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Prediction of fly ash size and chemical composition distributions: The random coalescence model
Twenty-Fourth Symposium (International) on Combustion/The Combustion Institute, 1992/pp. 1135-1144
PREDICTION OF FLY ASH SIZE AND CHEMICAL COMPOSITION DISTRIBUTIONS: THE RANDOM COALESCENCE MODEL L. E. BARTA, M. A. TOQAN, J. M. BEI~R AND A. F. SAROFIM Department of Chemical Engineering Massachusetts Institute of Technology. Cambridge MA, 02139, USA
In the course of combustion of pulverized coal, the coal minerals partially coalesce to form fly ash upon the complete burnout of the combustible matter. The probability of a fly ash particle impacting an obstacle in the flow e.g. heat exchange surface, depends largely on its size, and its retention in a deposit upon the chemical composition. The Random Coalescence Model (RCM) is an essential part of an overall model that follows the coal mineral matter transformation to deposit formation. Computer Controlled Scanning Electron Microscopy (CCSEM) of the size and chemical composition distributions of the mineral inclusions in the coal and analysis of the ion-exchangeable minerals form the inputs to the RCM calculations. A coal char combustion model provides limits for the coalescence of mineral inclusions as the char surface recedes during combustion. The calculation proceeds through steps determining the most probable values for the coal mineral size and chemical composition and the mean values and variants of the resultant fly ash size and chemical composition distributions. Experiments carried out with a Wyoming lignite in the pilot scale MIT Combustion Research Facility gave good agreement with results of the RCM calculations predicting the fly ash size and chemical composition distributions when CCSEM data of the coal minerals were used as input to the model.
Introduction Prediction of fouling tendencies of coal in pulverized coal combustion requires knowledge of the size and chemical composition of the fly ash. The fly ash is formed during combustion from partially coalesced individual mineral inclusions and organically bound coal minerals. There is interest in a model capable of predicting fly ash deposition tendencies from coal mineral properties. One such comprehensive model (Be6r et al. 1) contains a submodel describing the coal mineral matter (m.m.) transformation into fly ash. This entails the prediction of the fly ash size and chemical composition distributions for given values of the initial parameters of the coal e.g. coal particle size, density, ash content, included mineral size distribution, organically bound mineral fraction, etc., and also the random particle to particle variation of the above parameters by a series of weighted integrals. In the present contribution a theoretical study is presented of the random m.m. coalescence in a single coal particle, and fly ash properties are computed from experimentally determined parameters of the coal including the distributions of particle size, density, ash content, and size and chemical cornI135
position of mineral inclusions. Computer Controlled Scanning Electron Microscopy (CCSEM) 2 is used for the characterization of the included coal m.m. in individual coal particles. The Random Coalescence Model Fly Ash Size Distribution:
During the burnout of the coal particle, random coalescence of the mineral inclusions takes place which will reduce their number. This reduction can be given as: no = n + An
(1)
where no: the number of inclusions before coalescence, n: the number of inclusions after coalescence, An: the number reduction of inclusions. In the description of a model of the coalescence process two groups of mineral particles can be distinguished. One of these consisting of "n" number of particles is named the "acceptor" group, and the other in which there are "'An" inclusions is called the "captured" group. The particles in these groups
1136
COAL COMBUSTION
are referred to as "acceptor" and "captured" inclusions, respectively. Both groups of particles have the same size and chemical composition distributions. The captured particles are distributed randomly onto the acceptor particles of size x~; the number of acceptor particles with size xi is ni. The probability of coalescence between these two groups can be given as the fractional surface area (p(xi)) of the particles with size xi in the acceptor group. This formulation of the problem renders it amenable to the application of the probabilistic "urn" model, 3 which provides an analytical solution to the problem of particle to particle variation of mineral properties. In the urn model it is assumed that "balls" of different sizes (mineral inclusions) are randomly thrown into a number of "urns" (coal particles) of uniform size. In the present case, we consider the distribution of An * p(xi) particles having a size distribution off(x) onto ni acceptor particles. The total volume of captured particles that an acceptor particle can receive can be expressed as a gamma random variable with a mean value and variance as given by Equations 2 and 3, respectively. 1
"1"i"
E(vi) = Anp(xi) -- Ma -ni 6 Var(vi) = Anp(xi) -- M 6
p(x,)
(3)
n i X2 =
n
M2
where vi: volume of captured inclusions coalesced with aeceptor inclusions of size xi; Me: the second moment of the size distribution of the captured inclusions; M3: the third moment of the size distribution of the captured inclusions; M6: the sixth moment of the size distribution of the captured inclusions; The fly ash size distribution emerging from the above discussed allocation of the captured particles can be obtained by determining the distribution of the possible total volume of a fly ash particle after coalescence. The total volume of a single fly ash particle can be given as:
function of vi. The final size distribution of the fly ash is then obtained by integrating the size distribution functions of v~ for all possible values of i, and the cumulative distribution function of the fly ash so obtained can be given as: F,i~(y) =
fo'f(x)
a(x), A 6 (y - x3) dx
where An x 2 M~
~(x)
n M2 M6
X=
6
+ ,,,,
(4)
where v~: the total volume of a fly ash particle after the coalescence of the captured inclusions with the acceptor particles of size xi; The distribution function of the random variable v~ can be obtained directly from the distribution
6 M3
(6)
(7)
rr M6
F*: the incomplete gamma function; The step by step derivation of Eq. 5 is given elsewhere. 4
Fly Ash Chemical Composition Distribution: In the derivation of the chemical composition distribution, a similar procedure to that for size distribution is followed, except that in this case a joint size-chemical concentration distribution, f(x, c) is used. The random coalescence of mineral particles is described in the following by using the urn model and the concept of acceptor and captured particles. The number of acceptor particles of size y and chemical content c is designated by n(y, c). The probability that the captured particles coalesce with acceptor particles of size y and chemical compound concentration c, is given by the area fraction of these particles: p(y, c). The captured particles of chemical content ci are distributed randomly onto acceptor particles of size y and chemical compound concentration c. The total volume of captured particles coalesced with acceptor inclusions of size y and concentration c, is a gamma random variable (/xi), according to the urn model. 2 Its mean value and variance can be given by:
n(v, c) u2 E(ix~) = An f(c~) A c i n M2
x~ r ,'T =
(5)
1
• - -
n(y, c)
7'/"
M3 -
6
(8)
Var(/zi) = An f(ci) Aci n(y, c) y2 n Me
1 X
-
-
n(v, c)
M6
(#
(9)
FLY ASH SIZE AND CHEMICAL COMPOSITION Where /-~i = the volume of captured inclusions coalesced with acceptor inclusions of size y and concentration c. When an acceptor and a captured particle coalesce, the chemical composition of the emerging fly ash particle can be different from that of its parents. By taking into account the coalescence of the captured particles with all their possible chemical composition (/~, i = 1 ...), the concentration ~', of a chosen chemical compound in a fly ash particle can be given
Ol 1 ~
1137
An- y2 fot n M2 A1 f(c) (t - c)
-
71"
x M3(c) -- dc 6
(14)
I
f(c) (c - t) M3(c) 6 3-2 =
1
2
(15)
as: y3 7/"
c "/"
=
6
y3 77"
--
6
+ E c~/z~ i ~
(10)
a.z
An y'2 f l = ~ Az f(c) (c -- t) n Me
+ E /.ti i
7t"
The distribution of r can be obtained from convolution theory by using the distribution functions of kei (i = 1 ... ~). The final distribution function of the concentration of a chemical compound in a fly ash particle can be obtained by integrating the distribution functions of ~" for all possible values of y and c. The cumulative distribution of the concentration of a chemical compound in the fly ash can then be given as:
• M3(c)-dc 6
(16)
An
where - - is the captured particles as a fraction of n the number of acceptors; The details of the derivation of equations 12 . . . 16 are given elsewhere, a
Reduction of the Number of Inclusions During Coal Burnout: The following input parameters are necessary for the calculation of the final distribution functions of the fly ash size and the concentration of a chemical compound:
where
g(c, y, t) = Prob.(r < t)
(12)
is the cumulative distribution of a chemical species after capture by acceptor inclusions of a given size and concentration
a . / the size distribution of the acceptor particles; b . / the distribution of the concentration of a chemical compound, for example SiO2; c . / the joint distribution function of the size and the concentration of a chemical compound;
l fo __xL le 1-
when t -<
~6(t-c) F(ot2----~)
al,
- --if- (t - c)
where
))
dx
when t > c
d . / the number reduction of inclusions during the coal particle burnout. t
fo
71"
f(c) (t - c) M3(c) - dc 6
A1 =
t
n
(13)
The first three input parameters mined by CCSEM. The value of number reduction, however, has to In order to determine this value, model has to be assumed.
can be deterthe inclusion be calculated. a combustion
COAL COMBUSTION
1138
After the volatile matter in the coal particle burns away, an external diffusion limited combustion is assumed i.e. the char particle burns in the shrinking core mode. The inclusions and the mineral particles formed from the ion-exchangeable m.m. are attached to the receding char surface, and upon collision with other mineral particles they coalesce. At a radius (rtrans) of the char, the diffusion resistance diminishes and the oxygen penetration into the char particle becomes dominant. The combustion proceeds by internal burning where the radius of the char particle remains constant but its porosity increases. The internally burning char particle's outer surface is populated by the randomly allocated mineral inclusions. The char eventually disintegrates by reaching a critical porosity and the coalesced mineral inclusions (fly ash particles) are released. By assuming a certain radius for the char core (this will, generally, be dependent on the char reactivity and temperature), a surface area is determined onto which mineral particles with different size are randomly allocated. The mathematical problem of surface coverage by randomly allocated particles was studied by C. Macks who recommended the following relationship between the initial number of particles on the one hand, and the number of formed clusters (coalesced particles for our case), on the other,:
n = no
--
(-n~ -\ 8 A
exD
My))
(17)
Where A: is area to which the mineral particles are randomly allocated; When there are two m.m. types in the coal, namely inclusions and ion-exchangeable minerals, the ionexchangeable m.m. is distributed onto the inclusions randomly. Due to the large number of ionexchangeable nuclei per inclusion particle, the random distribution can be approximated by assuming that each inclusion would receive an allocation of ion-exchangeable m.m. proportional to its area fraction. After the redistribution of the ion-exchangeable m.m., the total number of particles will be the same as that of the inclusions, however, the distributions of size, and concentration of a chemical compound will be altered. Let the particles formed by the coalescence of ion-exchangeable and included minerals be named as "total" inclusions. The number of these "total" inclusions was not changed by their coalescence with the ion-ex-
changeable ash but it will change by coalescence among the "total" inclusion particles. For calculating the number reduction of the "total" inclusions, the char surface area (A) is approximated by that of a sphere with the radius of rtra,~. The initial number of inclusions (no) can be given as:
no
ainc D~ ffcoal
(18)
M3inc Pinc
where
ainc:
the inclusion content of the coal particle; the coal diameter, Pcoat: the coal density; Pinc: the average inclusion density; M3inc: the third moment of the inclusion's size distribution; In the case of monosize inclusions, Equation 17 can be simplified to: De:
n
e_l/S~2•215
~
(19)
no
where & the ratio of the critical char diameter to the coal original diameter; The expressions given by Equations 17 and 19 w similar results to that obtained by L. Monroe in his computer simulation of the fly ash formation for a swelling type coal. In the calculation of the number reduction of inclusions, the most important parameter is the ratio of the "total" inclusion projected surface area and the area to which the inclusions are randomly allocated. The same parameter was considered by A. Kerstein 7 to govern the final size distribution of the fly ash in his population-balance model. The ash growth number defined by Sh. G. Kangs can also be related to the number reduction of mineral particles by assuming that the separation distance (the average distance until a surface ash particle separates from the char surface) is proportional to the char shell thickness. Experimental The Experimental Coal
General Coal Characteristics: The experimental coal was a Wyoming lignite of 13.4% moisture, 43.8% volatile, 35.9% fixed carbon, 0.15% sulfur and 6.9% ash. The higher heating value was 23.8 MJ/kg. The sulfur free ash consisted of 39% SiO2 20% A1203, 24% CaO and 7% Fe203.
FLY ASH SIZE AND CHEMICAL COMPOSITION The volume based coal size distribution was determined by a laser diffraction particle size analyzer. The coal particle size is an important parameter for determining the initial number of inclusions in a coal particle and the number reduction of the inclusions during the burnout of a coal particle. The volumetric mean value and standard deviation of the distribution were calculated by using the method of lognormal curve fitting. The calculated mean particle size and standard deviation are 37.7 Ixm and 51.8 I~m, respectively.
Mineral Matter Distribution in the Coal: In the random coalescence model, no extraneous m.m. is taken into account. By definition the particles in coal with a density larger than 2.8 g/cm 3 are considered extraneous. Using a sink-float method the extraneous mineral content of the Wyoming lignite was determined as 0.087 wt%. Due to this relatively small amount the effect of the extraneous mineral matter upon the final size distribution of the fly ash was ignored. The ion-exchangeable m.m. was considered to have important effects on the size and chemical composition of the fly ash. Its mass fraction and chemical composition was therefore determined by the method of acetic acid extraction of the coal. The results show that 22% of the total ash content was ion-exchangeable. By taking the chemical composition of the ash determined by the ASTM method and that of the included m.m. determined by CCSEM together with the results of the ion-exchange analysis, the chemical composition of the leached m.m. could be calculated. The results showed that the ion-exchangeable mineral matter consisted of 82 wt% CaO, 12.5 wt% MgO and 5.5 wt% Na20. For the prediction of the concentration distribution of a chosen chemical compound in the fly ash, the concentration distribution of the same chemical compound in the mineral inclusions serves as an input function. In addition, the joint distribution of size and concentration of the same chemical compound is also necessary for the model calculations. The information provided by the CCSEM is sufficient to determine both distribution functions. In the following example SiO2 has been selected as the chemical compound for predicting its concentration distribution in the fly ash. The concentration distribution of SiO2 in the "'total" inclusions is plotted in Figure 1. The SiO2 content of a mineral particle was calculated after the redistribution of the ion-exchangeable m.m. onto the inclusion particles. A technique similar to that used by D. O. Loehden 9 was applied. The results show three distinct peaks in the distribution which indicate that there are three major SiO~ containing mineral types
0.~,~/ L ~ 0.1.1~-
Fly Ash
1139
Total Inclusions Mean=38.1%
Mean=38.3%
t~ 0.0
II
I1
~ o. ~
I
[[
o
9 t 0.0~ ^_r,
1~o 4o-~o
~o ~o do ~o ~o-ffo-16o
SiliCon DIoxltl@ Content(ate'/.)
FIG. 1. Mass based distributions of SiO~ content in the "total" inclusions and in the fly ash. The distribution of SiO~ changes during the burnout of the coal particles due to intensive coalescence. The mean SiO2 content remains constant but its standard deviation decreases due to the homogenizing effect of coalescence.
present in the lignite. The same three peaks are shown also in the joint size and SiO2 content distribution. 4
Size Distribution of Mineral Inclusions: The size distribution of the included minerals is one of the important inputs for the calculation of the final size distribution of the fly ash. The mineral inclusions' size distribution functions were determined by CCSEM. Abelian transformation was used for the stereological correction of the raw data (S.D. Wicksell). lo The moments of the size distribution (M1, M2, M3 and Ms) were also determined from experimental size distribution functions. The volume based size distribution of mineral inclusions in the coal is plotted in Figure 2. The volumetric mean particle size and standard deviation were approximated by using the method of lognormal curve fitting. The calculated mean particle size and standard deviation are 4.3 txm and 3.8 lain, respectively. Pulverized Coal Combustion Studies
Combustion Conditions: The MIT Combustion Research Facility (CRF) was used to burn the experimental Wyoming lignite. The arrangement consisted of a 1.2 m by 1.2 m by 4.75 m combustion chamber, followed by a 3 m long water cooled cylindrical section of 0.5 m diameter leading to the stack. The coal feed rate corresponded to 0.93 MW
1140
COAL COMBUSTION
1.2
~0.8
I Inclusions Mean Size 4.3 um
=
~y
Comparison of the Measured and the Predicted Distribution Functions of Fly Ash Size and Chemical Composition (SiOa)
/
The Model Calculation; the Calculation Procedure
ash
~
0.4 ~02 10
The "'logic diagram" of the calculation of the fly ash size and chemical composition distributions formed by the combustion of a single coal particle is plotted in Figure 3. The calculation starts by determining the most probable coal particle and m.m. properties followed by the calculation of fly ash properties.
Particle Diameter(urn)
FIG. 2. Volume based size distribution functions of the inclusions and the fly ash. The mean particle size and the variance of the inclusion size distribution increase from 4.3 Ixm to 12.6 Ixm and from 3.8 I~m to 7.0 ttm, respectively, due to coalescence during char burnout.
thermal input. The coal was carried by air from a coal silo at 1.21 air/coal mass ratio. The air flow rate was measured by an built-in impact tube, and the flow rate of the coal by a weigh belt. The primary, secondary and tertiary air flows, all monitored by Pitot tubes were preheated to 384 K, 514 K and 594 K, respectively. The total flow rate of the combustion air was set to give 14% excess air.
Measurements; Properties of the Sampled Fly Ash: Flue gas temperature and velocity measurements were taken by a suction pyrometer and a Pitot tube respectively for obtaining isokinetic fly ash samples from the cylindrical section of the facility. Fly ash samples were taken at 6.1 m from the burner, the gas temperature was 1339 K. The fly ash size distribution and chemical composition was determined by CCSEM. The volume based size distribution function of the fly ash is shown in Figure 2. The maximum fly ash particle size was 90 ~m and the calculated mean particle size was 12.6 I~m, and the standard deviation was 7.0 I,Lm. The chemical composition distribution of fly ash was also determined by CCSEM. The results are shown for the SiO2 content in Figure 1. The SiO2 distribution in the fly ash is significantly different from that of the mineral matter indicating extensive mineral coalescence; the standard deviation of the SiO2 content decreased by approximately 10% due to a homogenizing effect of the random m.m. coalescence.
The Most Probable Coal and Mineral Matter Property Distributions: 9 Select a coal particle of size De; 9 Determine the mean ash content and density of coal particles of size De; 9 Calculate the included and ion-exchangeable m.m. content; 9 Take the joint size-chemical composition distribution function of inclusions; 9 Calculate the inclusion size distribution function and its third moment; 9 Calculate the "total" inclusion number in a coal particle (Equ. 18.); 9 Calculate the joint size-chemical composition distribution function of the "total" inclusions (f(x, c)) by using the values of ai,c and aion;
The Most Probable Fly Ash Size Distribution: 9 Calculate the size distribution function of the "total" inclusions; 9 Compute its first, second, third and sixth moments; 9 Calculate the transition radius by using ~ = 0.26; 9 Calculate the number reduction of inclusions due to random coalescence by Equation 17; 9 Compute the size distribution function of the fly ash by Equations 5, 6 and 7;
The Most Probable Fly Ash Chemical Composition Distribution: 9 Calculate the chemical composition distribution of the "total" inclusions; 9 Obtain the third and sixth moments of the size distribution of the "total" inclusions as a function of the chemical composition (M3(c), Mr(c)); 9 Calculate the functions of a],2(t) and A].2(t); 9 Compute the chemical composition distribution by Eq. 11. In the most comprehensive case, even with monosize coal particles, the input parameters such
FLY ASH SIZE AND CHEMICAL COMPOSITION
~" I
8
p~,..,
p,..~
Coal Particle
1141
Coal
)
a,.~
f~.,,(x,c)
a,.,,
\ /
- l
size
\
/
RCM
Fly Ash
enem.
FIG. 3. Logic diagram of calculation for fly ash size and chemical composition distributions originating from a coal particle of a given size.
as inclusion size distribution, inclusion density, coal ash content and density are varying from coal particle to coal particle. In order to obtain the final distribution functions of the fly ash, all the input parameters have to be considered as random variables. Their distribution functions can be obtained by the application of the urn model.
The Variances of the Fly Ash Size and Chemical Composition Distribution: 9 Obtain the joint size-chemical composition distribution of the inclusions; 9 Calculate the number of inclusions of a given size and chemical composition; 9 Consider this value as the mean of a Poisson distribution; 9 Create a new random value by using this Poisson distribution for the number of inclusions of the given size and chemical composition; 9 Repeat the latter procedure for every possible value of inclusion size and chemical composition; (In this way a new random joint sizechemical composition distribution function can be obtained with a random total number of inclusions.)
9 Compute the probability of this new configuration by using the Poisson probabilities of each case; 9 Calculate the total mass of the newly developed inclusion particles; 9 Obtain the total volume of the coal matrix and the mass of ion-exchangeable m.m.; 9 Calculate the new mass ratio of ion-exchangeable m.m. to inclusions; (In this way, a new coal particle is created that can be used as an input to the calculational procedure.) 9 Integrate the Poisson probability weighted fly ash size and chemical composition distribution functions after each run.
Results of Model Calculations; Comparison with Experiments
The Fly Ash Size Distribution: The results of the calculation is plotted in Figure 4. The number based distribution function of the "total" inclusions and of the predicted fly ash are shown. The comparison between the measured and predicted cumulative size distribution functions were made by taking their volume based distributions.
1142
COAL COMBUSTION
1
~ 0.8" ~0.7~ 0.6-
Conclusions
0.9"
Ntm',berBased
IncluR~ons+lon.exch. byCCSF_M
"~ 0.520.40.2
t
~ 0.'1
%
........
T
Particle Diameter(um)
FIG. 4. Comparison of calculated and measured volume based fly ash size distributions (RCM).
The Kolmogorov-Smirnovzl test was applied to evaluate the fit between the two volume based cumulative distribution functions. The results showed that at 95% confidence level, the two cumulative distributions represent the same random variable.
A model of random m.m. coalescence in a burning pulverized coal particle has been developed. The model is capable of predicting the distributions of particle size and chemical composition of the fly ash formed when the coal has been burned. Coal mineral size and chemical composition distributions determined by CCSEM analyses serve as input to the calculations. A combustion model provides limits of the coalescence of the mineral inclusions in the course of the burn-out of the char particle. The calculation proceeds through steps determining the most probable values for the coal mineral size and chemical composition and the mean values and variants of the resultant fly ash size and chemical composition distributions. Experimental results obtained with a Wyoming lignite fired in the MIT Combustion Research Facility showed good agreement between predicted and experimental fly ash size and chemical composition distributions, when CCSEM analytical inputs were used in the random coalescence model.
Nomenclature
The Fly Ash Si02 Concentration Distribution: The cumulative distributions of SiO2 content in the "total" inclusions, in the fly ash are plotted in Figure 5. It can be seen that the SiO2 content distribution changed considerably due to intensive coalescence of the inclusions. The results also indicate that in addition to the coalescence of the ion-exchangeable m.m. and the mineral inclusions there is further coalescence between the "'total" inclusions. The applied Kolmogorov-Smirnov 11 test on the calculated and the predicted cumulative distributions showed similar results to that obtained in the size distribution case.
no: n: An: vi:
Xi;
Mlinc: M3inc: MI:
Mz: M3:
~I ~
M6:
0.8
0.7
~r
.y,.
~0.4 0.3 0.2,} v'~"
~
0~
10
z
L
"""
vT:
_
20
p(x,):
~.~t~dlcllonby]
30
40
60
Silicon Dioxide Content
0
80
90
the first moment of the size distribution of the inclusions; the third moment of the size distribution of the inclusions; the first moment of the size distribution of the captured particles; the second moment of the size distribution of the captured particles; the third moment of the size distribution of the captured particles; the sixth moment of the size distribution of the captured particles; the total volume of a fly ash particle after the coalescence of the captured inclusions with the acceptor particles of size Xi;
by ~2SEM
~
the number of inclusions in a coal particle before coalescence; the number of acceptor particles; the number reduction of inclusions; the volume of captured inclusions coalesced with acceptor inclusions of size
X)
(wt%)
FIG. 5. Calculated and measured cumulative distributions of the SiO2 content in the fly ash (RCM).
the area fraction of the acceptor particles of size xi; the number based size distribution of the f(x): "total" inclusions; Fsize(y): the cumulative number based distribution of the fly ash particles produced by a single coal particle; F*: the incomplete gamma function; /xi: the volume of captured inclusions co-
FLY ASH SIZE AND C H E M I C A L COMPOSITION alesced with acceptor inclusions of size y and concentration c; f(c): the distribution of the concentration of a chemical compound in a inclusion particle; r: the concentration of a chemical compound in a fly ash particle after the random coalescence of the captured particles with the acceptor particles of size y and concentration c; Fchem(t): the cumulative distribution of the concentration of a chemical compound in a fly ash particle; f ( y , c): the joint distribution function of particle size and concentration of a chemical compound of an inclusion particle; A: the area to where the inclusion particles are randomly allocated; De: the coal diameter; rtrans: the transition radius; 6: the ratio of 2*rtra,~/Dc; ainc: the inclusion content of the coal particle; aion: the ion-exchangeable mineral content of the coal particle; PcoaF the coal density; Pinc" the average inclusion density;
2.
3.
4.
5.
6.
7.
Acknowledgments
8.
The research was supported by the New England Power Service Co., ABB-Combustion Engineering, Public Service Electric & Gas Co., Empire State Electric Energy Research Corp., Ente Nazionale per 1" Energia Elettrica and EPRL The authors thank Valerie Wood for her valuable assistance in the microscopic analysis.
9.
10. REFERENCES
11.
I. BEI~R, J. M., SAROTIM,A. F. AND BARTA, L. E.: From Coal Mineral Properties to Fly Ash De-
1143
position Tendencies; A Modeling Route. Engineering Foundation Conference. March 1015, 1991. Florida. HUGGINS, F. E;, KOSMACK, D. A., HUFFMANN, G. P. AND LEE, F. R.: Coal Mineralogies by SEM Automated Image Analysis. Scanning Electron Microscopy, Vol. I., p. 531. 1980. BARTA, L. E., HORVATH, F., BEER, J. M. AND SAROFIM, A. F.: Twenty-Third Symposium International on Combustion, p. 1289, The Combustion Institute, 1991. Transformation of Coal Mineral Matter during Pulverized Coal Combustion. MIT Progress Report. 1991. MACK, C.: The Expected Number of Clumps when Convex Laminae are Placed at Random and with Random Orientation on a Plane Area. Proc. Camb. Phil. Soc. 50, 581-585. MONROE, L. S.: An Experimental and Modeling Study of Residual Fly Ash Formation in Combustion of a Bituminous Coal. Ph.D. Thesis, Department of Chemical Engineering, MIT. 1989, KERSTE1N, A. R.: Population-Balance Model of Physical Transformations of Ash during Char Oxidation. Combust. Flame 77. 187-99 1989. KANt, SH. G.: Fundamental Studies of Mineral Matter Transformation during Pulverized Coal Combustion: Residual Ash Formation. Ph.D. Thesis, Department of Chemical Engineering, MIT, 1991. LOEHDEN, D. O. : The Formation of Fouling and Slagging Deposits in Pulverized Coal Combustion. M.S. Thesis, Department of Mechanical Engineering, MIT, 1988. WICKSELL, S. D.: The Corpuscle Problem. Biometriea, 17. 1925. KOLMOCOROV-SMIRNOV.Test in Von Mises, R: Mathematical Theory of Probability and Statistics, New York, Academic Press. 1964.
COMMENTS Dr. George Domazetis, State Electricity Commission of Victoria, Australia. Your presentation implied that you require, as an input parameter, the final size of the ash particle. Is this the case? Can this approach be considered general and to be applied for all coals? Have you considered only one or two coals and what rank were they?
Author's Reply. The input parameters required for the model are the data of the CCSEM analysis, i.e. the size and chemical composition distributions of the included mineral matter in the coal, the amount of the ion exchangeable mineral matter, and chemical analysis and particle size distribution of
the coal. From these data the Model yields fly ash size and chemical composition distributions. The approach taken is quite general, it is applicable to a wide range of coal types. The coal types selected for example calculations and experiment are very different (subbituminous and bituminous, resp.) yet good agreement was obtained for both these coals between predicted and experimental fly ash property data. Computations were made and experiments carried out for several more coals to broaden our data base for model testing. The data from these studies are being evaluated and will be prepared for publication.
1144
COAL COMBUSTION
R. P. Gupta, University of Newcastle, Australia. Does your model take into account the mineral matter? For example, silica clays, pyrites and aukerites behave differently i.e. molten phases and fragmentation. How would the t e m p e r a t u r e and stoichiometrie ratios influence the resulting ash size distribution? Does the model give coarser fly ash for higher temperature and reducing atmosphere?
Author's Reply. The distribution of the coal minerals chemical composition is one of the inputs to the model. In particular, it serves for the calculations of the mineral matter and fly ash viscosity distributions and for the determination of the fly ash density distribution. These latter data are then used for calculating the particle impaction and sticking probabilities in the fly ash deposition process. In the "Random Coalescence" model it is assumed that during the combustion of the char particle all mineral inclusions (except quartz) are molten and readily coalesce upon touching each other. Their viscosity will, however, vary, dependent upon temperature
and chemical composition. The char combustion submodel takes account of the char particle temperature during combustion: the temperature affects the critical diameter of the burning char below which no further coalescence is assumed to occur, and hence influences the fly ash size in the same sense as implied in the question: higher temperature-coarser fly ash.
Colin Paulson, CSIRO, Australia. Does your model take into consideration particle disintigration and particle collisions? Author's Reply. Our model takes into account particle fragmentation and its effect on mineral matter coalescence, by means of the "'critical diameter" concept in the coal combustion submodel. The effects of particle collisions in the gas flow are not considered.
PREDICTION OF FLY ASH SIZE AND CHEMICAL COMPOSITION DISTRIBUTIONS: THE RANDOM COALESCENCE MODEL L. E. BARTA, M. A. TOQAN, J. M. BEI~R AND A. F. SAROFIM Department of Chemical Engineering Massachusetts Institute of Technology. Cambridge MA, 02139, USA
In the course of combustion of pulverized coal, the coal minerals partially coalesce to form fly ash upon the complete burnout of the combustible matter. The probability of a fly ash particle impacting an obstacle in the flow e.g. heat exchange surface, depends largely on its size, and its retention in a deposit upon the chemical composition. The Random Coalescence Model (RCM) is an essential part of an overall model that follows the coal mineral matter transformation to deposit formation. Computer Controlled Scanning Electron Microscopy (CCSEM) of the size and chemical composition distributions of the mineral inclusions in the coal and analysis of the ion-exchangeable minerals form the inputs to the RCM calculations. A coal char combustion model provides limits for the coalescence of mineral inclusions as the char surface recedes during combustion. The calculation proceeds through steps determining the most probable values for the coal mineral size and chemical composition and the mean values and variants of the resultant fly ash size and chemical composition distributions. Experiments carried out with a Wyoming lignite in the pilot scale MIT Combustion Research Facility gave good agreement with results of the RCM calculations predicting the fly ash size and chemical composition distributions when CCSEM data of the coal minerals were used as input to the model.
Introduction Prediction of fouling tendencies of coal in pulverized coal combustion requires knowledge of the size and chemical composition of the fly ash. The fly ash is formed during combustion from partially coalesced individual mineral inclusions and organically bound coal minerals. There is interest in a model capable of predicting fly ash deposition tendencies from coal mineral properties. One such comprehensive model (Be6r et al. 1) contains a submodel describing the coal mineral matter (m.m.) transformation into fly ash. This entails the prediction of the fly ash size and chemical composition distributions for given values of the initial parameters of the coal e.g. coal particle size, density, ash content, included mineral size distribution, organically bound mineral fraction, etc., and also the random particle to particle variation of the above parameters by a series of weighted integrals. In the present contribution a theoretical study is presented of the random m.m. coalescence in a single coal particle, and fly ash properties are computed from experimentally determined parameters of the coal including the distributions of particle size, density, ash content, and size and chemical cornI135
position of mineral inclusions. Computer Controlled Scanning Electron Microscopy (CCSEM) 2 is used for the characterization of the included coal m.m. in individual coal particles. The Random Coalescence Model Fly Ash Size Distribution:
During the burnout of the coal particle, random coalescence of the mineral inclusions takes place which will reduce their number. This reduction can be given as: no = n + An
(1)
where no: the number of inclusions before coalescence, n: the number of inclusions after coalescence, An: the number reduction of inclusions. In the description of a model of the coalescence process two groups of mineral particles can be distinguished. One of these consisting of "n" number of particles is named the "acceptor" group, and the other in which there are "'An" inclusions is called the "captured" group. The particles in these groups
1136
COAL COMBUSTION
are referred to as "acceptor" and "captured" inclusions, respectively. Both groups of particles have the same size and chemical composition distributions. The captured particles are distributed randomly onto the acceptor particles of size x~; the number of acceptor particles with size xi is ni. The probability of coalescence between these two groups can be given as the fractional surface area (p(xi)) of the particles with size xi in the acceptor group. This formulation of the problem renders it amenable to the application of the probabilistic "urn" model, 3 which provides an analytical solution to the problem of particle to particle variation of mineral properties. In the urn model it is assumed that "balls" of different sizes (mineral inclusions) are randomly thrown into a number of "urns" (coal particles) of uniform size. In the present case, we consider the distribution of An * p(xi) particles having a size distribution off(x) onto ni acceptor particles. The total volume of captured particles that an acceptor particle can receive can be expressed as a gamma random variable with a mean value and variance as given by Equations 2 and 3, respectively. 1
"1"i"
E(vi) = Anp(xi) -- Ma -ni 6 Var(vi) = Anp(xi) -- M 6
p(x,)
(3)
n i X2 =
n
M2
where vi: volume of captured inclusions coalesced with aeceptor inclusions of size xi; Me: the second moment of the size distribution of the captured inclusions; M3: the third moment of the size distribution of the captured inclusions; M6: the sixth moment of the size distribution of the captured inclusions; The fly ash size distribution emerging from the above discussed allocation of the captured particles can be obtained by determining the distribution of the possible total volume of a fly ash particle after coalescence. The total volume of a single fly ash particle can be given as:
function of vi. The final size distribution of the fly ash is then obtained by integrating the size distribution functions of v~ for all possible values of i, and the cumulative distribution function of the fly ash so obtained can be given as: F,i~(y) =
fo'f(x)
a(x), A 6 (y - x3) dx
where An x 2 M~
~(x)
n M2 M6
X=
6
+ ,,,,
(4)
where v~: the total volume of a fly ash particle after the coalescence of the captured inclusions with the acceptor particles of size xi; The distribution function of the random variable v~ can be obtained directly from the distribution
6 M3
(6)
(7)
rr M6
F*: the incomplete gamma function; The step by step derivation of Eq. 5 is given elsewhere. 4
Fly Ash Chemical Composition Distribution: In the derivation of the chemical composition distribution, a similar procedure to that for size distribution is followed, except that in this case a joint size-chemical concentration distribution, f(x, c) is used. The random coalescence of mineral particles is described in the following by using the urn model and the concept of acceptor and captured particles. The number of acceptor particles of size y and chemical content c is designated by n(y, c). The probability that the captured particles coalesce with acceptor particles of size y and chemical compound concentration c, is given by the area fraction of these particles: p(y, c). The captured particles of chemical content ci are distributed randomly onto acceptor particles of size y and chemical compound concentration c. The total volume of captured particles coalesced with acceptor inclusions of size y and concentration c, is a gamma random variable (/xi), according to the urn model. 2 Its mean value and variance can be given by:
n(v, c) u2 E(ix~) = An f(c~) A c i n M2
x~ r ,'T =
(5)
1
• - -
n(y, c)
7'/"
M3 -
6
(8)
Var(/zi) = An f(ci) Aci n(y, c) y2 n Me
1 X
-
-
n(v, c)
M6
(#
(9)
FLY ASH SIZE AND CHEMICAL COMPOSITION Where /-~i = the volume of captured inclusions coalesced with acceptor inclusions of size y and concentration c. When an acceptor and a captured particle coalesce, the chemical composition of the emerging fly ash particle can be different from that of its parents. By taking into account the coalescence of the captured particles with all their possible chemical composition (/~, i = 1 ...), the concentration ~', of a chosen chemical compound in a fly ash particle can be given
Ol 1 ~
1137
An- y2 fot n M2 A1 f(c) (t - c)
-
71"
x M3(c) -- dc 6
(14)
I
f(c) (c - t) M3(c) 6 3-2 =
1
2
(15)
as: y3 7/"
c "/"
=
6
y3 77"
--
6
+ E c~/z~ i ~
(10)
a.z
An y'2 f l = ~ Az f(c) (c -- t) n Me
+ E /.ti i
7t"
The distribution of r can be obtained from convolution theory by using the distribution functions of kei (i = 1 ... ~). The final distribution function of the concentration of a chemical compound in a fly ash particle can be obtained by integrating the distribution functions of ~" for all possible values of y and c. The cumulative distribution of the concentration of a chemical compound in the fly ash can then be given as:
• M3(c)-dc 6
(16)
An
where - - is the captured particles as a fraction of n the number of acceptors; The details of the derivation of equations 12 . . . 16 are given elsewhere, a
Reduction of the Number of Inclusions During Coal Burnout: The following input parameters are necessary for the calculation of the final distribution functions of the fly ash size and the concentration of a chemical compound:
where
g(c, y, t) = Prob.(r < t)
(12)
is the cumulative distribution of a chemical species after capture by acceptor inclusions of a given size and concentration
a . / the size distribution of the acceptor particles; b . / the distribution of the concentration of a chemical compound, for example SiO2; c . / the joint distribution function of the size and the concentration of a chemical compound;
l fo __xL le 1-
when t -<
~6(t-c) F(ot2----~)
al,
- --if- (t - c)
where
))
dx
when t > c
d . / the number reduction of inclusions during the coal particle burnout. t
fo
71"
f(c) (t - c) M3(c) - dc 6
A1 =
t
n
(13)
The first three input parameters mined by CCSEM. The value of number reduction, however, has to In order to determine this value, model has to be assumed.
can be deterthe inclusion be calculated. a combustion
COAL COMBUSTION
1138
After the volatile matter in the coal particle burns away, an external diffusion limited combustion is assumed i.e. the char particle burns in the shrinking core mode. The inclusions and the mineral particles formed from the ion-exchangeable m.m. are attached to the receding char surface, and upon collision with other mineral particles they coalesce. At a radius (rtrans) of the char, the diffusion resistance diminishes and the oxygen penetration into the char particle becomes dominant. The combustion proceeds by internal burning where the radius of the char particle remains constant but its porosity increases. The internally burning char particle's outer surface is populated by the randomly allocated mineral inclusions. The char eventually disintegrates by reaching a critical porosity and the coalesced mineral inclusions (fly ash particles) are released. By assuming a certain radius for the char core (this will, generally, be dependent on the char reactivity and temperature), a surface area is determined onto which mineral particles with different size are randomly allocated. The mathematical problem of surface coverage by randomly allocated particles was studied by C. Macks who recommended the following relationship between the initial number of particles on the one hand, and the number of formed clusters (coalesced particles for our case), on the other,:
n = no
--
(-n~ -\ 8 A
exD
My))
(17)
Where A: is area to which the mineral particles are randomly allocated; When there are two m.m. types in the coal, namely inclusions and ion-exchangeable minerals, the ionexchangeable m.m. is distributed onto the inclusions randomly. Due to the large number of ionexchangeable nuclei per inclusion particle, the random distribution can be approximated by assuming that each inclusion would receive an allocation of ion-exchangeable m.m. proportional to its area fraction. After the redistribution of the ion-exchangeable m.m., the total number of particles will be the same as that of the inclusions, however, the distributions of size, and concentration of a chemical compound will be altered. Let the particles formed by the coalescence of ion-exchangeable and included minerals be named as "total" inclusions. The number of these "total" inclusions was not changed by their coalescence with the ion-ex-
changeable ash but it will change by coalescence among the "total" inclusion particles. For calculating the number reduction of the "total" inclusions, the char surface area (A) is approximated by that of a sphere with the radius of rtra,~. The initial number of inclusions (no) can be given as:
no
ainc D~ ffcoal
(18)
M3inc Pinc
where
ainc:
the inclusion content of the coal particle; the coal diameter, Pcoat: the coal density; Pinc: the average inclusion density; M3inc: the third moment of the inclusion's size distribution; In the case of monosize inclusions, Equation 17 can be simplified to: De:
n
e_l/S~2•215
~
(19)
no
where & the ratio of the critical char diameter to the coal original diameter; The expressions given by Equations 17 and 19 w similar results to that obtained by L. Monroe in his computer simulation of the fly ash formation for a swelling type coal. In the calculation of the number reduction of inclusions, the most important parameter is the ratio of the "total" inclusion projected surface area and the area to which the inclusions are randomly allocated. The same parameter was considered by A. Kerstein 7 to govern the final size distribution of the fly ash in his population-balance model. The ash growth number defined by Sh. G. Kangs can also be related to the number reduction of mineral particles by assuming that the separation distance (the average distance until a surface ash particle separates from the char surface) is proportional to the char shell thickness. Experimental The Experimental Coal
General Coal Characteristics: The experimental coal was a Wyoming lignite of 13.4% moisture, 43.8% volatile, 35.9% fixed carbon, 0.15% sulfur and 6.9% ash. The higher heating value was 23.8 MJ/kg. The sulfur free ash consisted of 39% SiO2 20% A1203, 24% CaO and 7% Fe203.
FLY ASH SIZE AND CHEMICAL COMPOSITION The volume based coal size distribution was determined by a laser diffraction particle size analyzer. The coal particle size is an important parameter for determining the initial number of inclusions in a coal particle and the number reduction of the inclusions during the burnout of a coal particle. The volumetric mean value and standard deviation of the distribution were calculated by using the method of lognormal curve fitting. The calculated mean particle size and standard deviation are 37.7 Ixm and 51.8 I~m, respectively.
Mineral Matter Distribution in the Coal: In the random coalescence model, no extraneous m.m. is taken into account. By definition the particles in coal with a density larger than 2.8 g/cm 3 are considered extraneous. Using a sink-float method the extraneous mineral content of the Wyoming lignite was determined as 0.087 wt%. Due to this relatively small amount the effect of the extraneous mineral matter upon the final size distribution of the fly ash was ignored. The ion-exchangeable m.m. was considered to have important effects on the size and chemical composition of the fly ash. Its mass fraction and chemical composition was therefore determined by the method of acetic acid extraction of the coal. The results show that 22% of the total ash content was ion-exchangeable. By taking the chemical composition of the ash determined by the ASTM method and that of the included m.m. determined by CCSEM together with the results of the ion-exchange analysis, the chemical composition of the leached m.m. could be calculated. The results showed that the ion-exchangeable mineral matter consisted of 82 wt% CaO, 12.5 wt% MgO and 5.5 wt% Na20. For the prediction of the concentration distribution of a chosen chemical compound in the fly ash, the concentration distribution of the same chemical compound in the mineral inclusions serves as an input function. In addition, the joint distribution of size and concentration of the same chemical compound is also necessary for the model calculations. The information provided by the CCSEM is sufficient to determine both distribution functions. In the following example SiO2 has been selected as the chemical compound for predicting its concentration distribution in the fly ash. The concentration distribution of SiO2 in the "'total" inclusions is plotted in Figure 1. The SiO2 content of a mineral particle was calculated after the redistribution of the ion-exchangeable m.m. onto the inclusion particles. A technique similar to that used by D. O. Loehden 9 was applied. The results show three distinct peaks in the distribution which indicate that there are three major SiO~ containing mineral types
0.~,~/ L ~ 0.1.1~-
Fly Ash
1139
Total Inclusions Mean=38.1%
Mean=38.3%
t~ 0.0
II
I1
~ o. ~
I
[[
o
9 t 0.0~ ^_r,
1~o 4o-~o
~o ~o do ~o ~o-ffo-16o
SiliCon DIoxltl@ Content(ate'/.)
FIG. 1. Mass based distributions of SiO~ content in the "total" inclusions and in the fly ash. The distribution of SiO~ changes during the burnout of the coal particles due to intensive coalescence. The mean SiO2 content remains constant but its standard deviation decreases due to the homogenizing effect of coalescence.
present in the lignite. The same three peaks are shown also in the joint size and SiO2 content distribution. 4
Size Distribution of Mineral Inclusions: The size distribution of the included minerals is one of the important inputs for the calculation of the final size distribution of the fly ash. The mineral inclusions' size distribution functions were determined by CCSEM. Abelian transformation was used for the stereological correction of the raw data (S.D. Wicksell). lo The moments of the size distribution (M1, M2, M3 and Ms) were also determined from experimental size distribution functions. The volume based size distribution of mineral inclusions in the coal is plotted in Figure 2. The volumetric mean particle size and standard deviation were approximated by using the method of lognormal curve fitting. The calculated mean particle size and standard deviation are 4.3 txm and 3.8 lain, respectively. Pulverized Coal Combustion Studies
Combustion Conditions: The MIT Combustion Research Facility (CRF) was used to burn the experimental Wyoming lignite. The arrangement consisted of a 1.2 m by 1.2 m by 4.75 m combustion chamber, followed by a 3 m long water cooled cylindrical section of 0.5 m diameter leading to the stack. The coal feed rate corresponded to 0.93 MW
1140
COAL COMBUSTION
1.2
~0.8
I Inclusions Mean Size 4.3 um
=
~y
Comparison of the Measured and the Predicted Distribution Functions of Fly Ash Size and Chemical Composition (SiOa)
/
The Model Calculation; the Calculation Procedure
ash
~
0.4 ~02 10
The "'logic diagram" of the calculation of the fly ash size and chemical composition distributions formed by the combustion of a single coal particle is plotted in Figure 3. The calculation starts by determining the most probable coal particle and m.m. properties followed by the calculation of fly ash properties.
Particle Diameter(urn)
FIG. 2. Volume based size distribution functions of the inclusions and the fly ash. The mean particle size and the variance of the inclusion size distribution increase from 4.3 Ixm to 12.6 Ixm and from 3.8 I~m to 7.0 ttm, respectively, due to coalescence during char burnout.
thermal input. The coal was carried by air from a coal silo at 1.21 air/coal mass ratio. The air flow rate was measured by an built-in impact tube, and the flow rate of the coal by a weigh belt. The primary, secondary and tertiary air flows, all monitored by Pitot tubes were preheated to 384 K, 514 K and 594 K, respectively. The total flow rate of the combustion air was set to give 14% excess air.
Measurements; Properties of the Sampled Fly Ash: Flue gas temperature and velocity measurements were taken by a suction pyrometer and a Pitot tube respectively for obtaining isokinetic fly ash samples from the cylindrical section of the facility. Fly ash samples were taken at 6.1 m from the burner, the gas temperature was 1339 K. The fly ash size distribution and chemical composition was determined by CCSEM. The volume based size distribution function of the fly ash is shown in Figure 2. The maximum fly ash particle size was 90 ~m and the calculated mean particle size was 12.6 I~m, and the standard deviation was 7.0 I,Lm. The chemical composition distribution of fly ash was also determined by CCSEM. The results are shown for the SiO2 content in Figure 1. The SiO2 distribution in the fly ash is significantly different from that of the mineral matter indicating extensive mineral coalescence; the standard deviation of the SiO2 content decreased by approximately 10% due to a homogenizing effect of the random m.m. coalescence.
The Most Probable Coal and Mineral Matter Property Distributions: 9 Select a coal particle of size De; 9 Determine the mean ash content and density of coal particles of size De; 9 Calculate the included and ion-exchangeable m.m. content; 9 Take the joint size-chemical composition distribution function of inclusions; 9 Calculate the inclusion size distribution function and its third moment; 9 Calculate the "total" inclusion number in a coal particle (Equ. 18.); 9 Calculate the joint size-chemical composition distribution function of the "total" inclusions (f(x, c)) by using the values of ai,c and aion;
The Most Probable Fly Ash Size Distribution: 9 Calculate the size distribution function of the "total" inclusions; 9 Compute its first, second, third and sixth moments; 9 Calculate the transition radius by using ~ = 0.26; 9 Calculate the number reduction of inclusions due to random coalescence by Equation 17; 9 Compute the size distribution function of the fly ash by Equations 5, 6 and 7;
The Most Probable Fly Ash Chemical Composition Distribution: 9 Calculate the chemical composition distribution of the "total" inclusions; 9 Obtain the third and sixth moments of the size distribution of the "total" inclusions as a function of the chemical composition (M3(c), Mr(c)); 9 Calculate the functions of a],2(t) and A].2(t); 9 Compute the chemical composition distribution by Eq. 11. In the most comprehensive case, even with monosize coal particles, the input parameters such
FLY ASH SIZE AND CHEMICAL COMPOSITION
~" I
8
p~,..,
p,..~
Coal Particle
1141
Coal
)
a,.~
f~.,,(x,c)
a,.,,
\ /
- l
size
\
/
RCM
Fly Ash
enem.
FIG. 3. Logic diagram of calculation for fly ash size and chemical composition distributions originating from a coal particle of a given size.
as inclusion size distribution, inclusion density, coal ash content and density are varying from coal particle to coal particle. In order to obtain the final distribution functions of the fly ash, all the input parameters have to be considered as random variables. Their distribution functions can be obtained by the application of the urn model.
The Variances of the Fly Ash Size and Chemical Composition Distribution: 9 Obtain the joint size-chemical composition distribution of the inclusions; 9 Calculate the number of inclusions of a given size and chemical composition; 9 Consider this value as the mean of a Poisson distribution; 9 Create a new random value by using this Poisson distribution for the number of inclusions of the given size and chemical composition; 9 Repeat the latter procedure for every possible value of inclusion size and chemical composition; (In this way a new random joint sizechemical composition distribution function can be obtained with a random total number of inclusions.)
9 Compute the probability of this new configuration by using the Poisson probabilities of each case; 9 Calculate the total mass of the newly developed inclusion particles; 9 Obtain the total volume of the coal matrix and the mass of ion-exchangeable m.m.; 9 Calculate the new mass ratio of ion-exchangeable m.m. to inclusions; (In this way, a new coal particle is created that can be used as an input to the calculational procedure.) 9 Integrate the Poisson probability weighted fly ash size and chemical composition distribution functions after each run.
Results of Model Calculations; Comparison with Experiments
The Fly Ash Size Distribution: The results of the calculation is plotted in Figure 4. The number based distribution function of the "total" inclusions and of the predicted fly ash are shown. The comparison between the measured and predicted cumulative size distribution functions were made by taking their volume based distributions.
1142
COAL COMBUSTION
1
~ 0.8" ~0.7~ 0.6-
Conclusions
0.9"
Ntm',berBased
IncluR~ons+lon.exch. byCCSF_M
"~ 0.520.40.2
t
~ 0.'1
%
........
T
Particle Diameter(um)
FIG. 4. Comparison of calculated and measured volume based fly ash size distributions (RCM).
The Kolmogorov-Smirnovzl test was applied to evaluate the fit between the two volume based cumulative distribution functions. The results showed that at 95% confidence level, the two cumulative distributions represent the same random variable.
A model of random m.m. coalescence in a burning pulverized coal particle has been developed. The model is capable of predicting the distributions of particle size and chemical composition of the fly ash formed when the coal has been burned. Coal mineral size and chemical composition distributions determined by CCSEM analyses serve as input to the calculations. A combustion model provides limits of the coalescence of the mineral inclusions in the course of the burn-out of the char particle. The calculation proceeds through steps determining the most probable values for the coal mineral size and chemical composition and the mean values and variants of the resultant fly ash size and chemical composition distributions. Experimental results obtained with a Wyoming lignite fired in the MIT Combustion Research Facility showed good agreement between predicted and experimental fly ash size and chemical composition distributions, when CCSEM analytical inputs were used in the random coalescence model.
Nomenclature
The Fly Ash Si02 Concentration Distribution: The cumulative distributions of SiO2 content in the "total" inclusions, in the fly ash are plotted in Figure 5. It can be seen that the SiO2 content distribution changed considerably due to intensive coalescence of the inclusions. The results also indicate that in addition to the coalescence of the ion-exchangeable m.m. and the mineral inclusions there is further coalescence between the "'total" inclusions. The applied Kolmogorov-Smirnov 11 test on the calculated and the predicted cumulative distributions showed similar results to that obtained in the size distribution case.
no: n: An: vi:
Xi;
Mlinc: M3inc: MI:
Mz: M3:
~I ~
M6:
0.8
0.7
~r
.y,.
~0.4 0.3 0.2,} v'~"
~
0~
10
z
L
"""
vT:
_
20
p(x,):
~.~t~dlcllonby]
30
40
60
Silicon Dioxide Content
0
80
90
the first moment of the size distribution of the inclusions; the third moment of the size distribution of the inclusions; the first moment of the size distribution of the captured particles; the second moment of the size distribution of the captured particles; the third moment of the size distribution of the captured particles; the sixth moment of the size distribution of the captured particles; the total volume of a fly ash particle after the coalescence of the captured inclusions with the acceptor particles of size Xi;
by ~2SEM
~
the number of inclusions in a coal particle before coalescence; the number of acceptor particles; the number reduction of inclusions; the volume of captured inclusions coalesced with acceptor inclusions of size
X)
(wt%)
FIG. 5. Calculated and measured cumulative distributions of the SiO2 content in the fly ash (RCM).
the area fraction of the acceptor particles of size xi; the number based size distribution of the f(x): "total" inclusions; Fsize(y): the cumulative number based distribution of the fly ash particles produced by a single coal particle; F*: the incomplete gamma function; /xi: the volume of captured inclusions co-
FLY ASH SIZE AND C H E M I C A L COMPOSITION alesced with acceptor inclusions of size y and concentration c; f(c): the distribution of the concentration of a chemical compound in a inclusion particle; r: the concentration of a chemical compound in a fly ash particle after the random coalescence of the captured particles with the acceptor particles of size y and concentration c; Fchem(t): the cumulative distribution of the concentration of a chemical compound in a fly ash particle; f ( y , c): the joint distribution function of particle size and concentration of a chemical compound of an inclusion particle; A: the area to where the inclusion particles are randomly allocated; De: the coal diameter; rtrans: the transition radius; 6: the ratio of 2*rtra,~/Dc; ainc: the inclusion content of the coal particle; aion: the ion-exchangeable mineral content of the coal particle; PcoaF the coal density; Pinc" the average inclusion density;
2.
3.
4.
5.
6.
7.
Acknowledgments
8.
The research was supported by the New England Power Service Co., ABB-Combustion Engineering, Public Service Electric & Gas Co., Empire State Electric Energy Research Corp., Ente Nazionale per 1" Energia Elettrica and EPRL The authors thank Valerie Wood for her valuable assistance in the microscopic analysis.
9.
10. REFERENCES
11.
I. BEI~R, J. M., SAROTIM,A. F. AND BARTA, L. E.: From Coal Mineral Properties to Fly Ash De-
1143
position Tendencies; A Modeling Route. Engineering Foundation Conference. March 1015, 1991. Florida. HUGGINS, F. E;, KOSMACK, D. A., HUFFMANN, G. P. AND LEE, F. R.: Coal Mineralogies by SEM Automated Image Analysis. Scanning Electron Microscopy, Vol. I., p. 531. 1980. BARTA, L. E., HORVATH, F., BEER, J. M. AND SAROFIM, A. F.: Twenty-Third Symposium International on Combustion, p. 1289, The Combustion Institute, 1991. Transformation of Coal Mineral Matter during Pulverized Coal Combustion. MIT Progress Report. 1991. MACK, C.: The Expected Number of Clumps when Convex Laminae are Placed at Random and with Random Orientation on a Plane Area. Proc. Camb. Phil. Soc. 50, 581-585. MONROE, L. S.: An Experimental and Modeling Study of Residual Fly Ash Formation in Combustion of a Bituminous Coal. Ph.D. Thesis, Department of Chemical Engineering, MIT. 1989, KERSTE1N, A. R.: Population-Balance Model of Physical Transformations of Ash during Char Oxidation. Combust. Flame 77. 187-99 1989. KANt, SH. G.: Fundamental Studies of Mineral Matter Transformation during Pulverized Coal Combustion: Residual Ash Formation. Ph.D. Thesis, Department of Chemical Engineering, MIT, 1991. LOEHDEN, D. O. : The Formation of Fouling and Slagging Deposits in Pulverized Coal Combustion. M.S. Thesis, Department of Mechanical Engineering, MIT, 1988. WICKSELL, S. D.: The Corpuscle Problem. Biometriea, 17. 1925. KOLMOCOROV-SMIRNOV.Test in Von Mises, R: Mathematical Theory of Probability and Statistics, New York, Academic Press. 1964.
COMMENTS Dr. George Domazetis, State Electricity Commission of Victoria, Australia. Your presentation implied that you require, as an input parameter, the final size of the ash particle. Is this the case? Can this approach be considered general and to be applied for all coals? Have you considered only one or two coals and what rank were they?
Author's Reply. The input parameters required for the model are the data of the CCSEM analysis, i.e. the size and chemical composition distributions of the included mineral matter in the coal, the amount of the ion exchangeable mineral matter, and chemical analysis and particle size distribution of
the coal. From these data the Model yields fly ash size and chemical composition distributions. The approach taken is quite general, it is applicable to a wide range of coal types. The coal types selected for example calculations and experiment are very different (subbituminous and bituminous, resp.) yet good agreement was obtained for both these coals between predicted and experimental fly ash property data. Computations were made and experiments carried out for several more coals to broaden our data base for model testing. The data from these studies are being evaluated and will be prepared for publication.
1144
COAL COMBUSTION
R. P. Gupta, University of Newcastle, Australia. Does your model take into account the mineral matter? For example, silica clays, pyrites and aukerites behave differently i.e. molten phases and fragmentation. How would the t e m p e r a t u r e and stoichiometrie ratios influence the resulting ash size distribution? Does the model give coarser fly ash for higher temperature and reducing atmosphere?
Author's Reply. The distribution of the coal minerals chemical composition is one of the inputs to the model. In particular, it serves for the calculations of the mineral matter and fly ash viscosity distributions and for the determination of the fly ash density distribution. These latter data are then used for calculating the particle impaction and sticking probabilities in the fly ash deposition process. In the "Random Coalescence" model it is assumed that during the combustion of the char particle all mineral inclusions (except quartz) are molten and readily coalesce upon touching each other. Their viscosity will, however, vary, dependent upon temperature
and chemical composition. The char combustion submodel takes account of the char particle temperature during combustion: the temperature affects the critical diameter of the burning char below which no further coalescence is assumed to occur, and hence influences the fly ash size in the same sense as implied in the question: higher temperature-coarser fly ash.
Colin Paulson, CSIRO, Australia. Does your model take into consideration particle disintigration and particle collisions? Author's Reply. Our model takes into account particle fragmentation and its effect on mineral matter coalescence, by means of the "'critical diameter" concept in the coal combustion submodel. The effects of particle collisions in the gas flow are not considered.