The sequential elutriation behavior of wide particle size distributions

Powder Technology 286 (2015) 230–239

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The sequential elutriation behavior of wide particle size distributions Eloi Kewes a,b,⁎, Franck Dahlem a, Sandrine Bec a, Nicolas Estime b, Emmanuel Risse b, Jacques Grollemund b, Jean-Luc Loubet a a b

Laboratoire de Tribologie et Dynamique des Systemes, UMR CNRS 5513, Ecole Centrale de Lyon, 36 avenue Guy de Collongue, 69134 Ecully Cedex, France Bluestar Silicones France SAS, 1-55 avenue des Freres Perret, 69192 Saint-Fons Cedex, France

a r t i c l e

i n f o

Article history: Received 24 April 2015 Received in revised form 10 August 2015 Accepted 14 August 2015 Available online 21 August 2015 Keywords: Fluidization Elutriation Entrainment Wide particle size distribution Interparticle adhesion

a b s t r a c t Batch elutriation of a metallurgical-grade silicon powder with a wide particle size distribution in a laboratory scale fluidized bed was studied, highlighting the influence of carryover polydispersity. The smallest elutriable fines, namely superfines (b10 μm), whose terminal velocity Ut is far lower than the superficial gas velocity Ug are entrained first, while the largest elutriable particles (Ut ≈ Ug) begin to be entrained with a delay that is as long as the time required for the superfines to leave the bed, thus inducing sequential elutriation. When no superfines were present, the entrainment was not delayed. This peculiar phenomenon was observed at all of the tested gas velocities (0.05–0.2 m s−1) and for different wide particle size distributions belonging overall to the Geldart group A. The superfines thus seem to strongly limit the elutriation of the larger elutriable particles. In addition, the elutriation rate constants were found to increase with increasing superficial gas velocity and with decreasing particle size. When superfines were present, the elutriation rate constant leveled off under a critical size. Increasing the superfine particle content appears to reduce the elutriation rate constant of all of the elutriable particles. These phenomena are related to interparticle interactions within the bed and/or the freeboard and confirm the importance of polydispersity in the elutriation behavior. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Fluidized bed reactors are widely used in the chemical industry in fields as various as catalytic reactions, coal and biomass gasification, fluid catalytic cracking (FCC) in the petroleum industry, mineral processing, and other solid processing industries [1]. Yet, the complex phenomena involved in fluidization, including the entrainment of fines, still suffer from a lack of understanding. When a powder bed is fluidized by a gas, the superficial gas velocity Ug can overcome the free fall terminal velocity Ut of part or all of the particles of the bed, so that they are carried out of the fluidization column. Entrainment thus refers to the total flux of particles leaving the bed while elutriation refers to the classifying effect of entrainment because particles with different sizes or shapes can be entrained under different kinetics. Although this topic has been studied for years, a recent and very comprehensive review by Chew and co-workers [2] emphasized the dramatic discrepancies between the correlations proposed in the literature for the elutriation rate constant. They underlined the need for more physical understanding of the dominating parameters affecting entrainment. Most of entrainment studies use the elutriation rate constant approach, whose theory is developed in part 2 of the present paper. ⁎ Corresponding author at: Laboratoire de Tribologie et Dynamique des Systemes, UMR CNRS 5513, Ecole Centrale de Lyon, 36 avenue Guy de Collongue, 69134 Ecully Cedex, France. E-mail address: [email protected] (E. Kewes).

http://dx.doi.org/10.1016/j.powtec.2015.08.022 0032-5910/© 2015 Elsevier B.V. All rights reserved.

The determination of the elutriation rate constant is mainly empirical, with experimental work relying on pilot fluidization columns of various scales and with various designs, especially running batchwise (unsteady-state system) or recycling the entrained fines back to the bed (steady-state recirculating system) [3]. The fluidized powder itself, with a given true density and particle size distribution (PSD), will determine the fluidization properties as indicated in the Geldart classification [4]. This classification distinguishes among four groups of particles: D (spoutable; e.g., roast coffee beans), B (sand-like; e.g., coarse sand, glass beads), A (aeratable; e.g., FCC catalyst), and C (cohesive; e.g., dust). The nature of the material itself is usually taken into account for the true density of the powder. Many studies are devoted to the entrainment of well-separated binary PSDs, e.g., elutriable group C particles in a bed mainly composed of non-elutriable group A or group B particles [5–11]. Fully elutriable group A–group C mixtures [12–15] have also been studied but wider PSDs have attracted far less attention [16,17]. It seems well-established that the smaller the particle is, the more easily it is entrained out of the bed and the higher the elutriation rate constant until a critical size is reached, at which point smaller particles experience significant interparticle forces and the elutriation rate constant levels off or even decreases [1,7–9,12,14,15]. Nevertheless, it is not clear whether the entrained particles of different sizes behave independently or if they interact with each other. By implicitly stating that an elutriable particle of a given size class has no influence on the other elutriable size classes, the polydispersity of the elutriable fines is sometimes neglected [6,9]. This lack of influence is often explained by

E. Kewes et al. / Powder Technology 286 (2015) 230–239

the fact that in the bed, the fine-coarse interaction should be greater than fine–fine interaction. In addition, some researchers claim that the presence of superfines reduces the elutriation rate of larger elutriable fines. Li and co-workers [11] found the elutriation rate constant of group C and group A particles to be dependent on the weight fraction of the group C particles in the bed: an increased fraction of superfines decreases the elutriation rate of the fines because of increased interparticle adhesion. On the contrary, other researchers found that large entrainment of fines provoked an upward force on the particles in the freeboard, so that the elutriation rate of the larger fines is increased, even causing coarse bed particles whose terminal velocity Ut is less than the superficial gas velocity to be entrained [17–19]. The present work investigates the influence of the polydispersity of the entrained flux (or carryover) on entrainment by experimentally studying the entrainment out of a powder bed run batchwise with a wide PSD, ranging from group C to group B. The powder is metallurgical-grade silicon (MG-Si), obtained by comminution of silicon [20]. The ground powders have PSDs close to Rosin–Rammler distributions, that have proven useful in describing the product distribution of a number of comminution systems [21]. Such PSDs are therefore of significant interest for the fluidization of materials produced by size reduction in general and for the silicones industry in particular. In this latter industry, MG-Si is used in fluidized-bed reactors to synthesize dimethyldichlorosilane, a monomer of silicone polymers [22,23]. The impurity concentration in the reactive powder depends on particle size [24], emphasizing the importance of elutriation. 2. Theoretical background 2.1. Freeboard and transport disengagement height (TDH) The freeboard is the section of the fluidization column between the bed surface and the column outlet. Bubbles bursting at the bed surface spray particles in the freeboard: coarse particles (with Ut N Ug) can fall back to the bed, while so-called elutriable particles (with Ut b Ug) are entrained, regardless of the height of the column. A description of the upward and downward motion of the particles in the freeboard was proposed by Pemberton and Davidson [19]. A critical height over the bed surface called the transport disengagement height (TDH) is defined, yet ambivalently [5]: often considered to be the height over which the solid density in the freeboard does not vary with increasing height, it can also refer to the height above which coarse particles cannot be found; these heights are referred to as TDH(F) and TDH(C) respectively [5]. TDH(C) is usually calculated based on ballistic models [25]. On one hand, TDH(C) relies on the assumption that there is neither momentum transfer between particles in the freeboard nor interactions of any type. This assumption is valid only with low solid concentration in the freeboard. On the other hand, the definition of TDH(F) is more versatile because it takes into account the fact that interparticle interactions can occur in the freeboard. For example, entrained particles can form clusters or agglomerates whose terminal velocity Ut is different from that of the individual particles. A theoretical description is more complicated and TDH(F) is generally determined on the basis of empirical correlations [1,26]. This latter definition will be adopted in the present paper because of its validity in the case of larger entrainment fluxes and polydisperse carryover. Note that it has been suggested to refer to aggregates formed due to cohesive forces as agglomerates and formed due to hydrodynamic forces as clusters [27]. However, Cocco et al., who experimentally observed “clusters” in the freeboard of fluidized beds for the first time, proposed a more complex mechanism: the formation of clusters would be assisted by hydrodynamic forces inside the bed, locally making cohesive forces dominant [28]. Once formed, these agglomerates or clusters can be ejected in the freeboard. Entrainment studies are usually conducted with a freeboard height higher than the TDH, for the sake of reproducibility and because industrial applications generally attempt to minimize the carryover.

231

2.2. Definition of the elutriation rate constant The total entrainment flux E(h) (kg s−1 m−2) is the weight of particles entrained per unit area and time at height h. If the particle sizes are divided into discrete size intervals, then the fraction of E(h) due to particles of a given particle diameter dpi (belonging to size interval i) is Ei(h). The elutriation rate constant approach relies on the assumption that the entrainment flux Ei(h) is directly proportional to the weight fraction of this particle size in the bed xBi , with their ratio being the elutriation rate constant Ki⁎(h). Above TDH, the entrainment flux is nearly constant ⁎ , by definition: and the notation becomes Ki∞ K
i∞ ¼

Ei∞ : xBi

ð1Þ

In other words, a bed composed of particles with size dpi only (xBi = 1) ⁎ . The main interest of this constant is to yields an entrainment flux Ki∞ predict the individual Ei∞ and the total entrainment E∞ for a bed with any PSD: E∞ ¼

X

Ei∞ ¼

i

X

xBi K
i∞ :

ð2Þ

i

Nevertheless, as mentioned in the Introduction, correlations for the elutriation rate constant are reliable under a narrow sets of conditions, because it is not clear if or when the elutriation rate constant of size ⁎ is impacted by the bed weight fraction xBj or the entraindpi particles Ki∞ ment flux Ej∞ of the other particles j. 2.3. Back-calculation of the elutriation rate constant from batch experiments Starting from the definition in Eq. (1) and the definition of a flux, the following equation is obtained: Ei∞ ¼ −

1 d  B B x W ¼ xBi K
i∞ AB dt i

ð3Þ

where AB is the cross-sectional area of the bed (m2) and W B is the total weight of the bed (kg). For batch experiments, entrained particles are removed definitively, so that xBi and W B depend on time. However, if the total entrained weight is relatively small, e.g., less than 20% of the total bed weight, then W B may be regarded as constant for the integration [3]. Assuming the weight of fines adhered on the freeboard wall negligible, each particle leaving the bed is then entrained out of the column ðdtd wEi ¼ − dtd wBi Þ and Eq. (3) can be integrated as    K
AB wEi ðt Þ ¼ wBi ð0Þ 1− exp − i∞ B t : W

ð4Þ

In Eq. (4), wiE(t) is the total cumulative weight entrained out of the bed, and wiB(0) = xBi (0)WB is the total weight of particles of the size interval i in the initial powder bed. The exponential coefficient is often expressed as the rate Ki ∞: K i∞ ¼

K
i∞ AB WB

:

ð5Þ

⁎ must be used because it is supposed The elutriation rate constant Ki∞ to be unaffected by bed weight or column diameter [3] and does not depend on size discretization. Note that some authors alternatively ⁎ AB/(xBi (0)WB) [6,9]. chose to normalize: Ki∞ = Ki∞ The initial condition for the above integration relies on the hypothesis that every particle entrained after a long time was already present in the bed at the beginning of the experiment. This fact is not obvious, since particles can actually be created during fluidization. Colakyan and Levenspiel first presented a model accounting for elutriable

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particles created during batch experiments by interparticle abrasion [29]. Under this condition, Eq. (3) becomes: −

1 d  B B R x W ¼ xBi K
i∞ − i : AB AB dt i

ð6Þ

Ri is an abrasion rate that represents the weight of particles in size interval i created in the bed per time unit, due to interparticle abrasion. Under the assumption of a constant abrasion rate, the integration of Eq. (6) gives:   R wEi ðt Þ ¼ wBi ð0Þ− i ½1− expð−K i∞ t Þ þ Ri t: K i∞

ð7Þ

A convenient representation is the entrained fraction wiE(t)/wiB(0), that is the fraction of particles with size dpi initially present in the bed that have been entrained out of the column. If the carryover is considered to be a single size interval (neglecting the polydispersity of the E (t) = entrained fines), then the total cumulative entrained weight Wtot ∑wiE(t) is:   R ½1−expð−K ∞ t Þ þ Rt W Etot ðt Þ ¼ W Be ð0Þ− |{z} K∞ |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl ffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Particles becoming Particlesfreely elutriable in the initial bed

ð8Þ

elutriable during fluidization

where WEtot is the total cumulative entrained weight (kg), WeB(0) is the total weight of freely elutriable particles in the initial bed (kg) and R is the total production rate of elutriable particles (kg/s). If no interparticle abrasion or deagglomeration occur, then Ri = 0 and the model reduces to Eq. (4). R depends on the material: Colakyan and Levenspiel distinguish between attriting solids (e.g., sand) and nonattriting solids (e.g., polyethylene) [29]. This is illustrated in Fig. 1, which shows qualitative examples of entrained fraction curves for attriting and non-attriting cases. Non-attriting solids exhibit a slope of zero at long times (∀ i, Ri = 0) while attriting solids exhibit a positive slope (∃ i, Ri N 0). Note that the slope is Ri/wBi (0) for the entrained fraction graph and Ri for the total cumulative weight graph. The attrition rate is also expected to increase with increasing superficial gas velocity, bed height and especially with increasing gas speed at the distributor [30]. Fig. 1 also shows that the same weight of particles is entrained faster when the elutriation rate constant is higher (dashed–dotted lines). Liu and Kimura later stated that fines could initially be attached to larger non-elutriable particles [6]. Their generation from agglomerates due to interparticle friction would also contribute to the abrasion rate. In this view, wiB(0) should be regarded as the fraction of particles in the size interval i in the initial bed that can be freely entrained, in

Fig. 1. Entrained fraction of the size interval i versus time; wiE(t)/wiB(0) curves obtained from Eq. (7) for various values of Ki∞ at Ri = 0 (dashed–dotted lines) and various values of Ri at a fixed value of Ki∞ (line and circles). Solids with Ri ≠ 0 are attriting and those with Ri = 0 are non-attriting, following the definition by [29].

opposition to the particles in size interval i in the initial bed that are agglomerated and whose liberation is accounted for by Ri. Note that when all of the free elutriable particles are entrained (e.g., after a time longer than 3/Ki ∞), the exponential term in Eq. (7) is negligible compared to the linear term, the cumulative entrained weight curve thus becoming a straight line of slope Ri. Eqs. (7) and (8) have proven useful in interpreting the experimental batch elutriation curves to determine the elutriation rate constant and interparticle attrition in several studies [5,6,8,9,29].

3. Experimental The fluidization set-up is schematically represented in Fig. 2. The experiments were performed in a glass column (inner diameter of 75 mm and height of 2 m) and a gas distributor resulting in a pressure drop of 102 mBar at 0.05 m/s. The fluidizing gas was dry nitrogen (Air Liquide, 99.999999%) for all experiments. Metallurgical-grade silicon (MG-Si) powder was obtained by laboratory scale grinding and sieving, thus resulting in different wide particle size distributions (Fig. 3). The true density of silicon is 2.33 g cm− 3. PSD-1 was obtained by sieving at 400 μm. Fines have been removed at 0.075 m s−1 to obtain PSD-1b, whose median size is close to that of PSD-1, but the fine tail of the distribution is strongly different. PSD-2, obtained by further milling and sieving at 315 μm, has a median size of 101 μm. The PSDs are shown in Fig. 3 and the Sauter mean diameter D[3,2], the median size D50, the minimum fluidization velocity (MFV) and the Geldart group assignment are described in Table 1. The Sauter mean diameter (D[3,2], surface-to-volume diameter) is a statistical mean best characterizing the fluidization properties of a powder. If a unique Geldart group had to be assigned to each of these three powders based on their Sauter mean diameter, then they would all belong to group A (PSD-1b is at the boundary of group B and PSD-2 is at the boundary of group C). These powders could also be described by mixtures of groups A, B and C, but the decomposition of these wide PSDs would be arbitrary. The three powders experimentally exhibit the properties of group A powders. For each experiment, 2 kg of powder was fluidized batchwise at a constant superficial gas velocity, ranging from 0.05 to 0.2 m s−1. Sizing of powder sampled on top and bottom of the bed during fluidization showed that speeds larger than 0.05 m s−1 ensures the bed homogeneity. Furthermore, pressure drop measurements showed that the full circulating velocity (as defined by Gauthier et al. [31]) was less than 0.05 m s−1 for all tested powders. The static bed height is approximately 0.35 m. The fluidized bed height was never higher than 0.6 m, so the freeboard was always higher than 1.4 m. Particles with a terminal velocity Ut under the superficial gas velocity Ug can be entrained: the critical size for which Ut = Ug is given for the different superficial gas velocities in Table 2. Ut was computed using the Haider–Levenspiel correlation for the drag force [1]. Entrained fines were collected in a glass cyclone; the fines passing the cyclone are retrieved by an absolute filter. The whole fine collecting device adds a pressure drop of 10 mBar at 0.075 m s−1. The sampled fines are weighed and their size distribution is determined by laser diffraction using a Mastersizer 2000. Laser diffraction provides PSDs normalized on a volume basis, which is consistent with particle entrainment being quantified through the mass of the particles. Note that the internal porosity of MG-Si particles is low, so that volume and mass correspond to each other with a fixed density of 2.33 (true density of silicon). Experimental data have were fitted using the non-linear fitting algorithm of Matlab2014a to obtain the values of the parameters in Eqs. (4), (7) or (8). The confidence bounds on both the obtained parameters and the predicted values of the fit for a new observation were calculated from the Jacobian of the fit. Upper and lower confidence bounds plotted in the figures of this article represent the limits within which all of the values of an identical experimental should fall with a probability of 95%.

E. Kewes et al. / Powder Technology 286 (2015) 230–239

233

Fig. 2. Experimental device used to perform the elutriation tests. Particles of the bed are spashed in the freeboard: the disengaging zone includes upward motion of the entrained particles and downward motion of the disengaging particles, while the less dense transport zone only consists of an upward motion of elutriable particles. These particles are collected in the gas–solid separation unit, and then their weight and size distribution are determined.

4. Results 4.1. Batch entrainment of PSD-1 4.1.1. Total entrainment for PSD-1 E is plotted The experimental total cumulative entrained weight Wtot versus time in Fig. 4(a) for various gas velocities. The derivatives of these curves, namely the total entrainment rates, were calculated numerically using the experimental values and are plotted in Fig. 4(b). E (t) curves in Fig. 4(a) resemble the curves given by the theoretThe Wtot ical equation with interparticle abrasion (see Fig. 1). The total entrained weight increases with gas velocity because larger particles become elutriable at higher gas velocities (Fig. 4(a)). The entrainment rate peak sharpens and shifts toward shorter time when the gas velocity

increases, which is consistent with an easier entrainment as the gas velocity increases. Nevertheless, closer examination of these curves reveals counterintuitive facts. Because of more intense mixing and interparticle contact in the bed, the abrasion rate should be more intense at higher superficial gas velocities [9]. This more intense abrasion is not the case here: as seen in Fig. 4(b) after 300 min, all of the curves are superimposed, which demonstrates that the slope at large times (that is the total abrasion rate R) does not increase with gas velocity. In addition, the secondary peak observed after 110 min at 0.2 m s−1, which is also present as a shoulder after 130 min at 0.15 m s−1 in Fig. 4(b) can not taken into account by the elutriation–abrasion model of Eq. (8). Moreover, such a double entrainment rate peak behavior has never been reported to our knowledge. To explain these facts, the polydispersity of the entrained flux must be considered, as described in Section 4.1.2. 4.1.2. Entrainment of each size fraction for PSD-1: considering polydispersity At each sampling time, the PSD of the entrained flux was determined. Hence, the cumulative entrained weight by size interval wEi (t), from particles smaller than 1.4 μm to particles larger than 91.2 μm, was obtained and plotted for 0.075 m s−1 (Fig. 5(a)) and 0.2 m s− 1 (Fig. 5(b)). The curves at all speeds can be fitted with Eq. (4) that does not account for interparticle abrasion. The final slope for all size intervals under 30 μm is clearly zero. Larger particles are elutriated more

Table 1 Characteristics of the analyzed powders: Sauter mean diameter D[3,2], median size D50, minimum fluidization velocity and group of fluidization [4].

Fig. 3. Cumulative particle size distributions of powders 1, 1-b and 2 taken as the starting bed material, with Sauter mean diameters D[3,2] of 57, 93 and 20 μm, respectively. The inset in the top left corner represents the corresponding differential PSDs.

PSD

D[3,2] (μm)

D50 (μm)

MFV (10−2 m s−1)

Geldart group

PSD-1 PSD-1b PSD-2

57 93 20

186 184 101

0.3 0.6 0.8

A A A

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E. Kewes et al. / Powder Technology 286 (2015) 230–239

Table 2 Maximal particle size elutriable for various superficial gas velocities. Ug (m s−1) size dp with Ut(dp) = Ug

0.05 32.4

0.075 41.0

0.1 48.6

0.15 63.5

0.2 77.0

slowly and reach the zero slope within a longer time than plotted. This result indicates that MG-Si is a non-attriting solid at the tested superficial gas velocities according to Colakyan's theory (see Fig. 1). The largest elutriable fines appear to start being elutriated with a delay. This delay t0 was taken into account in Eq. (4) via substitution of t by t − t0. The sum of the fits on each size interval without attrition provides an E as shown in excellent fit for the total cumulative entrained weight Wtot Fig. 6 (fit represented as dashed lines). Note that a very satisfactory fit E (not shown). Howcan also be obtained by directly using Eq. (8) on Wtot ever, the use of Eq. (8) requires including in the model an abrasion rate that appears to have no physical sense. Indeed, as shown in Fig. 5 no interparticle abrasion occurs, despite the similar shape of the curves of WEtot in Fig. 4 and WEtot of the attriting solids (Fig. 1, case R ≠ 0). The cause of this shape is the largest elutriable fines starting to be entrained with a delay, which cannot be accounted for by the linear attrition rate R.

Fig. 5. Entrained fraction wiE(t)/wiB(0) for all elutriating fractions at 0.075 m s−1 (a) and 0.2 m s−1 (b) in the case of PSD-1. The symbols refer to experimental data while dashed lines are numerical fits using Eq. (4) (free elutriation without interparticle abrasion). Excellent fits are obtained both at low and high superficial gas velocities: no entrainment due to interparticle abrasion occurs. In both cases, the smaller elutriable particles are fully removed from the bed first, while the larger particles begin to be entrained with a delay of 50 to 100 min. (a) Ug = 0.075 m s−1. (b) Ug = 0.2 m s−1.

Fig. 4. Experimental data on the total entrainment for PSD-1 at different gas velocities. WEtot(t) is the total cumulative weight of the particles that have left the column at time t (a) and dtd W Etot ðtÞ is the instantaneous flux out of the column at time t (b), obtained by numerical derivation of the curves in (a). The curves at lower speeds appear to follow the behavior described by Eq. (8) and depicted in Fig. 1 with interparticle abrasion. Yet, as the superficial gas velocity increases, interparticle abrasion does not become larger and a secondary entrainment rate peak arises with a delay of approximately 100 min. (a) Total cumulative weight entrained WEtot(t) versus time. (b) Total entrainment rate versus time.

d W Etot ðtÞ dt

For PSD-1 at 0.075 m s−1 and 0.2 m s−1 bed samples taken at different fluidization times were observed by SEM, as can be seen in Fig. 7. The inserted graphs evidence the position of sampling times in the elutriation curve. As can be seen, for both speeds considered, the four sampling times correspond to (from left to right) (1) the beginning of superfines entrainment, (2) the end of superfines entrainment, (3) the beginning of larger elutriable fines entrainment and (4) middle/end of larger elutriable fines entrainment. A micrograph of the initial powder is shown: a large amount of superfines appear attached to larger particles. At the beginning of superfines entrainment (1), the adhesion of superfines on larger particles is still present and may be slightly stronger. Agglomerates of superfines attached on both medium fine and coarse particles are observed. Note that these will be referred to as “agglomerates” hereafter, although the precise mechanism of their formation (hydrodynamics, interparticle forces or a combination of both [28]) is not known. At the end of superfines entrainment (2), very few cohesion is observed, hardly any superfines coating larger particles are observed. At the beginning of larger elutriable fines entrainment (3), particles with size of a few tenth of microns appear as individual particles rather than agglomerates. As the entrainment of the larger elutriable fines proceeds (4), their number visibly decreases. This is more pronounced for the 0.2 m s−1 case, where larger particles can be entrained. These SEM observations of the bed are consistent with the superfines being entrained first, then larger elutriable fines.

E. Kewes et al. / Powder Technology 286 (2015) 230–239

235

dcrit under which the elutriation rate constant does not increase further with decreasing particle size due to interparticle interactions: dcrit ¼

10325 from ρ0:725 s

dcrit ¼

dcrit ¼

½12

ð9Þ

101000 g ρ0:731 s

from ½7

ð10Þ

101000 ρs g 0:731

from ½10

ð11Þ

where ρs is the true density of the powder and g is the gravity. The critical diameter for MG-Si is respectively 37 μm, 35 μm and 8 μm using Eqs. (9), (10) and (11), respectively. Note that in a subsequent paper, the correlation by Baeyens et al. (Eq. (9)) was found to be overestimating the experimental critical diameter [14]: for limestone (whose density ρs = 2580 kg m−3 is close to MG-Si), dcrit was approximately 10 μm at 0.1 m s−1 and 20 μm at 0.3 m s−1. In the present paper, at low superficial gas velocities, a plateau is reached at approximately 10 μm. Even if the critical diameter appears to increase at high superficial gas velocity, the interpretation is not straightforward because the time delay is not taken into account, as mentioned above. The general trend and order of magnitude of the elutriation rate constant versus particle size is similar to the results or correlations obtained by several authors [12,14,15,33]. The results obtained under other conditions of superficial gas velocities and/or particle sizes are far from the present values.

Fig. 6. Total cumulative entrained weight WEtot(t) at 0.075 m s−1 (a) and 0.2 m s−1 (b) in the case of PSD-1. Triangles are experimental data while solid lines are numerical fits using the sum of the fits of Fig. 5 obtained using Eq. (4) (free elutriation without interparticle abrasion). Dashed lines are the contributions of the particles larger than 30 μm (red) and smaller than 30 μm (blue) to the fit. A satisfactory fit is obtained; this fit accounts for the inflexion point due to the entrainment delay of the larger elutriable particles. (a) Ug = 0.075 m s−1. (b) Ug = 0.2 m s−1.

⁎ elutriation rate constant 4.1.3. Correlation for Ki∞ The elutriation rate constants were determined by fitting Eq. (4) to the experimental cumulative weight entrained for each size interval wEi . The elutriation rate constant is found to depend on the particle size, as shown in Fig. 8: Ki ⁎∞ increases with decreasing particle size ⁎ also inuntil a critical value where a plateau is reached. As expected, Ki∞ creases with increasing superficial gas velocity. Note in particular that the time delay t0 does not impact the calculation of the elutriation rate ⁎ at 0.2 m s−1 for particles larger constant here: thus, the values of Ki∞ than 30 μm plotted in Fig. 8 are the values obtained after the time delay, thus when the smallest elutriable fines have been already re⁎ for the finest and the largest moved from the bed. In other words, the Ki∞ fines were determined before and after the removal of superfines, i.e., not simultaneously. A large number of correlations for the elutriation rate constant have been proposed in the literature, as comprehensively reviewed by Chew et al. [2]. These authors demonstrated the consistency of all of the correlations to be bound to the range of superficial gas velocity, particle size and even experimental device used. Nevertheless, common trends arise: the elutriation rate constant was often found to level off or even decrease under a critical size [7–12,14,15,32], as is observed here as well. Interparticle interactions would be responsible for this plateau: as the particle size decreases, adhesion forces become stronger and limit the rate of entrainment. The interparticle interactions can be promoted inside the bed (e.g., between non-elutriable coarse particles and fines [7,10]) or in the freeboard via elutriable fine particle agglomerates whose apparent size is larger than the size of each particle of the agglomerate. Several authors [7,10,12] have proposed equations to determine the critical diameter

4.2. Effect of the initial superfine content: comparison of PSD-1 and PSD-1b To confirm that the finest particles are the cause for the delayed entrainment peak, PSD-1b was studied. As is obvious in Fig. 3, PSD-1b has the same particle size distribution as PSD-1 except particles finer than 100 μm are depleted and particles smaller than 10 μm (superfines) are absent. The cumulative entrained weight obtained at 0.2 m s−1 is represented in Fig. 9 (to be compared with Fig. 5(b)). It is obvious that without superfine particles, the entrainment of all particles is not delayed: the delay in entrainment observed for PSD-1 is related to superfines. The elutriation rate constants for PSD-1 and PSD-1b are compared in ⁎ are the same for particles larger than approximately Fig. 10. The Ki∞ 30 μm. The reader should remember that the time delay does not impact the calculation of the elutriation rate constant. When this fact is taken into account, it becomes clear that the entrainment of these particles occur at the same rate whether superfines are present or not. The only change is the time delay described before: when superfines are present, the entrainment curve is shifted toward larger time but has the same shape. In contrast, the smallest particles of PSD-1b (between 10 and 30 μm) have a higher elutriation rate constant, i.e., they are removed faster from the bed when no superfines are present. This observation ⁎ being caused by agglomerated is consistent with the plateau value of Ki∞ superfine particles. This result could also give an explanation for some discrepancies underlined by Chew and co-workers [2]: correlations for ⁎ based on experiments using powders including superfine particles Ki∞ (cohesive particles smaller than 10 μm, such as [10,12]), predict far lower elutriation rate constants than correlations built without these particles, e.g., [5,16]. This result would imply that the elutriation rate constant of size i particles Ki ⁎∞ can be impacted by the bed weight fraction xBj or the entrainment flux Ej∞ of the other particles j. 4.3. Effect of the initial PSD: comparison of PSD-1 and PSD-2 The same batch experiments were performed on PSD-2 which has a much smaller Sauter mean diameter (see Table 1). The total cumulative entrained weight is plotted versus time in Fig. 11; the same curve for PSD-1 is shown for comparison. It is striking that the entrainment rate

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Fig. 7. SEM micrographs, all with the same scale bar (indicated on the bottom right corner), of the initial powder (PSD-1) and of the powder sampled in the bed during elutriation at 0.075 m s−1 and 0.2 m s−1 at four different sampling times. The insert graphs correspond to Fig. 5 and the dashed lines evidence the sampling times in the entrainment curves.

is identical for both PSDs during the first 100 min. Subsequently, fines in PSD-1 are depleted and the entrainment rate decreases while it holds on longer for PSD-2 which has more initial fines to remove. The cumulative entrained weight per size fraction against time is shown in Fig. 12. The initial fine mass in the bed is higher than that in PSD-1 (wiB(0) (PSD-2) N wBi (0) (PSD-1)); as expected, this results in a higher plateau value at the end of entrainment. The entrainment of the largest elutriable fines (N 30 μm) is clearly shifted toward longer times, in contrast to the results of PSD-1. This result corresponds to the longer time required to remove the finest elutriable particles from the bed in the case of PSD-2. Despite having a higher weight fraction initially in PSD-

Fig. 8. Elutriation rate constant depending on particle size at different superficial gas velocities for PSD-1, values obtained by fitting the experimental data of Fig. 5 with Eq. (4). At a ⁎ increases with decreasing particle size until a critical size given superficial gas velocity, Ki∞ ⁎ levels off. under which Ki∞

2, fines are not entrained at a faster rate than in the case of PSD-1. This result is confirmed in Fig. 13: at the same superficial gas velocity, the elutriation rate constant seems slightly lower when more fines and superfines are initially present in the bed. This result is again consistent with the hypothesis of the finest fractions promoting adhesion and therefore increasing the residence time of larger fines in the bed. 5. Discussion Batch elutriation of MG-Si powder appears to be sequential, in that the smallest elutriable fines (Ut ≪ Ug) are entrained first, and then the

Fig. 9. Entrained fraction wiE(t)/wiB(0) for all elutriating fractions at 0.2 m s−1 in the case of PSD-1b. The symbols refer to experimental data while dashed lines are numerical fits using Eq. (4) (free elutriation without interparticle abrasion). Compared with Fig. 5, no delay is observed.

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Fig. 10. Elutriation rate constant at 0.2 m s−1 for PSD-1 (squares) and PSD-1b (triangles). ⁎ are unchanged for larger particles while they In the absence of superfines, the values Ki∞ are increased for smaller particles.

elutriation of the largest elutriable fines (U t bU g or even U t NU g ) starts, with a delay equal to the time required to remove almost all of the finest particles from the bed. Such behavior appears to be uniquely observed, with no paper referencing it to our knowledge. Only a recent paper briefly mentions an industrial case where a delayed total entrainment peak was observed when running batchwise [34]. When reproduced at the laboratory scale they found the delayed peak to follow the complete elutriation of the fine material (monitored by the median size of particles collected in a cyclone). Given this technical report, the sequential behavior is expected to be observed in industrial reactors as well. No previous paper explaining this phenomenon was found by these authors. Yet, the results of the present paper are consistent with previously reported phenomena. The model (Eq. (4)) describing batch entrainment kinetics was successfully used on the discretized size intervals of the carryover. However, the linear term added by Colakyan and Levenspiel [29] and improved by Liu and Kimura [6] that accounted for fines becoming elutriable during fluidization (either created by interparticle abrasion or by particle liberation from fine-coarse agglomerates in the bed) could not be used here. No elutriation due to interparticle attrition was observed and no indicator of wear was observed on coarse particles using a scanning electron microscope after a fluidization run. Instead, the finest elutriable particles appear to block the elutriation of the larger particles: the latter begin to be entrained only when the finest fractions are already elutriated. The kinetics were thus better described by adding a time delay t0 in Eq. (4) after which the elutriation of the largest elutriable fines actually starts. This delay is no longer present if the initial bed PSD does not include superfine particles. This is

Fig. 11. Total cumulative weight entrained WEtot versus time for PSD-1 and PSD-2 at a superficial gas velocity Ug of 0.075 m s−1. The curves are perfectly superimposed at the beginning of the entrainment test; subsequently the cumulative weight entrained increases faster for PSD-2, due to the larger amount of fine particles in the initial bed.

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Fig. 12. Entrained fraction wiE(t)/wiB(0) for all elutriating fractions at 0.075 m s−1 in the case of PSD-2. The symbols refer to experimental data while dashed lines are numerical fits using Eq. (4) (free elutriation without interparticle abrasion). Again, excellent fits are obtained both at low and high superficial gas velocities: no entrainment due to interparticle abrasion occurs. The smaller elutriable particles are fully removed from the bed first, while the larger particles begin to be entrained with a delay of 150 to 250 min.

supported by the SEM micrographs presented in Fig. 7, that evidences the cohesive influence of the superfines on the powder and the formation of agglomerates. When these superfines are removed, the larger elutriable particles are not retained in agglomerates anymore and therefore start to be entrained. Note that there is no reason for this phenomenon to be bound to batch processes. This suggests that continuously operating fluidized beds should be fed rapidly enough with new material (containing superfines) in order to limit the entrainment of larger particles. Several authors have already provided conclusions regarding the influence of the fine and superfine proportion in the bed on the elutriation of the larger size fractions. Baeyens et al. found the elutriation rate constant of group A particles to be reduced when the weight fraction of group C particles was increased [12]. This behavior occurred only at velocities of approximately 0.1 m s− 1 and did not persist at 0.6 m s− 1, which is why they regarded the effect of the superfines as an adhesion promoter inside the bed. The adhesion would play a role only at low gas velocities, while it is overruled at higher velocities, where hydrodynamic forces dominate. Li et al. observed that a greater fraction of particles smaller than 6 μm diminishes the carryover of group A particles in a recirculating fluidized bed; this observation was explained by the promotion of interparticle adhesion within the bed due to superfines [11]. In addition, Choi et al. obtained greater elutriation rate constants for particles for which U t NU g when increasing the fraction of particles for

Fig. 13. Elutriation rate constant depending on particle size at 0.075 m s−1 for PSD-1 and ⁎ PSD-2, values obtained by fitting experimental data of Figs. 5 and 12 with Eq. (4). Ki∞ values of especially the largest elutriable fines are reduced by the larger amount of fines in the bed.

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which Ut b Ug at superficial gas velocities between 0.6 and 2.2 m s−1 [16]. They attributed this fact to the momentum transfer from elutriating particles to coarse particles in the freeboard, thus adding an upward force. This phenomenon was first considered by Geldart et al. [18] and observed by Chew et al. [17]. Other authors have observed entrainment of particles for which U t NU g [5,15]. Given this somewhat contradictory background, several explanations are worth considering. Four hypotheses are proposed below: they locate the grounds of the phenomenon inside the bed for Hypothesis (i), in the transition from the bed to the freeboard for Hypothesis (ii) and inside the freeboard for Hypothesis (iii) and Hypothesis (iv). Hypothesis (i). The very fine particles promote interparticle adhesion inside the bed, thus forming agglomerates, which involve these particles, larger elutriable fines and/or coarse particles. These agglomerates are less likely to be ejected in the freeboard than the individual particles, which limits the rate of elutriation of agglomerated particles. When superfines are removed, a gradual liberation of particles from the agglomerates occurs, causing the rate of entrainment of larger elutriable particles to increase. Hypothesis (ii). The gradual change of the bed PSD (Sauter mean diameter shifting toward higher values) causes a change in the fluidization regime from bubbling to slugging. In the latter regime, particles would be ejected faster so that the elutriation increases. Hypothesis (iii). As in the first hypothesis, superfine-promoted agglomerates of superfines are formed in the bed and ejected in the freeboard or directly formed in the freeboard. Such agglomerates may comprise superfines only or both superfines and larger elutriable fines. The size of the agglomerate rather than that of individual particles has thus to be considered to state whether entrainment occurs. On the one hand, the apparent terminal velocity of agglomerates composed of superfines only still verify Ut b Ug and these agglomerates are thus entrained. On the other hand, agglomerates composed of superfines and larger elutriable fines may have an apparent terminal velocity larger than the gas velocity ðU t bU g Þ and fall back to the bed (even if the individual particles all had terminal velocities smaller than Ug). When all of the superfines are removed, agglomerate formation is not promoted anymore and larger elutriable fines, ejected as individual particles in the freeboard, are entrained. Hypothesis (iv). (a) Fine particles induce an upward force on slightly larger particles due to momentum transfer in the freeboard, but not on far larger particles. Thus, particles of a given size interval help the upper interval to be entrained and so on, resulting in the sequential elutriation. Yet, this argument can be reversed as follows: (b) when the smallest elutriable fines (Ut ≪ Ug) are entrained, the freeboard is densely filled by upward and downward flows of particles or agglomerates so that a global downward force is induced on particles with U t bU g , preventing them from being entrained. When the superfines are fully removed, the freeboard is less densely filled allowing larger particles to be entrained. Note that the agglomerates mentioned in Hypothesis (i) and Hypothesis (iii) are transient, as they result from the dynamic agglomeration and deagglomeration of particles, which are driven by interparticle adhesion and friction and impact forces, respectively. This dynamic equilibrium implies that some particles appear alternatively as individual particles and as agglomerates. The latter Hypothesis (iv) is based on papers describing operation at higher gas velocities than those of the present studies and thus seems less likely to be the case. Hypothesis (ii) is interesting because it explains the gradual change in entrainment behavior by the gradual change in fluidization regime. Hypothesis (ii) is also consistent with the fact that the transition appears when the Sauter mean diameter of the bed approaches the Geldart A to B boundary. Practically, a transition

from bubbling to slugging was actually observed for PSD-1 only, which is not surprising given the change in bed PSD. Nevertheless, this transition is not necessarily the cause for the entrainment behavior: Hypothesis (ii) implicitly states that the transport disengagement height is modified due to the regime transition, from a height greater than the freeboard height to a lower height. Indeed, if a column is high enough, then the initial velocity of the particles sprayed out by bubbles or slugs has no influence on the fact that large particles can disengage. This result implies that if the column was higher, then we would not observe any delay; however the delayed peak has been observed elsewhere at different scales (included industrial scale) [34]. Moreover, according to several correlations for the TDH, the freeboard height in the present study is greater than the TDH. Zenz and Othmer [35] (as cited in [36]) estimate the TDH to be less than 1 m at superficial gas velocities under 0.7 m s− 1 in a 0.075 m-diameter column. The majority of the correlations reviewed in [36] predict TDH between 1 and 1.4 m at a superficial gas velocity of 0.2 m s− 1, less than the experimental 1.5 to 1.7 m-high freeboard at the end of the delay. At an even lower superficial gas velocity of 0.075 m s−1, the phenomenon is still observed, while correlations predict a TDH of less than 1 m. Another feature of this hypothesis is that the variation of the particle size distribution in the bed should also affect the bubble size, which is known to determine the turbulence intensity in the freeboard [26]. This could lead to more intense gas fluctuations in the freeboard, with faster ascending gas motion, thus activating the entrainment of larger particles. Nevertheless, as the impact of bubble eruption on freeboard gas fluctuations diminishes with height, this again assumes that sufficiently high columns would not show this trend. Hence, this drawback of Hypothesis (ii) raises uncertainties that it is the only cause. As literature background suggests that the behavior should be governed by interparticle interactions at low superficial gas velocities, Hypothesis (i) and Hypothesis (iii) appear to be the most likely valid hypotheses. They are supported by the SEM micrographs presented in Fig. 7: superfines appear very cohesive and adhere on larger particles rather than forming agglomerates composed only of superfines. As the superfines are removed, agglomerate breakage occurs causing the entrainment of the larger elutriable particles that are not involved in agglomerates anymore. Hypothesis (i) and Hypothesis (iii) are also both consistent with the fact that group C influence the entrainment and the presence of the delayed peak at different scales. In addition, Hypothesis (iii) would explain the plateau value of the elutriation rate constant under a certain size: if the smallest particles are elutriated as agglomerates, then they are all entrained at the same rate. It is not unlikely that several of the proposed mechanisms co-exist: for example, agglomerate formation can occur both in the bed and in the freeboard (Hypothesis (i) and Hypothesis (iii)), or the bubbling–slugging transition could change the way solids are sprayed out and consequently the agglomerate formation. Among batch entrainment measurements, qualitative electrostatic measurements were performed, with the results indicating that strong electrostatic voltages build in the fluidization column, in correlation with entrainment. Because dry nitrogen was used to fluidize the powder, implying low relative humidity, electrostatic effects are expected to be dominant [37]. Different materials could behave differently because the ability to create tribocharges or to evacuate electrostatic charges strongly depends on the electric properties of the material. It has been observed on another electrostatic material that fines and coarse particles can acquire opposite charges upon fluidization [38]. The interparticle adhesion can be affected by the freeboard wall; nevertheless the same sequential elutriation phenomenon was observed by the authors in larger columns (150 and 400 mm). We therefore do not expect wall effects to be dominant. The nature of interparticle adhesion within the bed or in agglomerates within the freeboard could be due to electrostatic interactions and are currently under investigation to explain the cause of the sequential elutriation behavior of MG-Si.

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6. Conclusion Batch entrainment tests were performed on metallurgical-grade silicon powder fluidized by dry nitrogen at superficial gas velocities ranging from 0.05 to 0.2 m s− 1. Even if the total elutriation curve appears to follow the attriting behavior, dividing the carryover into discrete size intervals indicated that no entrainment due to interparticle attrition occurs and that the elutriation of the largest elutriable fines starts only after the complete removal of the finest elutriable fines from the bed. This phenomenon was observed at different superficial gas velocities and with different bed particle size distributions and results in a secondary delayed peak in the total entrainment curve. This delay is only present when the initial bed particle size distribution includes a sufficient concentration of cohesive superfine particles. Elutriation rate constants were back-calculated from experimental ⁎ is found to increase with dedata: at a given superficial gas velocity, Ki∞ creasing particle size and then levels off under a critical size. An increase in superfine particles content slightly decreases the elutriation rate constants of all of the elutriable particles. Overall, the presence of the finest elutriable particles (Ut ≪ Ug) appears to limit the elutriation of the largest elutriable particles ðU t bU g Þ, delaying the entire entrainment ⁎ , which is the rate at which entrainment phenomenon or decreasing Ki∞ occurs. Overall, this result indicates that the elutriation rate constant of a given particle size interval may depend on other particles. The explanation could lie within interparticle interactions, promoted by superfines (b 10 μm), changing the adhesion behavior inside the bed or between agglomerates inside the freeboard. The variation in the elutriation rate constant obtained here is analogous to previously observed plateau ⁎ with decreasing particle size, but the sequential entrainvalues in Ki∞ ment behavior had not been observed previously. Several intricate phenomena could cause this behavior, which could be linked with the polydispersity of the bed PSD and carryover or with the material itself because pure silicon is known for its high tendency to create tribocharges. References [1] W.-C. Yang, Handbook of Fluidization and Fluid–Particle Systems, Marcel Dekker, 2003. [2] J.W. Chew, A. Cahyadi, C.M. Hrenya, R. Karri, R.A. Cocco, Review of entrainment correlations in gas–solid fluidization, Chem. Eng. J. 260 (2015) 152–171. [3] D. Kunii, O. Levenspiel, Fluidization Engineering, 2nd edition ButterworthHeinemann, 1991. [4] D. Geldart, Types of gas fluidization, Powder Technol. 7 (1973) 285–292. [5] M. Sciazko, J. Bandrowski, J. Raczek, On the entrainment of solid particles from a fluidized bed, Powder Technol. 66 (1991) 33–39. [6] Y.-D. Liu, S. Kimura, Fluidization and entrainment of difficult-to-fluidize fine powder mixed with easy-to-fluidize large particles, Powder Technol. 75 (1993) 189–196. [7] X. Ma, K. Kato, Effect of interparticle adhesion forces on elutriation of fine powders from a fluidized bed of a binary particle mixture, Powder Technol. 95 (1998) 93–101. [8] D. Santana, J. Rodrìguez, A. Macias-Machin, Modelling fluidized bed elutriation of fine particles, Powder Technol. 106 (1999) 110–118. [9] J. Rodrìguez, J. Sánchez, A. Alvaro, D. Florea, A. Estévez, Fluidization and elutriation of iron oxide particles. A study of attrition and agglomeration processes in fluidized beds, Powder Technol. 111 (2000) 218–230.

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