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Trace elements emission factors from coal combustion
The Science of the Total Environment, 65 (1987) 95-107 Elsevier Science Publishers B.V., Amsterdam - - Printed in The Netherlands
TRACE ELEMENTS COMBUSTION
95
EMISSION FACTORS FROM COAL
S. CERNUSCHI and M. GIUGLIANO Istituto di Ingegneria Sanitaria, Politecnico di Milano, Via Gorlini 1, 20151 Milano (Italy)
(Received October 30th, 1986; accepted December llth, 1986)
ABSTRACT In the national energy policies of most of the European countries, including Italy, a large utilization of coal fired power plants to produce electricity is foreseen for the coming years. This will lead to an increase in the mobilization of trace elements in the environment, especially in the atmosphere. An accurate knowledge of the factors related to the mobilization, particularly the enrichment mechanism of trace elements in the emitted particulate matter, is of fundamental significance for environmental impact assessment studies. In this work an analytical method is presented to calculate the trace element emission factors taking into account the enrichment of trace elements, dependence on the size of the emitted particles and the probability density function of the particulate size distribution. The resulting equation is applied to the calculation of the emission factors for a typical pulverized coal fired power plant and to the evaluation of the expected global atmospheric mobilization of trace elements for the European Community Countries by the year 1990. INTRODUCTION The problems a r i s i n g from n u c l e a r p o w e r p r o d u c t i o n , the u n c e r t a i n t y in the t r e n d of fuel costs a n d t h e limited d e v e l o p m e n t and p r o d u c t i o n of a l t e r n a t i v e s o u r c e s of energy, m a k e coal an i m p o r t a n t s o u r c e of p r i m a r y energy, with large possibilities for e m p l o y m e n t even in n o n - p r o d u c i n g countries. F o r 1990, it is foreseen t h a t the m o r e developed c o u n t r i e s will use solid fuels to provide ~ 10-30% of t h e i r e n e r g y demand. The most i m p o r t a n t e n v i r o n m e n t a l i m p a c t of coal c o m b u s t i o n is due to the g a s e o u s emissions a n d p a r t i c u l a t e s from p o i n t a n d diffuse sources. The p a r t i c u l a t e m a t t e r emitted t h r o u g h the s t a c k has a t t r a c t e d a lot of a t t e n t i o n d u r i n g the last 10 years: it is e n r i c h e d - - i n c o m p a r i s o n with b o t t o m and fly ash collected by t h e p a r t i c u l a t e c o n t r o l e q u i p m e n t - - m a i n l y in t h o s e elements t h a t are p o t e n t i a l l y toxic (e.g. As, Cd, Pb, Sb, Se, Zn) [1]. The emission f a c t o r s for the t o t a l p a r t i c u l a t e emitted are easily derived from the ash c o n t e n t of coal, the type of b u r n e r a n d the p a r t i c u l a t e c o n t r o l equipm e n t used [2]. A similar e v a l u a t i o n for t r a c e elements is n o t as easy: t h e i r emission is c o m p l i c a t e d by e n r i c h m e n t p h e n o m e n a w h i c h give rise to an i r r e g u l a r d i s t r i b u t i o n of the elements b e t w e e n the different c o m b u s t i o n residues (bottom ash, fly ash, p a r t i c u l a t e m a t t e r a n d s t a c k gases). F u r t h e r m o r e ,
0048-9697/87/$03.50
© 1987 Elsevier Science Publishers B.V.
96
the emission factors of the trace elements emitted with the particulate matter have become very important for an impact assessment of the emitted particulate debris on its ultimate receptors (atmospheric aerosol, soil and fresh water). The aim of this paper is the formulation of an analytical method for the evaluation of trace elements emission factors. The method uses reliable models describing the dependence of trace element enrichment upon the granulometric size of particulates emitted, the size distribution of which is assumed to be log-normal. ENRICHMENT MECHANISMS Almost every experimental study concerning the behaviour of trace elements during the combustion of coal has demonstrated a significant size-dependent enrichment of certain elements in particulate phases [3-10]. The shape of the element concentration versus particle size profiles exhibits some variations between the different studies, mainly related to the trace element considered, the combustion conditions (type of boiler, residence time) and the chemical and physical nature of the coal burned. However, it is now generally recognized that the enrichment of some elements on the smaller particle sizes is significantly higher than that occurring on the larger fly ash particles, especially for the most volatile elements. While the particle size dependence of the trace elements concentration has been widely demonstrated, there are no definitive experimental data to fully describe the enrichment mechanism, especially for the submicron size range, which, from an environmental point of view, is the most interesting. One of the first field studies was conducted by Natusch and co-workers [3], who obtained a reasonable fit of their experimental data utilizing an inverse relationship between concentration and particle diameter, derived from purely geometrical considerations: C
=
a + b'dp
1
(1)
They explain the observed behaviour with a volatilization-condensation mechanism of the elements showing pronounced concentration trends, assuming the element volatilizes in the combustion chamber and subsequently condenses or adsorbs evenly onto the surface of fly ash particles, giving rise to the greatest deposited mass per unit weight for the smallest particles. Flagan and Friedlander [11] also studied the volatilization-condensation model and proposed an inverse dependence of the trace element concentration on the square of the particle diameter: C = a + b.dp 2
(2)
With their proposed dependence, Flagan and Friedlander were able to describe Natusch's data. Subsequent work by Smith [12] demonstrates that such a
97 dependence shows a good agreement with theory and allows us to describe the concentration-particle size data over most of the size range. Some disagreement between workers arises when the concentration-particle size data are examined in the submicron size range. In an experimental study conducted on several size fractions of fly ash collected from two pulverized coal fired plants, Smith [12] found that the concentrations of trace elements which show significant enrichments in the larger size fraction tend to become fairly constant in the well-resolved submicron size range, extending as low as 0.15#m (physical median diameter). In explaining the observed phenomena Smith suggests a different formation mechanism for the particles in the 0.1-1~m size range which involves the bursting of larger particles, due to internal gas release, followed by coagulation and concurrent condensation of volatilized material. However, Smith points out that the importance of the bursting mechanism in determining the formation of submicron particles would depend on the combustion conditions and the type of coal burned, so one does not necessarily have to expect a constant enrichment for the smallest particle sizes in all coal fired plants. Even if some disagreement exists for the enrichment phenomena, it is now generally accepted that the volatilization-condensation mechanism plays the main role in determining the observed fly ash enrichment profiles of trace elements, with a possible minor influence of other chemical processes such as surface segregation [13,14]. However, in view of the physical and chemical complexity of the combustion process and the extreme variability of the main factors that influence the enrichment, it has not yet been possible to explain the trace elements concentration dependence on particle size with a theoretical approach of general validity. EVALUATION OF THE TRACE ELEMENT EMISSION FACTOR For the reasons described above, there is a need for an evaluation of emission factors of the trace elements which considers the enrichment of each element and its variation with size in the emitted particulate matter. Generally the enrichment of each element is quantified by a so-called enrichment factor (EF), defined as the ratio between the concentration of the element before and after the process which causes the enrichment, usually normalized to an element that does not show any distinct redistribution between particles of different size, typically A1, Ti, Fe: EF
= (CI/CS)D/(CI/CS) v
(3)
where C I is the trace element concentration,CS the concentration of the reference element utilized for the normalization and the subscripts D and U indicate the ratios after and before the process producing the enrichment, respectively. All the data reported in the literature, on which the formulation of the above mechanisms is based, describe the enrichment factor, EF, as a
98
size-dependent property of fly ash. The dependence of the EF upon the particle size for homogeneous data [3, 5, 6, 15], and for the average data from different sources [16], is described by the relationship: EF = a . d ~
(4)
Equation (4) is in accordance with the fundamental volatilization-condensation model proposed to explain the enrichment phenomena [3, 11, 15]. Smith's data, and the derived model, show an enrichment factor fairly constant in the well-resolved sub-micron size range. Equation (4) can also be used for the description of such data, if b --- 0 is assumed, for particle size diameters in the range where the EF appears fairly constant (0.15-O.75 #m for Smith's data). The numerical values of constants a and b of Eqn (4), derived from the data reported by Gladney et al. [5], Coles et al. [6] and Smith et al. [15], and the corresponding coefficient of the correlation between EF and the particle size dp, are given in Table 1. The values of the constants were estimated by the least squares method. In the range 0.15-0.75 pm, the EF values for Smith's data can be described by the relationship EF = a
(5)
because EF is not dependent upon particle size. In Eqn (5), a is the constant of Eqn (4) estimated in the range 0.75-33 ~m. (The data from Smith are available up to 200 pm mean particle diameter; however, particle sizes > 30 pm can be TABLE 1 C o r r e l a t i o n coefficient o f e n r i c h m e n t f a c t o r (EF) v e r s u s particle size d a t a (EF = a d ~ ) Reference: Size r a n g e (urn):
Coles et al. [6] 2.4-18.5 a
As Cd Cr Cu Mn Mo Ni Pb Sb Sr V Zn
b
r
27.50 13.60 3.27 3.10
-1.08 -1.21 -0.40 -0.36
0.99 0.99 0.99 0.98
9.35 2.74 9.47 17.56 1.82 5.16 16.5
-0.83 -0.22 -0.65 -0.99 -0.21 -0.64 -0.98
0.99 0.91 b 0.99 0.99 0.93 b 0.99 0.98
ab=O. N o t s i g n i f i c a n t a t 95%.
G l a d n e y et al. [5] 0.175-30
S m i t h et al. [15] > 0.75-33
a
a
b
r
b
Smith et al. [15] a 0.15-0.75 r a
a'
8.6
-0.56
0.88
10.2
-0.76
0.98
10.2
9.17
1.63
-0.17
0.70 b
1.71 9.84 6.01
-0.11 -0.39 -0.50
0.56 b 0.86 0.84
3.57 4.58 1.71 5.6 3.15 10.22
-0.52 -0.22 -0.12 -0.49 -0.24 -0.56
0.96 0.89 0.88 0.96 0.93 0.98
3.57 4.58 1.71 5.60 3.15 10.22
3.13 3.66 1.67 5.43 2.83 9.20
1.12 2.53 5.99
0.13 -0.20 -0.60
0.98 0.81 0.96
1.12 2.53 5.99
1.10 2.03 4.33
1.65
-0.07
0.70 b
99
considered of little interest, because they are normally entirely collected by the control devices.) In the last column of Table 1, the value of the constant a' calculated by least squares interpolation of the EF experimental data is given for comparison with a. The difference between a and a' does not appear to be meaningful. In conclusion, Eqn (4) allows a fairly accurate description of the relationship EF-dD for most of the data reported in the literature. However, large differences can be observed between the constants for the different data series. These differences mainly arise from differences in combustion conditions (combustion chamber, oxygen excess, residence time), coal characteristics, size range considered and standardization element used in the EF evaluation. The trace element emission factor (TEEF) can thus be evaluated by: TEEF
= g~a" d~p(dp)d(dp)
(6)
0
where K is the trace element emission factor without considering the enrichment effect, a-d~ is the size enrichment function describing the enrichment factor-particle size relationship and p(dp) is the probability density of the particulate size distribution. The K value can be calculated by the following expression: g
= (1 -
E)(TPEF)(CC)(CA)
(7)
where E is the total efficiency of particulate collectors, TPEF is the total particulate emission factor for an uncontrolled source, CC is the trace element concentration in feed coal and CA is the coal/ash ratio in the feed coal. As far as a suitable particulate size distribution is concerned, it is well known that an ideal function model should have the following characteristics: (i) it should be able to describe the distributions over the entire size range of the particulate emission (0.001-100pm); (ii) number, surface area and volume or mass distribution should be equally well described over the entire range; (iii) the function should have some physical basis. It is very difficult to satisfy all these conditions at the same time; however, the log-normal distribution is nearest to the ideal situation. The log-normal model has been fitted with good agreement to very many particulate samples, obtained before and after the collection devices [17-20]. Furthermore, the log-normal distribution has been found equally suitable for the number, the surface area and the volume or mass of particulate. Since the overall efficiency of the collectors keeps the distribution of the emitted particulate substantially unchanged, the log-normal distribution can still be utilized for p(dp) in (6). If the dependence of EF upon dp is described by Eqn (4), the integral I in (6) can be found (see Appendix): I = a exp [b In Mg + (b In Sg)2/2]
(8)
100 where Mg and Sg are the geometric mean and the standard geometric deviation of the distribution. In the case where the dependence of EF upon dp is described by (4) and (5) for d, < 1 pm, the integral is (see Appendix): I = (a/2){[1 e r f ( u / 2 1 / 2 ) ] + [exp(blnMg + ( b l n S g ) 2 / 2 ) ] [ 1
-
erf(U/21/2)]}
(9)
where Mg and Sg are as previously described, erf is the error function, and: U u
= =
-
lnMg/lnSg
-
blnSg
lnMg/lnSg
Introducing I in to Eqn (6), we finally obtain for TEEF: TEEF -- (1 - E ) ( T P E F ) ( C C ) ( C A ) ( I )
(10)
APPLICATION AND CONCLUSIONS An example of the application of this method is in the evaluation of the TEEF for a typical coal fired power plant. The plant burns pulverized coal, and is equipped with electrostatic precipitators. The mass distribution of the particulate emitted was found to be log-normal in the range 1-100pm, with a geometric mean of 8.4 p and a standard geometric deviation of 2.2 [20]. The TEEF values calculated by (8) and (10) versus the observed values are shown in Figs. 1-3. The use of Eqn (5) does not give results which are substantially different from those calculated by (4), because the mass fraction of particles < 0.75#m in diameter is negligible (0.8% for a log-normal particulate size distribution with M s = 8.4 #m and Sg = 2.2). Using Coles' values for a and b [6], Eqn (8) and (10) describe with good accuracy the experimental TEEF values of nearly all elements considered (r = 0.99). There is a significant over-
~
ic
sr
8
N1
0.; O:
0.05 V
~
°v
r=0,99
MO
0.02
/ oc_,d , , , , , ~ , , 0.010.0~ 005 Q1 0.2 0.5 1 2 5 10 20 TEEFob6erved(g/tl
Fig. 1. Scatter diagram of observed TEEF values versus TEEF values calculated by ( 8 ) and (10), with a and b derived from Coles' data (r /> 0.60 is significantat 95%).
101 ,.~20
.
.
.
.
.
.
~
,
' / Sr~/
/ I
~ol~O0/
: "~ 0.1
/ Mo/A
0.05
/
r = 0.98 "
s 0
0.02 ~
o,~ o~
o.Ss o:~ o12
o.'s
~
~
-~
~
2o
TEEF observed (g/t)
Fig. 2. Scatter diagram of observed TEEF values versus TEEF values calculated by (8) and (10), with a and b derived from Smith's data (r I> 0.63 is significant at 95%). 2
i
i
i
i
F
~
/ ~, oa o~
~
0:1
r=O.6a
0.~
0.0~
001
J
I
0~02
006
l
Q1
I
0.2
I
I
G5 1 TEEF obeerved ( g / t }
Fig. 3. Scatter diagram of observed TEEF values versus TEEF values calculated by (8) and (10), with a and b derived from Gladney's data (r t> 0.81 is significant at 95%).
estimation for Sb, whose concentration, however, was near the analytical detection limit, and a slight underestimation for V. Also for Smith's values for a and b [12] the agreement with the experimental emission factors was good (r = 0.89), with more significant deviations for As and Zn, both of which are underestimated. The estimation obtained using the values of Gladney [5] was not as accurate (r = 0.63), with significant underestimations for As and Zn and overestimations for Sb and Pb. The disagreements observed are difficult to explain and obviously depend on the different operating conditions described previously. The method outlined, however, allows a good evaluation of the trace elements emission factors from the coal composition, the efficiency of the
102
particulate control equipment and size distribution parameters of the particulate emitted. It is also possible to utilize the method in any evaluation of the expected emissions for different control devices (typically electrostatic precipitators and bag filters) from their fractional removal efficiencies and the outlet particulate size distribution. Obviously, the method retains all the uncertainties in the parameters describing the enrichment phenomena. Another example of the application of the proposed method is to the prediction of the expected amount of coal to be burnt by 1990 in the power plants of nine countries of the European Community [21, 22]. The evaluation of the contribution of the fraction emitted into the atmosphere to the total amount of trace elements, MT, mobilized in the environment can be based on the following input data: (i) the mean trace element content (CC) of power plant coal of the European Community (Table 2) [21]; (ii) total particulate emission factor (TPEF) for a typical pulverized coal fired power plant equipped with an electrostatic precipitator (total collection efficiency 99.3% required to meet the standard in the Directive Proposal of CEC [23]); (iii) the mean coal/ash ratio (CA = 10); (iv) values of constants a and b derived from Coles et al. [6] (Table 1); (v) values of distribution parameter for single mode log-normal distribution (Mg = 4.9 pm, S~ = 4), selected as representative of typical particulate emitted from coal fired power plants equipped with electrostatic precipitators [18]. For the European Community the expected amount of coal to be burnt in power plants by 1990 is 240 × 106 metric tons [21], with a total estimated trace element mobilization into the environment reported in Table 2 (MT). The third TABLE 2 Trace element mean content (CC) of coal to be burnt in EC countries by 1990 and derived total trace element mobilization (MT) expected for the same year. TEEF give the trace element emission factors calculated by (8) and (10) and MA is the subsequent atmospheric mobilization. The last column gives the percentage of the total mobilization emitted into the atmosphere Trace element
CC
MT (tons year 1)
TEEF (g t o n - 1)
MA
(ppm)
As Cd Cr Cu Mo Ni Pb Sb Se V Zn
13.9 0.4 34.2 23.4 6.3 40.4 44.3 2.5 2.1 57.9 80.9
3340 100 8210 5620 1500 9700 10640 600 505 13900 19420
1.16 0.02 0.38 0.25 0.17 0.45 1.23 0.13 0.31 0.88 3.89
278 4.3 91.2 61.2 40.3 107.7 295 30.8 73.6 211.7 934.4
%
(tons year- 1) 8.3 4.3 1.1 1.1 2.7 1.1 2.8 5.1 14.6 1.5 4.8
103 c o l u m n of T a b l e 2 r e p o r t s the emission f a c t o r for e a c h t r a c e e l e m e n t ( T E E F ) c a l c u l a t e d using Eqns (8) and (10), and the s u b s e q u e n t a t m o s p h e r i c mobilization (MA) derived from the t o t a l e x p e c t e d coal usage by 1990. T h e last c o l u m n of Table 2 gives the p e r c e n t a g e of the t o t a l t r a c e elements mobilized emitted into the a t m o s p h e r e as p a r t i c u l a t e matter. T h e c o m p a r i s o n of o u r results with d a t a derived from the few mass b a l a n c e studies r e p o r t e d in the l i t e r a t u r e must obviously be based on a n a l o g o u s o p e r a t i n g conditions, especially for the t o t a l p a r t i c u l a t e emitted t h r o u g h the stack. T h e c o m p a r i s o n with the a t m o s p h e r i c mobilization d a t a d e r i v e d by Sabbioni et al. [22] from U.S.A. mass b a l a n c e studies is r e p o r t e d in T a b l e 3 as the p e r c e n t a g e of t r a c e e l e m e n t mobilized into the a t m o s p h e r e (columns 1 and 3) and as the same p e r c e n t a g e n o r m a l i z e d to the p e r c e n t a g e of t o t a l ash emitted t h r o u g h the stack (columns 2 and 4, % normalized -- % mobilized/% of the t o t a l ash emitted). T h e n o r m a l i z a t i o n allows a c o m p a r i s o n i n d e p e n d e n t of the o p e r a t i n g conditions (fly ash p r o d u c t i o n ) and of the efficiency of the p a r t i c u l a t e c o n t r o l devices. The d a t a show fairly good a g r e e m e n t : this confirms t h a t the e n r i c h m e n t p h e n o m e n a , i n d i c a t e d by the mass b a l a n c e s results, c a n be well described by an a n a l y t i c a l m e t h o d whose basic i n p u t data, for the e v a l u a t i o n of the t r a c e elements emission factor, are the coal compositions. F u r t h e r d a t a r e q u i r e d (fly ash production, p a r t i c u l a t e c o n t r o l efficiency, d i s t r i b u t i o n p a r a m e t e r s of the emitted p a r t i c u l a t e m a t t e r ) can be derived from the different o p e r a t i n g conditions. APPENDIX If the d e p e n d e n c e of E F u p o n dp is described by Eqn (4) and p(dp) is a single-mode log-normal distribution, the i n t e g r a l on the r i g h t - h a n d side of Eqn (6) becomes: TABLE 3 Atmospheric mobilization calculated in the present work compared with analogous data derived from Sabbioni et al. [22]. The percentages of the total ash emitted, utilized in the normalization, are 0.56% (present work) and 0.45% (Sabbioni et al.) Trace element As Cd Cr Cu Mo Ni Pb Sb Se V Zn
Present work
Sabbioni et al. [22]
% mobilized
% normalized
% mobilized
% normalized
8.3 4.3 1.1 1.1 2.7 1.1 2.8 5.1 14.6 1.5 4.8
14.8 7.7 2.0 2.0 4.8 2.0 5.0 9.1 26.1 2.7 8.6
2.9 2.7 1.0 0.7 1.2 0.4 1.8 2.4 14.3 1.0 1.8
6.4 6.0 2.2 15 2.7 0.9 4.0 5.3 31.8 2.2 4.0
104 oo
I = fa" d~{exp - [(ln(dp/Mg))2/2(ln Sg)2]/d, In Sg(2~)~/2}d(dp)
(I)
0
If
z = ln(dp/Mg)/ln Sg
(II)
then z(0) =
- oo
(III)
z(oo) = oo
(IV)
Substituting for dp the value obtained in (II) and for the limits of integration the values in (III) and (IV) gives: oo
I = [a/(2~) 1/2] exp (b In Mg) ~ exp (bz In Sg - z2/2)dz
(v)
-co
From tables of standard integrals: i exp ( - p2x2 + qx)dx
= exp (q2/4p2)(~l/2/p)
(VI)
-oo
In the present case, p = 2 -1/2
(VII)
q = blnSg
(VIII)
so finally one obtains: I = a exp [b In Mg + (b In 8g)2/2]
(IX)
If the dependence of EF upon dp is described, in the size range where the enrichment becomes constant, by Eqn (5), and p(dp) is still a single-mode log-normal distribution, the integral in right-hand side of (6) has to change to: 1
I =
{a{exp - [(ln(dp/Mg))2/2(lnSg)2]/dplnSg(2~)l/2 }d(dp) ./ 0
oo
+ f a . d~{exp - [(ln(dp/Mg))2/2(ln Sg)2]/dp In Sg(2~)1/2}d(dp)
(X)
1
where dp = 1 #m is the assumed value of the particulate matter diameter below which the enrichment becomes fairly constant with the particle size (see text for details). Substituting again for dp the value obtained with the transformation outlined in (II), and for the integration limits those obtained in (III) and (IV), leads to:
I = [a/(2r) 1/2] i exp ( - z2/2) dz + [a/(2r) 1/2] exp (b In Mg) o0
105
i
(XI)
exp ( - z2/2 + b In S g z ) d z
U
where u is the value of z for d p = 1 #m: u =
(XII)
- lnMg/lnSg
From tables of standard integrals: i exp ( - q 2 x 2 ) d x
=
[(~)1/2/2q] [1 + erf(qu)]
for q > 0
(XIII)
--OD
where erf is the error function. Applying (XIII) to the first integral of the right-hand side of (XI), we have q = 2-1/2
(XIV)
so one obtains: i exp ( - z2/2) dz = 0r/2) 1/2 [1 - erf (u/2~/2)]
(XV)
--OD
The second integral of the right-hand side of (XI) can easily be handled if the integration variable z is transformed to a new variable using: Z = z + B
(XVI)
where B =
- b In Sg
(XVII)
Applying this transformation, the integrand function becomes: exp ( - zS/2 + b In S g z )
=
exp [ ( - Z 2 + B2)/2]
(XVIII)
and the integral transforms to: 00
OO
j e x p ( - z2/2 + b l n S g z ) d z
=
exp (S2/2)lex p ( - Z2/2)dZ
(XIX)
U
where U
=
u + B
=
-
lnMg/lnSg-
blnSg
(XX)
In this way, the integral in (XIX) becomes a Gaussian function whose solution, derived from standard integral tables, is: ao
I
exp ( - Z 2 / 2 ) d Z
=
(~/2) '/2 [1 - erf(U/2'/2)]
where erf is, as in (XV), the error function.
(XXI)
106 U t i l i z i n g t h e s t a n d a r d i n t e g r a l s o u t l i n e d i n (XV) a n d (XXI), t h e s o l u t i o n o f t h e i n t e g r a l I i n (XI) c a n b e f o u n d : I
=
• [1 -
(a/2){[1 + erf(u/21t2)] + [exp ( b l n M g +
(blnSg)2/2)]
e r f (U/21/2)]}
(XXII)
w i t h u a n d U as d e f i n e d i n (XII) a n d (XX), r e s p e c t i v e l y . REFERENCES 1 2 3 4 5 6 7 8
9 10
11
12 13 14 15 16 17 18 19
T.F. Yen, The Role of Trace Metals in Petroleum, Ann Arbor Press, Ann Arbor, Michigan, 1975. US-EPA, Supplement 13 for compilation of air pollutant emission factors, Research Triangle Park, NC, 1982. D.F.S. Natusch, J.R. Wallace and C.A. Evans Jr., Toxic trace elements: preferential concentration in respirable particles. Science, 183 (1974) 202-204. J.M. Kaakinen, R.M. Jorden, M.H. Lawasani and R.E. West, Trace element behaviour in coal-fired plant, Environ. Sci. Technol., 9 (1975) 862 869. E.S. Gladney, J.A. Small, G.E. Gordon and W.H. Zoller, Composition and size distribution of in-stack particulate material at a coal-fired power plant, Atmos. Environ., 10 (1976) 1071-1077. D.G. Coles, R.C. Ragaini, J.M. Ondov, G.L. Fisher, D. Silberman and B. Prentice, Chemical studies of stack fly ash from a coal fired power plant, Environ. Sci. Technol., 13 (1979) 455-459. R.D. Smith, J.A. Campbell and K.K. Nielson, Characterization and formation of submicron particles in coal-fired plants, Atmos. Environ., 13 (1979) 607-617. J.M. Ondov, R.C. Ragaini and A.H. Biermann, Emission and particle size distribution of minor and trace elements at two western coal-fired power plants equipped with cold-side electrostatic precipitators, Environ. Sci. Technol., 13 (1979) 946-953. G.R. Markowski and R. Filby, Trace element concentration as function of particle size in fly ash from a pulverized coal utility boiler, Environ. Sci. Technol., 19 (1985) 796-804. M. Neville, R.J. Quann, B.S. Haynes and A.F. Sarofim, Vaporization and condensation of mineral matter during pulverized coal combustion. 8th Symp. Combustion, The Combustion Institute, 1981, pp. 1257-1274. R.C. Flagan and S.K. Friedlander, Particle formation in pulverized coal combustion--a review paper presented at the Symposium on Aerosol Science and Technology at the 82th National Meeting of the AICHE, Atlantic City, NJ, 1976. R.D. Smith, The trace element chemistry of coal during combustion and the emission from coal-fired plants, Prog. Energy Combust. Sci., 6 (1980) 53-119. C.D.Stinespring and G.W. Stewart, Surface enrichment of aluminosilicate minerals and coal combustion ash particles, Atmos. Environ., 15 (1981) 307 313. R.D. Smith and D.R. Baer, Fly ash surface formation and segregation during heating, Atmos. Environ., 17 (1983) 1399-1409. R.D. Smith, J.A. Campbell and K.K. Nielson, Concentration dependence upon particle size of volatilized elements in fly ash, Environ. Sci. Technol., 13 (1979) 553-558. J.M. Pacyna, Emission factors of trace metals from coal-fired power plants, Norwegian Institute for Air Research, Tekn. Rapp. N. 14/81, 1981. P. Bacci, G.M. Marcazzan, P. Redaelli and A. Ventura, Particulate emission and element behaviours in a large coal power plant, I1 Nuovo Cimento, 8C (1985) 907-922. R.J. Cheng, V.A. Mohen, I.I. Shen, M. Current and J.B. Hudson, Characterization of particulates from power plants, J. Air Pollut. Control Assoc., 26 (1976) 787-790. R.B. Candelaria and G.E. Palomino, Characterization of Navajo generating station emission measured during the June~July 1979 VISTTA field program, Atmos. Environ., 16 (1982) 2287-2298.
107 20
21
22
23
M. Cioni and L. Bonfanti, Characterization of solid emissions from a coal fired power plant, International Conference on Aerosols in Science Medicine and Technology, Garmish, 25-27 Sept. 1985. E. Sabbioni, L. Goetz, A. Springer and R. Pietra, Trace metals from coal-fired power plants: derivation of an average data base for assessment studies of the situation in the European Communities, Sci. Total Environ., 29 (1983) 213-217. E. Sabbioni, L. Goetz and G. Bignoli, Health and environmental implication of trace metals released from coal-fired power plants: an assessment study of the situation in the European Community, Sci. Total Environ., 40 (1984) 141-154. Concil of European Community, Directive proposal CoM (83) 704 def. (19/12/1983) EC Official Journal N. C49.
TRACE ELEMENTS COMBUSTION
95
EMISSION FACTORS FROM COAL
S. CERNUSCHI and M. GIUGLIANO Istituto di Ingegneria Sanitaria, Politecnico di Milano, Via Gorlini 1, 20151 Milano (Italy)
(Received October 30th, 1986; accepted December llth, 1986)
ABSTRACT In the national energy policies of most of the European countries, including Italy, a large utilization of coal fired power plants to produce electricity is foreseen for the coming years. This will lead to an increase in the mobilization of trace elements in the environment, especially in the atmosphere. An accurate knowledge of the factors related to the mobilization, particularly the enrichment mechanism of trace elements in the emitted particulate matter, is of fundamental significance for environmental impact assessment studies. In this work an analytical method is presented to calculate the trace element emission factors taking into account the enrichment of trace elements, dependence on the size of the emitted particles and the probability density function of the particulate size distribution. The resulting equation is applied to the calculation of the emission factors for a typical pulverized coal fired power plant and to the evaluation of the expected global atmospheric mobilization of trace elements for the European Community Countries by the year 1990. INTRODUCTION The problems a r i s i n g from n u c l e a r p o w e r p r o d u c t i o n , the u n c e r t a i n t y in the t r e n d of fuel costs a n d t h e limited d e v e l o p m e n t and p r o d u c t i o n of a l t e r n a t i v e s o u r c e s of energy, m a k e coal an i m p o r t a n t s o u r c e of p r i m a r y energy, with large possibilities for e m p l o y m e n t even in n o n - p r o d u c i n g countries. F o r 1990, it is foreseen t h a t the m o r e developed c o u n t r i e s will use solid fuels to provide ~ 10-30% of t h e i r e n e r g y demand. The most i m p o r t a n t e n v i r o n m e n t a l i m p a c t of coal c o m b u s t i o n is due to the g a s e o u s emissions a n d p a r t i c u l a t e s from p o i n t a n d diffuse sources. The p a r t i c u l a t e m a t t e r emitted t h r o u g h the s t a c k has a t t r a c t e d a lot of a t t e n t i o n d u r i n g the last 10 years: it is e n r i c h e d - - i n c o m p a r i s o n with b o t t o m and fly ash collected by t h e p a r t i c u l a t e c o n t r o l e q u i p m e n t - - m a i n l y in t h o s e elements t h a t are p o t e n t i a l l y toxic (e.g. As, Cd, Pb, Sb, Se, Zn) [1]. The emission f a c t o r s for the t o t a l p a r t i c u l a t e emitted are easily derived from the ash c o n t e n t of coal, the type of b u r n e r a n d the p a r t i c u l a t e c o n t r o l equipm e n t used [2]. A similar e v a l u a t i o n for t r a c e elements is n o t as easy: t h e i r emission is c o m p l i c a t e d by e n r i c h m e n t p h e n o m e n a w h i c h give rise to an i r r e g u l a r d i s t r i b u t i o n of the elements b e t w e e n the different c o m b u s t i o n residues (bottom ash, fly ash, p a r t i c u l a t e m a t t e r a n d s t a c k gases). F u r t h e r m o r e ,
0048-9697/87/$03.50
© 1987 Elsevier Science Publishers B.V.
96
the emission factors of the trace elements emitted with the particulate matter have become very important for an impact assessment of the emitted particulate debris on its ultimate receptors (atmospheric aerosol, soil and fresh water). The aim of this paper is the formulation of an analytical method for the evaluation of trace elements emission factors. The method uses reliable models describing the dependence of trace element enrichment upon the granulometric size of particulates emitted, the size distribution of which is assumed to be log-normal. ENRICHMENT MECHANISMS Almost every experimental study concerning the behaviour of trace elements during the combustion of coal has demonstrated a significant size-dependent enrichment of certain elements in particulate phases [3-10]. The shape of the element concentration versus particle size profiles exhibits some variations between the different studies, mainly related to the trace element considered, the combustion conditions (type of boiler, residence time) and the chemical and physical nature of the coal burned. However, it is now generally recognized that the enrichment of some elements on the smaller particle sizes is significantly higher than that occurring on the larger fly ash particles, especially for the most volatile elements. While the particle size dependence of the trace elements concentration has been widely demonstrated, there are no definitive experimental data to fully describe the enrichment mechanism, especially for the submicron size range, which, from an environmental point of view, is the most interesting. One of the first field studies was conducted by Natusch and co-workers [3], who obtained a reasonable fit of their experimental data utilizing an inverse relationship between concentration and particle diameter, derived from purely geometrical considerations: C
=
a + b'dp
1
(1)
They explain the observed behaviour with a volatilization-condensation mechanism of the elements showing pronounced concentration trends, assuming the element volatilizes in the combustion chamber and subsequently condenses or adsorbs evenly onto the surface of fly ash particles, giving rise to the greatest deposited mass per unit weight for the smallest particles. Flagan and Friedlander [11] also studied the volatilization-condensation model and proposed an inverse dependence of the trace element concentration on the square of the particle diameter: C = a + b.dp 2
(2)
With their proposed dependence, Flagan and Friedlander were able to describe Natusch's data. Subsequent work by Smith [12] demonstrates that such a
97 dependence shows a good agreement with theory and allows us to describe the concentration-particle size data over most of the size range. Some disagreement between workers arises when the concentration-particle size data are examined in the submicron size range. In an experimental study conducted on several size fractions of fly ash collected from two pulverized coal fired plants, Smith [12] found that the concentrations of trace elements which show significant enrichments in the larger size fraction tend to become fairly constant in the well-resolved submicron size range, extending as low as 0.15#m (physical median diameter). In explaining the observed phenomena Smith suggests a different formation mechanism for the particles in the 0.1-1~m size range which involves the bursting of larger particles, due to internal gas release, followed by coagulation and concurrent condensation of volatilized material. However, Smith points out that the importance of the bursting mechanism in determining the formation of submicron particles would depend on the combustion conditions and the type of coal burned, so one does not necessarily have to expect a constant enrichment for the smallest particle sizes in all coal fired plants. Even if some disagreement exists for the enrichment phenomena, it is now generally accepted that the volatilization-condensation mechanism plays the main role in determining the observed fly ash enrichment profiles of trace elements, with a possible minor influence of other chemical processes such as surface segregation [13,14]. However, in view of the physical and chemical complexity of the combustion process and the extreme variability of the main factors that influence the enrichment, it has not yet been possible to explain the trace elements concentration dependence on particle size with a theoretical approach of general validity. EVALUATION OF THE TRACE ELEMENT EMISSION FACTOR For the reasons described above, there is a need for an evaluation of emission factors of the trace elements which considers the enrichment of each element and its variation with size in the emitted particulate matter. Generally the enrichment of each element is quantified by a so-called enrichment factor (EF), defined as the ratio between the concentration of the element before and after the process which causes the enrichment, usually normalized to an element that does not show any distinct redistribution between particles of different size, typically A1, Ti, Fe: EF
= (CI/CS)D/(CI/CS) v
(3)
where C I is the trace element concentration,CS the concentration of the reference element utilized for the normalization and the subscripts D and U indicate the ratios after and before the process producing the enrichment, respectively. All the data reported in the literature, on which the formulation of the above mechanisms is based, describe the enrichment factor, EF, as a
98
size-dependent property of fly ash. The dependence of the EF upon the particle size for homogeneous data [3, 5, 6, 15], and for the average data from different sources [16], is described by the relationship: EF = a . d ~
(4)
Equation (4) is in accordance with the fundamental volatilization-condensation model proposed to explain the enrichment phenomena [3, 11, 15]. Smith's data, and the derived model, show an enrichment factor fairly constant in the well-resolved sub-micron size range. Equation (4) can also be used for the description of such data, if b --- 0 is assumed, for particle size diameters in the range where the EF appears fairly constant (0.15-O.75 #m for Smith's data). The numerical values of constants a and b of Eqn (4), derived from the data reported by Gladney et al. [5], Coles et al. [6] and Smith et al. [15], and the corresponding coefficient of the correlation between EF and the particle size dp, are given in Table 1. The values of the constants were estimated by the least squares method. In the range 0.15-0.75 pm, the EF values for Smith's data can be described by the relationship EF = a
(5)
because EF is not dependent upon particle size. In Eqn (5), a is the constant of Eqn (4) estimated in the range 0.75-33 ~m. (The data from Smith are available up to 200 pm mean particle diameter; however, particle sizes > 30 pm can be TABLE 1 C o r r e l a t i o n coefficient o f e n r i c h m e n t f a c t o r (EF) v e r s u s particle size d a t a (EF = a d ~ ) Reference: Size r a n g e (urn):
Coles et al. [6] 2.4-18.5 a
As Cd Cr Cu Mn Mo Ni Pb Sb Sr V Zn
b
r
27.50 13.60 3.27 3.10
-1.08 -1.21 -0.40 -0.36
0.99 0.99 0.99 0.98
9.35 2.74 9.47 17.56 1.82 5.16 16.5
-0.83 -0.22 -0.65 -0.99 -0.21 -0.64 -0.98
0.99 0.91 b 0.99 0.99 0.93 b 0.99 0.98
ab=O. N o t s i g n i f i c a n t a t 95%.
G l a d n e y et al. [5] 0.175-30
S m i t h et al. [15] > 0.75-33
a
a
b
r
b
Smith et al. [15] a 0.15-0.75 r a
a'
8.6
-0.56
0.88
10.2
-0.76
0.98
10.2
9.17
1.63
-0.17
0.70 b
1.71 9.84 6.01
-0.11 -0.39 -0.50
0.56 b 0.86 0.84
3.57 4.58 1.71 5.6 3.15 10.22
-0.52 -0.22 -0.12 -0.49 -0.24 -0.56
0.96 0.89 0.88 0.96 0.93 0.98
3.57 4.58 1.71 5.60 3.15 10.22
3.13 3.66 1.67 5.43 2.83 9.20
1.12 2.53 5.99
0.13 -0.20 -0.60
0.98 0.81 0.96
1.12 2.53 5.99
1.10 2.03 4.33
1.65
-0.07
0.70 b
99
considered of little interest, because they are normally entirely collected by the control devices.) In the last column of Table 1, the value of the constant a' calculated by least squares interpolation of the EF experimental data is given for comparison with a. The difference between a and a' does not appear to be meaningful. In conclusion, Eqn (4) allows a fairly accurate description of the relationship EF-dD for most of the data reported in the literature. However, large differences can be observed between the constants for the different data series. These differences mainly arise from differences in combustion conditions (combustion chamber, oxygen excess, residence time), coal characteristics, size range considered and standardization element used in the EF evaluation. The trace element emission factor (TEEF) can thus be evaluated by: TEEF
= g~a" d~p(dp)d(dp)
(6)
0
where K is the trace element emission factor without considering the enrichment effect, a-d~ is the size enrichment function describing the enrichment factor-particle size relationship and p(dp) is the probability density of the particulate size distribution. The K value can be calculated by the following expression: g
= (1 -
E)(TPEF)(CC)(CA)
(7)
where E is the total efficiency of particulate collectors, TPEF is the total particulate emission factor for an uncontrolled source, CC is the trace element concentration in feed coal and CA is the coal/ash ratio in the feed coal. As far as a suitable particulate size distribution is concerned, it is well known that an ideal function model should have the following characteristics: (i) it should be able to describe the distributions over the entire size range of the particulate emission (0.001-100pm); (ii) number, surface area and volume or mass distribution should be equally well described over the entire range; (iii) the function should have some physical basis. It is very difficult to satisfy all these conditions at the same time; however, the log-normal distribution is nearest to the ideal situation. The log-normal model has been fitted with good agreement to very many particulate samples, obtained before and after the collection devices [17-20]. Furthermore, the log-normal distribution has been found equally suitable for the number, the surface area and the volume or mass of particulate. Since the overall efficiency of the collectors keeps the distribution of the emitted particulate substantially unchanged, the log-normal distribution can still be utilized for p(dp) in (6). If the dependence of EF upon dp is described by Eqn (4), the integral I in (6) can be found (see Appendix): I = a exp [b In Mg + (b In Sg)2/2]
(8)
100 where Mg and Sg are the geometric mean and the standard geometric deviation of the distribution. In the case where the dependence of EF upon dp is described by (4) and (5) for d, < 1 pm, the integral is (see Appendix): I = (a/2){[1 e r f ( u / 2 1 / 2 ) ] + [exp(blnMg + ( b l n S g ) 2 / 2 ) ] [ 1
-
erf(U/21/2)]}
(9)
where Mg and Sg are as previously described, erf is the error function, and: U u
= =
-
lnMg/lnSg
-
blnSg
lnMg/lnSg
Introducing I in to Eqn (6), we finally obtain for TEEF: TEEF -- (1 - E ) ( T P E F ) ( C C ) ( C A ) ( I )
(10)
APPLICATION AND CONCLUSIONS An example of the application of this method is in the evaluation of the TEEF for a typical coal fired power plant. The plant burns pulverized coal, and is equipped with electrostatic precipitators. The mass distribution of the particulate emitted was found to be log-normal in the range 1-100pm, with a geometric mean of 8.4 p and a standard geometric deviation of 2.2 [20]. The TEEF values calculated by (8) and (10) versus the observed values are shown in Figs. 1-3. The use of Eqn (5) does not give results which are substantially different from those calculated by (4), because the mass fraction of particles < 0.75#m in diameter is negligible (0.8% for a log-normal particulate size distribution with M s = 8.4 #m and Sg = 2.2). Using Coles' values for a and b [6], Eqn (8) and (10) describe with good accuracy the experimental TEEF values of nearly all elements considered (r = 0.99). There is a significant over-
~
ic
sr
8
N1
0.; O:
0.05 V
~
°v
r=0,99
MO
0.02
/ oc_,d , , , , , ~ , , 0.010.0~ 005 Q1 0.2 0.5 1 2 5 10 20 TEEFob6erved(g/tl
Fig. 1. Scatter diagram of observed TEEF values versus TEEF values calculated by ( 8 ) and (10), with a and b derived from Coles' data (r /> 0.60 is significantat 95%).
101 ,.~20
.
.
.
.
.
.
~
,
' / Sr~/
/ I
~ol~O0/
: "~ 0.1
/ Mo/A
0.05
/
r = 0.98 "
s 0
0.02 ~
o,~ o~
o.Ss o:~ o12
o.'s
~
~
-~
~
2o
TEEF observed (g/t)
Fig. 2. Scatter diagram of observed TEEF values versus TEEF values calculated by (8) and (10), with a and b derived from Smith's data (r I> 0.63 is significant at 95%). 2
i
i
i
i
F
~
/ ~, oa o~
~
0:1
r=O.6a
0.~
0.0~
001
J
I
0~02
006
l
Q1
I
0.2
I
I
G5 1 TEEF obeerved ( g / t }
Fig. 3. Scatter diagram of observed TEEF values versus TEEF values calculated by (8) and (10), with a and b derived from Gladney's data (r t> 0.81 is significant at 95%).
estimation for Sb, whose concentration, however, was near the analytical detection limit, and a slight underestimation for V. Also for Smith's values for a and b [12] the agreement with the experimental emission factors was good (r = 0.89), with more significant deviations for As and Zn, both of which are underestimated. The estimation obtained using the values of Gladney [5] was not as accurate (r = 0.63), with significant underestimations for As and Zn and overestimations for Sb and Pb. The disagreements observed are difficult to explain and obviously depend on the different operating conditions described previously. The method outlined, however, allows a good evaluation of the trace elements emission factors from the coal composition, the efficiency of the
102
particulate control equipment and size distribution parameters of the particulate emitted. It is also possible to utilize the method in any evaluation of the expected emissions for different control devices (typically electrostatic precipitators and bag filters) from their fractional removal efficiencies and the outlet particulate size distribution. Obviously, the method retains all the uncertainties in the parameters describing the enrichment phenomena. Another example of the application of the proposed method is to the prediction of the expected amount of coal to be burnt by 1990 in the power plants of nine countries of the European Community [21, 22]. The evaluation of the contribution of the fraction emitted into the atmosphere to the total amount of trace elements, MT, mobilized in the environment can be based on the following input data: (i) the mean trace element content (CC) of power plant coal of the European Community (Table 2) [21]; (ii) total particulate emission factor (TPEF) for a typical pulverized coal fired power plant equipped with an electrostatic precipitator (total collection efficiency 99.3% required to meet the standard in the Directive Proposal of CEC [23]); (iii) the mean coal/ash ratio (CA = 10); (iv) values of constants a and b derived from Coles et al. [6] (Table 1); (v) values of distribution parameter for single mode log-normal distribution (Mg = 4.9 pm, S~ = 4), selected as representative of typical particulate emitted from coal fired power plants equipped with electrostatic precipitators [18]. For the European Community the expected amount of coal to be burnt in power plants by 1990 is 240 × 106 metric tons [21], with a total estimated trace element mobilization into the environment reported in Table 2 (MT). The third TABLE 2 Trace element mean content (CC) of coal to be burnt in EC countries by 1990 and derived total trace element mobilization (MT) expected for the same year. TEEF give the trace element emission factors calculated by (8) and (10) and MA is the subsequent atmospheric mobilization. The last column gives the percentage of the total mobilization emitted into the atmosphere Trace element
CC
MT (tons year 1)
TEEF (g t o n - 1)
MA
(ppm)
As Cd Cr Cu Mo Ni Pb Sb Se V Zn
13.9 0.4 34.2 23.4 6.3 40.4 44.3 2.5 2.1 57.9 80.9
3340 100 8210 5620 1500 9700 10640 600 505 13900 19420
1.16 0.02 0.38 0.25 0.17 0.45 1.23 0.13 0.31 0.88 3.89
278 4.3 91.2 61.2 40.3 107.7 295 30.8 73.6 211.7 934.4
%
(tons year- 1) 8.3 4.3 1.1 1.1 2.7 1.1 2.8 5.1 14.6 1.5 4.8
103 c o l u m n of T a b l e 2 r e p o r t s the emission f a c t o r for e a c h t r a c e e l e m e n t ( T E E F ) c a l c u l a t e d using Eqns (8) and (10), and the s u b s e q u e n t a t m o s p h e r i c mobilization (MA) derived from the t o t a l e x p e c t e d coal usage by 1990. T h e last c o l u m n of Table 2 gives the p e r c e n t a g e of the t o t a l t r a c e elements mobilized emitted into the a t m o s p h e r e as p a r t i c u l a t e matter. T h e c o m p a r i s o n of o u r results with d a t a derived from the few mass b a l a n c e studies r e p o r t e d in the l i t e r a t u r e must obviously be based on a n a l o g o u s o p e r a t i n g conditions, especially for the t o t a l p a r t i c u l a t e emitted t h r o u g h the stack. T h e c o m p a r i s o n with the a t m o s p h e r i c mobilization d a t a d e r i v e d by Sabbioni et al. [22] from U.S.A. mass b a l a n c e studies is r e p o r t e d in T a b l e 3 as the p e r c e n t a g e of t r a c e e l e m e n t mobilized into the a t m o s p h e r e (columns 1 and 3) and as the same p e r c e n t a g e n o r m a l i z e d to the p e r c e n t a g e of t o t a l ash emitted t h r o u g h the stack (columns 2 and 4, % normalized -- % mobilized/% of the t o t a l ash emitted). T h e n o r m a l i z a t i o n allows a c o m p a r i s o n i n d e p e n d e n t of the o p e r a t i n g conditions (fly ash p r o d u c t i o n ) and of the efficiency of the p a r t i c u l a t e c o n t r o l devices. The d a t a show fairly good a g r e e m e n t : this confirms t h a t the e n r i c h m e n t p h e n o m e n a , i n d i c a t e d by the mass b a l a n c e s results, c a n be well described by an a n a l y t i c a l m e t h o d whose basic i n p u t data, for the e v a l u a t i o n of the t r a c e elements emission factor, are the coal compositions. F u r t h e r d a t a r e q u i r e d (fly ash production, p a r t i c u l a t e c o n t r o l efficiency, d i s t r i b u t i o n p a r a m e t e r s of the emitted p a r t i c u l a t e m a t t e r ) can be derived from the different o p e r a t i n g conditions. APPENDIX If the d e p e n d e n c e of E F u p o n dp is described by Eqn (4) and p(dp) is a single-mode log-normal distribution, the i n t e g r a l on the r i g h t - h a n d side of Eqn (6) becomes: TABLE 3 Atmospheric mobilization calculated in the present work compared with analogous data derived from Sabbioni et al. [22]. The percentages of the total ash emitted, utilized in the normalization, are 0.56% (present work) and 0.45% (Sabbioni et al.) Trace element As Cd Cr Cu Mo Ni Pb Sb Se V Zn
Present work
Sabbioni et al. [22]
% mobilized
% normalized
% mobilized
% normalized
8.3 4.3 1.1 1.1 2.7 1.1 2.8 5.1 14.6 1.5 4.8
14.8 7.7 2.0 2.0 4.8 2.0 5.0 9.1 26.1 2.7 8.6
2.9 2.7 1.0 0.7 1.2 0.4 1.8 2.4 14.3 1.0 1.8
6.4 6.0 2.2 15 2.7 0.9 4.0 5.3 31.8 2.2 4.0
104 oo
I = fa" d~{exp - [(ln(dp/Mg))2/2(ln Sg)2]/d, In Sg(2~)~/2}d(dp)
(I)
0
If
z = ln(dp/Mg)/ln Sg
(II)
then z(0) =
- oo
(III)
z(oo) = oo
(IV)
Substituting for dp the value obtained in (II) and for the limits of integration the values in (III) and (IV) gives: oo
I = [a/(2~) 1/2] exp (b In Mg) ~ exp (bz In Sg - z2/2)dz
(v)
-co
From tables of standard integrals: i exp ( - p2x2 + qx)dx
= exp (q2/4p2)(~l/2/p)
(VI)
-oo
In the present case, p = 2 -1/2
(VII)
q = blnSg
(VIII)
so finally one obtains: I = a exp [b In Mg + (b In 8g)2/2]
(IX)
If the dependence of EF upon dp is described, in the size range where the enrichment becomes constant, by Eqn (5), and p(dp) is still a single-mode log-normal distribution, the integral in right-hand side of (6) has to change to: 1
I =
{a{exp - [(ln(dp/Mg))2/2(lnSg)2]/dplnSg(2~)l/2 }d(dp) ./ 0
oo
+ f a . d~{exp - [(ln(dp/Mg))2/2(ln Sg)2]/dp In Sg(2~)1/2}d(dp)
(X)
1
where dp = 1 #m is the assumed value of the particulate matter diameter below which the enrichment becomes fairly constant with the particle size (see text for details). Substituting again for dp the value obtained with the transformation outlined in (II), and for the integration limits those obtained in (III) and (IV), leads to:
I = [a/(2r) 1/2] i exp ( - z2/2) dz + [a/(2r) 1/2] exp (b In Mg) o0
105
i
(XI)
exp ( - z2/2 + b In S g z ) d z
U
where u is the value of z for d p = 1 #m: u =
(XII)
- lnMg/lnSg
From tables of standard integrals: i exp ( - q 2 x 2 ) d x
=
[(~)1/2/2q] [1 + erf(qu)]
for q > 0
(XIII)
--OD
where erf is the error function. Applying (XIII) to the first integral of the right-hand side of (XI), we have q = 2-1/2
(XIV)
so one obtains: i exp ( - z2/2) dz = 0r/2) 1/2 [1 - erf (u/2~/2)]
(XV)
--OD
The second integral of the right-hand side of (XI) can easily be handled if the integration variable z is transformed to a new variable using: Z = z + B
(XVI)
where B =
- b In Sg
(XVII)
Applying this transformation, the integrand function becomes: exp ( - zS/2 + b In S g z )
=
exp [ ( - Z 2 + B2)/2]
(XVIII)
and the integral transforms to: 00
OO
j e x p ( - z2/2 + b l n S g z ) d z
=
exp (S2/2)lex p ( - Z2/2)dZ
(XIX)
U
where U
=
u + B
=
-
lnMg/lnSg-
blnSg
(XX)
In this way, the integral in (XIX) becomes a Gaussian function whose solution, derived from standard integral tables, is: ao
I
exp ( - Z 2 / 2 ) d Z
=
(~/2) '/2 [1 - erf(U/2'/2)]
where erf is, as in (XV), the error function.
(XXI)
106 U t i l i z i n g t h e s t a n d a r d i n t e g r a l s o u t l i n e d i n (XV) a n d (XXI), t h e s o l u t i o n o f t h e i n t e g r a l I i n (XI) c a n b e f o u n d : I
=
• [1 -
(a/2){[1 + erf(u/21t2)] + [exp ( b l n M g +
(blnSg)2/2)]
e r f (U/21/2)]}
(XXII)
w i t h u a n d U as d e f i n e d i n (XII) a n d (XX), r e s p e c t i v e l y . REFERENCES 1 2 3 4 5 6 7 8
9 10
11
12 13 14 15 16 17 18 19
T.F. Yen, The Role of Trace Metals in Petroleum, Ann Arbor Press, Ann Arbor, Michigan, 1975. US-EPA, Supplement 13 for compilation of air pollutant emission factors, Research Triangle Park, NC, 1982. D.F.S. Natusch, J.R. Wallace and C.A. Evans Jr., Toxic trace elements: preferential concentration in respirable particles. Science, 183 (1974) 202-204. J.M. Kaakinen, R.M. Jorden, M.H. Lawasani and R.E. West, Trace element behaviour in coal-fired plant, Environ. Sci. Technol., 9 (1975) 862 869. E.S. Gladney, J.A. Small, G.E. Gordon and W.H. Zoller, Composition and size distribution of in-stack particulate material at a coal-fired power plant, Atmos. Environ., 10 (1976) 1071-1077. D.G. Coles, R.C. Ragaini, J.M. Ondov, G.L. Fisher, D. Silberman and B. Prentice, Chemical studies of stack fly ash from a coal fired power plant, Environ. Sci. Technol., 13 (1979) 455-459. R.D. Smith, J.A. Campbell and K.K. Nielson, Characterization and formation of submicron particles in coal-fired plants, Atmos. Environ., 13 (1979) 607-617. J.M. Ondov, R.C. Ragaini and A.H. Biermann, Emission and particle size distribution of minor and trace elements at two western coal-fired power plants equipped with cold-side electrostatic precipitators, Environ. Sci. Technol., 13 (1979) 946-953. G.R. Markowski and R. Filby, Trace element concentration as function of particle size in fly ash from a pulverized coal utility boiler, Environ. Sci. Technol., 19 (1985) 796-804. M. Neville, R.J. Quann, B.S. Haynes and A.F. Sarofim, Vaporization and condensation of mineral matter during pulverized coal combustion. 8th Symp. Combustion, The Combustion Institute, 1981, pp. 1257-1274. R.C. Flagan and S.K. Friedlander, Particle formation in pulverized coal combustion--a review paper presented at the Symposium on Aerosol Science and Technology at the 82th National Meeting of the AICHE, Atlantic City, NJ, 1976. R.D. Smith, The trace element chemistry of coal during combustion and the emission from coal-fired plants, Prog. Energy Combust. Sci., 6 (1980) 53-119. C.D.Stinespring and G.W. Stewart, Surface enrichment of aluminosilicate minerals and coal combustion ash particles, Atmos. Environ., 15 (1981) 307 313. R.D. Smith and D.R. Baer, Fly ash surface formation and segregation during heating, Atmos. Environ., 17 (1983) 1399-1409. R.D. Smith, J.A. Campbell and K.K. Nielson, Concentration dependence upon particle size of volatilized elements in fly ash, Environ. Sci. Technol., 13 (1979) 553-558. J.M. Pacyna, Emission factors of trace metals from coal-fired power plants, Norwegian Institute for Air Research, Tekn. Rapp. N. 14/81, 1981. P. Bacci, G.M. Marcazzan, P. Redaelli and A. Ventura, Particulate emission and element behaviours in a large coal power plant, I1 Nuovo Cimento, 8C (1985) 907-922. R.J. Cheng, V.A. Mohen, I.I. Shen, M. Current and J.B. Hudson, Characterization of particulates from power plants, J. Air Pollut. Control Assoc., 26 (1976) 787-790. R.B. Candelaria and G.E. Palomino, Characterization of Navajo generating station emission measured during the June~July 1979 VISTTA field program, Atmos. Environ., 16 (1982) 2287-2298.
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M. Cioni and L. Bonfanti, Characterization of solid emissions from a coal fired power plant, International Conference on Aerosols in Science Medicine and Technology, Garmish, 25-27 Sept. 1985. E. Sabbioni, L. Goetz, A. Springer and R. Pietra, Trace metals from coal-fired power plants: derivation of an average data base for assessment studies of the situation in the European Communities, Sci. Total Environ., 29 (1983) 213-217. E. Sabbioni, L. Goetz and G. Bignoli, Health and environmental implication of trace metals released from coal-fired power plants: an assessment study of the situation in the European Community, Sci. Total Environ., 40 (1984) 141-154. Concil of European Community, Directive proposal CoM (83) 704 def. (19/12/1983) EC Official Journal N. C49.