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Residence time distribution of sorbent particles in a circulating fluidised bed boiler
285
Powder Technology, 70 (1992) 285-292
Residence time distribution fluidised bed boiler Anders
Lyngfelt
of sorbent particles in a circulating
and Bo Leckner
Dept. of Energy Conversion, Chalmers Universi@ of Technology, 412 96 Gothenburg (Sweden)
Abstract The residence time distribution of limestone sorbent particles has been studied in order to increase the understanding of the conditions for sulphur capture in fluidised bed boilers. Two methods were used. The ‘steady state method’ involves the study of residence time for various particle size fractions. The ‘transient method’ is based on the transient increase in the amount of sorbent carryover with the fly ash, following initial limestone addition to a fresh bed (i.e. a bed with little or no sorbent). For the boiler investigated both methods gave similar results, showing that the major fraction of the sorbent, 80-85%, had a residence time of one hour or more.
Introduction Despite extensive research on limestone behaviour in the laboratory, as well as a large number of studies of global sulphur capture in commercial scale fluidised bed boilers (FBBs), a fundamental understanding of the parameters which limit the sulphur capture performance in FBBs is still lacking. The limiting factors for sulphur capture include: (1) Insufficient residence time, i.e. the sorbent spends too short a time in the boiler to be fully converted. Improvements can be made by changes in boiler design. (2) The saturation conversion, i.e. the sorbent is fully converted and will not attain significantly higher conversion with prolonged residence time. The sulphur capture performance can be improved by selecting a sorbent with a higher saturation conversion. (3) Reducing conditions, i.e. the conversion is low due to reductive decomposition of the reaction product, CaSO, [l]. Local in-bed reducing conditions may appear even at a substantial overall air excess, due to the bypass of air through the bed. Improvements can be obtained by changes in design and operation, such as lowered bed temperature and increased recirculation of elutriated particles. The latter increases the residence time of the sorbent particles under oxidising conditions in the upper part of the combustion chamber and in the cyclone. The present investigation is concerned with the first of these factors. Literature data regarding sorbent residence time distributions are hard to find, probably as a result of the practical and economic difficulties in-
volved with comprehensive tests in commercial boilers. The purpose of this study is to present residence time data for a boiler (under realistic operating conditions) as well as to illustrate practical methods for obtaining such data, meaning that the data should be derived from quantities that can be measured in practice. Limestone was used as the test material.
The system The system considered, Fig. 1, is composed of a combustion chamber and one or several gas-particle separators (e.g. cyclones), with the calcium flows crossing the system border. The main incoming flow of calcium is added limestone, but a minor amount of calcium also enters as part of the fuel ash. The solid material in the system is called the bed material, which includes not only the dense phase in the bottom part of the combustion chamber, but also the entrained particles which are present in the upper part of the combustion chamber and in the cyclone. Particles not captured by
Fig. 1. The boiler system considered.
0 1992 - Elsevier Sequoia. All rights reserved
286
the first particle separator may be caught by a secondary separator and returned to the combustion chamber. A final gas-particle separator (i.e. a bag-house filter or an electrostatic precipitator) removes the remaining particles from the flue gas. These particles constitute an exiting flow, termed fly ash or carryover material. Depending on the volume of the incoming solid flow and the exiting fly ash flow, the amount of bed material increases or decreases. If it decreases, makeup sand must be added; if it increases, bed material must be discharged. In the latter case we have two exiting flows, fly ash and spent bed material. The system also includes a buffer store of solid bed material, the silo. This store is not considered in the model for the following reasons. For steady state conditions it can be assumed that the flows passing between the silo and the boiler are identical in size and composition. For transient conditions, i.e. at the start of limestone addition, it is assumed that the interchange of material between the boiler and the silo is too slow to affect the results significantly. The bed material is assumed to be well mixed. This means that the size distribution of the spent bed material is identical with the size distribution of the bed material. The system was studied by means of analyses of incoming and exiting flows as well as bed material analyses.
the bed is obtained
as:
dn =ii,+6f-lie-?ib dt
However, if a fraction of size i is considered, the balance should also include calcium in particles of size i formed from the size reduction of larger particles fig i, and calcium in particles of size i reduced to a smaller size, n--d, i’.
Steady-state conditions At steady-state, dn/dt= 0 and an overall residence time is obtained as: n tie,+&
7=-z- n fi,+tif
(lb)
For particle size i, the ‘intrinsic’ average residence time is: ni
rr. i=
k,
i
+ri,
i+fi$
i
(34
which is also equal to:
Theory A total average residence time for the sorbent, r,,,, can be derived from the rate of sorbent addition, ii,, and the amount of sorbent in the bed at steady state, IZ, where: 7, = nl?i,
(1)
Such an average residence time may, however, give incomplete information. Due to differences in size, and therefore elutriability, we may have a fraction of (small) particles with a short residence time and another fraction of (large) particles with long residence time. An example of this is given: The lime in a stationary FBB has a total average residence time on the order of 30-40 h for a Ca/S molar ratio of 1.5. In reality, however, the material is divided in at least two fractions, of which the minor fraction, 15%, has a residence time on the order of 100 h, whereas the major fraction has a residence time on the order of a few hours or less [2]. The example illustrates that average residence time is not a sufficient measure and that a more detailed knowledge of the residence time distribution is needed. The overall calcium balance involves the flow rates of calcium in added limestone, A,, calcium in fuel ash, r&, carryover calcium, ii,, and calcium exiting in the form of spent bed material, A,,. Thus a balance over
The intrinsic residence time is not an expedient measure of residence time since it contains the internal flows for size decrease, til i and fii i, i.e. flows that do not enter or exit the system. Furthermore, the rates of size reduction, fid: i and ri; i, cannot be determined with the experimental data produced in this study. Therefore it is not possible to calculate the intrinsic average residence time without further knowledge about the mechanisms of size reduction. The definition of fractional residence time used in this work is based on the exiting flows: 4 Ti = ii,.
i+6b,
i
This residence time is equal to the average age of the particles if there is no size reduction [3], or if the particles are reduced in size immediately as they are introduced. A motivation for the use of this definition is given in the discussion section. ri can also be written:
(5) --t-
re,i
rb
Here r,, i=Qic,
i and (6)
287
since the spent bed material has the same calcium size distribution as the bed material, a consequence of the assumption of a well mixed bed material. It is assumed that for a given size the probability for a particle to leave the system is equal for all particles of that size. This assumption yields an exponential residence time distribution: P,(t) =e-t/n
(7)
where P,(t) is the probability for a particle of size i to attain the age t in the bed. This means that Pi is also the fraction of particles of size i attaining age t. A measure of the total residence time distribution is given by the sum of the residence time distributions for the various size fractions: P(t) = x f;:Pi(t) = 2 Ae-+
(7b)
where& is the fraction of the total calcium leaving the system which is of size i:
the start of limestone addition. The calcium balance over the bed is calcium in added material, r7,, less calcium in carryover and spent bed material: dn z
l-i$lf,(l-e-fln)
=iit
[
A comparison of eqns. (4) and (3b) shows that for all size fractions the intrinsic residence time is always less than the residence time, except in the case of no size reduction. Thus, since the intrinsic residence time involves internal flows, a weighted mean value for the intrinsic residence time will always be smaller than the total average residence time, 7,. In order to facilitate a discussion on the relative size of the internal flows, an alternative residence time, 7a, i, will also be studied. This alternative residence time is based on the added calcium and is obtained by neglecting the term tii in eqn. (3a). The fuel calcium, which has an unknown size distribution, is assumed to have the same size distribution as the added limestone, which yields:
(12) For steady state conditions t+ COeqn. (12) yields: n=&$JT
(13)
Introducing the known overall average residence time, the residence time for the calcium in the spent zd material, 7;, can be obtained from eqn. (13):
(14) Overall mass balances
At steady state, the fraction of calcium exiting the boiler in the form of fly ash is:
05) The fraction of calcium exiting with the spent bed material is 1 - &=. With &a the fractional exiting flows of calcium are determined: n’, i =fb,i (lfie,
i=fe.
ra,i=
fia,, i +Tff, i
i(lLif,ri,) ri,, ii,* ni
=
z
(10)
i4Cafit
4GJfit
v-9
(17)
The fractional amount of calcium in the bed material is: ni=nfb,
ni
(11)
Here the carryover calcium is assumed to consist of j - 1 fractions, and thejth fraction is the calcium removed with the spent bed material. Equation (11) can be integrated, which yields:
i-l
With eqns. (4) and (8) the relation between the fractional residence times and the total average residence time, eqn. (l), can be derived:
1
i
(18)
and for the calcium leaving the system, the fraction of size i is:
This alternative residence time is not suitable for calculating a residence time distribution. Transient conditions
The calcium in the bed material is represented by a number of fractions with different residence time distributions, cfi eqn. (7b). The flow of carryover calcium from a fraction will be a function of the time from
Experimental The experiments were carried out in a 40 MW circulating fluidised bed boiler in Nykiiping, Sweden.
288
The results reported here were obtained during a comprehensive study of emission control in this boiler [4]. Table 1 gives some design and operation data for the boiler, as well as data concerning the fuel and sorbent. A porous limestone called Ignaberga was used. The test period involved 29 days of continuous limestone addition. The bed sorbent content stabilised within approximately ten days. The fly ash mass flow in combination with calcium analysis of nine fly ash samples were used to determine the fraction of calcium exiting the system with the fly ash at steady state, +ca. The data used in the steady state method are obtained from three samples of fly ash and two samples of bed material taken at steady state conditions. These samples were sieved and calcium analysis of the sieved fractions was used to determine the calcium size distributions, fb, i and f,, i. The transient increase in the fraction of calcium in fly ash at the start of limestone addition was determined from 17 samples. The total number of calcium analyses employed in this study was 68. Some practical characteristics of the system studied should be mentioned: - The bed material samples are taken from the bottom of the combustion chamber. The samples may underestimate the content of small particles, since the part of the bed material present in the top of the combustion chamber and in the cyclone is made up of smaller particles than the dense bottom phase. - The system includes a device for regeneration of bed material which removes particles larger than 2 mm: This does not affect the size distribution of the removed calcium since the sorbent particles are smaller than 2 mm. Thus the size distribution of sorbent particles
TABLE
1. Test conditions
Boiler: design design load cross-section combustion chamber fuel feed fluidisation velocity excess air ratio
height
circulating FBB Gijtaverken 40 IvIw 11 m* 17 m with screw to comb. chamber 5-6 m s-r 1.2
Fuel: size moisture ash volatiles, daf sulphur, daf
English bitum. coal O-30 mm 12% 10.7% 34% 1.9%
Limestone: size CaCO,
Ignaberga 0.2-2 mm 90%
in the spent bed material is the same as in the bed material samples. - The size of the spent bed material flow was not measured. Thus the flow of calcium leaving the system with the bed material must be derived implicitly from the other flows, see eqn. (16). Results Steady-state The amount
of solid material in the combustion chamber is obtained from the pressure drop and the cross-sectional area. This amount, in addition to an unknown quantity of material in the cyclone, make up the total bed mass, which is estimated to be 10 000 kg. The calcium mass fraction in the bed is 25% at steady-state, which means that n = 2 500 kg. The total flow of added calcium, fi,, is 182.8 kg h-l (of which fii= 13.6 kg h-l). The fractional flows and amounts of calcium can be calculated with eqn. (16)-(18), the residence time from eqn. (5) and the calcium fractions with eqn. (19), see Table 2. The alternative residence time distribution according to eqn. (10) is presented in Table 3. In contrast to the residence time according to Table 2, the alternative residence time decreases with increasing size, an effect of the particle size reduction. For the largest particles, where tiz i is small, the result should reflect the intrinsic residence time according to eqn. (3). The short residence time obtained for the large particles evidently reflects the rapid disappearance of large particles by fragmentation and attrition. If the size reduction is negligible, the three fractional residence times will be equal, cfi eqns. (3), (4) and (10). This obviously does not apply to the limestone investigated, CJ Tables 2 and 3. It is of interest to relate the rate of size reduction to exiting or entering streams. This is done in Table 4, using the ratio between residence time and alternative residence time. The equations in Table 4 can be derived with eqns. (4), (lo), (2b) and with &J&=0. It can be clearly seen that for small particles, the formation of particles from size reduction is considerably larger than the addition of particles. Also it is seen that for large particles, the size reduction is much larger than the exiting flows. For intermediate sizes the computed ratios are smaller, but no conclusion can be drawn from this, since rid: i and iiz i may be of approximately equal size and thus cancel each other. Transient conditions The transient increase in calcium content in the fly
ash is shown in Fig. 2. From Fig. 2 the fraction of added calcium leaving the system can be derived, Fig. 3. A fit to the curve was obtained under the conditions
289 TABLE
2. Residence
time for the various size fractions Carryover
Bed Ca content
dP (mm)
fb. i
< 0.063 < 0.09 <0.125 <0.18 < 0.25 > 0.25
ni
Ca
fit,i 0% h-‘)
fe,i
(kg)
Residence
0.06253 6.63 0.2031 21.5 0.4046 42.9 0.3048 32.3 0.0249 2.64 =O, not measured Xl.0 8106.0 =fi,&c.
=O, not measured 0.0248 62.0 0.0835 209 0.1524 381 0.1620 405 0.5773 1443 X1.0 I;2500
time (h)
Tc,i
7
?
0.01” 2.65 4.24 8.66 26.9 32.6
2.88 4.87 11.8 153 m
Fraction fi
0.036 0.128 0.270 0.241 0.082 0.242
“Assumed. TABLE d, (mm)
3. Residence
time for various fractions Limestone
0.045 < 0.063 < 0.09 <0.125 <0.18 <0.25 < 0.355 < 0.5 < 0.71
(mm)
Residence
Bed Ca content
i
fit, i 0%
0.0006 0.0021 0.0046 0.0159 0.1426 0.0618 0.1131 0.1520 0.2035 0.1888 0.0833 0.031 Cl.0
0.11 0.38 0.84 2.91 26.1 11.3 20.7 27.8 37.2 34.5 15.2 5.7 2182.7 ?I,
TABLE 4. Ratio of size reduction
4
added
size distribution time
7% i fa.
<
based on added limestone
to entering
h-l)
fb, i
--
_ _ na, i+nf,
i _ i
0.15
-
3CO.10
-
@I
-
=O, not measured =O, not measured 0.0248 0.0835 0.1524 0.1620 0.1912 0.1813 0.1504 0.0433 0.0100 0.0012 x1.0
and exiting flows
Ad:i-nd.
nb, i (kg)
73.8 71.8 14.6 35.8 23.1 16.3 10.1 3.1 1.6 0.5
62.0 209 381 405 478 453 376 108 25.0 3.0 22500 =FI
2 8
< 0.09 <0.125 <0.18 < 0.25 < 0.355 <0.5 <0.71
26.8 15.9 (0.71) (0.33)
that the sum of fi and fi be equal to the fraction of calcium, dca, which leaves the boiler with the fly ash at steady-state. The fitted values are: fi=O.l, r1 = 0.29 h, fi= 0.48 and r,=5.0 h. With r,,, =nhi, = 16.4 h and fi =f3 = 1- +ea = 0.42, eqn. (14) yields 3 = TV= 27 h.
$ .* 2 0.05 : I._.‘:
0.00
11 12
14
16
16
Time,
20
22
24
h
Fig. 2. Calcium content, as weight fraction, of fly ash VS. time. Limestone addition starts at 15:32 h. The fraction present before start of limestone addition originates from the fuel ash.
Comparison Thus we have determined the average residence time for a number of fractions with two methods, the steadystate and the transient method. The residence time distribution for each of the two methods can be computed according to eqn. (7b). The result is shown in
residence times, eqn. (4). The transient method is more direct, with which the residence time distribution of the carryover material is determined by fitting measured data, as shown in Fig. 3. The steady state method accords with the theory of Yagi and Kunii [3]. A complication with the present system compared to that studied by Yagi and Kunii is the change in particle size. The significance of the residence time distribution obtained with the steady state method in a system with particle size reduction will be discussed in the following paragraph. Fig. 3. Fraction of calcium added leaving the system as carryover shown vs. time of limestone addition. Fuel ash calcium is excluded. Solid line shows fit.
go.60 3 0 2 0.40
0.20
0.00
Rksidence Fig. 4. Residence with eqn. (7b).
t!‘me,
time distribution
h
100
for the two methods obtained
Fig. 4. It is seen that both methods show a fairly similar total residence time distribution. The residence time of the smallest particles (<0.063 mm) was assumed for the steady-state method, but this fraction is only 3.6% and errors in this assumption have only a minor effect on the results, as shown in Fig. 4.
Discussion The correspondence of the residence time distribution calculated by the two methods is good. For the fraction of calcium which is removed with the bed material, I- &at which has a long residence time, the correspondence should be good, since the main difference between the methods is for the sorbent elutriated. The major fraction, SO-85%, of the calcium has a residence time of 1 h or more. The long residence time accords well with the high sulphur capture performance of the boiler and the high sulphation of the sorbent particles. The sulphation of the particles was 45-50% irrespective of particle size [5]. With the steady state method the residence time distribution is deduced from the average fractional
The definition of residence time for the steady state method The fractional average residence time used, eqn. (4),
is not necessarily the average age of the particles of a particular size leaving the system. By age is meant the time that a particle has spent in the system. The relation between average particle age and the residence time according to eqn. (4) is complicated and depends on the manner in which the size is reduced. In order to illustrate this, two extreme cases for size reduction will be discussed. Case I: Immediate size reduction as the sorbent enters the boiler and no reduction in size following this. This means that sorbent particles immediately after being introduced into the boiler achieve a size distribution identical to that of the sorbent particles leaving the system. Consequently the particles which are reduced in size are only a negligible part of the particles present in the bed. In this case the residence time as obtained by eqn. (4) is equivalent to the average age of the particles leaving the system, and accordingly a proper measure of residence time. Case 2: A slow reduction in size, at a rate independent of age. This means that the probability for particles to be fragmented/attrited is equal for all particles of a given size, irrespective of the time they have spent in the boiler. In this case eqn. (4) does not provide a correct measure of average particle age. The intrinsic residence time, on the other hand, does give a correct measure of age, but only the age of the particles in their final size. (A particle may have spent a long time in the bed as part of a larger particle.) Thus the intrinsic residence time excludes all calcium present in particles that will obtain a smaller size before they leave the system. The only reasonable way to include this excluded calcium is to assign it to the size it actually has when the residence time is computed, which results in eqn. (4). The fractional residence time is the ratio of the amount of particles in the bed of size i to the amount of particles leaving the system of size i. Accordingly, the fractional residence time can be seen as a measure
291
of the probability for particles of size i to be retained in the system. The total residence time distribution is simply a summing up of the fractional residence time distributions. Thus also in Case 2 the steady state method provides a relevant measure of the ability of a boiler to retain the particles of a given sorbent. It is, however, important to be aware of the significance of this residence time, i.e. that in this case it is not directly related to particle age. This means that in Case 2 the results should be used with discrimination as input data in sulphur-capture modelling. The question remains, which of the two cases is closer to the real conditions in the boiler with the present sorbent. Observations available support Case 1: l Laboratory experiments with Ignaberga limestone indicate that the size reduction is substantial during the initial heating and calcination. The limestone is thought to fragment due to the explosive evaporation of water inclusions. l Boiler experiments [2] show that the elutriation of old sorbent is very low, <1%/h, which is a result of a very slow attrition/fragmentation. l In the present test, the carryover fraction was approximately 70% of its steady state value, &, after 5 h, c$ Fig. 3, whereas the calcium in the bed at this time is only 10% of its steady state value. The production of fines, which is indicated by the carryover, should be proportional to the amount of calcium in the boiler in Case 2. This is obviously not the case. Available data thus indicate that the size reduction is rapid when the sorbent is fresh in the bed and then decreases to a very low level, i.e. the limestone studied is closer to Case 1 than to Case 2. In addition to the previously mentioned ‘explosive’ evaporation of water inclusions, two other explanations for Case 1 behaviour are possible: 0 The size reduction could be caused mainly by defects or irregularities in the particle structure such as cracks and edges. 0 The resistance to attrition/fragmentation of the particles may be increased by changes in the structure caused by chemical reactions, i.e. sulphation and reactions caused by local reducing conditions. The latter include cyclic sulphation and reductive decomposition of CaSO,, as well as the formation of smaller amounts of CaS which is reported to form a eutectic with CaSO,
PIIt should be stressed that the understanding of the size reduction processes is not complete. In view of the widely different properties of natural limestones, it is not possible to generalize from the results of single limestones. Thus the interesting question of whether limestones in general can be associated with Case 1 behaviour remains to be answered.
Conclusions It is possible to describe the residence time distribution with the two methods proposed. The methods require that the fraction of calcium leaving the system with the fly ash, &,, be determined. This can be achieved by a calcium balance where fly ash flow and calcium content are compared with added calcium under steady state conditions. The steady state ,method also requires sampling of bed material and fly ash under steady state conditions, and the sieving of these samples and analysis of each size fraction for its sulphur content. The transient method requires a known fly ash flow, and that its increasing content of calcium be obtained from the analyses of a number of fly ash samples. An advantage of the transient method is the low number of analyses needed compared to the steady state method. A disadvantage of the transient method is that it requires a fresh bed (i.e. free of sorbent) initially. The information produced with the steady state method is more detailed, as it involves the residence time for various particle sizes. This information can be used in a more comprehensive sulphur-capture modelling. For a Case 2 sorbent, i.e. if slow size reduction dominates, data should be used with discrimination in modelling. The residence time distribution obtained is dependent on the design and operation of the boiler as well as on the sorbent properties, and should be seen as an indicator of the possible sulphur-capture performance. If most of the sorbent has a long residence time, efficient sulphur capture should be expected if the sorbent is not exposed to reducing conditions or if it is not a very unreactive sorbent. In the boiler investigated, the major part of the sorbent has a long residence time. This is in accord with the efficient sulphur-capture performance of the boiler.
Acknowledgement This work has been financially supported by the Swedish National Energy Administration. The analyses were performed by Kazimiera Puromaki at the Dept. of Inorganic Chemistry, Chalmers University of Technology. Samples and experimental data were supplied by Margareta Mjornell and Maria Karlsson.
List of symbols fi
fa,i
fraction of calcium (with a given average residence time) fraction of total added calcium with size i
292
fraction of total bed material calcium with size
fb, i
i
fe, i
P(t) pi(t>
II
za,i Fi
b. i n-+d. i -_ n d. i Ae,
i
n, i
t
n,. i
fraction of total carryover calcium with size i fraction of total calcium, eqn. (7b) probability for a particle of given size to obtain a certain age, eqn. (7) calcium in bed, moles or kg calcium in bed of size fraction i, moles or kg calcium, added or removed, mol h-’ or kg h-l: added in the form of limestone rempved with spent bed material carryover, i.e. leaving with the fly ash added with the fuel total added, (ti, +fif) calcium, added or removed from a size fraction, mol h-l or kg h-l: added in the form of limestone removed with spent bed material added due to size reduction of larger particles removed due to size reduction into smaller particles carryover, i.e. leaving with the fly ash added with the fuel total added, (ii=, i+ri, i) time, h
re,i rb
ra,i
carryover fraction, eqn. (15) average residence time, h total residence time, eqn. (1) intrinsic fractional residence time, eqn. (3) fractional residence time used, steady-state eqn. (4) and transient eqn. (11) fractional residence time for carryover material, eqn. (5) residence time for spent bed material sorbent, eqn. (6) alternative residence time, based on added size distribution, eqn. (10)
References 1 A. Lyngfelt and B. Leckner, Chem. Eng. Sci., 44 (1989) 207. 2 A. Lyngfelt, Sulphur Capture in a 16 MW Fluidtied Bed Boiler - Decomposition of CaSO, at High Temperature, Report A88 - 169, Department of Energy Conversion, Chalmers University of Technology, Gothenburg, 1988. 3 S. Yagi and D. Kunii, Chem. Eng. Sci., 16 (1961) 364. 4 M. Mjiknell, B. Leckner, M. Karlsson and A. Lyngfelt, Proc. Znt. Con& Fluid. Bed Combustion, 11 (1991) 6.55. 5 A. Lyngfelt and B. Leckner, 5th Znt. Fluidked Combustion Co& London, December 1991. 6 A. Zinzen, VDZ Z., 88 (1944) 171.
Powder Technology, 70 (1992) 285-292
Residence time distribution fluidised bed boiler Anders
Lyngfelt
of sorbent particles in a circulating
and Bo Leckner
Dept. of Energy Conversion, Chalmers Universi@ of Technology, 412 96 Gothenburg (Sweden)
Abstract The residence time distribution of limestone sorbent particles has been studied in order to increase the understanding of the conditions for sulphur capture in fluidised bed boilers. Two methods were used. The ‘steady state method’ involves the study of residence time for various particle size fractions. The ‘transient method’ is based on the transient increase in the amount of sorbent carryover with the fly ash, following initial limestone addition to a fresh bed (i.e. a bed with little or no sorbent). For the boiler investigated both methods gave similar results, showing that the major fraction of the sorbent, 80-85%, had a residence time of one hour or more.
Introduction Despite extensive research on limestone behaviour in the laboratory, as well as a large number of studies of global sulphur capture in commercial scale fluidised bed boilers (FBBs), a fundamental understanding of the parameters which limit the sulphur capture performance in FBBs is still lacking. The limiting factors for sulphur capture include: (1) Insufficient residence time, i.e. the sorbent spends too short a time in the boiler to be fully converted. Improvements can be made by changes in boiler design. (2) The saturation conversion, i.e. the sorbent is fully converted and will not attain significantly higher conversion with prolonged residence time. The sulphur capture performance can be improved by selecting a sorbent with a higher saturation conversion. (3) Reducing conditions, i.e. the conversion is low due to reductive decomposition of the reaction product, CaSO, [l]. Local in-bed reducing conditions may appear even at a substantial overall air excess, due to the bypass of air through the bed. Improvements can be obtained by changes in design and operation, such as lowered bed temperature and increased recirculation of elutriated particles. The latter increases the residence time of the sorbent particles under oxidising conditions in the upper part of the combustion chamber and in the cyclone. The present investigation is concerned with the first of these factors. Literature data regarding sorbent residence time distributions are hard to find, probably as a result of the practical and economic difficulties in-
volved with comprehensive tests in commercial boilers. The purpose of this study is to present residence time data for a boiler (under realistic operating conditions) as well as to illustrate practical methods for obtaining such data, meaning that the data should be derived from quantities that can be measured in practice. Limestone was used as the test material.
The system The system considered, Fig. 1, is composed of a combustion chamber and one or several gas-particle separators (e.g. cyclones), with the calcium flows crossing the system border. The main incoming flow of calcium is added limestone, but a minor amount of calcium also enters as part of the fuel ash. The solid material in the system is called the bed material, which includes not only the dense phase in the bottom part of the combustion chamber, but also the entrained particles which are present in the upper part of the combustion chamber and in the cyclone. Particles not captured by
Fig. 1. The boiler system considered.
0 1992 - Elsevier Sequoia. All rights reserved
286
the first particle separator may be caught by a secondary separator and returned to the combustion chamber. A final gas-particle separator (i.e. a bag-house filter or an electrostatic precipitator) removes the remaining particles from the flue gas. These particles constitute an exiting flow, termed fly ash or carryover material. Depending on the volume of the incoming solid flow and the exiting fly ash flow, the amount of bed material increases or decreases. If it decreases, makeup sand must be added; if it increases, bed material must be discharged. In the latter case we have two exiting flows, fly ash and spent bed material. The system also includes a buffer store of solid bed material, the silo. This store is not considered in the model for the following reasons. For steady state conditions it can be assumed that the flows passing between the silo and the boiler are identical in size and composition. For transient conditions, i.e. at the start of limestone addition, it is assumed that the interchange of material between the boiler and the silo is too slow to affect the results significantly. The bed material is assumed to be well mixed. This means that the size distribution of the spent bed material is identical with the size distribution of the bed material. The system was studied by means of analyses of incoming and exiting flows as well as bed material analyses.
the bed is obtained
as:
dn =ii,+6f-lie-?ib dt
However, if a fraction of size i is considered, the balance should also include calcium in particles of size i formed from the size reduction of larger particles fig i, and calcium in particles of size i reduced to a smaller size, n--d, i’.
Steady-state conditions At steady-state, dn/dt= 0 and an overall residence time is obtained as: n tie,+&
7=-z- n fi,+tif
(lb)
For particle size i, the ‘intrinsic’ average residence time is: ni
rr. i=
k,
i
+ri,
i+fi$
i
(34
which is also equal to:
Theory A total average residence time for the sorbent, r,,,, can be derived from the rate of sorbent addition, ii,, and the amount of sorbent in the bed at steady state, IZ, where: 7, = nl?i,
(1)
Such an average residence time may, however, give incomplete information. Due to differences in size, and therefore elutriability, we may have a fraction of (small) particles with a short residence time and another fraction of (large) particles with long residence time. An example of this is given: The lime in a stationary FBB has a total average residence time on the order of 30-40 h for a Ca/S molar ratio of 1.5. In reality, however, the material is divided in at least two fractions, of which the minor fraction, 15%, has a residence time on the order of 100 h, whereas the major fraction has a residence time on the order of a few hours or less [2]. The example illustrates that average residence time is not a sufficient measure and that a more detailed knowledge of the residence time distribution is needed. The overall calcium balance involves the flow rates of calcium in added limestone, A,, calcium in fuel ash, r&, carryover calcium, ii,, and calcium exiting in the form of spent bed material, A,,. Thus a balance over
The intrinsic residence time is not an expedient measure of residence time since it contains the internal flows for size decrease, til i and fii i, i.e. flows that do not enter or exit the system. Furthermore, the rates of size reduction, fid: i and ri; i, cannot be determined with the experimental data produced in this study. Therefore it is not possible to calculate the intrinsic average residence time without further knowledge about the mechanisms of size reduction. The definition of fractional residence time used in this work is based on the exiting flows: 4 Ti = ii,.
i+6b,
i
This residence time is equal to the average age of the particles if there is no size reduction [3], or if the particles are reduced in size immediately as they are introduced. A motivation for the use of this definition is given in the discussion section. ri can also be written:
(5) --t-
re,i
rb
Here r,, i=Qic,
i and (6)
287
since the spent bed material has the same calcium size distribution as the bed material, a consequence of the assumption of a well mixed bed material. It is assumed that for a given size the probability for a particle to leave the system is equal for all particles of that size. This assumption yields an exponential residence time distribution: P,(t) =e-t/n
(7)
where P,(t) is the probability for a particle of size i to attain the age t in the bed. This means that Pi is also the fraction of particles of size i attaining age t. A measure of the total residence time distribution is given by the sum of the residence time distributions for the various size fractions: P(t) = x f;:Pi(t) = 2 Ae-+
(7b)
where& is the fraction of the total calcium leaving the system which is of size i:
the start of limestone addition. The calcium balance over the bed is calcium in added material, r7,, less calcium in carryover and spent bed material: dn z
l-i$lf,(l-e-fln)
=iit
[
A comparison of eqns. (4) and (3b) shows that for all size fractions the intrinsic residence time is always less than the residence time, except in the case of no size reduction. Thus, since the intrinsic residence time involves internal flows, a weighted mean value for the intrinsic residence time will always be smaller than the total average residence time, 7,. In order to facilitate a discussion on the relative size of the internal flows, an alternative residence time, 7a, i, will also be studied. This alternative residence time is based on the added calcium and is obtained by neglecting the term tii in eqn. (3a). The fuel calcium, which has an unknown size distribution, is assumed to have the same size distribution as the added limestone, which yields:
(12) For steady state conditions t+ COeqn. (12) yields: n=&$JT
(13)
Introducing the known overall average residence time, the residence time for the calcium in the spent zd material, 7;, can be obtained from eqn. (13):
(14) Overall mass balances
At steady state, the fraction of calcium exiting the boiler in the form of fly ash is:
05) The fraction of calcium exiting with the spent bed material is 1 - &=. With &a the fractional exiting flows of calcium are determined: n’, i =fb,i (lfie,
i=fe.
ra,i=
fia,, i +Tff, i
i(lLif,ri,) ri,, ii,* ni
=
z
(10)
i4Cafit
4GJfit
v-9
(17)
The fractional amount of calcium in the bed material is: ni=nfb,
ni
(11)
Here the carryover calcium is assumed to consist of j - 1 fractions, and thejth fraction is the calcium removed with the spent bed material. Equation (11) can be integrated, which yields:
i-l
With eqns. (4) and (8) the relation between the fractional residence times and the total average residence time, eqn. (l), can be derived:
1
i
(18)
and for the calcium leaving the system, the fraction of size i is:
This alternative residence time is not suitable for calculating a residence time distribution. Transient conditions
The calcium in the bed material is represented by a number of fractions with different residence time distributions, cfi eqn. (7b). The flow of carryover calcium from a fraction will be a function of the time from
Experimental The experiments were carried out in a 40 MW circulating fluidised bed boiler in Nykiiping, Sweden.
288
The results reported here were obtained during a comprehensive study of emission control in this boiler [4]. Table 1 gives some design and operation data for the boiler, as well as data concerning the fuel and sorbent. A porous limestone called Ignaberga was used. The test period involved 29 days of continuous limestone addition. The bed sorbent content stabilised within approximately ten days. The fly ash mass flow in combination with calcium analysis of nine fly ash samples were used to determine the fraction of calcium exiting the system with the fly ash at steady state, +ca. The data used in the steady state method are obtained from three samples of fly ash and two samples of bed material taken at steady state conditions. These samples were sieved and calcium analysis of the sieved fractions was used to determine the calcium size distributions, fb, i and f,, i. The transient increase in the fraction of calcium in fly ash at the start of limestone addition was determined from 17 samples. The total number of calcium analyses employed in this study was 68. Some practical characteristics of the system studied should be mentioned: - The bed material samples are taken from the bottom of the combustion chamber. The samples may underestimate the content of small particles, since the part of the bed material present in the top of the combustion chamber and in the cyclone is made up of smaller particles than the dense bottom phase. - The system includes a device for regeneration of bed material which removes particles larger than 2 mm: This does not affect the size distribution of the removed calcium since the sorbent particles are smaller than 2 mm. Thus the size distribution of sorbent particles
TABLE
1. Test conditions
Boiler: design design load cross-section combustion chamber fuel feed fluidisation velocity excess air ratio
height
circulating FBB Gijtaverken 40 IvIw 11 m* 17 m with screw to comb. chamber 5-6 m s-r 1.2
Fuel: size moisture ash volatiles, daf sulphur, daf
English bitum. coal O-30 mm 12% 10.7% 34% 1.9%
Limestone: size CaCO,
Ignaberga 0.2-2 mm 90%
in the spent bed material is the same as in the bed material samples. - The size of the spent bed material flow was not measured. Thus the flow of calcium leaving the system with the bed material must be derived implicitly from the other flows, see eqn. (16). Results Steady-state The amount
of solid material in the combustion chamber is obtained from the pressure drop and the cross-sectional area. This amount, in addition to an unknown quantity of material in the cyclone, make up the total bed mass, which is estimated to be 10 000 kg. The calcium mass fraction in the bed is 25% at steady-state, which means that n = 2 500 kg. The total flow of added calcium, fi,, is 182.8 kg h-l (of which fii= 13.6 kg h-l). The fractional flows and amounts of calcium can be calculated with eqn. (16)-(18), the residence time from eqn. (5) and the calcium fractions with eqn. (19), see Table 2. The alternative residence time distribution according to eqn. (10) is presented in Table 3. In contrast to the residence time according to Table 2, the alternative residence time decreases with increasing size, an effect of the particle size reduction. For the largest particles, where tiz i is small, the result should reflect the intrinsic residence time according to eqn. (3). The short residence time obtained for the large particles evidently reflects the rapid disappearance of large particles by fragmentation and attrition. If the size reduction is negligible, the three fractional residence times will be equal, cfi eqns. (3), (4) and (10). This obviously does not apply to the limestone investigated, CJ Tables 2 and 3. It is of interest to relate the rate of size reduction to exiting or entering streams. This is done in Table 4, using the ratio between residence time and alternative residence time. The equations in Table 4 can be derived with eqns. (4), (lo), (2b) and with &J&=0. It can be clearly seen that for small particles, the formation of particles from size reduction is considerably larger than the addition of particles. Also it is seen that for large particles, the size reduction is much larger than the exiting flows. For intermediate sizes the computed ratios are smaller, but no conclusion can be drawn from this, since rid: i and iiz i may be of approximately equal size and thus cancel each other. Transient conditions The transient increase in calcium content in the fly
ash is shown in Fig. 2. From Fig. 2 the fraction of added calcium leaving the system can be derived, Fig. 3. A fit to the curve was obtained under the conditions
289 TABLE
2. Residence
time for the various size fractions Carryover
Bed Ca content
dP (mm)
fb. i
< 0.063 < 0.09 <0.125 <0.18 < 0.25 > 0.25
ni
Ca
fit,i 0% h-‘)
fe,i
(kg)
Residence
0.06253 6.63 0.2031 21.5 0.4046 42.9 0.3048 32.3 0.0249 2.64 =O, not measured Xl.0 8106.0 =fi,&c.
=O, not measured 0.0248 62.0 0.0835 209 0.1524 381 0.1620 405 0.5773 1443 X1.0 I;2500
time (h)
Tc,i
7
?
0.01” 2.65 4.24 8.66 26.9 32.6
2.88 4.87 11.8 153 m
Fraction fi
0.036 0.128 0.270 0.241 0.082 0.242
“Assumed. TABLE d, (mm)
3. Residence
time for various fractions Limestone
0.045 < 0.063 < 0.09 <0.125 <0.18 <0.25 < 0.355 < 0.5 < 0.71
(mm)
Residence
Bed Ca content
i
fit, i 0%
0.0006 0.0021 0.0046 0.0159 0.1426 0.0618 0.1131 0.1520 0.2035 0.1888 0.0833 0.031 Cl.0
0.11 0.38 0.84 2.91 26.1 11.3 20.7 27.8 37.2 34.5 15.2 5.7 2182.7 ?I,
TABLE 4. Ratio of size reduction
4
added
size distribution time
7% i fa.
<
based on added limestone
to entering
h-l)
fb, i
--
_ _ na, i+nf,
i _ i
0.15
-
3CO.10
-
@I
-
=O, not measured =O, not measured 0.0248 0.0835 0.1524 0.1620 0.1912 0.1813 0.1504 0.0433 0.0100 0.0012 x1.0
and exiting flows
Ad:i-nd.
nb, i (kg)
73.8 71.8 14.6 35.8 23.1 16.3 10.1 3.1 1.6 0.5
62.0 209 381 405 478 453 376 108 25.0 3.0 22500 =FI
2 8
< 0.09 <0.125 <0.18 < 0.25 < 0.355 <0.5 <0.71
26.8 15.9 (0.71) (0.33)
that the sum of fi and fi be equal to the fraction of calcium, dca, which leaves the boiler with the fly ash at steady-state. The fitted values are: fi=O.l, r1 = 0.29 h, fi= 0.48 and r,=5.0 h. With r,,, =nhi, = 16.4 h and fi =f3 = 1- +ea = 0.42, eqn. (14) yields 3 = TV= 27 h.
$ .* 2 0.05 : I._.‘:
0.00
11 12
14
16
16
Time,
20
22
24
h
Fig. 2. Calcium content, as weight fraction, of fly ash VS. time. Limestone addition starts at 15:32 h. The fraction present before start of limestone addition originates from the fuel ash.
Comparison Thus we have determined the average residence time for a number of fractions with two methods, the steadystate and the transient method. The residence time distribution for each of the two methods can be computed according to eqn. (7b). The result is shown in
residence times, eqn. (4). The transient method is more direct, with which the residence time distribution of the carryover material is determined by fitting measured data, as shown in Fig. 3. The steady state method accords with the theory of Yagi and Kunii [3]. A complication with the present system compared to that studied by Yagi and Kunii is the change in particle size. The significance of the residence time distribution obtained with the steady state method in a system with particle size reduction will be discussed in the following paragraph. Fig. 3. Fraction of calcium added leaving the system as carryover shown vs. time of limestone addition. Fuel ash calcium is excluded. Solid line shows fit.
go.60 3 0 2 0.40
0.20
0.00
Rksidence Fig. 4. Residence with eqn. (7b).
t!‘me,
time distribution
h
100
for the two methods obtained
Fig. 4. It is seen that both methods show a fairly similar total residence time distribution. The residence time of the smallest particles (<0.063 mm) was assumed for the steady-state method, but this fraction is only 3.6% and errors in this assumption have only a minor effect on the results, as shown in Fig. 4.
Discussion The correspondence of the residence time distribution calculated by the two methods is good. For the fraction of calcium which is removed with the bed material, I- &at which has a long residence time, the correspondence should be good, since the main difference between the methods is for the sorbent elutriated. The major fraction, SO-85%, of the calcium has a residence time of 1 h or more. The long residence time accords well with the high sulphur capture performance of the boiler and the high sulphation of the sorbent particles. The sulphation of the particles was 45-50% irrespective of particle size [5]. With the steady state method the residence time distribution is deduced from the average fractional
The definition of residence time for the steady state method The fractional average residence time used, eqn. (4),
is not necessarily the average age of the particles of a particular size leaving the system. By age is meant the time that a particle has spent in the system. The relation between average particle age and the residence time according to eqn. (4) is complicated and depends on the manner in which the size is reduced. In order to illustrate this, two extreme cases for size reduction will be discussed. Case I: Immediate size reduction as the sorbent enters the boiler and no reduction in size following this. This means that sorbent particles immediately after being introduced into the boiler achieve a size distribution identical to that of the sorbent particles leaving the system. Consequently the particles which are reduced in size are only a negligible part of the particles present in the bed. In this case the residence time as obtained by eqn. (4) is equivalent to the average age of the particles leaving the system, and accordingly a proper measure of residence time. Case 2: A slow reduction in size, at a rate independent of age. This means that the probability for particles to be fragmented/attrited is equal for all particles of a given size, irrespective of the time they have spent in the boiler. In this case eqn. (4) does not provide a correct measure of average particle age. The intrinsic residence time, on the other hand, does give a correct measure of age, but only the age of the particles in their final size. (A particle may have spent a long time in the bed as part of a larger particle.) Thus the intrinsic residence time excludes all calcium present in particles that will obtain a smaller size before they leave the system. The only reasonable way to include this excluded calcium is to assign it to the size it actually has when the residence time is computed, which results in eqn. (4). The fractional residence time is the ratio of the amount of particles in the bed of size i to the amount of particles leaving the system of size i. Accordingly, the fractional residence time can be seen as a measure
291
of the probability for particles of size i to be retained in the system. The total residence time distribution is simply a summing up of the fractional residence time distributions. Thus also in Case 2 the steady state method provides a relevant measure of the ability of a boiler to retain the particles of a given sorbent. It is, however, important to be aware of the significance of this residence time, i.e. that in this case it is not directly related to particle age. This means that in Case 2 the results should be used with discrimination as input data in sulphur-capture modelling. The question remains, which of the two cases is closer to the real conditions in the boiler with the present sorbent. Observations available support Case 1: l Laboratory experiments with Ignaberga limestone indicate that the size reduction is substantial during the initial heating and calcination. The limestone is thought to fragment due to the explosive evaporation of water inclusions. l Boiler experiments [2] show that the elutriation of old sorbent is very low, <1%/h, which is a result of a very slow attrition/fragmentation. l In the present test, the carryover fraction was approximately 70% of its steady state value, &, after 5 h, c$ Fig. 3, whereas the calcium in the bed at this time is only 10% of its steady state value. The production of fines, which is indicated by the carryover, should be proportional to the amount of calcium in the boiler in Case 2. This is obviously not the case. Available data thus indicate that the size reduction is rapid when the sorbent is fresh in the bed and then decreases to a very low level, i.e. the limestone studied is closer to Case 1 than to Case 2. In addition to the previously mentioned ‘explosive’ evaporation of water inclusions, two other explanations for Case 1 behaviour are possible: 0 The size reduction could be caused mainly by defects or irregularities in the particle structure such as cracks and edges. 0 The resistance to attrition/fragmentation of the particles may be increased by changes in the structure caused by chemical reactions, i.e. sulphation and reactions caused by local reducing conditions. The latter include cyclic sulphation and reductive decomposition of CaSO,, as well as the formation of smaller amounts of CaS which is reported to form a eutectic with CaSO,
PIIt should be stressed that the understanding of the size reduction processes is not complete. In view of the widely different properties of natural limestones, it is not possible to generalize from the results of single limestones. Thus the interesting question of whether limestones in general can be associated with Case 1 behaviour remains to be answered.
Conclusions It is possible to describe the residence time distribution with the two methods proposed. The methods require that the fraction of calcium leaving the system with the fly ash, &,, be determined. This can be achieved by a calcium balance where fly ash flow and calcium content are compared with added calcium under steady state conditions. The steady state ,method also requires sampling of bed material and fly ash under steady state conditions, and the sieving of these samples and analysis of each size fraction for its sulphur content. The transient method requires a known fly ash flow, and that its increasing content of calcium be obtained from the analyses of a number of fly ash samples. An advantage of the transient method is the low number of analyses needed compared to the steady state method. A disadvantage of the transient method is that it requires a fresh bed (i.e. free of sorbent) initially. The information produced with the steady state method is more detailed, as it involves the residence time for various particle sizes. This information can be used in a more comprehensive sulphur-capture modelling. For a Case 2 sorbent, i.e. if slow size reduction dominates, data should be used with discrimination in modelling. The residence time distribution obtained is dependent on the design and operation of the boiler as well as on the sorbent properties, and should be seen as an indicator of the possible sulphur-capture performance. If most of the sorbent has a long residence time, efficient sulphur capture should be expected if the sorbent is not exposed to reducing conditions or if it is not a very unreactive sorbent. In the boiler investigated, the major part of the sorbent has a long residence time. This is in accord with the efficient sulphur-capture performance of the boiler.
Acknowledgement This work has been financially supported by the Swedish National Energy Administration. The analyses were performed by Kazimiera Puromaki at the Dept. of Inorganic Chemistry, Chalmers University of Technology. Samples and experimental data were supplied by Margareta Mjornell and Maria Karlsson.
List of symbols fi
fa,i
fraction of calcium (with a given average residence time) fraction of total added calcium with size i
292
fraction of total bed material calcium with size
fb, i
i
fe, i
P(t) pi(t>
II
za,i Fi
b. i n-+d. i -_ n d. i Ae,
i
n, i
t
n,. i
fraction of total carryover calcium with size i fraction of total calcium, eqn. (7b) probability for a particle of given size to obtain a certain age, eqn. (7) calcium in bed, moles or kg calcium in bed of size fraction i, moles or kg calcium, added or removed, mol h-’ or kg h-l: added in the form of limestone rempved with spent bed material carryover, i.e. leaving with the fly ash added with the fuel total added, (ti, +fif) calcium, added or removed from a size fraction, mol h-l or kg h-l: added in the form of limestone removed with spent bed material added due to size reduction of larger particles removed due to size reduction into smaller particles carryover, i.e. leaving with the fly ash added with the fuel total added, (ii=, i+ri, i) time, h
re,i rb
ra,i
carryover fraction, eqn. (15) average residence time, h total residence time, eqn. (1) intrinsic fractional residence time, eqn. (3) fractional residence time used, steady-state eqn. (4) and transient eqn. (11) fractional residence time for carryover material, eqn. (5) residence time for spent bed material sorbent, eqn. (6) alternative residence time, based on added size distribution, eqn. (10)
References 1 A. Lyngfelt and B. Leckner, Chem. Eng. Sci., 44 (1989) 207. 2 A. Lyngfelt, Sulphur Capture in a 16 MW Fluidtied Bed Boiler - Decomposition of CaSO, at High Temperature, Report A88 - 169, Department of Energy Conversion, Chalmers University of Technology, Gothenburg, 1988. 3 S. Yagi and D. Kunii, Chem. Eng. Sci., 16 (1961) 364. 4 M. Mjiknell, B. Leckner, M. Karlsson and A. Lyngfelt, Proc. Znt. Con& Fluid. Bed Combustion, 11 (1991) 6.55. 5 A. Lyngfelt and B. Leckner, 5th Znt. Fluidked Combustion Co& London, December 1991. 6 A. Zinzen, VDZ Z., 88 (1944) 171.