Bed porosity

Glaser and Thodos [Am. Jn.st. Chem. Eng. J., 4, 63 (1958)] give a correlation involving individual particle shape and bed porosity. Kunii and Suzuki [Jnt. ]. Heat Mass Tran.sfer, 10, 845 (1967)] discuss heat and mass transfer in packed beds of fine particles. 

In general bed voidage is dependent on the paeking eharaeteristies of the material (a funetion of the orientation of the partieles in the bed), whieh is both partiele size and shape dependent. Unfortunately, at present it is only possible to prediet bed porosity for eertain distributions of regular partieles. Porosity ean be related to erystallizer solids hold-up empirieally, however, by an expression of the form... 

The competitive adsorption isotherms were determined experimentally for the separation of chiral epoxide enantiomers at 25 °C by the adsorption-desorption method [37]. A mass balance allows the knowledge of the concentration of each component retained in the particle, q, in equilibrium with the feed concentration, < In fact includes both the adsorbed phase concentration and the concentration in the fluid inside pores. This overall retained concentration is used to be consistent with the models presented for the SMB simulations based on homogeneous particles. The bed porosity was taken as = 0.4 since the total porosity was measured as Ej = 0.67 and the particle porosity of microcrystalline cellulose triacetate is p = 0.45 [38]. This procedure provides one point of the adsorption isotherm for each component (Cp q. The determination of the complete isotherm will require a set of experiments using different feed concentrations. To support the measured isotherms, a dynamic method of frontal chromatography is implemented based on the analysis of the response curves to a step change in feed concentration (adsorption) followed by the desorption of the column with pure eluent. It is well known that often the selectivity factor decreases with the increase of the concentration of chiral species and therefore the linear -i- Langmuir competitive isotherm was used ... 

Parameters a and b are related to the diffusion coefficient of solutes in the mobile phase, bed porosity, and mass transfer coefficients. They can be determined from the knowledge of two chromatograms obtained at different velocities. If H is unknown, b can be estimated as 3 to 5 times of the mean particle size, where a is highly dependent on the packing and solutes. Then, the parameters can be derived from a single analytical chromatogram. 

Figure 5. Gas holdup (e0) and incremental bed porosity (eLO — eL) vs. superficial gas velocity with process development unit (PDU)...

Adlington and Thompson (Al) measured the gas-liquid interfacial area in beds of particles of from 0.3- to 3-mm diameter by oxygen absorption in a sodium sulfite solution. They found that the interfacial area decreased with decreasing bed porosity, and was less sensitive to changes in particle size. 

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. 

Also, Schier s experiments revealed the necessity to consider the directional influence of the walls of the filter bed on the bed porosity e. This effect is very important especially for small sized beds that are usually used in laboratories for investigations. For beds made of spherically shaped collectors several correlations exist describing the e(y/dc) function where y denotes the distance from the wall in the radial direction. However, for relative large bed diameters DB/dc ranging from 5 to 25 it proved to be sufficient to use an averaged e in Eq. (3.2.5), as proposed by Jeschar [6],... 

In the course of separating the droplets some liquid will be stored within the bed. The accumulated liquid lowers the value of e. However, in contrast to separation of solids the filter will not be blocked as the liquid can move out of the filter, as explained in Section 3.2.1. By introducing the saturation ft the change in bed porosity due to accumulated liquid can be accounted for. 

A well-substantiated correlation for air-water systems taken from the trickle bed literature (Morsi and Charpentier, 1981) was used for the volumetric mass transfer coefficients in the / , and (Rewap)i terms in the model. The hi term was taken from a correlation of Kirillov et al. (1983), while the liquid hold-up term a, in Eqs. (70), (71), (74), (77), and (79) were estimated from a hold-up model of Specchia and Baldi (1977). All of these correlations require the pressure drop per unit bed length. The correlation of Rao and Drinkenburg (1985) was employed for this purpose. Liquid static hold-up was assumed invariate and a literature value was used. Gas hold-up was obtained by difference using the bed porosity. 

Note that the initial slope of the adsorption isotherm can be easily obtained from the knowledge of the retention time associated to a small injection performed on a column, as this retention time is given by tR = t0 ji + 1 - -k where /0 = V/Q is tiie zero-retention time based on the external bed porosity e (commonly, e is about 0.36-0.4). 

In 1962 Jottrand and Grunchard (J7) reported on mass transfer to a small rectangular nickel plate immersed in a liquid fluidized bed of sand particles. Mass-transfer rates were five to ten times higher than those measured in an open pipe flow a maximum rate was measured at a bed porosity of 0.58. Le Goff et al. (Lie) later showed that this maximum is directly related to a maximum in the average kinetic energy of the fluidized particles per unit bed volume. 

The functional dependence of jD on Reynolds number has been the subject of study by many investigators [e.g., Thodos and his co-workers (77, 78), and Wilson and Geankoplis (79)]. A variety of equations have been proposed as convenient representations of the experimental data. Many of these correlations also employ the bed porosity (eB) as an additional correlating parameter. This porosity is the ratio of the void volume between pellets to the total bed volume. 

In view of the fact that our results are reasonably sensitive to the estimate of the bed porosity used in the analysis, these results are not bad. If one had employed a value of 0.3 or 0.5 rather than 0.4 for sB, jD would change significantly and this would have a major influence on the calculated concentration (or mole fraction) differences. Unfortunately, bed porosity data were not noted in the article cited. In an experimental program being conducted as an aspect of a reactor design, this parameter could easily be determined. 

Before proceeding to the next illustration, it is instructive to see if our assumption of constant total pressure was indeed appropriate. If one assumes 1/4 in. spherical pellets, a nominal gas viscosity of 0.09 lb/hr-ft and a bed porosity of 0.4, the Reynolds number of the gas is given by... 

Before the bed can become fluidized, however, the particles must dislodge from their packed state, which expands the bed. Thus, the porosity (s) in Eqs (14-5) and (14-9) is not the initial packed bed porosity but the expanded bed porosity at the point of minimum fluidization ( ml ), i.e., the minimum bed voidage in the bed just prior to fluidization. Actually, the values of C and C2 in Eq. (14-8) that give the best results for fluidized beds of uniform spherical particles have been found from empirical observations to be ... 

The minimum bed porosity at incipient fluidization for nonspherical particles can be estimated from... 

Water is pumped upward through a bed of 1 mm diameter iron oxide particles (SG = 5.3). If the bed porosity is 0.45, over what range of superficial water velocity will the bed be fluidized ... 

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