Transversal dispersion reactors

An alternative method to account for bed dispersion is to model the bed as a cascade of well stirred tank reactors, each with a uniform temperature and concentration (124,1 5) Transverse dispersion can be accounted for by staggering the cells so that each cell feeds into two different cells in the forward direction (126). When the value of L/d is large, say above 20, the two models are not very different if the number of cells in the cascade is chosen to equal N = PeL/2d. When Pe = 2, this amounts to considering... 

Rivers are close to the perfect environmental flow for describing the flow as plug flow with dispersion. The flow is confined in the transverse and vertical directions, such that a cross-sectional mean velocity and concentration can be easily defined. In addition, there is less variation in rivers than there is, for example, in estuaries or reactors - both of which are also described by the plug flow with dispersion model. For that reason, the numerous tracer tests that have been made in rivers are useful to characterize longitudinal dispersion coefficient for use in untested river reaches. A sampling of the dispersion coefficients at various river reaches that were... 

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. 

In addition to use of the axial dispersion model to represent the longitudinal distribution of residence times in a reactor, the transverse or radial dispersion characteristics can also often be adequately modeled with a diifusionlike equation. This is most often done for empty tubes or packed beds the latter has been thoroughly covered in Chapter 11. Further aspects of the topic can be found in Levenspiel and Bischoff [1] and Wen and Fan [2]. 

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