Analysis of literature data shows only a few studies for the anaerobic wastewater systems and indicates uncertainties to exist. Furthermore, the treatment of aerobic growth being well advanced but more development of the application of thermodynamic laws has to be directed to the study of anaerobic growth.
The treatment of McCarty (1972), for the analysis of wastewater treatment, gives an interesting application of the concept of Yave that expresses the yield in terms of grams of biomass per mole available electrons (which is defined as the number of electrons per C-mol electron donor upon combustion). The idea is that, assuming a constant Gibbs energy production per mole of electrons, the biomass yield per mole of available electrons might be constant. This parameter can be calculated using only black box information, but Yave is not a constant. This is due to the fact that the Gibbs energy of combustion per available electron depends strongly on the electron donor/acceptor couple. Furthermore, there is no intrinsic Second Law-based limit for Yave.
To study the anaerobic degradation of glucose Mosey (1983) used the YATP concept. This concept proposed by Beauchop and Elsden (1960) express the yield of biomass in terms of consumed ATP (YATP in grams of biomass dry weight/mol ATP). The YATP can be determined experimentally from growth yields studies. But this parameter is not a constant, and its value depends on the growth rate of the microorganism, on the substrate and on the composition of the cell material. And however the amount of ATP used for biosynthesis depends on the routes of carbon fixation, that is very difficult to define in a mixed culture like is present in anaerobic wastewater reactors. Moreover, for practical application one needs detailed biochemical knowledge. This concept, therefore, has no intrinsic limit based on the Second Law.
In the black box description the process is considered like an open system exchanging matter and energy with the environment and dissipating Gibbs energy. Only the chemistry of the conversion process is considered, and the biomass is specified by its elemental composition. Hence, it must be able to evaluate the biomass growth yield without having information about the intracellular biochemical properties of the microorganisms (e.g., electron transport chain or anabolic/catabolic properties).
Finally, applying elemental and energy balances, it is possible to evaluate the biomass or product yield, if one of them is known. But using the black description proposed by Heijnen et al. (1992), these yields are obtained in a theoretical manner.