where C and n are empirical coefficients. Combining these two equations and combining k, C, and XH|„ into a new coefficient K, called the treatability coefficient, gives:
When recirculation is not used, the applied soluble substrate concentration is just the concentration in the process influent wastewater. However, when recirculation is used, the influent is diluted by the recirculated effluent, making the applied substrate concentration less than the concentration in the untreated wastewater. In that case, the applied substrate concentration is given by Eq. 16.5. Combining Eqs. 19.8, 16.5, and 16.8, which defines the THL, gives the most common form of the modified Velz/ Germain equation:
This equation is dimensional, with the value of K depending on the value of n and the units used for flow rate, F, cross-sectional area, A^, and depth, L. Consequently, when a value of K is taken from the literature, particular attention must be paid to the units used and those units must be retained. Since K is a reaction rate coefficient, its value is temperature dependent. That dependency is typically expressed by Eq. 3.95, with the temperature coefficient 0 set to a value of 1.035. Sometimes Eq. 19.9 is made explicitly dependent on temperature by substituting Eq. 3.95 directly into it. Finally, in many applications of the Velz/Germain equation, the term F'A, is referred to as the unit wastewater application rate.
As discussed in Section 16.4.2, in the Eckenfelder"'17 model the treatability coefficient, K, is expressed as K,as where K, is another treatability coefficient and a, is the media specific surface area. As discussed previously in this chapter, this may be appropriate for applications where channeling of flow and media plugging are not likely to be important, but is inappropriate when they are. The Eckenfelder equation has received less use than the modified Velz/Germain equation and, consequently, the empirical data base from which to select appropriate model coefficients is much more limited. This reduces its practical utility. However, when sufficient data are available it may be a superior model with which to correlate full-scale or pilot-scale data.
Although the modified Velz/Germain and the Eckenfelder equations were developed theoretically, it is now recognized that their theoretical basis is flawed. Consequently, they must be viewed as empirical models which are best used to correlate performance data. Nevertheless, because the modified Velz/Germain equation has been widely used, a significant empirical database exists, and it has been used to estimate a variety of trickling filter performance characteristics.""'" Like the NRC* and Galler-Gotaas1* equations, it has been used to characterize the removal of organic matter by a trickling filter and secondary clarifier system. In these instances, the performance of the secondary clarifier is implicitly incorporated into the treatability coefficient. It has also been used to characterize the removal of organic matter across just the trickling filter itself. Furthermore, in some of those cases the relationship between the concentration of soluble organic substrate in the influent and effluent from the trickling filter is characterized, whereas in others the relationship between the total concentration of biodegradable organic matter in the influent and the concentration of soluble organic matter in the effluent is characterized. Due to this variation in usage, it is important that the basis for treatability coefficients taken from the literature be identified.
The available data"'indicate that the value of n in the modified Velz/Germain equation varies with the trickling filter media type and application, ranging from 0.3 to 0.7. However, it is a standard practice by some to use a value of 0.5 for all situations so that the relative treatability of various wastewaters can be assessed by
the numerical value of the treatability coefficient. Although this apprtach results in some sacrifice in precision, it does allow easy comparison of the relati\e performance of various trickling filter applications.
Experience indicates that a number of adjustments must be mad; to allow the modified Velz/Germain equation to accurately characterize the perfornance of full-scale trickling filter applications. Adjustments must be made for tht depth of the trickling filter media and for the influent waste strength. A correctiai can also be made if the THL is below the minimum required value of 1.8 m/hr.The need for these adjustments is related to the fact that this model is not fundamaital in nature. As discussed above, the best use of the modified Velz/Germain equaion is to correlate full-scale or pilot-scale performance data. It can be used to intapolate within a particular data set, but caution should be exercised if performance atimates are to be extrapolated beyond the existing data base. Detailed descriptionsof the use of the modified Velz/Germain equation to predict the performance of fullscale trickling filter applications are presented elsewhere.*1'""
Examination of Eq. 19.9 reveals that it contains eight terms: (1) he wastewater flow rate, F, (2) the wastewater soluble substrate concentration, Ss„, p) the desired effluent soluble substrate concentration, SSo (4) the treatability coefficent. K, (5) the exponent n, (6) the media depth, L, (7) the cross-sectional area, A, and (8) the recirculation ratio, a. In a design setting, F, SSo, SSc, K, and n are all ktown, leaving three unknowns. Since there is one equation and three unknowns, tvo will be free design variables and can be chosen at will, allowing the other to be alculated. One approach is to choose the recirculation ratio and the cross-sectional irea to set the THL within the allowable range, allowing the media depth, L, to be calculated. Another is to specify the depth, typically at the maximum unsupportet depth for the particular media, and then investigate the effects of the recirculation raio on the area required to maintain the minimum THL. Since total systems costs lepend on the media volume used, the amount of recirculation pumped, and the haght to which the wastewater and recirculation flow must be pumped, the opportinity exists for the designer to seek an optimal design that minimizes the system coss.
Example 184.108.40.206 illustrates use of the modified Velz/Germain quation to design a trickling filter for the removal of biodegradable organic matter
Consider the wastewater that was used in the examples of Section P.3.2, for which 65% of the BOD, is soluble. Use the modified Velz/Germain ecuation to size a trickling filter to produce an effluent with a soluble BOD, coraentration of 10 mg/L, which is essentially the same effluent quality achieved inExample 220.127.116.11. Assume a value for K of 0.4 (m/hr)"7m (which is equivalnt to the value of 0.075 gpm"7ft often reported in the literature''" ') and a valui for n of 0.5. The temperature is 20°C. The characteristics of the media are sud that the THL must to be maintained at a value of 1.8 m/hr or greater, the deph of one bundle is 0.61 m, and the unsupported depth must be no greater than 1.7 m (11 bundles).
a. What is the influent soluble BOD, concentration?
Since the total BOD, in the influent is 150 mg/L and 65% is souble, the soluble BOD, concentration is 97.5 mg/L.
b. What media volume is required if no recirculation is used and the cross-sectional area is selected to maintain a THL of 1.8 m/hr (43.2 m/day)? The required cross-sectional area can be calculated from the definition of THL, given by Eq. 16.8:
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