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Input rate = (2,000)(25) = 50,000 g/day Removal rate = (1.16)( 13,900) = 16,100 g/day Output rate = 50,000 - 16,100 = 33,900 g/day Effluent concentration = 33,900 + 2,000 = 17 mg N/L

The concentration is well above 5 mg/L, so the assumption of a zero-order rate is juslitied. Examination of the mass removal rate in stage 3 and comparison of it to the mass input rate into stage 4 suggests that the concentration in stage 4 will also be high enough to allow nitrification to occur at the zero-order rate. In this case, however, carbon oxidation has no effect, as indicated in Table E20.2. Thus, the rate will be 1.5 g NH;-N/(m -day). Repealing the procedure above for stage 4 reveals that the effluent ammonia-N concentration will be 6.5 mg/L. Since this is above 5 mg/L, the assumption that nitrification will occur at the zero-order rate is justified.

Since the ammonia-N concentration entering stage 5 is close to 5 mg/L, the effluent concentration from stage 5 will be less than 5 mg/L, causing the ammonia-N llux to be limited by the ammonia-N concentration. This requires use of an iterative procedure to estimate the effluent ammonia-N concentration, just as was done in Example 20.2.1.1. Application of that procedure reveals thai the effluent ammonia-N concentration from stage 5 is 2.0 mg/L.

Although the effluent ammonia-N concentration is slightly lower than the desired effluent concentration, the necessity to use full shafts of fixed area makes it unlikely that the media area could be reduced while still meeting the effluent requirement. Consequently, this is considered to be an acceptable design.

### 20.3.4 Pilot Plants

Pilot studies should be conducted using full-scale, i.e., 3.6 m diameter, units rotating at 1.4 to 1.6 rpm. This is because of the effects of disc diameter and rotational speed on process performance, as discussed in Section 17.2. In the past, small diameter pilot-scale units have been used without consideration for the differences in mass transfer characteristics between pilot-scale and full-scale units.14 The result has been full-scale units that did not perform as expected. Furthermore, as illustrated in Figure 17.5, scale-up by maintaining the same THL and peripheral velocity in the pilot unit as in full-scale units does not work either.1214 Consequently, the only safe approach is to use pilot units with full diameter discs. The shaft length is simply shorter.

Data from full-scale or pilot-scale units can be analyzed using the models and empirical relationships presented above. For the removal of biodegradable organic matter this consists of the first-order and second-order models. For nitrification this involves comparison of the measured ammonia-N flux with the typical values presented in Figure 20.5. In some instances, a Monod-type model has been fit to data from pilot units," although it should be recognized that in such cases the halfsaturation coefficient incorporates the mass transfer effects, as indicated in Eq. 19.5 for trickling filters. Any result that indicates zero-order organic substrate or ammonia-N fluxes greater than those presented in this chapter should be viewed with skepticism. They indicate that, for some reason, the pilot unit is achieving a greater oxygen transfer rate than is typical in full-scale units.

Graphical procedures provide an alternative approach for using pilot-scale data to size an RBC system, and they have been used successfully in several instances.'70 They are based on a mass balance across an RBC stage. The basic procedure will be illustrated for organic matter removal, but applies equally well for nitrification. To begin the procedure, pilot-plant data are used to calculate the removal rate per unit area, i.e., the flux, of organic matter, Js, for each stage and/or each loading. The rates are then plotted as a function of the residual concentration in the stage and a smooth curve is drawn through the data. Such a curve will generally have a shape like that illustrated in Figure 20.9. Since each stage in an RBC can be considered to be completely mixed, a steady-state mass balance on soluble substrate across stage N is:

where Js„ is the flux in stage N, which is related to the substrate concentration Ss.„ in that stage as illustrated in Figure 20.9. All other terms have been defined previously. Rearrangement of this equation provides the rationale for the graphical approach:

As depicted by Eq. 20.10 and illustrated in Figure 20.9, a line drawn from Js„ to the input substrate concentration, Ss.„ ,, on the abscissa will have a slope of — F/ A.,.,,, which is just the THL on the stage times —1.0. This line is called the operating line. Once the plot of flux versus substrate concentration has been drawn from the pilot-plant data, the THL required to decrease the substrate concentration from Ss „ , to Ss.„ in a single stage can be determined by drawing an operating line from Ss.„ , on the abscissa to the flux associated with Ss„ and measuring the slope. Since the

Figure 20.9 Illustration of the graphical procedure for determining the hydraulic loading required to reduce the soluble substrate concentration from Ss.„ , to Ss„ in a single-stage RBC.

Soluble Substrate Cone., g/m3

Figure 20.9 Illustration of the graphical procedure for determining the hydraulic loading required to reduce the soluble substrate concentration from Ss.„ , to Ss„ in a single-stage RBC.

flow rate is known, the required stage surface area can be determined. Furthermore, by recognizing the definition of the SOL, it can be seen that the intersection of the operating line with the ordinate is that loading. This allows the graphical procedure to also be used to determine the output concentration from any stage in an RBC train. The SOL on the stage is calculated with Eq. 20.1 and an operating line is drawn from the SOL on the ordinate to the influent substrate concentration on the abscissa. The intersection of that operating line with the curve gives the flux in that stage and the output substrate concentration, Ss„.

The graphical procedure can also be used to determine the output concentration from a staged RBC system or to determine the size system required to achieve a desired effluent concentration. The former can be done directly whereas the latter requires an iterative approach. For an existing system, the THL is calculated for each stage. The procedure, illustrated in Figure 20.10, is initiated by plotting an operating line with slope — F/A,u from the system influent substrate concentration, Ss.„ on the abscissa to the rate curve. The intersection of that operating line with the curve gives the output substrate concentration from stage 1, Ss.i. Since that concentration is also the influent concentration to stage 2 the procedure can be repeated to determine the output concentration from stage 2, and so on, until the final stage is reached, as shown in Figure 20.10. If all stages have the same hydraulic loading, then all of the operating lines will be parallel, as illustrated in the figure. For design of a new system, an iterative procedure must be used. Generally, the smallest system will result when the first stage is loaded with an SOL of 32 g BODs/(nr • day) because that will

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