Ideal Flow Conditions

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. 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 called the stimulus-response technique. In this section we 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 to determine the distribution function. 

The mathematical relations expressing the different amounts of time that fluid elements spend in a given reactor may be expressed in a variety of forms [see, e.g., Leven-spiel (1-3) and Himmelblau and Bischoff (4)]. In this book we utilize the cumulative residence-time distribution curve [F(0], as defined by Danckwerts (5) for this purpose. For a continuous flow system. Fit) is the volume fraction of 

Introduction to Chemical Engineering Kinetics and Reactor Design, Second Edition. Charles G. Hill, Jr. and Thatcher W. Root. 2014 John Wiley Sons, Inc. Published 2014 by John Wiley Sons, Inc. 

Because F t + dt) represents the volume fraction of the fluid having a residence time of less than t + dt, and F(f) represents fliat having a residence time of less than t, the differential of F(f), namely, dFit), will be the volume fraction of the effluent stream having a residence time between t and t + dt. Hence, dF(t) is known as the differential residence-time distribution fimction. From the principles of probability the average residence time (f) of a fluid element is given by 

1 Experimental Determination of Residence Time Distribution Functions 

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In the holding section of a continuous sterilizer, correct exposure time and temperature must be maintained. Because of the distribution of residence times, the actual reduction of microbial contaminants in the holding section is significantly lower than that predicted from plug flow assumption. The difference between actual and predicted reduction in viable microorganisms can be several orders of magnitude therefore, a design based on ideal flow conditions may fail. 

It is convenient to classify deviations from ideal flow conditions into two categories. 

For application in flow reactors the nanocarbons need to be immobilized to ensure ideal flow conditions and to prevent material discharge. Similar to activated carbon, the material can be pelletized or extruded into millimeter-sized mechanically stable and abrasion-resistant particles. Such a material based on CNTs or CNFs is already commercially available [17]. Adversely, besides a substantial loss of macroporosity, the use of an (organic) binder is often required. This material inevitably leaves an amorphous carbon overlayer on the outer nanocarbon surface after calcination, which can block the intended nanocarbon surface properties from being fully exploited. Here, the more elegant strategy is the growth of nanocarbon structures on a mechanically stable porous support such as carbon felt [15] or directly within the channels of a microreactor [14,18] (Fig. 15.3(a),(b)), which could find application in the continuous production of fine chemicals. Pre-shaped bodies and surfaces can be... 

A mixed-flow reactor requires uniform composition of the fluid phase throughout the volume while the fluid is constantly flowing through it. This requires a special design in order to be achieved in the case of gas-solid systems. These reactors are basically experimental devices, which closely approach the ideal flow conditions and have been devised by Carbeny (Levenspiel, 1972). This device is called a basket-type mixed reactor (Figure 3.6). The catalyst is contained in four rapidly spinning wire baskets. 

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. 

Koukou MK, Papayannakos N, Markatos NC, Bracht M, Van Veen HM, and Roskam A. Performance of ceramic membranes at elevated pressure and temperature Effect of non-ideal flow conditions in a pilot scale membrane separator. J. Membr. Sci. 1999 155(2) 241-259. 

When first put into use—and every few months thereafter— the flow conditions for optimum response of the FID should be determined. This can be done by the time-honored method of repeated injections while varying the flow rate of air and especially of hydrogen or by a faster method recently publicized (18). This test takes but a few minutes to execute but can improve analytical results considerably. To even mention FID optimization may well be redundant. It has been my experience, however, that most gas chromatographs equipped with flame ionization detectors are run under less than ideal flow conditions. In trace analysis, this oversight may be crucial. 

In practice, especially in large-scale reactors, plug-flow or complete mixing are rarely achieved, and it is desirable to quantify the deviation from those idealized flow conditions. Also, when a chemical reactor does not perform at the expected level, it is necessary to identify the reason. A diagnostic method that is applied in such situations is based on measuring the residence time distribution (RTD) in the reactor. An inert tracer is injected at the reactor inlet, and its concentration at the reactor outlet is measured with time. By comparing the outlet concentration curve to the inlet concentration curve, the RTD curve of the reacting fluid in the reactor can be constructed [1,7,10,43]. 

Chapter 11 Deviations from Ideal Flow Conditions... 

Chapter 11 Deviations from Ideal Flow Conditions equation (11.1.59) may be rewritten as... 

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