Particle Residence Time and Particle Mixing in a Scaled Internal

Apr 27, 2002 - A pilot plant is currently under construction in southern Italy operated with a circulating fluidized bed, and to predict the fluid dyn...
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Ind. Eng. Chem. Res. 2002, 41, 2637-2645

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Particle Residence Time and Particle Mixing in a Scaled Internal Circulating Fluidized Bed Ralf Kehlenbeck,† John G. Yates,*,† Renzo Di Felice,‡ Hermann Hofbauer,§ and Reinhard Rauch§ Department of Chemical Engineering, University College London, Torrington Place, London WC1E 7JE, U.K., Dipartimento di Ingegneria Chimica e di Processo, Universita` degli Studi di Genova, Via Opera Pia 15, 16145 Genova, Italy, and Institute of Chemical Engineering, Fuel and Environmental Technology, Getreidemarkt 9/159, 1060 Vienna, Austria

A process is under development for the steam gasification of biomass to produce a hydrogenrich gas for use with a fuel cell to generate electricity on a local scale. A pilot plant is currently under construction in southern Italy operated with a circulating fluidized bed, and to predict the fluid dynamic conditions within the plant, a cold laboratory rig was built according to existing scaling laws, and experimental studies were carried out. In this paper, we present the experimental results concerning the solids residence time of particles introduced into the system and the particle mixing in the “gasifier” section of the model. Both parameters are of fundamental importance for the operation of the pilot plant as they determine the performance of the gasification process. It is shown that the biomass particles spend sufficient time in the gasifier to be fully gasified, and an equation is derived to predict the mean residence time of the biomass particles as a function of the dimensionless mass turnover of the circulating bed material. In addition, it is shown that the biomass particles are well mixed within the circulating bed material. One reason for this is a result of the geometric design of the apparatus. Introduction Residence Time of Introduced Solids. The residence time of particles introduced into a circulating fluid bed is of fundamental importance for the performance of chemical reactions such as biomass gasification occurring in the system. Latif,1 for example, found that, after 170-310 min at a temperature between 700 and 800 °C, almond shells with a particle size of about 830 µm are completely gasified. Knowledge about the residence time within the system is also of fundamental importance for other applications such as particle drying. Nevertheless, there are few literature references to solids residence times in circulating fluidized beds. Kuramoto et al.2 investigated several different types of particle and came to the conclusion that injected particles do not circulate if their density is less than the bulk density of the circulating bed material because of an increased segregation effect around the minimum fluidization velocity umf. Harris et al.3 have also investigated this question. Particle Mixing in Fluidized Beds. Most of the work on particle mixing in gas fluidized beds has been carried out on binary systems of particles in bubbling beds. It has been shown that segregation due to differences in size and/or density leads to a variation of particle concentration over the bed height. Commonly, the particles with a tendency to rise in the bed are called flotsam, while the particles tending to sink are called jetsam. The main variables effecting particle segregation in a fluidized bed are found to be the superficial velocity * To whom correspondence should be addressed. † University College London. ‡ Universita ` degli Studi di Genova. § Institute of Chemical Engineering, Fuel and Environmental Technology.

and the minimum fluidization velocities of the solids. Particle mixing in circulating fluidized beds, however, is rarely discussed in the literature. In bubbling beds, it was found that both particle mixing and segregation are caused solely by rising gas bubbles.4-6 In the wake region of a bubble, particles are carried up to the surface of the bed, and as a consequence, other particles move downward into the bubblefree regions. In a rapidly bubbling bed, the particle mixing is thus very good, although difficulties with particle segregation caused by density and size differences can occur.4,6-8 These separation effects are caused mainly by density rather than size differences of particles.5 Kunii and Levenspiel9 showed that, at gas velocities close to umf, the segregation of jetsam particles is more dominant than at higher velocities. Verloop et al.10 reported that gas fluidized beds approach perfect mixing for u0 > 1.5umf, whereas other investigators gave much higher values. Peeler and Huang,4 for example, investigated the mixing of sand particles having particle sizes of 208 and 2020 µm and found perfect mixing for u0 > 15umf. To describe the mixing in a fluidized bed, Rowe et al.6 defined a mixing index, Mmix, as

Mmix )

cjetsam cbed,jetsam

(1)

where cjetsam gives the concentration of jetsam particles in the uniform upper part of the bed and cbed,jetsam is the concentration of jetsam particles within the whole bed. Thus, Mmix takes values between 0 for complete segregation and 1 for perfect mixing. Several models have been proposed to calculate particle mixing in a gas fluidized bed. Gibilaro and

10.1021/ie010513u CCC: $22.00 © 2002 American Chemical Society Published on Web 04/27/2002

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Figure 1. Mixing index, Mmix, as a function of the velocity ratio, u0/umf,floatsam.

Rowe7 derived a model describing the segregation patterns, and Peeler and Huang4 listed some empirical equations calculating Mmix as

Mmix ) (1 + e-Φ)-1

(2)

with the dimensionless velocity term, Φ, derived by Rice and Brainovich10

( ) {

x

Φ)(

u0 - uTO u0 + for u > u | |exp f - for u0 < uTO u0 - umf,flotsam uTO 0 TO (3)

where uTO is the takeover velocity. By definition, u0 ) uTO when the mixing index equals 0.5; as u0 becomes large, the mixing index approaches unity (Figure 1). Nienow et al.11 calculated Φ as

Φ)

(

) ( )

u0 - uTO u0 exp u0 - umf,flotsam uTO

(4)

Rice and Brainovich10 gave the following equation for the takeover velocity

( )

hbed uTO ) 2 D

-0.2

xumf,flotsamumf,jetsam

(5)

Peeler and Huang4 calculated uTO as

uTO ) 0.54

x

djetsam u u dfloatsamx mf,flotsam mf,jetsam

(6)

Scaling Parameters. Scaling is a procedure frequently used to characterize and study the design of large-scale units such as aircraft and industrial boilers. With specially developed scaling rules, a small-scale laboratory model can be built having hydrodynamic behavior similar to that of a large plant. Thus, initial experiments can be carried out on a low-cost laboratory rig to verify the operating conditions of an industrial unit. Several authors have developed scaling parameters for fluidized beds,13-21 but probably the best known and most widely used parameters are those derived by Glicksman et al.,21 who, on the basis of the governing equations of conservation of mass and momentum of fluid and particles, derived a set of nondimensional parameters that must be matched to obtain hydrodynamic similarity between a model and a full-scale plant.

Figure 2. Sketch of the cold model.

Their so-called “full” set of scaling parameters is

Gs FfFsdp3g Fs u02 Ffu0D , , , , 2 Ff gD η Fs u 0 η

(7)

which are, respectively, the Archimedes number, the solid-to-fluid density ratio, the Froude number, the Reynolds number, and the dimensionless solid circulation rate. In addition, the two units should have the same geometry, and the bed particles should have the same sphericity and particle size distribution. By matching this set of parameters, hydrodynamic similarity is obtained, as has been confirmed by several experimental investigations.18-21 Experimental Apparatus For the purpose of biomass gasification to produce a hydrogen-rich gas, a circulating fluidized bed system was developed with the objective of feeding the product gas into a fuel cell to produce “clean” electricity. The fluid dynamic behavior of the unit was simulated in a one-fifth-scaled cold laboratory model based on the full set of scaling parameters proposed by Glicksman et al.,21 a sketch of which is shown in Figure 2. Biomass (wood chips) will be introduced in the pilot plant, currently under construction in southern Italy, in the gasifier shown on the left-hand side in Figure 2. There, it will be gasified and circulated together with the bed material (olivine) into a combuster (riser) where the resulting char from the gasification process will be burned. This exothermic reaction will heat the bed

Ind. Eng. Chem. Res., Vol. 41, No. 11, 2002 2639 Table 1. Particles and Fluidizing Gases Used in the Cold Model circulating bed material material density F (kg/m3) particle size d (µm) minimum fluidization velocity (m/s) viscosity η (Pa s)

simulated biomass gasified non-gasified

fluidizing gas gasifier

riser

bronze 8900 180 0.11

resin 1500 1500 0.28

ZrO2 3900 1800 1.2

55:45% He/air 0.63 -

air 1.19 -

-

-

-

1.87 × 10-5

1.72 × 10-5

material, which then recirculates via a downcomer and a siphon into the gasifier. The inlets for the respective gases to fluidize the particles are shown in Figure 2. According to the scaling parameters, in the cold model, the particle-gas system listed in Table 1 was used. In the whole system, the total mass load of circulating bed material was 12 kg of bronze, and the flow rate of / ) 200 L/min if not gas into the gasifier was Vgasi indicated otherwise. The flow rate into the bottom zone of the riser was kept constant with V/prim ) 30 L/min, while V/sec was used as an operating parameter. Because the cold laboratory model was designed according to generally accepted and industrially used scaling parameters, it can be expected that the fluid dynamic behavior in the model is similar to that in the pilot plant. The experimental apparatus is described in more detail elsewhere.22 Furthermore, Kehlenbeck et al.23 defined a new scaling parameter giving the dimensionless mass turnover as

m*Driser M) mut

(8)

where m* is the mass flow, m is the total mass load in the apparatus, Driser is the riser diameter, and ut is the terminal settling velocity of particles used The experimental data could be correlated using the equation

M ) aU2 - 1.6aU + 0.64a where

U ) u0/ut

(9)

a ) 1.5 × 10-3 which was shown to be valid for 0 e M e 7 × 10-4. Solid circulation starts at U ) 0.8. Under normal conditions both the cold model and the pilot plant should be operated at M ) 1.5 × 10-4. Experiments on Biomass Circulation and Residence Time The following were considered to be possible fates of the biomass within the apparatus: it could (i) be blown directly out of the gasifier because of its low density, (ii) float on the top surface of the particle bed in the gasifier, (iii) not circulate into the combustor at all, (iv) circulate into the riser without spending enough time in the gasifier to be gasified, and/or (v) circulate into the combustor as planned. To determine the residence time distribution (RTD) and the mean residence time of the scaled biomass particles in the system, about 20 biomass-representing particles were introduced into the particle bed of the

Figure 3. RTDs of different biomass-representing particles for M ) 1.21 × 10-4.

gasifier from the top. Just below the siphon, a wire mesh was placed inside the gasifier so that particles could be collected after completing a cycle in the system. This time was measured with a stopwatch. The amount of particles exiting the siphon at a specific time divided by the total amount of introduced particles gave the cumulative curve F. In the following experiments, silicone rubber particles with a density of 1500 kg/m3 and a size of about 1.5 mm were used. These particles roughly represent the gasified biomass inside the pilot plant. In addition, ZrO2 particles with a mean particle size of 1.8 mm and a density of 3900 kg/m3 were used. These particles should simulate the behavior of the nongasified biomass in the pilot plant. It was observed that these particles under the given conditions were circulating in the bed as shown in Figure 3, where the RTDs obtained for both the gasified and nongasified biomass are shown for a dimensionless mass turnover of M ) 1.21 × 10-4. It can be seen that no difference in residence time between these different types of particle was observed. To investigate the reproducibility of the experiments, the measurements were rerun four times as shown in Figure 4, and it is clear that the results are very reproducible. The experimental data follow the curve calculated with

F ) 1 - exp[-y(t - z)]

(10)

which is in accordance with Verloop et al.10 and Levenspiel,24 giving the equation for a continuously stirred tank reactor (CSTR) in series with a plug-flow reactor (PFR). The parameter z gives the time when the first particle exits the siphon and was found to be quite constant with

z ) 2 min ) constant

(11)

According to Verloop et al.10 and Levenspiel,24 z gives the residence time of particles in the PFR, tres,PFR,

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Figure 4. Reproducibility of RTD for representing gasified biomass.

Figure 6. Influence of M on the RTD.

Figure 7. Mean residence time as a function of the dimensionless mass turnover, M. / Figure 5. Influence of the flow rate into the gasifier, Vgasi , on the RTD at M ) 1.21 × 10-4.

whereas the parameter 1/y gives the mean residence time of particles in the CSTR, tres,CSTR. Hence, the mean residence time of particles in the entire system is

tres ) tres,PFR + tres,CSTR

(12)

Because the gasifier was fluidized at the base immediately before the transfer line to the riser, it was thought that a higher gasifier flow rate could affect the residence time of the biomass, leading to the particles spending a longer time in the gasifier. Kehlenbeck et al.,23 however, showed that the solid circulation of the / . circulating bed material is not at all affected by Vgasi In Figure 5, the RTD of the introduced particles is / / ) 100 L/min and Vgasi ) 200 L/min. It shown for Vgasi can be seen that, as expected, the solids residence time / ) 100 L/min is lower that that for the higher for Vgasi flow rate; the mean value is decreased by about 14% from 12.2 to 10.5 min. In fact, this result can be explained with a smaller generated bubble in the bottom zone of the gasifier. Larger bubbles prevent the biomass from flowing down into the intersection of the gasifier and combustor. Because it was expected that the residence time of the biomass in the system would depend on the solid circulation of the bed material, experiments were carried out with varying dimensionless mass turnover in the range 3.43 × 10-5 e M e 2.09 × 10-4. The results obtained are shown in Figure 6 for a gasifier flow rate of 200 L/min.

From Figure 6, it becomes evident that the particle residence time is strongly dependent on the solid circulation rate of the bed material. The parameter y could be correlated with

y ) 4 × 10-3 exp(4 × 105M)

(1s)

(13)

Thus, eq 12 becomes

tres ) 2 +

-3

4 × 10

1 exp(4 × 105M)

(14)

In Figure 7, the mean residence time, tres, is shown as a function of the dimensionless mass turnover, M. It can be seen that, with increasing M, the mean residence time decreases exponentially. Similar results were found by Latif,1 who studied the residence time of almond shells in a circulating fluid bed as a function of the superficial velocity in the riser. He observed that, with increasing velocity and increasing mass load in the system, and thus with increasing solid circulation, the mean residence time decreased. No mathematical correlation, however, was derived. Discussion of the RTD Results An equation was derived with which it is possible to approximate the mean residence time and the residence time distribution as a function of the mass turnover of the circulating bed material. It was shown that, with increasing circulation rate, the residence time decreases exponentially. Thus, for low solid circulation, a small change in M affects tres of the biomass particles quite

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strongly, whereas for high circulation rates, small changes in M have a negligible effect on tres. For the operation of the pilot plant, this means that, if the temperature in the gasifier is too low, the solid circulation can be increased to a certain extent to increase the biomass circulation into the combustor where more heat is provided by the exothermic combustion reaction. That means, however, that less time for the gasification process is available so that an optimum has to be found during the pilot-plant operation. At present, however, it cannot be said for certain how much time the biomass particles spend in the different sections of the system. The flow patterns in the riser are highly complex; close to the riser wall, particles are overall flowing downward in a dense phase as stated by Werther and Hirschberg25 and as also observed visually in the cold model. The particles rising in the lean phase in the core of the riser could not be observed visually. However, because the gasifier is vigorously bubbling with very large generated bubbles in the bottom zone and very good particle mixing (as observed visually), it is expected that the biomass spends most of its time in the gasifier. Fiorentino et al.26 derived a mathematical model for the gasification of biomass that was fairly confirmed experimentally.27 They observed particle segregation during the gasification process. In the initial stage of the biomass gasification, the velocity of the biomass particles was directed downward in the bed, which would most likely decrease the residence time in the gasifier of the pilot plant. However, as soon as the particles started to descend, they decelerated, their flow reversed, and the biomass started to rise within the particle bed. Thus, most likely, the biomass residence time in the pilot plant will be higher than that obtained with the cold model because of the gasification process. However, as discussed below in the particle mixing section, the gasifier at the operating conditions discussed here is a perfectly mixed reactor (CSTR). Coming back to the explanations discussed before, the riser would be a PFR. Thus, in a first approach, it can be assumed that the biomass particles spend about 2 min in the riser and, hence, that the time the particles spend in the gasifier depends on the solid circulation rate. To verify this statement, some further experiments need to be carried out. Experiments on Particle Mixing in the Gasifier In this section, experimental results for the solid mixing of particles in the cold model “gasifier” are discussed. Because the particle bed in the pilot plant contains a catalyst, good mixing of the biomass with the bed material is desirable for a high biomass conversion efficiency. For the particle mixing experiments in the cold model, two different bed materials were used: (1) zirconium oxide (ZrO2) particles with a mean particle diameter of 1800 µm and a density of about 3900 kg/ m3, which were chosen because they roughly represent the nongasified biomass as it would enter the pilot plant, and (2) resin particles with a diameter of about 670 µm and a density of about 1500 kg/m3, which were thought to represent the biomass particles in the pilot plant in a gasified state. For the experiments, the respective particles simulating the biomass used in the pilot plant were added to the circulating bed material of 12 kg of bronze. It was

Figure 8. Dependency of the superficial velocity, u0, on the diameter of the gasifier minimum for different volumetric flow / rates, Vgasi .

thought that the concentration of the introduced particles might influence the mixing behavior within the gasifier, and therefore, experiments were run at two volume concentrations of about 0.3 and 0.6 m3 of biomass/m3 of bed material, giving mass loadings of 2 and 3 kg of ZrO2 and 0.5 and 1 kg of resin, respectively. In addition, the flow rate into the gasifier was varied from 40 to 200 L/min, while the riser flow rate was kept constant at about 550 L/min. After the bed material was introduced into the system, the particles were circulated in the apparatus for some 20 min to obtain steady-state conditions before the flow rates into the rig were switched off abruptly. The particles fell back to form a fixed bed, which was then removed layer by layer (steps of 1.5 cm) using a vacuum pump. In this way, the gasifier was emptied down to the level of the distributor plate of the windbox. All particles below this point were considered to be in the combustor. Once one layer of particles was removed from the gasifier, the mass fraction and, by multiplication with the density, the volume fraction of the respective particles were determined. Superficial and Minimum Fluidization Velocity in the Gasifier. Owing to the conical shape of the gasifier, the diameter varies with height above the distributor, as shown in Figure 2; also the superficial velocity, u0, in the gasifier varies with height and, thus, with diameter. In Figure 8, the dependency of the superficial velocity on the diameter of the gasifier is / . Furshown for different volumetric flow rates Vgasi thermore, the minimum fluidization velocity of the respective bed materials used for the solid mixing experiments is indicated. Several conclusions can be drawn from this graph: (1) At the investigated volumetric flow rates, the maximum superficial velocity is about one-half of the umf value of the ZrO2 particles. (2) Only for the experiments carried / out at Vgasi ) 200 L/min were the bronze particles fluidized completely over the entire height of the particle / bed. (3) A flow rate of Vgasi ) 40 L/min is equivalent to about umf,bronze. Particle Mixing Results. Figures 9 and 10 show the experimental results obtained for the mixing of the ZrO2 / particles in the gasifier for different values of Vgasi . The

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Figure 9. Particle mixing (2 kg of ZrO2 in 12 kg of bronze) for different flow rates into the gasifier.

Figure 10. Particle mixing (3 kg of ZrO2 in 12 kg of bronze) for different flow rates into the gasifier.

Figure 11. Mixing index for ZrO2 particles as a function of the velocity ratio u0/umf,ZrO2 (u0 calculated at the bottom of the gasifier, D ) 80 mm).

Figure 12. Particle mixing (0.5 kg of resin in 12 kg of bronze) for different flow rates into the gasifier.

volume fraction of ZrO2 in bronze is shown as a function of the relative bed height in the gasifier

hrel )

hi htotal

(15)

where hi is the actual height in the gasifier and htotal is the total particle bed height; hrel ) 0 gives the top of the particle bed, and hrel ) 1 is the bottom of the bed just above the gas distributor. It can be seen that the particle mixing results for the two concentrations are very similar. At flow rates down to about 100 L/min, perfect mixing is achieved, although the ZrO2 particles on their own would not be fluidized at these velocities. Below flow rates of 100 L/min, the particle mixing becomes worse, with the ZrO2 particles floating on top of the bed. In Figure 11, the calculated mixing indices for both biomass concentrations are plotted as a function of the velocity ratio of u0/umf,ZrO2, where the superficial velocity was calculated for the bottom of the gasifier giving the highest value for u0. It can be seen that perfect mixing is obtained at velocities well below umf,ZrO2. Chiba et al.8 observed that, if the bigger component (here ZrO2) is less dense than the bulk density of the smaller particles (bronze), the smaller particles sink and are considered to be jetsam, a result also obtained here. In Figures 12 and 13 the particle mixing results obtained for resin particles at volumetric concentrations of about 0.3 and 0.6 are shown. Also here, no significant

Figure 13. Particle mixing (1 kg of resin in 12 kg of bronze) for different flow rates into the gasifier.

difference is obtained for different resin concentrations. It becomes clear that, to achieve perfect mixing with / has to be about the resin particles, the flow rate Vgasi 200 L/min or higher. For lower flow rates the resin particles become flotsam. Perfect mixing is now obtained at velocity ratios of about u0/umf,resin ≈ 2.5, as can be seen in Figure 14, in which the mixing index is shown as a function of u0/umf,resin. The mixing patterns of the resin particles also agree with the observations of Chiba et al.8 that the lighter but larger particles float on top of the bed, thus confirming that the particle density, rather than the particle size drives segregation.

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Figure 14. Mixing index for resin particles as a function of the velocity ratio u0/umf,resin (u0 calculated at the bottom of the gasifier, D ) 80 mm).

Figure 17. Mixing index, Mmix, as a function of the gas velocity parameter, Φ, for the ZrO2 and resin particles. Table 2. Calculated and Measured Values for uTO

Rice and Brainovich11 Peeler and Huang4 experimental

Figure 15. Volume fraction of resin and ZrO2 in the gasifier for / (for lower mass loads). different values of Vgasi

uTO,ZrO2 (m/s)

uTO,resin (m/s)

0.28 0.06 0.13

0.13 0.05 0.2

Mmix can be predicted quite well. For low values of Φ, however, the curve has to decrease much faster than calculated. As indicated, if the superficial velocity in the gasifier equals zero, a mixing index of 0.4 is predicted, which physically is not possible. Also, for the resin particles, it can be seen from Figure 17 that, for low values of Φ, the mixing index has to decrease much faster than is actually calculated. Comparing the calculated values of uTO with the experimental values listed in Table 2, it becomes clear that no correlation predicts the turnover velocity with good accuracy. Discussion of the Particle Mixing Results

Figure 16. Concentrations of resin and ZrO2 in the gasifier for / different values of Vgasi (for higher mass loads).

In Figures 15 and 16, the ZrO2 and resin concentra/ . It can tions are shown for the different flow rates Vgasi be seen that the volume concentration in the gasifier increases exponentially with decreasing flow rate from a constant value at perfect mixing. Similar curves were obtained by Latif.1 The differences in the course of the curves for ZrO2 and resin indicate a different mixing behavior of these particle types. In Figure 16, the mixing index, Mmix, for the ZrO2 and resin particles is plotted as a function of the velocity term, Φ, as defined by Rice and Brainovich;11 uTO was determined from the experiments shown in Figure 11. For ZrO2, it can be seen that, for Φ > 0, the trend of

The reasons for the very good particle mixing at very low velocities can be explained as follows. In a standard fluidized bed, solid mixing is thought to be driven solely by rising bubbles, as discussed in earlier studies.4-6 A circulating fluidized bed can be well mixed, however, whereas, for a noncirculating bed, complete segregation occurs, as also mentioned by Di Felice et al.28 in a study of liquid fluidized beds. The imposed solid circulation causes particles to flow from the top to the bottom of the bed, thereby replacing the particles that are circulating into the riser. Thus, as long as particles are circulating within the system, the dense bed tends to mix well. Superimposed is an additional mixing effect caused by the rising bubbles in the bed. If the dense bed is no longer well fluidized but both types of particles are still circulating in the system, jetsam particles coming out of the return system stay on top of the dense particle bed, and segregation occurs. Because there is still solid circulation, however, these particles will slowly flow down to replace the bed particles flowing into the riser and thus, there is still some particle mixing. Because the bronze particles are considered to be in group B of the Geldart classification, bubbling occurs as soon as umf is reached. Therefore, also at the lowest flow rate of 40 L/min, gas bubbles are rising within the dense bed enhancing the particle mixing effect.

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Table 3. Velocity Ratios for Used Particles material

terminal settling velocity ut (m/s)

superficial velocity u0 (m/s)

riser velocity ratio u0/ut

ZrO2 resin

16.31 4.51

3.9 3.9

0.24 0.86

In summary, it can be said that none of the existing theories for captive fluidized beds fully predict the particle mixing in a circulating fluidized bed. It is clear that these equations were derived for superficial velocities in excess of the minimum fluidization velocity of the flotsam particles. One reason for the very good particle mixing for very low flow rates is the geometry of the gasifier, as its cone shape promotes internal circulation even at very low velocities. In addition, all of the existing equations were derived for noncirculating fluidized beds; in a circulating bed, however, the return flow of the particles also contributes to the particle mixing and thus has to be considered. Conclusions The behavior of particles in the circulating fluidized bed is very complex as not only the conditions in a bubbling bed but also the conditions in the riser have to be taken into account to predict residence times and particle mixing. It was stated above that solid circulation in the system starts for u0/ut ) 0.8. All of the experiments were carried out at flow rates of V/prim + V/sec ) 530 L/min. The resulting velocity ratios are listed in Table 3. It can be seen that, whereas the resin particles should just start to circulate, the ZrO2 particles are far from that point. This consideration is true for single-particle systems only. For a particle mixture, solid circulation of particles with higher ut values starts at lower velocity ratios. Di Felice et al.28 accounted for that effect by considering the particles with higher ut to be fluidized by a so-called pseudo-fluid having the physical properties of the particle-fluid suspension. Whereas the suspension viscosity can be approximated by the viscosity of the pure fluid, the density is now given by

Fsuspension )

csFs + F cs + 

(16)

where cs and Fs are the concentration and the density, respectively, of the particles having the lower ut. Assuming that the total solids concentration is constant in the upper part of the riser and using the concentration measurements resulting from particle mixing (Figures 15 and 16), the resulting pseudo-density is now 5560 times higher than that of the pure fluid, which could explain why the ZrO2 particles circulate throughout the entire system. At some point, however, the concentration of ZrO2 particles becomes so high that these particles will just rest as a fixed bed at the bottom of the riser; the fixed bed height will increase with increasing ZrO2 concentration. At even higher concentrations, the connection to the gasifier becomes completely blocked, and solid circulation stops. Thus, the occupied volume determines this point rather than the mass concentration, and for this reason, the results are plotted here as a function of volume concentration and not of mass concentration as is commonly found in the literature. At the point where solid circulation breaks down, the particle mixing in the gasifier will be com-

pletely different, because then the particle mixing is only driven by the generated gas bubbles in the gasifier. In general, it can be said that, for very low velocities in the gasifier, solids mixing can be achieved as a result of the novel shape of the gasifier as well as the overall gross circulation of the particles. Existing correlations predicting the solid mixing, however, are not applicable for this system, and more experiments using different types of particles need to be carried out in the future to derive a new correlation for this type of fluidized bed. Here, the complex influence of the different bubbling behaviors at different flow rates into the gasifier have to be taken into account. Particles simulating both the nongasified and the gasified biomass were used, and no difference in residence time was observed. The residence time of the particles during one complete cycle in the unit was related to the mass turnover of the circulating bed material. Here, a novel correlation was derived to predict the mean residence time of the biomass particles. This equation is applicable for circulating fluidized beds having a geometric design similar to that of the pilot plant under construction in Italy. For other systems, the exponential dependency of tres and M was also observed so that only the numerical parameters need to be adapted. The result reported by Kuramoto et al.2 that particles having a bulk density lower than the bulk density of the bed material will not circulate was not observed. The time spent by the biomass particles in the gasifier was found to be sufficient for the gasification process and to depend strongly on the mass turnover. Acknowledgment The authors thank the European Commission for funding this project within the framework Joule III program, Contract JOR3CT970196. Notation Φ ) velocity term F ) density (kg/m3) η ) viscosity (Pa s) c ) volume fraction (m3/m3) d ) particle diameter (m) D ) apparatus diameter (m) Gs ) solids mass flux (kg/m2s) h ) height (m) M ) dimensionless mass turnover m ) mass (kg) m* ) mass flow (kg/s) Mmix ) mixing index t ) time (s) u ) velocity (m/s) U ) dimensionless velocity ratio (u0/ut) u0 ) superficial velocity (m/s) umf ) minimum fluidization velocity (m/s) uTO ) takeover velocity (m/s) V* ) volumetric flow (m3/s) y ) rate of increase (1/s) z ) start of solid circulation (s) Indices gasi ) gasifier i ) counter prim ) primary rel ) relative res ) residence

Ind. Eng. Chem. Res., Vol. 41, No. 11, 2002 2645 sec ) secondary CSTR ) continuously stirred tank reactor PFR ) plug-flow reactor

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Received for review June 15, 2001 Revised manuscript received February 4, 2002 Accepted February 11, 2002 IE010513U