Local porosity

J. Gotz, K. Zick, C. Heinen, T. Konig 2002, (Visualisation of flow processes in packed beds with NMR imaging Determination of the local porosity, velocity vector and local dispersion coefficients), Chem. Eng. Process. 41 (7), 611-630. 

The difference between V- and D-tessilations is as follows each of V-polyhedra includes one network point (or particle) and a void that is closer to this point than to others, each of D-polyhedra includes one cavity and parts of the particles that are the closest to the center of the cavity and all windows that are on the borders with other neighboring cavities. It is convenient to term the latter as PBU/C, where C means cavity. The local coordination number of cavities Zc is equal to the number of the faces of PBU/C (D-polyhedra or D-polygons), and their local porosity e (or eA in 2D space) is equal to the unoccupied volume. Typical D-polyhedra are shown in Figure 9.30 and Figure 9.31. 

The following measurement of the monochromatic scatming topography of a SiC-sample with the mass density p = 3,22 g/cm represents the spatially resolved properties of the mean porosity. The local porosity p variation is in the range of about +/- 3 %. It decreases from p= 62 % on the right side (which represents the centre of the sample) to p = 58 % at the left perimeter. 

FIGURE 22.59-A Wei-Ming Lu, Frank M. Tiller, et al, A New Method to Determine Local Porosity and Filtration Resistance of Filter Cakes, Journal of Chinese Institute of Chemical Engineers, vol. 1, 1970, Journal of Chinese Institute of Chemical Engineers, p. 50, Figure 8, vol. 1, 1970. 

Flow resistance can be interpreted as the time that a particle would take in travelling a given distance assuming that it travels with a velocity equal to the specific discharge (i.e., as if the local porosity is equal to I). 

The adsorbent pellets are spheres and the differences of the local porosities in the bed are small... 

Figure 10.15 Experimental set-up. The local flow structure is measured with the PIV method. The local porosity and CO2 concentration are obtained from local through beam IR absorbance measurements.

Here dw( ) is the macroscopic EOF velocity (Darcy velocity) field through the neutrally charged porous medium inside the microcapillary. < ) = < )(r) is the local porosity distribution of the porous medium, determined by Eq. 9. The Darcy permeability K is defined by the Carman-Kozeny equation [7], K = a — ( )), and the inertial coefficient F =, with a = 150 and b = 1.75... 

Figure 6. Pellet intruded to 1 Ibara. Alloy now intrudes in all mesopores in stmcture down to 1 pm. Only intragranular pores and channels are not now intruded. An idea of the variation in local porosity can now be observed. No apparent differences are seen at x20, x25, or x50 at 20bara.

The porous sphere approach by Vanni (2000) adopts essentially the same concept for the internal aggregates structure. Yet, this approach yields smaller hydrodynamic diameters than the multipole expansion method because the local porosity at the convex huU, i.e. the decisive parameter of the model, is systematically underestimated when the aggregate is considered spherical. 

It is now certain that the only truly rigorous approach to filtration theory is by using point values of a within the cake itself and those can only be obtained from studies of flow and local porosities in practical cakes. This is inevitably very complicated and beyond the scope of this book. The reader is referred to the already mentioned review by Tiller et al and to a theoretical paper by Wakeman . 

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