Yang Fluidization, Solids Handling, and Processing

Figure 52. Improving fluidizing characteristics by fines addition, solid groups: A-A and B-A. (Yang, Tung, and Kwauk, 1985.)

Figure 53 is a similar plot, but for the ten sets of Group B-C mixtures. Most curves show that the value of Θ for Group B-C binaries give maxima at certain intermediate compositions. The presence of these maxima suggests that not only fine particles belonging to Group C may improve the fluidizing characteristics of such coarse solids as Group B, but the coarse particles may also improve the fluidizing characteristics of the fine particles, which are known to possess the notorious tendency towards channelling before fluidization sets in.

This synergism of Group B-C mixtures testifies to the significance of particle size selection and particle size distribution design, in order to tailor a solid particulate material to certain desired fluidizing characteristics.

A mathematical model has been proposed to account for the mutual synergistic action of either particle component on the other in increasing the value of the dimensionless time Θ as shown in Fig. 53, in terms of the mass fraction x2 of fines, and two empirical parameters n1 and n2:

Θ = Θ1 (1 - x2) (1 + x2n1 ) + Θ2 x2 [1 + (1 - x2) n2]

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Mutual synergism of binary mixtures containing fine particles can be quantified in terms of the departure of the Θ-x2 curve from a linear tie line, which signifies absence of synergism, joining Θ1 and Θ2 for the respective components, as shown in Fig. 54. A convenient measure of this departure is the shaded area lying between the Θ-x2-curve and the linear tie line. This can be derived analytically in terms of what will be called the Synergism number Sy, normalized with respect to Θ1+Θ2 of both the coarse and the fine particles:

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9.1The Energy-Minimized Multiscale (EMMS) Model

With respect to the highly disparate nature of G/S and L/S fluidization, even at an early stage, the aggregative tendency of L/S fluidization was already discovered when large and/or heavy solid particles were used, and, moreover, clustering of these particles was also reported (Wilhelm and Kwauk, 1948). The particulate phenomenon present in certain G/S systems was noted, however, much later in connection with certain Geldart A-type solids, e.g., the graded, spheroidal FCC catalyst. Aggregative tendency of the normally particulate L/S fluidization on the one hand, and particulate tendency of the normally aggregative G/S fluidization on the other, led to the concept of interpolating these opposite tendencies toward an intermediate regime of transition.

Physically the EMMS model consists of a dense phase of clusters dispersed in a dilute phase composed of more or less discrete suspended particles, as shown in Fig. 55 (Li, Tung and Kwauk, 1988). The total fluid flow Ug to the system is divided into two streams, one through the densephase clusters Uc and one through the surrounding dilute phase Uf. Clusters are suspended by the fluid flowing inside them as well as outside them, while the discrete particles in the dilute phase are being entrained by their surrounding fluid. The dense clusters occupy a volume fraction f of the bed volume, the remaining (1 - f) fraction belonging to the dilute phase. Figure 55 also tabulates the symbols for velocity U, for voidage ε and for drag coefficient CD referring to the dense and the dilute phases.

There are thus three scales of interaction between the fluid and the particles:

a. Microscale of particle size—drag on particle for both the dense and dilute phases

b. Mesoscale of cluster size—interaction between dilutephase fluid and clusters

c. Macroscale for the overall two-phase flow system, involving its interaction with its boundaries, such as walls and internals.

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The above six equations for continuity and force balance do not, however, afford a complete description of a heterogeneous particle-fluid system in which a dense phase and a dilute phase coexist. An additional constraint needs to be identified to account for the stability of the system.

This constraint is to be provided through the concept of minimal energy. According to this concept, particles in a vertical flow system tend toward certain dynamic array which results in minimal energy.

The total energy associated with a flowing particle-fluid system is thus considered to consist of the sum of two portions, one used in suspending and transporting the particles, and one consumed in energy dissipated in particle collision and circulation. Alternately, in terms of the power per unit weight of solids, the total power N is composed of the suspension and transporting portion NST and the energy dissipation portion NED. The former can be split into that for particles suspension NS and transport NT, and in accordance with the multiscale model, also into portions for the dense cluster phase, the surrounding dilute phase and interaction between the two, that is

Consequently, modeling of a two-phase flow system is subject to both the constraints of the hydrodynamic equations and the constraint of minimizing N. Such modeling is a nonlinear optimization problem. Numerical solution on a computer of this mathematical system yields the eight parameters:

ε f, ε c , f, Uf, Uc, l, Udf, Udc

plus the various constituent power terms.

9.2Reconciling L/S and G/S Systems

Figure 56 compares the computed results for the FCC/air system against those for the glass/water system, to illustrate the disparate behaviors of G/S and L/S fluidization.

The first three insets on the left-hand side show the change of voidages, ε f, ε c and ε , cluster phase fraction f, and slip velocity Us, for the FCC/air system. In the corresponding insets for the L/S system, however, the three voidages ε f, ε c and ε are identical, and the cluster phase fraction f is zero, indicating the absence of clusters throughout the velocity range of Ug, that is, fluidization is homogeneous. Also, the slip velocity Us between solid particles and the surrounding liquid is always less than the terminal velocity Ut of the particles, which remains the asymptotic value for the increasing slip velocity Us as the entering liquid velocity Ug increases.

The lowest two insets of Fig. 56 compares the power for suspending and transporting the solid particles NST for the G/S and L/S systems. For the FCC/air system, NST is always less than the total energy N, until it jumps to the latter value at the point of sudden change, while for glass/water, NST is always the same as N in view of its homogeneous nature.

Figure 57 shows the gradual transition of the homogeneous glass/ water fluidization to the highly heterogeneous or aggregative glass/air fluidization, as the particle/fluid density ratio ρp /ρf increases from water through ethyl ether, and carbon dioxide under different stages of decreasing pressure from its critical condition, to atmospheric air. The appearance and gradual growth of the two-phase structure is evident in the order of the fluids listed. For instance, the curves in the top left inset show that at ρp/ρf = 2.55 for glass/water, f = 0 throughout the range of gas velocity Ug, indicating a homogeneous particle-fluid system. When the ratio ρp/ρf has increased to 3.19 for glass/ethylether, however, the two-phase structure appears for gas velocities Ug up to 0.4 m/s. This velocity range broadens through carbon dioxide under decreasing pressures from its critical point, until at ρp/ρf = 2,162 for glass/air, this two-phase structure has extended beyond

Ug = 2 m/s.

While Fig. 56 demonstrates, from modeling, the disparate nature between G/S and L/S fluidization, Fig. 57 shows continuity in particle-fluid behavior through properly selected intermediate systems, thus reconciling through theory the phenomenological discrimination between aggregative and particulate fluidization.