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23-Chem-B4 Biochemical Engineering · December 2016

Question 4 of 5: The Air-On/Air-Off (Dynamic Gassing-Out) Method for q O2 and k L a

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

National Exam 04-Chem-B4, Biochemical Engineering — December 2016. 3 hours, Closed-Book Exam (one approved Casio or Sharp calculator model permitted). Per the exam notes, FIVE (5) questions constitute a complete paper and all five must be answered; most require a short-essay-format answer.

Reference texts: Shuler & Kargi, Bioprocess Engineering: Basic Concepts, 2nd ed.; Bailey & Ollis, Biochemical Engineering Fundamentals, 2nd ed.; Madigan et al., Brock Biology of Microorganisms, 13th ed.

Question 4: The Air-On/Air-Off (Dynamic Gassing-Out) Method for qO2 and kLa (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.

The air-on/air-off (dynamic gassing-out) method determines both the specific oxygen uptake rate qO2 and the volumetric mass-transfer coefficient kLa from a single dissolved-oxygen (DO) trace recorded during an actual fermentation, without interrupting the culture for long or requiring a separate sulfite-oxidation experiment. It rests on the unsteady dissolved-oxygen balance for a well-mixed bioreactor:

$$\frac{dC}{dt}=k_La(C^{*}-C)-q_{O2}X$$

where C is the dissolved oxygen concentration, C* the saturation concentration, X the biomass concentration, and qO2X the oxygen uptake rate (OUR) of the culture.

DOtimeair OFF: slope = -qₒ₂·Xair ONC* (saturation)C_crit
Fig. 4 — idealized DO(t) trace: each air-OFF segment (red) falls linearly with slope −qO2X; each air-ON segment (blue) recovers toward C* according to the full unsteady balance. The trace must be kept between C* and the critical DO Ccrit throughout.

Air-off step — measuring qO2

Aeration (or agitation) is briefly stopped while the DO probe continues recording. With no gas transfer, kLa(C*−C)=0 and the balance reduces to dC/dt=−qO2X: the DO falls perfectly linearly with time, and the (negative) slope is the oxygen uptake rate OUR directly. Dividing by an independently measured biomass concentration X (e.g. dry cell weight) gives the specific respiration rate qO2=OUR/X. The air-off interval must be started well above and stopped well before the DO reaches the critical dissolved-oxygen concentration Ccrit (below which respiration itself becomes oxygen-limited) — otherwise the measured slope no longer reflects the true, oxygen-unlimited qO2.

Air-on step — measuring kLa

Aeration is resumed and the DO recovers toward saturation. Because qO2 was just measured (and is taken as roughly constant over the short recovery window), it can be substituted back into the full unsteady balance and the equation rearranged to isolate the only remaining unknown:

$$k_La=\frac{dC/dt+q_{O2}X}{C^{*}-C}$$

In practice, dC/dt is read at several points along the rising trace (or (dC/dt+qO2X) is plotted against C, which for constant kLa and C* gives a straight line of slope −kLa and intercept kLaC*), and kLa is obtained by linear regression rather than from a single point, which reduces sensitivity to measurement noise.