Reaeration coefficients

Under equiUbrium or near-equiUbrium conditions, the distribution of volatile species between gas and water phases can be described in terms of Henry s law. The rate of transfer of a compound across the water-gas phase boundary can be characterized by a mass-transfer coefficient and the activity gradient at the air—water interface. In addition, these substance-specific coefficients depend on the turbulence, interfacial area, and other conditions of the aquatic systems. They may be related to the exchange constant of oxygen as a reference substance for a system-independent parameter reaeration coefficients are often known for individual rivers and lakes. 

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.

Measurements of reaeration coefficients have been made at a number of locations over the years, and it is natural that individuals would try to correlate these measurements with the measured parameters of the river so that predictions can be made elsewhere. A partial compilation of measurements is given in Figure 9.2. Although there is scatter in flume measurements, this is exceeded by a factor of 10 in field measurements. 

Figure 9.2. Measurements of reaeration coefficient in laboratory flumes and in the field. Present authors are Gulliver and Halverson (1989). St is a Stanton number, Ki/u. ...

Moog and Jirka then calibrated the lead coefficient and studied the predictive capability of 10 calibrated empirical equations to predict reaeration coefficients that were the result of 331 field studies. The result was surprising, because the best predictive equation was developed by Thackston and Krenkel s (1969) from laboratory flume studies, and the comparison was with field equations. In dimensionless form, Thackston and Krenkel s (1969) cahbrated (multiplying the lead coefficient by 0.69) equation can be converted to a dimensionless form utilizing Sherwood, Schmidt, Reynolds, and Froude numbers ... 

Now, consider a natural river, illustrated in Figure 9.3. 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 on reaeration coefficient, without the dampening effect of stream depth. The measurement of p and surface vorticity in a field stream remains a challenge that has not been adequately addressed. The mean values that are determined with field measurements are not appropriate. Most predictive equations for reaeration coefficient use an arithmetic mean velocity, depth, and slope over the entire reach of the measurement (Moog and Jirka, 1998). The process of measuring reaeration coefficient dictates that these reaches be long to insure the accuracy of K2. Flume measurements, however, have generally shown that K2 u /hor K2 (Thackston and Krenkel, 1969 ... 

Gulliver and Halverson, 1989). If this is truly the case, we should be taking the mean of and the mean of to use the predictive equations to estimate reaeration coefficient. Example 9.1 will investigate whether this is an important consideration. 

The ramihcations of the poor K2 predictive ability are that we cannot do an adequate job of planning for oxygen concentrations during low flow events or for spills, unless we have performed held measurements of reaeration coefficient. This will be explored in Example 9.2. 

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. 

The effluent from a sewage treatment plant on a river with an upstream biochemical oxygen demand (BOD) of 2 g/m has a discharge of 10 m /s and a BOD of 15 g/m. Determine the best choice of stream reaeration coefficient,... 

FIGURE 2-13 Air-water reaeration coefficients for oxygen in a reach of Walker Branch, a stream in Oak Ridge, Tennessee. Measured coefficients (dashed line) and calculated coefficients from several published predictive equations (solid lines) are shown. Until better predictive relationships are developed, highly accurate estimates of gas exchange appear to require experimental determination (data from Genereux and Hemond, 1992). 

In the absence of tracer data, estimates of gas exchange coefficients in streams can be made from a number of empirical equations, which typically depend on a combination of the stream mean velocity and depth (V and d, respectively). Some equations contain other parameters, such as shear velocity, width, and Froude number (u, w, and N, respectively) of the stream. The Froude number is equal to (V/ fgd), and is the ratio of stream velocity to the travel speed of a shallow-water surface wave. By convention, the empirical equations given for streams are usually for a reaeration coefficient, which is the gas exchange coefficient for oxygen divided by the average stream depth. Examples of empirical equations for reaeration coefficients are shown in Table 2-5. 

Negelescu, M. and Rojanski, V. (1969). Recent Research to Determine Reaeration Coefficients. Water Research 3(3), 189-202. 

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... 

Table II. Predicted Atmospheric Reaeration Coefficients (k2) as a Function of Stream Flow in the Jackson River"...

Several empirical relationships for reaeration coefficients were recently reviewed and tested by Moog and Jirka (1995), who found that the form of the relationship given in Eq. (20.15) best characterized stream reaeration rates. A liquid mass transfer coefficient for each compound, ki can then be determined from a ratio of the Schmidt numbers (Mackay and Yven, 1983) ... 

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... 

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