Cascade of stirred tank reactors

In order to reduce the disparities in volume or space time requirements between an individual CSTR and a plug flow reactor, batteries or cascades of stirred tank reactors ard employed. These reactor networks consist of a number of stirred tank reactors confiected in series with the effluent from one reactor serving as the input to the next. Although the concentration is uniform within any one reactor, there is a progressive decrease in reactant concentration as ohe moves from the initial tank to the final tank in the cascade. In effect one has stepwise variations in composition as he moves from onfe CSTR to another. Figure 8.9 illustrates the stepwise variations typical of reactor cascades for different numbers of CSTR s in series. In the general nonisothermal case one will also en-... 

The ratio of equations 8.3.58 and 8.3.57 gives the relative total space time requirement for a cascade of stirred tank reactors vis a vis a plug flow reactor. 

Analysis of CSTR Cascades under Nonsteady-State Conditions. In Section 8.3.1.4 the equations relevant to the analysis of the transient behavior of an individual CSTR were developed and discussed. It is relatively simple to extend the most general of these relations to the case of multiple CSTR s in series. For example, equations 8.3.15 to 8.3.21 may all be applied to any individual reactor in the cascade of stirred tank reactors, and these relations may be used to analyze the cascade in stepwise fashion. The difference in the analysis for the cascade, however, arises from the fact that more of the terms in the basic relations are likely to be time variant when applied to reactors beyond the first. For example, even though the feed to the first reactor may be time invariant during a period of nonsteady-state behavior in the cascade, the feed to the second reactor will vary with time as the first reactor strives to reach its steady-state condition. Similar considerations apply further downstream. However, since there is no effect of variations downstream on the performance of upstream CSTR s, one may start at the reactor where the disturbance is introduced and work downstream from that point. In our generalized notation, equation 8.3.20 becomes... 

We can characterize the mixed systems most easily in terms of the longitudinal dispersion model or in terms of the cascade of stirred tank reactors model. The maximum amount of mixing occurs for the cases where Q)L = oo or n = 1. In general, for reaction orders greater than unity, these models place a lower limit on the conversion that will be obtained in an actual reactor. The applications of these models are treated in Sections 11.2.2 and 11.2.3. 

Determination of Conversion Levels Based on the Cascade of Stirred Tank Reactors Model... 

ILLUSTRATION 11.7 USE OF THE CASCADE OF STIRRED TANK REACTORS MODEL TO PREDICT REACTOR PERFORMANCE... 

Use the model based on a cascade of stirred tank reactors to predict the conversion that will be attained in the reactor of Illustration 11.1. Assume that the value of the first-order rate constant is 3.33 x 10 3sec-1. 

The system mostly applied in practice for supply of ozone is the bubble column and the stirred tank reactor. With these reactor systems it is always possible to set up the complete reactor modification as a plug flow reactor, a continuous flow single stirred tank reactor or a cascade of stirred tank reactors. 

In the hydrogenation of benzoic acid, decarboxylation of the cyclohexane carboxylic acid product can occur. Therefore, a cascade of stirred-tank reactors is preferred here... 

Figure 8.2 Types of continuous-flow stirred-tank reactors (a) three-stage cascade of stirred-tank reactors (b) vertically staged cascade of three stirred tanks. Compartmented versions of a battery of stirred tanks in a single horizontal shell may also be employed. (Adapted from J. R. Couper, W. R. Penney, J. R. Fair, and S. M. Walas. Chemical Process Equipment Selection and Design. Copyright 2010. Used with permission of Elsevier.)...

The space time required to accomplish the specified conversion in a plug flow reactor (18.6 h) is sufficiently long that it makes the use of a tubular reactor impractical for the operating conditions specified. For these conditions a cascade of stirred-tank reactors would be more appropriate for use. 

S.3.2.2 Algebraic Approach to the Analysis of Cascades of Stirred-Tank Reactors Operating at Steady State... 

Thus, the pertinent area in this case is the rectangle shown in Figure 93b. For a staged cascade of stirred-tank reactors, a similar analysis indicates that the pertinent area is that given by the sum of the rectangles corresponding to the individual tanks. 

A continuous cascade of stirred tank reactors consists of N tanks in series as shown below. 

In the first commercial plant (20,000 t/a), a cascade of stirred tank reactors are operated at 170°C between 10 and 17 bar. The catalyst (palladium supported on charcoal) is separated from the liquid product by centrifugation. Small amounts of catalyst are recovered at the bottom of the cyclohexanoe carboxylic acid distillation column. A plant of 100,000 t/a capacity is no in operation. 

The desired production capacity and the required reaction time (residence time) are two of the most important criteria when selecting a reactor suitable for a homogeneous process. Trambouze et al. [ 1 ] have proposed a chart that suggests the applicability limits of different kinds of reactors for various reactions (Figure 3.8). For slow reactions and low production capacities, a BR is typically chosen, whereas for larger production voliunes, a continuous reactor is preferred a cascade of stirred tank reactors or a tube reactor. In the next section, the mass and energy balances for homogeneous reactors will be considered in detail. 

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