Powder Technology 145 (2004) 113 – 122 www.elsevier.com/locate/powtec
Volume contraction behaviour of binary solid–liquid fluidized beds Mohammad Asif * Department of Chemical Engineering, King Saud University, P.O. Box 800, Riyadh-11421, Saudi Arabia Received 6 November 2002; received in revised form 4 March 2004; accepted 28 June 2004 Available online 19 August 2004
Abstract Contrary to the widely held notion that the total bed height of a binary solid fluidized bed will be the sum of heights of the two individual mono-component beds fluidized at the same velocity, significant negative deviations have been observed in our experimental investigation. The negative deviations, signifying a contraction of the total volume of the binary solid fluidized bed, could sometimes be as high as 25% of the actual volume. The volume contraction has been found to depend mainly upon the degree of solids mixing prevailing in the bed irrespective of whether it is fully fluidized or not. The composition of the binary solid fluidized was another important factor that influenced the contraction behaviour of the bed besides the size ratio of the two constituent solid species of the binary present in the bed. D 2004 Elsevier B.V. All rights reserved. Keywords: Binary solid; Liquid fluidized bed; Volume contraction; Mixing
1. Introduction The presence of two different solid species in a binary solid–liquid fluidized bed, such that the larger one is lighter and the smaller one is denser, is known to reveal interesting hydrodynamic features, including the phenomenon of the layer inversion. It is, in fact, various stages of the mixing of the two solid components in the fluidized bed that causes it to exhibit the phenomenon of the layer inversion. A good deal of literature is available discussing various aspects of the layer inversion phenomenon and models for the prediction of its occurrence [1–12]. There are, however, not many studies that discuss the role of the solids mixing on the overall expansion of the fluidized bed. The common notion is that the mixing does not affect the expansion behaviour of the fluidized bed containing two or more solid species. Its obvious consequence is that the total bed height will be equal to the sum of the heights of individual mono-component beds fluidized at the same velocity. The model that embodies this notion is known as the serial model. The most commonly cited work in
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[email protected]. 0032-5910/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2004.06.007
this connection is the one of Epstein et al. [13]. Attributing the origin of the serial model to Lewis and Bowerman [14], they reported a good agreement with the serial model in their experimental investigation involving several binaries. The binary with the largest difference of the size of the two constituent solids in their study was the one of the size ratio of 5, which exhibited a broad spectrum of mixing stages over the range of fluidizing velocities considered, and yet showed very little deviation from the serial model predictions. Contrary to this, a little-known work of Chiba [15], using ambient tap water as the fluidizing medium, presented explicit experimental evidence of a negative deviation from the predictions of the serial model, signifying a volume contraction in a completely mixed liquid fluidized bed. The height of the mixed bed in the case of the binary of size ratio 4.75 in his work was as low as 75% of the one predicted by the serial model. Even the binary of size ratio as small as 2.4 was found to reveal a significant discrepancy. The comparison of his experimental findings with the predictions of the unit cell model of Moritomi et al. [5] was, however, not always satisfactory. More recently, Asif [16] also observed a significant volume contraction in a binary solid fluidized bed containing two solid species with over a 10-fold difference of the size and a substantial difference of the
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Table 1 Physical properties of particle samples used Solid species
Polyethylene terephthalate resin (PET) Sand Glass
Size (Am)
Density (kg/m3)
Richardson–Zaki correlation parameters Ut
n
2790
1396
96.6
2.66
250–300 425–500
2664 2465
34.7 59.1
3.79 3.1
density. Using a sand sample of wide size distribution (212– 300 Am) as the smaller component, the contraction behaviour observed in his study was found to be strongly related to the solids mixing prevailing in the bed. However, he considered only a limited range of the bed composition. It was, however, interesting to see the implication of the volume contraction on the overall bulk density of the binary solid bed in his work. In addition to above-mentioned experimental studies, models capable of predicting the composition dependence of the layer-inversion phenomenon are also likely to predict a volume contraction. One such example is the unit cell model as seen in the work of Chiba [15]. A few others have been pointed out by Asif [12]. However interesting, this issue will not be pursued here in view of a lack of relevance to the experimental focus of the present study. Needless to say, the issue of the existence of the volume contraction in the expansion behaviour of the binary solid– liquid fluidized bed is of fundamental importance from a hydrodynamics standpoint. Its proper understanding is an important prerequisite for understanding other hydrodynamic features of binary solid fluidized beds. In view of the above discussion, a careful experimental investigation has been carried out here using tap water maintained at 20 8C to study specifically the volume contraction behaviour of binary solid fluidized beds containing solid species which differ significantly in size as well as in density and exhibit a broad spectrum of mixing stages during the fluidization. Three solid species constituting two different binaries are considered here. These binaries mainly differ in their size ratios, being 10 for one and 6 for the other. For both cases, a wide range of bed compositions varying from 0.15 to 0.86 (volume fraction of the larger component) has been investigated. The range of liquid velocity studied included even the defluidized state of the binary solid bed.
orifices was used. The diameter of these distributor orifices was 2 mm, which were drilled on a square pitch to keep open only 4% of the total distributor area. This configuration gives about 1.3 holes/cm2 (of the distributor area). It has been pointed out before by Asif et al. [17,18] that such a distributor with high density of small orifices eliminates the presence of dead zones in the distributor region due to the liquid channeling even when low-density solid particles, which normally require operation at low liquid velocities, are used. To prevent the clogging of the distributor with solid particles, both faces of the distributor were covered with a fine mesh of 26% open area and negligible pressure drop. As an added precaution to eliminate entry effects, if any, a 0.5-m-long calming section packed with 3-mm glass beads was employed preceding the distributor. Throughout the present experimental investigation, particular care was observed to maintain the temperature of the tap water, used as the fluidizing medium, at 20F0.2 8C. This was important in view of the fact that any change in the water temperature significantly affects the viscosity and will consequently affect the bed height. The flow rate of the water was adjusted using one of three calibrated flowmeters of a suitable range. An immersion cooler was used to remove the heat generated by the water pump and maintain the water temperature constant in the water recirculation tank. The bed heights were read visually with the help of a ruler along the length of the column. The pressure drop along the bed was measured using an inverted air–water manometer. The observation included measuring the flow rate, the bed height and the pressure drop across the bed. 2.1. Solid particles There were three different kinds of solid samples used in the present experimental investigation. Their sizes and densities are tabulated in Table 1. Both sand and glass were sieved samples retained between two adjacent sieves. While the particles of sand and glass samples can be considered
2. Experimental The test section used for the present fluidization studies was a 1.5-m-tall transparent acrylic column. Its internal diameter was 60 mm. An important aspect of the design of the experimental setup was to eliminate the effect of the distributor, especially the presence of dead zones and the fluid channeling. Towards this end, a perforated plate (9 mm thick) with high density of uniformly distributed small
Fig. 1. Expansion behaviour of mono-component of beds of solid species in Table 1 along with their parameters of Richardson and Zaki correlation.
M. Asif / Powder Technology 145 (2004) 113–122 Table 2 Binary makeup
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Table 3 PET–glass system (binary I)
Binary
Component 1
Component 2
Size ratio
I II
PET PET
glass sand
6 10
nearly spherical, the slightly cylindrical PET resin had a Wadell’s shape factor of 0.85. The mono-component expansion behaviour of all the three solid samples was individually studied as shown in Fig. 1. The Richardson and Zaki correlations [19] parameters, U t and n, were evaluated from the expansion data as shown in the figure and are tabulated in Table 1. As shown in Table 2, two different binaries were considered here. Binary I was a PET–glass mixture, while the binary II was a PET–sand mixture. Both binaries show layer-inversion behaviour. In order to gain a better understanding of the mixing and segregation behaviour of two components in the binary solid fluidized bed, the bulk density profiles of individual particle species during monocomponent fluidization is shown in Fig. 2. The greater the difference in the bulk density profiles of the two components, one expects a higher degree of segregation. As the two bulk density profiles approach one another, the degree of mixing in the binary solid fluidized bed is likely to increase. As seen in the figure, the bulk density profile of sand intersects that of PET at about 23 mm/s. On the other hand, the same occurs at 48 mm/s for the glass and PET. As shown in Table 3, there were 10 experiments carried out for binary I including mono-component expansion studies. The binary solid fluidized bed composition, X 1, which is the fluid-free volume fraction of PET, was varied from 0.15 to 0.86. In experiments 1–7, the amount of glass was held constant, and the amount of PET was changed to get the desired composition of the bed. In the last two experiments, on the other hand, the amount of PET was held constant, and the amount of sand sample was changed. Thus, experiments 6 and 9 have different solid charges in spite of the same composition. Similarly, experiment 8 has much less total solid volume than 7 for X 1=0.86. This is
Experiment
1 2 3 4 5 6 7 8 9 10
Weight (g) PET
Glass
Total solid volume (cm3)
0.0 48.5 97.0 184.0 412.0 825.0 1723.0 690.0 690.0 690.0
500.0 500.0 500.0 500.0 500.0 500.0 500.0 200.0 418.0 0.0
202.8 237.6 272.3 334.6 498.0 793.8 1437.1 575.4 663.8 494.3
X1
Runs
0.000 0.146 0.255 0.394 0.593 0.744 0.859 0.859 0.745 1.000
4 1 2 2 2 2 1 2 1 4
mainly due to the limitation imposed by the height of the fluidization column. Note that a minimum of two runs were made for most bed compositions as seen in Table 3. Nine experiments were carried out for binary II as shown in Table 4. For the first seven experiments, the total amount of sand sample was held constant in the bed, while the PET charge was varied to get the desired bed composition. As in the case of binary I, the last two experiments for higher X 1 were carried out with much less total solid volume. The total solid volume and the bed compositions in these experiments were intentionally kept similar to the ones before, should there arise a need to make a comparison between the two binaries.
3. Results and discussion In the following, the definition of the volume contraction of the binary solid fluidized bed is first presented. The contraction behaviour of the binary I and binary II is discussed next. A comparison of the two binaries is presented last. The fractional volume change of a binary solid fluidized bed can be defined as a ratio of the difference between the composite and the actual bed heights to the actual bed height. The term composite here means the sum of the heights of the two individual mono-component layers fluidized at the same velocity and is, in fact, the height
Table 4 PET–sand system (binary II)
Fig. 2. Effect of liquid velocities on the overall bulk densities of the monocomponent beds of solid species considered in the present study.
Experiment
Weight (g) PET Sand
Total solid volume (cm3)
X1
Runs
1 2 3 4 5 6 7 8 9
0.0 44.5 97.5 195.0 412.0 825.0 1723.0 500.0 500.0
198.4 230.3 268.2 338.1 493.5 789.4 1432.6 415.7 478.3
0.000 0.138 0.260 0.413 0.598 0.749 0.862 0.862 0.749
2 1 2 2 1 1 2 1 1
528.5 528.5 528.5 528.5 528.5 528.5 528.5 153.3 320.0
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predicted by the serial model. Instead of the height, it is often more convenient to use the specific volume, V, which is the bed volume occupied by the unit volume of the solid. Thus, one can write, Volume changeð%Þ ¼
VSM VActual 100 VActual
In the above definition, 1 VActual ¼ 1 eActual
ð1Þ
ð2Þ
where e Actual is the overall void fraction of the binary solid fluidized bed, and V SM is the volume mean of the specific volumes of the mono-component fluidized beds that can be written as, VSM ¼ X1 V1 þ ð1 X1 ÞV2
ð3Þ
where V 1 and V 2 are specific volumes of mono-component bed of components 1 and 2, respectively, when fluidized at the same superficial velocity as the binary solid fluidized bed. Note that Eq. (3) is a statement of the serial model written in terms of specific volumes. From the above definition of the fractional volume change, it is clear that its positive value will indicate a contraction of the bed. It is also worthwhile to point out at this stage that mono-component values of specific volumes needed to compute the composite bed height (V SM) can be obtained in two ways. First, the actual (experimentally measured) value of the mono-component expansion is used. Second, the experimental mono-component expansion data are fitted with the Richardson–Zaki equation, yielding correlation parameters which can subsequently be used to predict the mono-component specific volumes. The first approach is apparently more accurate and will therefore be followed in the present work unless otherwise mentioned. 3.1. Binary I: PET–glass system The first experiment for this binary involved four runs carried out to study the mono-component expansion behaviour of glass. A good agreement among them was observed. For most other binary-bed compositions, a minimum of two runs were carried out. The volume contraction behaviour in both runs of each experiment is shown together in Fig. 3. It can be seen here that the overall agreement between individual runs of the same experiment is excellent at lower liquid velocities. Some deviations are clearly visible at higher liquid velocities. In this connection, it is important to mention that swirling instability was seen developing at a velocity of 42 mm/s and above for the mono-component fluidized bed of glass. The same phenomenon was also observed for binary solid fluidized beds in the
Fig. 3. Volume contraction behaviour of binary solid fluidized beds of binary I at different compositions.
upper glass layer at these liquid velocities. Note that experiments 3 and 5, although shown together, have different compositions.
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Runs of each experiment are averaged and presented in Fig. 4. It is seen here that both the liquid velocity as well as the bed composition significantly affect the contraction behaviour of the binary solid fluidized bed. Below a liquid velocity of 30 mm/s, the bed contraction is seen to be similar for all compositions. This, however, changes at higher velocities. Now, the contraction behaviour strongly depends upon the composition of the binary solid bed. For higher X 1, the degree of contraction keeps on increasing with the velocity before decreasing as seen for the cases of X 1=0.75 (experiments 6 and 9) and X 1=0.86 (experiments 7 and 8). In this way, one maximum is noted for each these two compositions. The degree of bed contraction for lower X 1, on the other hand, first decreases and then increases as the velocity is increased beyond 33 mm/s. As a result, a minimum is observed for each of these compositions around a liquid velocity of 40 mm/s. It is important at this stage to examine the correlation between the contraction behaviour of the binary solid fluidized bed and the observed degree of mixing of two components prevailing in the fluidized bed of binary I. This is presented in Fig. 5, which shows total bed heights as well as heights of mixed PET–glass layers. At lower liquid velocities, a layer of pure glass constitutes the lower layer, whereas a mixed layer of PET–glass constitutes the upper layer, so the location of its top is the same as the total height of the bed. At this stage, a relatively high degree of segregation is observed with most glass in the mixed layer present close to the interface of the two layers. As the liquid velocity is increased, the fluidized bed expands and the glass from the lower mono-component layer starts to move into the upper mixed layer increasing its size. This continues till a uniform mixing of both components prevails throughout the bed. This state of complete mixing of the two components is termed as the onset of the layer inversion in the literature. An increase in the liquid velocity now leads to the development of a mono-component layer of glass above the mixed PET–glass layer. With a further increase of the liquid velocity, this segregation tendency increases, which is reflected by the continued shortening of the lower mixed
Fig. 4. Effect of the liquid velocity and the bed composition on the volume contraction behaviour of binary solid fluidized bed containing binary I.
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Fig. 5. Effect of the liquid velocity and the bed composition on the total bed height and the height of the mixed PET–glass layer.
layer and the growth of the upper mono-component layer of glass. It is seen in Fig. 5 that the appearance of a layer of glass takes place between the liquid velocity of 30–44 mm/s, depending upon the bed composition. The presence of larger amount of PET at higher X 1 delays the appearance of the upper glass layer. Comparing Figs. 4 and 5, the peak observed in the profile of the bed contraction for a given bed composition appears to correspond to the complete mixing of the two components. From the foregoing description of the mixing and segregation behaviour of the binary solid fluidized bed, it is clear that the degree of contraction is related to the degree of mixing of the two components prevailing in the binary solid fluidized bed. The question still remains as to why should there be a contraction phenomenon associated with the mixing of the two components. Its most plausible explanation appears to be the absorption of the smaller glass beads into the interstitial spaces of the porous matrix of the larger component. As a result, a fraction of the glass beads and/ or its associated void space are lost as far as its contribution, the overall expansion of the binary solid fluidized bed, is concerned. Therefore, as the fraction of the larger particle species is increased in the fluidized bed, its capability to accommodate the smaller component also increases simultaneously. This explains the increase in the degree of contraction with an increase in X 1. The trend, however, reverses for X 1=0.86 in experiment 8. Now, the amount of the larger component in the fluidized bed is much higher and is therefore capable of accommodating much higher amount of smaller component than that which is available at this composition. This causes a lowering of the bed contraction. The above explanation of the mixing-induced contraction phenomenon is mainly based on the visual observation of the binary solid bed when the bed is partially segregated. Especially when the fraction X 1 is 0.6 and higher, one can clearly see the smaller glass trapped in the interstices of the matrix of the PET layer. On the other hand, when the two components are substantially mixed at higher liquid velocities, another plausible mechanism of contraction
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could prevail. Noting that the denser (but smaller) component will have a larger associated void space as compared to the larger (but lighter) component, the glass could hold the PET in its interstitial space causing a contraction. Yet an entirely different mechanism could actually prevail at higher liquid velocities for smaller X 1. Due to its smaller population, the larger component fails to evolve a neighborhood consisting of particles its kind and gets individually caught up in the rather more vigorous motion of the denser component. This leads to an increase in the void space surrounding the PET particles, which could ultimately cause a negative value of contraction as seen in Fig. 4. Despite an increase in the segregation behaviour of the binary solid fluidized beds after the layer-inversion phenomena as seen in Fig. 5, an increase in the degree of contraction is once again witnessed in Fig. 4 for X 1 less than 0.75 and velocities above 40 mm/s. This is at variance with the explanation of the mixing-induced contraction phenomenon put forward before. This is apparently due to the swirling instability observed in the glass layer at the two highest flow rates reported here. For higher X 1, on the other hand, the mixed PET–glass layer dominates the major portion of the binary solid fluidized bed, which either delays or attenuates the appearance of the swirling. This type of bed contraction can therefore be termed as the swirlinginduced contraction phenomenon. As pointed out earlier that the composite bed height, or V SM, in Eq. (3) can either be based on the actual bed void fraction or predicted from the fitted parameters of the Richardson–Zaki correlation reported in Table 1. In the foregoing, the results presented were all based on actual values of the void fraction. It is, nevertheless, worthwhile at this stage to examine the effect on the contraction behaviour when predicted values of the mono-component bed expansion are used. Towards this end, the difference between the predicted and actual values of the expansion of the monocomponent bed of glass is first compared at different liquid velocities. This is shown in Fig. 6, which presents the data
Fig. 6. Mono-component-specific volumes for all the four runs, their average along with the fitted values using the Richardson–Zaki correlation for the mono-component bed of glass. The chart window shows the difference between fitted and averaged experimental values.
Fig. 7. Bed contraction behaviour of binary solid fluidized bed of PET– glass using predicted composite bed height.
for all the four runs and their average, in addition to the fitted values for the bed of glass. The chart window highlights the percentage difference between the average and the fitted values of the specific volumes. It is obvious that the maximum deviation between the two does not exceeds 3%. A similar exercise for the expansion of the mono-component bed of PET yielded a maximum deviation that was less than 2%. The smoothing effect of using the predicted values of the mono-component expansion is visible in Fig. 7. While not much difference (from Fig. 4) is seen in contraction profiles for higher X 1, the occurrence of a minimum for lower X 1 is more accentuated now at about 40 mm/s. 3.2. Binary II: PET–sand system This system differs from the previous one mainly in the size ratio. This caused a considerable difference on their defluidization dynamics. This issue is discussed in detail elsewhere [20]. Suffice it to say that during the defluidization process, the capacity of the upper mixed layer to accommodate its smaller counterpart is significantly enhanced when the size ratio of the two components increases. The dependence of the bed contraction on the liquid velocity for different compositions of binary II is depicted in Fig. 8. The bed contraction is seen to depend upon both X 1 and U o. For all velocities, as X 1 increases from 0.14 in experiment 2 to 0.60 in experiment 5, the bed contraction tends to increase. On further increasing X 1, the degree of contraction, however, depends upon U o. At the highest velocities considered here, the contraction increases with X 1. However, this behaviour changes as the liquid velocity is lowered. When U o is around 17 mm/s, the maximum contraction occurs for X 1=0.75. In a completely defluidized bed, on the other hand, the maximum contraction occurs for X 1=0.60, which tends to decreases with any further increase in X 1. The dependence of the volume contraction of the bed on the liquid velocity, on the other hand, is more complex. For
M. Asif / Powder Technology 145 (2004) 113–122
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Fig. 8. Effect of the liquid velocity and the bed composition on the volume contraction behaviour of the binary solid fluidized bed containing binary II.
a binary solid fluidized bed of a given composition, the bed contraction is lower at higher liquid velocities but tends to increase initially as the liquid velocity is lowered and shows a maximum in the range of 15–20 mm/s. With a further lowering of the liquid velocity, the contraction begins to decrease down to around 11 mm/s, which is the minimum fluidization velocity of the PET resin. If the liquid velocity is lowered further, the degree of contraction, unlike binary I, again shows a significant increase for the bed compositions in the range of 0.25–0.75. As seen earlier for the case of the binary I, the observed volume contraction behaviour of binary II is also found to be closely tied to the degree of mixing of the two components in the bed. At higher liquid velocities, the bed is segregated with a pure layer of sand being at the top and a mixed layer of PET and sand in the lower region of the fluidized bed. This can be seen in Fig. 9a, which shows a photograph of the fluidized bed for X 1=0.60 in experiment 5. As the liquid velocity is lowered, a downward migration of the sand from the upper mono-component layer into the lower mixed layer takes place till both components are uniformly mixed throughout the bed. The liquid velocity at which the complete mixing or the layer inversion takes place depends upon the composition of the bed as seen in Table 5. One finds the same trend of peaks of contraction profiles in Fig. 8. Further lowering the liquid velocity leads to the segregation again with a mono-component layer of sand developing below and a mixed PET–sand layer above. This can be seen in Fig. 9b. The segregation tendency at lower velocities leads to a lowering of the bed contraction again. However, if the liquid velocity is lowered even below the U mf of the PET resin, the sand of the lower layer starts to move into the interstices of the PET layer above. This leads to an enhanced degree of mixing of the two components and reflects into an increase in the degree of contraction. A detail description of the defluidization dynamics of such binaries and their dependence on the bed composition is described elsewhere [20]. Thus, one sometimes notices two maxima in the contraction profiles of Fig. 8. One occurs during the fluidization
Fig. 9. Photos of binary solid fluidized bed before and after the layer inversion in Experiment 5. White particles are PET resin and the dark is sand.
when the two components are uniformly mixed, whereas the other one occurs during the defluidization. Very often, both maxima appear to be of comparable magnitude, except the one for X 1=0.86 in experiment 7. In this case, the degree of contraction during the defluidized state progressively decreases with the lowering of the liquid velocity. The question arises why the volume contraction at this composition (X 1=0.86) is so high during the fluidized state. This can be explained by taking into account the void fraction associated with the expansion of the smaller component. At higher liquid velocities, the presence of smaller component in the interstices of the mixed PET–sand layer entails not only its loss but also of
Table 5 Liquid velocity in millimeters per second at which complete mixing occurs for binary II (based on Fig. 3a and b in Ref. [12]) Experiments
Velocity
2 3 4 5 6 7 8 9
15.0 15.3 15.5 16.5 19.0 20.0 20.5 19.0
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Fig. 10. Effect of the total solids volume on the volume contraction behaviour for the fluidized bed containing binary II.
its associated void fraction, which progressively increases with the increase of the liquid velocity. In order to examine the effect of the total volume of solids present in the PET–sand solid fluidized bed, a comparison is made in Fig. 10 showing experiments of same composition but with different total solid volumes (see Table 4). It should be kept in mind that the difference in the total solid volume in the fluidized bed translates into a proportionate difference in the height of the fluidized bed so long as the composition is the same. Not much difference is seen between experiments 6 and 9 (X 1=0.75), where the total solids volume difference is little less than twofold except at U o=23.6 mm/s. On the other hand, experiments 7 and 8 (X 1=0.86) with much greater difference in their total
Fig. 11. Comparison of contraction profiles of binaries I and II. The solid makers represent binary I, and empty markers represent binary II. The x-axis is normalized velocity as discussed in the text.
M. Asif / Powder Technology 145 (2004) 113–122
solid volumes show clear differences at higher liquid velocities, being prominent for 23.6 mm/s. Thus, when the total solids volume is smaller, the contraction is often larger at higher liquid velocities. This appears to be due to the nonuniform distribution of the sand into the mixed PET– sand layer, which tends to delay the appearance of the upper mono-component sand layer, thereby increasing the degree of contraction. 3.3. Comparison of contraction behaviour of binaries I and II Since the two binaries considered in the present experimental investigation significantly differ in their size ratios, it is interesting at this stage to examine the effect of the size difference on their contraction behaviour. The difficulty in this connection arises from the fact that the two binaries exhibit a complete mixing, and therefore, the peaks in their contraction profiles occur at different liquid velocities. In order to circumvent this problem, the liquid superficial velocities are normalized using the velocity at which the bulk density profiles of the two components of a binary intersect. These values are 23 mm/s for the binary I and 48 mm/s for the binary II as seen in Fig. 2. The results are shown in Fig. 11. There are six charts in this figure for the six binary compositions considered here. The contraction profiles of both binaries of similar compositions are presented together for the sake of comparison. It is clear from these figures that the velocity normalization carried out here does help to align the contraction peaks of the two binaries. The general trend seen here is that an increase in the size ratio commonly leads to an increase in the contraction behaviour. The reason for this phenomenon is simple. As the difference in the size of the two components increases, the larger component can accommodate greater amount of smaller counterpart in its interstitial void space. This feature is found to be more prominent for high X 1. This is due to the fact that a greater amount of the larger component could absorb a greater amount of the smaller component. This absorption capacity of the larger component increases as the size difference of the two components increases. By the same token, as the amount of larger component is decreased in the bed, the effect of the difference of the size ratio increasingly gets blurred. Unlike the case of PET–glass, however, no swirling-induced contraction is seen for PET– sand case. Another issue, which is not directly related to the issue of the bed contraction, nonetheless, comes into picture due to the velocity normalization procedure adopted here. This is the occurrence of the peak of the contraction curves. If one explains the phenomenon of the layer inversion based on the equality of bulk densities of the two components, one would expect its occurrence when the value of the normalized velocity is unity. However, it is always seen to
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be less than unity in all cases here. For lower X 1, its value is around 0.70 and is hardly seen going beyond 0.85 for higher X 1.
4. Conclusions Several types of mixing effects have been observed to prevail in binary solid fluidized bed. The most common is the occurrence of the volume contraction of the bed due to the mixing of the two solid components present in the bed. Factors, e.g., liquid velocity, bed composition and the size ratio of the binary that normally affect the solids mixing also influence the contraction behaviour of the bed. Besides the predominant mechanism of the mixinginduced volume contraction, an altogether different type of mechanism is sometimes found to prevail at lower concentrations of the larger component as seen in the case of PET– glass. Instead of a contraction, this mechanism leads to a positive deviation from the serial model predictions. However, another type of volume contraction, which is not related to the solids mixing, arises from the swirling instability observed in the fluidized bed at high liquid velocities. In the present study, the mono-component bed of glass or its layer in binary I was found to be more susceptible to such a behaviour. It is seen here that a significant contraction could also occur when the bed is either partially or fully defluidized. In such a case, a much stronger influence of the size ratio is observed. Of several plausible explanations, the occurrence of the phenomenon of mixing-induced contraction appears mainly due to the filling of the interstitial void space of the larger component by the smaller component.
Symbols used n Richardson–Zaki correlation index (–) PET polyethylene terephthalate resin (–) U mf minimum fluidization velocity (mm s1) Uo liquid superficial velocity (mm s1) Ut Richardson–Zaki correlation parameter (U o=U t for e=1), (mm s1) total bed volume V overall specific volume ¼ total solids volume (–) Vi mono-component specific volume of i th species (–) V SM specific volume predicted by the serial model (–) X1 fluid-free volume fraction of particle species 1 (–) e overall bed void fraction (–)
Acknowledgement This work was supported by the Research Center, College of Engineering, King Saud University. Help of Dr. A. Ibrahim and Engr. A. Ismail with the experimental work is greatly appreciated.
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References [1] H. Moritomi, T. Iwase, T. Chiba, A comprehensive interpretation of solid layer inversion in liquid fluidized beds, Chem. Eng. Sci. 37 (1982) 751 – 757. [2] G. Van Duijn, K. Rietema, Segregation of liquid-fluidized solids, Chem. Eng. Sci. 37 (1982) 727 – 733. [3] N. Epstein, B.P. LeClair, Liquid fluidization of binary particle mixtures: II. Bed inversion, Chem. Eng. Sci. 40 (1985) 1517 – 1526. [4] L.G. Gibilaro, R. Di Felice, S.P. Waldram, P.U. Foscolo, A predictive model for the equilibrium composition and inversion of binary solid–liquid fluidized beds, Chem. Eng. Sci. 41 (1986) 379 – 387. [5] H. Moritomi, Y. Yamagishi, T. Chiba, Prediction of complete mixing of liquid-fluidized binary solid particles, Chem. Eng. Sci. 41 (1986) 297 – 305. [6] R.H. Jean, L.S. Fan, On the criterion of solid layer inversion in liquid–solid fluidized bed containing a binary mixture of particles, Chem. Eng. Sci. 41 (1986) 2811 – 2821. [7] N. Funamizu, T. Takakuwa, An improved Richardson–Zaki formula for computing mixed layer composition in binary solid–liquid fluidized beds, Chem. Eng. Sci. 50 (1995) 3025 – 3032. [8] N. Funamizu, T. Takakuwa, A minimal potential energy model for predicting stratification pattern in binary and ternary solid–liquid fluidized beds, Chem. Eng. Sci. 51 (1996) 341 – 351. [9] J.F. Richardson, E. Afiatin, Fluidization and sedimentation of binary mixtures of particles in a liquid, 9th International Conference on Transport and Sedimentation of Solid Particles, 2–5 September 1997, Cracow, Poland (1997).
[10] M. Asif, Segregation velocity model for fluidized suspension of binary mixture of particles, Chem. Eng. Process. 37 (1998) 279 – 286. [11] M. Asif, Generalized Richardson–Zaki correlation for liquid fluidization of binary solids, Chem. Eng. Technol. 21 (1998) 77 – 82. [12] M. Asif, Predicting binary solid fluidized bed behaviour using averaging approaches, Powder Technol. 127 (2002) 226 – 238. [13] N. Epstein, B.P. LeClair, B.B. Pruden, Liquid fluidization of binary particle mixtures: I. Overall bed expansion, Chem. Eng. Sci. 36 (1981) 1803 – 1809. [14] E.W. Lewis, E.W. Bowerman, Fluidization of solid particles in liquids, Chem. Eng. Progr. 48 (1952) 603 – 608. [15] T. Chiba, Bed contraction of liquid-fluidized binary solid particles at complete mixing, in: K. Yoshida, S. Morooka (Eds.), Proc. of Asian Conf. on Fluidized-Bed and Three-Phase Reactors, Soc. of Chem. Eng, Japan, 1988, pp. 385 – 392. [16] M. Asif, Expansion behaviour of a binary solid–liquid fluidized bed with large particle size difference, Chem. Eng. Technol. 24 (2001) 1019 – 1024. [17] M. Asif, N. Kalogerakis, L.A. Behie, Distributor effects in liquid fluidized beds of low-density particles, AIChE J. 37 (1991) 1825 – 1831. [18] M. Asif, N. Kalogerakis, L.A. Behie, Hydrodynamics of liquid fluidized beds including the distributor region, Chem. Eng. Sci. 47 (1992) 4155 – 4166. [19] J.F. Richardson, W.N Zaki, Sedimentation and fluidization: I, Trans. Inst. Chem. Eng. 32 (1954) 35 – 52. [20] M. Asif, A.A. Ibrahim, Minimum fluidization velocity and defluidization behaviour of binary solid–liquid-fluidized beds, Powder Technol. 126 (2002) 241 – 254.
