Reactors with Real Behavior

In practice, smaller or larger deviations from the above-described ideal behavior occur. The magnitude of the deviation and thus the first step in evaluating the true situation in a given reactor is an analysis of the residence-time behavior. 

The selectivity and conversion of a chemical reactor depend not only on the kinetics of the reaction but also on the time for which the reaction partners are available for the reaction, that is, the hydrodynamic behavior. By determining the residence-time behavior of a reactor, one can determine its deviation from ideal hydrodynamic behavior (boundary cases plug flow and complete backmixing) and hence decide with which reactor model the real reactor can best be modeled. 

Na2S04) by means of two ball valves and measuring the electrical conductivity at the reactor outlet (conductivity meter Q). In practice, radioactive labels are used, since even traces which do not influence the reaction are readily detectable. 

The result of the measurement is the cumulative residence-time curve F(t) (Equation 2.2-22)  

Differentiation of P(t) (dimensionless) gives the residence-time distribution function (dimensions s Equation 2.2-23)  

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There is an interior optimum. For this particular numerical example, it occurs when 40% of the reactor volume is in the initial CSTR and 60% is in the downstream PFR. The model reaction is chemically unrealistic but illustrates behavior that can arise with real reactions. An excellent process for the bulk polymerization of styrene consists of a CSTR followed by a tubular post-reactor. The model reaction also demonstrates a phenomenon known as washout which is important in continuous cell culture. If kt is too small, a steady-state reaction cannot be sustained even with initial spiking of component B. A continuous fermentation process will have a maximum flow rate beyond which the initial inoculum of cells will be washed out of the system. At lower flow rates, the cells reproduce fast enough to achieve and hold a steady state. 

In addition to the one-parameter models of lanks-in-series and dispersion. many other one-parameter models exist w hen a combination of ideal reactors is to model the real reactor as shown in Section 13.5 for reactors with bypassing and dead volume. Another example of a one-parameter model would be to model the real reactor as a PFR and a CSTR in series with the one parameter being the fraction of the total volume that behaves as a CSTR. We can dream up many other situations that would alter the behavior of idea) reactors in a way that adequately describes a real reactor. However, it may be that one parameter is not sufficient to yield an adequate comparison between theory and practice. We explore these situations with combinations of ideal reactors in the section on two-parameter models. 

There is an interior optimum. In this numerical example it occurs when 40% of the reactor volume is in the initial CSTR and 60% is in the downstream PFR. The model reaction is chemically unrealistic but illustrates behavior that can arise with real reactions. An excellent process for the bulk polymerization of styrene consists of a CSTR followed by a tubular postreactor. 

It was found, however, that the reactor showed oscillatory behavior in certain ranges [see Bush, 1972]. Therefore, the second dynamic criterion, (10.4.2-10) was also checked with relationships similar to (10.4.2-12), but also accounting for some of the additional complexities in the real (gas phase) experimental system. The results are shown in Fig. I0.4.2.A-2, where the left-hand side (LHS) and right-hand side (RHS) of the criterion are plotted. A central region exists where the criterion is violated. 

Real reactors deviate more or less from these ideal behaviors. Deviations may be detected with re.sidence time distributions (RTD) obtained with the aid of tracer tests. In other cases a mechanism may be postulated and its parameters checked against test data. The commonest models are combinations of CSTRs and PFRs in series and/or parallel. Thus, a stirred tank may be assumed completely mixed in the vicinity of the impeller and in plug flow near the outlet. 

Chapter 2 treated multiple and complex reactions in an ideal batch reactor. The reactor was ideal in the sense that mixing was assumed to be instantaneous and complete throughout the vessel. Real batch reactors will approximate ideal behavior when the characteristic time for mixing is short compared with the reaction half-life. Industrial batch reactors have inlet and outlet ports and an agitation system. The same hardware can be converted to continuous operation. To do this, just feed and discharge continuously. If the reactor is well mixed in the batch mode, it is likely to remain so in the continuous mode, as least for the same reaction. The assumption of instantaneous and perfect mixing remains a reasonable approximation, but the batch reactor has become a continuous-flow stirred tank. 

From Figure 7 it is deduced that the number of the equilibrium states depends on the number of points where the straight line yo = constant intersects with the curve defined by Eq.(13). With a value of yo 0.025, there are three equilibrium points Pi, P2, P3, being P stable, P2 unstable and P3 can be stable or unstable depending on the real part of the eigenvalues of the linearized system at this point. When the line yo = constant is tangent to the curve yo = fiy ) (be. point M) a new behavior of the reactor appears, which can be characterized from dyo/dy = 0 in Eq.(13) as follows ... 

The CSTR with complete mixing and the PFR with no axial mixing are limiting behaviors that can be only approached in practice. Residence time distributions in real reactors can be found with tracer tests. 

Reaction studies with model compounds representative of the metal species in petroleum are discussed to provide insight into the fundamental rate processes which occur. It will be demonstrated that this information can be used to successfully interpret the behavior of real feedstocks in commercial hydrotreating reactors. 

Figure 4.3.1 Catalyst characterization under reaction conditions spans all length scales from real reactors to the atomic structure with the catalytically active site as well as many orders in timescales considering long-term behavior in a real process and rapid changes of the structure and extremely fast surface processes.

The reactors treated in the book thus far—the perfectly mixed batch, the plug-flow tubular, and the perfectly mixed continuous tank reactors—have been modeled as ideal reactors. Unfortunately, in the real world we often observe behavior very different from that expected from the exemplar this behavior is tme of students, engineers, college professors, and chemical reactors. Just as we must learn to work with people who are not perfect, so the reactor analyst must learn to diagnose and handle chemical reactors whose performance deviates from the ideal. Nonideal reactors and the principles behind their analysis form the subject of this chapter and the next. 

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