Stirred-Tank Reactor Cascade

For any continuous stirred-tank reactor, n, in a cascade of reactors (Fig. 3.13) the reactor n receives the discharge from the preceding reactor, n-1, as its feed and discharges its effluent into reactor n+1, as feed to that reactor. 

Thus the balance equations for reactor, n, simply become 

Thus the respective rate expressions depend upon the particular concentration and temperature levels, that exist within reactor, n. The rate of production of heat by reaction, rg, was defined in Sec. 1.2.5 and includes all occurring reactions. Simulation examples pertaining to stirred tanks in series are CSTR, CASCSEQ and COOL. 

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This section is concerned with batch, semi-batch, continuous stirred tanks and continuous stirred-tank-reactor cascades, as represented in Fig. 3.1 Tubular chemical reactor systems are discussed in Chapter 4. 

For steady-state operation of a continuous stirred-tank reactor or continuous stirred-tank reactor cascade, there is no change in conditions with respect to time, and therefore the accumulation term is zero. Under transient conditions, the full form of the equation, involving all four terms, must be employed. 

CONTINUOUS STIRRED TANK REACTOR CASCADE (CSTR)... 

Ravindranath and Mashelkar 151 Continuous Esterification Stirred tank reactor cascade... 

The autoclave reactors used today in the high-pressure polymerization of ethylene are single stirred-tank reactors, cascades of stirred autoclaves, and multi-chamber autoclaves. 

During the manufacturing process, if the grafting increases during early stages of the reaction, the phase volume will also increase, but the size of the particles will remain constant [146-148]. Furthermore, reactor choice plays a decisive role. If the continuous stirred tank reactor (CSTR) is used, little grafting takes place and the occlusion is poor and, consequently, the rubber efficiency is poor. However, in processes akin to the discontinuous system(e.g., tower/cascade reactors), the dispersed phase contains a large number of big inclusions. 

An alternative method to account for bed dispersion is to model the bed as a cascade of well stirred tank reactors, each with a uniform temperature and concentration (124,1 5) Transverse dispersion can be accounted for by staggering the cells so that each cell feeds into two different cells in the forward direction (126). When the value of L/d is large, say above 20, the two models are not very different if the number of cells in the cascade is chosen to equal N = PeL/2d. When Pe = 2, this amounts to considering... 

Crameri et al. (1997) have reported an asymmetric hydrogenation constituting an important step in the production of a new calcium antagonist, Mibefradil (POSICOR) (of Hoffmann-LaRoche). Pilot-scale synthesis of (S)-2-(4-flurophenyl)-3-methylbutanoic acid by the asymmetric hydrogenation of 2-(4-fluorophenyl)-3-methyl but-2-enoic acid with a [Ru (/ )-MeOBIPHEP)(OAc)2]-catalyst has been described. The hydrogenation was performed in a continuous mode in a cascade stirred-tank reactor system at a pressure of 270 bar. A large reduction in total reactor volume compared to the batch mode was realized. 

Fig. 5.4-23 shows a sketch drawing of a BSC (Brogli et al., 1981). The stirred-tank reactor made of glass (a metal version is also available) is surrounded by a jacket through which a heat-transfer fluid flows at a very high rate the jacket is not insulated. The temperature of the circulation loop is regulated by a cascaded controller so that the heat evolution in the reactor is equilibrated by heat transfer through the reactor wall. The temperature in the loop is adjusted by injection of thermostatted hot or cold fluid. 

Figure 3.13. Cascade of continuous stirred-tank reactors.

A cascade of three continuous stirred-tank reactors arranged in series, is used to carry out an exothermic, first-order chemical reaction. The reactors are jacketed for cooling water, and the flow of water through the cooling jackets is countercurrent to that of the reaction. A variety of control schemes can be employed and are of great importance, since the reactor scheme shows a multiplicity of possible stable operating points. This example is taken from the paper of Mukesh and Rao (1977). 

Figure 5.23. A typical stirred tank reactor control scheme, temperature cascade control, and reagent ...

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-... 

Size Comparisons Between Cascades of Ideal Continuous Stirred Tank Reactors and Plug Flow Reactors. In this section the size requirements for CSTR cascades containing different numbers of identical reactors are compared with that for a plug flow reactor used to effect the same change in composition. 

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... 

The Stirred Tanks in Series Model Another model that is frequently used to simulate the behavior of actual reactor networks is a cascade of ideal stirred tank reactors operating in series. The actual reactor is replaced by n identical stirred tank reactors whose total volume is the same as that of the actual reactor. 

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... 

In Section 11.1.3.2 we considered a model of reactor performance in which the actual reactor is simulated by a cascade of equal-sized continuous stirred tank reactors operating in series. We indicated how the residence time distribution function can be used to determine the number of tanks that best model the tracer measurement data. Once this parameter has been determined, the techniques discussed in Section 8.3.2 can be used to determine the effluent conversion level. 

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 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-... 

Figure 4.13 Enzymatic by-product removal synthesis of dinitrodibenzyl from nitrotoluene applying a cascade of continuous stirred-tank reactors while degassing with nitrogen...

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. 

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