Segregated feed model

In what follows, both macromixing and micromixing models will be introduced and a compartmental mixing model, the segregated feed model (SFM), will be discussed in detail. It will be used in Chapter 8 to model the influence of the hydrodynamics on a meso- and microscale on continuous and semibatch precipitation where using CFD, diffusive and convective mixing parameters in the reactor are determined. 

Figure 8.1 Segregated Feed Model (SFM) (after Zauner and Jones, 2000b)...

Use the segregated flow model to predict the effluent concentration of species A and V for the reactor network whose F(t) curve was determined in part (a). The feed contains only species A at an initial concentration Aq. 

The feed consists of pure A at 2 atm and 400°C. Each of the reactions of interest is first-order in the reactant Use the segregated flow model to derive an expression for the effluent concentration of species B. What is this concentration if the values of k, andkj are 16.0,1.0,... 

Here, Xjeg is the dimensionless concentration vector (normalized, e.g., by a feed concentration), R(X) is the corresponding rate vector, and is the dimensionless output concentration of the segregated flow system with a residence time 7. We allow the objective function, /, to be specified by the designer as any function of and t. One can see that the differential equation system can be uncoupled from the rest of the model and solved offline if the dimensionless feed concentration, Xq, is prespecified. Once the vectors Xseg are determined, we merely solve for/(r), which satisfies an additional set of linear constraints. If Gaussian quadrature on finite elements is applied to the above model over the domain [0, r axl we get... 

The lateral segregation mechanism of FPR desensitization in neutrophils (Figure 2) may be an attractive model that integrates the receptor-mediated actin polymerization/depolymerization and feed-back regulation of receptor fimction. What do we know about FPR binding to cytoskeletal proteins and membrane disribution of FPR as a function of the activation state of neutrophils to support such an idea ... 

Bourne and coworkers [21-23] have developed the mathematics and applied their model to predict the effects of stoichiometric ratio, startup of a semi-batch reactor, effect of volumetric feed ratio, batch vs. continuous operation, etc. They have also experimentally demonstrated the use of reaction systems with well-characterized kinetics to determine the level of micro-mixing. Thus chemical reactions can be considered as molecular probes to be used to study segregation. Other... 

In simple laminar flows (e.g. one-dimensional shear or elongation) the time evolution of some mixing parameters (e.g. striation thickness or intensity of segregation) has been calculated in a number of cases (Chapter 11 for general information). In turbulent, single-phase fluids it is very difficult to model the transport phenomena in full physical detail. Qualitatively, however, the following sequence may be visualized after the feed streams have met ... 

In fact, it is extremely complex to predict the influence of mixing on product selectivity. This would require detailed modeling of an incompletely mixed reactor and kinetic data, difficult to obtain for multistep reactions, without any prohibitive effort. However, with knowledge of the reaction mechanism, but withoutthe kinetics, a simple method can be applied which does not determine quantitatively the extent of a mixing effect but rather indicates qualitatively how partial segregation and feed configuration influence the rates of formation of the desired and undesired products and hence the selectivity [66, 67]. 

Representation of partial segregation of the initiator feed-stream is possible by the lEM-model. The concentration of initiator in fresh aggregates is given by... 

Ibid. A two parameter model for partial segregation. Application to flow reactors with pre- and unmixed feed. 36 (1981), 839-844... 

However, the fluid leaving the first CSTR may not become mixed on a molecular level before it enters the second reactor. In the limit, the fluid elements in this stream may remain completely segregated between the two reactors. For this situation, the procedure described in the preceding paragraph is not appropriate because the stream entering the second CSTR is not uniform on a molecular level. Rather, the feed to the second CSTR consists of packets of fluid with different compositions. In this case, the macrofluid model must be used, with the measured RTD for the whole reactor, i.e., the reactor that was being modeled as a series of equal-volume CSTRs. In the case of a fluid that remains as a macrofluid, there is no need to fit the CIS model to the measured RTD. The macrofluid model must be applied directly. 

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