44. Oxygen transfer was measured in a stirred tank bioreactor using dynamic method.
The dissolved oxygen tension was found to be 80% air saturation under steady state conditions.
The measured oxygen tensions at 7 s and 17 s were
55% and 68% air saturation, respectively.
The volumetric mass transfer coefficient
KLa is __________ s−1.
Volumetric Mass Transfer Coefficient KLa Calculation in a Stirred Tank Bioreactor
The volumetric mass transfer coefficient KLa in a stirred tank bioreactor
can be calculated using the dynamic (gassing-out) method.
From the given dissolved oxygen tension data, the calculated value is
0.07339 s−1, which corresponds to Option B
in standard biochemical engineering MCQs.
Dynamic Method Explained
The dynamic method involves temporarily reducing the dissolved oxygen (DO) concentration,
usually by nitrogen sparging, and then observing its recovery after re-aeration.
The oxygen balance follows:
where:
- C(t) = dissolved oxygen at time t (% air saturation)
- C* = steady-state dissolved oxygen (% air saturation)
- KLa = volumetric mass transfer coefficient
Rearranging logarithmically:
Hence:
Step-by-Step Calculation
Driving force = 80% − 55% = 25%
Driving force = 80% − 68% = 12%
ln(12/80) = ln(0.15) ≈ −1.897
Δt = 17 − 7 = 10 s
≈ 0.07339 s−1
Option Analysis
- 7.339 s−1: Incorrect. Unrealistically high for bioreactors and ignores logarithmic normalization.
- 0.07339 s−1: ✅ Correct. Matches the dynamic method calculation.
- 0.339 s−1: Incorrect. Overestimates due to improper handling of driving force.
- 7339 s−1: Incorrect. Decimal misplacement and physically impossible.
KLa Fundamentals
The volumetric mass transfer coefficient quantifies oxygen transfer:
In stirred tank bioreactors, KLa depends on agitation speed, aeration rate,
impeller design, and broth rheology.
Practical Applications
- Bioreactor design and scale-up
- Optimization of aerobic fermentations
- Production of antibiotics, enzymes, and biomass
- Control of dissolved oxygen using DO probes
