Residence time distribution, application

Tailoring of the particle size of the crystals from industrial crystallizers is of significant importance for both product quality and downstream processing performance. The scientific design and operation of industrial crystallizers depends on a combination of thermodynamics - which determines whether crystals will form, particle formation kinetics - which determines how fast particle size distributions develop, and residence time distribution, which determines the capacity of the equipment used. Each of these aspects has been presented in Chapters 2, 3, 5 and 6. This chapter will show how they can be combined for application to the design and performance prediction of both batch and continuous crystallization. 

Glaser and Litt (G4) have proposed, in an extension of the above study, a model for gas-liquid flow through a b d of porous particles. The bed is assumed to consist of two basic structures which influence the fluid flow patterns (1) Void channels external to the packing, with which are associated dead-ended pockets that can hold stagnant pools of liquid and (2) pore channels and pockets, i.e., continuous and dead-ended pockets in the interior of the particles. On this basis, a theoretical model of liquid-phase dispersion in mixed-phase flow is developed. The model uses three bed parameters for the description of axial dispersion (1) Dispersion due to the mixing of streams from various channels of different residence times (2) dispersion from axial diffusion in the void channels and (3) dispersion from diffusion into the pores. The model is not applicable to turbulent flow nor to such low flow rates that molecular diffusion is comparable to Taylor diffusion. The latter region is unlikely to be of practical interest. The model predicts that the reciprocal Peclet number should be directly proportional to nominal liquid velocity, a prediction that has been confirmed by a few determinations of residence-time distribution for a wax desulfurization pilot reactor of 1-in. diameter packed with 10-14 mesh particles. 

An investigation into the applicability of numerical residence time distribution was carried out on a pilot-scale annular bubble column reactor. Validation of the results was determined experimentally with a good degree of correlation. The liquid phase showed to be heavily dependent on the liquid flow, as expected, but also with the direction of travel. Significantly larger man residence times were observed in the cocurrent flow mode, with the counter-current mode exhibiting more chaimeling within the system, which appears to be contributed to by the gas phase. 

Mass transfer of a solute dissolved in a fluid is not only the fundamental mechanism of mixing processes, it also determines the residence-time distribution in micro fluidic systems. As mentioned in Section 1.4, in many applications it is desir-... 

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).]... 

Most chemical reaction engineering textbooks contain material on residence time distribution theory. Levenspiel [17] and Hill [18] present particularly useful introductions as do refs. 9 and 16. The proceedings of a recent summer school [19] contains a brief overview of the field [8] as well as papers describing many specific applications of RTD theory in chemical engineering contexts. Nauman s comprehensive invited review cited earlier [4] is an extremely thorough and yet highly readable contribution to the literature. The book by Nauman and Buffham [20], will no doubt fill a most important gap in the literature on mixing in continuous flow systems. 

This chapter deals in large part with the residence time distribution (or RTD) approach to nonideal flow. We show when it may legitimately be used, how to use it, and when it is not applicable what alternatives to turn to. 

De Baun, R. M., and Katz, S., Approximations to residence time distribution in mixing systems and some applications thereof. Chem. Eng. Sci. 16, 97 (1961). (I IV)... 

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 residence time distribution of particles is related to the properties of the particles and the gas flow, including the size distribution, and the velocity of gas flow and its profile. In practically applicable impinging stream devices, the particles being processed usually have relatively narrower size distribution the diameter of the tube to particles size ratio, d Jd,h is normally very large ( 15) while the gas velocity is high... 

It is well known that the measurement of residence time distribution usually employs the dynamic method [54], the so-called input-response technique. However, for measuring RTD of solid particles the input signal is a difficult and troublesome problem. The author of the present book employs an arbitrary known function as the input signal so that this problem is solved. This procedure is also applicable, in principle, to the measurements of RTD of solid materials in other devices. 

It should be noted that Eq. (3.31) is an approximate relationship. This is because both the individual flow rates of the particles A and B vary with time, although the total flow rate, i.e. the flow rate of A plus that of B, is stable, while the variation of particle flow rate may affect RTD. However, since the variations of the flow rates of particles A and B are not so large, the possible deviation of Function F caused by this factor may be neglected, just like the generalized (dimensionless) residence time distribution function can be extended for application in a certain range [57]. 

The fluidized bed reactor can also handle fast, complex reactions, with mixing and temperature control being especially good when stirring is provided. Unfortunately, the extent of back mixing is difficult to assess so that the residence time distribution of the reactants in the reactor is uncertain. In addition, only small catalyst particles can be used, and attrition, with the consequent breakdown and loss of catalyst, is a problem. Finally, a catalyst bed is adequately fluidized over only a comparatively narrow range of flow rates. More information about kinetic reactors can be found in reviews [33,34,50], Applications of the basket-type mixed reactor to liquid-solid systems are discussed by Suzuki and Kawazo [62] and by Teshima and Ohashi [63], and the development of a laminar flow, liquid-solid reactor by Schmalzer et al. [64], In the latter reactor the wall is coated with a catalyst layer. 

Topics that acquire special importance on the industrial scale are the quality of mixing in tanks and the residence time distribution in vessels where plug flow may be the goal. The information about agitation in tanks described for gas/liquid and slurry reactions is largely applicable here. The relation between heat transfer and agitation also is discussed elsewhere in this Handbook. Residence time distribution is covered at length under Reactor Efficiency. A special case is that of laminar and related flow distributions characteristic of non-Newtonian fluids, which often occurs in polymerization reactors. 

Equations describing velocity profiles can be used, among other applications, to study the effect of different rheological models on the distribution of velocities and to understand the concept of residence-time distribution across the cross-section of a pipe or a channel. 

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