Channel residence time distribution

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. 

This is the first reactor reported where the aim was to form micro-channel-like conduits not by employing microfabrication, but rather using the void space of structured packing from smart, precise-sized conventional materials such as filaments (Figure 3.25). In this way, a structured catalytic packing was made from filaments of 3-10 pm size [8]. The inner diameter of the void space between such filaments lies in the range of typical micro channels, so ensuring laminar flow, a narrow residence time distribution and efficient mass transfer. 

The precise and, where needed, short setting of the residence time allows one to process oxidations at the kinetic limits. The residence time distributions are identical within various parallel micro channels in an array, at least in an ideal case. A further aspect relates to the flow profile within one micro channel. So far, work has only been aimed at the interplay between axial and radial dispersion and its consequences on the flow profile, i.e. changing from parabolic to more plug type. This effect waits to be further exploited. 

Figure 3.42 Evolution of a pulse at the entrance of a micro channel for different diffusion coefficients. Calculated concentration profile (left) and cumulative residence time distribution curve (channel 300 pm x 300 pm x 20 mm flow velocity 1 m s f = 10 s) [27],...

GL 1[ [R 1[ [P la[ The residence time distribution between the individual flows in the various micro channels on one reaction plate of a falling film micro reactor was estimated by analysing the starting wetting behavior of an acetonitrile falling film [3]. For a flow of 20 ml h it was found that 90% of all streams were within a 0.5 s interval for an average residence time of 17.5 s. 

With the development of modern computation techniques, more and more numerical simulations occur in the literature to predict the velocity profiles, pressure distribution, and the temperature distribution inside the extruder. Rotem and Shinnar [31] obtained numerical solutions for one-dimensional isothermal power law fluid flows. Griffith [25], Zamodits and Pearson [32], and Fenner [26] derived numerical solutions for two-dimensional fully developed, nonisothermal, and non-Newtonian flow in an infinitely wide rectangular screw channel. Karwe and Jaluria [33] completed a numerical solution for non-Newtonian fluids in a curved channel. The characteristic curves of the screw and residence time distributions were obtained. 

In a final RTD experiment, a sheet of dye was frozen as before and positioned in the feed channel perpendicular to the flight tip. The sheet positioned the dye evenly across the entire cross section. After the dye thawed, the extruder was operated at five rpm in extrusion mode. The experimental and numerical RTDs for this experiment are shown in Fig. 8.12, and they show the characteristic residence-time distribution for a single-screw extruder. The long peak indicates that most of the dye exits at one time. The shallow decay function indicates wall effects pulling the fluid back up the channel of the extruder, while the extended tail describes dye trapped in the Moffat eddies that greatly impede the down-channel movement of the dye at the flight corners. Moffat eddies will be discussed more next. Due to the physical limitations of the process, sampling was stopped before the tail had completely decreased to zero concentration. 

A characteristic of micro-channel reactors is their narrow residence-time distribution. This is important, for example, to obtain clean products. This property is not imaginable without the influence of dispersion. Considering only the laminar flow would... 

In macroscopic reactors, knowledge of the velocity profile in the channel cross-section is a necessary and sufficient prerequisite to describe the material transport. In microscopic dimensions down to a few micrometers, diffusion also has to be considered. In fact, without the influence of diffusion, extremely broad residence time distributions would be found because of the laminar flow conditions. Superposition of convection and diffusion is called dispersion. Taylor [91] was among the first to notice this strong dominating effect in laminar flow. It is possible to transfer his deduction to rectangular channels. A complete fluid dynamic description has been given of the flow, including effects such as the influence of the wall, the aspect ratio and a chemical wall reaction on the concentration field in the cross-section [37]. 

A characteristic of micro channel reactors is their narrow residence-time distribution. This is important, for example, to obtain clean products. This property is not imaginable without the influence of dispersion. Just considering the laminar flow would deliver an extremely wide residence-time distribution. The near wall flow is close to stagnation because a fluid element at the wall of the channel is, by definition, fixed to the wall for an endlessly long time, in contrast to the fast core flow. The phenomenon that prevents such a behavior is the known dispersion effect and is demonstrated in Figure 3.88. 

One reason to use micro structured reaction chambers is certainly the possibility of describing the fluid dynamic behavior in these structures due to the laminar flow regime. With the following calculations the reactive gas flow in a square micro structure with coated catalytically active walls will be studied in detail. The task was to find a channel arrangement and to calculate the residence time distribution of this arrangement numerically (Figure 4.93). 

Residence Time Distribution for Guided Flow in Channels... 

The influence of channels, i.e. flow-guiding internal structures, also accounts for the overall residence time distribution in the square. This will be demonstrated by the observation of particles emitted at the structure inlet. The path of such an... 

The maximum relative deviation is 36%. The parabolic velocity profile in the micro channels will not influence the residence time distribution, otherwise the deviation would be much larger. The reason for this is the fast balancing of the concentration in a small channel by dispersion. 

The residence time of such a well is again best visible at the exit. The parabolic profile this time is much wider than for the structured case. The maximum relative deviation amounts to 233%, which is 6.5 times larger than for the structured well. This is important because it demonstrates that micro structures are indeed a means to obtain a narrow overall residence time distribution. The error introduced by manufacturing tolerances (estimated 5 pm absolute tolerance in a 320 pm wide channel) is 1.6% in width, a value which does not influence this evaluation. 

Figure 4.97 Calculated cumulative residence time distribution function for a multi-channel well, a laminar flow reactor and a plug flow reactor [147] (by courtesy of VDI-Verlag GmbH).

Fig. 9.14 Values of F(y) for a 6-in-diameter, 20 1 IVD extruder at constant flow rate (500 lb/h) with screw speed as a parameter. Simulation was made for a square pitched screw with a constant channel depth of 0.6 in. [Reprinted by permission from G. Lidor and Z. Tadmor, Theoretical Analysis of Residence Time Distribution Functions and Strain Distribution Functions in Plasticating Extruders, Polym. Eng. Sci., 16, 450-462 (1976).]...

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. 

A number of elegant studies over the past few years have also addressed the need to minimize particle size distributions through the use of segmented flow microfluidic systems. Such an approach removes the possibility of particle deposition on channels and eliminates the problems of residence time distributions that occur in single phase systems (where drag at the channel walls sets up a velocity distribution inside the channel). For example, Shestopalov et al. reported the two-step synthesis... 

The time spent by reactants and intermediates at reaction conditions determines conversion (and perhaps selectivity). It is therefore often important to understand the residence time distribution (RTD) of reaction species in the reactor. This RTD could be considerably different from what is expected. Reasons for the deviation could be channeling of fluid, recycling of fluid, or creation of stagnant regions in the reactor, as illustrated in Fig. 19-6. 

Generally, this implies the use of ideal reactors of the plug flow or well stirred tank type with well defined residence times and residence time distributions under isothermal conditions (with some exceptions, as will be indicated). By-passing part of the catalyst by channeling in a packed bed or uneven flow distributions must be avoided. In three-phase systems (gas/liquid/solid), the even distribution of both fluid phases over the catalyst is crucial. 

In the channel model, the residence-time distribution function is bimodal if the streams are not sufficiently mixed, a situation which occurs if a2/y2 > about 1/20. For larger values, local hot-spots are likely to develop, and the correlation to be described does not apply. This puts a lower limit on the parameter k of that model. ... 

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