Unsegregated model

Ramkrishna et al.m proposed a similar model at about the same time—this too was an unsegregated model which also divided the biomass into two compartments. They referred to the material in the two compartments as G-mass and D-mass, respectively, and suggested that these materials were formed in parallel. They also proposed that the micro-organism produced a toxic substance which inhibited its growth. They produced a set of differential equations obtained from material-balance considerations, to describe the behaviour of such a system in both batch and continuous culture. For batch culture ... 

Thus, the segregated flow model is based on the fundamental assumption that the fluid elements are independent or do not mix (macromixing model). Until now, we considered a perfect mixture in the mass balance and concentration uniform, no interaction between the fluid elements (micromixing), called unsegregated model. 

The calculation begins with an initial fluid of specified isotopic composition. The model, by mass balance, assigns the initial compositions of the solvent and each aqueous species. The model then sets the composition of each unsegregated mineral to be in equilibrium with the fluid. The modeler specifies the composition of each segregated mineral as well as that of each reactant to be added to the system. 

The relatively simple unsegregated-structured model is based on an internal key compound e of the biomass. The activity of this compound is expressed in terms of the concentrations of the substrate Cs, of the product Cp and of the compound Ce of the biomass itself. Thus the rate of formation of the key compound e is given by... 

Therefore, comparing the conversions of a first-order irreversible reaction of unsegregated (Equation 24.23) and segregated models (Equation 24.28), we obtain identical results. These results depend only on the parameter zk, independently of average residence time. We conclude that only the time, not the degree of mixing, can determine the conversion of a first-order irreversible reaction. 

For the model unsegregated (micromixing) from the molar balance equation in a... 

In the literature there are several ways of classifying different types of models (cf. Roels and Kossen, 1978, and Sect. 2.4.3). From the viewpoint of process engineering, in this book distinctions will be made among macrokinetic, microkinetic, formal kinetic, and process kinetic models (see Fig. 2.14). The formal models that will be discussed individually in Chap. 5 are sometimes referred to in the literature as unsegregated or unstructured models that have a descriptive or predictive nature. 

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