Segregated-flow reactor model

The segregated-flow reactor model (SFM) represents the micromixing condition of complete segregation (no mixing) of fluid elements. As noted in Section 19.2, this is one extreme model of micromixing, the maximum-mixedness model being the other. 

The first equation describes the concentrations available from segregated flow. The model equations for a recycle reactor starting from any feasible point are described by the second and third equations. The fourth equation gives the concentration at the exit of the recycle reactor. Here, the vectors I and u are lower and upper bounds, respectively, on the exit concentration vector. Thus, if 7rr > Jp2> then the recycle reactor provides an advantageous extension over (P2). 

This equation is a general equation for the calculation of conversion in any segregated flow reactor. For a laminar flow reactor, that is modelled as a segregated flow reactor, we get an equation for XAfhy substituting Equations 3.369 and 3.365 in 3.370 ... 

The completely segregated stirred tank can be modeled as a set of piston flow reactors in parallel, with the lengths of the individual piston flow elements being distributed exponentially. Any residence time distribution can be modeled as piston flow elements in parallel. Simply divide the flow evenly between the elements and then cut the tubes so that they match the shape of the washout function. See Figure 15.12. A reactor modeled in this way is said to be completely segregated. Its outlet concentration is found by averaging the concentrations of the individual PFRs ... 

These two types of deviations occur simultaneously in actual reactors, but the mathematical models we will develop assume that the residence time distribution function may be attributed to one or the other of these flow situations. The first class of nonideal flow conditions leads to the segregated flow model of reactor performance. This model may be used... 

In the segregated flow model the contents of the volume elements of the fluid do not mix with one another as they move through the reactor. Each element may be considered as a small closed system that moves through the reactor. The different systems spend varying amounts of time in the reactor, giving rise to the measured residence time distribution func-... 

The basic premise of the segregated flow model is that the various fluid elements move through the reactor at different speeds without mixing with one another. Consequently, each little fluid element will behave as if it were a batch reactor operating at constant pressure. The conversions attained within the various fluid elements will be equal to those in batch reactors with holding times equal to the residence times of the different fluid elements. The average conversion level in the effluent is then given by... 

ILLUSTRATION 11.5 USE OF THE SEGREGATED FLOW MODEL TO DETERMINE THE CONVERSION LEVEL OBTAINED IN A NON-IDEAL FLOW REACTOR... 

Use the F(t) curve generated in Illustration 11.1 to determine the fraction conversion that will be achieved in the reactor if it is used to carry out a first-order reaction with a rate constant equal to 3.33 x 10 3 sec-1. Base the calculations on the segregated flow model. 

Use the F(t) curve for two identical CSTR s in series and the segregated flow model to predict the conversion achieved for a first-order reaction with k = 0.4 ksec-1. The space time for an individual reactor is 0.9 ksec. Check your results using an analysis for two CSTR s in series. 

In this chapter, we focus on the characteristics of the ideal-flow models themselves, without regard to the type of process equipment in which they occur, whether a chemical reactor, a heat exchanger, a packed tower, or some other type. In the following five chapters, we consider the design and performance of reactors in which ideal flow occurs. In addition, in this chapter, we introduce the segregated-flow model for a reactor as one application of the flow characteristics developed. 

Equation 13.5-2 is the segregated-flow model (SFM) with a continuous RTD, E(t). To what extent does it give valid results for the performance of a reactor To answer this question, we apply it first to ideal-reactor models (Chapters 14 to 16), for which we have derived the exact form of E(t), and for which exact performance results can be compared with those obtained independently by material balances. The utility of the SFM lies eventually in its potential use in situations involving nonideal flow, wheic results cannot be predicted a priori, in conjunction with an experimentally measured RTD (Chapters 19 and 20) in this case, confirmation must be done by comparison with experimental results. 

Micromixing between these two extremes (partial segregation) is possible, but not considered here. A model for (1) is the segregated-flow model (SFM) and for (2) is the maximum-mixedness model (MMM) (Zwietering, 1959). We use these in reactor models in Chapter 20. 

In addition to these two macromixing reactor models, in this chapter, we also consider two micromixing reactor models for evaluating the performance of a reactor the segregated flow model (SFM), introduced in Chapters 13 to 16, and the maximum-mixedness model (MMM). These latter two models also require knowledge of the kinetics and of the global or macromixing behavior, as reflected in the RTD. 

This chapter discusses four methods of gas phase ceramic powder synthesis by flames, fiunaces, lasers, and plasmas. In each case, the reaction thermodynamics and kinetics are similar, but the reactor design is different. To account for the particle size distribution produced in a gas phase synthesis reactor, the population balance must account for nudeation, atomistic growth (also called vapor condensation) and particle—particle segregation. These gas phase reactors are real life examples of idealized plug flow reactors that are modeled by the dispersion model for plve flow. To obtain narrow size distribution ceramic powders by gas phase synthesis, dispersion must be minimized because it leads to a broadening of the particle size distribution. Finally the gas must be quickly quenched or cooled to freeze the ceramic particles, which are often liquid at the reaction temperature, and thus prevent further aggregation. 

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