ARTICLE pubs.acs.org/IECR
A Population Balance Model on Sorbent in CFB Combustors: The Influence of Particle Attrition Fabio Montagnaro,† Piero Salatino,*,‡ Fabrizio Scala,§ and Massimo Urciuolo§ †
Dipartimento di Chimica, Universita degli Studi di Napoli Federico II, Complesso Universitario del Monte di Sant'Angelo, 80126 Naples, Italy ‡ Dipartimento di Ingegneria Chimica, Universita degli Studi di Napoli Federico II, Piazzale Vincenzo Tecchio 80, 80125 Naples, Italy § Istituto di Ricerche sulla Combustione, Consiglio Nazionale delle Ricerche, Piazzale Vincenzo Tecchio 80, 80125 Naples, Italy ABSTRACT: A population balance model on sorbent particles in an atmospheric circulating fluidized bed combustor fueled with sulfur-bearing solid fuel is developed. The model aims at the prediction of the following quantities establishing at the steady state in the combustor: sorbent inventory and particle size distribution, partitioning of the sorbent between fly and bottom ash, desulfurization efficiency, and the mass flow rate of the sorbent circulating around the loop of the combustor. The core of the model is represented by the population balance equations on sorbent particles, which embody terms expressing the rate of sorbent attrition/fragmentation. The effect of the progress of sulfation on attrition is taken into account by the selection of appropriate constitutive equations. Model results are presented and discussed with the aim of clarifying the influence of particle attrition. In particular, the effect of attrition on bed sorbent partitioning between lime and sulfated lime and on SO2 capture efficiency is highlighted. The model enables one to assess the balance between opposed effects of attrition on desulfurization: on one hand, attrited fines are characterized by a better reactivity with respect to SO2, when compared with the mother particles; on the other hand, attrition is responsible for larger amounts of unsulfated material reporting to the fly ash. A sensitivity analysis is also carried out with reference to relevant operational parameters of the combustor in order to correlate changes in ash partitioning and desulfurization efficiency with the extent of sorbent attrition and solids circulation.
1. INTRODUCTION Particle size distribution (PSD) of the bed material is an important factor in fluidized bed (FB) combustors, as it affects fluid dynamics, heat transfer, and pollutant formation. When the bed material contains a SO2 sorbent, like limestone or dolomite, its PSD also affects the desulfurization efficiency in the boiler. The existence of an optimum sorbent PSD has been suggested.1 If the sorbent particles are too fine, they rapidly escape as fly ash, and calcium conversion decreases because of the insufficient residence time. On the contrary, if the sorbent particles are too coarse, conversion decreases because of limited penetration of sulfur into the particle. The PSD of the sorbent establishing at a steady state in the boiler cannot be a priori determined simply on the basis of the PSD of the feed sorbent, but it is the result of the interplay of a number of processes. In particular, attrition and fragmentation phenomena can substantially affect the sorbent PSD and, in turn, the performance of the desulfurization process.24 Attrition and fragmentation of limestone during the FB combustion of sulfur-bearing fuels have been thoroughly characterized over the past decade.414 Key phenomenological features and mechanistic pathways of sorbent attrition in FB combustors have been disclosed with the aid of a comprehensive test protocol consisting of different and mutually complementary test procedures.4,6,1113 In particular, sorbent attrition phenomena have been classified into (Table 1) the following: (i) primary fragmentation, which occurs immediately after the injection of sorbent particles into the hot bed as a consequence of thermal stresses and internal overpressures due to CO2 emission; r 2011 American Chemical Society
(ii) attrition by abrasion, related to the occurrence of surface wear as the FB emulsion phase is sheared by the passage of bubbles, generating mostly fine/quickly elutriable fragments; and (iii) secondary fragmentation, a result of high-velocity impacts of sorbent particles against targets (bed material, reactor walls/internals), occurring mostly in the jetting region of the FB and in the exit region of the riser and the cyclone of circulating FB (CFB) reactors. The critical influence of the progress of calcination and sulfation on the attrition of limestone in FB combustors has long been recognized.2,4,11 These reactions bring about extensive modifications of the mechanical and morphological properties of the sorbent particles, which significantly affect the mechanisms and extent of particle breakage. For example, the progress of sulfation decreases the attrition rate with respect to that of the native porous lime due to the formation of a more compact and tougher sulfate shell at the periphery of the particle.4 The extent of impact fragmentation of the sorbent has also been found to be largely dependent on the chemical transformations suffered by the particles.11 Models aimed at predicting the size distribution of bed particles in fluidized bed combustors under the influence of particle attrition have been recently developed. Some of these models have been focused on the simulation of the PSD of bed Received: January 18, 2011 Accepted: July 11, 2011 Revised: July 11, 2011 Published: July 11, 2011 9704
dx.doi.org/10.1021/ie2001204 | Ind. Eng. Chem. Res. 2011, 50, 9704–9711
Industrial & Engineering Chemistry Research
ARTICLE
Table 1. Main Features of Attrition/Fragmentation Mechanisms mechanism
caused by...
location:
generation of...
primary fragmentation (decrepitation)
thermal/mechanical stresses
dense bed/splashing zone
coarse/fine fragments
attrition by abrasion (surface wear)
rubbing of bed solids
dense bed
fine fragments
secondary fragmentation (impact fragmentation)
collisions against targets
jetting region + riser exit/cyclone
coarse/fine fragments
Figure 2. Schematic representation of the CFB combustor loop with indication of relevant sorbent fluxes.
Figure 1. Framework for the assessment of the fate of sorbent particles in a fluidized bed.
ash particles, relevant to the case when no sorbent is present in the bed.1517 More limited effort has been devoted to modeling sorbent PSD in fluidized beds in the presence of attrition and its influence on the desulfurization efficiency.1820 The effect of chemical reactions on particle attrition was not considered in these models. Accordingly, the models were not able to discriminate between the partitioning of the different sorbent components (CaO, CaSO4) in the outlet streams. In this work, a population balance model is presented, which aims at predicting the sorbent inventory and particle size distribution, the partitioning of sorbent between fly and bottom ash, the sulfur capture efficiency, and the mass flow rate of sorbent circulating around the loop of an air-blown CFB combustor during steady operation. The distinctive feature of the model is the consideration of the influence of particle attrition on the main output variables. The sorbent is lumped into two fractions, lime and sulfated lime, and attrition parameters are estimated separately for each of them. A sensitivity analysis is also carried out to correlate changes in ash partitioning and desulfurization efficiency with the extent of attrition and the solid circulation rate.
2. MODEL A conceptual framework for analyzing the effect of sulfation and attrition on the fate of sorbent particles in the FB is represented in Figure 1. Some simplifying assumptions underlie this framework. The populations of sorbent particles (of different ages and sulfation degrees) have been arbitrarily lumped into two fractions, namely, lime (L) and sulfated lime (SL). The transfer of sorbent from lime to sulfated lime has been assumed to occur according to a global sulfation rate which is proportional to the
SO2 concentration and the lime bed inventory. Calcination and primary fragmentation occur over a much shorter time-scale than sulfation.4 Accordingly, in the framework of the model, calcination and primary fragmentation (“1” in Figure 1) have been assumed to take place instantaneously upon feeding, so that the inventory of the raw limestone (CaCO3) in the bed is negligible. Calcination gives rise to a distribution of lime particles that can be drained as bottom ash, elutriated in fly ash, or sulfated—“3”—to become sulfated lime. Analogously, sulfated lime particles can be either drained as bottom ash or elutriated in fly ash. Attrition by abrasion (and secondary fragmentation) of coarse particles —“2”—shifts the PSD (both of L and SL) toward finer sizes. From the standpoint of particle attrition, the sorbent particles have been divided into coarse and fine particles, where fine particles represent those which are not subjected to further attrition in the fluidized bed. This assumption is closely related to the concept of natural grain size21 according to which particles smaller than a critical size do not undergo attrition to a significant extent. A schematic representation of a CFB combustor loop with indication of the relevant sorbent fluxes is reported in Figure 2 (see also the Notation for symbols). Population balance equations have been referred to the sorbent present at steady state in the combustor. In principle, each particle in the population is characterized by two variables: the particle size (d) and the sulfation degree (XS). The two-dimensional population balance is simplified on the basis of the assumption that the sorbent can be lumped into two classes as far as XS is concerned: the unconverted lime (L) and the sulfated lime (SL). It is assumed that sorbent undergoes sulfation according to a prevailing coreshell pattern.22 Therefore, SL consists of particles characterized by a CaSO4-rich shell and a nearly unconverted CaO core. With this simplification, the population balance in the dXS domain simplifies, yielding two onedimensional population balance equations in the d domain. Upon discretization of the domain and referring to the ith particle size bin, equations concerning the L and SL components 9705
dx.doi.org/10.1021/ie2001204 |Ind. Eng. Chem. Res. 2011, 50, 9704–9711
Industrial & Engineering Chemistry Research
ARTICLE
read, respectively mP _ 0 ðdi ÞΔd þ
¼
R iþ1, L W iþ1, L þ Δd
n
∑ ka, L U j¼i þ 1
W j, L Pa, L ðdi ÞΔd dj
R i, L W i, L þ ai, L þ ei, L þ bi, L þ kCSO2 W i, L Δd
ð1Þ
kCSO2 W i, L ½ð1 X S, i ÞMW L þ X S, i MW SL MW L n
∑ ka, SLU j¼i þ 1
W j, SL Pa, SL ðdi ÞΔd dj
þ
R iþ1, SL W iþ1, SL þ Δd
¼
R i, SL W i, SL þ ai, SL þ ei, SL þ bi, SL Δd
ð2Þ
The LHS of eq 1 consists of three inlet terms, namely, (1) A term related to the sorbent feeding. (2) A term accounting for the migration of mother particles, due to continuous particle shrinkage by attrition, from the (i+1)th to the ith size bin. Shrinkage by attrition is expressed as23,24 ka U R ¼ 3
ka, L UW i, L di
ð4Þ
(3) Sorbent loss by elutriation at the cyclone: ei, L ¼ ½1 ηðdi Þg i, L
ð5Þ
where the lime flow rate entering the cyclone gi,L is computed as a function of Wi,L according to Wirth:25 g i, L ¼
βi Fð1 εmf ÞU 0 W i, L W
The cyclone collection efficiency is expressed as
ð3Þ
Particle swelling or shrinkage caused by chemical reactions has been neglected in the model. (3) A term under summation which takes into account new particles generated by attrition of the coarse mother particles that fall into the ith size bin. The RHS of eq 1 consists of five outlet terms, namely (1) Continuous particle shrinkage (in this case, accounting for the migration of particles from the ith to the (i1)th size bin). (2) Particles generated by attrition of particles of size di that leave the size bin to enter into finer size bins, where4,21 ai, L ¼
Figure 3. Outline of sulfation regimes. Stage I: buildup of the sulfated layer of thickness δ up to a maximum local sulfation degree in the outer shell. Stage II: attrition-enhanced sulfation regime.
ð6Þ
The nondimensional parameter βi is expressed as
8 2 2 > < β ¼ 1 U t, i C Fri with C ¼ 0:00533 and for U t, i < U 0 i U0 4ð1 εmf Þ > : β ¼ 0 for U t, i g U 0 i
ð7Þ
ηðdi Þ ¼
ð9Þ
for di < 120 μm, otherwise η = 1 (see Redemann et al.16). (4) Bed drain expressed, according to the hypothesis of perfect mixing of bed material in the bottom bed, as bi, L W i, L ¼ b W
ð10Þ
(5) Transfer from the L to the SL phase, driven by sulfation. It has been discussed8,26,27 that sorbent sulfation in FB combustors takes place along two subsequent stages (Figure 3): stage I, associated with the initial buildup of a sulfate-rich particle shell, and stage II, associated with a slower attritionenhanced sulfation promoted by continuous removal of the sulfated material from the particle surface. Assuming that the contribution to SO2 capture given by stage II is negligible, the global sulfation kinetic constant used in the model has been estimated by averaging over the time the sulfation rate in stage I measured during differential FB experiments.4 Similarly, eq 2 for SL particles is written considering that the first term is now related to the transfer from the L to the SL phase (by sulfation), and that SL particles present a sulfation degree dependent on particle size and well below unity. In particular, it is assumed X S, i ¼ X shell S
d3i ðdi 2δÞ3 d3i
ð11Þ
if di > 2δ (where δ is the thickness of the sulfated layer); otherwise XS,i = Xshell S . The overall SO2 capture efficiency can be calculated as n
as a function of the particle terminal velocity Ut,i and Froude number Fri: U0 Fr i ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi F Ff di g c Ff
1 c dcut 1 þ di
kCSO2 cap
ð8Þ
ηdes
9706
F 2 ¼ SO ¼ inlet FSO 2
∑ ðW i, LX S, i Þ i¼1
MW L m_ MW L r Ca=S
ð12Þ
dx.doi.org/10.1021/ie2001204 |Ind. Eng. Chem. Res. 2011, 50, 9704–9711
Industrial & Engineering Chemistry Research
ARTICLE
Table 2. Main Input Parameters of the Model 2 1
2000
m_ [kg m
W [kg m2]
250
δ [μm]a
U [m s1]
2.5
Xshell [] S
0.55
ka,L []b
5 109
k [ppm1 s1]c
106
ka,SL []b rCa/S []
109 2.5
dcut [μm] c []
10 4
Cinlet SO2
[ppm]
s ]
0.0077 50
a
Estimated from refs 28 and 29. b Estimated from experimental tests4,6,11,31 as detailed in section 3.2. c Estimated from experimental tests4 as detailed in section 3.1.
It is noteworthy that the overall sorbent sulfation rate in eq 12 is proportional to an “effective” SO2 concentration CSO2 experienced by sorbent particles during their lifetime in the combustor. Considering that most of the sorbent resides in the bottom bed and in the splashing region of the riser, where extensive backmixing is promoted by vigorous fluidization, CSO2 has been computed under the assumption of perfect mixing as CSO2 ¼ Cinlet SO2 ð1 ηdes Þ
ð13Þ
where Cinlet SO2 is the concentration of SO2 that would be established in the primary region of the riser (i.e., below the secondary air feeding level) without desulfurization. Partitioning of the sorbent between fly and bottom ash is expressed by a partitioning factor f, defined as e ð14Þ f ¼ e þ b
3. RESULTS AND DISCUSSION 3.1. Evaluation of Model Parameters. The model was solved in the MATLAB environment. Input parameters have been assigned according to values corresponding to realistic design/ operating parameters of industrial-scale CFB combustors and are reported in Table 2. The SO2 concentration related to the combustion of the sulfur-bearing solid fuel in the absence of desulfurization was set at Cinlet SO2 = 2000 ppm. The total bed inventory in the riser per unit cross-sectional area was assumed to be equal to 800 kg m2, a typical figure based on admissible pressure drops across the riser in practical operation of CFB combustors. On the basis of realistic sorbent feeding rates and fuel ash content, it was further assumed that the total bed inventory consists of W = 250 kg m2 of sorbent (L + SL) and 550 kg m2 of fuel ash. By taking into account the values of the fluidization velocity (2.5 m s1) and of Cinlet SO2 in the primary region of the riser and by considering a typical calcium-to-sulfur inlet molar ratio of 2.5, the value for m_ (the lime mass feed rate) could be calculated (m_ = 0.0077 kg m2 s1) for the CFB combustor operated at 850 °C and 1 atm. The sulfated shell of SL particles was assumed to have a thickness of 50 μm (see Montagnaro et al.28 and Abanades et al.29), characterized by a maximum sulfation degree of 55%. This theoretical value was estimated by taking into account the molar volumes of CaO and CaSO4 and further assuming that sulfation occurs without significant particle swelling. By working out the XS-versus-time experimental results obtained by Scala et al.4 under differential reaction conditions, and by considering the average rates of reaction in stage I (see Figure 3), it was assumed that the sulfation rate could be expressed as a linear
function of both SO2 concentration and lime inventory, the kinetic constant being k = 106 ppm1 s1. The PSD of the lime immediately after calcination/primary fragmentation, P0, was expressed as a log-normal function extending over the particle size range 02000 μm, with a mean Sauter diameter (dS) of 110 μm, about 28% by mass of particles with d < 100 μm and about 4% by mass of particles with d > 1000 μm. As can be observed in Figure 4, the peak of the distribution was at 66 μm, and the d50 value was 180 μm. The size distribution of particles generated by attrition, Pa, was expressed as an exponential function for both L and SL: 1 di Pa, L ðdi Þ ¼ Pa, SL ðdi Þ ¼ exp ð15Þ d̅ d̅ with d = 35 μm. Attrition was considered to be active only for particles coarser than 50 μm, while its occurrence was neglected (ka,L = ka,SL = 0) for finer particles. Values of F = 2000 kg m3, εmf = 0.42, and U0 = 6 m s1 were used in eq 6. 3.2. Evaluation of the Attrition Rate Constant for Coarse Sorbent Particles. Particular attention was devoted to the correct evaluation of the attrition rate constants ka,L and ka,SL, in view of their influence on model results. These constants were evaluated separately for lime and sulfated lime particles and take into account attrition by both surface wear4,6 and impact (secondary) fragmentation.11 The reason for the separate evaluation of the constants for L and SL particles lies in the experimental finding that L particles undergo much more extensive attrition than SL particles, because of the surface hardening effect brought about by the sulfation of lime.4,6 An Italian limestone whose attrition behavior has been extensively studied4,6,11 was taken as a reference sorbent. The attrition constant was assumed as the sum of two separate constants related to surface abrasion and secondary fragmentation, respectively. The first contribution was estimated on the basis of reported experimental data4 collected during batch attrition tests. Since the attrition rate of fresh sorbent decreases with time as a result of particle rounding off, the attrition rate data for lime have been averaged over a reasonable residence time before appreciable sulfation occured (30 min). In addition, it is known that surface abrasion of the sorbent is dependent on the presence and nature of other inert particles in the bed (sand, ash, etc.). In the present model, no sand was assumed to be contained in the bed, which consists of sorbent and fuel ash only. Unfortunately, no attrition data of limestone in the ash has been reported to date in the literature. However, since ash is usually softer than the sorbent, it was assumed that the largest contribution to attrition was due to collisions of sorbent particles with other sorbent particles. On the basis of the above assumptions, the surface wear attrition constants were estimated to be 3 109 and 2 1010 for L and SL components, respectively. The second contribution (secondary fragmentation) was estimated on the basis of experimental data of limestone breakage upon high-velocity impacts.11 It was assumed that the largest contribution to secondary fragmentation was given by particle collisions in the jetting region near the gas distributor. The entrainment rate and average velocity of sorbent particles into the jets, required to calculate the frequency and kinetic energy of impacts, were estimated according to Massimilla.30 The fractional mass of fragments formed upon a single impact was estimated at the relevant impact velocities from data reported 9707
dx.doi.org/10.1021/ie2001204 |Ind. Eng. Chem. Res. 2011, 50, 9704–9711
Industrial & Engineering Chemistry Research
ARTICLE
Figure 4. Model results without attrition: (a) PDF of particle sizes and (b) cumulative PSD for lime feed, bottom and fly ash, and circulating material.
Figure 5. Model results with attrition: (a) PDF of particle sizes and (b) cumulative PSD for lime feed, bottom and fly ash, and circulating material.
by Scala et al.11 for both L and SL particles. These values were then reduced by a factor of 10 on account of the experimental finding that the fractional mass of fragments decreases with the number of successive impacts experienced by the same particles.31 The total particle entrainment rate in the jets (per unit cross-section of the combustor) and the fractional mass of fragments formed upon impact were combined to extract pseudoattrition rate constants for secondary fragmentation, which were estimated to be 2 109 and 8 1010 for lime and sulfated lime, respectively. The two contributions from surface abrasion and secondary fragmentation were summed to give ka,L = 5 109 and ka,SL = 1 109. It must be noted that in the above derivation the possible contributions of attrition in the upper riser region and in the cyclone were neglected. As a final remark, the accumulated experience6,12 suggests that the attrition resistance of fully sulfated sorbents derived from different limestones appears to be very similar, depending on the mechanical properties of the sulfate shell. On the other hand, lime particles obtained from different parent limestones usually exhibit a much broader variability of attrition parameters, which usually retain memory of the mechanical and textural properties of the parent limestone. These features must be taken into account when considering the extension of the model to sorbents different from the Italian limestone taken as a reference in the present study.
3.3. Model Results. The influence of attrition on the performance of the combustor has been assessed by comparing results obtained from computations performed neglecting attrition (i.e., ka = 0 for both L and SL) with those in which attrition was more realistically taken into account. 3.3.1. No-Attrition Case. Results of computations for the noattrition case are reported in Figures 4 and 6 and Table 3. Figure 4a shows the probability density functions (PDF) of particle sizes for bottom and fly ashes and for the sorbent stream (g) leaving the riser and engaging the cyclone (Figure 2). The particle size distributions are reported as cumulatively undersized in Figure 4b. Data referring to the lime feeding (P0) are also reported for reference. A noticeable shift toward coarser particles can be observed for material reporting to bottom ash as compared with the lime feeding. In fact, for the bottom ash stream (b), the PDF peak is located at 120 μm and dS = 207 μm. Particles finer than 50 μm are hardly found, and only 5% by mass of particles has d < 100 μm (d50 = 229 μm). On the other hand, the PDF peak is located at 72 μm (dS = 50 μm; d50 = 64 μm) for the population reporting to the fly ash (e). Particles coarser than 120 μm are not present in this stream (see eqs 5 and 9), and 93% by mass of particles have d < 100 μm. The g stream consisting of the circulating material is characterized by a more uniform particle size distribution. The PDF peak is substantially equal to that of bottom ash (and, in turn, of bed material, see eq 10). Its dS (139 μm) and d50 (143 μm) are both 9708
dx.doi.org/10.1021/ie2001204 |Ind. Eng. Chem. Res. 2011, 50, 9704–9711
Industrial & Engineering Chemistry Research
ARTICLE
comprised between those of fly and bottom ash streams. The mass rate of sorbent material carried over along the riser is 56 kg m2 s1: taking into account that the mass rates of the sorbent lost by elutriation at the cyclone and drained as bottom ash are on the order of 103 and 102 kg m2 s1, respectively, this value can be assumed as a quantitative indication of the mass rate of sorbent circulating in the combustor (see ref 32). The inventory of lime (WL) is 15 kg m2, corresponding to 6% of the total sorbent inventory (fixed at 250 kg m2). Figure 6 shows that sorbent reporting to fly ash accounts for f = 23% of the total outlet streams even without attrition, due to the non-negligible presence of elutriable fines in the sorbent feeding (see Figure 4). From the same figure, it can be observed that SO2 capture efficiency corresponds to ηdes = 0.80 when attrition is neglected. 3.3.2. Attrition Case. Model results considering the effect of attrition are reported in Figures 5 and 6 and Table 3. Plots in Figure 5 display the same general features as those corresponding to the no-attrition case. However, data in Table 3 show that attrition induces a shift of the curves toward coarser particle sizes for bottom ash/bed material (due to the circumstance that attrition leaves in the bottom bed prevailingly coarser particles) and, as expected, toward finer sizes for fly ash and circulating ash. Moreover, consideration of attrition entails an increase in the f value (up to 49%, see Figure 6) with a corresponding decrease in the mass flow rate of circulating sorbent material (g = 54 kg m2 s1). The lime inventory decreases (WL = 12 kg m2, i.e., 4.8% of the total sorbent inventory) since attrition of L particles (more extensive than that of SL particles, see Table 2) determines finer L-particle sizes and, in turn, a better Ca exploitation for SO2
Figure 6. Results of sensitivity analysis. Effect of the lime attrition constant (ka,L) on the partitioning between fly and bottom ash, expressed as f = e/(e + b), and on the SO2 capture efficiency.
capture (see eq 11). It is noteworthy that this feature does not imply an improvement in ηdes, which decreases from 0.80 to 0.76 (see Figure 6). This finding can be related to competing effects of attrition: on one hand, attrition may enhance desulfurization through better Ca exploitation that characterizes fine attrited particles compared with parent particles; on the other, attrition brings about a larger fractional loss of unsulfated material at the cyclone which reports to the fly ash. Under the operating conditions selected for this study, the negative effect associated with fine sorbent loss at the cyclone overweighs the positive effect of a more extensive degree of Ca exploitation, resulting in a less favorable SO2 capture. Full validation of the model is prevented by a lack of detailed characterization of sorbent streams issuing from atmospheric CFB combustors, similar to what was reported for pressurized CFB combustors by Shimizu et al.8 An analysis of the partitioning of sorbents between fly and bottom ash based on experimental data from full-scale operation of a CFB combustor with different limestones has been reported by Rozelle et al. and related to the limestone petrography.10 Although the detailed operating conditions assumed in the present computations do not exactly match those reported in the quoted paper, it can be noted that the actual partitioning of sorbent between fly and bottom ash obtained from model computations with consideration of attrition is similar (nearly 50%) to that measured by Rozelle et al. for micritic limestones.10 3.3.3. Sensitivity Analysis. A sensitivity analysis has been carried out with reference to the attrition constant of L particles (ka,L) on account of its inherent broad variability from sorbent to sorbent, which, instead, does not characterize the values of ka,SL. An additional sensitivity test has been performed on the value of the constant C appearing in the expression of the solids carry-over parameter βi (eq 7). This analysis was justified by the broad uncertainty associated with the empirical assignment of this parameter and its likely impact on the solids circulation rate. Figure 6 and Table 3 display the main results obtained when ka,L was increased by a factor as large as 10 with respect to the basecase value, keeping all of the other operating conditions/parameters at the base-case levels. The model sensitivity was appreciable: enhanced attrition gives rise to decreased dS values for fly ash (as small as 28 μm), g values (as small as 48 kg m2 s1), and lime inventories (as small as 2% of the total sorbent inventory). On the other hand, dS increases as ka,L increases for both bottom ash and circulating material: the greater relevance of coarser particles in these streams is consistent with the presence of finer particles in fly ash, promoted by the increase in the attrition constant. A similar trend is observed if reference is made to the d50 values. Correspondingly, f increases up to 65%, and ηdes is as low as 55% when ka,L is taken to be 10 times the base-case value.
Table 3. Selected Output Parameters of the Model fly ash
bottom ash
circulating material
dS [μm]
d50 [μm]
dS [μm]
d50 [μm]
dS [μm]
d50 [μm]
g [kg m2 s1]
WL [kg m2]
f []
ηdes []
without attrition
207
229
50
64
139
143
56
15
0.23
0.80
with attrition (base case)
213
252
33
52
132
138
54
12
0.49
0.76
sensitivity on ka,L
ka,L 5 ka,L 10
225 234
272 287
30 28
44 41
134 136
142 144
50 48
6 5
0.58 0.65
0.63 0.55
sensitivity on C
C 0.25
191
236
29
42
111
120
16
14
0.44
0.79
9709
dx.doi.org/10.1021/ie2001204 |Ind. Eng. Chem. Res. 2011, 50, 9704–9711
Industrial & Engineering Chemistry Research
ARTICLE
Further analysis of data enabled quantitative correlation of f and ηdes with ka,L: f ðka, L Þ ¼ f ðka, L ¼ 0Þ þ Rka, L γ R ¼ 13:5; γ ¼ 0:21
ð16Þ
ηdes ðka, L Þ ¼ R½ηdes ðka, L ¼ 0Þ þ γ expð θk a, L Þ R ¼ 0:61; γ ¼ 0:52; θ ¼ 3:1 107
ð17Þ
Results of the sensitivity test on parameter C in eq 7 are also reported in Table 3. The value of C was decreased by a factor of 4, keeping the other model variables at the base-case level. As expected, decreasing C is directly reflected by a decrease of the g value (which turns out to be as small as 16 kg m2 s1) and indirectly by an increase in the lime inventory. The combined effect gives rise to a general shift of the bottom ash, fly ash, and circulating material particle size distributions toward finer sizes. The partitioning factor f decreases from 49% to 44%, and ηdes increases from 0.76 to 0.79 when C is decreased by a factor of 4. The positive effect of decreasing C on the desulfurization efficiency is clearly associated with the decreased sorbent loss at the cyclone, confirming the general result that desulfurization efficiency is largely controlled by sorbent partitioning between fly and bottom ash, expressed by f.
4. CONCLUSIONS A population balance model on sorbent particles in a circulating fluidized bed combustor has been developed to investigate the influence of particle attrition on sorbent inventory and particle size distribution, partitioning of the sorbent between fly and bottom ash, desulfurization efficiency, and the mass rate of the sorbent circulating around the loop of the combustor. The model takes into account attrition and fragmentation phenomena and the kinetics of SO2 capture by sorbent particles. Altogether, model computations confirm the relevance of attrition and fragmentation to the performance of circulating fluidized bed combustors, since these phenomena modify to a significant extent the sorbent particle size distributions and affect the course of in situ desulfurization. The comparison of computations carried out with consideration of attrition/fragmentation with those in which attrition was deliberately neglected indicates that attrition enhances (by a factor of nearly 2) the amount of sorbent reporting to fly ash and reduces (by 20%) the lime inventory in the bottom bed. Desulfurization is less favorable when attrition is at work: the desulfurization efficiency decreases from 80% to 76%. This effect is related to the larger amount of unsulfated material lost at the cyclone and reporting to the fly ash, which overweighs the effect related to a better calcium exploitation for SO2 capture of attrited fine lime particles. The sensitivity of the model on attrition parameters and solids circulation rates is remarkable. Correlations could be established between ash partitioning and desulfurization efficiency with the attrition constant of the unsulfated lime. It is highlighted that, for example, the partitioning factor increases by more than 30%, and the desulfurization efficiency decreases by nearly 30% if the attrition constant is increased by a factor of 10. A clear crosscorrelation of SO2 capture efficiency with sorbent partitioning between fly and bottom ash can be recognized. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ NOTATION a = attrition rate [kg m2 s1] b = mass flow rate of sorbent in bed drain per unit cross-sectional area of the combustor [kg m2 s1] C = constant appearing in eq 7 [] c = exponent appearing in eq 9 [] CSO2 = SO2 concentration [ppm] Cinlet SO2 = SO2 inlet concentration [ppm] Δd = particle diameter interval [m] d = particle diameter [m] d = mean diameter of attrited fragments [m] d50 = median value of the cumulative distribution [m] dcut = cyclone cutoff diameter [m] dS = mean Sauter diameter [m] e = mass flow rate of sorbent in fly ash per unit cross-sectional area of the combustor [kg m2 s1] f = partitioning factor [] Fr = Froude number [] Fcap SO2 = molar rate of SO2 captured by the sorbent per unit crosssectional area of the combustor [kgmol m2 s1] inlet FSO2 = molar rate of SO2 at the inlet per unit cross-sectional area of the combustor [kgmol m2 s1] g = overall net mass flux of circulating material [kg m2 s1] gc = acceleration due to gravity [m s2] k = sulfation kinetic constant [ppm1 s1] ka = attrition constant [] m_ = mass feed rate of lime per unit cross-sectional area of the combustor [kg m2 s1] MW = molecular weight [kg kgmol1] P0 = particle size distribution of lime after primary fragmentation [m1] Pa = particle size distribution of attrited fragments [m1] R = rate of particle shrinkage due to attrition [m s1] rCa/S = calcium to sulfur inlet molar ratio [] U = gas superficial velocity in the primary region of the riser [m s1] U0 = gas velocity in the riser [m s1] Ut = particle terminal velocity [m s1] W = overall mass of sorbent in the bed per unit cross-sectional area of the combustor [kg m2] XS = sulfation degree [] = sulfation degree in the sulfated shell [] Xshell S Greek symbols
β = parameter appearing in eq 6 [] δ = thickness of the sulfated shell [m] εmf = bed voidage at minimum fluidization [] η = cyclone collection efficiency [] ηdes = SO2 capture efficiency [] F = particle density [kg m3] Ff = fluid density [kg m3] Subscripts
i, j, n = refers to particles in the ith, jth, and nth size bin L = refers to lime particles SL = refers to sulfated lime particles
’ REFERENCES (1) Lyngfelt, A.; Leckner, B. Sulphur Capture in Circulating FluidizedBed Boilers: Can the Efficiency be Predicted? Chem. Eng. Sci. 1999, 54, 5573. (2) Chandran, R. R.; Duqum, J. N. Attrition Characteristics Relevant for Fluidized Bed Combustion. In Fluidization VI; Grace, J. R., Shemilt, 9710
dx.doi.org/10.1021/ie2001204 |Ind. Eng. Chem. Res. 2011, 50, 9704–9711
Industrial & Engineering Chemistry Research L. W., Bergougnou, M. A., Eds.; Engineering Foundation: New York, 1989. (3) Couturier, M. F.; Karidio, I.; Steward, F. R. Study on the Rate of Breakage of Various Canadian Limestones in a Circulating Transport Reactor. In Circulating Fluidized Bed Technology IV; Avidan, A. A., Ed.; American Institution of Chemical Engineers: New York, 1993. (4) Scala, F.; Cammarota, A.; Chirone, R.; Salatino, P. Comminution of Limestone during Batch Fluidized-Bed Calcination and Sulfation. AIChE J. 1997, 43, 363. (5) Di Benedetto, A.; Salatino, P. Modelling Attrition of Limestone during Calcination and Sulfation in a Fluidized Bed Reactor. Powder Technol. 1998, 95, 119. (6) Scala, F.; Salatino, P.; Boerefijn, R.; Ghadiri, M. Attrition of Sorbents during Fluidized Bed Calcination and Sulphation. Powder Technol. 2000, 107, 153. (7) Anthony, E. J.; Granatstein, D. L. Sulfation Phenomena in Fluidized Bed Combustion Systems. Prog. Energy Combust. Sci. 2001, 27, 215. (8) Shimizu, T.; Peglow, M.; Sakuno, S.; Misawa, N.; Suzuki, N.; Ueda, H.; Sasatsu, H.; Gotou, H. Effect of Attrition on SO2 Capture by Limestone under Pressurized Fluidized Bed Combustion ConditionsComparison between a Mathematical Model of SO2 Capture by Single Limestone Particle under Attrition Condition and SO2 Capture in a Large-Scale PFBC. Chem. Eng. Sci. 2001, 56, 6719. (9) Chen, Z.; Lim, C. J.; Grace, J. R. Study of Limestone Particle Impact Attrition. Chem. Eng. Sci. 2007, 62, 867. (10) Rozelle, P. L.; Pisupati, S. V.; Scaroni, A. W. Prediction of Sorbent Performance in a Circulating Fluidized Bed Boiler Based on Petrographic Properties. J. Eng. Gas Turb. Power 2007, 129, 565. (11) Scala, F.; Montagnaro, F.; Salatino, P. Attrition of Limestone by Impact Loading in Fluidized Beds. Energy Fuels 2007, 21, 2566. (12) Scala, F.; Montagnaro, F.; Salatino, P. Sulphation of Limestones in a Fluidized Bed Combustor: the Relationship between Particle Attrition and Microstructure. Can. J. Chem. Eng. 2008, 86, 347. (13) Montagnaro, F.; Salatino, P.; Scala, F. The Influence of Temperature on Limestone Sulfation and Attrition under Fluidized Bed Combustion Conditions. Exp. Therm. Fluid Sci. 2010, 34, 352. (14) Yao, X.; Zhang, H.; Yang, H.; Liu, Q.; Wang, J.; Yue, G. An Experimental Study on the Primary Fragmentation and Attrition of Limestones in a Fluidized Bed. Fuel Process. Technol. 2010, 91, 1119. (15) Cammarota, A.; Chirone, R.; Marzocchella, A.; Salatino, P. Assessment of Ash Inventory and Size Distribution in Fluidized Bed Coal Combustors. In Proc. 16th Int. Conf. FBC; Geiling, D. W., Ed.; ASME: New York, 2001. (16) Redemann, K.; Hartge, E. U.; Werther, J. A Particle Population Balancing Model for a Circulating Fluidized Bed Combustion System. Powder Technol. 2009, 191, 78. (17) Pallares, D.; Johnsson, F.; Palonen, M. Modeling of the Solids Inventory in CFB Boilers. In Fluidization XIII; Kim, S. D., Kang, Y., Lee, J. K., Seo, Y. C., Eds.; Engineering Conferences International: New York, 2010. (18) Saastamoinen, J. J. Particle-Size Optimization for SO2 Capture by Limestone in a Circulating Fluidized Bed. Ind. Eng. Chem. Res. 2007, 46, 7308. (19) Saastamoinen, J.; Pikkarainen, T.; Tourunen, A.; R€as€anen, M.; J€antti, T. Model of Fragmentation of Limestone Particles during Thermal Shock and Calcinations in Fluidised Beds. Powder Technol. 2008, 187, 244. (20) Saastamoinen, J. J.; Shimizu, T.; Tourunen, A. Effect of Attrition on Particle Size Distribution and SO2 Capture in Fluidized Bed Combustion under High CO2 Partial Pressure Conditions. Chem. Eng. Sci. 2010, 65, 550. (21) Ray, Y. C.; Jiang, T. S.; Wen, C. Y. Particle Attrition Phenomena in a Fluidized Bed. Powder Technol. 1987, 49, 193. (22) Dam-Johansen, K.; Østergaard, K. High-Temperature Reaction between Sulphur Dioxide and Limestone-II. An Improved Experimental Basis for a Mathematical Model. Chem. Eng. Sci. 1991, 46, 839. (23) Arena, U.; D’Amore, M.; Massimilla, L. Carbon Attrition during the Fluidized Combustion of a Coal. AIChE J. 1983, 29, 40.
ARTICLE
(24) Chirone, R.; Massimilla, L.; Salatino, P. Comminution of Carbons in Fluidized Bed Combustion. Prog. Energy Combust. Sci. 1991, 17, 297. (25) Wirth, K. E. Fluid Mechanics of Circulating Fluidized Beds. Chem. Eng. Technol. 1991, 14, 29. (26) Saastamoinen, J. J.; Shimizu, T. Attrition-Enhanced Sulfur Capture by Limestone Particles in Fluidized Beds. Ind. Eng. Chem. Res. 2007, 46, 1079. (27) Scala, F.; Salatino, P. Limestone Attrition under Simulated Oxyfiring Fluidized-Bed Combustion Conditions. Chem. Eng. Technol. 2009, 32, 380. (28) Montagnaro, F.; Salatino, P.; Scala, F. The Influence of Sorbent Properties and Reaction Temperature on Sorbent Attrition, Sulfur Uptake, and Particle Sulfation Pattern during Fluidized-Bed Desulfurization. Combust. Sci. Technol. 2002, 174, 151. (29) Abanades, J. C.; Anthony, E. J.; García-Labiano, F.; Jia, L. Progress of Sulfation in Highly Sulfated Particles of Lime. Ind. Eng. Chem. Res. 2003, 42, 1840. (30) Massimilla, L. Gas Jets in Fluidized Beds. In Fluidization II; Davidson, J. F., Clift, R., Harrison, D., Eds.; Academic Press: London, 1985. (31) Scala, F.; Salatino, P. Attrition of Limestones by Impact Loading in Fluidized Beds: the Influence of Reaction Conditions. Fuel Process. Technol. 2010, 91, 1022. (32) P€uttmann, A.; Kramp, M.; Thon, A.; Hartge, E. U.; Werther, J. Particle Breakage in the Cyclones of Fluidized Bed Systems. In Fluidization XIII; Kim, S. D., Kang, Y., Lee, J. K., Seo, Y. C., Eds.; Engineering Conferences International: New York, 2010.
9711
dx.doi.org/10.1021/ie2001204 |Ind. Eng. Chem. Res. 2011, 50, 9704–9711
