Q.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 1×10-4 g oxygen consumed / g biomass s-1 and 60 min-1, respectively.
If the oxygen solubility is 8×10-3 kg m-3 under the operating conditions, based only on oxygen dynamics, the maximum possible cell concentration is ________ kg m-3. (Answer in integer)
Calculating Maximum Cell Concentration in Aspergillus niger Bioreactor for Citric Acid Production
The maximum possible cell concentration is 80 kg/m³ based on oxygen transfer limitations.
Core Concept
At steady state in aerated bioreactors, oxygen transfer rate (OTR) equals oxygen uptake rate (OUR). Maximum biomass occurs when dissolved oxygen approaches zero, so OTRmax = kLa × C*, where kLa is the volumetric mass transfer coefficient and C* is oxygen solubility.
Step-by-Step Calculation
Convert units first: kLa = 60 min-1 = 1 s-1; qO2 = 1×10-4 g O2/g biomass·s = 10-7 kg O2/kg biomass·s; C* = 8×10-3 kg/m³.
OTRmax = kLa × C* = 1 s-1 × 8×10-3 kg/m³ = 8×10-3 kg O2/m³·s.
Maximum cell concentration Xmax = OTRmax / qO2 = (8×10-3) / (10-7) = 80,000 g/m³ = 80 kg/m³.
Unit Consistency Check
| Parameter | Given | Converted | Role |
|---|---|---|---|
| kLa | 60 min-1 | 1 s-1 | Transfer efficiency |
| qO2 | 1×10-4 g/g·s | 10-7 kg/kg·s | Specific uptake |
| C* | 8×10-3 kg/m³ | Same | Solubility limit |
| Xmax | – | 80 kg/m³ | Calculated |
Common Errors Explained
- Skipping kLa unit conversion (min-1 to s-1) yields ~4.8 kg/m³—incorrect.
- Wrong qO2 conversion (e.g., keeping g instead of kg) gives 800 kg/m³—off by factor of 10.
- Ignoring steady-state OTR=OUR assumption overestimates by not setting C=0.
