Segregated Tanks in Series

Two different cases should be mentioned for the segregated tanks-in-series model firstly, every reactor in the series can be segregated, and secondly, the tanks in series as an entity can be segregated. These two initial assumptions lead to different results. 

Let us first consider the case in which the tank series as an entity is segregated. Thus, for a reactant A, we obtain 

FIGURE 4.28 An individually segregated tank series (complete backmixing between each unit). 

In the second case, let us assume that each individual CSTR is segregated. As a result, the following derivation is valid, provided that the volume elements are broken up and mixed with each other between each step in the series  

For irreversible, second-order reaction kinetics with an arbitrary stoichiometry, the generation rates of the reactants are as follows  

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The above expressions are inserted into the appropriate balance equations, for example, for tanks-in-series, segregated tanks-in-series, and maximum-mixed tanks-in-series models. The models are solved numerically [3], and the results are illustrated in the diagrams presented in Figure 4.29, which displays the differences between the above models for second-order reactions. The figure shows that the differences between the models are the most prominent in moderate Damkohler numbers (Figure 4.29). For very rapid and very slow reactions, it does not matter in practice which tanks-in-series model is used. For the extreme cases, it is natural to use the simplest one, that is, the ordinary tanks-in-series model. 

FIGURE 4.29 yj (tanks in series), yur (maximum-mixed tanks in series), and ysT (segregated tanks in series) at M = 1.00, M = vaCob/(vbCoa)> R = kAtcoA h/ AyR = DamkOhler number. 

What value can the substrate (S) obtain in case the reactor is described by the segregated tanks-in-series model with j = 2, and the tanks in series as an entity is completely segregated ... 

Segregated tanks-in-series model (the tanks in series as a whole segregated)... 

The limits for part (b) are at the endpoints of a vertical line in Figure 15.14 that corresponds to the residence time distribution for two tanks in series. The maximum mixedness point on this line is 0.287 as calculated in Example 15.14. The complete segregation limit is 0.233 as calculated from Equation (15.48) using/(/) for the tanks-in-series model with N=2 ... 

Part (c) considers the mixing extremes possible with the physical arrangement of two tanks in series. The two reactors could be completely segregated so one limit remains 0.233 as calculated in part (b). The other limit corresponds to two CSTRs in series. The first reactor has half the total volume so that Uinkii = 2.5. Its output is 0.463. The second reactor has (ai )2ki2 = 1.16, and its output is 0.275. This is a tighter bound than calculated in part (b). The fraction unreacted must lie between 0.233 and 0.275. 

A reactor has a residence time distribution like that of that of two equal completely mixed tanks in series. The rate equation is -dC/dt = 0.5C1-5. Inlet concentration is C0 = 1.2 lbmol/cuft and the feed rate is 10 Ibmol reactant/min. Conversion required is 95%. Find the reactor volume needed (a) assuming segregated flow (b) in a two stage CSTR. 

The case of maximum mixedness corresponding to a given CTD has been simulated using a stirred-tanks-in-series configuration, each tank of which has a zero degree of segregation. Volumes of all the tanks have been assumed to be equal. To be exact, such a... 

Tanks-iti-Series Versus Segregation for a First-Order Reaction We have already stated that the segregation and maximum mixedness models are equivalent for a first-order reaction. The proof of this statement was left as an exercise in Problem P13-3b, Wc now show the tanks-in-series model and the segregation models are equivalent for a first-order reaction. 

Ideal PFR Ideal CSTR Ideal laminar Row reactor Segregation Maximum mixedness Dispersion Tanks in series... 

A continuous bulk polymerization process with three reaction zones in series has been developed. The degree of polymerization increases from the first reactor to the third reactor. Examples of suitable reactors include continuous stirred tank reactors, stirred tower reactors, axially segregated horizontal reactors, and pipe reactors with static mixers. The continuous stirred tank reactor type is advantageous, because it allows for precise independent control of the residence time in a given reactor by adjusting the level in a given reactor. Thus, the residence time of the polymer mixtures can be independently adjusted and optimized in each of the reactors in series (8). 

The concept of a well-stirred segregated reactor which also has an exponential residence time distribution function was introduced by Dankwerts (16, 17) and was elaborated upon by Zweitering (18). In a totally segregated, stirred tank reactor, the feed stream is envisioned to enter the reactor in the form of macro-molecular capsules which do not exchange their contents with other capsules in the feed stream or in the reactor volume. The capsules act as batch reactors with reaction times equal to their residence time in the reactor. The reactor product is thus found by calculating the weighted sum of a series of batch reactor products with reaction times from zero to infinity. The weighting factor is determined by the residence time distribution function of the constant flow stirred tank reactor. 

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