As discussed in Section 2.4.3, soluble microbial products are thought to arise from two processes, one growth associated and the other non-growth-associated. ""
Growth associated product formation results directly from biomass growth and substrate utilization. If soluble microbial product formation was occurring in appreciable amount, it would be necessary to modify the stoichiometric equation for microbial growth to account for it. Letting SMP represent the concentration of soluble microbial products in COD units and YM1. the product yield in units of product COD formed per unit of substrate COD used, Eq. 3.31 can be rewritten to account for soluble microbial product formation:
This shows that less electron acceptor is used when soluble products are formed because part of the COD of the substrate remains in the medium as those products. Rewriting this equation in the form of Eq. 3.9 with biomass as the reference constituent gives:
This tells us:
Combining Eq. 3.72 with Eq. 3.35 for rXn gives:
The fact that rSMP is proportional to (jl shows that it is growth-associated.
Non-growth-associated product formation, also called biomass-associated product formation,lt" occurs as a result of cell lysis and decay. Rewriting Eq. 3.53 to incorporate soluble product formation into the COD-based stoichiometry of the traditional approach to decay gives:
Biomass COD + [ — (1 — f„ — fMP)]0: equivalents of electron acceptor -» f„ biomass debris COD + fMI, soluble product COD (3.74)
where fMP is the fraction of active biomass contributing to biomass-associated products. Using this with Eq. 3.56 gives the rate of production of biomass-associated product:
By analogy to biomass debris formation, a similar approach could be used to account for soluble microbial product formation in the lysis:regrowth approach, giving a parameter fy,> which is smaller than fMP in the same way that fi, is smaller than f0.
Combining Eqs. 3.73 and 3.75 suggests that the specific rate of soluble microbial product formation is linearly related to the specific growth rate. While such a relationship may be adequate for slowly growing cultures like those found in activated sludge systems, it is not adequate for more rapidly growing systems4" and thus Eqs. 3.73 and 3.75 cannot be considered to be of general applicability to all systems. Although a relatively large body of research on soluble microbial product formation has been conducted,4"it is still not sufficient to allow consensus on the rate expressions to be used. Thus, in spite of its known importance, soluble microbial product formation will not be incorporated into the models in Parts II and IV.
Insufficient information is available to provide typical values for fMP and f«,., but, as indicated in Section 2.4.3, YMP values have been found to be less than 0.1/42
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