Radial porosity distribution

Mueller, G.E. (1991), Prediction of radial porosity distribution in randomly packed fixed beds of uniformly sized spheres in cylindrical containers, Chem. Eng. Sci., 46,706. 

Figure 5.24 Computer-generated catalyst bed and its radial porosity distribution function averaged over axial coordinate (solid line). Mean bed porosity f = 0.47 (dashed line), aspect ratios di/dp = 3.9, L/dp = 18.5, r/R = 1 corresponds to the inner wall of the membrane.

Goodling, J.S., Vachon, R.I., Stelpflug, W.S., Ying, S.J. and Khader, M.S., 1983. Radial Porosity Distribution in Cylindrical Beds Packed with Spheres. Powder Technology, 35(1) 23-29. 

JS Goodling, RI Vachon, WS Stelpflug, SJ Ying, MS Khader. Radial porosity distribution in cylindrical beds packed with spheres. Powder Technol 35 23 29, 1983. 

In addition to these kinetic investigations the catalyst was characterized with respect to the following parameters internal surface area, porosity, pore diameter, radial coke distribution within the particle und the tortuosity. Thereby also the change of these parameters for different carbon loads during deactivation and regeneration were determined. 

Ktifner, R. and Hofmann, H., 1990. Implementation of Radial Porosity and Velocity Distribution in a Reactor Model for Heterogeneous Catalytic Gas-Phase Reactions (Torus-Model). Chemical Engineering Science, 45(8) 2141-2146. 

U. Kiirten, M. van Sint Annaland and J. A. M. Kuipers, Oxygen distribution in packed-bed membrane reactors for partial oxidations Effect of the radial porosity profiles on the product selectivity, Ind. Eng. Chem. Res., 2004, 43, 4753 760. 

Two-phase pressure drop in micropacked beds is very large, particularly, for particles with small diameter, and is significantly influenced by capillary forces, especially at higher reactor-to-partide diameter ratios [94]. The two-phase flow in micro packed bed reactors with radially nonuniform porosity distribution was simulated by solving a two-dimensional hydrodynamic model based on the volume-averaged mass and momentum conservation equations. 

Abstract In this chapter, an exothermic catalytic reaction process is simulated by using computational mass transfer (CMT) models as presented in Chap. 3. The difference between the simulation in this chapter from those in Chaps. 4,5, and 6 is that chemical reaction is involved. The source term in the species conservation equation represents not only the mass transferred from one phase to the other, but also the mass created or depleted by a chemical reaction. Thus, the application of the CMT model is extended to simulating the chemical reactor. The simulation is carried out on a wall-cooled catalytic reactor for the synthesis of vinyl acetate from acetic acid and acetylene by using both c — Sc model and Reynolds mass flux model. The simulated axial concentration and temperature distributions are in agreement with the experimental measurement. As the distribution of lx shows dissimilarity with Dj and the Sci or Pri are thus varying throughout the reactor. The anisotropic axial and radial turbulent mass transfer diffusivities are predicted where the wavy shape of axial diffusivity D, along the radial direction indicates the important influence of catalysis porosity distribution on the performance of a reactor. 

Schiesser and Lapidus (S3), in later studies, measured the liquid residencetime distribution for a column of 4-in. diameter and 4-ft height packed with spherical particles of varying porosity and nominal diameters of in. and in. The liquid medium was water, and as tracers sodium chloride or methyl orange were employed. The specific purposes of this study were to determine radial variations in liquid flow rate and to demonstrate how pore diffusivity and pore structure may be estimated and characterized on the basis of tracer experiments. Significant radial variations in flow rate were observed methods are discussed for separating the hydrodynamic and diffusional contributions to the residence-time curves. 

Comparing with the conventional three-phase beds, the axial solid holdup distribution is much more uniform and the radial distribution of gas holdup (sg) is much flatter in circulating beds, due to the relatively high Ul and solid circulation. The values of Eg and bed porosity can be predicted by Eqs. (7) and (8) with a correlation coefficient of 0.94 and 0.95, respectively. 

Similarly, in 3D-radial geometries of interest for petroleum engineers, an equivalent wellbore radius re is defined. The near-wellbore region, including radially distributed wormholes from rw up to re, is infinitely permeable and therefore becomes a mere radial extension of the wellbore itself. Equation 2 can be used to calculate the pseudodecrease of the skin when an undamaged primary porosity formation of permeability k0 includes wormholes as described hereabove ... 

The intrapellet porosity or void volume fraction Sp is given by an average over the radial part of the distfibution function h(r). l en all cylindrical pores are oriented parallel to the x direction (i.e., perpendicular to the external surface), the angular part of the distribution function is spiked at 6> = 0, which implies that... 

Rocha and Paixao [38] proposed a pseudo two-dimensional mathematical model for a vertical pneumatic dryer. Their model was based on the two-fluid approach. Axial and radial profiles were considered for gas and solid velocity, water content, porosity, temperatures, and pressure. The balance equations were solved numerically using a finite difference method, and the distributions of the flow field characteristics were presented. This model was not validated with experimental results. 

The interior of a reactor is represented by a random-close arrangement of hard impermeable spherical catalyst particles packed in a confining cylindrical container (Fig. 5.24). The radial-distribution function of interparticle porosity shows... 

Figure 9.1 The multiple length scales of mussel adhesion. (A) Centimeter length scale pertains to the radial distribution of threads around an individual mussel, Mytilus edulis. (B) The foot is shown extended in the process of making a new thread. (C) The millimeter scale refers to the spatulate geometry of threads and plaques. (D) The micrometer scale is seen in a cross-sectional slice through a plaque, as in B, and reveals an extensive porosity. The nanometer scale is best captured by a portion of a single adhesive protein adsorbed to a target surface featuring the two most abundant side chains lysine and Dopa.

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