Cascades of CSTRs

Cross-flow reactors are fed continuously with streams of components of the reaction mixture whereby some components are introduced at the inlet, while others are introduced at other locations. The reaction mixture flows out continuously from the end of the reaction zone. A cascade of CSTRs with additional feeds to individual reactors represents a cross-flow reactor system. Cross-flow reactors are also operated at steady-state conditions ... 

Parallel reactions, oai = om2, a i = am = 0, Ei > E2. The. selectivity to the desired product increases with temperature. The highest allowable temperature and the highest reactant concentrations should be applied. A batch reactor, a tubular reactor, or a cascade of CSTRs is the best choice. 

Consecutive reactions, isothermal reactor cmi < cw2, otai = asi = 0. The course of reaction is shown in Fig. 5.4-71. Regardless the mode of operation, the final product after infinite time is always the undesired product S. Maximum yields of the desired product exist for non-complete conversion. A batch reactor or a plug-flow reactor performs better than a CSTR Ysbr.wux = 0.63, Ycstriiuix = 0.445 for kt/ki = 4). If continuous operation and intense mixing are needed (e.g. because a large inteifacial surface area or a high rate of heat transfer are required) a cascade of CSTRs is recommended. 

ILLUSTRATION 8.8 DETERMINATION OF REACTOR SIZE REQUIREMENTS FOR A CASCADE OF CSTR s—ALGEBRAIC APPROACH... 

These relations support our earlier assertion that for the same overall conversion the total volume of a cascade of CSTR s should approach the plug flow volume as the number of reactors in the cascade is increased. 

The physical situation in a fluidized bed reactor is obviously too complicated to be modeled by an ideal plug flow reactor or an ideal stirred tank reactor although, under certain conditions, either of these ideal models may provide a fair representation of the behavior of a fluidized bed reactor. In other cases, the behavior of the system can be characterized as plug flow modified by longitudinal dispersion, and the unidimensional pseudo homogeneous model (Section 12.7.2.1) can be employed to describe the fluidized bed reactor. As an alternative, a cascade of CSTR s (Section 11.1.3.2) may be used to model the fluidized bed reactor. Unfortunately, none of these models provides an adequate representation of reaction behavior in fluidized beds, particularly when there is appreciable bubble formation within the bed. This situation arises mainly because a knowledge of the residence time distribution of the gas in the bed is insuf-... 

The bioreactor has been introduced in general terms in the previous section. In this section the basic bioreactor concepts, i.e., the batch, the fed-batch, the continuous-flow stirred-tank reactor (CSTR), the cascade of CSTRs and the plug-flow reactor, will be described. 

A comparison of the various types of reactor concepts, in a general sense, is actually only possible between the batch, the CSTR and the PFR. The cascade of CSTRs, depending on the number of vessels n in the series, more or less behaves as an ideal mixer for n->l or an ideal plug flow for n- - . The fed-batch reactor is more difficult to situate. Although the concentration of compounds important for the rate of reaction can be controlled optimally during the whole fed period, the reactor volume is only partially utilized, especially in the beginning. Nevertheless, this reactor concept certainly has decisive advantages in many cases, as shown by the fact that it is one of the most widely used. 

Remark 5 Note also that reactors of various distribution functions can be treated with this approach, on the grounds that different distribution functions are usually approximated via cascades of CSTRs. In this case, we can treat the number of CSTRs as a variable or provide a variety of alternative reactors each featuring different numbers of CSTRs. Kokossis and Floudas (1990), present examples for batch, semibatch reactors and different distribution functions. 

Pibouleau et al. (1988) provided a more flexible representation for the synthesis problem by replacing the single reactor unit by a cascade of CSTRs. They also introduced parameters for defining the recovery rates of intermediate components into the distillate, the split fractions of top and bottom components that are recycled toward the reactor sequence, as well as parameters for the split fractions of the reactor outlet streams. A benzene chlorination process was studied as an example problem for this synthesis approach. In this example, the number of CSTRs in the cascade was treated as a parameter that ranged from one up to a maximum of four reactors. By repeatedly solving the synthesis problem, an optimum number of CSTRs was determined. 

For a 100 times slower reaction, the heat exchange becomes fully uncritical, but the conversion of 99% can only be reached with a volume of 90 m3, which is unrealistic. The situation improves with a higher reactor temperature or with a different combination of reactors cascade of CSTRs or CSTR followed by a tubular reactor. 

Another way to decrease the width of the particle size distribution generated is to use a cascade of CSTRs, where the output from the ith reactor is the input for the (i + l)1h reactor. If nucleation occurs in the first tank of the cascade, followed by growth in all subsequent tanks, then the population leaving the last (A/th) reactor is given by Abe and Balakrishnan [100] as... 

As an alternative to a cascade of CSTR trains, a novel continuous reactor with a Couette-Taylor vortex flow (CTVF) has been proposed, which can realize any flow pattern between plug and perfectly mixed flows [361-366]. A continuous Couette-Taylor vortex flow reactor (CCTVFR) consists of two concentric cylinders with the inner cylinder rotating and with the outer cylinder at rest. Figure 29 shows a typical flow pattern caused by the rotation of the inner cylinder. 

The polymerization time in continuous processes depends on the time the reactants spend in the reactor. The contents of a batch reactor will all have the same residence time, since they are introduced and removed from the vessel at the same times. The continuous flow tubular reactor has the next narrowest residence time distribution, if flow in the reactor is truly plug-like (i.e., not laminar). These two reactors are best adapted for achieving high conversions, while a CSTR cannot provide high conversion, by definition of its operation. The residence time distribution of the CSTR contents is broader than those of the former types. A cascade of CSTR s will approach the behavior of a plug flow continuous reactor. 

Figure 1.2 Continuous reactors (a) tubular reactor, (b) continuous stirred-tank reactor (CSTR), and (c) cascade of CSTRs.

Consider a liquid-phase, first-order reaction of the form A P + R in an isothermal cascade of CSTRs where only reactant A is fed to the system. Taking the inlet stream to the cascade as the reference stream and since only reactant A is fed, y o = 1- Using Eq. 8.2.3, the design equation for the nth CSTR is... 

Figure 8.5 Graphical presentation of the design equation for a cascade of CSTRs.

In practice, the cascade usually consists of either equal-size reactors or a set of specified numbers of CSTRs in which the volume of each is selected such that total volume of the cascade, for a given outlet conversion, is the smallest. A cascade of equal-size CSTRs is represented in Figure 8.4 by rectangles whose areas are the same, and a cascade with the total smallest volume is represented by a given number of rectangles whose combined area is the smallest. Below, we consider the performance of a cascade of CSTRs when the reaction rate is given. 

Cascade of CSTRs In several processes, a cascade of CSTRs may be used to obtain the desired polymer properties and maximize monomer conversion. Conversion of monomer increases from reactor to reactor and thus the solids content and viscosity would increase and heat transfer coefficients decrease for each progressive reactor. For each reactor, an energy balance can be performed using Equation 13.9 by replacing the temperature... 

Given the autocatalytic nature of the growth cycle for microorganisms, an alternative solution to circumventing problems associated with the absence of reactor productivity during the lag phase is to employ a cascade of CSTRs, The stirred tanks may differ in size, with the first reactor operating at a point in the growth cycle where the... 

The design equations for batteries of chemostats can be derived by appropriate extensions of the material balance relations developed in Section 8.3.2 for cascades of CSTRs. Steady-state operation is assumed for each stirred tank, but students must be careful in writing the reaction rate terms that appear in these relations. Details... 

As we saw in Section 8.3.2, one can develop equations describing the performance of an arbitrary CSTR in a cascade of CSTRs. We can also develop the corresponding equations for the nth bioreactor in an extended cascade of stirred tanks by conducting an analysis on the nth bioreactor. The feed stream exiting bioreactor n - 1 and entering reactor n has a volumetric flow rate V, a concentration of the hmiting substrate equal to s , and a biomass concentration. This stream enters well-stirred reactor n, which... 

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