if the gas velocity is higher than minimum fluidization velocity (Umb = Umf ). With an increase in velocity beyond minimum bubbling velocity, large instabilities with bubbling and channeling of gas are observed. At high gas velocities, the movement of solids becomes more vigorous. Such a bed is called a bubbling bed or heterogeneous fluidized bed (Fig. 1.9). In this regime, gas bubbles generated at the distributor coalesce and grow as they rise through the bed. For deep beds of small diameter, these bubbles eventually become large enough to spread across the diameter of the vessel. This is called a slugging bed regime. In large diameter columns, if gas velocity increases still further, then instead of slugs, turbulent motion of solid clusters and voids of gas of various size and shape are observed. Entrainment of solids becomes appreciable. This regime is called a turbulent fluidized bed regime (Fig. 1.9, Fig. 12.3). With further increase in gas velocity, solids entrainment becomes very high so that gas-solid separators (cyclones) become necessary. This regime is called a fast fluidization regime. For a pneumatic transport regime, even higher gas velocity is needed, which transports all the solids out of the bed. As one can imagine, the characteristics of gas-solid flows of these different regimes are strikingly different. It is, therefore, necessary to determine the prevailing flow regime in order to select an appropriate mathematical model to represent it.

Several regime maps have been proposed in the literature. One widely used regime map developed by Grace (1986) is shown in Fig. 12.4. This map is developed



FIGURE 12.4 General flow regime map for gas-solids flows (from Kunii and Levenspiel, 1991).

using two dimensionless numbers defined in Fig. 12.4. The main conclusions to be drawn from this regime map can be summarized as follows:

For fine solids (class A and B), stable operation of a bubbling bed exists over a wide range of operating conditions. For larger particles (class D), the operating range is relatively narrow.

For small particles, bubbling starts at a gas velocity much higher than minimum fluidization velocity (3-8 times Umf) and continues way beyond the terminal velocity Ut. For large particles, bubbling occurs at a gas velocity close to Umf.

• Fast fluidization is possible for small particles at very high gas velocity (around

1000 Umf).

There are several empirical correlations to predict minimum fluidization velocity and minimum bubbling velocity, which can be used to examine whether bubbles will exist or not (see for example, correlations summarized by Kunii and Levenspiel, 1991). Generally, most of these correlations predict similar results for fine particles (< 100 ^m). However, for large solid particles, there is a considerable scatter in the predictions of different published correlations. When there is a wide size distribution and non-spherical particles, it is often necessary to use experiments to make reliable estimates of minimum fluidization and minimum bubbling velocity. Bubbles in a bubbling bed can be quite irregular in shape and vary greatly in size. In beds of fine solid particles, bubbles grow quickly to a few centimeters in size and remain at that size as a result of equilibrium between coalescence and splitting. For larger particle beds, bubbles grow steadily in the bed and reach tens of centimeters in size. Several correlations have been proposed to estimate bubble sizes and bubble growth in fluidized beds (Mori and Wen, 1975; Darton et al., 1977; Werther, 1978 and so on). Similarly several correlations have been proposed to estimate bubble rise velocity (Davidson and Harrison, 1963; Werther, 1983). Since the types of turbulent fluidized bed regime are not very well defined, the transition between bubbling bed and turbulent regime and that between turbulent and fast fluidization regime, are also not very clearly defined. A recent review by Bi et al. (2000) may be consulted to estimate these transition velocities. With this brief introduction to gas-solid flows in fluidized bed reactors, major reactor engineering issues, conventional design practices and the role of computational flow modeling to facilitate better reactor engineering are discussed below.

12.1.2. Reactor Engineering

For good reactor operation, it is desirable to realize effective gas and solid contact leading to maximum mass and energy exchange between gas and solid particles. The objective of a reactor engineer is to realize such an effective gas-solid contact without compromising other desirable characteristics such as residence time distribution (RTD), backmixing and so on. Prevailing flow regimes obviously play an important role in determining gas-solid contacting characteristics.

Bubbling fluid beds are generally used when excellent solids mixing and bed to wall heat transfer characteristics are desired. RTD and degree of backmixing is a strong function of such bubbling characteristics as mean bubble size, size distribution, bubble rise velocity, bubbling frequency and bubble shape. Knowledge of bubble size and rise velocity can then be used to estimate transport coefficient between bubble and dense phase and also to estimate solids circulation and mixing. Studies indicate that the fluidized bed reactor can be operated in different modes either to promote solid mixing or segregation. In bubbling fluidized beds, bubbling of gas causes gross circulation of solid particles. When a bed of wide particle size distribution and of widely varying density is fluidized, denser particles tend to settle at the bottom of the bed. This phenomenon is counter-balanced by circulation of solids. At very large gas velocity (Uo > Umf, where Uo is superficial gas velocity) solids circulation dominates the process and at gas velocity close to Umf solids segregation dominates the process. Mixing and segregation of solids in the bed is set up by the dynamic equilibrium between the two competing mechanisms.

From a reactor engineering point of view, macroscale circulation of solid particles enhances backmixing, which lowers the conversion and selectivity of the fluidized bed reactor. In bubbling fluidized beds, severe by-passing of reactant gas is possible through fast rising large gas bubbles. It is generally believed that gas by-passing can be avoided in high velocity fluidized beds (turbulent or fast-fluidization regimes). High velocity fluidized bed reactors are attractive for high-pressure applications, since the reactor diameter is reduced for the same gas throughput.

In riser reactors, which are operated in a fast-fluidized regime (Uo > 20Ut, where Uo is gas superficial velocity and Ut is terminal settling velocity of solid particles), solids backmixing and radial distribution of solids play a central role in determining overall performance. Fast-fluidized beds are characterized by downflow of solids in the near wall region and upflow of solids through the central core. Solid volume fractions exhibit distinct peaks near the walls. In order to make realistic simulations, it is essential to predict such wall peaking of solids volume fraction accurately. The possibility of formation of clusters and their influence on the efficiency of gas-solid contacting is also an important design issue. Clusters formation and their properties are not yet well understood and several conflicting reports about their significance have been published (see a review by Chen, 1995). Cluster formation may increase or decrease local transport coefficient and may alter the fluid dynamics of riser reactors. Compared to the large body of empirical information/correlations available for the case of bubbling beds, empirical information available for fast-fluidized bed reactors and turbulent fluidized bed reactors is much less and contains a significant amount of scatter (Zijerveld, 1998; Venderbosch, 1998; Bi et al., 2000 for reviews of recent data).

Conventional design practices involve making use of such accumulated empirical information to develop reaction-engineering models (two- or three-phase models for bubbling beds and axial dispersion models for turbulent and fast fluidized beds). Such models are invariably based on very simplified fluid dynamics (Kunii and Levenspiel, 1991). These models are used to understand the sensitivity of reactor performance to operating and model parameters. In many cases, transition from bubbling to turbulent fluidization is not sharp and significant uncertainty exists about the location of the transition. Thompson et al. (1999) developed a generalized bubbling-turbulent (GBT) model based on a probabilistic approach to overcome such difficulties. Kunii and Levenspiel (2000) recently discussed a reaction-engineering model for circulating fluidized beds operated in a fast-fluidized regime. These models and sensitivity studies using these models, coupled with prior experience in designing fluidized bed reactors, are used to evolve an experimental program to collect the required information about hydrodynamics with adequate accuracy. Experimental data obtained at two or more scales is then used to develop an appropriate fluid dynamic basis for the specific gas-solid system under consideration. This information is used again with reactor performance models to evaluate designs of industrial fluidized bed reactors. Scale-up experiments need to be carried out to ensure that the hydrodynamics of large-scale industrial reactors (with different gas distributors and internals) is not very different from that of pilot-scale reactors showing satisfactory reactor performance. Obviously, such a procedure restricts options for reactor configurations and it also has a significant amount of uncertainty due to the empiricism employed.

Moreover, these conventional models are not useful to understand the influence of details of the hardware configuration on reactor performance. Detailed hydrodynamic models are necessary to resolve hardware-related issues. For example, distributor design of an industrial fluidized bed reactor involve several aspects including shape and location of distributor, number of holes, distribution of holes, orientation of holes and so on. Empirical information suggests that if pressure drop across the distributor is small (less than 20% of the pressure drop across the fluidized bed), gas mal-distribution and by-passing (due to formation of large bubbles at the distributor holes) may occur. This information is not adequate to optimize distributor design and to estimate its influence on gas and solid dynamics within the fluidized bed. Non-optimum distribution of holes may result in local settling of solids and may lead to erosion-related problems, as was mentioned for the OXY reactor case in Chapter 9. Similar comments are applicable to designing the feed nozzle system (diameter, shape, orientation, number of nozzles, location of nozzles and so on). Feed nozzle design affects local gas-(liquid-)solid contacting and therefore, overall performance. To design improved feed systems for riser or bubbling bed reactors, detailed knowledge of local fluid dynamics is necessary. Apart from the distributor and feed nozzle design, to resolve other reactor-engineering issues such as designing internals etc. it would be necessary to develop detailed fluid dynamic models. In analyzing important issues such as the formation of local hot spots, by-passing, solids entrain-ment in a free board and so on, CFD-based models can contribute uniquely. With such contributions, computational flow modeling may greatly accelerate the entire reactor development program with enhanced confidence levels and better performance. CFD models can significantly reduce the demands on pilot planting by providing efficient and effective interpolation and extrapolation tools. A typical reactor engineering program for fluidized bed reactors based on CFD models is shown in Fig. 12.5.

Operating regime Bubbling/turbulent fast-flui dilation

Capacity Mass and energy balance: flowrates of gas and solid phases

Reaction engineering model Conversion/yield Sensitivity with respect to operating parameters/ operating flow regime

Preliminary Design Selection of mode of operation, Single-particle reactor models, Preliminary sizing/ hardware configuration A

Characterization of gas-solids system Relevant physico-chemical properties, fluidization behavior

Computational flow model Model development/

validation Distributor designs Feed/outlet nozzle designs Reactor internals Provide required information to reaction engineering models ) Examine local hot spots ori segregation phenomena Short-list most promising configurations Scale-up/scale-down guidelines Interpretation of bench- and pilot-scale experiments Extrapolation of pilot-scale experiments/cold flow simulations to desired operating conditions and scale

Experiments Bench and pilot scale Model validation Decision on final configuration/ design

Final Reactor Design

FIGURE 12.5 Reactor engineering of fluidized bed reactors.

It should, however, be noted that the physics of gas-solid contacting is extremely complex, and as yet, has defied rigorous representation in mathematical models. As shown in Fig. 12.5, some experimentation will be necessary. Keeping the specific objectives in mind, the reactor engineer has to judiciously formulate a model for the reactor. Key predictions of such a model need to be validated by comparison with experimental data before they can be used for reactor engineering applications (to evaluate different configurations, to short-list the most promising ones, to provide the relevant information of fluid dynamics to the reaction engineering models, to optimize distributor, feed system and reactor internals, to scale-up and to scale-down and so on). As mentioned in previous chapters, it is necessary to use different modeling approaches (hierarchy of models) to construct a useful picture of industrial fluidized bed reactors. A brief review of modeling strategies and some recent results are discussed in the following section. Some applications of CFD models to reactor engineering are then discussed.

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