Residence time distribution channeling effect

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. 

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. 

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. 

This type of reactor is very widely used because it is one of the simplest to construct and it is cheap. Sampling and analysis of the product streams are generally easy, but they can be difficult to obtain effectively at low conversions. Isothermality of the reactor is generally attainable, particularly at low heat release. Residence-time distribution measurements can be difficult because of channeling problems, but this can be somewhat reduced by running the reactor vertically rather than horizontally. 

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. 

Ariga et al. [48] have investigated the behavior of the monolith reactor in which Echerichia coli with P-galactosidase or Saccharomyces cerevisiae was immobilized within a thin film of K-carragcenan gel deposited on the channel wall. The effects of mass transfer resistance and axial dispersion on the conversion were studied. Those authors found that the monolith reactor behaved like the plug-flow reactor. The residence-time distribution in this reactor was comparable to four ideally mixed tanks in series. The influence of gas evolution on liquid film resistance in the monolith reactor was also investigated. It was shown that at low superficial gas velocities, the gas bubble may adhere to the wall, which decreases the effective surface area available for the reaction. The authors concluded that the reactor was very effective in the reaction systems accompanied by gas evolution, such as fermentations. 

The axial dispersion in a single channel is low due to the very thin film surrounding the bubbles. For the low conversion that is usually obtained in a single pass through the monolith reactor, the residence-time distribution within the channels will have an insignificant effect on conversion. However, the difference between the channels can be important. In downflow where the velocity is controlled by gravity, the linear velocity will be almost the same in all channels, but the gas hold-up will be different in the channels due to uneven liquid distribution over the cross section. 

Microscale reactions have been studied mostly to demonstrate proofs of cmicept. There is a lack of reaction optimization studies on the microscale with respect to flow rates, stoichiometiy, concentrations, mixing design, residence time distribution, and temperature. Conditions obtained from conventional-scale synthesis do not necessarily apply to microscale reactions. Only a few systematically studied reactions have been translated into real industrial technology. The mixing strategy, the parameters of the channel geometry, and the fabrication tolerance affect the microreaction conditions. The effects of the microscale on reactions are detailed in the following sections. 

Flow dispersion in the channel using both experimental residence time distribution [44,45] and computational fluid dynamics mass transport smdies, including the effect of manifolds [46,47]. 

Correct modeling of the flow near the front of a stream requires a rigorous solution of the hydrodynamic problem with rather complicated boundary conditions at the free surface. In computer modeling of the flow, the method of markers or cells can be used 124 however this method leads to considerable complication the model and a great expenditure of computer time. The model corresponds to the experimental data with acceptable accuracy if the front of the streamis assumed to be flat and the velocity distribution corresponds to fountain flow.125,126 The fountain effect greatly influences the distribution of residence times in a channel and consequently the properties of the reactive medium entering the mold. 

The sixth reactor design criterion requires that the pressure drop at the minimum residence time be less than 100 psi. For a small diameter channel, the flow through that channel wiU be laminar for all flow rates of interest for this particular applicahon. Neglecting end effects, the solutions to the equations of continuity and of motion for steady-state laminar flow of an incompressible Newtonian fluid are well-known, yielding a parabolic velocity distribution and the Hagen-Poiseuille equahon for pressure drop, as given in Eqs. (9) and (10) ... 

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