Ind. Eng. Chem. Res. 2008, 47, 4953–4961
4953
Prediction of Hydrodynamic Properties of Mixed-Particle Systems and Theoretical Analysis of Loop Pressure Profile in a CFB Unit Mitali Das, B. C. Meikap,* and R. K. Saha Department of Chemical Engineering, Indian Institute of Technology (IIT), Kharagpur, Dist: Midnapur(W), West Bengal, Pin - 721 302, India
The hydrodynamic behaviors of mixed system of particles were investigated in a circulating fluidized bed (CFB) unit consisting of fast column (riser) with an inner diameter of 0.1016 m and a height of 5.62 m. Particle mixtures containing a Geldart group-A-like fluid catalytic cracking (FCC) catalyst with group-B-like sand and iron ore with coal were used to study the hydrodynamic features including static pressure, voidage, and loop pressure profile. The mixed system consisting of FCC catalyst and sand contained 20, 50, and 80 mass % sand, and the coal-iron ore mixture contained 80 mass % coal. The superficial air velocity ranged between 2.01 and 4.681 m/s, and the corresponding mass fluxes were 12.5-50 kg/(m2 s). A comparison of the available experimental values for static pressure profiles at different operating conditions for mixedparticle systems shows good agreement with those predicted from the single-particle systems. Using experimental data on the loop pressure balance, a simplified theoretical analysis was performed to predict the pressure profile in the CFB loop. The deviations between the two sets of values are within reasonable limits of accuracy. Introduction Fast fluidized beds (FFBs) represent an emerging technology, having applications in chemical, mineral, and metallurgical industries, as well as in the the power sector. FFB technology assumes importance where high specific transfer rates, large solid throughputs, and thermal uniformity within the reactor are required. A fast fluidized bed has been described by Yerushalmi et al.1 as a dense entrained suspension, characterized by an aggregative state in which much of the solid is segregated in relatively large and densely packed groups of particles. The solid is highly turbulent and displays extensive back-mixing. As a high velocity gas is used to circulate an appropriate quantity of solid particles during operation, it is possible to maintain almost all of the hydrodynamic regimes of a fluidized-bed system, from bubbling to pneumatic conveying, with FFBs lying in the middle. A fast bed consists of a dense phase near the bottom, a dilute phase at the top, and a transition region in between. With a gradual increase in gas velocity for a fixed-solids circulation rate, the dense phase at the bottom further expands and slowly transforms into a dilute bed. Similarly, with an increase in the solids circulation rate at a constant gas velocity, the height of the dense zone at the bottom steadily rises, and the system is said to be converted into a dense-bed transport regime. A review of the literature indicates that studies on the effects of operating pressure and voidage on gas-solid fluidized-bed behavior with the development of coal combustion processes have drawn immense interest among researchers since as early as the 1970s. These studies began with discussions of the effects of pressurized conditions on nonbubbling fluidization and the presentation of several methods for improving the prediction of the minimum fluidization velocity at elevated pressure. The effects of pressure on nonbubbling bed expansion in the region between minimum fluidization and minimum bubbling velocities were considered, and areas of uncertainty or disagreement were * To whom correspondence should be addressed. Tel.: +91-3222283958. Fax: +91-3222-282250. E-mail:
[email protected] or
[email protected].
highlighted. Recently, only limited research has been reported on mixed-particle systems. Batsevych et al.2 studied the dynamic properties of a binary mixture of magnetic and nonmagnetic particles using the method of nonequilibrium statistical operator, deriving and analyzing the generalized hydrodynamic equations. The hydrodynamics of a mixed-particle system containing millet and ragi in which the millet had an average diameter 2250 µm and a density of 1163.9 kg m-3 and the ragi particles had an average diameter of 1500 µm and a density of 1310.4 mg m-3 with a mass fraction of 0.5 was studied in an annular circulating fluidized-bed drier. Dilute-phase flow and dense-phase slugging flow regime models were verified for this system by Sivasanmugam and Lakshmi.3 Ajbar et al. 4 studied the hydrodynamic behavior of Geldart group D particles mixed with a small proportion of Geldart group B particles using pressure fluctuations data. Recent research on the hydrodynamics and mixing of biomass particles in fluidized beds has been reviewed by Cui and Grace.5 A critical review of the literature dealing with the hydrodynamics of mixed-particle systems reveals that the work carried out in the past decade includes particles within a narrow range. The studies were mainly carried out for noncatalytic processes in a circulating fluidized bed (CFB). Few studies have been reported for catalytic systems with very high solids circulation. The unique features and advantages of CFB reactors have resulted in their being considered for both noncatalytic gas-solid reactions involving energy conversion processes (such as those occurring in combustors, gasifiers, and incinerators) and solidcatalyzed gas-phase reactions including thos occurring in fluid catalytic cracking (FCC) reactors. The common features in each group of applications are that they are operated with bed solids that are not identical. However, very few reports have been published on the wide range of particles used in CFBs and the hydrodynamics of mixtures of particle systems. Therefore, in the present work, an attempt was made to study the hydrodynamic characteristics of a CFB with mixed particles (binary systems). Experiments were carried out with five different bed materials. The first class of bed materials consisted of a mixture of quartz sand and spent FCC catalyst, each of 18-kg inventory
10.1021/ie800477w CCC: $40.75 2008 American Chemical Society Published on Web 06/12/2008
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Figure 1. (a) Schematic diagram and (b) photographic view of the experimental setup.
but with the amount of sand varying from 20 to 80 mass %. The second class of bed material comprises a binary mixture of coal (80 mass %) and iron ore (20 mass %), each 20 kg in weight. The fourth bed material thus has differences in both sizes and densities. Experimental Setup and Procedure The experimental setup is schematically shown in Figure 1a. The setup consists of a blower (A), air lines provided with orifice meters (D), a fast bed column (G), a cyclone separator (J) with a bag filter (K), a downcomer with a butterfly valve (I), a slow bed column (H), and a solids control valve (L) fitted in a solids transfer line. For visual observation, the setup was made of Perspex. For pressure drop measurements, 22 pressure taps connected to manometers were installed along the CFB loop. Along the whole riser, seven sampling probes were installed at different locations, specifically, at heights of h ) 0.67, 1.20, 1.57, 3.53, 4.3, 4.77, and 5.09 m above the distributor plate. It consisted of a riser, a cyclone and a bag filter to separate the fines, a downcomer, a slow bed, and a transfer line connecting the slow and fast beds. After passing through the fast bed, the solids entered the riser where they were separated in the cyclone and bag filter, descended downward through the downcomer, were collected in the slow bed, and were then transferred back into the riser. A photograph of the experimental CFB system being used here is shown in Figure 1b, and detailed equipment characteristics are listed in Table 1. Air, at controlled rates, was supplied to the fast bed (0.1015 m in diameter × 5.83 m in height) from a root blower through a multihole distributor plate
Table 1. Equipment Characteristics
riser column slow bed column solid transfer line cyclone recirculating column
diameter (m)
height (m)
0.1016 0.2032 0.1016 0.258 0.1016
5.62 1.88 0.42 0.99 2.22
having 12% open area. A small amount of air from a bypass line was also sent to the slow bed to keep it at minimum fluidizing conditions. For smooth transfer of aerated solids back into the riser, a transfer line inclined at 60° from the horizontal with a control valve to regulate the flow of solids independently was used. In most of the work reported earlier, L valves have been used for this purpose; this, however, gave large variations in the pressure drop compared to the smooth flow reported here. Various procedures have been reported in the literature to measure the solids circulation rate, but in the present case, a butterfly valve was used for reasons including simplicity in operation and no loss in the solids circulated back into the riser. For pressure drop measurements, 21 pressure taps were located along the CFB loop. The superficial gas velocities into the riser and slow bed were obtained from pressure drop measurements across the standard calibrated orifice meters installed in the air supply lines. The physical properties of the bed materials used in the experiments are listed in Table 2. Results and Discussion The pressure profiles obtained for the mixed-particle system of FCC catalyst and sand at various flow conditions are shown
Ind. Eng. Chem. Res., Vol. 47, No. 14, 2008 4955 Table 2. Physical Properties of Bed Materials bed materials FCC catalyst-sand FCC catalyst-sand FCC catalyst-sand coal-iron ore coal-iron ore
particle diameters (µm) FCC FCC FCC coal, coal,
catalyst, 119; sand, 471 catalyst, 119; sand, 471 catalyst, 119; sand, 471 335; iron ore, 140 168; iron ore, 166
CFB inventory (kg)
density (kg/m3)
16 18 IS 20 20
1805 2049 2365 1781 1781
in Figures 2 and 3. It can be seen from these figures that the system exhibits two distinct zones: an initial sharp decay and a later less-rapid decay. The former is usually seen when the flow is in a developing zone, whereas the latter corresponds to the developed flow conditions. In the developing flow region, the upward-flowing core particles experience a relatively large upward drag force and vigorous interactions with other particles (forming clumps or clusters). The steep decline in the pressure profiles with height is due to the combined effects of particle acceleration and net radial movement of solids from the upwardflowing core suspension to the predominantly downward-flowing wall region. In the developed flow region, the decay in the pressure profile is small, as the solids concentration and the variation in the particle velocity with height are rather low. Effect of Air Velocity on Static Pressure Profiles. Figure 2 shows the effect of the air velocity on the pressure profiles. At a constant solids circulation rate (Gs) of 24.75 kg/(m2 s) for the mixed system of FCC catalyst-sand, as the air velocity (Ug) increases from 2.907 to 4.681 m/s, there is a considerable variation in the static pressure as shown in Figure 2a-c. It can be seen from these plots that the effect of the gas velocity on the static pressure is lower at the top of the riser than at the bottom. The static pressure at the riser top was found to be nearly 0.20 kPa, whereas that at the bottom ranged from 0.20 to 1.60 kPa. At a superficial gas velocity of 2.907 m/s, the static pressure at the bottom of the riser had a typical value of 1.80 kPa for the 20 mass % FCC catalyst system. However, under the same operating conditions, the systems with 50 and 80 mass % FCC catalyst exhibited static pressures of 1.60 and 1.55 kPa, respectively. This might be because, as the percentage of fine particle increases, some of the fines are washed away from the bed and move toward the upper zone of the riser as a result of the decrease in static pressure. For lower percentages of fine particles, the coarse particles remain in the lower part of the bed, and the solid flux is higher because the static pressure at the bottom is higher. Again, at a higher superficial gas velocity of 4.681 m/s, the static pressure at the bottom of the riser was found to be 1.28 kPa for the 20 mass % FCC catalyst system, whereas for the same solids circulation and velocity, the corresponding static pressures for the 50 and 80 mass % FCC catalyst mixed-particle systems were 0.70 and 0.60 kPa. This dramatic reduction in static pressure might be due to the same reasons as explained earlier. The static pressure at higher velocity is lower than that at lower velocity. This is due to the fact, that at higher velocity, dense zone shifts toward the dilute zone. As a result, the static pressure at the bottom decreases. It is therefore important to note that the static pressure profile is much better for mixed-particle systems than for the corresponding single-particle systems with respect to energy dissipation. Effect of Solids Circulation Rate on Pressure Profile. Figure 3 shows the typical effect of the solids circulation rate on the static pressure profile for the FCC catalyst-sand system at a constant velocity of 4.681 m/s. It is observed that the static pressure at the bottom of the riser increases as the solids circulation rate is increased from 24.75 to 50 kg/(m2 s).
bed composition (mass %) 80% 50% 20% 80% 80%
FCC FCC FCC coal, coal,
catalyst, 20% sand catalyst, 50% sand catalyst, 80% sand 20% iron ore 20% iron ore
Umf (m/s)
Ut (m/s)
εmf
0.131 0.131 0.131 0.122 0.122
2.16 2.16 2.16 1.4 1.4
0.44 0.44 0.44 0.45 0.45
Considering the top of the column, it is noted that the variation in the static pressure is relatively low. At the different solids circulation rates, namely, 24.75, 45.38, and 50.0 kg/(m2 s), the decrease in static pressure in the dense zone was very sharp. It was also found that, as the percentage of sand was increased from 20 to 80 mass %, the static pressure increased from 0.78 to 1.40 kPa. This might be due to the higher particle concentration in the dense zone of the riser. Voidage Profiles. The axial voidage profile in fast fluidized beds has been found to be dependent on the particle size distribution and solids loading in the riser. A review of the literature shows that most research groups have concentrated on Geldart’s group A or B particles individually. Scant attention has been paid to mixed systems of these types of particles. However, in the present work, an attempt was made to report the voidage profile for a mixed-particle system of two sets of particles. Specifically, mixtures of coal and iron ore were examined in which the particle diameters of the coal and iron were quite different (dP,coal ) 335 µm and dP,iron ) 140 µm) and and in which the particle diameters were similar (dP,coal ) 168 µm and dP,iron ) 166 µm). Results were obtained for the voidage profiles at various operating conditions (air velocity and solids circulation rate) for the mixtures. In general, the voidage was found to increase along the riser height.Effect of Air Velocity on Voidage Profile. The effect of air velocity on the voidage profile for the coal-iron ore system with similar particle diameters (dP,coal ) 168 µm and dP,iron ) 166 µm) is shown in Figure 4. It was observed that the gas velocity has an almost negligible effect in the dilute zone but that there is a considerable change in voidage in the dense zone. The general tendency for the dense region is to expand with decreasing gas flow at a constant solids circulation rate.Effect of Solids Circulation Rate on Voidage Profile. The effect of the circulation rate on the voidage profile for the coal-iron ore mixture of particles with a broader range in size (dP,coal ) 335 µm and dP,iron ) 140 µm) is shown in Figure 5. It was observed that the voidage in the dilute zone was between 0.997 and 0.999. However, there was a sharp change in voidage in the dense zone that varied from 0.975 to 0.9997. The solids circulation rates employed were 23, 34, and 44.0 kg/(m2 s). As the solids circulation rate was increased, the voidage profiles showed a decreasing trend along the riser height. Hydrodynamic Properties for Mixed-Particle Systems. In the present work, an attempt was made to predict the hydrodynamic behavior of mixed-particle systems in a circulating fluidized bed from the hydrodynamic profiles of the singleparticle systems. The following equation can be used to calculate the hydrodynamic properties such as pressure profile for mixed system Pmixture ) x1PS1 + x2PS2
(1)
where x1 and x2 are the weight fractions of components 1 and 2, respectively, in the mixed system and PS1 and PS2 are the corresponding hydrodynamic properties of the two singleparticle systems S1 and S2 at a particular set of operating conditions.
4956 Ind. Eng. Chem. Res., Vol. 47, No. 14, 2008
Figure 2. Effect of superficial gas velocity on static pressure profile (system: FCC catalyst, sand): (a) 20, (b) 50, and (c) 80 mass % FCC catalyst.
A comparison was made between the available experimental values at different operating conditions and the values predicted from model eq 1. Figure 6 shows that the static pressure profile obtained experimentally for the mixed-particle system of coal and iron ore agrees well with that predicted from the singleparticle systems. Loop Pressure Profile. Literature survey reveals that the smooth performance of a CFB system depends on a number of complex variables including the solids circulation rate, gas
velocity, and bed materials, which again depend on the geometric configuration (downcomer, transfer line, control valve, riser exit geometry, and so on). The riser cannot therefore be considered in isolation but must be treated as an element in the circulating loop.6–8 One should accordingly take into account the behavior of each subsystem and the interactions among subsystems. For example, the solids content in a fast column is closely related to the pressure drop across the riser, which, in turn, is governed by the circulating load in the downcomer, slow
Ind. Eng. Chem. Res., Vol. 47, No. 14, 2008 4957
Figure 3. Effect of solids circulation rate on static pressure profile (system: FCC catalyst, sand): (a) 20, (b) 50, and (c) 80 mass % FCC catalyst.
bed, and other sections of the system. Three major principles must be incorporated in understanding the pressure variations in a circulating loop.8 The first principle relates to a material balance on the particles. That is, the total quantity of particles in the fast bed and other sections of the CFB, including the cyclone, solids transfer line, and so on, must equal the total quantity of solids charged to the system. Any increase in the amount of particles in the fast bed must be accompanied by a corresponding decrease in the amounts of particles in other beds.
The second principle relates to the interrelationship among the entertainment rate, gas velocity, and disengaging height at the dense bed level and gas outlet. The third principle relates to the pressure balance according to which the sum of the differential pressures around the circulating loop must be equal to zero. The operating characteristics of a CFB system can then be determined by the solution of a set of equations incorporating all three of these principles.7–9Analysis of Data. Figure 7 shows a typical measured pressure profile in the CFB loop, and Figure
4958 Ind. Eng. Chem. Res., Vol. 47, No. 14, 2008
Figure 4. Effect of superficial gas velocity on voidage profile (system, coal-iron ore).
Figure 5. Effect of solids circulation rate on voidage profile (system, coal-iron ore).
8 shows the various zones of the experimental CFB system. The pressure drop in the riser was taken from pressure tap points 2-13. On the other hand, the pressure drop around the elbow was measured at points 13 and 14. At the top of the riser was a 90° bend that forced the gas and particles to change their direction. Evidently, the particles collided within the bend surface, so that the pressure drop increased. Thereafter, the gas-solid mixture entered the cyclone where the solid was separated from the gas. The pressure drop around the cyclone was measured at points 14 and 15 shown in Figure 8. After the cyclone, the gas and particles entered the downcomer, and pressure recovery began at points 15-18. Actually, the dilute phase started at point 15 and continued slightly below point 18, where a standpipe separated the interface of the dilute and
Figure 6. Prediction of pressure profile along the riser for 80 mass % coal-20 mass % iron ore system.
dense phases. The pressure at the bottom of the slow bed (fluidized) was measured as indicated at point 21. The transfer of solid from the slow bed to the riser is shown in the diagram by the tie line (TL) that lies between pressure taps 19 and 20 (in the slow bed) and pressure taps 3 and 4 (in the riser). As there was no pressure tap in the transfer line, the pressure drop around the valve could not be measured.Pressure Balance in the CFB Loop. In any CFB, there exists a pressure balance for any set of conditions. The pressure change from a point along the loop is zero when the same point is again reached; that is, the pressure change between two points in a CFB is the same in both directions. The pressure change in the present CFB loop can be divided into three sections. The first is the conveying
Ind. Eng. Chem. Res., Vol. 47, No. 14, 2008 4959 Table 3. Contributions of Different Terms to the Total Pressure Drop (Coal-Iron System)a riser height (m)
∆PT (kPa)
∆PS (kPa)
∆Pf (kPa)
∆Pa (kPa)
0.02 0.22 0.36 0.66 0.96 1.26 1.76 2.26 2.96 3.66 4.36 5.06 5.62
1.51 0.61 0.52 0.20 0.08 0.05 0.04 0.03 0.03 0.02 0.02 0.02 0.02
0.92 0.37 0.31 0.12 0.04 0.02 0.01 0.01 0.01 0.005 0.005 0.003 0.003
0.08 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01
0.59 0.22 0.19 0.07 0.02 0.01 0.008 0.006 0.006 0.003 0.003 0.002 0.002
a
Figure 7. Typical pressure profile around the CFB loop.
Figure 8. Various zones of the experimental CFB system.
pressure drop, from the point at which gas enters the loop to the point at which it leaves the loop, given by the range from
Ug ) 3.12 m/s, Gs ) 24 kg/(m2 s).
point 2 to point 15 in Figure 8. The second is the pressure recovery in the standpipe between points 15 and 20). The third is the control pressure drop between points 19 and 20 and points 3 and 4 in the transfer line. The conveying pressure drop determines the energy requirement. This is the pressure drop of the gas when it passes through the unit. Its maximum value is determined by the blower and the height of the standpipe. The conveying pressure drop consists of two components, one due to the flow restrictions in the CFB loop (such as the bend, cyclone, and so on) and the other due to the presence of solid particles in the gas phase of the riser. Pressure recovery in the standpipe is due to the dilute- and dense-phase regions, the latter being predominant. Pressure recovery depends on the dense-phase height and the flow pattern of solid particles. If the particles in the standpipe are well fluidized, then the velocity in the standpipe in fluidized conditions (USB) is greater than Umf/ε, and the pressure recovery is at its maximum. This value increases with increasing densephase height. In this case, the estimation of the pressure recovery is relatively simple. On the other hand, if USB < Umf/ε, the particles are not fluidized, packed-bed flow might occur, and it becomes difficult to predict the pressure recovery in the standpipe correctly. It is imperative that the solids flow rate in a CFB be controlled. When the solids flow through control devices such as slide valves, L valves, and/or butterfly valves, there is some pressure drop that varies with the rate of flow of the solids. A minimum control pressure drop is needed to ensure the smooth circulation of the solid particles, as well as operational stability. The pressure balance in a CFB determines the solid particle concentration and solids circulation rate in the riser. The pressure drop in the riser is dictated by the pressure difference between pressure recovery and control pressure drop. Experimental data further reveal that the maximum solids circulation rate in the riser occurs for the maximum pressure recovery and minimum control pressure drop. The higher the solids circulation rate, the higher the pressure drop and solid particle concentration in the riser. Theoretical Analysis of the CFB Loop Pressure Drop. Based on an understanding of experimental data on the loop pressure balance, a simplified theoretical analysis was performed to predict the pressure profile in the CFB loop. The analysis took into account the flow regimes in various sections of the CFB loop, namely, the acceleration zone and dilute zone in the riser, bend, cyclone, downcomer-standpipe lean-phase region, slow bed, and transfer line. The computational sequence and equations used are presented below.Riser. The pressure profile and voidage data along the riser indicate that the riser consists
4960 Ind. Eng. Chem. Res., Vol. 47, No. 14, 2008
of an accelerating zone (developing zone) at the bottom, followed by a dilute zone (developed zone) at the top. The pressure drop is due to acceleration, static head, and friction and can be expressed as ∆PT ) ∆Pa + ∆PS + ∆Pf
(2)
Each component of the pressure drop is made up of contributions from both the gas and the particles. Thus ∆PS ) ∆PS,P + ∆PS,g
(3)
∆PS,P ) FP(1 - ε)g∆L
(4)
∆PS,g ) Fgεg∆L
(5)
∆Pf ) ∆Pf,g + ∆Pf,p
(6)
∆Pf,g)2fgFgUg2∆L/Dt
(7)
∆Pf,p)2fsFp(1 - ε)Us∆L/Dt
(8)
The particles in the riser bottom are accelerated from zero velocity at the inlet to a certain value. The acceleration pressure drop consists of four terms, which account for the solid particle gravity, gas friction, solid friction, and kinetic energy of the solid particles at the accelerating length Lacc
∆PT )
Lacc
∫ F (1 - ε)g dL + ∫ p
0
0
Lacc
∫ 0
2fgFgUg dL + Dt 2
2fs(1 - ε)FpUs2 dL + FP(1 - ε)US2 (9) Dt
where Lacc is the acceleration length. Yang’s9 correlation can be used to calculate Lacc as follows US2
Lacc )
∫ (3/4)C
US1
US dUS
2 dsFg(Ug - Us)
ε4.7(Fp - Fg)dP
2fsUS2 -gDt
(10)
Equation 10 can also be deduced from the gas-solid momentum balance along the riser. At the riser top, where the particle velocity becomes constant, the last term in eq 9 is absent. These values were used in the present case to predict the pressure drop in the riser. Table 3 lists the contribution of each term to the total pressure drop in the riser. Whereas the accelerating pressure drop can vary from 9% to 40%, the frictional pressure drop due to the solids is 1% of the total pressure drop at the top of the riser where the dilute zone prevails.Bend. The solid particles in suspension from the riser pass through the bend to the cyclone separator in the CFB. During passage through the top bend, the gas velocity remains unchanged. As particles collide with the bend surface, friction increases, and the solid particle velocity decreases. The pressure drop in this case can be calculated using the Kunii and Levenspiel10 expression ∆PBC)fbF¯Ug2
(11)
In general, fb can vary from 0.125 to 0.375 depending on the riser diameter.Cyclone. The pressure drop in the cyclone, ∆Pcyc, was calculated from the relationship ∆Pcyc)fcFgUcyc2
(12)
where fc is the friction factor for the gas-solid mixture with the cyclone wall and Ucyc is the tangential gas velocity at the cyclone.Downcomer. The downcomer-cum-standpipe acts as a pressure recovery system. The pressure recovery occurs in two regions: the lean phase and the dense phase. In the present case,
the dense phase operated in the bubbling fluidized regime. The pressure recovery in the lean phase, arising from falling of the particles, can be calculated from the relationship ∆Pd)Gsg∆L/Ut
(13)
If, however, the flow of the gas-solid mixture is stick-slip flow, Ergun’s equation for the pressure drop can be applied. In stick-slip flow, the movement of gas relative to solids (and not relative to the wall) determines the pressure gradient. This is because the frictional resistance between the gas and the solids overshadows that between the gas and the wall. Thus, Ergun’s equation can be written as
( )[
][
]
|U| (1 - ε) 150(1 - ε)µg ∆P ) + 1.75|U|Fg L gCdP dP ε3
(14)
where |U| is the linear velocity of gas relative to solid. Again |U|)(Ug/ε) - Us
(15)
If |U| > Umf, the flow is aerated. Accordingly ∆Pd ) ε0(h2-h1)/gc + ∆Pf
(16)
Slow Bed. The slow bed in the present case was operated in the bubbling fluidized zone. The pressure drop in this case can be found from ∆PSB ) FP(1 - εden)Lg
(17)
The overall voidage in the bed can be expressed as εden ) (1 - εB)εP - εB
(18)
where εP is the voidage of the particulate phase and εB is the fraction of the dense phase occupied by bubbles or slugs. These values can be calculated depending on the type of particle (as classified in Geldart’s chart, giving the corresponding relationship available in the literature).Solids Control Valve. The pressure losses through the solids control valve can be calculated from the equation of Leung and Jones11 ∆PV )
[( )( )]
Gs At 1 2[FP(1 - ε)] CD A0
2
(19)
where CD is the discharge coefficient for the valve.Solids Transfer Line. For aerated solids, the pressure drop is given by two terms, the static pressure and the frictional loss. The pressure drop in an inclined solid transfer line can be calculated using the equation ∆PTL ) FP(1 - εmf)gLTL sin θ
(20)
where θ is the angle of inclination of the transfer line. Figure 9 compares the experimental and predicted pressure profiles in the CFB loop. The dark line represents the theoretical values calculated for the various sections in the loop, using the above equations. The experimental values are also included in the same plot (light line). As can be seen, the deviations between the two sets of values are within reasonable limits of accuracy. Conclusions On the basis of the present investigation, the following conclusions can be made about the hydrodynamics of mixed systems of particles: At a constant solids circulation rate (Gs), as the air velocity increases (Ug), the static pressure shows a decreasing trend. This possibly occurs because of a large carry over of particles at higher velocities. Effects of the solids circulation rate on the
Ind. Eng. Chem. Res., Vol. 47, No. 14, 2008 4961 LTL ) length of solids transfer line (m) ∆PBC ) pressure drop in bend (kPa) ∆P ) pressure drop (kPa) ∆Pcal ) calculated pressure drop (kPa) ∆Pcyc ) pressure drop in cyclone (kPa) ∆Pd ) pressure drop in downcomer (kPa) ∆Pf ) pressure drop due to friction (kPa) ∆Pf,g ) pressure drop due to gas friction (kPa) ∆Pf,p ) pressure drop due to solid friction (kPa) ∆PL ) pressure drop in dense bottom zone of riser (kPa) ∆PR ) pressure drop in riser (kPa) ∆PS ) pressure drop due to static head (kPa) ∆PSB ) pressure drop in slow bed (kPa) ∆PS,g ) pressure drop due to gas static head (kPa) ∆PS,p ) pressure drop due to weight of solid (kPa) ∆PT ) total pressure drop in riser (kPa) ∆PTL ) pressure drop in solids transfer line (kPa) ∆PV ) pressure drop through solids control valve (kPa) |U| ) linear velocity of gas relative to solid (m/s) Ucyc ) tangential gas velocity at cyclone entrance (m/s) Ug ) superficial gas velocity (m/s) Umf ) minimum fluidization velocity (m/s) Us ) solid velocity (m/s) Ut ) terminal settling velocity (m/s) Greek Letters Figure 9. Comparison of experimental and predicted loop pressure profiles (system: FCC catalyst, sand).
static pressure profile for the FCC catalyst-sand and coal-iron ore systems were observed. The static pressure at the bottom of the riser decreases sharply when the solids circulation rate increases. In contrast, the changes in pressure the top of the column are relatively low. The effect of air velocity on the voidage profile at constant solids circulation rate is apparent. As the velocity increases, the voidage increases, and as the solids circulation rate is increased, the voidage profile shows a decreasing trend along the riser height. Predictions of the hydrodynamic behavior for mixed-particle systems from those of the single systems were made, and the results were compared and plotted with the available experimental values at different operating conditions. The plots show a good match between the predicted and experimental curves. Based on an understanding of experimental data on loop pressure balance, a simplified theoretical analysis was performed to predict the pressure profile in the CFB loop. The deviations between the two sets of values were found to be within reasonable limits of accuracy. Nomenclature A ) aspect ratio A0 ) cross-sectional area of the valve opening in solids transfer lines (m2) CD ) coefficient of orifice Cds ) drag coefficient dP ) particle diameter (m) Dt ) tube diameter (m) fb ) friction factor in bend fc ) friction factor in cyclone separator fg ) gas friction factor fs ) solid friction factor g ) acceleration due to gravity (m/s2) Gs ) solids circulation rate [kg/(m2 s)] L ) height of the column (m) Lacc ) accelerating (or mixing) length (m)
ε ) voidage εB ) fraction of dense phase occupied by bubbles or slugs εmf ) minimum fluidization velocity εden ) overall voidage in slow bed µg ) gas viscosity [kg/(m s)] F ) average density of the bed (kg/m3) Fg ) gas density (kg/m3) Fp ) solids density (kg/m3)
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ReceiVed for reView March 26, 2008 ReVised manuscript receiVed April 21, 2008 Accepted May 2, 2008 IE800477W
