Residence-time distributions ideal reactors

In Chapter 1 two new sections have been added. In the first of these is a discussion of non-ideal flow conditions in reactors and their effect on residence time distribution and reactor performance. In the second section an important class of chemical reactions—that in which a solid and a gas react non-catalytically—is treated. Together, these two additions to the chapter considerably increase the value of the book in this area. 

Ideal and Real Reactors, Residence Time Distribution, and Reactor Modeling... 

Figure 3.29. Reactor design procedure with reactors having residence time distributions deviating from those of ideal reactors.

Tanks-in-series reactor configurations provide a means of approaching the conversion of a tubular reactor. In modelling, they are employed for describing axial mixing in non-ideal tubular reactors. Residence time distributions, as measured by tracers, can be used to characterise reactors, to establish models and to calculate conversions for first-order reactions. 

Two template examples based on a capillary geometry are the plug flow ideal reactor and the non-ideal Poiseuille flow reactor [3]. Because in the plug flow reactor there is a single velocity, v0, with a velocity probability distribution P(v) = v0 16 (v - Vo) the residence time distribution for capillary of length L is the normalized delta function RTD(t) = T 1S(t-1), where x = I/v0. The non-ideal reactor with the para-... 

For a few highly idealized systems, the residence time distribution function can be determined a priori without the need for experimental work. These systems include our two idealized flow reactors—the plug flow reactor and the continuous stirred tank reactor—and the tubular laminar flow reactor. The F(t) and response curves for each of these three types of well-characterized flow patterns will be developed in turn. 

Note that in this case the right side of equation 11.1.68 is zero for t = 0 and unity for t = 00. Figure 11.9 contains several F(t) curves for various values of n. As n increases, the spread in residence time decreases. In the limit, as n approaches infinity the F(t) curve approaches that for an ideal plug flow reactor. If the residence time distribution function given by 11.1.69 is differentiated, one obtains an... 

In the previous section we indicated how various mathematical models may be used to simulate the performance of a reactor in which the flow patterns do not fit the ideal CSTR or PFR conditions. The models treated represent only a small fraction of the large number that have been proposed by various authors. However, they are among the simplest and most widely used models, and they permit one to bracket the expected performance of an isothermal reactor. However, small variations in temperature can lead to much more significant changes in the reactor performance than do reasonably large deviations inflow patterns from idealized conditions. Because the rate constant depends exponentially on temperature, uncertainties in this parameter can lead to design uncertainties that will make any quantitative analysis of performance in terms of the residence time distribution function little more than an academic exercise. Nonetheless, there are many situations where such analyses are useful. 

The physical situation in a fluidized bed reactor is obviously too complicated to be modeled by an ideal plug flow reactor or an ideal stirred tank reactor although, under certain conditions, either of these ideal models may provide a fair representation of the behavior of a fluidized bed reactor. In other cases, the behavior of the system can be characterized as plug flow modified by longitudinal dispersion, and the unidimensional pseudo homogeneous model (Section 12.7.2.1) can be employed to describe the fluidized bed reactor. As an alternative, a cascade of CSTR s (Section 11.1.3.2) may be used to model the fluidized bed reactor. Unfortunately, none of these models provides an adequate representation of reaction behavior in fluidized beds, particularly when there is appreciable bubble formation within the bed. This situation arises mainly because a knowledge of the residence time distribution of the gas in the bed is insuf-... 

The available models mostly refer to ideal reactors, STR, CSTR, continuous PFR. The extension of these models to real reactors should take into account the hydrodynamics of the vessel, expressed in terms of residence time distribution and mixing state. The deviation of the real behavior from the ideal reactors may strongly affect the performance of the process. Liquid bypass - which is likely to occur in fluidized beds or unevenly packed beds - and reactor dead zones - due to local clogging or non-uniform liquid distribution - may be responsible for the drastic reduction of the expected conversion. The reader may refer to chemical reactor engineering textbooks [51, 57] for additional details. 

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. 

Simulation examples demonstrating non-ideal mixing phenomenon in tank reactors are CSTRPULSE, NOCSTR and TUBEMIX. Other more general examples demonstrating rank-based residence time distributions are MIXFLOl, MIXFL02, GASLIQ1, GASLIQ2 and SPBEDRTD. 

Continuous Multicomponent Distillation Column 501 Gas Separation by Membrane Permeation 475 Transport of Heavy Metals in Water and Sediment 565 Residence Time Distribution Studies 381 Nitrification in a Fluidised Bed Reactor 547 Conversion of Nitrobenzene to Aniline 329 Non-Ideal Stirred-Tank Reactor 374 Oscillating Tank Reactor Behaviour 290 Oxidation Reaction in an Aerated Tank 250 Classic Streeter-Phelps Oxygen Sag Curves 569 Auto-Refrigerated Reactor 295 Batch Reactor of Luyben 253 Reversible Reaction with Temperature Effects 305 Reversible Reaction with Variable Heat Capacities 299 Reaction with Integrated Extraction of Inhibitory Product 280... 

For isothermal, first-order chemical reactions, the mole balances form a system of linear equations. A non-ideal reactor can then be modeled as a collection of Lagrangian fluid elements moving independe n tly through the system. When parameterized by the amount of time it has spent in the system (i.e., its residence time), each fluid element behaves as abatch reactor. The species concentrations for such a system can be completely characterized by the inlet concentrations, the chemical rate constants, and the residence time distribution (RTD) of the reactor. The latter can be found from simple tracer experiments carried out under identical flow conditions. A brief overview of RTD theory is given below. 

Figure 1.4. Sketch of the residence time distribution (RTD) in a non-ideal reactor. 

Thus, for known kinetics and a specified residence time distribution, we can predict the fractional conversion of reactant which the system of Fig. 9 would achieve. Recall, however, that this performance is also expected from any other system with the same E(t) no matter what detailed mixing process gave rise to that RTD. Equation (34) therefore applies to all reactor systems when first-order reactions take place therein. In the following example, we apply this equation to the design of the ideal CSTR and PFR reactors discussed in Chap. 2. The predicted conversion is, of course, identical to that which would be derived from conventional mass balance equations. 

The notions of different combinations of ideal reactors and residence time distributions are essential in analyzing these problems and in suggesting appropriate solutions. We summarize the many applications of chemical reaction engineering in Figure 8-18, which indicates the types of molecules, reactors, and reactors we can handle. 

The following equations are written for absorption (of any gas) in a continuous-flow stirred tank reactor (CFSTR) under the assumption that the gas and liquid phases are ideally mixed (Figure B 1-2). The assumption of an ideally mixed phase can be checked by determining the residence time distribution in the reactor (e. g. Levenspiel, 1972 Lin and Peng, 1997 Huang et al., 1998). 

After an iPP particle reached the FBR, co-polymerization of ethylene-propylene starts preferrably inside the porous PP matrix. Depending on the individual residence time, the particle will be filled with a certain amount of ethylene-propylene rubber, EPR, that improves the impact properties of the HIPP. It is important to keep the sticky EPR inside the preformed iPP matrix to avoid particle agglomeration that could lead to wall sheeting and termination of the reactor operation. Ideally a "two phase" structure, see Fig.5.4-3, is produced. Finally, a "super-high impact" PP results that contains up to 70% EPR. How much EPR is formed per particle depends on three factors catalyst activity in the FBR, individual particle porosity, and individual particle residence time in the FBR. All particle properties are therefore influenced by the residence time distribution, and finally, a mix of particles with different relative amounts of EPR is produced - a so called "chemical distribution" see, for example, [6]. 

In this section, several cases where there is a spread in drop size distribution will be calculated first for an ideal piston flow reactor in which all liquid parts have the same residence time distribution, and, finally, also the case of a CSTR in which there is a spread in drop size will be calculated, but only for the case of zero-order drop conversion. 

A graphical representation of the cumulative residence time distribution function is given in Figure 4.97 for a structured well, a laminar flow reactor and an ideal plug flow reactor assuming the same average residence time and mean velocity in each reactor. 

The SSE is an important and practical LCFR. We discussed the flow fields in SSEs in Section 6.3 and showed that the helical shape of the screw channel induces a cross-channel velocity profile that leads to a rather narrow residence time distribution (RTD) with crosschannel mixing such that a small axial increment that moves down-channel can be viewed as a reasonably mixed differential batch reactor. In addition, this configuration provides self-wiping between barrel and screw flight surfaces, which reduces material holdback to an acceptable minimum, thus rendering it an almost ideal TFR. 

An important advantage of the use of EOF to pump liquids in a micro-channel network is that the velocity over the microchannel cross section is constant, in contrast to pressure-driven (Poisseuille) flow, which exhibits a parabolic velocity profile. EOF-based microreactors therefore are nearly ideal plug-flow reactors, with corresponding narrow residence time distribution, which improves reaction selectivity. 

The three ideal reactors form the building blocks for analysis of laboratory and commercial catalytic reactors. In practice, an actual flow reactor may be more complex than a CSTR or PFR. Such a reactor may be described by a residence time distribution function F(t) that gives the probability that a given fluid element has resided in the reactor for a time longer than t. The reactor is then defined further by specifying the origin of the observed residence time distribution function (e.g., axial dispersion in a tubular reactor or incomplete mixing in a tank reactor). 

Ideal reactors work under very simple limiting conditions, mainly concerning the residence time distribution. The operation of an ideal reactor is essentially controlled by chemical kinetics and thus the kinetic analysis of a chemical reaction is facilitated by the use of such a reactor. Furthermore, most laboratory and industrial reactors operate under conditions very near to ideality or may be modelled by simple combinations of ideal reactors. There are three main types of ideal reactors ... 

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