Any method employing changing DO concentrations during the OTE measurement is called “non-steady state” method. If DO increases during the measurement, it is called “absorption” method. If it decreases, it is called “desorption” method.

The methods widely used to measure OTE and standardized OTE (SOTE), which are found in ASCE Method #002-84 (1991), fall into non-steady state absorption method, where OTE and STOE are estimated from the DO increasing rate. In this method, after filling a tank with clean water, bisulfite and cobalt catalysts are added to remove dissolved oxygen before bubbling starts. Typically sodium bisulfite (NaSO_{3}) is added in the amount equals to 125 or 175% of the stoichiometric requirement and approximately 0.05 mg/L of cobalt chloride is also added as cobaltous ions (Stenstrom, 2006). Subsequently air bubbling starts while DO is measured real time. Finally, SOTE is mathematically calculated from the DO curveÂ against zero DO and zero salinity at 20^{Â o}C.

One drawback of non-steady state method is that the accuracy of the experiment largely relies on *OUR,* which are often questionable. For example, when the OUR measured *ex situ* in test bottles was compared to the OTE measured *in situ* in aeration basin, *ex situ* method always produced higher OUR by up to 40% (Krause, 2003). It was attributed to the high shear rate caused by a micro-mixer in the test bottles used in OUR measurement, which broke down microbial flocs and increased the expose of microorganisms to dissolved oxygen. The *in situ* methods are discussed here.

Following summarizes the procedure of calculating OTE and SOTE based on non-steady state absorption method.

**Measurement of apparent mass transfer coefficient in clean water,***k*_{L}a_{0}

Oxygen transfer (or dissolution) rate in clean water can be described by equation (1) using an apparent mass transfer coefficient,Â *k _{L}a_{0}*, where DO increasing rate is proportional to

*k*

_{L}a_{0}**Â**and the difference between saturated DO ()and the DO at time t,

*C*.

_{o,t}Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â —————————-(1)

where

*C _{o,t}*Â Â Â = DO at time t in clean water (mg/L)

Â Â Â Â = average saturated DO in clean water (mg/L)

*t*Â Â Â Â Â = elapsed time (hr)

*k*Â = apparent mass transfer coefficient in clean water (/hr)

_{L}a_{0}In above equation,Â Â represents an average saturated DO in the tank and can be calculated using the equation (4) here. The above equation can be integrated using two boundary conditions, *i.e*. C_{0,t}=C_{i}Â at t=0 and *C _{0,t}*Â =Â

*C*Â at t=t.

_{0,t}Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â —————————-(2)

The log-term in the left side of the equation can be plotted against *t* to obtain Â *k _{L}a_{0}*Â from the slope.

**Measurement of apparent mass transfer coefficient in process water,Â***k*_{L}a_{0}

This step is required only to calculate *OTE*, not *SOTE*. In MBR, volumetric oxygen consumption is measured by oxygen uptake rate (OUR). At steady state, the oxygen dissolution rate equals to oxygen consumption rate (*OUR*) as described as equation (3)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â —————————-(3)

where

*C _{SS}*Â Â Â = DO in mixed liquor at steady state (mg/L)

*C*Â Â Â Â = concentrated DO in mixed liquor (mg/L)

^{*}*k*Â = apparent mass transfer coefficient in mixed liquor (/hr)

_{L}aÂ Â*Â C ^{*}, which equals toÂ Î²,*Â can be calculated byÂ usingÂ the equation (3) and equation (4) here for the experimental condition.

*OUR*Â is experimentally measured according to the Method 2710 (APHA, 1999). Finally

*k*Â can be estimated using equation (3) in this page.

_{L}a_{0}**Calculation of oxygen transfer rate,***OTR*

Standard *OTR* at zero DO in clean water, *OTR _{0}*,Â can be calculated using equation (4).

*OTR*rates at a given DO (

*C*) in process water (

_{ss}*OTR*, kg O

_{2}/hr) can be also calculated using a similar equation.

In above equations, V indicates reactor volume in m^{3}.

**Calculation of***SOTE*and*OTE*

Oxygen transfer efficiency in clean water (SOTE) and in mixed liquor (OTE) are estimated as follow.

where Q_{air}Â is air flow rate in Nm^{3}/hr at 20^{o}C and 1 atm. The factor in denominator, 0.279, is the oxygen density at 20 ^{o}C, 1 atm, and 0% relative humidity, but it becomes 0.275 at 20 ^{o}C, 1 atm and 36% relative humidity where most blowers are rated for.

By definition, Î±-factor can be calculated as follow from the ratio between *k _{L}a*Â and

*k*. It represents the relative ratio of oxygen dissolution in process water against that in clean water.

_{L}a_{0}Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â —————————-(6)

Â© Seong Hoon Yoon