Yang Fluidization, Solids Handling, and Processing

		Pressure and Temperature Effects		125
Eq. (8)	uε = nut(1 -ε )ε n−1
	ue =
Eq. (9)		[3.2gd p (1− ε )(ρ p − ρ g )] ρ p

where n is the Richardson and Zaki exponent.

If ue > uε , the bed is STABLE

If ue > uε , the bed will BUBBLE

Equating ue and uε and manipulating the resulting expression leads to the following stability criterion:

	Term 1 (T1)							Term 2 (T2)
	égd		p	(ρ	p	- ρ )ù0.5
Eq. (10)	ê					g	ú -0.56n(1-ε			)0.5ε n−1	= C
				2					mb
	ê				ρp		ú			mb
				ut
	ë						û

If C > 0 (if Term 1 is > Term 2), the bed is STABLE

If C < 0 (If Term 1 is < Term 2), the bed BUBBLES

The Hydrodynamic Theory of Foscolo and Gibilaro has been shown to predict the increase in εmb with temperature and pressure very well. This is shown in Figs. 7 and 8, respectively, for the data of Rapagna (1994) and Crowther et al., (1978). Jacob and Weimer (1987) also reported that the Foscolo and Gibilaro theory successfully predicted the increase in εmb with increasing pressure.

1.4Bubble Size and Frequency

Temperature and pressure also interact with particle size to affect bubble size and frequency in fluidized beds. Information on the effect of temperature on bubble size in the literature is somewhat inconsistent. However, the information that does exist suggests that bubble size decreases slightly with temperature for Group A materials (Geldart and

126 Fluidization, Solids Handling, and Processing

Kapoor, 1976; Kai and Furusaki, 1985; Yoshida et al., 1976). Although less information exists for larger particle sizes, bubble size appears to not change with temperature for Group B materials (Sishtla et al., 1986; Wittman et al., 1981), and to increase with temperature for Group D materials (Sittiphong et al. 1981).

Workers generally report that bubble frequency increases with temperature (Mii et al., 1973; Otake et al., 1975; Yoshida et al., 1974). There is an initial rapid increase in frequency with temperature near ambient, which then tapers off at higher temperatures.

As reported above, investigators have reported that fluidization appears smoother when beds are operated at high pressure. They also report that there is a “slow motion” quality about the bed. This behavior has been attributed to a decrease in the bubble size with pressure. Indeed, there is ample experimental evidence (Barreto et al., 1984; Chan et al., 1987; Rowe et al., 1984; Weimer and Quarderer, 1983) which shows that increasing pressure causes bubble size to decrease in Group A materials. The same evidence shows that the pressure effect on bubble size decreases as the particle size increases, and that pressure does not affect bubble size significantly for large Group B, and Group D materials. The effect of pressure on bubble size for 66 micron and 171 micron material is shown in Fig. 9 from Weimer and Quarderer. As can be seen from the figure, pressure has a significant effect only for the smaller particles.

Although there is some disagreement among researchers in this area, it is generally believed that bubbles divide by splitting from the roof due to Taylor instabilities (Clift and Grace, 1972), and that the smaller bubbles observed in high-pressure beds of Group A solids are a result of the increased expansion of the dense phase with pressure. This results in an effective decrease in the viscosity of the dense phase. Taylor instability (an instability in the roof of the bubble/dense-phase interface) increases with a decrease in the viscosity of the dense phase. This results in a collapse of the bubble roof more frequently at high pressures. King and Harrison (1980) used x-rays to obtain images of bubble breakup and found that bubble breakup occurred because of “fingers” of material penetrating the bubble from the roof. This is schematically depicted in Fig. 10.

Experimental observations show that the dense-phase viscosity for small Group A particles decreases significantly with pressure (King and Harrison et al., 1980; May and Russell, 1953) as shown in Fig. 11. However, the dense-phase viscosity of Group B and Group D particles

128 Fluidization, Solids Handling, and Processing

Particles Penetrate Into Bubble Roof Due to Taylor Instability

When Penetration Completely Pierces Bubble - Bubble Splits

Figure 10. Schematic drawing of bubbles splitting from the roof.

	0.005
	0.002				475 microns
m/s
2	0.001
Viscosity,
	0.0005
	0.0002				101 microns
Kinematic
	0.00005	Material: Ballotini
	0.0001
					64 microns
		Gas
	0.00002	Nitrogen
		Nitrogen
	0.00001	Carbon Dioxide
		5	10	15	20	25
	0

Pressure, bar

Figure 11. Kinematic viscosity versus pressure. (King & Harrison.)

Pressure and Temperature Effects 129

Pressure also appears to cause bubble frequency to increase. This has been reported by both Rowe et al., (1984) and Chan et al., (1987). Rowe et al., (1984) also reported that bubbles were flatter at elevated pressures.

1.5Bed-to-Surface Heat Transfer Coefficient

In general, gas-to-particle or particle-to-gas heat transfer is not limiting in fluidized beds (Botterill, 1986). Therefore, bed-to-surface heat transfer coefficients are generally limiting, and are of most interest. The overall heat transfer coefficient (h) can be viewed as the sum of the particle convective heat transfer coefficient (hpc), the gas convective heat transfer coefficient (hgc), and the radiant heat transfer coefficient (hr).

Eq. (11) h = hpc + hgc + hr

The radiant heat transfer coefficient becomes important above about 600°C, but is difficult to predict. Baskakov et al. (1973) report that depending on particle size, hr increases from approximately 8% to 12% of the overall heat transfer coefficient at 600°C, to 20 to 33% of h at 800°C.

Therefore, for beds operating below 600°C

Eq. (12)

h = hpc + hgc

Botterill et al. (1982) measured the overall heat transfer coefficient as a function of particle size for sand at three different conditions: 20°C and ambient pressure, 20°C and 6 atmospheres, and 600°C and ambient pressure. They found that there was a significant increase in h with pressure for Group D particles, but the pressure effect decreased as particle size decreased. At the boundary between Groups A and B, the increase of h with pressure was very small.

The effect of pressure on the heat transfer coefficient is influenced primarily by hgc (Botterill and Desai, 1972; Xavier et al., 1980). This component of h transfers heat from the interstitial gas flow in the dense phase of the fluidized bed to the heat transfer surface. For Group A and small Group B particles, the interstitial gas flow in the dense phase can be assumed to be approximately equal to Umf /εd . Umf is extremely small for

Pressure and Temperature Effects 131

Increasing temperature has a large effect on h for small particles near and below the Group A/B boundary. Increasing temperature causes h to increase for these particles. The effect of temperature is less pronounced for Group B particles, and h decreases with temperature for Group D materials.

The primary effect of temperature on h is due to the particle convective component of the overall heat transfer coefficient. The particle convective heat transfer coefficient, hpc, depends upon heat transfer from particle “packets” to the surface. It is influenced by factors which affect the solids circulation rate. The greatest resistance to heat transfer for particle convection is when heat has to flow between particles through the gas, which has a relatively low thermal conductivity. Heat transfer is especially low for Group A and B particles, for which the flow of interstitial gas is laminar. Therefore, because increasing the temperature of the gas increases its thermal conductivity, increasing temperature increases hpc. Increasing system pressure has little effect upon hpc except for Group A particles where pressure causes an increased expansion of the dense phase, and greater heat transfer because of the increased area available to transfer heat (Botterill, 1986).

1.6Entrainment and Transport Disengaging Height

Entrainment from fluidized beds is also affected by temperature and pressure. Increasing system pressure increases the amount of solids carried over with the exit gas because the drag force on the particles increases at higher gas densities. May and Russell (1953) and Chan and Knowlton (1984) both found that pressure increased the entrainment rate from bubbling fluidized beds significantly. The data of Chan and Knowlton are shown in Fig. 13.

Increasing gas viscosity also increases the entrainment rate from fluidized beds because the drag force on the particles increases with increasing gas viscosity. Findlay and Knowlton (1985) varied gas viscosity in their experimental system (by changing system temperature) while maintaining gas density constant (by adjusting system pressure) in order to determine the effect of gas viscosity on the entrainment rate from a fluidized bed of char and limestone. They found that increasing gas viscosity significantly increased the entrainment rate from fluidized beds as shown in Fig. 14.

132 Fluidization, Solids Handling, and Processing

Entrainment Rate, kg/m 3

4

3.5

3

2.5

2

1.5

1

0.5

0

0

Material: Sand Gas: Nitrogen Diameter: 30 cm Particle Size:

200 microns

Pressure, bar

4.4

11.2

21.4

31.6

(Knowltonand Hirsan)

0.1

0.2

0.3

0.4

0.5

Superficial Gas Velocity, m/s

Figure 13. The effect of system pressure on entrainment. (Knowlton & Hirsan.)

Pressure and Temperature Effects 133

Entrainment Rate, kg/h

50

Material: 65% Lignite Char/35% Limestone Particle Size: -250 microns

Column Diameter: 20 cm Gas Density: 5.8 kg/m 3

20

10

5

2

Viscosity, kg/m-s

1

0.065 (27 C) 0.115 (427 C)

0.146 (760 C)

0.5
0.05	0.1	0.2	0.3	0.5

Superficial Gas Velocity, m/s

Figure 14. The effect of gas viscosity on entrainment. (Findlay & Knowlton.)

134 Fluidization, Solids Handling, and Processing

Chan and Knowlton (1984) also investigated the effect of system pressure on the transport disengaging height (TDH) over a pressure range of 1 to 30 bar. They found that TDH increased linearly with pressure over this range (Fig. 15). The effect of gas viscosity on TDH has not been determined experimentally by anyone thus far.

TDH, m

3

Material: Sand

Gas: Nitrogen

Column Diameter: 30 cm

2.5Particle Size: 200 microns

Gas Velocity, m/s

2	0.198
	0.229
	0.259

1.5

1

0.5

0

10

20

30

40

Pressure, bar

Figure 15. The effect of pressure on TDH. (Knowlton & Hirsan.)

1.7Particle Attrition at Grids

Particle attrition not due to thermal or chemical reaction effects (i.e., mechanical attrition) occurs much more rapidly in the grid region of fluidized beds than in the bulk of the bed. This is due to high-velocity gas