oxygen at the given temperature and pressure.
In order to determine the value of kLa, you would need to use the equilibrium concentration of oxygen in the broth (C*AL) and the dissolved oxygen data provided during the re-oxygenation step.
C*AL (equilibrium concentration of oxygen in the broth) is given as 7.9 * 10^-3 kg/m^3. This represents the concentration of dissolved oxygen when the system has reached equilibrium at the specified conditions.
To calculate kLa, you can use the following formula:
kLa = (1 / t) * ln((C*AL - CAL) / (C*AL))
Where t is the time taken during the re-oxygenation step, CAL is the measured dissolved oxygen concentration at that particular time, and C*AL is the equilibrium concentration of oxygen in the broth.
By plugging in the appropriate values from the provided data into the formula, you can determine the value of kLa for the given fermentor system.