The complex nature of the events occurring in RBC systems is discussed in Chapter 17. Because of that complexity, fundamental design models for the RBC process are still in the developmental stage. Consequently, empirical approaches are currently used for design. Most of those approaches express the SOL in terms of BOD< so we will do the same herein. This section describes the design procedures for RBCs that remove organic matter and nitrify, both separately and together. The use of pilot plants to develop site-specific design data is also discussed. Some general comments on RBC design procedures are also provided.

20.3.1 Removal of Biodegradable Organic Matter

General Approach. The general approach to the design of an RBC system to remove biodegradable organic matter consists of the following steps:

• Select a design expression.

• Select an effluent quality goal. As discussed in Section 9.4.4, the selection of that goal should consider uncertainty and variability in process performance.

• Use the design expression and the effluent quality goal to calculate the total media surface area required.

• Determine the media surface area required in the first stage to keep the stage SOL below 32 g BOD,/(m2 • day) to prevent excessive growth of Beggiatoa.

• Select the number of trains to be used, the number stages in each train, and the number of shafts in each stage.

Several empirical design approaches have been presented in recent design manuals. 27 ,1 This section presents two equations which have been found to most accurately characterize the performance of full-scale systems treating domestic wastewaters, the first-order and the second-order models. Both can be used to estimate the total media area required for domestic wastewaters. The design of RBC systems to treat industrial wastewaters generally requires full-scale experience with the same or a similar wastewater, or a pilot study.

After the total media surface area and the area in the first stage have been determined, engineering experience and judgement must be used to configure the system. Generally, a minimum of four trains is desirable from an operational perspective because when one train is out of service for maintenance, three-quarters of the total media volume will remain in service. This will generally be sufficient to produce an acceptable quality effluent in the short term. Guidance concerning the number of stages is provided in Table 20.2. Even though the total media volume may have been selected to give the desired effluent substrate concentration, staging that media as recommended in the table will provide a factor of safety in the design. Finally, the number of shafts in the first stage is determined by the minimum area required to prevent oxygen limitations. The number of shafts in the remaining stages can be selected based on the experience of the designer and other considerations. However, at no time should the loading on any stage exceed 32 g BOD,/(m • day).

First-Order Model. The first-order model is analogous to the Velz/Germain equation used to design trickling filters. It was first presented by Benjes," ^ as follows:

where Sv and SM, are the concentrations of total biodegradable organic matter in the clarified process effluent and influent, respectively, VM is the media volume, F is the influent flow rate, and k, is a first-order reaction rate coefficient. It should be noted that even though the first-order model is similar to the Velz/Germain equation, it is based on concentration of total organic matter entering and leaving the process rather than on the soluble organic matter as was done in Eq. 19.6. Based on a review of operating data from 27 full-scale municipal wastewater treatment plants, a value for k, of 0.3 was selected when SSl. and Ss() are measured as BOD,, VM is expressed in ft1, and F is expressed in gallons per minute.'2. Figure 20.8" compares the predictions of this equation with the results from the plants and indicates a generally good fit. Note that the plot was prepared with 100[(SS1) — SSl)/SS(,] as the ordinate and the SOL as the abscissa. Because of the nature of the abscissa, a separate curve results from Eq. 20.4 for each influent substrate concentration and the plant data have been grouped into three sets to show that effect. Nevertheless, the data scatter indicates that some facilities may perform less efficiently than indicated by the equation. As a consequence, some design manuals suggest the use of a more conservative k, value in the range of 0.2 to 0.25."''''

Because Eq. 20.4 was developed using standard density RBC shafts that contain media with a specific surface area of 35 ft /ft\ i.e., 115 m /m\ it can be converted into an expression based on media surface area. Using metric units and a value for k; of 0.3, the expression becomes:

where A^, is the total media surface area expressed in m: and F is the wastewater flow rate in m'/day. Even though Eq. 20.5 was developed for standard density media,

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