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V dt

Thus, the dispersion number foT a nonideal reactoT can be approximated by determining the slope of the F(t) curve at the time equal to one HRT and using Eq. 4.25. There are also several ways of determining the dispersion number using the £(t) curve and they are discussed in detail elsewhere."

Figure 4.8 Step input tracer response for the axial dispersion model.

Time, t

Figure 4.8 Step input tracer response for the axial dispersion model.

After the dispersion number has been determined, the performance of the reactor can be determined by using Eq. 4.23 with the appropriate reaction rate expressions. This often requires numerical techniques. Because of the complexity of such an approach, CSTRs in series have been used more frequently to model system performance in environmental engineering practice. However, the dispersion number is often used to characterize the flow patterns in reactors for other purposes.'

### 4.4.3 Representation of Complex Systems

The reactor systems used for some suspended growth biochemical operations are quite simple, whereas those used for others are complex, as seen in Table 1.2. Luckily, the concepts presented in this chapter suggest thai many of the complex systems can be modeled simply as CSTRs in scries, although those CSTRs may be of different size or may contain different biochemical environments (i.e., aerobic or anoxic). In Chapter 7 we will use this technique to investigate the theoretical performance of several systems.

Sometimes the flow patterns in reactor systems are so complex that the RTDs cannot be modeled by the techniques discussed above. In that case, it may be necessary to model the system as a complex network of flow regions with various modes of flow between and around them. This technique was proposed by Cholette and Cloutier* and is based on the premise that just as adding different numbers of tanks in series changes the RTD, so will adding different types of mixers in series and parallel. The main difference is that by adding different types of regions and flows it is possible to reproduce almost any RTD. As one might expect, however, the techniques for doing this can be quite complex. The reader is referred to other sources for information about their use.'"

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