Reactor models, applications Laminar flow

A laminar-flow reactor (LFR) is rarely used for kinetic studies, since it involves a flow pattern that is relatively difficult to attain experimentally. However, the model based on laminar flow, a type of tubular flow, may be useful in certain situations, both in the laboratory and on a large scale, in which flow approaches this extreme (at low Re). Such a situation would involve low fluid flow rate, small tube size, and high fluid viscosity, either separately or in combination, as, for example, in the extrusion of high-molecular-weight polymers. Nevertheless, we consider the general features of an LFR at this stage for comparison with features of the other models introduced above. We defer more detailed discussion, including applications of the material balance, to Chapter 16. 

As our first application, we consider the classical Taylor-Aris problem (Aris, 1956 Taylor, 1953) that illustrates dispersion due to transverse velocity gradients and molecular diffusion in laminar flow tubular reactors. In the traditional reaction engineering literature, dispersion effects are described by the axial dispersion model with Danckwerts boundary conditions (Froment and Bischoff, 1990 Levenspiel, 1999 Wen and Fan, 1975). Here, we show that the inconsistencies associated with the traditional parabolic form of the dispersion model can be removed by expressing the averaged model in a hyperbolic form. We also analyze the hyperbolic model and show that it has a much larger range of validity than the standard parabolic model. 

Data Assume that the reactors are long enough for the dispersion model to be applied and that laminar flow prevails at all points. The Beer Lambert law of light intensity, I, is applicable I/Io = exp(aCL), where a is absorptivity of the reactant gas mixture at a concentration, C, which absorbs the light of the CO2 laser and L is the path length. 

Wilck M. and Stratmann F. (1997) A 2-D multicomponent modal aerosol model and its application to laminar flow reactors. J. Aerosol. Sci. 28, 959-972. 

Considerations along the above lines lead to analogous correlations for the Sherwood number for the description of mass transfer in a single channel. The application of the rather simple Nusselt and Sherwood number concept for monolith reactor modeling implies that the laminar flow through the channel can be approached as plug flow, but it is always limited to cases in which homogeneous gas-phase reactions are absent and catalytic reactions in the washcoat prevail. If not, a model description via distributed flow is necessary. 

For comparison the case of a tubular reactor with laminar flow but without molecular diffusion is also shown in Figure 4.10.61, which is formally represented by Bo 6, see also Figure 4.10.58. Values of Bo that are less than this value are only reached for very low values of Re x Sc and low L/d values, whereby we have to keep in mind that the model and thus Eqs. (4.10.117b) and (4.10.114) are only applicable for L/dt > 0.04Re x Sc. 

Microreactors are developed for a variety of different purposes, specifically for applications that require high heat- and mass-transfer coefficients and well-defined flow patterns. The spectrum of applications includes gas and liquid flow as well as gas/liquid or liquid/liquid multiphase flow. The variety and complexity of flow phenomena clearly poses major challenges to the modeling approaches, especially when additional effects such as mass transfer and chemical kinetics have to be taken into account. However, there is one aspect that makes the modeling of microreactors in some sense much simpler than that of macroscopic equipment the laminarity of the flow. Typically, in macroscopic reactors the conditions are such that a turbulent flow pattern develops, thus making the use of turbulence models [1] necessary. With turbulence models the stochastic velocity fluctuations below the scale of grid resolution are accounted for in an effective manner, without the need to explicitly model the time evolution of these fine details of the flow field. Heat- and mass-transfer processes strongly depend on the turbulent velocity fluctuations, for this reason the accuracy of the turbulence model is of paramount importance for a reliable prediction of reactor performance. However, to the... 

Currently, one of the most developed, hence most illustrative, examples of practical application of SM is provided by the GRI-Mech project [1]. In its latest release, the GRI-Mech 3.0 dataset is comprised of 53 chemical species and 325 chemical reactions (with a combined set of 102 active variables), and 77 peer-reviewed, well-documented, widely trusted experimental observations obtained in high-quality laboratory measurements, carried out under different physical manifestations and different conditions (such as temperature, pressure, mixture composition, and reactor conhguration). The experiments have relatively simple geometry, leading to reliably modeled transport of mass, energy, and momentum. Typical experiments involve flow-tube reactors, stirred reactors, shock tubes, and laminar premixed flames, with outcomes such as ignition delay, flame speed, and various species concentration properties (location of a peak, peak value, relative peaks, etc.). 

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