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Figure 8.1 Plot of Eq. 8.7 for the determination of Y„ and b,,.

Making the same substitutions and linearizing gives:

A plot of (Sri) — S()/(fA X,) vs. t will give a straight line with a slope of bH/Y„ and an ordinate intercept of 1/Y„. This is illustrated in Figure 8.2.

This technique is better than alternative linearizations when the error is either normally or log-normally distributed and the coefficient of variation is less than 11%, or when the error is uniformly distributed, regardless of the coefficient of variation."8

### 8.2.3 Determination of fD

The value of f„ can be determined from Eq. 5.26 using nonlinear least squares analysis with b„ as a fixed value obtained from the preceding analysis:

Alternatively, rearrangement gives:

A plot of l/fA vs. 0t will give a straight line with a slope of fu bM. The ordinate intercept should pass through 1.0. Because b„ is known, l'„ can be calculated.

Figure 8.2 Plot of Eq. 8.8 for determination of Y„ and b„

Figure 8.2 Plot of Eq. 8.8 for determination of Y„ and b„

8.2.4. Estimation of Inert Soluble Chemical Oxygen Demand, S,

Before the kinetic parameters describing microbial growth and substrate utilization can be estimated, data must be available on the soluble substrate concentration, Ss. This requires knowledge of the inert soluble COD, S,, as shown in Eq. 8.4. The easiest way to determine S, is to remove an aliquot of the mixed liquor from one of the bioreactors operating at an SRT of 10 days or more, place it in a batch reactor, and aerate it. The soluble COD should be measured over time and when it reaches a stable residual value, that value can be considered to be equivalent to the concentration of inert soluble COD in the feed.1"

Mamais et al.:J have suggested that S, can be estimated as the truly soluble COD remaining in the effluent from a bioreactor operated with a long SRT. The rationale for this technique is that at longer SRTs, the amount of soluble, readily biodegradable COD remaining in the effluent will be negligibly small. Consequently, essentially all soluble COD remaining will be nonbiodegradable. The truly soluble COD is obtained by flocculating an effluent sample from the bioreactor with the longest SRT with ZnS04 at pH 10.5 (forming Zn(OH)2 floe) prior to filtration through a 0.45 p.m membrane filter. The flocculation step effectively removes colloidal organic matter that might pass through the filter, leaving only S,.

Both of the above techniques are approximations. As discussed in Section 3.4, bacteria produce soluble microbial products as they degrade organic matter. Consequently, part of the inert organic matter remaining will actually be of microbial origin. However, because the models employed herein do not explicitly account for soluble microbial products, it is acceptable to consider it as part of the inert soluble

COD as long as a constant influent soluble COD, S(ll, is used in the treatability study. Germirli et al.': have proposed a simple technique whereby the residual COD from the test described above may be partitioned into inert soluble COD from the influent and from microbial activity. It may be used in situations irt which it is necessary to explicitly account for soluble microbial products.

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