Fluidized catalyst beds bubbles

III. Turbulent-Flow Phenomena in Bubble Columns and Fluidized Catalyst Beds... 

It is interesting to see how far modern technology for fluidized catalyst beds has served to achieve good fluidization. Our criterion of good fluidization is a gas-fluidized bed of a low viscosity liquid (such as water), where the low-viscosity liquid would set the lower limit to the fluidity of the emulsion. Such a gas-fluidized liquid bed is the well-known bubble column, which has been studied extensively. Our objective is to understand the behavior in the recirculation flow regime, since the superficial gas velocity of practical interest is usually more than 30 cm/sec for fluidized catalyst beds and for these conditions intense recirculation of the emulsion has been observed (note Fig. 2 and Section II,D,3). 

Currently available data for the flow properties of the fluidized catalyst bed are fragmentary, since the local motion of the emulsion phase is diflicult to measure experimentally. Therefore, it is useful to clarify the flow properties of the bed in terms of our knowledge of bubble columns. First, the fluid-dynamic properties of the bubble columns will be explained then, the available data will be adapted to apply to fluid catalyst beds. The reader will be able to picture an emulsion phase of carefully prepared catalyst particles operating in intense turbulence for fluidized beds under conditions of practical interest. This turbulence distinguishes the flow properties of fluid catalyst beds from those of widely studied teeter beds. 

The mean bubble size in a fluidized bed has been discussed in Section II,B. As discussed, for a fluidized catalyst bed of good fluidity may be taken as approximately 5.0 cm [cf. Figs. 10 and 11, and Eq. (2-11)] for Uc, > 10 cm/sec. With Eq. (3-33), this (I32 gives = 49.5 cm/sec, which is shown in Fig. 34 as a dashed line. It is interesting that the mean slip velocity is essentially the same as for a bubble column, when Uq > 20 cm/sec. As noted in Section II,B, and Mg are very sensitive to change in particle size, size distribution, shape, and density. 

In summary, the calculations show convincingly that modern fluidized-catalyst-bed technology has attained an emulsion fluidity nearly equivalent to that of low-viscosity liquids. With such fluidity, data obtained for a bubble column shed light on the performance of a fluidized catalyst bed, and vice versa. 

Longitudinal dispersion in the continuous phase (the liquid phase for a bubble column, and the emulsion phase for a fluidized catalyst bed) is closely related to flow properties of the equipment. Here, we wish to describe the longitudinal dispersion phenomena in terms of the fluid-dynamic properties of the equipment. The prime purpose is to test whether the fluid-dynamic analysis developed earlier is sound, but lon-... 

A gas bubble column is taken here as a model equipment undergoing longitudinal dispersion of the continuous phase. The theory obtained is equally applicable to a fluidized catalyst bed of good fluidity exhibiting similar flow properties. The following procedure is from Miyauchi (M27). 

In regard to axial dispersion in unbaffled bubble-flow equipment like liquid-liquid spray columns, gas bubble columns, or fluidized catalyst beds, a close similarity has been supposed as a result of bubble flow and of turbulence induced by bubbles (B3, M33). Baird and Rice (B3) have assumed that the Kolmogoroflf concept for eddy viscosity in isotropic turbulence is applicable to evaluate E in the unbaffled bubble column under turbulent conditions, concluding that Ezt >s 0.35 in cm-sec units,... 

When the velocity profile of the emulsion phase is similar to that of the liquid phase in a bubble column, Eq. (4-11) will apply to the fluidized catalyst bed. This similarity seems to be well justified as mentioned in Sections III,A,4-5, although there is no direct calculation of the turbulent kinematic viscosity from the measurement of velocity profile in the fluidized catalyst bed. 

The turbulent kinematic viscosity vt of the fluidized catalyst bed has been determined, as Eq. (3-3 la), from the use of axial dispersion coefficient This is a natural consequence of the analogy between the bubble column and the fluidized catalyst bed of good fluidity (such as in fluidized catalytic cracking). The mean gas holdup (Fig. 36) and the mean bubble velocity along the bed axis (Fig. 37) are reasonably well predicted by applying Eq. (3-3 la) for the fluidized cracking catalyst bed. 

III,D,5). In this chapter, the equation is further examined in relation to bed performance, since the turbulence properties of the bed result from interaction between bubbles and the continuous phase. As shown in Fig. 34, the mean slip velocity of bubbles in a fluidized catalyst bed of good fluidity is essentially the same as that for a bubble column when Uq > 20 cm/sec. A criterion under which bubble size approaches a dynamic equilibrium is obviously needed for predicting or evaluating the performance of scaled-up beds. 

The mean bubble size that concerns us here is on the order of 5 cm, so that the Eotvos number Eo (equal to dlgpi/a) is well over 40 for usual bubble-column liquids. The bubbles are of spherical-cap type under this condition, which is essentially equivalent to a Weber-number criterion We (equal to dy piul/a) > 20, since Ug = Vgrfb/2 (H4, H5). The bubbles in a fluidized catalyst bed satisfy the above criterion, since a- 0. Consequently, surface tension has relatively little effect, and instead the splitting is closely related to disturbances induced by the bulk turbulence, the intensity and the scale of which are mainly governed by the fluidity of the continuous phase and the operating gas velocity. 

Scientific approaches to improve bed fluidity are potentially important for fluidized bed technology. Also, further quantitative relations between bubble splitting and bed properties would be very helpful in planning and scaling-up fluidized catalyst beds. 

Heat and mass transfer constitute fundamentally important transport properties for design of a fluidized catalyst bed. Intense mixing of emulsion phase with a large heat capacity results in uniform temperature at a level determined by the balance between the rates of heat generation from reaction and heat removal through wall heat transfer, and by the heat capacity of feed gas. However, thermal stability of the dilute phase depends also on the heat-diffusive power of the phase (Section IX). The mechanism by which a reactant gas is transferred from the bubble phase to the emulsion phase is part of the basic information needed to formulate the design equation for the bed (Sections VII-IX). These properties are closely related to the flow behavior of the bed (Sections II-V) and to the bubble dynamics. 

Kai T, Takahashi T, Misawa M, Tiseanu I, Ichikawa N, Takada N. Observation of rising bubbles in a fluidized catalyst bed using a fast X-ray CT scanner. Proc, 5th SCEJ S)mip. on Fluidization, Tsukuba, 1999, pp. 435-440. 

Consider the reaction A - B taking place in the dense, or particulate, phase of a bubbling bed of fluidized catalyst particles (Fig. 10). It is in steady opera-... 

In our discussion of surface reactions in Chapter 11 we assumed that each point in the interior of the entire catalyst surface was accessible to the same reactant concentration. However, where the reactants diffuse into the pores within the catalyst pellet, the concentration at the pore mouth will be higher than that inside the pore, and we see that the entire catalytic surface is not accessible to the same concentration. To account for variations in concentration throughout the pellet, we introduce a parameter known as the effectiveness factor. In this chapter we will develop models for diffusion and reaction in two-phase systems, which include catalyst pellets and CVD reactors. The types of reactors discussed in this chapter will include packed beds, bubbling fluidized beds, slurry reactors, and trickle beds. After studying this chapter you will be able to describe diffusion and reaction in two- and three-phase systems, determine when internal pore diffusion limits the overall rate of reaction, describe how to go about eliminating this limitation, and develop models for systems in which both diffusion and reaction play a role (e.g., CVD). 

Figure 5 shows typical expansion data measured by Morooka et al. (M41) using unclassified FCC catalyst particles. As soon as the bed reaches minimum fluidization, it starts to expand. After bubbles start to form (i.e., under aggregative fluidization) the bed expands slowly and then... 

The averaged volume fraction Cb. calculated by Eq. (3-25), is shown in Fig. 36, for bubble columns and also for FCC-catalyst beds (M40). The mean slip velocity of bubbles is again taken as ii , = 49.5 cm/sec. Also, Vi is calculated by Eq. (3-31a) for curve FQF and by Eq. (3-31) for curve FQP, while curve EE is an empirical fit of the data. As in the case of a bubble column, curve FQP matches better with curve EE, although FQP is consistently higher. Curve EE tends to decrease the slope for Uq s 7-8 cm/sec, perhaps due to the decrease in Ms the scatter of data makes the behavior unclear. This is explained by the difference in the region of Uc < 20 cm/sec. The bubble column shows higher 6b values than those for the fluidized bed, which is due to the bubble column s lower Us (cf. Fig. 34). 

The direct contact model has some difiiculties, however. In fluidized beds, gas bubbles of very low solid content are usually considered to exist in the dense phase (H14, K13, T19). Also, the cloud layer is negligibly thin, due to small (/ r for the usual fluid catalyst beds, according to equa-ticMis of Davidson and Harrison (D3) and Murray (M47). The streamlines of gas phase through a bubble have been observed to pass through the cloud, but not through the bubble wake (R17). Thus there seems little possibility of believing that the bubble gas is in direct contact with a substantial amount of catalyst in the bubble phase (see also Secticxi VI,A). Furthermore, the direct contact model is applied to the data by Gilliland and Knudsen, and v in Eq. (7-9) is calculated to fit the data. Calculation (M26) shows that the volume of catalyst, with an apparent density the same as for the emulsion, which contacts the bubble gas freely exceeds the volume of bubble gas itself (v/ib = 3.3, 2.0, and 1.5, respectively, for Uc. = 10, 20, and 30 cm/sec). This seems to be unsound physically. 

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