Dynamic (gassing-out) method for kLa: the technique is fundamentally based on which oxygen balance principle in an aerated fermenter?

Introduction / Context:
The dynamic (gassing-out) method is widely used to estimate the volumetric oxygen transfer coefficient, kLa, directly in a bioreactor under process conditions. Unlike purely chemical methods, it uses the transient dissolved-oxygen (DO) response while cells are consuming oxygen.

Given Data / Assumptions:

• Bioreactor is equipped with a DO probe and aeration can be switched or stepped.
• Cells consume oxygen at a rate OUR (oxygen uptake rate).
• Henry’s equilibrium saturation C* is known for the operating conditions.

Concept / Approach:
The liquid-phase oxygen balance is dC/dt = kLa*(C* − C) − OUR. By imposing a step (e.g., turning air on/off or changing gas composition) and recording DO versus time, one can regress kLa while accounting for OUR. This distinguishes the dynamic method from chemical sulfite oxidation tests, which measure kLa in the absence of cells.

Step-by-Step Solution:
1) Create a controlled change in aeration or agitation and log DO continuously.2) Model the transient using dC/dt = kLa*(C* − C) − OUR.3) Estimate kLa (and possibly OUR) from the transient profile.

Verification / Alternative check:
Comparing dynamic-method kLa to off-line sulfite oxidation values often shows differences due to broth rheology and cell presence; the dynamic method better reflects real process conditions.

Why Other Options Are Wrong:
Option B ignores OUR, a key term during growth; C describes a different chemical method; D is too vague; E lacks necessary liquid-phase information.

Common Pitfalls:
Neglecting probe response time and calibration, or assuming OUR is constant when it varies with biomass and conditions.

Final Answer:
Oxygen material balance in an aerated batch fermenter during microbial growth (kLa(C* − C) − OUR)