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Particle-Size Optimization for SO2 Capture by Limestone in a Circulating Fluidized Bed J. J. Saastamoinen* VTT Technical Research Centre of Finland, P.O. Box 1603, FIN-40101 JyVa¨skyla¨, Finland
Sulfur capture by limestone particles in a circulating fluidized bed is studied by modeling. Small particles are reactive but they have a short residence time depending on the separation efficiency of the cyclone. With large particles, the residence time is longer, but the rate and degree of sulfur capture are lower. Then the large particles removed in the bottom ash flow may have reached a lesser degree of conversion (from CaO to CaSO4), especially if the rate of attrition is low. The optimum particle size or particle-size distribution to minimize the limestone feed rate to achieve a given efficiency of sulfur capture is discussed. A methodology to calculate the optimum size is presented. 1. Introduction Limestone particles are used in circulating fluidized beds for sulfur capture. There is extensive literature on modeling of sulfur capture by limestone particles, and some of this literature has been discussed earlier.1,2 Several models for sulfur retention in fluidized-bed (FB) or circulation fluidized-bed (CFB) boilers have been presented.3-14 The residence time and conversion and their effect on optimum particle size in sulfur capture have been studied.12,15,16 The optimum size was about 0.2-0.4 mm for the limestone used; then the particles were sufficiently large so that they did not escape as fly ash.15 Below this optimum, the conversion decreases because of reduced residence time, and above this size, the conversion decreases because of insufficient penetration of sulfur to the particle’s interior.15 A model that incorporates detailed laboratory data on limestone together with boiler data on particle-size distributions, as well as residence times for the various particle sizes, has been presented.12 Modeling could produce measured results for a reactive limestone, but laboratory measurements gave much lower conversion compared to measurements in a large-scale CFB boiler.15 The reason for this was attributed to alternating oxidizing and reducing conditions, which obviously promote diffusion of sulfur dioxide into the particles. Fragmentation and attrition may also have a great effect. After a rapid initial stage, the reaction rate of limestone particles becomes very slow because of the formation of a product layer on the particle surface. The pores may become totally plugged, hindering further SO2 diffusion into the particle. The rate and extent of conversion of sulfur capture by limestone particles increases with decreasing particle size, since a greater part of the mass has been reacted before this pore plugging at the particle surface has been completed. Using small particles, rapid conversion is achieved, but the residence time of the particle may remain short depending on the separation efficiency of the cyclone. With larger particles, the residence time is longer, which may lead to maximum conversion with a specific particle size. This is illustrated in Figure 1. The optimum particle size depends both on the conversion curve X, which is different for different initial particle sizes, and on the residence time of the * Corresponding author. Tel.: +358 20 722 2547. Fax: +358 20 722 2597. E-mail:
[email protected].
Figure 1. Optimum particle size of limestone.
particle in the boiler, which depends on the particle size and the curve of separation efficiency of the cyclone. The effect of mixing on SO2 has been discussed.17,18 SO2, sorbent, and oxygen must be located in the same place, which makes the effect of lateral mixing important. This causes a difference between commercial and pilot plants. For highvolatile coals, the operation of commercial units has been found to be poorer than that of the pilot scale.18 CaO is distributed more evenly than SO2. The nonuniform distribution is due to the SO2 released from volatiles. Also, O2 concentration is small in the area where the volatiles are released. The ratio [commercial Ca/S]/[pilot Ca/S] increases with an increasing amount of volatiles.18 Over half of the sulfur was released with volatiles for the coal studied.19 The density and reactivity of coal affect the location of S release; if more S is released above the bed, smaller limestone size seems better. Some measured concentration profiles of SO2 in fluidized beds have been reported.18,20-22 In the present method, the effect of the SO2 concentration profile is approximately accounted for by using a logarithmic average value. It has been found in a 30 MWe CFB boiler that the majority of both calcium and sulfur fed to the boiler was removed with the fly ash, regardless of the sorbent. It was thought that attrition may play a key role in overall sorbent performance.23 Thus, a model that includes the effect of attrition is important. Attrition may have an enhancing effect on sulfation because of the removal of the sulfated surface layer with low diffusivity. The effect of attrition is not clearly seen in laboratory-scale reactivity tests because of their short duration and usually less-abrading environment. Attrition may also be more effective in full scale with alternating oxidizing and reducing conditions since, because of the release of SO2 under reducing conditions, the CaO, which is less hard than CaSO4, is formed at the surface. A model
10.1021/ie070567p CCC: $37.00 © 2007 American Chemical Society Published on Web 09/06/2007
Ind. Eng. Chem. Res., Vol. 46, No. 22, 2007 7309 Table 1. Conversion X ()Xb) and Rate of Conversion as a Function of Time t
a
model
conversion rate as function of X
1 2 3 4 5 6a 7b 8 9 10c
comprehensive models comprehensive models dX/dt ) X′ ) k(Xmax - X) X′ ) k1/nn(Xmax - X)[-ln(1 - X/Xmax)](n-1)/n dX/dt ) X′ ) aCg e-KX X′ ) (k/2)/[(1 - X)-1/3 - 1] X′ ) 3k(1 - X)2/3 X′ ) nk(1 - X)(n-1)/n X′ ) (1 - X)n+1k/n X′ ) k/Y′
11d
X′ ) 3(1 - X)2/3/τ
relation between conversion X and time t numerically analytically X ) Xmax(1 - e-kt) X ) Xmax[1 - exp(-k1tn)] X ) (1/K) ln(aCgKt + 1) 1 - 3(1 - X)2/3 + 2(1 - X) ) kt 1 - (1 - X)1/3 ) kt 1 - (1 - X)1/n ) kt (1 - X)-n ) kt 3{R - [R + (1 - R)(1 - X)]2/3}/ (R - 1) - 3(1 - X)2/3 ) Y ) kt (t - t0)/τ ) (1 - X0)1/3 - (1 - X)1/3
b
ref e.g. 2, 8, 11, 37 7, 14 3-4, 6, 13, 31, 38-40 6, 30 12, 33 27 27 29 29 27 34
c
Shrinking core model for diffusion control. Shrinking core model for chemical reaction control. Shrinking core model accounting for change in volume. d Shrinking core model for long-term conversion after time t0.
incorporating reaction, attrition, and residence time of particles in the boiler has been applied to study the optimum particle size of limestone.1 The effect of cyclone was not considered in this previous model, but the particles were assumed to escape the reactor when reaching a critical size. The increase in cyclone efficiency can lead to a significant decrease in the limestone consumption.24 The new model presented here to evaluate the residence-time distribution (RTD) of particles includes the effects of cyclone efficiency, bottom ash removal, and circulation time. The RTD of particles can be combined from three fates of solid matter: mother particles escaping as bottom ash and in fly ash and attrition products escaping in fly ash. When considering a single sorbent particle, the initial reaction rate is relatively fast and then greatly decreases. The degree of conversion reached during the initial stage (∼2 h) is an interplay between reaction rate and diffusion. A dense product layer is formed on the particle surface during the initial stage, restricting diffusion of SO2 inside, and even stopping further reaction, when the pores are plugged. Attrition removes a product layer. Since the residence time of the particles is long in the boiler, it can improve long-term SO2 capture. Long-term (∼20-50 h) residual activity of particles can take place. The amount of the sorbent in the bed mass in the slow regime can be great. This influences the SO2 level since the “starved” sulfur capture may take place after several days. The purpose of the work is to give guidelines for the optimum choice of particle size or particle-size distribution (PSD) of limestone. In reality, PSD cannot be freely chosen but is formed in the grinding process, but the method shows the best PSD of a given set of PSDs. This guideline is presented in the form of a calculation method that can be sufficiently easily applied but requires information from the laboratory scale. Even if laboratory data is not available, the method gives a means to achieve understanding by simulation. It is necessary to understand many interactions for the optimum selection of limestone and its size. In the optimization, the effective PSD of the input (i.e., the PSD of mother particles), which is optimized, is the PSD after primary fragmentation due to thermal shock and calcination. The change in particle size in the primary fragmentation and how to determine the effective PSD of the input from the real PSD of the limestone feed are discussed in another paper.25 The method also suits the optimum selection of a limestone from a given set of limestones. The developed model can be used to study the effects of (i) limestone (PSD, reactivity properties, and attrition), (ii) process conditions (temperature, SO2 concentration, and CO2 partial pressure), (iii) coal properties (S content, amount of ash, and PSD of fuel’s ash), (iv) cyclone efficiency, and (v) bottom ash removal rate.
2. Model For optimizing the particle size or PSD, a model for the sulfur capture in the boiler accounting for the most influential parameters is required. The model presented here is based on the combination of the reaction and comminution rate information on the limestone with the residence-time distribution of the particles in the boiler. Even though the model is rather simple and relies on submodels for which experimental parameters are required, it is believed that it can predict the trends in a correct way and can assist planning. 2.1. Single-Particle Models for Conversion of Limestone in SO2 Capture. SO2 is captured by calcined limestone in the sulfation reaction CaO + SO2 + 1/2O2 f CaSO4 under atmospheric conditions. In pressurized conditions, the partial pressure of carbon dioxide is so high that CaCO3 is not calcined. Then SO2 capture takes place directly to calcium carbonate: CaCO3 + SO2 + 1/2O2 f CaSO4 + CO2. Various methods to calculate the conversion of a limestone particle as a function of time have been presented in the literature.2 The most general method is to solve the conservation equation of SO2 inside a particle with consideration to conversion-dependent diffusivity and reaction rate inside the particle and shrinkage of particles due to attrition.2 However, there is a lack of knowledge of the properties (reactivity and diffusivity) and their dependence on conversion, and this information is difficult to find by measurements. Simpler semiempirical models can also be applied for conversion of limestone (from CaO to CaSO4). For example, Borgwardt and Bruce compare five different rate equations for conversion.26 Equations of different forms have been summarized in refs 27 and 28. Some models currently applied for the conversion of limestone particles are shown in Table 1. If attrition is important, the conversion X should be determined in an abrasive environment corresponding to the real operation. Models with a final maximum conversion are not good in a case of long residence time and strong attrition since conversion does not reach a final value. It could also be possible to directly apply the measured conversion curves X(t) for different particle sizes in the optimization calculations. This requires that the SO2 level has been adjusted to be approximately constant in the experiments, which is easy in a thermobalance but more difficult in benchscale FB if the batch is large. Degrees of sulfation of different limestones as a function of time have been widely reported in the literature (see, e.g., refs 29-35). Intrinsic chemical reaction rate and diffusivity are important limestone (or CaO) properties affecting sulfur capture. These
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Figure 2. Dependence of maximum conversion on particle size d estimated from different sources in the literature: 9 Ko¨ping,33 2 sample 1,29 0 sample 2,29 4 sample 3,29 b sample 4,29 [ Elmtree,39 and O Havelock.39
properties along with the particle size and the process conditions (temperature and SO2 concentration) determine the reaction rate of a single particle characterized by the conversion of particles as a function of time X(t). The effects of high CO2 partial pressure (in pressurized or high O2 concentration atmospheres), which affect the diffusivity of the product layer, are accounted for using X(t) measured in those conditions. The curve X(t) is measured on the laboratory scale by mimicking the conditions of the large scale, and the accuracy then depends on the correspondence between these conditions. The residence time of a particle can be long and the residual activity of the particles can be influential,34 so the conversion curve should be known for longer times. The attrition rate, which is important for calculating the fly ash rate, can be characterized by the curve describing the change of particle diameter as a function of time d/d0 ) f(t). The density of limestone is also an important parameter. In addition to the conversion of the mother particles Xb(t) presented in Table 1, an estimation of the conversion of the attrition fines Xfa(t) is needed. After the initial stage (when mass transfer Biot number is large), it can be assumed to be the chemical limit since the fines are abraded from the particle surfaces, which have long been exposed to SO2. Another possibility (and for initial period) is to use experimental results (see, e.g., ref 36). The conversion functions and their reaction constants should correspond to the operational conditions of the reactor (temperature, pressure, and SO2 concentration). Thus, the effect of temperature and SO2 concentration is included in the reaction rate constant k. In practice, the SO2 concentration varies along the reactor, and the logarithmic average (see ref 1) is applied. X(t) (or k and Xmax) also depends on particle size, as illustrated in Figure 1. The dependence of maximum conversion on particle size is shown in Figure 2 for various limestones. They have been estimated from different conversion curves presented in the literature, but the estimation of the asymptote of the curve is not very accurate (as can be deduced from Figure 1). Model 3 is the most common description of the conversion used in the literature. The reactivity can be described by two parameters k and Xmax, which are both important properties affecting the optimum PSD. Parameter k describes the rapidity of the reaction. Its inverse, reaction time constant τr ) 1/k, is the time at which 63.2% conversion has been reached. Other time constants of the process are given later. The concept of time constant is useful, since it gives the possibility to compare the characteristic times or rates of different processes such as the rates of chemical reaction, attrition, bottom ash removal,
and particle loss from cyclone. Parameter Xmax describes the ultimate extent of the conversion. Values of Xmax and k for model 3 in Table 1 have been reported for several limestones;39 also, a correlation for the effect of particle diameter d and SO2 concentration on conversion at a chosen time is given. It can be seen from Figure 2 that Xmax ≈ 1/dn, where n varies in a broad range of n ) 0.08...0.8. The correlations k0 ) 110 + (k0,ref - 110)d/dref and Xmax ) 1 - (Xmax,ref)(d/dref)1/3 30 have been proposed to express the particle-size dependence of the reaction rate parameters for model 3 (Table 1) when the values for the reference values (ref) have been measured. Other relations for the particle-size dependence including the effects of SO2 and O2 have been presented.40 The drawback to the simple model 3 is that it cannot describe the long-term starved reaction in which no ultimate conversion Xmax is reached but the reaction will continue in reality. The second drawback is that it cannot predict the continuing reaction caused by attrition, which extends the reaction time by removing the reacted layer from the particle surface. Models of types 5-11, which contain no ultimate conversion Xmax, are then better suited. Besides the type of limestone and particle size, Xmax depends on SO2 concentration. In sulfur capture with precalcined limestone at 1113 K, an optimum calcination temperature 1223 K was found.41 A decrease or increase in the calcination temperature led to a decrease in the extent of conversion. This was explained so that the average pore size of the calcined limestone reached a maximum at this temperature.41 An empirical correlation for the conversion depending on porosity and purity has been suggested based on 12 limestones.42 For microfine particles (5 µm), the ultimate conversion of sulfation, Xmax, reached 1.0 in the range of temperatures from 1023 to 1273 K, but Xmax was always
