Ind. Eng. Chem. Process Des. Dev. 1981, 20, 705-708
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COMMUNICATIONS Minimum Fluidization Velocity at High Temperatures Minimum fluidization velocities of sand particles at various temperatures are investigated in a 13.2 cm diameter hot fluidized bed. Qualityof fluidization was fwnd to be good at h@ temperatures. The minimum fluidization velocity is a function of temperature and can be correlated with the changes in gas properties as a function of temperature. The minimum fluidization velocity decreases with increasing temperature for small particles (less than about 2 mm for sand with hot air a s fluidizing medium) but increases for large particles with temperature (>2 mm for sand). Wen and Yu’s equation whiih is developed based on room temperature operation is found to be vali for calculating minimum fluidization velocity at high temperatures. The experimental data do not indicate any increasing or decreasing trend for e,,,, with increase in temperature. Introduction Fluidized bed combustion (FBC) of coal with limestone or dolomite as bed material offers a way of burning highsulfur coals to meet environmental regulations. Fluidized bed combustors typically operate with superficial velocities in the range of 1 to 4 m/s. In order to avoid excessive elutriation losses and to achieve reasonable sorbent utilization, the average bed material size used in FBC is in the range of 2 to 3 mm. The fluidization characteristics of such large particles are not well understood, especially at elevated temperatures. Based on the pressure-drop correlation for fixed beds developed by Ergun (1952) and drag force considerations of a single particle in a multi-particle system, Wen and Yu (1966) proposed two methods for predicting the minimum fluidization velocity. Ergun’s (1952) equation for pressure drop in fixed beds requires the detailed knowledge of sphericity and bed voidage. To circumvent this difficulty, Wen and Yu (1966) introduced two empirical constants for voidage-shape factor functions based on all the available data in literature. Kunii and Levenspiel (1969) simplified Wen and Yu’s equation to approximate minimum fluidization velocity depending on the range of particle Reynolds number. Goroshko et al. (1958) proposed an equation containing the bed voidage at minimum fluidization, e&, based on Ergun’s equation for estimating the minimum fluidization velocity. However, the method of evaluation is sensitive to the value of emf used. It is difficult to estimate emf accurately under all operating conditions, particularly at high temperatures. Botterill and Toeman (1980) have measured the minimum fluidization velocity of small and large particles at high temperature. Goroshko’s equation (1958) was fitted to the data points by choosing emf values at various operating conditions. Recently, McKay and McLain (1980) measured the minimum fluidization velocities of large cuboid particles and found that Wen and Yu’s equation predicts the minimum fluidization velocity reasonably well even a t higher Reynold’s numbers. The present study shows that Botterill’s data and the data in the present investigation can be represented well by the Wen and Yu equation. Experimental Section Apparatus. The experimental technique involves the measurement of pressure drop across the bed material at various velocities at a constant temperature. The exper0196-4305/81/1120-0705$01.25/0
Table I. Experimental Conditions and Properties of Materials Used bed material sand size range of bed material investigated 240-3376 pm fluidizing medium air 2.63 specific gravity of sand temperature range 25-850 “C bed diameter 13.2 cm static bed height 8-10 cm
imental apparatus (Figure 1)consists of 13.2 cm diameter, 30 cm high mild steel column, fitted with a mild steel perforated plate distributor at the bottom. The bed is heated electrically by two ceramic heaters which surround the bed. The bed is well insulated to avoid heat losses. There is a provision for heating the bed with propane also, but the temperature in the bed can be maintained by electric heaters. Pressure taps are provided at appropriate points to measure the pressure drops. A thermocouple is inserted into the bed from the top to monitor the bed temperature. Pressure drop across the bed is determined by subtracting the pressure drop across the distributor from the total pressure drop. Measurement by this technique is compared with that of Botterill and Toeman (1980), where a stainless steel tube with holes drilled around the perimeter of its blocked end was inserted down to the distributor level for measuring the pressure drop across the bed. The agreement between the two methods is good. The experimental conditions and the material properties are shown in Table I. Discussion Pressure Drop Considerations. A number of workers, including Blake (1922), Carman (1937),Kozeny (1927), and Ergun (1952), have developed correlations for pressure drop through fixed beds. Ergun’s correlation can be used for nonspherical particles over a wide range of Reynolds’s numbers. Ergun has shown that the total pressure drop across a fixed bed is dependent on flow rate, voidage, particle shape, and size. The total pressure drop across the bed is the sum of viscous and kinetic energy losses. For low Reynold’s numbers (i.e., small particles and at high temperature), the viscous loss is dominant compared to the kinetic loss and the total pressure drop can be a p proximated by viscous energy loss alone. For high Reynolds numbers (i.e., large particles), the kinetic loss dominates and the total pressure drop across the bed can be 0 1981 American Chemical Soclety
706
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 4, 1981
li
1
Table 11. Values of emf at Various Temperatures (Material: Sand; Size: 462 pm)
t
rii
f
IIn i i oi n
Figure 1. Experimental setup for measuring U d
approximated as kinetic loss alone. The Ergun equation can be written as _ -- 150(1 - C ) ~ ~ L L U 1.75(1 - c)u2p (1) L 4s2t3 d,2 e3.4sdp
-+
Equating the pressure drop across the bed at incipient fluidization to the pressure drop predicted by eq 1, a quadratic equation in Remfis obtained 1,75C1Re,f2 + 150C2Red = Ar (2) (kinetic term) (viscous term) where (3)
The shape factor-voidage functions C1and Cz have been approximated by Wen and Yu (1966) based on more than 250 data points covering a wide range of fluid properties, particle sizes, and densities C1 N 14; Cz 11 (4) Using this approximation, eq 1 can be written as Remf= [(33.7)2+ 0.0408Ar]1/2- 33.7 (5) The validity of eq 5 has been tested at low temperatures for small and large particles over a wide range of Reynolds numbers (McKay and McLain, 1980; Wen and Yu, 1966) and the agreement between the experimental values and those calculated from eq 5 is within f34%. The validity of eq 5 is tested for high-temperature conditions by calculating the values of voidageshape factor functions using experimental values of Ar and Red For low Reynolds number, Red < 5, C2 is calculated by neglecting the kinetic term in eq 2. The calculated values of C2at various temperatures are shown in Figure 2. The assumption that C2 is approximately equal to 11 seems to be valid even at high temperatures as shown in Figure 2. It is clear from eq 2 that, for small Reynolds numbers, 150C2Remf= Ar or jiUd = constant. Viscosity increases with increase in temperature for a gas so that U, decreases with temperature.
mi
emf
temp, “C
from eq 1
from eq 6
18 281 391 551 611 625 786 921
0.437 0.419 0.431 0.451 0.451 0.446 0.455 0.461
0.415 0.385 0.395 0.410 0.411 0.404 0.414 0.412
For large Reynolds numbers, 1.75ClRed2 = Ar or pUd2 = constant. Density of gas decreases with increase in
temperature so that Ud increases with temperature. Values of td are calculated from the experimental data of Botterill et al., using Ergun’s and Goroshko’s equations, and the results are shown in Table 11. emf does not show an increasing trend with temperature. For sand and limestone particles, it is unlikely that shape factor changes with temperature. Since the voidage-shape factor function, C2,is essentially constant (Figure 2), e& does not show any decreasing or increasing trend with temperature. Goroshko et al. (1958) proposed the following correlation for estimation of the minimum fluidization velocity Ar =
150.emf
emf
This equation requires the estimation of emf. Recently, McKay and McLain (1980) have studied the fluidization characteristics of cuboid particles of various sizes and correlated their data with the equation
This equation also requires the estimation of under various operating conditions. It was shown by McKay and McLain (1980) that their data correlated reasonably well with Wen and Yu’s equation. Minimum fluidization velocities of different particle sizes at elevated temperatures are determined experimentally and the calculated values using different equations are compared in Figures 3 to 6. It can be seen that the Botterill data and the data from the present investigation agree well with the values calculated from Wen and Yu’s equation. It is clear from Figure 6 that Ud increases with increase in temperature for large particles where kinetic forces are dominant.
Ind. Eng. Chem. Process Des. 0 lhla l a r k
240 U SAND
-
__
0 3 2 c Re c 0 74
I
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--Wna L VI [11111 - O m a h l o I C q :0 4 2 I - tnrlIn I ~r :o B cm, :o 42 1
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---
/I//
400
o
800
600
'
I 200
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3376 am SA10 o EWl lthla work
-WEN
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l o I
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Figure 6. Effect o f temperature on U,, 3376-pm sand.
Figure 3. Effect o f temperature on U,, 240-pm sand. 20,
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R
d
Dev., Vol. 20, No. 4, 1981
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200 I
2 mm for sand with hot air as fluidizing medium) but increases for large particles with temperature (>2 mm for sand). (2) For small particles and a t high temperature, the viscous forces are dominant. For larger particles, kinetic forces are dominant. (3) The voidage-shape factor function approximations introduced by Wen and Yu (1966) are found to be valid even at high temperature. Wen and Yu's equation was shown to be valid even at high Reynolds numbers for very large particles (McKay and McLain, 1980).
EIPl WEN L VU 11966 1
1
I
400
600
.
I
800
I
1:c
Figure 4. Effect o f temperature on U,, 462-pm sand.
Acknowledgment The authors wish to acknowldege the support of this work by the Energy Research Center of West Virginia University under Grant ST-81-CC-2. The assistance of Che-An Ku in preparing the figures is appreciated. Nomenclature Ar = Archemedes number, (dp3p(pp- p ) g ) / r 2 C1= voidage-shape factor function, l/4sed3 Cz = voidage-shape factor function, (1- ed)/4s2ed3 d, = particle diameter, m g = gravitational acceleration, m L = bed height, m AP = pressure drop, N m-2 Re = Reynolds number based on particle diameter, U d # / p Remf= Reynolds number at minimum fluidization velocity, UmfdPPIr
0
1
I
200
400 T.
1
I
600
BOO
I C
Figure 5. Effect o f temperature on Ud,1310-pm sand.
For vesicular particles such as particles of coke with rugged edges, it has been shown by Feldmann et al. (1972) that the minimum fluidization velocity is greater than that calculated from the Wen and Yu equation. This is because such particles tend to hook at the edges and interlock with each other and behave as if they were larger particles. Conclusions (1)The minimum fluidization velocity decreases with increasing temperature for small particles (less than about
U = fluid superficial velocity, m s-l Ud = minimum fluidization velocity, m s-l Greek Letters e = voidage, dimensionless emf = voidage at minimum fluidization, dimensionless 4s = sphericity, dimensionless p = fluid viscosity, N s m-2 p = fluid density, kg m-3 p, = particle density, kg m-3 Literature Cited Blake, F. C. Trans. Am. Chem. Eng. 1922, 14, 415. Botterlil, J. S. M.; Toeman, Y. Proceedings of the 2nd Englneering Foundation Conference on Fluidization at Hennlker, 1980. p 93. Carman, P. C. T"I Inst. Chem. Eng. 1997. 15, 150. Ergun, S. Chem. Eng. prog. 1952, 48. 89. Feldmann, H. F.; Wen, C. Y.; Simons, W. H.; Yavorsky, P. M. Paper presented at the 71st National Meeting, AIChE, Dallas, Texas, 1972.
