Question 2 of 5: The Air-On/Air-Off Method and the Principles of Batch Sterilization

Question 2: The Air-On/Air-Off Method and the Principles of Batch Sterilization (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.

(i) Air-On/Air-Off (dynamic gassing-out) method

The air-on/air-off method determines both the specific oxygen uptake rate q_O2 and the volumetric mass-transfer coefficient k_La from a single dissolved-oxygen (DO) trace recorded during an actual fermentation, without a separate sulfite-oxidation experiment. It rests on the unsteady DO balance for a well-mixed bioreactor:

where C is the dissolved oxygen concentration, C* the saturation concentration, X the biomass concentration, and q_O2X the oxygen uptake rate (OUR) of the culture.

Air-off step. Aeration is briefly stopped while the DO probe keeps recording. With no gas transfer, k_La(C*−C)=0 and the balance reduces to dC/dt=−q_O2X: the DO falls perfectly linearly, and the (negative) slope is the oxygen uptake rate OUR directly; dividing by an independently measured biomass concentration X gives q_O2=OUR/X. The interval must stay above the critical DO C_crit, or the culture itself becomes oxygen-limited and the slope no longer reflects the true, unlimited q_O2.

Air-on step. Aeration is resumed and the DO recovers toward saturation. With q_O2 now known (and roughly constant over the short recovery window), the full balance rearranges to isolate the one remaining unknown:

In practice dC/dt is read at several points along the rise (or (dC/dt+q_O2X) is regressed against C, giving slope −k_La), so k_La comes from a regression rather than a single noisy point. The key advantage over the sulfite method is that both parameters are measured in the SAME broth under the SAME operating conditions (rheology, surfactants, agitation) as the real fermentation.

(ii) Principles of batch sterilization

Both batch and continuous sterilization share the same design tool: the Del factor (∇), a lumped measure of spore "kill" obtained by integrating an Arrhenius death-rate constant $k_d(T)=A\,e^{-E_d/RT}$ over the medium's whole time–temperature history: $$\nabla=\int_0^{t_{total}}k_d(T)\,dt=\ln\!\left(\frac{N_0}{N_f}\right)$$ Because nutrients degrade thermally with a lower activation energy than spore destruction, the ∇ needed for sterility can be delivered with far less nutrient damage by a short burst at high T than by a long soak at low T — this is the design principle both approaches try to exploit, and batch sterilization's limitations follow directly from how well it can do so.

In batch (in-situ) sterilization the entire medium charge is heated, held, and cooled inside the production fermenter itself, heated by steam in the jacket/coils and/or live steam sparged directly into the medium. The design follows from the Del factor: the required total is set by the whole charge, $\nabla_{total}=\ln(n_0V/N_f)$ (typically $N_f=10^{-3}$, one chance in a thousand of a surviving spore), and it is split across the three stages, $\nabla_{total}=\nabla_{heat}+\nabla_{hold}+\nabla_{cool}$. The heat-up and cool-down contributions are integrated from the measured T(t) ramps, and the holding time at the sterilization temperature (typically 121°C) is whatever remains: $t_{hold}=\nabla_{hold}/k_d(T_{hold})$. Because the whole vessel's contents (plus, often, particulate ingredients that heat more slowly than the bulk liquid) constitute a large thermal mass relative to the available heat-transfer area, the heat-up and cool-down ramps are slow (tens of minutes for an industrial-scale batch). The medium spends a correspondingly long time at intermediate temperatures, where nutrients degrade with comparatively little useful spore-kill credit per unit of thermal exposure — the ramps still contribute real ∇ toward the sterilization target, but a disproportionate share of the nutrient loss happens during those same slow ramps rather than the controlled hold. Batch sterilization remains the practical default at small/pilot scale, for particulate-laden or delicate media that would foul or lag in a narrow continuous exchanger, and where the simplicity of using the fermenter itself (no dedicated heater/holding-tube/cooler train) outweighs the nutrient penalty of slow ramps.