Multiple tanks in series

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. 

Tanks-in-Series Model Versus Dispersion Model. We have seen that we can apply both of these one-parameter models to tubular reactors using the variance of the RTD. For first-order reactions the two models can be applied with equal ease. However, the tanks-in-series model is mathematically easier to use to obtain the effluent concentration and conversion for reaction orders other than one and for multiple reactions. However, we need to ask what would be the accuracy of using the tanks-in-series model over the dispersion model. These two models are equivalent when the Peclet-Bodenstein number is related to the number of tanks in series, n, by the equation ... 

The Ideal Stirred Tank 533 Multiple Stirred Tanks in Series 536 Applicability of the CSTC Model 536... 

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. 

Now let us examine the case of multiple capacities in series. Consider the two noninteracting tanks in series shown in Figure 3.28. 

---