A Multiple Tanks in Series

Consider the case of three, constant-volume tanks in series, as represented in Fig. 2.11, in which the tanks have differing volumes Vlf V2, V3, respectively. Assuming well-mixed tanks, the component balance equations are 

In this case, three time constants in series, tj, t2 and T3, determine the form of the final outlet response C3. As the number of tanks is increased, the response curve increasingly approximates the original step-change input signal, as shown in Fig. 2.12. The response curves for three stirred tanks in series, combined with chemical reaction are shown in the simulation example CSTRPULSE. 

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This chapter develops the techniques needed to analyze multiple and complex reactions in stirred tank reactors. Physical properties may be variable. Also treated is the common industrial practice of using reactor combinations, such as a stirred tank in series with a tubular reactor, to accomplish the overall reaction. 

It is possible to employ either multiple individual tanks in series or units containing multiple stages within a single shell (see Figure 8.2). Multiple tanks are more expensive, but provide more flexibility in use, since they are more readily altered if process requirements change. In order to minimize pump requirements and maintenance, one often chooses to allow for gravity flow between stages. When the reactants are of limited miscibility, but differ... 

A computational model will be developed for numerous water quality parameters in the Platte River, Nebraska. In many locations, this river splits into multiple channels that are joined back together downstream. One significant split is the Kearney Canal diversion, illustrated in Figure E6.7.1, where 20% of the flow splits off into a second river at the city of Overton, only to return 20 km downstream at the city of Kearney. A tracer pulse was put into the river at location x = 0 and time t = 0, upstream of the diversion. Downstream of the diversion s return, the pulse at location x = 25 km is given in Figure E6.7.2. Develop a model for this reach that contains equal size tanks-in-series for the main channel and a similar number of tanks-in-series with the addition of a possible plug flow for the side channel, as illustrated in Figure E6.7.3. 

The other two methods are subject to both these errors, since both the form ofi the RTD and the extent of micromixing are assumed. Their advantage is that they permit analytical solution for the conversion. In the axial-dispersion model the reactor is represented by allowing for axial diffusion in an otherwise ideal tubular-flow reactor. In this case the RTD for the actual reactor is used to calculate the best axial dififusivity for the model (Sec. 6-5), and this diffusivity is then employed to predict the conversion (Sec. 6-9). This is a good approximation for most tubular reactors with turbulent flow, since the deviations from plug-flow performance are small. In the third model the reactor is represented by a series of ideal stirred tanks of equal volume. Response data from the actual reactor are used to determine the number of tanks in series (Sec. 6-6). Then the conversion can be evaluated by the method for multiple stirred tanks in series (Sec. 6-10). 

In Section 8.3.1.4, 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 CSTRs 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 non-steady-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 farther downstream. However, since there is no effect of variations downstream on the performance of upstream CSTRs, 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... 

Multi-zone, Tanks-in-Series, and Axial dispersion models (Fig. 12.3-1 F) Other, less fundamental approaches accounting for mixing limitations in reactors are described in Section 12.7. They are based on simplified descriptions of the mixing pattern, e.g., a ID axial dispersion approach, or on the decomposition of the complex flow reactor into multiple interconnected regions or zones, each of these being described by a different idealized mixing pattern. Such semi-empirical models contain model parameters which have to be determined, experimentally or a posteriori from PDF, CFD, or RTD data. 

The two procedures primarily used for continuous nitration are the semicontinuous method developed by Bofors-Nobel Chematur of Sweden and the continuous method of Hercules Powder Co. in the United States. The latter process, which uses a multiple cascade system for nitration and a continuous wringing operation, increases safety, reduces the personnel involved, provides a substantial reduction in pollutants, and increases the uniformity of the product. The cellulose is automatically and continuously fed into the first of a series of pots at a controlled rate. It falls into the slurry of acid and nitrocellulose and is submerged immediately by a turbine-type agitator. The acid is deflvered to the pots from tanks at a rate controlled by appropriate instmmentation based on the desired acid to cellulose ratio. The slurry flows successively by gravity from the first to the last of the nitration vessels through under- and overflow weirs to ensure adequate retention time during nitration. The overflow from the last pot is fully nitrated cellulose. 

Example 14.6 derives a rather remarkable result. Here is a way of gradually shutting down a CSTR while keeping a constant outlet composition. The derivation applies to an arbitrary SI a and can be extended to include multiple reactions and adiabatic reactions. It is been experimentally verified for a polymerization. It can be generalized to shut down a train of CSTRs in series. The reason it works is that the material in the tank always experiences the same mean residence time and residence time distribution as existed during the original steady state. Hence, it is called constant RTD control. It will cease to work in a real vessel when the liquid level drops below the agitator. 

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). 

It is possible to extend this treatment to the case of multiple CSTR s operating in series by adapting the procedure outlined by Denbigh and Turner (2). Let (ACA)U (ACA)2, and (ACA)h represent the changes in the concentration of species A that take place in tanks one, two, and i, respectively. 

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