Particles in the dilute phase

Possible agglomeration and sintering of fine particles in the dilute phase under certain conditions (e.g., high temperature). 

Perhaps the influence of dilute phase on the progress of reaction must have appeared in the minds of many investigators, but it was never formulated. It was stated (M33) that Visually the particles in the dilute phase are dispersed rather uniformly, so that under these flow conditions this portion of the particles may take part in increasing the catalytic conversion. Interesting discussions by Riley (R12) are another example. 

In the dilute phase the catalyst population decreases with increasing axial height from the dense-bed surface (Secticm II). It has been shown (M26) that the amount of directly contacting catalyst is approximately equal to a of Lewis et al. (LI2), if one takes the amount as the volume of catalyst existing above Z.,. The data are compared in Fig. 69. Here, L, is taken as the height above the distributor where the volume fraction of the emulsion equals that of the bubbles, i.e., Ce = Cb becomes meaningless in the dilute phase or in the transiticm zone, since Zb becomes dubious. However, Zed (instead of ie) is used as the hypothetical volume fraction if the dispersed particles in the dilute phase are concentrated into the same density as the emulsion. This treatment is convenient in calculating conversion in the dilute phase. 

The bubble gas, with initial concentration c , leaves the dense phase at z = Lf with concentration Ci and enters the dilute phase. For the dilute phase the diffusion-model approach is more general, since a fair amount of gas mixing is observed in a large-diameter bed (H19). Here, however, the usual piston-flow assumption is made for simplicity, since in small-scale beds the particles in the dilute phase are suspended rather uniformly. Actually the observed flow properties of the phase, including the transition zone, seem to be more complicated. 

Diffusion of gaseous reactant j through the bulk gas in the dilute phase to the surface of soHd particles in the dilute phase and the surface of clusters in the dense phase ... 

Particles in the dilute phase. In practice, some particles rain through bubbles as they rise and coalesce. While the fraction of the bubble volume occupied by particles is small (typically only 0.1 to 1%), even such a small fraction can have an appreciable influence on the reactor performance for fast reactions and slow interphase transfer. 

Expression 1 of Table 4-3 gives the particle velocity written in terms of the terminal velocity. This expression can be used generally for fine particles in the dilute-phase regime. Large particle sizes generally cause the particle velocity to be quite small and in some cases negative when inappropriate averaging has been done. Hinkle... 

As flue gas leaves the dense phase of the regenerator, it entrains catalyst particles. The amount of entrainment largely depends on the flue gas superficial velocity. The larger catalyst particles, 50p-90p, fall back into the dense bed. The smaller particles, O 0.-5O i, are suspended in the dilute phase and carried into the cyclones. 

On the other hand, an increase in the fines (particles <40 p) content of the circulating catalyst usually points to an attrition source or a change in the fresh catalyst PSD. Attrition in the dilute phase will not be reflected in the inventory PSD. 

The random thermal motions of each B-particle will occasionally cause a vapor-phase molecule to be captured in the liquid phase (heavy arrow), or a liquid-phase molecule to escape into the vapor phase (light arrow). In the limit that solute molecules are so dilute that solute-solute interactions can be neglected, the probability of each such capture/escape event is simply proportional to the number density (or mole fraction) of solute particles in the originating phase. We therefore expect that... 

SGP T TWSEC vise VISCL Vt VTGOl VTWO wc wd specific gravity of production water at system temperature T system temperature, °F time for water drop in oil phase to fall, s viscosity of liquid, gas or oil at system temperature T, cP viscosity of liquid or oil at system temperature T, cP terminal velocity of particle, ft/s particle velocity in oil phase, ft/s terminal velocity of water particle in the oil phase, ft/s BS W of treated desalter outlet crude oil, percentage by volume Barrels of dilution water per day mixed with the crude oil fluid upstream of the desalter... 

As shown in Step 1 of Fig. 3, the fluid flowing in the dilute phase has to support the discrete particles it contains as well as the clusters in suspension, and the combined forces result in a pressure drop equal to that of the parallel dense-phase fluid flow ... 

The contact in the dilute phase and the transition zone is different from that in the dense phase. The former is related to mass transfer between the gas phase and an agglomerate of solid particles, whereas the latter is mainly related to mass transfer between bubbles and emulsion including a certain amount of directly contacting catalyst. Upcm consideration of hindered settling of the swarm of particles (S16, Z7), we also find contact efficiency to be a function of the population density of particles. Normalizing by the Ig of the main dense phase, eg.de, e/ e.de is chosen as a variable... 

In calculating temperature distribution in the dilute phase, solid motion must be accounted for. Solid motion in the dilute phase is shown in Sections II and VI. Laboratory-scale fluid beds exhibit a circulating flow of solid particles with ascending central core and descending peripheral region. The enthalpy balances for both ascending and descending zcHies for the steady state are... 

In this section, calculations were carried out for the case of tjc = 1> (V ex 1. and Ced = (Z - Zt)Ce. de/(l - Zt). The last relation means that catalyst density decreases linearly with bed height from the top of the dense phase to some point (Zt) in the dilute phase. This Z, is not the total bed height, but a hypothetical intermediate height where the amount of catalyst particles becomes negligible. 

As the gas rate is increased above Go, more solids are entrained in the gas leaving the bed, until at very high flow rates the whole of the particles are in suspension in the dilute phase. The flow of fluids through packed and fluidized beds is discussed in more detail by Leva et alfi and Van Heerden. ... 

In a gas—sohd CFB with heterogeneous reactions and mass transfer, in Hne with the structural characteristics of the SFM model (Hong et al, 2012), as shown in Fig. 12, the mass transfer and reaction in any local space can be divided into components of the dense cluster (denoted by subscript c), the dilute broth (denoted by subscript f), and in-between (denoted by subscript i), respectively. And these terms can be represented by Ri (1 = gc, gf, gi, sc, sf, si). Both the dense and dilute phases are assumed homogenous and continuous inside, and the dense phase is fiarther assumed suspended uniformly in the dilute phase in forms of clusters of particles. Then the mass transfer terms can be described with Ranz-Marshall-hke relations for uniform suspension of particles (Haider and Basu, 1988). In particular, the mesoscale interaction over the cluster will be treated as is for a big particle with hydrodynamic equivalent diameter of d. Due to dynamic nature of clusters, there are mass exchanges between the dilute and dense phases with rate ofTk (k = g, s), pointing outward from the dilute to the dense phase. 

Penetration and diffusion of reactant j through the porous framework of sohd particles in the dilute and dense phases where adsorption and reaction take place ... 

If there is no chemical reaction but mass exchange between phases, such as evaporation, subfimation, and condensation, we can replace the reaction rate with certain mass exchange rate tm, and similarly define the heterogeneity index for structure-dependent mass transfer. For example, assume that the concentration of transferred species at particle surface is saturated further, the diffusion rate from the particles to the gas in the dense phase is equal to that from the gas in the dense phase to the gas in the dilute phase and we get... 

Here Cdc and represent the drag coefficient and superficial shp velocity for particles inside the dense phase k, respectively. With these relations, one can determine all the superficial sHp velocities of each dense phase and the superficial fluid velocities of the dilute and dense phases by using binary search method. Then, each particle in the dense phase k experiences two drag components, one suffering from the fluid in the dense phase and the other from the dilute phase as a whole and equally distributed over each particle in the dense phase. So, the drag force acting on each particle in the dense phase is... 

Miyauchi and Furusaki, 1974). A bubble-free emulsion then flows down the bed peripherally. This situation clearly leads to some reaction in the dilute phase. An elegant model that accounts for reaction in both the bubbling and dilute regions of the bed has been proposed by Miyauchi (1974), and another by Kunii and Levenspiel (1991) (more in line with their fine particle model). 

Chen and Wen (76) tried to improve on this model by allowing for axial dispersion of gas in the freeboard region and by means of assumptions which give more realistic profiles of particle holdup in the dilute phase. Entrainment is calculated from their recent correlation (77) which leads to an exponentially decreasing solids mass flux and makes allowance for solids returning to the bed surface along the vessel walls. Ejected particles were... 

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