DISTRIBUTIONS OF RESIDENCE TIMES FOR CHEMICAL REACTORS

Distributions of Residence Times for Chemical Reactors Chap. 13... 

Flow conditions may cause a more or less broad distribution of residence times for individual fluid packets or molecules. Effects of variable residence times have to be taken into account in the design and operation of large industrial reactors with adequate precautions the chemical engineer can prevent the undesirable effects of a residence time distribution, or utilize them. 

The DVD-ROM contains PDF files of the last live chapters from the fourth edition of the Elements of Chemical Reaction Engineering, which is mostly graduate material. These chapters, which were omitted from this book but are included on the DVD-ROM are DVD Chapter 10. Catalyst Decay DVD Chapter 11, External Diffusion Effects on Heterogeneous Reactions DVD Chapter 12. Diffusion and Reaction DVD Chapter 13, Distribution of Residence Times for Reactors DVD Chapter 14. Models for Non Ideal Reactors and a new chapter. DVD Chapter 15, Radial and Axial Temperature Variations in a Tubular Reactor. 

Given k fit) for nny reactor, you automatically have an expression for the fraction unreacted for a first-order reaction with rate constant k. Alternatively, given ttoutik), you also know the Laplace transform of the differential distribution of residence time (e.g., k[f(t)] = exp(—t/t) for a PER). This fact resolves what was long a mystery in chemical engineering science. What is f i) for an open system governed by the axial dispersion model Chapter 9 shows that the conversion in an open system is identical to that of a closed system. Thus, the residence time distributions must be the same. It cannot be directly measured in an open system because time spent outside the system boundaries does not count as residence but does affect the tracer measurements. 

Except for the case of an ideal plug flow reactor, different fluid elements will take different lengths of time to flow through a chemical reactor. In order to be able to predict the behavior of a given piece of equipment as a chemical reactor, one must be able to determine how long different fluid elements remain in the reactor. One does this by measuring the response of the effluent stream to changes in the concentration of inert species in the feed stream—the so-called stimulus-response technique. In this section we will discuss the analytical form in which the distribution of residence times is cast, derive relationships of this type for various reactor models, and illustrate how experimental data are treated in order to determine the distribution function. 

Since these two types of processes have drastically different effects on the conversion levels achieved in chemical reactions, they provide the basis for the development of mathematical models that can be used to provide approximate limits within which one can expect actual isothermal reactors to perform. In the development of these models we will define a segregated system as one in which the first effect is entirely responsible for the spread in residence times. When the distribution of residence times is established by the second effect, we will refer to the system as mixed. In practice one encounters various combinations of these two limiting effects. 

Vessels in which chemical reactions are conducted in the plant or laboratory are of various shapes and internal arrangements. The distribution of residence times in them of various reacting molecules or aggregates, the RTD, is a key datum for determining the performance of a reactor, either the expected conversion or the range in which the conversion must fall. How the RTD is measured or calculated and applied is the subject of this chapter. The main application of interest here is to find how nearly a particular vessel approaches some standard ideal behavior, or what its efficiency is. 

This assumes that all chemical species have the same residence time distribution, and is very convenient to compute the reaction paths for different contacting patterns. Matsuyama and Miyauchi [16] have also considered some aspects of this. An important conclusion of Wei [15] is that for a reactor with distribution of residence times, all reactions are slowed down in comparison with those in a plug flow reactor, but the faster reactions are slowed down a great deal more than the slower ones. Consequently, the occurrence of distribution of residence times makes all reaction rates of the characteristic species nearly equal. That is, the differences between the various reaction rates are decreased, thereby decreasing the selectivity. This is similar to the diffusion effects considered in Chapter 3. 

Obviously the residence time distribution has consequences for the conversion of a chemical reaction taking place in the fluid, since conversions generally increase with time. A distribution of residence times will generally reduce the conversion (except for reactions of zero order, or of a negative order). The residence time distribution is a physical characteristic of a continuous flow reactor, so that it can be determined by physical measurements. Consider a vessel and a fluid flow passing through it at a constant flow rate, from an entrance to an exit port. The flow conditions in the vessel are not known. By injecting a tracer component into... 

A factor in addition to the RTD and temperature distribution that affects the molecular weight distribution (MWD) is the nature of the chemical reaciion. If the period during which the molecule is growing is short compared with the residence time in the reactor, the MWD in a batch reactor is broader than in a CSTR. This situation holds for many free radical and ionic polymerization processes where the reaction intermediates are very short hved. In cases where the growth period is the same as the residence time in the reactor, the MWD is narrower in batch than in CSTR. Polymerizations that have no termination step—for instance, polycondensations—are of this type. This topic is treated by Denbigh (J. Applied Chem., 1, 227 [1951]). 

The time that a molecule spends in a reactive system will affect its probability of reacting and the measurement, interpretation, and modeling of residence time distributions are important aspects of chemical reaction engineering. Part of the inspiration for residence time theory came from the black box analysis techniques used by electrical engineers to study circuits. These are stimulus-response or input-output methods where a system is disturbed and its response to the disturbance is measured. The measured response, when properly interpreted, is used to predict the response of the system to other inputs. For residence time measurements, an inert tracer is injected at the inlet to the reactor, and the tracer concentration is measured at the outlet. The injection is carried out in a standardized way to allow easy interpretation of the results, which can then be used to make predictions. Predictions include the dynamic response of the system to arbitrary tracer inputs. More important, however, are the predictions of the steady-state yield of reactions in continuous-flow systems. All this can be done without opening the black box. 

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. 

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