Real Reactors and Residence Time Distribution RTD

In Chapter 2, the design of the so-called ideal reactors was discussed. The reactor ideahty was based on defined hydrodynamic behavior. We had assumedtwo flow patterns plug flow (piston type) where axial dispersion is excluded and completely mixed flow achieved in ideal stirred tank reactors. These flow patterns are often used for reactor design because the mass and heat balances are relatively simple to treat. But real equipment often deviates from that of the ideal flow pattern. In tubular reactors radial velocity and concentration profiles may develop in laminar flow. In turbulent flow, velocity fluctuations can lead to an axial dispersion. In catalytic packed bed reactors, irregular flow with the formation of channels may occur while stagnant fluid zones (dead zones) may develop in other parts of the reactor. Incompletely mixed zones and thus inhomogeneity can also be observed in CSTR, especially in the cases of viscous media. 

The abovementioned phenomena lead to a nonuniform residence time of the fluid elements in tubular reactors, which may have a detrimental effect on the reactor performance and product yield. 

In this chapter, residence time distribution (RTD) of ideal and nonideal reactors along with the method of determination are described in detail. The influence of nonideality and RTD on the reactor performance, the target product yield, and selectivity, including complex reactions, is presented. 

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Real reactors deviate more or less from these ideal behaviors. Deviations may be detected with residence 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. 

Residence time distribution (RTD) is a classical tool in the prediction of the comportment of a chemical reactor provided that the reaction kinetics and mass transfer characteristics of the system are known, the reactor performance can be calculated by combining kinetic and mass transfer models to an appropriate residence time distribution model. RTDs can be determined experimentally, as described in classical textbooks of chemical reaction engineering (e.g. Levenspiel 1999). RTD experiments are typically carried out as pulse or step-response experiments. The technique is principally elegant, but it requires the access to the real reactor system. In large-scale production, experimental RTD studies are not always possible or allowed. Furthermore, a predictive tool is needed, as the design of a new reactor is considered. 

The deviation of a real reactor from ideal systems is deduced by a widely used method of inquiry, the stimulus-response experiment with a nonreactive tracer. The goal is not knowledge of all the hydrodynamic details of the real flow, but to know how long the molecules stay in the reactor or, more precisely, determination of the residence time distribution (RTD). Based on the RTD and a respective link to the mass balance and conversion equation, respectively, the conversion of a reactant in a real reactor can then be calculatecL We will learn this in Sections 4.10.5.2 and 4.10.6.2, limiting ourselves to the case of single-phase flow and steady-state operation. 

The deviation of a real (continuously operated) reactor from ideal systems is deduced from the residence time distribution (RTD), which is measured by a pulse or by a step experiment. For a pulse experiment, a small amount of tracer is introduced into the feed stream, and the exit tracer concentration is measured with time ( function). For a step experiment, at time t = 0 we switch to a fluid with a tracer of constant concentration, and the exit tracer concentration versus time is measured (Ffunction). 

Transient experiments with inert tracers are used to determine residence time distributions. In real systems, they will be actual experiments. In theoretical studies, the experiments are mathematical and are applied to a dynamic model of the system. Table 1-1 lists the types of RTDs that can be measured using tracer experiments. The simplest case is a negative step change. Suppose that an inert tracer has been fed to the system for an extended period, giving Ci = Cout = Q for t < 0. At time t = 0, the tracer supply is suddenly stopped so that Cm = 0 for t > 0. Then the tracer concentration at the reactor outlet will decrease with time, eventually approaching zero as the tracer is washed out of the system. This response to a negative step change defines the washout function, W(t). The responses to other standard inputs are shown in Table 1-1. Relationships between the various functions are shown in Table 1-2. 

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