Void fraction space average

The basic mechanism for transition from bubble to slug flow appears to be the same as in vertical pipe flow. That is, as the gas flow rate is increased for a given liquid flow rate, the bubble density increases, many collisions occur and cell-type Taylor bubbles are formed, and the transition to slug flow takes place. As shown in the case of vertical pipe upflow, Taitel et al. (1980) assumed that this transition takes place when ac = 0.25. This criterion is also applicable here. However, because of the preferable geometry in the rod bundle, where the bubbles are observed to exist, instead of in the space between any two rods, this void fraction of 0.25 applies to the local preferable area only, a.L. The local voids, aL, can be related to the average void by (Venkateswararao et al., 1982)... 

Given the gas and liquid flow rates and the pipe diameter, it is now possible to calculate ULS and UGS from Eqs. (3-107) and (3-108), and the space average void fraction, a, from Eq. (3-114). 

Packing Nominal size, in. Approximate average weight per ft3 of tower volume, lb Approximate average total surface area of packing, ft /ft3 of tower volume Percent tree-gas space = t x 100 Packing factor, ap/e3, effective surface area/(void fraction)1, ft3 per ft3 of tower volume (dry-packed values for use with Fig. 16-20)... 

Conversion efficiency is definitely affected by the large void fraction, which is apparent in the results from changes in the total throughput, or space velocity (0.56 versus 1.11 sec ), shown in Fig. 7. In this comparison, the concentration of unconverted hexane increased tenfold when the flow rate was doubled. The impact of improvements in conductive heat transfer, combined with the mass transfer limitations associated with the cell size and honeycomb design, and a catalyst loading that was nearly one-half Chat of commercial pellet catalysts (average, 11.5% versus 19.2%) suggested that both carbon formation and steam/hydrocarbon reactions were better controlled with monolithic supports under the conditions employed. This comparison was made where the extent of the endothermic reaction is equal between the pellet bed and the hybrid cordierite/metal monolith bed. 

From the helium-mercury measurements the pore volume, the solid density, and the porosity of the catalyst particle can be determined. Values of p are of the order of 0.5, indicating that the particle is about half void space and half solid material. Since overall void fractions in packed beds are about 0.4, a rule of thumb for a fixed-bed catalytic reactor is that about 30% of the volume is pore space, 30% is solid catalyst and carrier, and 40% is void space between catalyst particles. Individual catalysts may show results considerably different from these average values, as indicated in Examples 8-4 and 8-5. 

A large reactor with many two-inch tubes will operate at the same space velocity but with a superficial velocity of 3.0 ft/sec. The estimated void fraction in the bed is 0.40. What conversion is expected if the average temperature is the same as in the lab reactor ... 

In two-phase pipe flows, the slip velocity or, equivalently, the drift flux is related to the void fraction. This leads to the occurrence of kinematic waves which convey void fraction signals. Kinematic waves have been investigated experimentally in air-water two-phase flows by inducing small void fraction disturbances at the inlet of vertical ducts, the average void fraction varying from 0.01 (bubbly flows) to 0.41 (slug flows). The temporal fluctuations of the void fraction are detected in regularly spaced cross sections by non intrusive impedance probes. The statistical... 

The random pore model, or macro- micro-pore model, of Wakao and Smith [1962, 1964] is intended for application to pellets manufactured by compression of small particles. The void fraction and pore radius distributions are each replaced by two averaged values 8m, I m for the macro and for the micro distribution (often a pore radius of -100 A is used as the dividing point between macro and micro). The particles which contain the micro-pores are randomly positioned in the pellet space. The interstices are the macro-pores of the pellet (see Fig. 3.5.2.1-1). The diffusion flux consists of three parallel contributions the first through the macro-pores, the second through the micro-pores and the third through interconnected macro-micro-pores in which the dominant resistance lies in the latter. The contributions to the diffusivity are added up to yield ... 

Throat size distribution is given from the intrusion profile. Pore body size distribution is given from the retraction profile (refs. 8-9). The ratio of the pore size to throat size at a given fraction of pore volume filled provides an indication of the shape or dimension of the void space. The amount of retained mercury (difference between intruded volume and extruded volume) gives some indication about the average connectivity and network size of the void space. Finally, total porosity in the range of 0.(X)5-0.5 microns in opening diameter is obtained from the total amount of mercury intmded and the solid densities from mercury displacement at 1 Bar. 

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