Question 9 of 10: Measuring Oxygen Uptake Rate and $k_La$ in a Bioreactor

Question 9: Measuring Oxygen Uptake Rate and $k_La$ in a Bioreactor (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(a) Parameters needed for the steady-state gas-balance method. The oxygen uptake rate (OUR) is obtained from a steady-state O₂ mass balance across the fermenter gas phase, which requires measuring: the inlet and exit gas volumetric flow rates ($F_{g,in}$, $F_{g,out}$ — or an inert-gas, e.g. N₂, balance if only $F_{g,in}$ is metered directly); the O₂ mole fraction (or partial pressure) in the inlet air ($y_{O_2,in}$, normally $\approx0.209$) and in the exit gas ($y_{O_2,out}$), from a paramagnetic or mass-spectrometric O₂ analyzer; the total pressure and temperature of the gas stream (to convert flows to molar terms via the ideal gas law); the liquid working volume $V_L$; and the biomass concentration $X$ (dry weight), needed to convert the volumetric OUR into the specific rate $q_{O_2}=\text{OUR}/X=(F_{g,in}y_{O_2,in}-F_{g,out}y_{O_2,out})/(V_LX)$.

(b) Why the gas-balance method is often inaccurate. The oxygen actually consumed is the small difference between two comparable, similarly-sized numbers — the O₂ content of the inlet gas and the O₂ content of the exit gas (e.g. 20.9% in vs. 19–20.5% out is typical) — so any small absolute error in either gas-analyzer reading, or in the metered flow rates, is amplified into a large relative error in the computed OUR. This problem is worst exactly when it matters most for process control: at low respiration rates (e.g. early growth, low biomass density) where the in/out O₂ difference is smallest, and in large, heavily-aerated fermenters where high air throughput dilutes the depletion signal further. Additional error is introduced whenever the exit flow $F_{g,out}$ is not measured directly but is back-calculated from an inert-gas balance, compounding the uncertainty from two measurements instead of one.

(c) Choosing between the dynamic and steady-state methods for $k_La$. The dynamic (gassing-out) method briefly interrupts aeration, lets the dissolved-oxygen (DO) probe register the fall caused by ongoing respiration ($dC/dt=-q_{O_2}X$, giving $q_{O_2}X$ directly), then resumes aeration and fits the exponential DO-recovery transient ($dC/dt=k_La(C^*-C)-q_{O_2}X$) to extract $k_La$. This method is preferable when the culture's respiration rate is high enough to produce a clean, measurable DO dip within a practical time without starving the cells of oxygen, and when a fast-responding DO probe is available to resolve the transient — i.e. for actively growing, well-aerated aerobic cultures, and when an in-situ, real-time measurement with minimal process disturbance is wanted. The steady-state (gas-balance) method is preferred when the culture's respiration is too weak to produce a resolvable dynamic signal (very low biomass density, an early growth stage, or systems with such high $k_La$ that the transient collapses faster than the probe can track it), when no fast-responding DO probe is available, for abiotic calibration tests (e.g. the sulfite-oxidation method, which has no biological respiration to exploit at all), or whenever even a brief interruption of aeration would unacceptably stress a sensitive culture.