Many people have expressed concerns about my recent Forum paper, such as this one:

"You're confusing oxygen transfer mechanisms with respiration.  The respiration determines the OTR which is then matched by the oxygen transfer rate."

My reply:

The respiration determines OUR that equates to the OTR at steady-state. The understanding that "The respiration determines the OUR which is then matched by the oxygen transfer rate." concurs with my thesis, and indeed is correct. But in submerged aeration, there is the phenomenon known as gas-side oxygen depletion, so that the oxygen transfer rate is affected by this effect and this effect (incorrectly) changes the value of Klaf. To make the correction, the OTR is therefore given by Klaf (C*inff - c)-R under the principle of superposition in physics. This is then matched by the oxygen transfer rate OTR at steady-state, which is equal to R.

Therefore,

Klaf (C*inff -c)-R = R.

"We did try to take time and explain that to you... There is no double R term.  R is NOT a part of the oxygen transfer mechanism."

My reply:

Yes, R is not part of the oxygen transfer mechanism, but gas-side oxygen depletion is. If R is non-variant, then it can be determined in a gas flow steady state, where R is matched by the gas depletion rate in the bubbles which affects the value of the OTR. This has led to THE ABOVE EQUATION when Klaf is understood to be (alpha.Kla) where alpha is a function of the wastewater characteristics only. The current alpha as used in the conventional model treats it as a lumped parameter that envelopes both effects (water characteristics and gas depletion), making it a highly variable parameter that is indeterminate. The concept of gas-side depletion of oxygen from air bubbles, at first glance, appears to be simple and straightforward, but is in fact less readily understood than it may seem. In ordinary air bubble aeration, the OTE is typically 10 ~ 20%, since oxygen gas is only slightly soluble in water. This 10 ~ 20% by weight is the actual amount of oxygen successfully being transferred to the liquid. This quantity is exactly equal to the quantity of gas depleted from the air bubbles.

In fact, if in the absence of free surface gas transfer, gas-side gas depletion as the bubbles rise to the free surface is the ONLY means of oxygen transfer, including any oxygen transfer at the bubble formation. Therefore, any modeling of oxygen transfer into any liquid (tap water, sewage, industrial wastes, etc.) must include the gas depletion effect, otherwise, the model cannot be valid.

In the review paper by Lars Uby (2019), in section 6.1, it was stated that "Among the CEN and DWA standard test methods, no result dependence on initial conditions (supersaturation or depletion of oxygen and nitrogen) has been detected (Wagner, 1991), but a rigorous uncertainty analysis is lacking. This has been fully accepted in German and European practice (DWA, 2007; CEN, 2003). Gas side depletion of oxygen from air bubbles has been shown to be a minor concern under common conditions (Baillod and Brown, 1983; Jiang and Stenstrom, 2012), corroborating this approach [of this paper]. In the interest of standardization and uncertainty quantification, the difference should be quantified, though experience speaks for at most a minor impact." IN my opinion, the above understanding by Lars is absolutely incorrect. It should be understood only in the context of the results of a clean water test, where the parameters Cs (saturation value) and Kla(mass transfer coefficient) are estimated. The reason why no result dependence on initial conditions (supersaturation or depletion of oxygen and nitrogen) has been detected, is because these effects have already been absorbed in the Standard Model. In other words, the calculated results of the two parameters have already included dependence on these effects, even though such dependence is not detected. In the application of clean water results to sewage or other liquid, these effects will change in accordance with changes in the gas depletion which is the same as changes in oxygen transfer under a changed environment. The bacterial and other microbial composition and their metabolic functioning, in particular, constitute drastic changes in the oxygen gas depletion rate which then drastically affect the value of the gas transfer parameters. Standardization and uncertainly analysis by all means, but they will not significantly improve on the clean water test results. On the other hand, if clean water test results are to be translated to other fluids, mixed liquor for example, then the principle of superposition must be applied to the Standard Model to take into account this all important gas depletion effect in diffused aeration, without which nothing in terms of oxygen transfer happens.