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Characterization of the upward motion of an object immersed in a bubbling fluidized bed of fine particles
Chemical Engineering Journal 280 (2015) 26–35
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Chemical Engineering Journal journal homepage: www.elsevier.com/locate/cej
Characterization of the upward motion of an object immersed in a bubbling fluidized bed of fine particles Farzam Fotovat a,⇑, Jamal Chaouki b,⇑ a b
Department of Chemical and Biological Engineering, University of British Columbia, Vancouver V6T 1Z3, Canada Department of Chemical Engineering, École Polytechnique de Montréal, C.P. 6079 succ., Centre Ville, Montreal, QC H3C 3A7, Canada
h i g h l i g h t s Two characteristics velocities are defined to describe the rise of the objects. Drift of bubbles is recognized as the main reason of the object rise. A correlation is proposed to predict the mean rise velocity of the immersed objects. The upward velocity of the objects is modeled based on the force balance in the drift region. The object rise frequency depends on the characteristics of the bed material.
a r t i c l e
i n f o
Article history: Received 1 March 2015 Received in revised form 21 May 2015 Accepted 22 May 2015 Available online 6 June 2015 Keywords: Gas–solid fluidization Radioactive particle tracking Object circulation Bubble Object rise frequency
a b s t r a c t The axial motion of HDPE, Acetal, and PTFE spheres immersed in a 3-D bed of the conventional fluidization materials was studied using the non-invasive radioactive particle tracking (RPT) technique. Coarse and fine sand as well as FCC were chosen as the fluidization material. The experiments were carried out at two excess gas velocities, i.e. Ue = 0.25 m/s and Ue = 0.50 m/s. Rise of an object immersed in a bubbling fluidized bed can be descried by two characteristic velocities, i.e. rise and upward velocity. When circulation pattern is fully established, the mean upward and rise velocity to the mean bubble velocity ratios become comparable. It is shown that the object rise takes place principally in the drift of bubbles. The mean object rise velocity is primarily influenced by the excess gas velocity. Comparatively, the ratio between the physical properties of the fluidization medium and the object such as size and density has trivial impact on the rise velocity of the object. The mean object upward velocity can satisfactorily be predicted with a theoretical model with no adjustable parameter. The frequency of the object rise along the bed is independent of the object properties but influenced by the fluidization material. Comparing to coarse sand and FCC, the objects immersed in fine sand rise less frequently. This is attributed to the relatively longer residence time of the object in the emulsion phase of fine sand particles. The intermittent circulation of the medium and large size Acetal spheres in beds of FCC and fine sand is featured by the low upward and rise object velocities and the very limited height travelled by the object. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction Due to unique features such as excellent solids mixing and heat transfer; fluidized beds are one of the best and widely used systems for handling multiphase chemical and physical processes. In practice, many of the industrial fluidized beds involve objects that
⇑ Tel.: +1 604 827 5921, +1 514 340 4711x4034; fax: +1 514 340 4159. E-mail addresses: [email protected] (F. Fotovat), [email protected] (J. Chaouki). http://dx.doi.org/10.1016/j.cej.2015.05.130 1385-8947/Ó 2015 Elsevier B.V. All rights reserved.
are irregular in terms of size, density and shape. Fuel particles (such as coal, biomass or waste materials), catalysts and agglomerates are some examples of these objects. Characterization of the motion of the irregular objects within the bed is crucial to prevent the operational problems such as emergence of hot or cold spots and the appearance of defluidized zones due to the formation of agglomerates [1]. Occurrence of segregation in fluidized beds involving dissimilar components such as irregular objects and conventional materials is another phenomenon that could have detrimental effects on the
F. Fotovat, J. Chaouki / Chemical Engineering Journal 280 (2015) 26–35
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Nomenclature Symbols Ac Ao Cd D db do dp Fod H Re Ub Ue Uf Umf Uo Ur Uu Up g g(e) Vo
catchment area of the single distributor hole (m2) cross sectional area of the spherical object (m2) drag coefficient (–) internal diameter of the bed (m) bubble diameter (m) object diameter (m) particle diameter (m) object rise frequency (–) dense bed height (m) Reynolds number (–) bubble rise velocity (m/s) excess gas velocity (m/s) fluid (gas) velocity (m/s) superficial gas of velocity of fluidization material at minim fluidization condition (m/s) object velocity (m/s) object rise velocity (m/s) object upward velocity (m/s) particle velocity (m/s) gravitational constant (m/s2) voidage function (–) object volume (m3)
process if chemical reactions take place in the system. On the other hand, segregation could beneficially be exploited to facilitate the operation of fluidized bed separators or classifiers used for coal cleaning, ore processing, and separation of the solid waste components [2]. On the basis of the experimental observations, objects rise by the action of ascending bubbles and sink in the bed with the dense phase. Since the downward flow of the dense phase is governed by the bubbles, they are responsible for the motion and circulation of the objects in the bed. Moreover, it has been shown that the bubbling characteristics of the segregating systems influence the degree and pattern of mixing/segregation of the constituting substances [3]. Profound understanding of the combustion or gasification of carbonaceous particles in bubbling fluidized beds depends on having detailed knowledge of circulation of large/light objects in a bed of fine/heavy particles. In these systems fuel particles tend to move up to the bed surface. Since fuel particles rise very fast and the time needed to reach the bed temperature increases dramatically with the size of fuel particles, thermal fragmentation and the consecutive reactions mostly take place at the top of the bed and the resulting reaction products and heat are released in the freeboard. This could dramatically reduce yield of desired reactions, increase tar formation and lead to occurrence of the hot spots, all deteriorating the reactor performance. Hence, it is of vital importance to gain a better insight into the rise pattern of objects differing in size and density in a variety of fluidization materials. Such insight could be helpful to improve the reactor performance by choosing the optimal fuel and bed material in terms of physical properties such as size and density. Motion of objects moving in bubbling fluidized beds has been studied using different experimental techniques. Rios et al. [4] explored the free motion of large light objects with various sizes and densities in 2-D and 3-D gas fluidized bed of heavy fine particles by employing cinematographic and radioactive tracing techniques. As they reported, the mean rise velocity of the objects is much lower than the bubble velocity (30%) since rise of an object to the bed surface is achieved by several jumps or jerks induced by passing bubbles. They also observed that the tendency of the object
trise tsink z
time spent by the object in a rising path (s) time spent by the object in a sinking path (s) height above the distributor (m)
Greek letters b parameter defined in Eq. (7) (–) e bed voidage (–) lf dynamic viscosity of fluid (gas) (Pa.s) qf fluid (gas) density (kg/m3) qo object density (kg/m3) qp particle density (kg/m3) sr relaxation time (s) Subscripts cal calculated exp experimental f fluid m mean value mf minimum fluidization o object p particle
to be involved in large amplitude displacement is increased with decreased size and increased density. Lim and Agarwal [5] used automated image analysis of a 2-D bubbling fluidized bed to characterize the circulation pattern and measure the velocity profile of large spherical objects and coal particles mixed with glass beads. Like Rios et al. [4], they reported that the mean rise velocity of the fluidized object is 30% of the mean bubble velocity along the bed. However, by studying the circulation characteristics of a variety of objects with different densities and sizes Soria-Verdugo et al. [1] found that the ratio of the mean rise velocity of the objects to the mean velocity of bubbles is around 20%. Moreover, they observed that the object rising velocity hardly varies with its density or size. Employing the radioactive particle tracking (RPT) technique, Fotovat et al. [6–8] provided insight into the circulation behavior and velocity profile of large cylindrical biomass particles fluidized with sand under bubbling conditions. RPT is a powerful non-invasive method that provides the instantaneous 3-D position of the tracked particle in a Lagrangian framework. Post-processing of the RPT data is helpful to reveal the characteristics of the motion of the tracer in the multiphase flow systems. Use of the computer-automated radioactive particle tracking (CARPT) technique for studying the solid circulation pattern of large objects in 3 phase fluidized beds involving binary mixtures was initially introduced by Larachi et al. [9]. Cassanello et al. [10] adopted this technique to investigate solids mixing in gas–liquid–solid fluidized beds. More recently, Upadhyay and Roy [11] employed this method to explore the mixing and hydrodynamic behavior in a bed consisting of equal weight percentages of the same size particles differing in density. On the basis of the RPT data, Fotovat et al. [6] realized that the average rise velocity of biomass particles is about 20% of the average bubble rise velocity, consistent with the findings of Soria-Verdugo et al. [1]. Measuring the rise velocity of a single sphere for a limited ratio of U/Umf in a bubbling and slugging fluidized bed, Rees et al. [12] demonstrated that this velocity is linearly correlated with the superficial gas velocity and the slope of this linear correlation was linked to the fluidization regime. In addition, like the
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preceding researchers [13], they observed that the rising objects carry on a defluidized hood of particles on their top. In a bubbling fluidized bed involving fine particles, it has been well established that bubbles induce rise of particles by carrying them upward in the bubble wake, i.e. the solids occupying the bottom of the completed sphere bubble, and in the drift, i.e. the region behind the completed sphere [14]. Particles rising inside the bubble wake exhibit a constant velocity at the same velocity as the bubble. The drift induced by the bubble motion generally moves at a velocity proportionally lower than the bubble velocity [15]. In the case of drift, particles undergo net displacement outside the wake due to the passage of bubbles, upwards near the bubble axis and downwards at several bubble radii from the axis [16]. The upward motion of the particles is offset by their downward flow in an emulsion phase close to the bed wall. Particles in the emulsion phase exhibit a Brownian-like motion, moving randomly in any direction [17]. Although these facts have been well known for the conventional fluidization material particles such as sand and FCC, further research is required to gain an insight into the mechanisms of solids displacement in case of irregularly large and light objects. In spite of the several studies conducted on fluidization of the large objects in a bed of conventional fine materials, no clear explanation has yet been provided to elucidate the phenomenological relationship between the bubbling and object rise velocities. Addressing this issue, the velocity profiles of a variety of spherical objects with different sizes and densities are scrutinized in this work by means of the RPT technique in order to shed light on the mechanisms governing rise of the object. Moreover, the impact of three different fluidization media, i.e. coarse and fine sand as well as the fluid catalytic cracking (FCC) catalyst, on the rise of immersed objects is studied. A comparison is also made between the experimental mean rise velocities of the objects and the corresponding values predicted by a model, which has been developed on the basis of the forces exerted on the object.
Table 2 Properties of the spherical objects. Designation
Material
do (mm)
qo (kg/m3)
HDPE PTFE Acetal-S Acetal-M Acetal-L
HDPE PTFE Acetal Acetal Acetal
9.5 9.5 4.8 9.5 19.0
929 2166 1381 1368 1347
To make a radioactive tracer from each object for the RPT tests, a tiny piece of metallic scandium is embedded into a small hole made on each polymeric sphere so that the size and density of the final tracer would not be different from those of the original particle. The tracer is then activated in the SLOWPOKE nuclear reactor of École Polytechnique de Montréal up to an activity of 70 lCi. The produced isotope 46Sc emits c-rays, which are counted by 12 NaI scintillation detectors placed around the column. Before each test, the desired tracer is dropped into the column and system is fluidized for a few minutes to ensure steady fluidization prior to starting data acquisition. The static bed height of each test is set to 228 mm (H/D = 1.5). A high speed data acquisition system counts the number of c-rays detected by each detector. These counts are analyzed later to calculate the coordinates of the tracer. Details of the system calibration and the inverse reconstruction strategy for determining tracer position can be found elsewhere [18,19]. In each experiment, the location of the tracer is tracked every 10 ms for about 4 h until around one and half million points are finally acquired. The excess superficial gas velocities, i.e. (Ue = U Umf), chosen for the tests are Ue = 0.25 m/s and Ue = 0.50 m/s. To this purpose, the desired air flow rate of each run is adjusted through a set of rotameter and orifice plate to reach the intended superficial gas velocity ranging from 0.25 to 1 m/s. It should be noted that the single tracer dropped into the bed was the only large object mixed with the bed materials.
3. Results and discussion 2. Experimental 3.1. Rise velocity of the object All experiments are conducted in a cylindrical Plexiglas column 152 mm in diameter equipped with a perforated plate as an air distributor. Under the ambient conditions, air is injected into the column through 163 holes of the distributor, which are 1 mm in diameter and arranged in a triangular pitch. Fine and coarse sand as well as FCC particles are used as the bed material. Five small polymeric spheres differing in size and density are chosen to be used as the object fluidized in a bed of fine particles. Tables 1 and 2 list properties of all materials used in this study. The true density is measured with a gas pycnometer (Micromeritics, AccuPyc II 1340) while the bulk density is measured with a graduated cylinder. Umf values of bed materials are determined experimentally in a 75 mm i.d. column equipped with a perforated plate. S, M, and L in designation of the spherical Acetal objects stand for the small, medium, and large size, respectively. The respective densities of these objects are not significantly different; however, all of them are made from Acetal upon the supplier claim.
The RPT result, which is the instantaneous position of the immersed object, can be processed in order to attain the velocity profile of the tracer. For this purpose, the local axial, radial and angular velocities are determined; however only the axial velocity of the tracer is a matter of interest in this study. As introduced by Mostoufi and Chaouki [17], when the tracer is displaced in the wake or drift of bubbles, its axial coordinates of the trajectory vs. time exhibit a straight line with a positive slope. It is also expected that when the tracer sink as a consequence of bubble drift, its trajectory would be a straight line with a negative slope. In order to distinguish between the different mechanisms governing the object displacement, it is assumed that the straight lines on the axial trajectory of the tracer correspond to stable bubbles, whereas, nonlinear parts of the trajectory correspond to either the random movement of the object in the emulsion or bubbles which have not reached their stable size. Accordingly, the axial trajectory of the tracers used in this study is analyzed to
Table 1 Properties of the bed materials. Material
Particle size range (lm)
dp,m (lm)
qP (kg/m3)
qb (kg/m3)
Voidage (–) (fixed bed)
Umf (m/s)
Geldart classification
Coarse sand Fine sand FCC
400–2000 50–700 30–300
770 220 80
2650 2650 1690
1350 1406 928
0.49 0.47 0.45
0.44 0.05 0.004
B–D B A
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characterize the mechanisms provoking jump of the large objects immersed in a bed of fine particles. As explained, jump of the objects is linked to the linear segments of the axial trajectory having positive slopes. These segments are detected through a computer program by applying the following criteria. 1. The segments are demarcated by the local minima and maxima of the axial trajectory of the object. 2. The correlation coefficient of the segment correlated with a line should be equal or greater than 0.995. 3. The minimum number of points in each segment should be equal or greater than 10 to ensure that the object displacement has been directly influenced by a bubble during a significant period. Fig. 1 depicts 30 s of the axial trajectory of Acetal-S submerged in a bed of fine sand fluidized at Ue = 0.50 m/s. The positive slope of the linear segments meeting the above criteria is considered as the respective rise velocity. Fig. 2 depicts the distribution of the normalized object rise velocity, the ratio of the object rise velocity to the mean bubble velocity (U r =U b ), of Acetal-S immersed in a bed of coarse sand fluidized at Ue = 0.25 m/s and Ue = 0.50 m/s. Bubble size and velocity are calculated by using Darton et al. [20] and Davidson and Harrison [21] equations, (Eqs. (1) and (2)), respectively. To calculate the mean bubble rise velocity, the latter equation is integrated and averaged along the bed height. It should
0.4
z (m)
0.3
0.2
0.1
0.0 0
5
10
15
20
25
30
t (s) Fig. 1. A sample axial trajectory of Acetal-S circulating in a bed of fine sand at Ue = 0.50 m/s.
pffiffiffiffiffi0:8 db ¼ 0:54g 0:2 ðU U mf Þ0:4 z þ 4 Ac qffiffiffiffiffiffiffiffi U b ¼ 0:711 gdb þ ðU U mf Þ
(b)
40
30
20
10
ð1Þ ð2Þ
Ranging from 0 to 0.5, the distribution profiles shown in Fig. 2 exemplify the velocity distribution of any object examined in the present study with a recurrent circulation behavior along the bed. The maximum of the normalized rise velocities are always far less than 1, implying that the objects never associate with the bubble wake, presumably due to their large sizes. Moreover, regardless of the excess gas velocity peaks of the distributions of the normalized object rise velocity take place around U r =U b 0:2. These facts signify that the object is not genuinely attached to the rising bubbles and suggest that the drift induced by the bubbles is principally responsible for rise of the object in the bubbling regime. Further studies are required to illustrate the mechanism of object displacement in turbulent or other fluidization regimes in which bubbles do not exist any longer. Fig. 3 shows the ratio of the mean object rise velocity to the mean bubble velocity, (U r =U b ), in beds of coarse and fine sand as well as FCC for two excess gas velocities, i.e. Ue = 0.25 m/s and Ue = 0.50 m/s. As indicated by the dashed lines, the mean value of U r =U b of all objects shown by white symbols in Fig. 3 is 0.22 regardless of the properties of the object and fluidization medium as well as the excess gas velocity. Nonetheless, the U r =U b values of Acetal-M in FCC and Acetal-M and Acetal-L in fine sand at Ue = 0.50 m/s, which are shown in gray, significantly deviates from those of the other objects. Fig. 4 compares the axial trajectories of Acetal-S and Acetal-L in a bed of fine sand (Ue = 0.50 m/s). While the former shows a steady circulation, the latter floats and sinks intermittently along the bed featuring a non-established circulation pattern of the object. Fig. 4a and b represent the displacement behavior of all objects with established and non-established circulation patterns, respectively. When the object circulation cannot be fully established, the axial displacement is constrained to the occasional jumps and for the rest of the time object vibrates narrowly in the grid zone. It denotes lack of the constant large and energetic enough bubbles in the bed, since it is believed that only these bubbles are able to trigger the object rise. It should be remarked that this situation is different from the conditions that the object cannot be displaced by any means and remains permanently stagnant on the
Probability density (%)
Probability density (%)
(a)
be remarked that the properties of the object and bed material may influence the bubbling features of the bed [22,23]; nonetheless the following equations are the most suitable ones that can be used in the absence of more comprehensive correlations.
25 20 15 10 5 0
0 0.0
0.1
0.2
0.3
Ur/Ub (-)
0.4
0.5
0.0
0.1
0.2
0.3
0.4
0.5
Ur/Ub (-)
Fig. 2. Distribution of the normalized rise velocity of Acetal-S in a bed of coarse sand fluidized at (a) Ue = 0.25 m/s (b) Ue = 0.50 m/s.
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0.5
Ur/Ub (-)
0.4
(b) HDPE Acetal-S Acetal-L
0.3 0.2
0.5 0.4
Ur/Ub (-)
(a)
Ur/Ub = 0.22
0.3 0.2
HDPE Acetal-S Acetal-M Acetal-L P Ur/Ub = 0.22
0.1
0.1
0.0
0.0 FCC
Fine Sand
Coarse Sand
Fluidization material
FCC
Fine Sand
Coarse Sand
Fluidization material
Fig. 3. The ratio of the mean object rise velocity to the mean bubble velocity at (a) Ue = 0.25 m/s (b) Ue = 0.50 m/s. Dashed lines show the mean values of U r =U b for the objects with a well-established circulation pattern represented by the white symbols. (The gray symbols represent the systems in which the object circulation is not fully established as described in the text.).
Fig. 4. The axial trajectory of (a) Acetal-S (b) Acetal-L fluidized for 4 h in a bed of fine sand at Ue = 0.50 m/s.
distributor. These are the cases that have not been featured in this work. Further studies are required to characterize the conditions leading to the intermittent fluidization of an object immersed in a bed of fine particles. Eq. (3) derived by data fitting demonstrates the correlation between the mean rise velocity of the objects and fine particle to
object density and size ratios as well as the excess gas velocity. The corresponding power of each term reflects the level of significance of that parameter on influencing the rise of the object. Accordingly, density and size ratios of the fluidization material to the object have corresponding effect on the excess gas velocity, which is substantially lower than that of the excess gas velocity.
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F. Fotovat, J. Chaouki / Chemical Engineering Journal 280 (2015) 26–35
This implies that as long as the dissimilar physical properties of the bed contents do not lead to sever segregation, the axial displacement of the immersed objects is principally controllable through adjusting the superficial gas velocity. The values obtained from Eq. (3) vs. the corresponding experimental values have been compared in Fig. 5. As depicted, discrepancy between the experimental and the respective calculated values is ± 15%. The correlation coefficient of Eq. (3) is about 0.9.
0:1 0:1 qp dp U r ¼ 0:41 ðU U mf Þ0:6 qo do
ð3Þ
3.2. Upward velocity of the object The object upward velocity, Uu is defined as any instantaneous positive velocity of the object. Therefore, all positive velocities that are determined by dividing the subtraction of two consecutive axial positions of the object by the relevant time interval can be considered as the upward velocity. Fig. 6 displays the ratio of the mean object upward velocity to the mean bubble velocity, (U u =U b ), in beds of coarse and fine sand as well as FCC for two excess gas velocities, i.e. Ue = 0.25 m/s and Ue = 0.50 m/s. Dashed line in each plot denotes the mean value of U u =U b (0.23) of all objects shown by white symbols in Fig. 6, which are those objects that constantly circulate in the bed. No notable impact of the object size and density and the excess gas velocity on U u =U b ratio is observed for such objects. The systematic deviation of U u =U b of the objects immersed in a bed of fine sand from that of the other objects, however, needs further scrutiny that will be addressed later. As discussed in Section 1, rise of an immersed object can take place in wake or drift of bubbles or in the emulsion phase through the Brownian-like motion. While the upward velocity (Uu) encompasses all upward displacements of the object regardless of the causing mechanism, the rise velocity (Ur) describes object rise when it is merely displaced in the bubble wake or drift. The parity
of the mean values of this two velocities for the objects circulating constantly along the bed implies that bubbles are exclusively responsible for the rise of such objects. The distribution profile of the object rise velocity, i.e. Fig. 2, elucidates that the objects mainly rise in the drift (and not in the wake) of bubbles. On the other hand, disparity between the corresponding mean values in case of the objects showing indefinite circulation pattern signifies the marked effect of the emulsion phase on limited displacement of the objects. Comparing rise and upward velocities of different combinations of objects and fluidization materials illustrates that the physical properties of the bed inventory does not influence the rise mechanism of the object provided that the vigorous bubbling conditions are established in the bed. The average object velocity in the bubble drift region could be estimated on the basis of the force balance in the vertical direction by neglecting the object-particle interaction forces [15]. Gravity, buoyancy and drag are the main forces exerted on the rising object as formulated below:
qo V o
dU o 1 ¼ ðqf qo ÞgV o þ C D Ao qf ðU f U o Þ2 dt 2
CD is the drag coefficient which can be given as a function of the object Reynolds number (Reo) and local bed voidage (e) [24–26] 2! 24 Re3o gðeÞ Re < 1000 CD ¼ 1þ Reo 6
ð5Þ
C D ¼ 0:44 gðeÞ Re P 1000 where Reo and g(e) are defined as
qf jU f U o jdo lf b gðeÞ ¼ e
Reo ¼
"
b ¼ 3:7 0:65 exp
ð6Þ
2
ð1:5 log Reo Þ 2
#
0.30 0.25
U r corr
0.20 0.15 0.10 0.05 0.00 0.00
0.05
0.10
0.15 U rexp
HDPE, Coarse sand, Ue=0.25 m/s Acetal-S, Coarse sand, Ue=0.25 m/s Acetal-L, Coarse sand, Ue=0.25 m/s HDPE, Fine sand, Ue=0.25 m/s Acetal-S,Fine sand, Ue=0.25 m/s HDPE, FCC, Ue=0.25 m/s Acetal-S, FCC, Ue=0.25 m/s
± 15%
ð4Þ
0.20
0.25
0.30
HDPE, Coarse sand, Ue=0.50 m/s Acetal-M, Coarse sand, Ue=0.50 m/s PTFE, Coarse sand, Ue=0.50 m/s Acetal-S, Coarse sand, Ue=0.50 m/s Acetal-L, Coarse sand, Ue=0.50 m/s HDPE, Fine sand, Ue=0.50 m/s Acetal-S, Fine sand, Ue=0.50 m/s HDPE, FCC, Ue=0.50 m/s Acetal-S, FCC, Ue=0.50 m/s
Fig. 5. The mean rise velocity of the objects circulating constantly along the bed as obtained from Eq. (3) vs. the corresponding experimental values.
ð7Þ ð8Þ
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F. Fotovat, J. Chaouki / Chemical Engineering Journal 280 (2015) 26–35
(a)
(b)
0.30
0.20
0.25 Uou/Ub = 0.23 U /Ub = 0.23 u
U /Ub = 0.23 u
Uu/Ub (-)
Uu/Ub (-)
0.25
0.15 0.10 0.05 0.00
0.30
0.20 0.15 0.10
HDPE Acetal-S Acetal-L
0.05 0.00
FCC
Fine Sand
HDPE Acetal-S Acetal-M Acetal-L PDFE
Coarse Sand
FCC
Fluidization material
Fine Sand
Coarse Sand
Fluidization material
Fig. 6. The ratio of the mean object upward velocity to the mean bubble velocity at (a) Ue = 0.25 m/s (b) Ue = 0.50 m/s. Dashed lines show the mean values of U u =U b for the objects with a well-established circulation pattern represented by white symbols. (The gray symbols represent the systems in which the object circulation is not fully established.).
0.30 0.25
0.15
U
umodel
0.20
0.10 0.05 0.00 0.00
0.05
0.10
0.15
0.20
0.25
0.30
U uexp HDPE, Coarse sand, Ue=0.25 m/s Acetal-S, Coarse sand, Ue=0.25 m/s Acetal-L, Coarse sand, Ue=0.25 m/s HDPE, Fine sand, Ue=0.25 m/s Acetal-S, Fine sand, Ue=0.25 m/s HDPE, FCC, Ue=0.25 m/s Acetal-S, FCC, Ue=0.25 m/s ± 15%
HDPE, Coarse sand, Ue=0.50 m/s Acetal-M, Coarse sand, Ue=0.50 m/s PTFE, Coarse sand, Ue=0.50 m/s Acetal-S, Coarse sand, Ue=0.50 m/s Acetal-L, Coarse sand, Ue=0.50 m/s HDPE, Fine sand, Ue=0.50 m/s Acetal-S, Fine sand, Ue=0.50 m/s HDPE, FCC, Ue=0.50 m/s Acetal-S, FCC, Ue=0.50 m/s
Fig. 7. The mean upward velocity of the objects circulating constantly along the bed as obtained from Eq. (4) vs. the corresponding experimental values.
Eqs. (4)–(9) are solved numerically assuming e = emf in the drift region. The initial condition is set to Uo = 0.5Ub at t = 0 as the maximum rise velocity of the object in the drift region as obtained from the distribution of the normalized object rise velocity shown in Fig. 2. As explained by Stein et al. [15], the average velocity of Uo can be obtained by using the following equation.
Uo ¼
1
Z sr
sr
0
from the corresponding experimental results that is fairly low to ensure that all impactful forces have been taken into account to derive Eq. (4). This again confirms that bubble drifts are predominantly responsible for the upward displacement of the large objects immersed in a bubbling bed of fine particles.
3.3. Rise frequency of the object
U o dt
ð9Þ
where sr, known as the relaxation time, is the time when the object becomes part of the emulsion phase and moves very slowly at minimum fluidization conditions. Since the initial condition of Eq. (4) is a function of bed height, Uo varies with the bed height. The height-averaged particle velocity is obtained by averaging the Uo values along the bed. Fig. 7 compares the experimental and modelled mean upward velocity of all objects circulating regularly along the bed. As noted, almost all values obtained from the proposed model deviate ±15%
In addition to the object rise velocity, the frequency of the occurrence of the object rise in the bubble drift characterizes the circulation pattern of the large objects fluidized with the help of fine particles. This parameter, which is defined as the number of the object jumps per unit time, is illustrated in Fig. 8 for all studied systems. As can be seen, the properties of the bed material affect the object rise frequency. It is particularly remarkable at low excess gas velocity, i.e. Ue = 0.25 m/s. The objects immersed in fine sand show the lowest rise frequency whereas those are fluidized in a bed of coarse sand rise more frequently in the bubble drift.
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F. Fotovat, J. Chaouki / Chemical Engineering Journal 280 (2015) 26–35
(a)
(b)
3.0
2.5
Fod*10 (1/s)
2.0
2
2
Fod*10 (1/s)
2.5
1.5 1.0 0.5 0.0
3.0
HDPE Acetal-S Acetal-L
2.0 1.5 1.0 0.5 0.0
FCC
Fine Sand
Coarse Sand
HDPE Acetal-S Acetal-M Acetal-L PTFE FCC
Fluidization material
Fine Sand
Coarse Sand
Fluidization material
Fig. 8. The object rise frequency at (a) Ue = 0.25 m/s (b) Ue = 0.50 m/s.
2.2
Σtsink/Σtrise (-)
2.0 1.8
(b)
HDPE Acetal-S Acetal-L
2.2 2.0
Σtsink/Σtrise (-)
(a)
1.6 1.4 1.2 1.0 0.8
1.8 1.6
HDPE Acetal-S Acetal-M Acetal-L PTFE
1.4 1.2 1.0 0.8
0.6
0.6 FCC
Fine Sand
Coarse Sand
Fluidization material
FCC
Fine Sand
Coarse Sand
Fluidization material
Fig. 9. The ratio of the time spent by the object in downward motion to the time spent by the object in upward motion in different fluidization media at (a) Ue = 0.25 m/s (b) Ue = 0.50 m/s.
The dependence of the object rise frequency on the type of fluidization material can be interpreted in light of the characteristics of the object sink in the emulsion phase. The time spent by the object in a cycle consists of the time that the object rises in a bubble drift (trise) and the time that object sinks in the emulsion phase (tsink). As revealed by comparing Figs. 8 and 9, the ratio between the total tsink and trise values shown in Fig. 9 is correlated with the object rise frequency. It is explained by considering this fact P that for a certain period of time the longer tsink is equivalent to P the shorter trise, which brings about the lower probability of the object rise along the bed. P P As exhibited in Fig. 9, tsink/ trise values corresponding to the objects immersed in a bed of fine sand is appreciably larger than those related to coarse sand and FCC. This infers that the objects spend comparatively longer time in the emulsion phase when the fluidization medium is fine sand. In other words, in the presence of fine sand particles sinking process is slower in comparison with other materials used in this study. This is attributed to the relevance of the buoyant forces during the sinking process as reported P P by Soria-Verdugo et al. [1]. In view of the different tsink/ trise values shown in Fig. 9, the impact of the buoyant forces on the downward motion of the objects in a bed of fine sand is evident, P P since, for example, the largest tsink/ trise, which denotes the slowest sink of the object, corresponds to HDPE, that is the lightest object. Due to the large difference between the densities of the bed material and the object a considerable buoyant force is exerted on HDPE impeding its sinking. Increasing size of the objects made of Acetal counterbalances the effect of the buoyant force, therefore P P tsink/ trise decreases from Acetal-S to Acetal-L (see Fig. 9b).
The reason that the effect of the buoyant force is rather outstanding for the fine sand compared to FCC and coarse sand is connected to the bulk characteristics of each material. A lower density difference between the object and the surrounding bed exists when FCC is used as the bed material in comparison with sand. Hence the magnitude of the buoyant force exerted on the object is less significant. In case of use of coarse sand, the higher gas hold up (voidage) of the emulsion phase, as inferred from the e values reported in Table 2, reduces the density felt by the object surrounded by the bed material. As a result, since the sinking of the objects takes place in a relatively looser and more permeable bed the impact of the buoyant force diminishes and the object encounters less resistance during its descent. Moreover, it is believed that the momentum transfer between the object and the fluidization medium is more effective when their respective sizes are closer to each other that is the case for coarse sand and the immersed objects. As the effect of buoyant forces on the object motion is reduced by increasing the gas velocity [1], it is expected that objects would be exposed to less hydrodynamic resistance and sink more smoothly. This results in the higher accessibility of the objects for the ascending journeys. Thus, it is likely that the rise frequency of all objects approaches a corresponding value by increasing the gas velocity. Such a trend is noticeable in this study for the objects immersed in a bed of FCC when Ue increases from 0.25 m/s to 0.50 m/s as their rise frequencies grow to become comparable with those of the objects fluidized in a bed of coarse sand.The distribution of the time spent by the object in the bubble drift or in the emulsion phase is of importance form the practical point of view.
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To compare the impact of biomass properties on the efficiency of a biomass combustor, Dos Santos and Goldstein [27] defined a parameter, namely BOE, indicating the occurrence of biomass particles outside the emulsion phase. Based on the experimental evidence, they concluded that the bubbling fluidized bed combustors should match the fuel characteristics such that the amount of biomass outside the emulsion (BOE) is minimized and the overall combustion efficiency optimized. It is because the presence of biomass particles in the bubbles leads to the release of the most energy of biomass in the freeboard rather than into the bed. Alternatively, choose of an appropriate fluidization medium can bring about a similar result by augmenting the biomass residence time in the emulsion phase. The higher U u =U b values of the objects in fine sand in comparison with the other fluidization media, which was discussed earlier (Fig. 6), can also be elucidated in light of the time spent by the object in the emulsion phase. It has been shown that the sinking path of an object is characterized by small periods, where the object falls fast, with high negative velocities, and periods of object vibration over a given position, in which both negative and positive velocities are present [28]. As the object stays longer in the emulsion phase, e.g. in case of use of fine sand as the bed material, the probability of the occurrence of the object vibration increases. As a result, the contribution of the positive velocities, which occurs as the object associates with the emulsion phase, increases in the mean object upward velocity and a larger U u =U b is expected. It is interesting that as seen in Fig. 8 the object rise frequency is not substantially different for the objects with non-established circulation pattern, i.e. Acetal-M in a bed of FCC and Acetal-M and Acetal-L in a bed of fine sand at Ue = 0.50 m/s. Fig. 10a and b demonstrate the distribution of the normalized height travelled by the object in bubble drifts for Acetal-S and Acetal-L in fine sand as the objects with established and non-established circulation pattern, respectively. As seen in Fig. 10b, in case of unsteady cycling of Acetal-L in a bed of fine sand (Ue = 0.50 m/s), more than 70% of the object vertical displacement is limited to very short ascents (Dzd/H 0.04). On the other hand, the steady circulation of Acetal-S under the same operating conditions (Fig. 10a) is featured by a wide distribution of the ascent lengths ranging from Dzd/H 0.04 to Dzd/H = 1.5. Performing a sensitivity analysis verifies that the results shown in Fig. 10 are almost independent of the value chosen as the minimum number of the points (10) considered for the second criterion of the algorithm used in this study. The results achieved from Figs. 8 and 10 imply that the frequent displacement of the object in the bubble drift does not necessarily result in good mixing conditions. This means that the object rise
4. Conclusions The upward motion of large objects immersed in a bubbling fluidized bed was studied by using the RPT technique. In this regard, the effects of the physical properties of the object and the fluidization medium as well as the impact of the excess gas velocity were explored by fluidization of a variety of polymeric spheres in beds of fine and coarse sand and FCC at Ue = 0.25 m/s and Ue = 0.50 m/s. Raising the excess gas velocity from 0.25 m/s to 0.50 m/s could bring about constant circulation of all studied objects in the presence of coarse sand whereas for FCC and fine sand, it could just give rise to the circulation of the objects with low or medium densities and those having the largest size and density remained stagnant on the distributor. Post-processing of the RPT data provided two characteristic velocities, i.e. the object upward and rise velocity describing any positive velocity of the object and the velocity of the object when it gets involved in the bubble drift, respectively. The distribution profile of the normalized rise velocity of the object revealed that it is unlikely that the object would attach to the bubbles and upward motion of the object in the bubble drift is the main mechanism of the object rise along the bed. When the circulation pattern is fully established, the ratio between the mean upward and rise velocity to the mean bubble velocity becomes independent of the object size and density as well as the excess gas velocity. As evidenced by the correlation proposed on the basis of the experimental results, the mean rise velocity of the objects is chiefly governed by the excess gas velocity. On the other hand, fluidization material to object density and size ratios have secondary impact on the rise velocity of the studied objects. Allowing for the gravity, buoyant and drag forces, the mean upward velocity of the object was estimated based on a theoretical model describing the force balance in the drift region. Remarkable consistency between the mean upward velocities obtained from the experiments and the corresponding modelled values substantiates that bubble drift are primarily responsible for the upward displacement of the objects. It was demonstrated that the object rise frequency depends on the characteristics of the bed material, particularly at low excess
(b)
8
Probability density (%)
Probability density (%)
(a)
frequency is not a suitable indicator of the effective circulation of the immersed objects. In other words, steady circulation of the object along the bed is guaranteed only when the large and energetic bubbles rise constantly in the bed. It should be noted that the level of the required vigorousness of bubbles in order to establish a stable circulation in each system depends on the physical properties of the object such as size and density.
6
4
2
80
60
40
20
0
0 0.0
0.2
0.4
0.6
0.8
Δzd/H
1.0
1.2
1.4
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Δzd/H
Fig. 10. Distribution of the normalized height travelled by the object as rises in the bubble drift for (a) Acetal-S (b) Acetal-L fluidized in a bed of fine sand at Ue = 0.50 m/s.
F. Fotovat, J. Chaouki / Chemical Engineering Journal 280 (2015) 26–35
gas velocities. Such dependence was remarkable for the objects immersed in a bed of fine sand due to the dominance of the buoyant force resulting in the lower opportunities for the exposure of the objects to the rising bubbles. The displacement of the objects in three cases, i.e. Acetal-M and Acetal-L in fine sand and Acetal-M in FCC (Ue = 0.50 m/s), was restricted to the occasional and intermittent rise and sink paths, possibly because of the lack of the vigorous enough bubbles all along the fluidization. As a consequence, the height travelled by these objects was very limited. Moreover, while U r =U b and U u =U b ratios were substantially lower than those of the other objects featured by a well-established circulation pattern, the respective rise frequencies were corresponding. Acknowledgement The authors are most grateful to Dr. John Grace for his constructive comments on this work. References [1] A. Soria-Verdugo, L.M. Garcia-Gutierrez, N. Garcia-Hernando, U. Ruiz-Rivas, Buoyancy effects on objects moving in a bubbling fluidized bed, Chem. Eng. Sci. 66 (2011) 2833–2841. [2] F. Fotovat, J.-P. Laviolette, J. Chaouki, The separation of the main combustible components of municipal solid waste through a dry step-wise process, Powder Technol. (2014) (Submitted). [3] J.W. Chew, C.M. Hrenya, Link between bubbling and segregation patterns in gas-fluidized beds with continuous size distributions, AIChE J. 57 (2011) 3003– 3011. [4] G.M. Rios, K. Dang Tran, H. Masson, Free object motion in a gas fluidized bed, Chem. Eng. Commun. 47 (1986) 247–272. [5] K.S. Lim, P.K. Agarwal, Circulatory motion of a large and lighter sphere in a bubbling fluidized bed of smaller and heavier particles, Chem. Eng. Sci. 49 (1994) 421–424. [6] F. Fotovat, J. Chaouki, J. Bergthorson, Distribution of large biomass particles in a sand-biomass fluidized bed: Experiments and modeling, AIChE J. (2014). [7] F. Fotovat, Characterization of Hydrodynamics and Solids Mixing in Fluidized Beds Involving Biomass, École Polytechnique de Montreal, 2013. [8] F. Fotovat, R. Ansart, M. Hemati, O. Simonin, J. Chaouki, Sand-assisted fluidization of large cylindrical and spherical biomass particles: experiments and simulation, Chem. Eng. Sci. 126 (2015) 543–559.
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[9] F. Larachi, M. Cassanello, M. Marie, J. Chaouki, C. Guy, Solids circulation pattern in 3-phase fluidized-beds containing binary-mixtures of particles as inferred from RPT, Chem. Eng. Res. Des. 73 (1995) 263–268. [10] M. Cassanello, F. Larachi, C. Guy, J. Chaouki, Solids mixing in gas-liquid-solid fluidized beds: experiments and modelling, Chem. Eng. Sci. 51 (1996) 2011– 2020. [11] R.K. Upadhyay, S. Roy, Investigation of hydrodynamics of binary fluidized beds via radioactive particle tracking and dual-source densitometry, Can. J. Chem. Eng. 88 (2010) 601–610. [12] A.C. Rees, J.F. Davidson, J.S. Dennis, A.N. Hayhurst, The rise of a buoyant sphere in a gas-fluidized bed, Chem. Eng. Sci. 60 (2005) 1143–1153. [13] T.H. Nguyen, J.R. Grace, Forces on objects immersed in fluidized beds, Powder Technol. 19 (1978) 255–264. [14] D. Geldart, Gas Fluidization Technology, Wiley, 1987. [15] M. Stein, Y.L. Ding, J.P.K. Seville, D.J. Parker, Solids motion in bubbling gas fluidised beds, Chem. Eng. Sci. 55 (2000) 5291–5300. [16] C.T. Crowe, Multiphase Flow Handbook, Taylor & Francis, Florida, USA, 2010, pp. 5–93. [17] N. Mostoufi, J. Chaouki, Flow structure of the solids in gas-solid fluidized beds, Chem. Eng. Sci. 59 (2004) 4217–4227. [18] F. Larachi, J. Chaouki, G. Kennedy, 3-D mapping of solids flow-fields in multiphase reactors with RPT, AIChE J. 41 (1995) 439–443. [19] F. Larachi, G. Kennedy, J. Chaouki, A gamma-ray detection system for 3-D particle tracking in multiphase reactors, Nucl. Instrum. Methods Phys. Res. Sect. A 338 (1994) 568–576. [20] R.C. Darton, R.D. LaNauze, J.F. Davidson, D. Harrison, Bubble growth due to coalesence in fluidised beds, Trans. Inst. Chem. Eng. 55 (1977) 274–280. [21] J.F. Davidson, D. Harrison, Fluidised Particles, Cambridge University Press, Cambridge, 1963. [22] G. Sun, J.R. Grace, Effect of particle size distribution in different fluidization regimes, AIChE J. 38 (1992) 716–722. [23] F. Fotovat, J. Chaouki, J. Bergthorson, The effect of biomass particles on the gas distribution and dilute phase characteristics of sand–biomass mixtures fluidized in the bubbling regime, Chem. Eng. Sci. (2013). [24] R. Di Felice, The voidage function for fluid-particle interaction systems, Int. J. Multiphase Flow 20 (1994) 153–159. [25] J. Leboreiro, G.G. Joseph, C.M. Hrenya, D.M. Snider, S.S. Banerjee, J.E. Galvin, The influence of binary drag laws on simulations of species segregation in gasfluidized beds, Powder Technol. 184 (2008) 275–290. [26] C.T. Crowe, J.D. Schwarzkopf, M. Sommerfeld, Y. Tsuji, Multiphase flows with droplets and particles, CRC Press, 2011. [27] F.J. Dos Santos, L. Goldstein Jr., Experimental aspects of biomass fuels in a bubbling fluidized bed combustor, Chem. Eng. Process. 47 (2008) 1541–1549. [28] A. Soria-Verdugo, L.M. Garcia-Gutierrez, S. Sanchez-Delgado, U. Ruiz-Rivas, Circulation of an object immersed in a bubbling fluidized bed, Chem. Eng. Sci. 66 (2011) 78–87.
Contents lists available at ScienceDirect
Chemical Engineering Journal journal homepage: www.elsevier.com/locate/cej
Characterization of the upward motion of an object immersed in a bubbling fluidized bed of fine particles Farzam Fotovat a,⇑, Jamal Chaouki b,⇑ a b
Department of Chemical and Biological Engineering, University of British Columbia, Vancouver V6T 1Z3, Canada Department of Chemical Engineering, École Polytechnique de Montréal, C.P. 6079 succ., Centre Ville, Montreal, QC H3C 3A7, Canada
h i g h l i g h t s Two characteristics velocities are defined to describe the rise of the objects. Drift of bubbles is recognized as the main reason of the object rise. A correlation is proposed to predict the mean rise velocity of the immersed objects. The upward velocity of the objects is modeled based on the force balance in the drift region. The object rise frequency depends on the characteristics of the bed material.
a r t i c l e
i n f o
Article history: Received 1 March 2015 Received in revised form 21 May 2015 Accepted 22 May 2015 Available online 6 June 2015 Keywords: Gas–solid fluidization Radioactive particle tracking Object circulation Bubble Object rise frequency
a b s t r a c t The axial motion of HDPE, Acetal, and PTFE spheres immersed in a 3-D bed of the conventional fluidization materials was studied using the non-invasive radioactive particle tracking (RPT) technique. Coarse and fine sand as well as FCC were chosen as the fluidization material. The experiments were carried out at two excess gas velocities, i.e. Ue = 0.25 m/s and Ue = 0.50 m/s. Rise of an object immersed in a bubbling fluidized bed can be descried by two characteristic velocities, i.e. rise and upward velocity. When circulation pattern is fully established, the mean upward and rise velocity to the mean bubble velocity ratios become comparable. It is shown that the object rise takes place principally in the drift of bubbles. The mean object rise velocity is primarily influenced by the excess gas velocity. Comparatively, the ratio between the physical properties of the fluidization medium and the object such as size and density has trivial impact on the rise velocity of the object. The mean object upward velocity can satisfactorily be predicted with a theoretical model with no adjustable parameter. The frequency of the object rise along the bed is independent of the object properties but influenced by the fluidization material. Comparing to coarse sand and FCC, the objects immersed in fine sand rise less frequently. This is attributed to the relatively longer residence time of the object in the emulsion phase of fine sand particles. The intermittent circulation of the medium and large size Acetal spheres in beds of FCC and fine sand is featured by the low upward and rise object velocities and the very limited height travelled by the object. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction Due to unique features such as excellent solids mixing and heat transfer; fluidized beds are one of the best and widely used systems for handling multiphase chemical and physical processes. In practice, many of the industrial fluidized beds involve objects that
⇑ Tel.: +1 604 827 5921, +1 514 340 4711x4034; fax: +1 514 340 4159. E-mail addresses: [email protected] (F. Fotovat), [email protected] (J. Chaouki). http://dx.doi.org/10.1016/j.cej.2015.05.130 1385-8947/Ó 2015 Elsevier B.V. All rights reserved.
are irregular in terms of size, density and shape. Fuel particles (such as coal, biomass or waste materials), catalysts and agglomerates are some examples of these objects. Characterization of the motion of the irregular objects within the bed is crucial to prevent the operational problems such as emergence of hot or cold spots and the appearance of defluidized zones due to the formation of agglomerates [1]. Occurrence of segregation in fluidized beds involving dissimilar components such as irregular objects and conventional materials is another phenomenon that could have detrimental effects on the
F. Fotovat, J. Chaouki / Chemical Engineering Journal 280 (2015) 26–35
27
Nomenclature Symbols Ac Ao Cd D db do dp Fod H Re Ub Ue Uf Umf Uo Ur Uu Up g g(e) Vo
catchment area of the single distributor hole (m2) cross sectional area of the spherical object (m2) drag coefficient (–) internal diameter of the bed (m) bubble diameter (m) object diameter (m) particle diameter (m) object rise frequency (–) dense bed height (m) Reynolds number (–) bubble rise velocity (m/s) excess gas velocity (m/s) fluid (gas) velocity (m/s) superficial gas of velocity of fluidization material at minim fluidization condition (m/s) object velocity (m/s) object rise velocity (m/s) object upward velocity (m/s) particle velocity (m/s) gravitational constant (m/s2) voidage function (–) object volume (m3)
process if chemical reactions take place in the system. On the other hand, segregation could beneficially be exploited to facilitate the operation of fluidized bed separators or classifiers used for coal cleaning, ore processing, and separation of the solid waste components [2]. On the basis of the experimental observations, objects rise by the action of ascending bubbles and sink in the bed with the dense phase. Since the downward flow of the dense phase is governed by the bubbles, they are responsible for the motion and circulation of the objects in the bed. Moreover, it has been shown that the bubbling characteristics of the segregating systems influence the degree and pattern of mixing/segregation of the constituting substances [3]. Profound understanding of the combustion or gasification of carbonaceous particles in bubbling fluidized beds depends on having detailed knowledge of circulation of large/light objects in a bed of fine/heavy particles. In these systems fuel particles tend to move up to the bed surface. Since fuel particles rise very fast and the time needed to reach the bed temperature increases dramatically with the size of fuel particles, thermal fragmentation and the consecutive reactions mostly take place at the top of the bed and the resulting reaction products and heat are released in the freeboard. This could dramatically reduce yield of desired reactions, increase tar formation and lead to occurrence of the hot spots, all deteriorating the reactor performance. Hence, it is of vital importance to gain a better insight into the rise pattern of objects differing in size and density in a variety of fluidization materials. Such insight could be helpful to improve the reactor performance by choosing the optimal fuel and bed material in terms of physical properties such as size and density. Motion of objects moving in bubbling fluidized beds has been studied using different experimental techniques. Rios et al. [4] explored the free motion of large light objects with various sizes and densities in 2-D and 3-D gas fluidized bed of heavy fine particles by employing cinematographic and radioactive tracing techniques. As they reported, the mean rise velocity of the objects is much lower than the bubble velocity (30%) since rise of an object to the bed surface is achieved by several jumps or jerks induced by passing bubbles. They also observed that the tendency of the object
trise tsink z
time spent by the object in a rising path (s) time spent by the object in a sinking path (s) height above the distributor (m)
Greek letters b parameter defined in Eq. (7) (–) e bed voidage (–) lf dynamic viscosity of fluid (gas) (Pa.s) qf fluid (gas) density (kg/m3) qo object density (kg/m3) qp particle density (kg/m3) sr relaxation time (s) Subscripts cal calculated exp experimental f fluid m mean value mf minimum fluidization o object p particle
to be involved in large amplitude displacement is increased with decreased size and increased density. Lim and Agarwal [5] used automated image analysis of a 2-D bubbling fluidized bed to characterize the circulation pattern and measure the velocity profile of large spherical objects and coal particles mixed with glass beads. Like Rios et al. [4], they reported that the mean rise velocity of the fluidized object is 30% of the mean bubble velocity along the bed. However, by studying the circulation characteristics of a variety of objects with different densities and sizes Soria-Verdugo et al. [1] found that the ratio of the mean rise velocity of the objects to the mean velocity of bubbles is around 20%. Moreover, they observed that the object rising velocity hardly varies with its density or size. Employing the radioactive particle tracking (RPT) technique, Fotovat et al. [6–8] provided insight into the circulation behavior and velocity profile of large cylindrical biomass particles fluidized with sand under bubbling conditions. RPT is a powerful non-invasive method that provides the instantaneous 3-D position of the tracked particle in a Lagrangian framework. Post-processing of the RPT data is helpful to reveal the characteristics of the motion of the tracer in the multiphase flow systems. Use of the computer-automated radioactive particle tracking (CARPT) technique for studying the solid circulation pattern of large objects in 3 phase fluidized beds involving binary mixtures was initially introduced by Larachi et al. [9]. Cassanello et al. [10] adopted this technique to investigate solids mixing in gas–liquid–solid fluidized beds. More recently, Upadhyay and Roy [11] employed this method to explore the mixing and hydrodynamic behavior in a bed consisting of equal weight percentages of the same size particles differing in density. On the basis of the RPT data, Fotovat et al. [6] realized that the average rise velocity of biomass particles is about 20% of the average bubble rise velocity, consistent with the findings of Soria-Verdugo et al. [1]. Measuring the rise velocity of a single sphere for a limited ratio of U/Umf in a bubbling and slugging fluidized bed, Rees et al. [12] demonstrated that this velocity is linearly correlated with the superficial gas velocity and the slope of this linear correlation was linked to the fluidization regime. In addition, like the
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preceding researchers [13], they observed that the rising objects carry on a defluidized hood of particles on their top. In a bubbling fluidized bed involving fine particles, it has been well established that bubbles induce rise of particles by carrying them upward in the bubble wake, i.e. the solids occupying the bottom of the completed sphere bubble, and in the drift, i.e. the region behind the completed sphere [14]. Particles rising inside the bubble wake exhibit a constant velocity at the same velocity as the bubble. The drift induced by the bubble motion generally moves at a velocity proportionally lower than the bubble velocity [15]. In the case of drift, particles undergo net displacement outside the wake due to the passage of bubbles, upwards near the bubble axis and downwards at several bubble radii from the axis [16]. The upward motion of the particles is offset by their downward flow in an emulsion phase close to the bed wall. Particles in the emulsion phase exhibit a Brownian-like motion, moving randomly in any direction [17]. Although these facts have been well known for the conventional fluidization material particles such as sand and FCC, further research is required to gain an insight into the mechanisms of solids displacement in case of irregularly large and light objects. In spite of the several studies conducted on fluidization of the large objects in a bed of conventional fine materials, no clear explanation has yet been provided to elucidate the phenomenological relationship between the bubbling and object rise velocities. Addressing this issue, the velocity profiles of a variety of spherical objects with different sizes and densities are scrutinized in this work by means of the RPT technique in order to shed light on the mechanisms governing rise of the object. Moreover, the impact of three different fluidization media, i.e. coarse and fine sand as well as the fluid catalytic cracking (FCC) catalyst, on the rise of immersed objects is studied. A comparison is also made between the experimental mean rise velocities of the objects and the corresponding values predicted by a model, which has been developed on the basis of the forces exerted on the object.
Table 2 Properties of the spherical objects. Designation
Material
do (mm)
qo (kg/m3)
HDPE PTFE Acetal-S Acetal-M Acetal-L
HDPE PTFE Acetal Acetal Acetal
9.5 9.5 4.8 9.5 19.0
929 2166 1381 1368 1347
To make a radioactive tracer from each object for the RPT tests, a tiny piece of metallic scandium is embedded into a small hole made on each polymeric sphere so that the size and density of the final tracer would not be different from those of the original particle. The tracer is then activated in the SLOWPOKE nuclear reactor of École Polytechnique de Montréal up to an activity of 70 lCi. The produced isotope 46Sc emits c-rays, which are counted by 12 NaI scintillation detectors placed around the column. Before each test, the desired tracer is dropped into the column and system is fluidized for a few minutes to ensure steady fluidization prior to starting data acquisition. The static bed height of each test is set to 228 mm (H/D = 1.5). A high speed data acquisition system counts the number of c-rays detected by each detector. These counts are analyzed later to calculate the coordinates of the tracer. Details of the system calibration and the inverse reconstruction strategy for determining tracer position can be found elsewhere [18,19]. In each experiment, the location of the tracer is tracked every 10 ms for about 4 h until around one and half million points are finally acquired. The excess superficial gas velocities, i.e. (Ue = U Umf), chosen for the tests are Ue = 0.25 m/s and Ue = 0.50 m/s. To this purpose, the desired air flow rate of each run is adjusted through a set of rotameter and orifice plate to reach the intended superficial gas velocity ranging from 0.25 to 1 m/s. It should be noted that the single tracer dropped into the bed was the only large object mixed with the bed materials.
3. Results and discussion 2. Experimental 3.1. Rise velocity of the object All experiments are conducted in a cylindrical Plexiglas column 152 mm in diameter equipped with a perforated plate as an air distributor. Under the ambient conditions, air is injected into the column through 163 holes of the distributor, which are 1 mm in diameter and arranged in a triangular pitch. Fine and coarse sand as well as FCC particles are used as the bed material. Five small polymeric spheres differing in size and density are chosen to be used as the object fluidized in a bed of fine particles. Tables 1 and 2 list properties of all materials used in this study. The true density is measured with a gas pycnometer (Micromeritics, AccuPyc II 1340) while the bulk density is measured with a graduated cylinder. Umf values of bed materials are determined experimentally in a 75 mm i.d. column equipped with a perforated plate. S, M, and L in designation of the spherical Acetal objects stand for the small, medium, and large size, respectively. The respective densities of these objects are not significantly different; however, all of them are made from Acetal upon the supplier claim.
The RPT result, which is the instantaneous position of the immersed object, can be processed in order to attain the velocity profile of the tracer. For this purpose, the local axial, radial and angular velocities are determined; however only the axial velocity of the tracer is a matter of interest in this study. As introduced by Mostoufi and Chaouki [17], when the tracer is displaced in the wake or drift of bubbles, its axial coordinates of the trajectory vs. time exhibit a straight line with a positive slope. It is also expected that when the tracer sink as a consequence of bubble drift, its trajectory would be a straight line with a negative slope. In order to distinguish between the different mechanisms governing the object displacement, it is assumed that the straight lines on the axial trajectory of the tracer correspond to stable bubbles, whereas, nonlinear parts of the trajectory correspond to either the random movement of the object in the emulsion or bubbles which have not reached their stable size. Accordingly, the axial trajectory of the tracers used in this study is analyzed to
Table 1 Properties of the bed materials. Material
Particle size range (lm)
dp,m (lm)
qP (kg/m3)
qb (kg/m3)
Voidage (–) (fixed bed)
Umf (m/s)
Geldart classification
Coarse sand Fine sand FCC
400–2000 50–700 30–300
770 220 80
2650 2650 1690
1350 1406 928
0.49 0.47 0.45
0.44 0.05 0.004
B–D B A
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characterize the mechanisms provoking jump of the large objects immersed in a bed of fine particles. As explained, jump of the objects is linked to the linear segments of the axial trajectory having positive slopes. These segments are detected through a computer program by applying the following criteria. 1. The segments are demarcated by the local minima and maxima of the axial trajectory of the object. 2. The correlation coefficient of the segment correlated with a line should be equal or greater than 0.995. 3. The minimum number of points in each segment should be equal or greater than 10 to ensure that the object displacement has been directly influenced by a bubble during a significant period. Fig. 1 depicts 30 s of the axial trajectory of Acetal-S submerged in a bed of fine sand fluidized at Ue = 0.50 m/s. The positive slope of the linear segments meeting the above criteria is considered as the respective rise velocity. Fig. 2 depicts the distribution of the normalized object rise velocity, the ratio of the object rise velocity to the mean bubble velocity (U r =U b ), of Acetal-S immersed in a bed of coarse sand fluidized at Ue = 0.25 m/s and Ue = 0.50 m/s. Bubble size and velocity are calculated by using Darton et al. [20] and Davidson and Harrison [21] equations, (Eqs. (1) and (2)), respectively. To calculate the mean bubble rise velocity, the latter equation is integrated and averaged along the bed height. It should
0.4
z (m)
0.3
0.2
0.1
0.0 0
5
10
15
20
25
30
t (s) Fig. 1. A sample axial trajectory of Acetal-S circulating in a bed of fine sand at Ue = 0.50 m/s.
pffiffiffiffiffi0:8 db ¼ 0:54g 0:2 ðU U mf Þ0:4 z þ 4 Ac qffiffiffiffiffiffiffiffi U b ¼ 0:711 gdb þ ðU U mf Þ
(b)
40
30
20
10
ð1Þ ð2Þ
Ranging from 0 to 0.5, the distribution profiles shown in Fig. 2 exemplify the velocity distribution of any object examined in the present study with a recurrent circulation behavior along the bed. The maximum of the normalized rise velocities are always far less than 1, implying that the objects never associate with the bubble wake, presumably due to their large sizes. Moreover, regardless of the excess gas velocity peaks of the distributions of the normalized object rise velocity take place around U r =U b 0:2. These facts signify that the object is not genuinely attached to the rising bubbles and suggest that the drift induced by the bubbles is principally responsible for rise of the object in the bubbling regime. Further studies are required to illustrate the mechanism of object displacement in turbulent or other fluidization regimes in which bubbles do not exist any longer. Fig. 3 shows the ratio of the mean object rise velocity to the mean bubble velocity, (U r =U b ), in beds of coarse and fine sand as well as FCC for two excess gas velocities, i.e. Ue = 0.25 m/s and Ue = 0.50 m/s. As indicated by the dashed lines, the mean value of U r =U b of all objects shown by white symbols in Fig. 3 is 0.22 regardless of the properties of the object and fluidization medium as well as the excess gas velocity. Nonetheless, the U r =U b values of Acetal-M in FCC and Acetal-M and Acetal-L in fine sand at Ue = 0.50 m/s, which are shown in gray, significantly deviates from those of the other objects. Fig. 4 compares the axial trajectories of Acetal-S and Acetal-L in a bed of fine sand (Ue = 0.50 m/s). While the former shows a steady circulation, the latter floats and sinks intermittently along the bed featuring a non-established circulation pattern of the object. Fig. 4a and b represent the displacement behavior of all objects with established and non-established circulation patterns, respectively. When the object circulation cannot be fully established, the axial displacement is constrained to the occasional jumps and for the rest of the time object vibrates narrowly in the grid zone. It denotes lack of the constant large and energetic enough bubbles in the bed, since it is believed that only these bubbles are able to trigger the object rise. It should be remarked that this situation is different from the conditions that the object cannot be displaced by any means and remains permanently stagnant on the
Probability density (%)
Probability density (%)
(a)
be remarked that the properties of the object and bed material may influence the bubbling features of the bed [22,23]; nonetheless the following equations are the most suitable ones that can be used in the absence of more comprehensive correlations.
25 20 15 10 5 0
0 0.0
0.1
0.2
0.3
Ur/Ub (-)
0.4
0.5
0.0
0.1
0.2
0.3
0.4
0.5
Ur/Ub (-)
Fig. 2. Distribution of the normalized rise velocity of Acetal-S in a bed of coarse sand fluidized at (a) Ue = 0.25 m/s (b) Ue = 0.50 m/s.
30
F. Fotovat, J. Chaouki / Chemical Engineering Journal 280 (2015) 26–35
0.5
Ur/Ub (-)
0.4
(b) HDPE Acetal-S Acetal-L
0.3 0.2
0.5 0.4
Ur/Ub (-)
(a)
Ur/Ub = 0.22
0.3 0.2
HDPE Acetal-S Acetal-M Acetal-L P Ur/Ub = 0.22
0.1
0.1
0.0
0.0 FCC
Fine Sand
Coarse Sand
Fluidization material
FCC
Fine Sand
Coarse Sand
Fluidization material
Fig. 3. The ratio of the mean object rise velocity to the mean bubble velocity at (a) Ue = 0.25 m/s (b) Ue = 0.50 m/s. Dashed lines show the mean values of U r =U b for the objects with a well-established circulation pattern represented by the white symbols. (The gray symbols represent the systems in which the object circulation is not fully established as described in the text.).
Fig. 4. The axial trajectory of (a) Acetal-S (b) Acetal-L fluidized for 4 h in a bed of fine sand at Ue = 0.50 m/s.
distributor. These are the cases that have not been featured in this work. Further studies are required to characterize the conditions leading to the intermittent fluidization of an object immersed in a bed of fine particles. Eq. (3) derived by data fitting demonstrates the correlation between the mean rise velocity of the objects and fine particle to
object density and size ratios as well as the excess gas velocity. The corresponding power of each term reflects the level of significance of that parameter on influencing the rise of the object. Accordingly, density and size ratios of the fluidization material to the object have corresponding effect on the excess gas velocity, which is substantially lower than that of the excess gas velocity.
31
F. Fotovat, J. Chaouki / Chemical Engineering Journal 280 (2015) 26–35
This implies that as long as the dissimilar physical properties of the bed contents do not lead to sever segregation, the axial displacement of the immersed objects is principally controllable through adjusting the superficial gas velocity. The values obtained from Eq. (3) vs. the corresponding experimental values have been compared in Fig. 5. As depicted, discrepancy between the experimental and the respective calculated values is ± 15%. The correlation coefficient of Eq. (3) is about 0.9.
0:1 0:1 qp dp U r ¼ 0:41 ðU U mf Þ0:6 qo do
ð3Þ
3.2. Upward velocity of the object The object upward velocity, Uu is defined as any instantaneous positive velocity of the object. Therefore, all positive velocities that are determined by dividing the subtraction of two consecutive axial positions of the object by the relevant time interval can be considered as the upward velocity. Fig. 6 displays the ratio of the mean object upward velocity to the mean bubble velocity, (U u =U b ), in beds of coarse and fine sand as well as FCC for two excess gas velocities, i.e. Ue = 0.25 m/s and Ue = 0.50 m/s. Dashed line in each plot denotes the mean value of U u =U b (0.23) of all objects shown by white symbols in Fig. 6, which are those objects that constantly circulate in the bed. No notable impact of the object size and density and the excess gas velocity on U u =U b ratio is observed for such objects. The systematic deviation of U u =U b of the objects immersed in a bed of fine sand from that of the other objects, however, needs further scrutiny that will be addressed later. As discussed in Section 1, rise of an immersed object can take place in wake or drift of bubbles or in the emulsion phase through the Brownian-like motion. While the upward velocity (Uu) encompasses all upward displacements of the object regardless of the causing mechanism, the rise velocity (Ur) describes object rise when it is merely displaced in the bubble wake or drift. The parity
of the mean values of this two velocities for the objects circulating constantly along the bed implies that bubbles are exclusively responsible for the rise of such objects. The distribution profile of the object rise velocity, i.e. Fig. 2, elucidates that the objects mainly rise in the drift (and not in the wake) of bubbles. On the other hand, disparity between the corresponding mean values in case of the objects showing indefinite circulation pattern signifies the marked effect of the emulsion phase on limited displacement of the objects. Comparing rise and upward velocities of different combinations of objects and fluidization materials illustrates that the physical properties of the bed inventory does not influence the rise mechanism of the object provided that the vigorous bubbling conditions are established in the bed. The average object velocity in the bubble drift region could be estimated on the basis of the force balance in the vertical direction by neglecting the object-particle interaction forces [15]. Gravity, buoyancy and drag are the main forces exerted on the rising object as formulated below:
qo V o
dU o 1 ¼ ðqf qo ÞgV o þ C D Ao qf ðU f U o Þ2 dt 2
CD is the drag coefficient which can be given as a function of the object Reynolds number (Reo) and local bed voidage (e) [24–26] 2! 24 Re3o gðeÞ Re < 1000 CD ¼ 1þ Reo 6
ð5Þ
C D ¼ 0:44 gðeÞ Re P 1000 where Reo and g(e) are defined as
qf jU f U o jdo lf b gðeÞ ¼ e
Reo ¼
"
b ¼ 3:7 0:65 exp
ð6Þ
2
ð1:5 log Reo Þ 2
#
0.30 0.25
U r corr
0.20 0.15 0.10 0.05 0.00 0.00
0.05
0.10
0.15 U rexp
HDPE, Coarse sand, Ue=0.25 m/s Acetal-S, Coarse sand, Ue=0.25 m/s Acetal-L, Coarse sand, Ue=0.25 m/s HDPE, Fine sand, Ue=0.25 m/s Acetal-S,Fine sand, Ue=0.25 m/s HDPE, FCC, Ue=0.25 m/s Acetal-S, FCC, Ue=0.25 m/s
± 15%
ð4Þ
0.20
0.25
0.30
HDPE, Coarse sand, Ue=0.50 m/s Acetal-M, Coarse sand, Ue=0.50 m/s PTFE, Coarse sand, Ue=0.50 m/s Acetal-S, Coarse sand, Ue=0.50 m/s Acetal-L, Coarse sand, Ue=0.50 m/s HDPE, Fine sand, Ue=0.50 m/s Acetal-S, Fine sand, Ue=0.50 m/s HDPE, FCC, Ue=0.50 m/s Acetal-S, FCC, Ue=0.50 m/s
Fig. 5. The mean rise velocity of the objects circulating constantly along the bed as obtained from Eq. (3) vs. the corresponding experimental values.
ð7Þ ð8Þ
32
F. Fotovat, J. Chaouki / Chemical Engineering Journal 280 (2015) 26–35
(a)
(b)
0.30
0.20
0.25 Uou/Ub = 0.23 U /Ub = 0.23 u
U /Ub = 0.23 u
Uu/Ub (-)
Uu/Ub (-)
0.25
0.15 0.10 0.05 0.00
0.30
0.20 0.15 0.10
HDPE Acetal-S Acetal-L
0.05 0.00
FCC
Fine Sand
HDPE Acetal-S Acetal-M Acetal-L PDFE
Coarse Sand
FCC
Fluidization material
Fine Sand
Coarse Sand
Fluidization material
Fig. 6. The ratio of the mean object upward velocity to the mean bubble velocity at (a) Ue = 0.25 m/s (b) Ue = 0.50 m/s. Dashed lines show the mean values of U u =U b for the objects with a well-established circulation pattern represented by white symbols. (The gray symbols represent the systems in which the object circulation is not fully established.).
0.30 0.25
0.15
U
umodel
0.20
0.10 0.05 0.00 0.00
0.05
0.10
0.15
0.20
0.25
0.30
U uexp HDPE, Coarse sand, Ue=0.25 m/s Acetal-S, Coarse sand, Ue=0.25 m/s Acetal-L, Coarse sand, Ue=0.25 m/s HDPE, Fine sand, Ue=0.25 m/s Acetal-S, Fine sand, Ue=0.25 m/s HDPE, FCC, Ue=0.25 m/s Acetal-S, FCC, Ue=0.25 m/s ± 15%
HDPE, Coarse sand, Ue=0.50 m/s Acetal-M, Coarse sand, Ue=0.50 m/s PTFE, Coarse sand, Ue=0.50 m/s Acetal-S, Coarse sand, Ue=0.50 m/s Acetal-L, Coarse sand, Ue=0.50 m/s HDPE, Fine sand, Ue=0.50 m/s Acetal-S, Fine sand, Ue=0.50 m/s HDPE, FCC, Ue=0.50 m/s Acetal-S, FCC, Ue=0.50 m/s
Fig. 7. The mean upward velocity of the objects circulating constantly along the bed as obtained from Eq. (4) vs. the corresponding experimental values.
Eqs. (4)–(9) are solved numerically assuming e = emf in the drift region. The initial condition is set to Uo = 0.5Ub at t = 0 as the maximum rise velocity of the object in the drift region as obtained from the distribution of the normalized object rise velocity shown in Fig. 2. As explained by Stein et al. [15], the average velocity of Uo can be obtained by using the following equation.
Uo ¼
1
Z sr
sr
0
from the corresponding experimental results that is fairly low to ensure that all impactful forces have been taken into account to derive Eq. (4). This again confirms that bubble drifts are predominantly responsible for the upward displacement of the large objects immersed in a bubbling bed of fine particles.
3.3. Rise frequency of the object
U o dt
ð9Þ
where sr, known as the relaxation time, is the time when the object becomes part of the emulsion phase and moves very slowly at minimum fluidization conditions. Since the initial condition of Eq. (4) is a function of bed height, Uo varies with the bed height. The height-averaged particle velocity is obtained by averaging the Uo values along the bed. Fig. 7 compares the experimental and modelled mean upward velocity of all objects circulating regularly along the bed. As noted, almost all values obtained from the proposed model deviate ±15%
In addition to the object rise velocity, the frequency of the occurrence of the object rise in the bubble drift characterizes the circulation pattern of the large objects fluidized with the help of fine particles. This parameter, which is defined as the number of the object jumps per unit time, is illustrated in Fig. 8 for all studied systems. As can be seen, the properties of the bed material affect the object rise frequency. It is particularly remarkable at low excess gas velocity, i.e. Ue = 0.25 m/s. The objects immersed in fine sand show the lowest rise frequency whereas those are fluidized in a bed of coarse sand rise more frequently in the bubble drift.
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F. Fotovat, J. Chaouki / Chemical Engineering Journal 280 (2015) 26–35
(a)
(b)
3.0
2.5
Fod*10 (1/s)
2.0
2
2
Fod*10 (1/s)
2.5
1.5 1.0 0.5 0.0
3.0
HDPE Acetal-S Acetal-L
2.0 1.5 1.0 0.5 0.0
FCC
Fine Sand
Coarse Sand
HDPE Acetal-S Acetal-M Acetal-L PTFE FCC
Fluidization material
Fine Sand
Coarse Sand
Fluidization material
Fig. 8. The object rise frequency at (a) Ue = 0.25 m/s (b) Ue = 0.50 m/s.
2.2
Σtsink/Σtrise (-)
2.0 1.8
(b)
HDPE Acetal-S Acetal-L
2.2 2.0
Σtsink/Σtrise (-)
(a)
1.6 1.4 1.2 1.0 0.8
1.8 1.6
HDPE Acetal-S Acetal-M Acetal-L PTFE
1.4 1.2 1.0 0.8
0.6
0.6 FCC
Fine Sand
Coarse Sand
Fluidization material
FCC
Fine Sand
Coarse Sand
Fluidization material
Fig. 9. The ratio of the time spent by the object in downward motion to the time spent by the object in upward motion in different fluidization media at (a) Ue = 0.25 m/s (b) Ue = 0.50 m/s.
The dependence of the object rise frequency on the type of fluidization material can be interpreted in light of the characteristics of the object sink in the emulsion phase. The time spent by the object in a cycle consists of the time that the object rises in a bubble drift (trise) and the time that object sinks in the emulsion phase (tsink). As revealed by comparing Figs. 8 and 9, the ratio between the total tsink and trise values shown in Fig. 9 is correlated with the object rise frequency. It is explained by considering this fact P that for a certain period of time the longer tsink is equivalent to P the shorter trise, which brings about the lower probability of the object rise along the bed. P P As exhibited in Fig. 9, tsink/ trise values corresponding to the objects immersed in a bed of fine sand is appreciably larger than those related to coarse sand and FCC. This infers that the objects spend comparatively longer time in the emulsion phase when the fluidization medium is fine sand. In other words, in the presence of fine sand particles sinking process is slower in comparison with other materials used in this study. This is attributed to the relevance of the buoyant forces during the sinking process as reported P P by Soria-Verdugo et al. [1]. In view of the different tsink/ trise values shown in Fig. 9, the impact of the buoyant forces on the downward motion of the objects in a bed of fine sand is evident, P P since, for example, the largest tsink/ trise, which denotes the slowest sink of the object, corresponds to HDPE, that is the lightest object. Due to the large difference between the densities of the bed material and the object a considerable buoyant force is exerted on HDPE impeding its sinking. Increasing size of the objects made of Acetal counterbalances the effect of the buoyant force, therefore P P tsink/ trise decreases from Acetal-S to Acetal-L (see Fig. 9b).
The reason that the effect of the buoyant force is rather outstanding for the fine sand compared to FCC and coarse sand is connected to the bulk characteristics of each material. A lower density difference between the object and the surrounding bed exists when FCC is used as the bed material in comparison with sand. Hence the magnitude of the buoyant force exerted on the object is less significant. In case of use of coarse sand, the higher gas hold up (voidage) of the emulsion phase, as inferred from the e values reported in Table 2, reduces the density felt by the object surrounded by the bed material. As a result, since the sinking of the objects takes place in a relatively looser and more permeable bed the impact of the buoyant force diminishes and the object encounters less resistance during its descent. Moreover, it is believed that the momentum transfer between the object and the fluidization medium is more effective when their respective sizes are closer to each other that is the case for coarse sand and the immersed objects. As the effect of buoyant forces on the object motion is reduced by increasing the gas velocity [1], it is expected that objects would be exposed to less hydrodynamic resistance and sink more smoothly. This results in the higher accessibility of the objects for the ascending journeys. Thus, it is likely that the rise frequency of all objects approaches a corresponding value by increasing the gas velocity. Such a trend is noticeable in this study for the objects immersed in a bed of FCC when Ue increases from 0.25 m/s to 0.50 m/s as their rise frequencies grow to become comparable with those of the objects fluidized in a bed of coarse sand.The distribution of the time spent by the object in the bubble drift or in the emulsion phase is of importance form the practical point of view.
34
F. Fotovat, J. Chaouki / Chemical Engineering Journal 280 (2015) 26–35
To compare the impact of biomass properties on the efficiency of a biomass combustor, Dos Santos and Goldstein [27] defined a parameter, namely BOE, indicating the occurrence of biomass particles outside the emulsion phase. Based on the experimental evidence, they concluded that the bubbling fluidized bed combustors should match the fuel characteristics such that the amount of biomass outside the emulsion (BOE) is minimized and the overall combustion efficiency optimized. It is because the presence of biomass particles in the bubbles leads to the release of the most energy of biomass in the freeboard rather than into the bed. Alternatively, choose of an appropriate fluidization medium can bring about a similar result by augmenting the biomass residence time in the emulsion phase. The higher U u =U b values of the objects in fine sand in comparison with the other fluidization media, which was discussed earlier (Fig. 6), can also be elucidated in light of the time spent by the object in the emulsion phase. It has been shown that the sinking path of an object is characterized by small periods, where the object falls fast, with high negative velocities, and periods of object vibration over a given position, in which both negative and positive velocities are present [28]. As the object stays longer in the emulsion phase, e.g. in case of use of fine sand as the bed material, the probability of the occurrence of the object vibration increases. As a result, the contribution of the positive velocities, which occurs as the object associates with the emulsion phase, increases in the mean object upward velocity and a larger U u =U b is expected. It is interesting that as seen in Fig. 8 the object rise frequency is not substantially different for the objects with non-established circulation pattern, i.e. Acetal-M in a bed of FCC and Acetal-M and Acetal-L in a bed of fine sand at Ue = 0.50 m/s. Fig. 10a and b demonstrate the distribution of the normalized height travelled by the object in bubble drifts for Acetal-S and Acetal-L in fine sand as the objects with established and non-established circulation pattern, respectively. As seen in Fig. 10b, in case of unsteady cycling of Acetal-L in a bed of fine sand (Ue = 0.50 m/s), more than 70% of the object vertical displacement is limited to very short ascents (Dzd/H 0.04). On the other hand, the steady circulation of Acetal-S under the same operating conditions (Fig. 10a) is featured by a wide distribution of the ascent lengths ranging from Dzd/H 0.04 to Dzd/H = 1.5. Performing a sensitivity analysis verifies that the results shown in Fig. 10 are almost independent of the value chosen as the minimum number of the points (10) considered for the second criterion of the algorithm used in this study. The results achieved from Figs. 8 and 10 imply that the frequent displacement of the object in the bubble drift does not necessarily result in good mixing conditions. This means that the object rise
4. Conclusions The upward motion of large objects immersed in a bubbling fluidized bed was studied by using the RPT technique. In this regard, the effects of the physical properties of the object and the fluidization medium as well as the impact of the excess gas velocity were explored by fluidization of a variety of polymeric spheres in beds of fine and coarse sand and FCC at Ue = 0.25 m/s and Ue = 0.50 m/s. Raising the excess gas velocity from 0.25 m/s to 0.50 m/s could bring about constant circulation of all studied objects in the presence of coarse sand whereas for FCC and fine sand, it could just give rise to the circulation of the objects with low or medium densities and those having the largest size and density remained stagnant on the distributor. Post-processing of the RPT data provided two characteristic velocities, i.e. the object upward and rise velocity describing any positive velocity of the object and the velocity of the object when it gets involved in the bubble drift, respectively. The distribution profile of the normalized rise velocity of the object revealed that it is unlikely that the object would attach to the bubbles and upward motion of the object in the bubble drift is the main mechanism of the object rise along the bed. When the circulation pattern is fully established, the ratio between the mean upward and rise velocity to the mean bubble velocity becomes independent of the object size and density as well as the excess gas velocity. As evidenced by the correlation proposed on the basis of the experimental results, the mean rise velocity of the objects is chiefly governed by the excess gas velocity. On the other hand, fluidization material to object density and size ratios have secondary impact on the rise velocity of the studied objects. Allowing for the gravity, buoyant and drag forces, the mean upward velocity of the object was estimated based on a theoretical model describing the force balance in the drift region. Remarkable consistency between the mean upward velocities obtained from the experiments and the corresponding modelled values substantiates that bubble drift are primarily responsible for the upward displacement of the objects. It was demonstrated that the object rise frequency depends on the characteristics of the bed material, particularly at low excess
(b)
8
Probability density (%)
Probability density (%)
(a)
frequency is not a suitable indicator of the effective circulation of the immersed objects. In other words, steady circulation of the object along the bed is guaranteed only when the large and energetic bubbles rise constantly in the bed. It should be noted that the level of the required vigorousness of bubbles in order to establish a stable circulation in each system depends on the physical properties of the object such as size and density.
6
4
2
80
60
40
20
0
0 0.0
0.2
0.4
0.6
0.8
Δzd/H
1.0
1.2
1.4
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Δzd/H
Fig. 10. Distribution of the normalized height travelled by the object as rises in the bubble drift for (a) Acetal-S (b) Acetal-L fluidized in a bed of fine sand at Ue = 0.50 m/s.
F. Fotovat, J. Chaouki / Chemical Engineering Journal 280 (2015) 26–35
gas velocities. Such dependence was remarkable for the objects immersed in a bed of fine sand due to the dominance of the buoyant force resulting in the lower opportunities for the exposure of the objects to the rising bubbles. The displacement of the objects in three cases, i.e. Acetal-M and Acetal-L in fine sand and Acetal-M in FCC (Ue = 0.50 m/s), was restricted to the occasional and intermittent rise and sink paths, possibly because of the lack of the vigorous enough bubbles all along the fluidization. As a consequence, the height travelled by these objects was very limited. Moreover, while U r =U b and U u =U b ratios were substantially lower than those of the other objects featured by a well-established circulation pattern, the respective rise frequencies were corresponding. Acknowledgement The authors are most grateful to Dr. John Grace for his constructive comments on this work. References [1] A. Soria-Verdugo, L.M. Garcia-Gutierrez, N. Garcia-Hernando, U. Ruiz-Rivas, Buoyancy effects on objects moving in a bubbling fluidized bed, Chem. Eng. Sci. 66 (2011) 2833–2841. [2] F. Fotovat, J.-P. Laviolette, J. Chaouki, The separation of the main combustible components of municipal solid waste through a dry step-wise process, Powder Technol. (2014) (Submitted). [3] J.W. Chew, C.M. Hrenya, Link between bubbling and segregation patterns in gas-fluidized beds with continuous size distributions, AIChE J. 57 (2011) 3003– 3011. [4] G.M. Rios, K. Dang Tran, H. Masson, Free object motion in a gas fluidized bed, Chem. Eng. Commun. 47 (1986) 247–272. [5] K.S. Lim, P.K. Agarwal, Circulatory motion of a large and lighter sphere in a bubbling fluidized bed of smaller and heavier particles, Chem. Eng. Sci. 49 (1994) 421–424. [6] F. Fotovat, J. Chaouki, J. Bergthorson, Distribution of large biomass particles in a sand-biomass fluidized bed: Experiments and modeling, AIChE J. (2014). [7] F. Fotovat, Characterization of Hydrodynamics and Solids Mixing in Fluidized Beds Involving Biomass, École Polytechnique de Montreal, 2013. [8] F. Fotovat, R. Ansart, M. Hemati, O. Simonin, J. Chaouki, Sand-assisted fluidization of large cylindrical and spherical biomass particles: experiments and simulation, Chem. Eng. Sci. 126 (2015) 543–559.
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[9] F. Larachi, M. Cassanello, M. Marie, J. Chaouki, C. Guy, Solids circulation pattern in 3-phase fluidized-beds containing binary-mixtures of particles as inferred from RPT, Chem. Eng. Res. Des. 73 (1995) 263–268. [10] M. Cassanello, F. Larachi, C. Guy, J. Chaouki, Solids mixing in gas-liquid-solid fluidized beds: experiments and modelling, Chem. Eng. Sci. 51 (1996) 2011– 2020. [11] R.K. Upadhyay, S. Roy, Investigation of hydrodynamics of binary fluidized beds via radioactive particle tracking and dual-source densitometry, Can. J. Chem. Eng. 88 (2010) 601–610. [12] A.C. Rees, J.F. Davidson, J.S. Dennis, A.N. Hayhurst, The rise of a buoyant sphere in a gas-fluidized bed, Chem. Eng. Sci. 60 (2005) 1143–1153. [13] T.H. Nguyen, J.R. Grace, Forces on objects immersed in fluidized beds, Powder Technol. 19 (1978) 255–264. [14] D. Geldart, Gas Fluidization Technology, Wiley, 1987. [15] M. Stein, Y.L. Ding, J.P.K. Seville, D.J. Parker, Solids motion in bubbling gas fluidised beds, Chem. Eng. Sci. 55 (2000) 5291–5300. [16] C.T. Crowe, Multiphase Flow Handbook, Taylor & Francis, Florida, USA, 2010, pp. 5–93. [17] N. Mostoufi, J. Chaouki, Flow structure of the solids in gas-solid fluidized beds, Chem. Eng. Sci. 59 (2004) 4217–4227. [18] F. Larachi, J. Chaouki, G. Kennedy, 3-D mapping of solids flow-fields in multiphase reactors with RPT, AIChE J. 41 (1995) 439–443. [19] F. Larachi, G. Kennedy, J. Chaouki, A gamma-ray detection system for 3-D particle tracking in multiphase reactors, Nucl. Instrum. Methods Phys. Res. Sect. A 338 (1994) 568–576. [20] R.C. Darton, R.D. LaNauze, J.F. Davidson, D. Harrison, Bubble growth due to coalesence in fluidised beds, Trans. Inst. Chem. Eng. 55 (1977) 274–280. [21] J.F. Davidson, D. Harrison, Fluidised Particles, Cambridge University Press, Cambridge, 1963. [22] G. Sun, J.R. Grace, Effect of particle size distribution in different fluidization regimes, AIChE J. 38 (1992) 716–722. [23] F. Fotovat, J. Chaouki, J. Bergthorson, The effect of biomass particles on the gas distribution and dilute phase characteristics of sand–biomass mixtures fluidized in the bubbling regime, Chem. Eng. Sci. (2013). [24] R. Di Felice, The voidage function for fluid-particle interaction systems, Int. J. Multiphase Flow 20 (1994) 153–159. [25] J. Leboreiro, G.G. Joseph, C.M. Hrenya, D.M. Snider, S.S. Banerjee, J.E. Galvin, The influence of binary drag laws on simulations of species segregation in gasfluidized beds, Powder Technol. 184 (2008) 275–290. [26] C.T. Crowe, J.D. Schwarzkopf, M. Sommerfeld, Y. Tsuji, Multiphase flows with droplets and particles, CRC Press, 2011. [27] F.J. Dos Santos, L. Goldstein Jr., Experimental aspects of biomass fuels in a bubbling fluidized bed combustor, Chem. Eng. Process. 47 (2008) 1541–1549. [28] A. Soria-Verdugo, L.M. Garcia-Gutierrez, S. Sanchez-Delgado, U. Ruiz-Rivas, Circulation of an object immersed in a bubbling fluidized bed, Chem. Eng. Sci. 66 (2011) 78–87.