GATE 2024 BT – Question 55
Aspergillus niger is grown in a 10,000 L stirred batch bioreactor under aerated conditions to produce citric acid. At steady state oxygen transfer conditions, the specific oxygen uptake rate of the organism and the volumetric mass transfer coefficient are $1\times10^{-4}$ g oxygen consumed/g biomass s$^{-1}$ and 60 min$^{-1}$, respectively. If the oxygen solubility is $8\times10^{-3}$ kg m$^{-3}$ under the operating conditions, based only on oxygen dynamics, the maximum possible cell concentration is ________ kg m$^{-3}$ (Answer in integer).
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Correct answer: 80
Explanation
Oxygen supply equals demand: $k_La\,C^* = q_{O_2}X$ at the largest X (dissolved oxygen near zero). $k_La = 60/60 = 1$ s$^{-1}$, so $X = \frac{1 \times 8\times10^{-3}}{1\times10^{-4}} = 80$ kg m$^{-3}$.