Transverse dispersion coefficient

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... 

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 ... 

River type/river Transverse dispersion coefficients (m2/sec) Discharge during dispersion measurement (m3/sec)... 

This noninvasive method could allow the differentiation between the various packing materials used in chromatography, a correlation between the chromatographic properties of these materials that are controlled by the mass transfer kinetics e.g., the coliunn efficiency) and the internal tortuosity and pore coimectivity of their particles. It could also provide an original, accurate, and independent method of determination of the mass transfer resistances, especially at high mobile phase velocities, and of the dependence of these properties on the internal and external porosities, on the average pore size and on the parameters of the pore size distributions. It could be possible to determine local fluctuations of the coliunn external porosity, of its external tortuosity, of the mobile phase velocity, of the axial and transverse dispersion coefficients, and of the parameters of the mass transfer kinetics discussed in the present work. Further studies along these lines are certainly warranted. 

The total transverse dispersion coefficient is the snm of the diffnsion coefficient in the porons medinm (which is the same as in the longitndinal direction nnless the porons medinm is anisotropic) and the transverse convective dispersion coefficient. Perkins and Johnston (1963) presented the correlation for the transverse dispersion coefficient in Eq. 2.54. 

FIGURE 2.6 Transverse dispersion coefficients for porous media. Source Perkins and Johnston (1963). 

Finally, we compare the values of longitudinal and transverse dispersion coefficients at typical reservoir flow conditions. Using Eqs. 2.53 and 2.54, we have... 

Eidsath et al. (1983) used finite element methods to numerically investigate dispersion in two dimensional, low Reynolds number flow through spatially periodic arrays of cylinders with a porosity of 0.37. They found that a e 1.7 in K P - Edwards et al. (1991) also used finite element methods to compute the longitudinal and transverse dispersion coefficients for a two-dimensional, spatially periodic array of cylinders. Their results differed from the results of Eidsath et al. (1983), possibly due to differences in the details of the numerical methods. 

Tables 9.2 and 9.3 list some of the closed-form solutions and correlations for the longitudinal and transverse dispersion coefficients for ordered and disordered media.

A fairly good correlation (within a factor of two) has been reported between u and the transverse dispersion coefficient, Dt, for two t)q)es of channels ... 

River Type/River Transverse Dispersion Coefficients (m /sec) Discharge During Dispersion Measurement (m /sec)... 

Hassinger, R.C. and von Rosenberg, D.U. 1968. A mathematical and experimental investigation of transverse dispersion coefficients. Society of Petroleum Engineers Journal 8(2) 195-204. 

Robbins, G.A. 1989. Methods for determining transverse dispersion coefficients of porous media in laboratory column experiments. Water Resources Research 25(6) 1249-1258. 

Zhang, X., Qi, X., Zhou, X. and H. Pang. 2006. An in situ method to measure the longitudinal and transverse dispersion coefficients of solute transport in soil. Journal of Hydrology 328 614-619. 

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