Transverse dispersivity

Naturally, there are two more Peclet numbers defined for the transverse direction dispersions. In these ranges of Reynolds number, the Peclet number for transverse mass transfer is 11, but the Peclet number for transverse heat transfer is not well agreed upon (121, 122). None of these dispersions numbers is known in the metal screen bed. A special problem is created in the monolith where transverse dispersion of mass must be zero, and the parallel dispersion of mass can be estimated by the Taylor axial dispersion theory (123). The dispersion of heat would depend principally on the properties of the monolith substrate. Often, these Peclet numbers for individual pellets are replaced by the Bodenstein numbers for the entire bed... 

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... 

Dispersion in packed tubes with wall effects was part of the CFD study by Magnico (2003), for N — 5.96 and N — 7.8, so the author was able to focus on mass transfer mechanisms near the tube wall. After establishing a steady-state flow, a Lagrangian approach was used in which particles were followed along the trajectories, with molecular diffusion suppressed, to single out the connection between flow and radial mass transport. The results showed the ratio of longitudinal to transverse dispersion coefficients to be smaller than in the literature, which may have been connected to the wall effects. The flow structure near the wall was probed by the tracer technique, and it was observed that there was a boundary layer near the wall of width about Jp/4 (at Ret — 7) in which there was no radial velocity component, so that mass transfer across the layer... 

In the calculation results (Fig. 21.4), benzene again is retarded by sorption and attenuates due to sorption, biodegradation, and dispersion along the direction of flow. In this case, it further attenuates due to transverse dispersion, by mixing with clean water flowing beside the plume. 

Dispersion Coefficients in Groundwater Flow. In a uniform media of particles, the longitudinal dispersion coefficient, Dl, and the transverse dispersion coefficient, Dt, are both functions of the grain diameter and velocity. (In our previous example, Dl... 

Koch and Brady (1985) have characterized transverse dispersion coefficient as a fraction of longitudinal dispersion coefficient ... 

Thus, longitudinal dispersion coefficient is roughly 10 times the value of transverse dispersion coefficient in a uniform media. 

Convert to transverse dispersion coefficient, Dt, and eliminate the image ... 

The solution to equation (E6.13.2) for this application is given in Figure E6.13.1 at various lateral distances from the peak concentration. The capture zone mean is 0.42 g/m or almost 100 times the recommended limit, which would raise concern in New Brighton. The leakage from the capture zone at x = 4,000 m for this scenario is computed to be 47 g, or sufficient mass to result in a concentration of 9 x 10 g/m for a similar capture zone. It is possible then that almost all of the plume was captured by the city of New Brighton, so the problem may not cover a wider area than the immediate downstream cities. This, at least, is one positive result of the low transverse dispersion of groundwater plumes. 

In the first instance, the effects of dispersion will be disregarded. Then the effects of dispersion in the axial (longitudinal) direction only will be taken into account and this discussion will then be followed by considerations of the combined contributions of axial and radial (transverse) dispersion. 

The magnitude of the dispersion effect due to transverse or radial mixing can be assessed by relying on theoretical predictions " and experimental observations " which confirm that the value of the Peclet number Pe(= udp/D, where dp is the particle diameter) for transverse dispersion in packed tubes is approximately 10. At bed Reynolds numbers of around 100 the diffusion coefficient to be ascribed to radial dispersion effects is about four times greater than the value for molecular diffusion. At higher Reynolds numbers the radial dispersion effect is correspondingly larger. 

The use of the Coanda effect is based on the desire to have a second passive momentum to speed up mixing in addition to diffusion [55, 163], The second momentum is based on so-called transverse dispersion produced by passive structures, which is in analogy with the Taylor convective radial dispersion ( Taylor dispersion ) (see Figure 1.180 and [163] for further details). It was further desired to have a flat ( in-plane ) structure and not a 3-D structure, since only the first type can be easily integrated into a pTAS system, typically also being flat A further design criterion was to have a micro mixer with improved dispersion and velocity profiles. 

M 87] [P 77] Simulations show that, as intended, transverse dispersion is achieved at the Coanda structure and mixing is completed after passing four Tesla structures (see Figure 1.183 and 1.184) [163],... 

However, there is a severe disadvantage with one-dimensional models they do not take into account the dilution due to the transversal dispersion. Consequently a mass M, that is not susceptible to any chemical reaction, occurs blurred at a point x downstream from xo (the location of M input) due to longitudinal dispersion. The dispersion leads to a smaller maximum concentration, however, and the mass integral equals the mass added at xo. Thus, the impulse of mass remains constant along any simulated one-dimensional distance. 

In reality, however, transversal dispersion Dt causes mass exchange in y and z direction leading to dilution. This dilution is a function of Dt and the flow velocity... 

In particular, the gravity-viscous force ratio and the ratio of transverse dispersion to longitudinal convection rate were made as close as possible to the prototype oil reservoir. These ratios control respectively the extent of gravity segregation and the extent of viscous fingering (for ai given unfavorable mobility ratio). 

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