Nonideal Reactors Residence Time Distributions

The residence time considers the time that each fluid element or group of molecules remains in the reactor it also depends on the velocity of the molecules within the reactor, and therefore the flow in the reactor. The residence time can be equal to the space time if the velocity is uniform within a cross section of the reaction system, as is the case of an ideal PFR. However, this situation is not the same for tank-type reactor, because the velocity distribution is not uniform. In most nonideal reactors, residence time is not the same for all molecules. This result in variations in concentration along the reactor radial, i.e., its concentration inside and outlet tank reactors are not uniform. This means a need to define the residence time and calculate their distribution for each system. 

From this example of a fast, competitive consecutive reaction scheme we can see that nonideal mixing can cause a decrease in selectivity in both continuous and semibatch reactors. Residence time distribution issues can cause a reduction in yield and selectivity for both slow and fast reactions (see Chapter 1), but for fast reactions, the decrease in selectivity and yield due to inefficient local mixing can be greater than that caused by RTD issues alone. In semibatch reactors, poor bulk mixing can also cause these reductions (see Example 13-3). 

Different reactor networks can give rise to the same residence time distribution function. For example, a CSTR characterized by a space time Tj followed by a PFR characterized by a space time t2 has an F(t) curve that is identical to that of these two reactors operated in the reverse order. Consequently, the F(t) curve alone is not sufficient, in general, to permit one to determine the conversion in a nonideal reactor. As a result, several mathematical models of reactor performance have been developed to provide estimates of the conversion levels in nonideal reactors. These models vary in their degree of complexity and range of applicability. In this textbook we will confine the discussion to models in which a single parameter is used to characterize the nonideal flow pattern. Multiparameter models have been developed for handling more complex situations (e.g., that which prevails in a fluidized bed reactor), but these are beyond the scope of this textbook. [See Levenspiel (2) and Himmelblau and Bischoff (4).]... 

These two types of deviations occur simultaneously in actual reactors, but the mathematical models we will develop assume that the residence time distribution function may be attributed to one or the other of these flow situations. The first class of nonideal flow conditions leads to the segregated flow model of reactor performance. This model may be used... 

In general, each form of ideal flow can be characterized exactly mathematically, as can the consequences of its occurrence in a chemical reactor (some of these are explored in Chapter 2). This is in contrast to nonideal flow, a feature which presents one of the major difficulties in assessing the design and performance of actual reactors, particularly in scale-up from small experimental reactors. This assessment, however, may be helped by statistical approaches, such as provided by residence-time distributions. It... 

In this chapter, we consider nonideal flow, as distinct from ideal flow (Chapter 13), of which BMF, PF, and LF are examples. By its nature, nonideal flow cannot be described exactly, but the statistical methods introduced in Chapter 13, particularly for residence time distribution (RTD), provide useful approximations both to characterize the flow and ultimately to help assess the performance of a reactor. We focus on the former here, and defer the latter to Chapter 20. However, even at this stage, it is important to realize that ignorance of the details of nonideal flow and inability to predict accurately its effect on reactor performance are major reasons for having to do physical scale-up (bench —> pilot plant - semi-works -> commercial scale) in the design of a new reactor. This is in contrast to most other types of process equipment. 

The TIS and DPF models, introduced in Chapter 19 to describe the residence time distribution (RTD) for nonideal flow, can be adapted as reactor models, once the single parameters of the models, N and Pe, (or DL), respectively, are known. As such, these are macromixing models and are unable to account for nonideal mixing behavior at the microscopic level. For example, the TIS model is based on the assumption that complete backmixing occurs within each tank. If this is not the case, as, perhaps, in a polymerization reaction that produces a viscous product, the model is incomplete. 

We will not attempt to solve the preceding equations except in a few simple cases. Instead, we consider nonideal reactors using several simple models that have analytical solutions. For this it is convenient to consider the residence time distribution (RTD), or the probability of a molecule residing in the reactor for a time f. 

The asymptotic mean size is 59A reached at 0.5 m, assuming that the reactor is an ideal plug flow reactor where all the particles are the same size. To further this anal3 is, we can add dispersion into this reactor analysis and correct for the nonideal nature of this reactor. The dispersion analysis allows the prediction of the geometric standard deviation of the partice size distribution due to variations in the residence time distribution. 

For a continuous reactor with a nonideal flow pattern, characterized by the differential residence time distribution E t), the following expression holds for the conversion nonideai. which is attained in case complete segregation of all fluid elements passing through the reactor can be assumed ... 

Figure 1-6 shows a residence time distribution from a tracer experiment studying the mixing characteristics of a nozzle-type reactor [15] that behaves nonideally. 

Overview In this chapter we learn about nonideal reactors, that is, reactors that do not follow the models we have developed for ideal CSTRs, PFRs, and PBRs. In Pan I we describe how to characterize these nonideal reactors using the residence time distribution function (/), the mean residence time the cumulative distribution function Fit), and the variance a. Next we evaluate E t), F(t), and for idea) reactors, so that we have a reference proint as to how far our real (i.e., nonideal) reactor is off the norm from an ideal reactor. The functions (f) and F(r) will be developed for ideal PPRs. CSTRs and laminar flow reactors, Examples are given for diagnosing problems with real reactors by comparing and E(i) with ideal reactors. We will then use these ideal curves to help diagnose and troubleshoot bypassing and dead volume in real reactors. 

In Pan 2 we will learn how to use the residence time data and functions to make predictions of conversion and exit concentrations. Because the residence time distribution is not unique for a given reaction system, we must use new models if we want to predict the conversion in our nonideal reactor. We present the five most common models to predict conversion and then close the chapter by applying two of these models, the segregation model and the maximum mixedness model, to single and to multiple reactions. 

The basic ideas that are used in the distribution of residence times to charac terize and model nonideal reactions are really few in number. The two majo uses of the residence time distribution to characterize nonideal reactors are... 

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