Segregation model

The highest conversion value of the segregation model can be determined since it yields an extreme value of the degree of reactant conversion, that is, the highest or the lowest, depending on the reaction kinetics. We can show that the conversion obtained with the 

FIGURE 4.21 Coupling (1) yields a better conversion in case of, for example, a reaction with the following rate equation —va =, if m 1. Both modes of coupling will yield the 

Each droplet acts like a batch reactor 

It is necessary to know the density function, E t), if the segregation model is applied. E(t) can be determined either experimentally or theoretically. Since it is possible to derive the residence time functions for many flow models, the segregation model is very flexible. According to the segregation model, the average concentration at the reactor outlet is obtained from the relation 

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A real system must lie somewhere along a vertieal line in Figure 9-5. Performanee is within the upper and lower points on this line namely maximum mixedness and eomplete segregation. Equation 9-10 gives the eomplete segregation limit. The eomplete segregation model with side exits and the maximum mixedness model are diseussed next. 

COMPLETE SEGREGATION MODEL WITH SIDE EXITS ... 

Lee and Bethke (1996) presented an alternative technique, also based on mass balance equations, in which the reaction modeler can segregate minerals from isotopic exchange. By segregating the minerals, the model traces the effects of the isotope fractionation that would result from dissolution and precipitation reactions alone. Not unexpectedly, segregated models differ broadly in their results from reaction models that assume isotopic equilibrium. 

The segregated conversions are intermediate to plug flow and CSTR battery. The only way to tell which of the segregated models is superior is to check them with actual conversion data. 

Unstructured and non-segregated models allow the most simplified representation of cellular complexity. As indicated in Figure 8.1, in these models, the entire cell population is represented by only one kind of cell (the average cell). Differences between cells within the population are not considered and thus, the cell population is considered homogeneous. 

Although an unstructured and non-segregated model includes simplifications of the cellular complexity, it is often used in culture simulation, because it is an adequate compromise between the available data, the difficulties involved in model formulation, and the desired model precision. 

The unstructured and segregated model considers the cell culture as a heterogeneous population, with individual cells characterized by age, mass, or size. The variation of properties follows a statistical distribution. The most concise way to deal with such population heterogeneity is through a population balance model (PBM). These models can become mathematically complex because the equations that describe the population have to consider that the properties vary in the population and... 

The complexity involved in cell structured and segregated models is increased with the necessity of their integration and can explain why some authors define the structured and segregated models as the next challenge for animal cell modeling. These difficulties are reflected by the scarce number of publications dealing with this integration. This advanced research field is beyond the scope of this book. 

The mathematical modeling of animal cell processes was reviewed by Tziampazis and Sambanis (1994), Portner and Schafer (1996), and Sidoli et al., (2004). These authors focused on non-structured and non-segregated models, certainly the most abundant models in literature, and also discussed the evolution of the use of other models, mainly the structured and segregated ones. 

As stated previously, unstructured and non-segregated models are those most commonly employed for simulating cell culture, due to their simplicity in representing the biological complexity of the system. It is should be restated that these models consider the cell population as homogeneous and do not distinguish between individual cells. 

Many of the equations employed in unstructured and non-segregated models derive from those of enzymatic kinetics (Sinclair and Kristiansen, 1987 Nielsen and Nikolajsen, 1988). Cells are considered as chemical reactors that support thousands of complex reactions catalyzed by enzymes that allow the conversion of substrates into secreted products. The equation formulated by Michaelis and Menten represents the enzymatic conversion rate of a unique substrate into one product (Equation 14). 

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