AN ANALYSIS OF LOOP SEAL OPERATIONS IN A CIRCULATING FLUIDIZED BED by alextt

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									0263±8762/00/$10.00+0.00 q Institution of Chemical Engineers Trans IChemE, Vol. 78, Part A, October 2000

AN ANALYSIS OF LOOP SEAL OPERATIONS IN A CIRCULATING FLUIDIZED BED
P. BASU and L. CHENG*
Mechanical Engineering Department, Dalhousie University, Nova Scotia, Canada *Institute for Thermal Power Engineering, Zhejiang University, PR China

T

he operation of a loop seal in a circulating ¯uidized bed is studied on the basis of pressure balance of the circulation loop. The sharp-crested theory of free surface ¯ow is applied to analyze the solids ¯ow rate through a loop seal. Factors, which in¯uence the solids ¯ow rate through the loop seal, include loop seal air velocity, initial bed inventory, standpipe size, loop seal slit size and particle size. The solids ¯ow could occur only between two limiting values of each of those parameters. The analysis also presented pressure distributions along the loop for different circulation rates. Results from above theoretical analyses were compared with experimental results. A good agreement between the results con®rmed the validity of the present analysis. Keywords: loop seal; solids recycle device; circulating ¯uidized bed

INTRODUCTION A typical circulating ¯uidized bed (CFB) system comprises a fast ¯uidized bed (riser), a gas-solid separator, a standpipe (dipleg) and a solids recycle system. Solids particles move around these components in sequence and the solids recycle system is a key component of the CFB loop. A nonmechanical valve is commonly used in this system because it is robust, inexpensive and simple in construction. Serious erosion of moving parts, high solids ¯ow rate requirement and high operating temperature preclude the use of mechanical valves. Solids in a non-mechanical valve are moved by air or gas. In certain sections of the valve the solids exhibit a liquid-like behaviour when aeration air is added. The solids ¯ow through the valve when the drag of the aeration air exceeds the resistance holding the solids together. Several types of non-mechanical solid recycle valves are used in a CFB system. They are L-valve, V-valve, J-valve, seal pot and loop seal (¯uo seal). Some data are available on L-valve1,2 and V-valve3 but information on loop seal is very limited. Some experimental investigations4,5 were reported, but a comprehensive analysis of the performance of the loop seal is not available in published literature. The present paper presents an analysis of the performance of the loop seal using free surface theory and pressure balance equations. Based on their experiments on a 200 mm ´ 200 mm cross section loop seal, Luo et al.4 presented empirical equations to calculate the standpipe height and solids ¯ow rate. The accuracy and general applicability of their equations have not been veri®ed. Horio6 discussed the total pressure balance around a CFB loop taking the loop seal as a simple ori®ce or valve. The pressure drop across the seal was obtained by an empirical equation. None of the models consider the in¯uence of solids inventory on solids recycle rates. 991

The present work analyses the loop seal taking into account all relevant factors including loop seal air velocity, initial bed inventory, standpipe size, loop seal slit size and particle size. THEORETICAL ANALYSIS Figure 1 shows a CFB loop with a loop seal where solids are in a fast ¯uidized condition in the riser. Particles enter the cyclone after they exit from the riser and particles, separated in the cyclone, accumulate in the standpipe. The standpipe drops the solids into the loop seal, which is split into two sections, supply and recycle chambers (Figure 1). These two sections are connected by a rectangular opening, called slit. Both chambers can be ¯uidized from the bottom. The recycle chamber has an over¯ow weir, which connects it to a discharge pipe leading the solids to the riser. Solids collected in the standpipe, drop into the supply chamber. Aeration given at the bottom of the loop seal helps this solids move through the slit into the ¯uidized recycle chamber. The ¯uidized solids spill over the weir into the recycle pipe, which leads the solids into the riser. Thus the solids move around the CFB loop without a mechanical pump. The pressure difference between the standpipe and the riser drives the solids through the system. So under a steady state, there would be a pressure equilibrium around the loop. Pressure Balance in a Circulation Loop For a pressure balance the algebraic sum of pressure drop across each section of the circulation loop should be equal to zero. Pa Pb Pe Pb Pf Pc Pf Pc Pg Pd Pg Pd Pa Pe 0 1

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BASU and CHENG

Figure 1. Loop seal solids recycle system.

Point D in Figure 1 is the solids surface in the standpipe. The friction on the discharge pipe (G-A) can be neglected as it is rarely full. Also, the section of the cyclone (C-D) offers very low resistance. So, if any resistance at the exit of the riser is neglected, Pb Pc 0, Pc Pd 0 and Pg Pa 0 can be written. The above pressure balance equation now simpli®es as: Pa Pb Pd Pe Pe Pf Pf Pg 0 2 Pressure Drop in the Riser The pressure drop along the riser height is determined by its axial voidage pro®le. Two main methods are used to estimate the axial voidage pro®le. The axial voidage pro®le may be divided into two parts, a denser section and a leaner section. The transition point between these two may be estimated for riser reactors at a given set of operating and geometric conditions7 . In a CFB boiler this point coincides with the secondary air injection point8 . So, the axial voidage pro®le in the leaner section may be calculated using the entrainment model of Kunii and Levenspiel9 . The voidage decay constant of the leaner section and voidage of the lower dense bed were based on experimental results9 . Thus, the bed is divided into lower dense region and

upper dilute region along the bed height. The total pressure drop across the riser A-B, also includes the frictional loss including acceleration loss, D Pab . Then the total pressure drop Pa Pb becomes: Pa Pb 1 «
den

ghden

1

«

dil

ghdil

D Pab

3

Where « den and « dil are voidages in lower dense region and upper dilute region respectively, hden is dense region height in bed, hdil is the dilute region height, which is riser height less the dense region height. Kunii and Levenspiel10 compared voidages in the lower dense regions of a ¯uidized bed (Table 1). A typical value for the fast ¯uidized bed is chosen in the present model calculation. Bed internals may affect the axial voidage pro®le. There is also an effect of the bed exit11 . However, if one assumes that the furnace is so tall that all particles are completely
Table 1. Comparison of voidage in the lower dense region of a ¯uidized bed. Fluidized bed Bubbling bed Turbulent bed Fast ¯uidization Voidage 0.45±0.60 0.60±0.78 0.78±0.84

Trans IChemE, Vol 78, Part A, October 2000

AN ANALYSIS OF LOOP SEAL OPERATIONS IN A CIRCULATING FLUIDIZED BED dispersed near its exit, and there is no re¯uxing, then the solids ¯ux leaving the bed may be given by the following equation: Gs 1 «
dil

993

expansion, derived by King17 , is used. «
r

»s Ab

4

ur ur

1 2

10

Where « dil is the voidage in the upper region, up is the absolute velocity of solids particle. As the voidage is very high, up can be approximated by the equation12 : up ug ut 5 Where ug is the super®cial gas velocity in the bed, ut is the particle terminal velocity. Pressure Drop in the Standpipe Particles move down slowly as a moving packed bed ¯ow in the standpipe. Assume the voidage to have identical values in the standpipe and in the supply chamber. So, the pressure drop per unit length is obtained by a slight modi®cation of the Ergun equation13 : Pe Ls Pd 150 1 « « 3 s
3 s

where ur is the ¯uidizing velocity in the recycle chamber. Solids Flow Rate at the Weir of the Recycle Chamber Once the recycle chamber is ¯uidized, the solids in it ¯ow like a liquid. The ¯uidized bed expands above the height of the weir (Figure 1), and the solids ¯ow into the riser through the inclined recycle pipe. The inclined pipe is generally not ®lled with solids. So the over¯ow rate of solids is a direct function of excess bed height above the weir, which increases with the ¯uidizing velocity. This situation is similar to that of free surface ¯ow of a liquid over a sharp crested weir. So from sharp-crested theory18 the volume ¯ow Qs of ¯uidized solids can be written as: Qs cg1/2 D h3/2 W 11 where c is an experimentally derived constant, D hr is the bed level above the weir, W is the width of the weir and g is the acceleration due to gravity. Thus the solids ¯ow rate Gs can be calculated by: Gs 1 «
r

mg D u w s dp
3 s 2 2

1.75 1 « « 3 s

»g D u w s dp

6

Where « s is the solids voidage in the standpipe, D u is the relative velocity of gas with respect to the solids.

»s Qs

c1

«

r

»s g1/2 D h3/2 v r

12

D u

uo

us

7

The super®cial rise velocity of gas up the standpipe, uo , is small. This ¯ow rate is a fraction d of the air ¯ow of the loop seal, Q. Here d is taken as 0.095 from Cheng and Basu14 . Pressure Drop Across the Slit Solids from the supply chamber ¯ow to the recycle chamber through an opening (slit) at the bottom of the division wall between these two chambers. The pressure drop across this opening can be calculated by the following equation suggested by Cheng and Basu14 . It is based on the experimental data of Jin et al.15 and Kuramoto et al.16 , Pe Pf 0.66 As Asc
1.2

Assuming that the total amount of solids and their size distribution do not change during operations, the sum of solids in each component of the CFB loop system should be equal to the original solids inventory M0 . Thus a material balance gives us the following equation, 1 «
den

»s Ab hden « «
s

1

« lsc

dil

»s Ab hdil 1 M0 «
s

1 1

»s Asp Ls »s Arc hr

»s Asc lsc 13

r

D hr

Gs

8

where As and Asc are cross section areas of the slit and the supply chamber, respectively. Pressure Drop in the Recycle Chamber Solids in the recycle chamber are ¯uidized by the air entering from its bottom. The bed level must rise above the weir (Figure 1) in order to over¯ow into the recycle pipe. Considering the bed to expand to a height D hr over the recycle chamber weir height hr (Figure 1): Pf Pg 1 «
r

where Ab , Asp , Asc and Arc are areas of the riser, standpipe, supply chamber and recycle chamber respectively. Neglecting the frictional loss and substituting equations (3), (6), (8) and (9) into (2), relations among different parameters are established. The above model can be used for both understanding the operating behaviour and the design of a loop seal. For example, the solids circulation rate and gas velocity in the riser may be speci®ed as input parameters, and then compute the aeration rate required in the loop seal. To validate the above model, it would be used ®rstly to interpret the observed behaviour of the loop seal, then the results compared. EXPERIMENTS The tests were carried out in a 152 mm diameter circulating ¯uidized bed with a 100 mm width rectangular loop seal. The system is shown in Figure 1. Three size sands, 480 mm, 355 mm and 250 mm were used in the tests and two techniques were used to measure the solids ¯ow rates. Experimental details are reported in Basu et al.5 so they are not reported here.

hr

D hr »s

9

For ®rst approximation, a simpli®ed expression for bed Trans IChemE, Vol 78, Part A, October 2000

994 RESULTS AND DISCUSSION

BASU and CHENG loop seal aeration rate results in an increased solids ¯ow through the loop seal. This can be explained by equation (12), which shows that the solids ¯ow rate increases when D hr increases. Equation (10) shows that higher aeration rate or higher velocity expands the bed in the recycle chamber and increases the D hr . However, the pressure seal of solids in the standpipe is broken if the loop aeration is increased continuously without a corresponding increase in the riser gas velocity. This de®nes the maximum operable velocity of the loop seal. Similarly, if the loop seal velocity is reduced much, the pressure drop across the standpipe solids falls below that required to drive the solids. This de®nes the lower limit of loop seal aeration. The lines in Figure 2 give the predicted operating range of the aeration velocity. Within this operating range, the solids ¯ow rate increases with loop seal air velocity. The solids ¯ow also increases as the riser gas velocity increases. However, at a higher riser gas velocity the operating range of the loop seal aeration decreases. Thus, the control range of the solids ¯ow rate reduces at a higher riser velocity. A limited change in the aeration rate gives a very large change in the ¯ow rate, and ®nally there is a breakdown in the ¯ow. Since the solids carrying capability of the riser increases at higher riser velocities, the solids level in the standpipe increases. This exerts a higher hydrostatic pressure on the loop seal moving more solids from the standpipe. So the solids recycle rate increases even when the loop seal aeration rate is unchanged. Figure 3 shows how the solids ¯ow rate increases with the riser gas velocity at a ®xed loop seal aeration rate. A high riser velocity results in high solids ¯ow from the riser to the standpipe. This results in a higher relative velocity between gas and the solids at a given supply chamber aeration. This gives a higher pressure drop across the standpipe. Higher resistance in the standpipe would cause less air to ¯ow through the supply chamber to maintain the pressure balance. This would increase the air ¯ow through the recycle chamber which in turn increases the recycle rate. The solids circulation rate, predicted from the present models, were plotted on Figure 2 along with experimental data. The latter was shown by points while the predictions are shown by lines. It shows a good agreement between the model and experiments.

The loop seal operates steadily when the pressure balance equation (1) is satis®ed but its operation becomes irrational or it stops entirely when the pressure balance is lost. A very common failure occurs when the pressure drop across the standpipe falls below that required to drive the solids through the loop seal and into the riser. Under this condition, the aeration air takes a short cut from the loop seal to the cyclone directly through the standpipe. When the riser operates at a high gas velocity, the solids transfer rate from the riser to the cyclone and standpipe increases. If there is no corresponding increase in the loop seal aeration, the solids return rate will be less than that leaving the riser. So there would be an imbalance in solids ¯ow rate breaking down the loop system pressure balance. Similarly, the balance breaks down with a combination of low riser gas velocity and high loop seal aeration air rate. Under this condition, the solids height in the standpipe drops lowering to an extent that the loop seal air takes the low resistance path through the cyclone, resulting in a drop in cyclone separation ef®ciency. This adversely affects the operation of a CFB. In the present model, the calculation was terminated either when an imbalance in the loop pressure or air bypassing in the standpipe occurred. Air by-passing happens when the relative velocity of gas and solids is higher than the minimum ¯uidizing velocity of the solids. Under this condition, further increases in relative velocity do not increase the resistance of the standpipe. So, the pressure drop in the standpipe reaches its peak making the solids recycle unstable. In all calculations, it is found that the loop system operated only within a certain range of loop seal aeration air rate for a given riser gas velocity. When the riser gas velocity varies the operating range of the loop seal aeration also changes. Besides this the solids inventory also affects the operating range of the loop seal. Reasons for these behaviour are explained in subsequent sections. Solids Flow Rate Figure 2 shows the relationship between the solids ¯ow rate and the loop seal aeration velocity at different riser gas velocities. At a ®xed riser gas velocity, an increase in the

Figure 2. A comparison of theoretical and experimental variation of the solids ¯ow rate with loop seal air velocity (points are experimental data at different loop seal slit height).

Figure 3. Solids ¯ow rate increases with the super®cial velocity at a ®xed loop seal air rate.

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AN ANALYSIS OF LOOP SEAL OPERATIONS IN A CIRCULATING FLUIDIZED BED

995

Figure 4. Solids height in standpipe decreases with increasing loop seal air velocity.

Figure 6. Pressure pro®le along the circulation loop at different solids circulation rate around the CFB loop.

Solids Height in Standpipe Figure 4 shows that the height of solids in the standpipe decreases with increasing loop seal aeration rate. As the loop seal aeration air increases, more solids would ¯ow out of the standpipe, giving a higher circulation rate. This would, in turn, make the riser denser. Thus, there is an increase of solids inventory in the riser at the cost of that in the standpipe. This causes the solids level in the standpipe to drop. There is, however, a minimum solids height in the standpipe for a given solids inventory in the system. From Figure 5 it is found that the pressure drop per unit height Pe Pd /Ls increases with the gas-solid relative velocity in the standpipe. So, if the pressure across the riser (Pa Pb ) increases for any reason, a larger fraction of the aeration moves to the standpipe to increase the standpipe head (Pe Pd ). However, it can increase only up to a certain maximum valve. Thus if Ls drops too far, the resultant (Pe Pd ) will not be able to balance the increased pressure drop (Pa Pb ) in the riser. So a solids height lower than the minimum will result in an air by-pass through the standpipe. It should be noted that a higher height of solids in the standpipe does not mean that a higher pressure is produced. The pressure drop in the standpipe is determined not only by the solids height but also by the relative velocity between solids and gas (Figure 5). If the loop seal aeration rate is too small, the pressure produced by the solids in the standpipe will not be enough to balance the loop system pressure and this would stop solids recycle rate (Figure 4).

This aeration rate, as explained earlier, de®nes the lower operating limit of the loop seal. Pressure Drops and Pressure Balance Pressure drops across different sections of the CFB loop vary with changes in the loop seal aeration rate. As discussed above, the solids ¯ow rate increases with the loop seal aeration rate, and so does with the solids inventory in the riser. Thus, the pressure drop in the riser increases with the increment in the loop seal aeration rate. The riser pressure drop also increases with the riser gas velocity at a given aeration rate. The pressure drop across the standpipe is a combined result of the solids height and the relative velocity between solids and gas in it (Figure 5). With increasing aeration rates the relative velocity increases, but the solids height decreases in the standpipe (Figure 4). This explains why the rate of increase of pressure drop drops off at higher aeration rates. The pressure drop across the opening between the two chambers of the loop seal increases with a rise in the loop seal aeration rate. The slit is like an ori®ce through which gas-solids ¯ow. At higher aeration rates, there is a higher ¯ow through the slit which in turn causes higher pressure drops. The equation used to calculate the slit pressure drop was taken from the experimental data of Jin15 and Kuramoto16 . The voidage of the recycle chamber increases as the loop seal aeration rate increases. Thus, the pressure drop in the recycle chamber decreases with the loop seal aeration rate. The bed expansion equation (10) gives a steady decline in bed density except at very high super®cial gas velocities. Figure 6 shows the pressure drops along the whole loop and their change at different solids ¯ow rates. This ®gure explains the pressure balance and shows how it is maintained at varying solids ¯ow rates. Similar pressure distributions around the CFB loop were found in the experiments of Basu et al.5 . Effect of Solids Inventory Li and Kwauk19 used the results of Weinstein et al.20 to suggest that axial voidage pro®les are affected by the solids inventory in the system. This implies that the system solids inventory has an effect on the pressure distribution

Figure 5. Variation of pressure drop across the unit height of the standpipe with increasing gas solids slip velocity in the standpipe.

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BASU and CHENG

Figure 7. Solids ¯ow rate increases with loop seal air velocity at different solids inventories (ug = 3 ms ±1).

Figure 9. Solids ¯ow rate varies with the loop seal air rate at different slit heights (ug = 3 ms ±1).

around the loop. Similar results were obtained by the present work. Figure 7 shows that at a ®xed aeration rate the solids ¯ow rate changes with the system solids inventory. At a given loop seal aeration rate, the solids ¯ow rate increases as the solids inventory increases. And the operational range of the loop seal aeration rate also increases with the solids inventory. Effect of Standpipe Size In¯uence of standpipe diameter on the solids ¯ow rate is shown in Figure 8. It shows that a smaller size standpipe can handle a given solids ¯ow rate at a smaller loop seal aeration rate. However, this decreases the solids storage capacity in a smaller standpipe. There would be a large change in the solids height in the standpipe for a relatively small change in the solids ¯ow rate. This makes the system less stable. Effect of Loop Seal Slit Height The slit height does not play an important role as long as it does not provide signi®cant resistance (Figure 9). The solids ¯ow rates do not change much at different slit heights. This is a result of smaller values of the linear velocity of solids through the slit (0.005 0.06 m s 1 in Figure 9) which offers a resistance small compared to that in other components in the loop.

Effect of Particle Size Solids particle size has an effect on the solids ¯ow rate (Figure 10). Smaller size particle has higher solids ¯ow rate at a ®xed loop seal aeration rate. At a given riser gas velocity, smaller size of solids has lower umf , and therefore, higher relative velocity (ug umf ). This gives larger pressure drops across the standpipe, which result in higher solids ¯ow rate through the loop seal. Effect of Adjusting Parameters Finally, the adjusting parameters in the model are discussed. There are two main adjusting parameters in the model calculation. One is the fraction of the loop seal air entering the supply chamber of the loop seal and this parameter can be obtained from experiments14 . It was taken as a constant in the present model and it might change with the pressure distribution in the loop seal. A lower value gives lower solids ¯ow rate at a given loop seal aeration rate, but the operating range of the loop seal air rate increases (Figure 11). Another parameter is the constant c of the sharp-crested theory in the equation (11). As the pressure drop across this section is not large compared to that in other places, the in¯uence of c can be neglected.

Figure 8. Solids ¯ow rate increases with loop seal air velocity for different standpipe sizes (ug = 3 ms ±1).

Figure 10. The variation of solids ¯ow rate with loop seal air velocity for different particle sizes (ug = 3 ms ±1).

Trans IChemE, Vol 78, Part A, October 2000

AN ANALYSIS OF LOOP SEAL OPERATIONS IN A CIRCULATING FLUIDIZED BED
Q Qs u0 ug umf up ur us usg ut D u W F « Figure 11. Solids ¯ow rate increases with the loop seal air velocity at different air fractions (ug = 3 ms ±1). « « «
s

997

d
den dil r s

mg

CONCLUSION A simple model of the operation of the loop seal in circulating ¯uidized beds is developed on the basis of pressure balance. It showed that the sharp-crested theory can be applied to estimate solids ¯ow rate through the loop seal. The loop system operated only within a certain range of loop seal aeration rate for a given riser gas velocity. At a given riser gas velocity the system can not be made to operate well at any solids recycle rate even through adjustments of the loop seal aeration. When the riser gas velocity varies the operating range of loop seal aeration rate also changes. Other observations made are: 1) The solids ¯ow rate increases with the loop seal air velocity. 2) The solids inventory in the system has an effect on the solids ¯ow rate. At a given loop seal aeration rate the solids ¯ow rate increases as the solids inventory increases. 3) The solids ¯ow rate decreases as the standpipe size increases at a certain loop seal air rate. 4) The slit size of the loop seal does not have a major effect on the solids ¯ow rate if the slit is adequately wide. 5) At a given loop seal aeration rate, smaller particles will have a higher solids ¯ow rate. NOMENCLATURE
Ab Arc As Asc Asp c dp ds g Gs hg hden hdil hr D hr Ls lsc M0 Pi D Pi j cross-section area of the riser, m2 area of the loop seal recycle chamber, m2 area of slit between two chambers in the loop seal, m2 cross-section area of the supply chamber, m2 cross-section area of the standpipe, m2 constant in equations (11) and (12) solids particle diameter, m standpipe, diameter, m acceleration due to gravity, m s 2 solids ¯ow rate, kg s 1 loop-seal gap height, m dense region height in the riser, m dilute region height in the riser, m recycle chamber height, m suspended solids height above the weir, m height of solids above the air distributor of supply chamber, m height of supply chamber, m solids inventory of the system, kg pressure at Point I, i a, b, c, d, e, f, g, Pa friction loss including acceleration loss in IJ section, ij ab, bc, cd, de, ef, fg, ga, Pa

»g »s

air ¯ow of the loop seal, m3 s 1 solids volume ¯ow, m3 s 1 velocity of gas in the standpipe, m s 1 velocity of gas in the riser, m s 1 minimum ¯uidizing velocity, m s 1 absolute velocity of solids particle, m s 1 ¯uidizing velocity in the recycle chamber, m s 1 super®cial velocity of solids in the standpipe, m s 1 actual gas velocity in the standpipe, ms ±1 particle terminal velocity, m s 1 super®cial gas velocity in the standpipe, m s 1 weir width, m sphericity of a particle, average fraction of the overall air entered the supply chamber of loop seal, voidage in lower dense region of the riser, voidage in upper dilute region of the riser, voidage in the recycle chamber, voidage in the standpipe, viscosity of gas, kg ms 1 density of gas, kg m 3 density of solids, kg m 3

REFERENCES
1. Knowlton, T. M., 1988, Non mechanical solids feed and recycle devices for circulating ¯uidized beds, Circulating Fluidized Bed Technology II, Basu, P. and Large, J. F. (eds) (Pergamon Press, Oxford) pp. 31±41. 2. Yang, W. C., 1993, L-valve equations, Powder Technology, 77: 49±54. 3. Chong, Y. O., O’Dea, D. P., Leung, L. S. and Nicklin, D. J., 1988, Design of standpipe and non-mechanical V valve for a circulating ¯uidized bed, Circulating Fluidized Bed Technology II, Basu, P. and Large, J. F. (eds) Pergamon Press, Oxford) pp. 493±500. 4. Luo, Z. Y., Ni, M. J., Zhou, J. H., Cheng, L. M., Chang, Z. J. and Cen, K. F., 1989, Solids recycle systems for circulating ¯uidized beds, Proceedings of the 1989 International Conference on Fluidized Bed Combustion, Manaker, A. M. (ed), (ASME, New York) pp. 557±562. 5. Basu, P., Luo, Z. Y., Boyd, M., Cheng, L. M. and Cen, K. F., 1999, An experimental investigation into a loop seal in a circulating ¯uidized bed, 6th Inter Conf on Circulating Fluidized Beds, August 22±27, Wurzburg, Germany pp. 805±810. 6. Horio, M., 1997, Circulating ¯uidized beds, Grace, J. R., Avidan, A. A. and Knowlton, T. M. (eds), Chapter 2, Hydrodynamics, (Chapman & Hall, London) pp. 61±65. 7. Li, J. H., Tung, Y. K. and Kwauk, M., 1988, Axial voidage pro®les of fast ¯uidized beds in different operation regions, Circulating Fluidized Bed Technology II, Basu, P. and Large, J. F. (eds), (Pergamon Press, Oxford) pp. 193±203. 8. Basu, P. and Fraser, S. A., 1991, Circulating ¯uidized bed boilersÐ design and operations, Chapter 2, Hydrodynamics, (ButterworthHeinemann, Boston) pp. 43±44. 9. Kunii, D. and Levenspiel, O., 1990, Flow modeling of fast ¯uidized beds, Circulating Fluidized Bed Technology III, Basu, P., Horio, M. and Hasatani, M. (eds) (Pergamon Press, Oxford) pp. 91±98. 10. Kunii, D. and Levenspiel, O., 1991, Fluidization Engineering, 2nd edn, Chapter 3, Fluidization and Mapping of Regimes, pp 80±82; Chapter 8, High-velocity Fluidization, p 200; Chapter 15, Circulation Systems, pp 374±375 (Butterworth-Heinemann, Boston). 11. Werther, J., 1993, Fluid mechanics of large-scale CFB units, Circulating Fluidized Bed Technology IV, Avidan, A. A. (ed) (AIChE, New York) pp. 1±14. 12. Rhodes, M. J., 1990, Principles of Powder Technology, M. J. Rhodes (ed), Chapter 7, Pneumatic Conveying (John Wiley & Sons, New York) pp. 148. 13. Ergun, S., 1952, Fluid ¯ow through packed columns, Chemical Eng Progress, 48 (2): 89±94. 14. Cheng, L. M., Basu, P., 1999, Effect of pressure on loop seal operation for a pressurized circulating ¯uidized bed, Powder Technology, Vol 103: 203±211. 15. Jin, Y., Wang, Z. W., Zhu, J. X. and Yu, Z. Q., 1985, A study on particle ¯ow between ¯uidized beds, Fluidization ’85, Science and Technology, Kwauk, M. and Kunii, D. (eds), (Science Press, Beijing China, Elsevier, Amsterdam) pp. 172±185.

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BASU and CHENG
Kunii, D. and Toei, R. (eds), (Engineering Foundation, United Engineering Trustees, Inc., New York) pp. 299±306.

16. Kuramoto, K., Kunii, D. and Furusawa, T., 1986, Flow of dense ¯uidized particles through an opening in a circulation system, Powder Technology, 47: 141±149. 17. King, D. F., 1989, Estimation of dense bed voidage in fast and slow ¯uidized beds of FCC catalyst, Fluidization VI, Grace, J. R., Shemilt, L. W. and Bergougnou,M. A. (eds), (Engineering Foundation, United Engineering Trustees, Inc, New York) pp. 1±8. 18. Whites, F. M., 1994, Fluidized Mechanics, 3rd ed, (McGraw-Hill, Inc, New York) pp. 622±623. 19. Li, J. H. and Kwauk, M., 1994, Particle-¯uid two-phase Flow, the Energy-minimization Multi-scale Method, (Metallurgical Industry Press, Beijing) pp. 140±148. 20. Weinstein, W., Graff, R. A., Meller, M., Shao, M. J., 1983, The effect of the imposed pressure drop across a fast ¯uidized bed, Fluidization,

ADDRESS
Correspondence concerning this paper should be addressed to Dr P. Basu, Department of Mechanical Engineering, Dalhousie University, Halifax, Nova Scotia, Canada B3J 2X4. E-mail: Prabir.Basu@Dal.Co The manuscript was communicated via our International Editor for Canada, Professor Philippe Tanguy. It was received 19 March 1999 and accepted for publication after revision 6 September 2000.

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