Article pubs.acs.org/IECR
Evolution of Limestone Particle Size Distribution in an Air-Jet Attrition Apparatus Gang Xiao,*,† John R. Grace,‡ and C. Jim Lim‡ †
State Key Laboratory of Clean Energy Utilization, Institute for Thermal Power Engineering, Zhejiang University, Hangzhou 310027, China ‡ Department of Chemical & Biological Engineering, University of British Columbia, 2360 East Mall, Vancouver, Canada V6T 1Z3 ABSTRACT: Attrition is very important in fluidized-bed reactors, especially for limestone-based sorbents used to capture SO2 and CO2. The initial size distribution of the sorbent particles is commonly used to predict the rate of attrition, but the distribution changes during the process. Limestone samples of narrow particle size distributions (PSDs) were tested in an ASTM air-jet attrition apparatus, and the evolution of the PSDs was investigated. The entropies of information on log-normal functions, a measure of the disorder of particles being entrained into the jets, remained almost unchanged during the attrition process. This indicates that particles of greater entropy generally experience attrition at a greater rate in an air-jet apparatus, except for particles which are too large to be mobilized or too small to stay in the bed.
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INTRODUCTION Fluidized beds are widely used as catalytic reactors and for gas− solid processes such as combustion.1,2 Particle attrition is very important in these processes, as it affects efficiency, entrainment, and operational costs to replace material lost through elutriation.3 Limestone is a common sorbent for SO2 capture and is receiving widespread attention for CO2 capture in fluidized beds.4,5 The CO2 capture capacity and attrition characteristics of CaO-based materials is affected by SO2 concentrations and calcium looping cycles.6 The attrition rate is an important factor in determining the reactor design and in optimizing operating conditions.3−6 Two main attrition mechanisms have been identified: abrasion and fragmentation. Abrasion occurs on the surface of the particles, producing fines by dislodging crystallites and asperities from the outermost layer. The size distribution of the major particles changes only slightly when abrasion is the predominant mechanism, but the production of the much finer particles results in overall bimodal distributions. Fragmentation refers to breakage of particles into two or more particles which are smaller than, but of the same order of magnitude in size as, the original particles. This process is much less likely to result in a bimodal size distribution. There are two standard methods for measuring and assessing attrition.7 One, introduced by Gwyn,8 relies on the rate of mass loss by elutriation in fluidized beds, or fines accumulation in the filter. Gwyn7,8 proposed a simple equation to represent timedependent attrition in an air-jet apparatus: W = k t t mt
material hardness Kh, critical stress intensity Kc, and gas or jet velocity ug (or particle velocity up). For gas velocity, it is common to subtract a minimum gas velocity umin for attrition,11,12 i.e. to write W = kug(ug − umin)mug
where kug is a constant and mug is an index. When ug exceeds umin, attrition occurs. If ug ≫ umin, e.g. for a sonic air jet, umin can be neglected. For a batchwise fluidized bed, Werther and Reppenhagen12 provided a model for the overall attrition rate: ̇ Ẇ = Ẇjet + Ẇ bubble + Wcyclone = norC jd pbρg dor 2uor 3 + Kbmb(usf − umin)3 + ṁc,ind pc uc,in 2 σc
(3)
where Ẇ is the total rate of mass loss by entrainment, whereas Ẇ jet, Ẇ bubble, and Ẇ cyclone are the rates of mass loss caused by grid jet attrition, bubble-induced attrition, and cyclone attrition, respectively. Another empirical method for representing attrition, proposed by Epstein,14 focuses on fragmentation.7 Two functions, S(x) and B(x, y), are utilized. S(x) represents the probability of fragmentation of particles of size x in a specific time interval, whereas B(x, y) describes the fraction of fragmentation products smaller than size x from a particle of size y. Broadbent and Callcott15 extended Epstein’s concept, defining S(x) and B(x, y) as vectors and matrices, respectively, with
(1)
where W is the fraction of particles smaller than a defined size, called fines, t is time, kt is a constant which is a function of the initial particle size and jet characteristics, and mt is an exponent, approximately independent of the initial particle size. Many factors have been considered based on similar formulations,9−13 such as particle diameter dp, shape factor φ, orifice diameter dor, number of orifices nor, gas density ρg, particle density ρp, © 2014 American Chemical Society
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Received: Revised: Accepted: Published: 15845
April 28, 2014 August 15, 2014 September 19, 2014 September 19, 2014 dx.doi.org/10.1021/ie501745h | Ind. Eng. Chem. Res. 2014, 53, 15845−15851
Industrial & Engineering Chemistry Research B (x , y ) =
Article
1 − exp( −x /y) 1 − exp( −1)
16,17
located at the top of the upper cone. The fines collector, a stainless steel cylinder containing a ceramic filter with opening diameters of ∼0.1 μm, is connected to the upper cone. Fines are trapped in the collector, while the gas exits from the top of the ceramic filter. The limestone tested in the batch attrition tests was Strassburg limestone, an American limestone tested extensively in previous reactivation, sorption, and attrition studies at UBC.5,20,22,23 The average density of this limestone is 2719 kg/ m3, with a standard deviation of 110 kg/m3, determined by a helium pycnometer (PN-75152) provided by Quantachrome Instruments. All tests reported in this paper lasted 5 to 96 h, with air at room temperature (20 ± 5 °C). The raw Strassburg limestone particles were of a wide size range. These particles were divided into several fractions by sieving for 20 min using Tyler sieves. The resulting fractions were of narrow particle size distributions (PSD) with 90% confidence intervals of roughly, e.g. 710−850, 500−600, 355−425, 250−300, 125−180 μm, etc. For simplification, these fractions are used to label these intervals, i.e. 710−850 μm, etc. After leak checking, 50 ± 0.1 g of limestone was added through the feeding port, which was then closed. An air flow rate of 10.0 ± 0.1 standard L/min, adjusted by a valve based on readings from a mass flow meter (Omega FMA5526), was then delivered to the apparatus through the distributor. The upstream pressure of the feeding air was ∼2.4 bar. During the attrition period, the air mass flow was held constant, and its upstream pressure increased by 0 to 0.3 bar, depending on the attrition rate and time, because of the fines captured by the filter and retained by the fines collector. The attrition tube and settling chamber were tapped for 10 min every 12 h and at the end of each run to encourage adhering fines to join either the material remaining supported by the distributor, called “material on distributor” below, or the fines elutriated into the fines collector. After the run, the fines and material on distributor were collected separately. The size distributions of the fines were analyzed by a Malvern laser diffraction apparatus (Mastersizer 2000) using the “catalyst” model, while the material on the distributor was sieved for 5 min using standard Tyler sieves and weighed using a GR-200 balance, provided by Pacific Industrial Scale Co. Ltd., Japan. Selected samples were also viewed by a scanning electron microscope (SEM, S3000N) provided by Hitachi Ltd., Japan.
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Austin extended the ideas of Epstein and Reid and developed a model to estimate the particle size distribution. McMillan et al.19 added assumptions and procedures to calculate the parameters of the model. For example, larger particles were assumed to break into pairs of smaller particles of diameter dp,large = dp,mother/(γ + 1)1/3 and dp,small = dp,mother/(1/γ + 1)1/3, where γ is a symmetry coefficient, equal to 0.8 in this model. Small particles would no longer break when their size was less than a critical size, 18 μm in their research. To simplify the attrition model, Chen et al.20 postulated that all particles have the same probability of fragmentation, scattering randomly into smaller size intervals. In previous research, initial or feed particle sizes have commonly been applied to predict attrition rates, even though the particle size distribution changes profoundly during the attrition process. This paper attempts to determine whether attrition rates depend only on the initial particle sizes, to find a simple way to describe the attrition rates and to provide a more fundamental understanding of attrition.
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EXPERIMENTAL EQUIPMENT AND METHOD The air jet attrition apparatus, based on the ASTM D5757-00 method,21 is shown in Figure 1. It employs a three-orifice
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MODES OF PARTICLE ATTRITION Previous Studies on Jet Attrition. Xiao et al.23 investigated the attrition rates (i.e., fines generation rates) of limestone particles of seven narrow size intervals and found that the attrition rate was probably controlled by cumulative fatigue caused by successive particle−particle impacts. The attrition rate was constant during the stable stage, representing most of the attrition process, while the mean particle size decreased. Merry24 studied flows of particles and fluid in the vicinity of vertical jets and found that particles entrained into a jet were from a limited area at the bottom of the jet. His work also indicated that the entrainment rate remained constant for a specific jet if ug ≫ umin. Qi et al.25 compared previous studies on saturation carrying capacity of gas and proposed a correlation, which indicated that the saturation carrying capacity was nearly independent of particle size if the gas velocity was sufficiently high.
Figure 1. Schematic of air-jet apparatus.22,23
distributor plate, an attrition tube, a settling chamber, and a fines collector. The distributor plate has three upward-facing orifices of diameter 397 ± 3 μm, equidistant from each other, each centered 10.01 ± 0.25 mm from the axis of the column. The distributor plate is attached to the bottom of the attrition tube, a 710 mm-long stainless steel cylindrical column of 35 mm inside diameter. The settling chamber, connected to the top of the attrition tube, consists of a lower diverging cone of height 230 mm, a 300 mm long cylinder of 110 mm inside diameter, and an upper cone of height 100 mm, converging to an inside diameter of 30 mm. The particle feeding port is 15846
dx.doi.org/10.1021/ie501745h | Ind. Eng. Chem. Res. 2014, 53, 15845−15851
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Figure 2. Photographs of particles remaining in 710−850 μm interval after beginning with particles of the same size interval.
Figure 3. Photographs of particles in different size intervals after 48 h of attrition.
Overall, these previous studies indicate that (1) the number of effective collisions is a very important factor for particle attrition; (2) particles are entrained into the jet from a limited area; and (3) the entrainment rate remains nearly constant over an extended time interval. Particles Entrained into Jets. Xiao et al.22 identified three categories of materials in limestone air-jet attrition tests entrained fines, material on distributor, and particles adhering to column wall. The latter could mostly be dislodged by tapping. In this paper, the material on the distributor is subdivided into two parts, one entrained into the jets and the other remaining stagnant, i.e. not mobilized by the jets. Cocco et al.26 noted that there is always a “stagnant region” in an attrition apparatus. For the air-jet apparatus, this region is probably between and around the jet orifices, where particles are rarely involved in attrition.22 These unbroken particles were always found among the material collected on the distributor. Most unattrited particles were larger than the maximum size that could be displaced by the jets, and could be separated by sieving. However, particles in the stagnant region were occasionally entrained into the jets after being activated by a sudden disturbance. As a result, the mass of particles in the stagnant region decreased very slowly with passing time.22 To calculate the mass of particles entrained into the jets, particles in the stagnant regions should be excluded from the material on distributor. It is not easy to determine the mass of particles in stagnant regions, because these particles are intermixed with material on distributor, whose amount changes slowly with time. For attrition beginning with 710−850 μm particles, photographs of particles still in this sieve size confidence interval after 48 and 96 h of operation are shown
in Figure 2. These indicate that only particles which did not decrease in size (unattrited) remained in the stagnant regions after 96 h, for these particles were rough and in the same size interval as the initial particles, whereas the attrited particles were smooth and smaller.22 Figure 3 displays photographs indicating also that only unattrited particles were left in the stagnant regions after 48 h of operation. In order to simplify analysis of the attrition process in the airjet attrition apparatus, it is postulated that the mass of entrained particles equals the mass of material on the distributor minus the mass of unattrited particles. Model to Describe Particle Size Distribution. In this study, material on the distributor was collected and sieved using standard Tyler sieves, providing information on the evolution of the particle size distributions. For the ith size interval of particles ranging from dp,i to dp,i+1, the average volume mean diameter, d, is defined as d=
3
(d p, i 3 + d p, i + 13)/2
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As suggested by Epstein,14 all particles size distributions in this paper are assumed to be log-normal, given by, ⎛
F (d ) =
⎞2
−⎜ln d ⎟ A e ⎝ dc ⎠ 2π σd
/2σ 2
(6)
where F(d) is the relative mass frequency distribution function (μm−1); A is the relative mass; σ is the standard deviation; and dc is the median diameter (μm). Let us assume that the saturation carrying capacity of the air jets was stable and that the masses of particles involved in jet 15847
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attrition per unit time remained constant24,25 and nearly independent of particle size. For particles entrained into jets, the entrainment rate is then assumed to be constant and nearly independent of particle size, although the mass and average size of material remaining in the column decreased as the test proceeded. For a constant entrainment rate, the size distribution of particles being entrained could be expressed by a normalized log-normal function, based on the size distribution of material on distributor, regardless of the unattrited particles, given by ⎛
f (d ) =
⎞
−⎜ln d ⎟ 1 e ⎝ dc ⎠ 2π σd
random variable within bounds. To a certain extent, more disorder of the size means more breakage-inducing collisions and a higher rate of attrition. Entropy of information can be used to quantify the disorder of the size of particles being entrained into the jet. The entropy of information on a lognormal size distribution function is given by H=
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2
∫0
∞
⎛ 1 ⎞ 1 1 f (d) ln⎜ ⎟ = + ln(2πσ 2) + ln(dc) 2 2 ⎝ f (d ) ⎠ (8)
EXPERIMENTAL RESULTS AND ANALYSIS Size Distribution. After 96 h of attrition beginning with a relatively narrow and coarse initial size range shown by the 0 h line in Figure 5, the mass density functions of material on
/2σ 2
(7)
where f(d) is the normalized mass density function of particles in inverse micrometers. Attrition Mode. The attrition rate remained approximately constant over an extensive time interval, suggesting that the number of breakage-inducing impacts does not decrease significantly as the mean particle size is reduced. Similar-size particles entrained into the jet from nearby points should travel along similar trajectories with similar velocities, so that breakage-inducing collisions are rare. We assume that collisions between similarly sized particles can be ignored, and that attrition occurred predominantly in the jets, rather than in their entry and exit zones, given the low velocities in the entry and exit zones of the jets. When the particles had been entrained into jets, the accelerating process of a particle of a certain size differed from that of particles of other sizes. Thus, they would have velocity differences, and would likely collide, resulting in attrition. Hence, the particle size distribution plays an important role in producing velocity differences which determine the attrition rate. The PSD is therefore a function of the attrition rate, which is in turn a function of the PSD, with particles of differing sizes colliding, resulting in breakage. Based on this mechanism, a schematic of particle collisions in a jet is displayed in Figure 4. From the theories of Boltzmann and Shannon,27 entropy is a measure of the disorder associated with a random variable. For particles entrained into the jet, the size of the particles is a
Figure 5. Size distribution of limestone particles remaining after 0−96 h of attrition, beginning with particles of size interval 500−600 μm.
distributor evolved as displayed by the other lines. Most particles initially larger than 500 μm remained in the stagnant region and are excluded from the 16, 24, and 48 h data. For material on the distributor after 96 h of attrition, the small number of large particles probably corresponded to particles in the stagnant region, whose proportion decreased after longterm operation, whereas the peak of mean size ∼100 μm represents particles entrained into the jets. The normalized lognormal distributions of particles entrained into the jets are displayed in Figure 6.
Figure 4. Schematic of particle collisions in a jet (Adapted from the work of Xiao et al.23 Copyright 2012 American Chemical Society).
Figure 6. Normalized size distribution of particles entrained into jets, beginning with particles of size interval 500−600 μm. 15848
dx.doi.org/10.1021/ie501745h | Ind. Eng. Chem. Res. 2014, 53, 15845−15851
Industrial & Engineering Chemistry Research
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Using the same method of data treatment, normalized lognormal fittings of size distributions of the particles entrained into the jets, beginning with particles of size confidence intervals of 710−850, 355−425, 250−300, and 125−180 μm are plotted in Figures 7−10, and the corresponding values of dc
Figure 10. Normalized size distribution of limestone particles remaining after 0−24 h of attrition, beginning with particles of size interval 125−180 μm.
ation of small particles when the attrition time exceeded 48 h and the mass of 0−106 μm particles was small. The areas under the normalized particle size distribution (PSD) curves of the raw materials are 1, while those of other curves are not equal to 1. There are two reasons. One is because there were always stagnant regions during the attrition process, as discussed above, and the particles in these zones are excluded from the PSD curves. The second reason is because the attrition fines were elutriated and, hence, were not included in the PSD curves. Figure 11 shows a sample of agglomeration of small particles, where some large particles are surrounded by small ones. The outer layers are often full of small particles (mainly
