Article pubs.acs.org/EF
Prediction of Coal Primary Fragmentation and Char Particle Size Distribution in Fluidized Bed Milijana J. Paprika,*,† Mirko S. Komatina,‡ Dragoljub V. Dakić,§ and Stevan Đ. Nemoda† †
Vinča Institute of Nuclear Sciences, University of Belgrade, P.O. Box 522, 11001 Belgrade, Serbia Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11000 Belgrade, Serbia § Innovation Center of Mechanical Faculty, University of Belgrade, Kraljice Marije 16, 11000 Belgrade, Serbia ‡
ABSTRACT: The combination of temperature gradient and volatile release has been identified as the main cause for primary fragmentation (breakage of fuel particles during devolatilization). A mathematical model of the primary fragmentation in a fluidized bed has been developed, incorporating both causes. It takes into account the type of the coal, size of the coal particles, and the fluidized bed temperature. The model simulates fragmentation of a batch of coal particles. For each particle in the batch, the model follows propagation and merging of cracks, starting from randomly distributed pre-existing pores, leading to possible breakage of the particle. The model calculates volume of the fragmented particles and volume diameters, classifying them into size classes. For each size class, the number of particles is counted, and the mass fraction is calculated. The results are the distribution of mass and number of char particles after the devolatilization and the primary fragmentation parameters.
■
et al.2) indicated that the quantity and pressure of volatiles contribute to the particle breakage. On the other hand, experiments designed to show the influence of the FB temperature and the size of coal particles2,13,19,21,22 testify to the role of thermal stress. However, these two phenomena have not been coupled in a single model, until the work of Senneca et al.23 The processes occurring during the devolatilization of a coal particle are complex, interlinked, and overlapping. A detailed model of the primary fragmentation should describe processes of heat and mass transfer, as well as poroelasticity of the coal particle, using a series of partial differential equations, requiring a large set of thermal, chemical, and mechanical characteristics of coal. Such detailed models and experimental findings of other authors were analyzed here in order to find patterns of fragmentation and to create a practical tool for the investigation of coal behavior in FB. The developed model simulates the breakage of a particle, not by a series of equations describing processes and conditions that are causing it, but by patterns of initialization, propagation, and merging of cracks. The model uses a smaller corpus of input parameters and simpler mathematical tools, still respecting the phenomenology and stochastic nature of the process.
INTRODUCTION Comprehension of the primary fragmentation (breakage during devolatilization) of coal in a fluidized bed (FB) over a wide range of coal sizes and FB temperatures is useful, sometimes even essential, in understanding and optimizing the practical coal combustion1,2 and creating credible combustion models.3,4 The process is importantly concomitant with devolatilization and, therefore, influences behavior of the fluidized bed inventory, char and ash formation, and emission of pollutants. Primary fragmentation affects the key parameter for the proper operation of a fluidized bed combustorthe particle size distribution (PSD) of the bed inventory.1,5 It influences hydrodynamics of the FB (both bubbling and circulating), the fuel mixing behavior, and the residence time of fuel particles. Consequently, the fragmentation influences in-furnace profiles of temperature, gas concentration, and char distribution.6,7 Also, the fragmentation increases the exposed surface of the fuel particle and, therefore, the rate of abrasion of fines of elutriable size.7,8 Neglecting this phenomenon might lead to an error as high as 63% in modeling of a circulating fluidized bed combustor, namely, in carbon loading and distribution of carbon particles in the riser.9 This is emphasized for cocombustion systems burning coal and biomass.10 Together with the attrition, the primary fragmentation influences the ash particle size distribution,11 which is significant in determination of the design parameters of a CFB boiler,12 especially for the boilers where coal ash is used as the fluidizing bed material instead of sand.13 Two phenomena have been reported as the causes for the primary fragmentation of coal: rapid change of the temperature and the formation of volatiles within the particle. Some authors have given priority to the mechanical stress generated by the pressure of volatiles,2,14−17 whereas others prioritized the thermal stress.13,18−20 Reduced primary fragmentation of pretreated coal (mildly prepyrolyzed anthracite in work of Chirone et al.17 and devolatilized Chinese coals done by Zhang © 2013 American Chemical Society
■
MODEL OF PRIMARY FRAGMENTATION
Primary fragmentation experiments reported in the literature10,19,24,25 resulted in two patterns of fragmentation: smaller fragments (relative to the original coal particle) originate from the outer shell of the particles, whereas the larger fragments are formed due to the fracture of the inner core. The smaller fragments are formed shortly after the coal particle has been introduced to the hot environment, whereas the larger fragments are formed later during the devolatilization. Received: May 10, 2013 Revised: July 24, 2013 Published: July 24, 2013 5488
dx.doi.org/10.1021/ef400875q | Energy Fuels 2013, 27, 5488−5494
Energy & Fuels
Article
Figure 1. Model of the particle primary fragmentation. (a) The inner and outer zone; distribution of the initial points, (b) cracks, (c−f) fragmentation of the outer zone, (g) fragmentation of the inner zone, (h) final fragment count. Spatial distribution of radial and tangential stresses within a fuel particle during the devolatilization19,23,26 can explain the behavior. Radial stresses, generated due to the pressure of released volatiles and thermal expansion, are compressive and continuously decreasing toward the particle surface. Tangential stresses, predominantly thermal in nature, change from compressive in the region of the particle center to tensile in the outer shell, close to the particle surface. Hence, in the outer shell of the particle close to the particle surface, the tangential stresses prevail, whereas in the central region of the particle the radial stresses prevail. Taking into account the presented experimental observations and stress analysis, a scenario of the process has been established: A newly formed crack is propagating through the particle, merging and connecting with others. In some cases, that leads to fragmentation. In the outer region of the particle where the tangential stresses prevail, the particle breaks tangentially, exfoliates. The border of that region is the radius of the transition between tensile and compressive tangential stresses. The thickness of the region depends on the FB temperature, coal thermal diffusivity, and residence time.19 In the central region of the particle, during the heat-up, volatiles start to release, moving through the particle in the direction of lower pressureeither toward the surface or toward the already emptied cracks, depending on what is closer. The latter mechanism produces coarser fragments. A fracture is initiated at the position of irregularities in the coal structure when the stresses exceed the failure strength of the coal. The strength of a coal particle (compressive strength, gridability, fracture toughness) shows a trend relative to the rank of the coal, and to the size of the specimen. It is also highly affected by the distribution, type, and condition of irregularities in the coal structure. The pores of the coal are those irregularities, pre-existing crackspossible initial points of the failure. Therefore, a model of the network of possible initial points of cracks in a coal particle should include pore characterization (total pore volume and average diameter of pores) and coal characterization (type of coal, related to the compressive strength of the coal: content of fixed carbon and volatiles). On the basis of the presented analysis, a mathematical model has been developed, aimed to predict the fragmentation behavior of a batch of coal particles devolatilizing in a fluidized bed of a constant temperature. For each particle in the batch, the model follows initialization, growth, and merging of the cracks, which leads to possible breakage. After the simulation of the fragmentation, the model calculates the volume and mass of the fragments and assigns a size class to the fragments.
The model input data are the coal type characteristics (volatile and carbon content, porosity, mean pore diameter), the FB characteristics (FB temperature), and the inlet coal particle size distribution. The model output data are the resulting char particle size distribution (number and mass fractions of char particles) and the primary fragmentation parameters, as introduced by Zhang et al.2 The main primary fragmentation parameters are as follows: • Primary fragmentation ratio (intensity, particle multiplication factor): Nf = Nout/Nin. Here, Nout is the number of the char particles, and Nin is the number of the original coal particles. • Changing ratio of coal particle size (variation factor of fed particles): Fd = ∑n1XiDiDc. Here, Xi is the mass fraction of particles with size i, n is the total number of size classes, Di is the average diameter of coal particles with size i after the fragmentation, and Dc is the diameter of the original coal particles. • Primary fragmentation index: Sf = Nf/Fd. That is the most comprehensive parameter of the process, taking into account the changes in number and size of particles. General assumptions of the model are as follows: 1. The coal particle is a porous sphere, divided into outer and inner zones, with homogeneous thermal and chemical characteristics. There is no occurrence of swelling or attrition. The model is dealing with a particle cross-section (Figure 1a). 2. The thickness of the outer zone, which is susceptible to exfoliation (the ratio of inner diameter D1 and particle diameter Dc, Figure 1a), depends on the FB temperature and the particle size. The values of the ratio D1/Dc for Tb = 900 °C is 0.7,18 and for Tb = 500 °C is 0.97.19 For the rest of the FB temperatures from range Tb = 500− 900 °C, a linear connection between those two points is proposed here: D1/Dc = − 6.75 × 10−4 Tb + 1.3075
(1)
3. The particle breakage is preceded by initialization, propagation, and merging of cracks. A crack, starting from an initial point, is propagating in a straight line, in the direction of the particle surface. The initial points are randomly distributed over the particle crosssection (Figure 1a). 4. In the outer zone, a crack starts at the associated initial point and propagates tangentially both ways to the particle surface (Figure 1b). In this zone, one crack causes separation of one fragment (Figure 1c,d,e). 5. In the inner zone, a crack is propagating from its associated initial point, depending on what is closer: either toward the particle surface, 5489
dx.doi.org/10.1021/ef400875q | Energy Fuels 2013, 27, 5488−5494
Energy & Fuels
Article
along the particle radius, or toward another initial point with greater radius (Figure 1b). The cracks are connecting, which leads in some cases to fragmentation. Thus, mergers of the cracks cause the possible breakage (Figure 1f,g,h) 6. The particle breaks along the planes perpendicular to the particle cross-section, following the cracks (Figure 2).
Figure 3. Types of cracks of the inner zone. of the spherical cap whose base diameter is the chord), Figure 1b,c. The model calculates the equivalent diameter of the sphere with the same volume as that of the fragment (volume diameter) and assigns a size class to it. 5. The model finds the next initial point with the greatest radius in the inner zone j(Ri,φi) and calculates the angle between the points i and j − φij, volume of the separated fragment, and volume diameter, assigning a size class to it. Point 5 of the calculation procedure is repeated until φij ≤ 2π. 6. If φij > 2π, the model corrects the particle diameter:
Figure 2. A view to the fragmented inner zone of the particle. 7. The total number of the initial points in a coal particle depends on the total pore area, amount of volatiles, and fixed carbon in the coal. Total pore area is calculated on the basis of the definition of porosity:
A tot = 2εDc3π /3Dpore
(2)
(Dc)new = 2(Dc3/8 − 3 ∑ Vk /4π )1/3
where ε is the porosity of the coal and Dpore is the average pore diameter. 8. The propagating potential of an initial point is represented by its equivalent pore area. The equivalent pore area of an initial point i, with the radial position Di, is estimated to be
Ai = (Di2π /4)(Cfix /Vol)·100
where ∑Vk is sum of volumes of the separated fragments from the outer zone. 7. Points 4−6 of the Calculation procedure are repeated until there are no more initial points in the outer zone, Figure 1d,e,f). 8. In the inner zone (Ri < D1/2), the model finds the initial point closest to the particle center m(Rm,φm) and calculates its distance to the particle center Dm. The model finds the pair of the initial points i and j, with the minimal sum of distances to the initial point m − dij. If dm ≤ dij, the initial point m is connected with the particle surface; if dm > dij, the initial point m is connected with the initial points i and j. The initial point m is the center of a fragment. The first crack is the line segment mi on one side and mj on the other. 9. For the initial point i(Ri,φi), the model calculates the distance to the particle surface di and finds the minimal distance to all the unconnected initial points with greater radii min(di1). If di ≤ min(di1), the initial point i is connected with the particle surface. 10. If d > min(di1), the initial point i is connected with the initial point i1. The next crack is ii1, and the model records a sequence of numbers i − i1. Point 10 of the calculation procedure is repeated until the initial point i is connected with the surface. 11. Points 9 and 10 are repeated for the initial point j(Rj,φj). 12. The model checks whether the cracks of the inner zone are bordering a fragment and whether the fragment is going to separate from the particle. 13. The separated fragment from the inner zone is a complex geometric body; its volume is calculated as a sum of the spherical segments bordered by cracks, Figure 2. The model calculates the equivalent diameter of the sphere with same volume as the fragment (volume diameter) and assigns the size class to it. 14. Points 8−13 of the calculation procedure are repeated for all of the unconnected initial points in the inner zone. 15. Points 2−14 of the calculation procedure are repeated for each particle in the batch. 16. For each size class, the number of fragments is counted and the mass fraction calculated. The model calculates the primary
(3)
if the initial point is in the inner zone and
Ai = ((Dc2π − Di2π )/4)(Cfix /Vol)·100
(5)
(4)
if it is in the outer zone of the particle cross-section. Cfix is the amount of fixed carbon in the coal, and Vol is the amount of volatiles in the coal, according to data from proximate analysis of the coal. 9. There are three types of crack mergers in the inner zone, Figure 3cracks are surrounding a fragment, but they make a loop and the fragment cannot separate from the particle (i), cracks are not bordering a fragment (ii), and cracks are bordering a fragment which can separate (iii). The calculation procedure is as follows: 1. The model starts with loading PSD (or dimensions and total number) of coal particles in the investigated batch, size classes of the fragments, data on fixed carbon and volatile content, and the fluidized bed temperature. 2. For a coal particle from the batch, the thickness of the outer zone D1 and the total pore area Atot (eq 1) is calculated. 3. The model randomly distributes one by one initial point on the cross-section of the coal particle (Figure 1a). An initial point i is defined by its radial position i(Ri,φi). When the initial point i is generated, its equivalent pore area Ai is calculated (eq 2 or 3). A new initial point is generated as long as the sum of the equivalent pore areas is smaller than Atot: ∑ni=0Ai ≤ Atot n − total number of initial points. 4. In the outer zone (D1/2 ≤ R1 < Dc/2), the model finds the initial point with the greatest radius i(Ri,φi) and calculates the length of the corresponding chord and volume of the separated fragment (volume 5490
dx.doi.org/10.1021/ef400875q | Energy Fuels 2013, 27, 5488−5494
Energy & Fuels
Article
fragmentation ratio, the changing ratio of coal size, and the primary fragmentation index.
■
RESULTS AND DISCUSSION The results of the model were compared with the experimental findings.2,13,22 In the comparison, characteristics of the experiments were consideredhow the particles had been handled during the collecting, sieving, and image analysis or weighing; whether the particles smaller than bed material had been taken into account; etc. Also, the processes of the devolatilization of an original coal particle and combustion of the fragments separated from the particle in early stages of fragmentation sometimes are overlapping (especially for larger coal particles). That was the reason for comparison between the combustion times of the fragments from the outer particle zone and the devolatilization time of the original coal particle. The model of the temperature of the coal particle burning in FB27 was used for calculation of the devolatilization and combustion times. In the case that the check showed that it is possible for the fragment to burn out during the devolatilization of the coal particle, those fragments were discarded from the calculation of the fragmentation parameters. Also, the fragments smaller than the bed material particles were discarded from the results. The experimental work of Zhang et al.,2 gave information on the primary fragmentation of the variety of coals, explaining influences of factors such as the FB temperature, size of coal particles, coal rank, and fluidizing medium. Figure 4 shows the
Figure 5. Primary fragmentation index, comparison with experimental results of Zhang et al.,2 variation of FB temperature.
Chinese bituminous coal, Jixi, was chosen,22 with 6−8 mm original size particles in an 850 °C FB. Results of the simulation are presented in Figures 6 and 7. Figure 6 presents “before” and
Figure 6. Number fraction of char particles, before/after the simulation.
Figure 4. Primary fragmentation index, comparison with experimental results of Zhang et al.,2 variation of size of coal.
“after” pictures of the number fraction distribution of coal particles for the size classes. As in the experiments,22 the simulation resulted in a large number of smaller fragments, whereas shares of coarser particles in total number were smaller. Figure 7 shows the normalized particle weight distribution (distribution of mass fraction of a size class divided by the class width, usual for comparisons with PSD). The simulation resulted in a bimodal distribution of fragmentsseparate distributions for smaller and larger char sizes. Although its contribution is small, the section of fines (particles smaller than 2 mm) in primary fragmentation products cannot be omitted, because it represents, according to some authors,11,28 a contribution to elutriable particles. Plots of the cumulative PSDs of the fine and coarse fragment sections in the Weibull, log-normal, and logistic coordinate
experimental and the simulation results of primary fragmentation indexes for two types of coals (Xinglong and Zhangcun) with seven coal sizes (5−7, 3.2−5, 2.5−3.2, 1.25−2.5, and 0.63−1.25 mm). Figure 5 presents the experimental and simulation results of primary fragmentation indexes for two other types of coals (Wanggan and Datong) at five temperatures (500−900 °C) of fluidized bed. A reasonably good agreement was achieved (Pearson correlation coefficient for the Zhangcun coal is 0.90, Xinglong coal 0.80, Wanggan 0.99, Datong 0.97), although the model gave slightly higher values, despite the modifications. The model gives the particle size distribution (PSD) of char particles after devolatilization of a batch of coal particles with defined size or particle size distribution. For this investigation, a 5491
dx.doi.org/10.1021/ef400875q | Energy Fuels 2013, 27, 5488−5494
Energy & Fuels
Article
separating the fine and larger char fraction (Df), and shape (α) and scale (β) parameters of the Weibull distributions, are shown in Table 1. Primary fragmentation of the Jixi coal was simulated for inlet coal particle sizes 1−3 mm, 3−6 mm, and 6−8 mm, and the FB temperature of 700 °C. As seen in Figure 8 and Table 1, border
Figure 7. Normalized particle weight of char particles, results of the simulation and Weibull distribution.
systems showed that they follow Weibull distribution (also known as Rosin−Rammler distribution). Shape α and scale β parameters of the Weibull distribution for both sections were estimated by linear regression. Df is the diameter separating the fine fragment section and the large fragment section. The cumulative distribution function is as follows:
Figure 8. Results of the simulationPSD of the bitumious coal, Tb = 700 °C, original coal particle size varied.
diameters Df (0.75 mm, 1.56 mm, 2 mm) are increasing for larger inlet sizes. In the same respect, the shape (α) and scale (β) parameters also increase, for both fine and large fragment sections of char. As seen in Figure 8, looking at the mass fraction of fragments that originated from the 1−3 mm inlet coal, there is a large number of the original particles which did not break. However, for the larger inlet coal particle sizes, the distribution was more dispersemost original coal particles had fragmented. Same fragmentation behavior was noted in the experimental investigation.22 The same bituminous coal, Jixi, inlet particle size 6−8 mm, was tested on the increase of FB temperature. The resulting size of the border diameter was increasing, as well as the shape and scale parameters for the fine fragment section. On the other hand, for the large fragment section, the shape and scale parameters were decreasing, as seen in Figure 9. As in the experiments,22 for the higher FB temperatures, the coal is fragmenting more intensely and the fine fragment section of char is more abundant. In experiments designed to examine the influence of coal rank,2,13,18,20 the coals showed different fragmentation behavior: bituminous and lignite coals broke on an inner radial
m(
