The Reaeration Coefficient

In the expressions for the gas exchange coefficient employed previously, it is evident that the air-water gas exchange flux density is proportional to the difference between a chemical concentration in the water (Cw) and the corresponding equilibrium concentration (Cw H) in air. Consequently, the difference between actual and equilibrium concentration in the water tends to decay exponentially, as expected for any first-order process. In many situations, exponential decay may provide a useful model of a volatile chemical concentration in a surface water. A classic example is degassing of a dissolved gas from a stream if the gas is present at concentration C0 upstream, atmospheric concentration of the gas is negligible, and flow is steady and uniform along the stream, then the gas concentration in the stream is given by 

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Determination of reaeration relies on the measurement of the air-water oxygen transfer coefficient (Section 4.4.2). Measurement of this coefficient — the reaeration coefficient — in gravity sewer lines follows basically the methods that have been developed for and applied in rivers. Methods for determination... 

Vary the reaeration coefficient Kair and see how this influences the dissolved oxygen profiles. 

Figure 9.1. Gas tracer pulses for the James River (North Dakota) used to measure the reaeration coefficient. GC, gas chromatograph SFe, suiter hexafloride.

As described in equation (6.59), longitudinal dispersion coefficient has a 67% confidence interval that is a factor of 1.7 times the best estimate. If the distribution of multiplicative uncertainty is normal, the 95% confidence interval would be at a factor of 3.4 times the best estimate. The reaeration coefficient has are MME of 1.8 for the Thackston and Krenkel equation (equation (9.7)). Again, if the multiplicative distribution is normal, the MME is 0.4 times the 95% confidence interval. Then the 95% confidence interval is a multiplicative factor of 4.5. 

Figure 6 shows the relationship between the reaeration coefficient (k2) and V/H15 where V is stream velocity in feet per second and H is... 

By convention, empirical equations for gas exchange in streams are often expressed as reaeration coefficients. The reaeration coefficient is the gas exchange velocity for oxygen divided by average river or stream depth and thus has units of [T ]. A reaeration coefficient can be thought of as a depth-normalized piston velocity. Examples of empirical equations for reaeration coefficients are shown in Table 2.5. 

In the case of oxygen-depleted streams, such as typically occur downstream of wastewater outfalls, the flux of O2 is from the atmosphere into the streams. In a stream with steady, uniform flow and no sources or sinks of oxygen other than the atmosphere, an oxygen deficit decays exponentially with downstream travel time. The classic Streeter-Phelps model, discussed in Section 2.5, considers not only dissolution of O2 into a stream but also simultaneous O2 consumption due to microbial degradation of organic waste within the stream. By tradition, the reaeration coefficient in Streeter-Phelps modeling is designated fCoj. 

The rate of O2 reaeration (the third term in Eq. 2.62) is proportional both to the O2 deficit, which is the difference between the saturated O2 concentration and the actual O2 concentration, and to the reaeration coefficient. The reaeration coefficient for oxygen equals the gas exchange velocity (the piston velocity) for oxygen divided by average stream depth (Section 2.3.2) thus, the gas exchange velocity equals the product of the reaeration coefficient and depth. Total flux [M/T] of atmospheric O2 into the control volume by reaeration is thus... 

Rivers are generally considered as a plug flow reactor with dispersion (Levenspiel, 1960), where the mixing is provided by the velocity profile and turbulence in the flow field. This concept is applied to the measurement of K /H = Kia in rivers, where H is depth of flow and K a = Ki AIV = K2 is generally called the reaeration coefficient, and a is the specific surface area. 

Now consider a natural river, illustrated in Figure 9.6. There are many sources of vorticity in a natural river that are not related to bottom shear. Free-surface vortices are formed in front of and behind islands, and at channel contractions and expansions. These could have a direct influence upon surface renewal, and the reaeration coefficient, without the dampening effect of stream depth. The measurement of r and surface vorticity in a field stream remains a challenge that has not been adequately addressed. 

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