Targeting segregated flow

Given the reaction stoichiometry and rate laws for an isothermal system, a simple representation for targeting of reactor networks is the segregated-flow model (see, e.g., Zwietering, 1959). A schematic of this model is shown in Fig. 2. Here, we assume that only molecules of the same age, t, are perfectly mixed and that molecules of different ages mix only at the reactor exit. The performance of such a model is completely determined by the residence time distribution function,/(f). By finding the optimal/(f) for a specified reactor network objective, one can solve the synthesis problem in the absence of mixing. 

The solution to this problem provides a good lower bound for the targeting problem. Also, the segregated flow model is often sufficient for the reactor synthesis problem. The solution to this simple formulation thus could be chosen... 

The segregated-flow model described by (P2) forms a basis to generate an AR. We now develop conditions for the closure of this space with respect to the operations of mixing and reaction by means of a PFR, a CSTR, or a recycle PFR (RR). Consider the region depicted by the constraints of (P2). Our aim is to develop conditions that can be checked easily for the reaction system in question so that, if these conditions are satisfied, we need to solve only (P2) for the reactor targeting problem. We will analyze these conditions based on PFR trajectories projected into two dimensions. Here, a PFR, which is an n-dimen-sional trajectory in concentration space and parametric in time, is generated by the solution of the initial value differential equation system in (PI). Figure 3 illustrates a PFR trajectory and its projections in three-dimensional space, where the solid line represents the actual PFR trajectory and the dotted lines represent the projected trajectories. 

The utility criterion supposes the selection (flow analysis) of the reaction set the most important for the particular behavior of the system, or for the particular product formation and transformations. This approach is very useful for the segregation of reactions, in which a particular substance (target product, leading radical, or key branching intermediate) forms or transforms. As a result, the analysis of the process under different conditions, or at different stages (when the ratio of various elementary reactions is changing) becomes available. 

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