In a well aerated and agitated microbial culture, the ‘supply'

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In a well aerated and agitated microbial culture, the ‘supply' of oxygen is equal to ‘demand' (uptake) of the growing culture. The K_La for such a system will be (K_La = volumetric mass transfer coefficient, C* = dissolved oxygen concentration in liquid in equilibrium with gaseous oxygen,C = instantaneous value of dissolved oxygen concentration, ‘r' = specific oxygen uptake rate per unit weight of cells, X = dry weight of the cells per unit volume)

1. (r X)/ (C* – C)
2. (r)/ X(C* – C)
3. (C* – C)/ (r X)
4. (X)/ r(C* – C)

Correct Option: A

The “gas out-gas in” method can directly determine the volumetric mass transfer coefficient in a bioreactor system and provide estimates of the volumetric microbial oxygen uptake rate and the average oxygen saturation concentration at the gas-liquid interface. The rate of oxygen transfer from the bubble air to the liquid phase is described by the equation :
dC_L / dt = K_La (C* – C_L)
⇒ K_La = dC_L/dt * 1/ (C* – C_L)
⇒ K_La = r*X/(C* – C_L)
Where r*X = dC_L/dt, r is the specific oxygen uptake rate per unit weight of cells and X is the dry weight of cells per unit volume.
For reliable measurements, deconvolution of the oxygen probe measurements must be made.