Non-steady state absorption method

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 (NaSO3) 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 curve against zero DO and zero salinity at 20 oC.

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.

  1. Measurement of apparent mass transfer coefficient in clean water, kLa0

Oxygen transfer (or dissolution) rate in clean water can be described by equation (1) using an apparent mass transfer coefficient, kLa0, where DO increasing rate is proportional to kLa0 and the difference between saturated DO (1)and the DO at time t, Co,t.

1¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† —————————-(1)
Co,t     = DO at time t in clean water (mg/L)
1       = average saturated DO in clean water (mg/L)
t          = elapsed time (hr)
kLa0  = apparent mass transfer coefficient in clean water (/hr)

In above equation, 1 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. C0,t=Ci at t=0 and C0,t = C0,t at t=t.

1¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬†—————————-(2)

The log-term in the left side of the equation can be plotted against t to obtain  kLa0 from the slope.

  1. Measurement of apparent mass transfer coefficient in process water, kLa0

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)

1¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬†—————————-(3)
CSS     = DO in mixed liquor at steady state (mg/L)
C*      = concentrated DO in mixed liquor (mg/L)
kLa    = apparent mass transfer coefficient in mixed liquor (/hr)

¬†C*, which equals to¬†ő≤1-1,¬†can be calculated by¬†using¬†the equation (3) and equation (4) here for the experimental condition. OUR¬†is experimentally measured according to the Method 2710 (APHA, 1999). Finally kLa0¬†can be estimated using equation (3) in this page.

  1. Calculation of oxygen transfer rate, OTR

Standard OTR at zero DO in clean water, OTR0, can be calculated using equation (4). OTR rates at a given DO (Css) in process water (OTR, kg O2/hr) can be also calculated using a similar equation.

1¬†or¬†1¬† ———————–(4)

In above equations, V indicates reactor volume in m3.

  1. Calculation of SOTE and OTE

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

1¬†or¬†1¬† ¬† ¬† —————————-(5)

where Qair is air flow rate in Nm3/hr at 20oC and 1 atm. The factor in denominator, 0.279, is the oxygen density at 20 oC, 1 atm, and 0% relative humidity, but it becomes 0.275 at 20 oC, 1 atm and 36% relative humidity where most blowers are rated for.

By definition, őĪ-factor can be calculated as follow from the ratio between kLa¬†and kLa0. It represents the relative ratio of oxygen dissolution in process water against that in clean water.

1¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬† ¬†—————————-(6)


© Seong Hoon Yoon