Equilibria for Magnesia Wet Scrubbing of Gases Containing Sulfur Dioxide Clyde H. Rowland' and Abdul H. Abdulsattar Bechtel National, Inc., P.O. Box 3965, San Francisco, Calif. 941 19
ficient for SO2 is set equal to unity. There remain four species whose individual ion activity coefficients affect the calculated equilibria: SO;-, SO:-, HSO,, and Mg2+.The activity coefficient for SO:- is assumed to be equal to that for SO:- in Mg-SO2-SO3 solutions, because activity coefficient data are available for MgSO4, but not for MgSO3. Calculated values are required for the activity coefficients of HSO, and Mg2+,designated here as 71 and 7 2 , respectively, and for the mean salt activity coefficient of MgS04, y+.The latter coefficient is the square root of the product of the activity coefficients for Mg2+ and SO:-. There are a total of 18 unknowns (excluding temperature): the molalities of the 10 dissolved species, the SO2 partial pressure, the three total molalities (Mg, SOP,SO3)in the liquid phase, the degree of MgS03.6H20 saturation, and the three activity coefficients (71, yz, y+). A set of 15 equations (shown below) can be written in terms of these unknowns, leaving three variables that are specified. From a practical standpoint, these three specified variables should be chosen from among the following six: partial pressure of S02, pH, fraction of saturation ( S )with solid MgS03-6H20, total magnesium molality, total SO2 molality (or alternatively, total sulfur molality including sulfate), and fraction of dissolved sulfur species oxidized to sulfate (Ox). Table I lists convenient choices.
H A chemical model is described that predicts thermodynamic equilibria for aqueous magnesium-sulfite-sulfate solutions in the range 15-60 "C. If three of the following variables are specified, then the other three are predicted: partial pressure of sulfur dioxide, pH, degree of saturation with solid magnesium sulfite hexahydrate, molality of dissolved magnesium, molality of dissolved sulfite, and fraction of dissolved sulfur species oxidized to sulfate. Published experimental data are used to test the model. The model predicts that the solubility of magnesium sulfite hexahydrate is independent of liquor composition for dissolved mole ratios of sulfite to active magnesium between 1.0 and 2.0, and that the solubility increases with increasing temperature. A simple set of correlations derived from the model predicts liquor composition and sulfur dioxide partial pressure for solutions saturated with magnesium sulfite.
A variety of wet sulfur dioxide (S02) scrubbing processes using magnesium have been applied or proposed (1-6). The design and operation of such magnesia-based scrubbing processes require an understanding of the lic,uor chemistry. Experimental data are available for sulfur dioxide partial pressure, pH, and magnesium sulfite solubility in some aqueous magnesium-sulfite-sulfate solutions (7-15). The chemical model described here predicts equilibria. The model can be simplified for solutions saturated with magnesium sulfite hexahydrate (MgS03~6H20);for this special case, a set of correlations derived from the model predicts liquor composition and SO2 partial pressure. The model has also been used to prepare parametric plots.
Equations i n the Model Once the three specified variables have been chosen, the other unknowns are calculated by Equations 1-15. Activity and fugacity coefficients assumed to be unity are not shown in these equations. Ionic equilibria:
Variables i n the Model In the formulation employed here for the Mg-SOZ-SO3 system, there are 13 species: H+, Mg2+,SO,'-, HSO;, SO,(aq), SO:-, MgSOg, MgSO:, OH-, MgOH+, H20(1), SOz(g), and MgSO3*6H20(~). Other species that were considered but not retained in the model are HSO,, MgHSO;, and MgS03-3H20(s). Use of a value of 0.0104 for the dissociation constant of HSO; a t 25 "C (16) indicated that dissociation is complete for magnesia-SO2 scrubbing. The ion complex MgHS0; had no significance in explaining experimental data. The hexahydrate solid form of MgS03 is thermodynamically stable, or lower in solubility than trihydrate, at temperatures as high as 59 "C (17).Although trihydrate solid is occasionally encountered a t temperatures of 50-60 "C ( I ) , it is assumed here that compositions of liquors saturated with MgS03 a t temperatures below 60 "C are adequately predicted from hexahydrate solubilities. The activity coefficients of the three minor ionic species included in the modei, X+, OH-, and MgOH+, are arbitrarily set equal to unity, because the concentrations of these species are too low to affect the ionic and mass balances. The equations given below to describe the system determine the activity of each of these minor species. The individual activity coefficients of the neutral dissolved species SOAaq), MgSO:, and MgSO! are also set equal to unity because data for such coefficients are scarce and reported values are close to unity. For example, Rabe and Harris (18) determined that the activity coefficient for SO2 (aq) is 0.98 in seawater, which has an ionic strength of about 0.67. Atmospheric pressure is assumed; therefore, the fugacity coef1158
Environmental Science & Technology
(5) K, = (H+)(OH-)
(6)
where quantities in parentheses are molalities of dissolved species . Vapor-liquid equilibrium:
pso* = Hso*[SO2(aq)l
(7)
where Pso2 is the partial pressure of S02, atm, and H S O is~ Henry's constant for S02. Liquid-solid equlibria:
where S is the fraction of MgSO3-6H20saturation. Mass balances: (Total Mg)
(MgZt)= (MgSO!) l+-+(Mg2+)
0013-936X/78/0912-1158$01.00/0
(MgS09) (Mg2+)
+
(MgOH+) (Mg2+)
(9)
@ 1978 American Chemical Society
Table 1. Computational Modes for Model Input/Output
purpose/ process
speclf led varlables
calcd varlables
S, p ~ OX ,
design/slurry
varlable calcd by electroneutrallty equatlon
log (so;-)
pSo2,Mg, so2
Pso2,S, so2
design/liquor operation
pH, Mg, Ox PH, Mg, total sulfur
operation operation (overspecified)
Mg, SOP, OX Pso,, pH, S PH, Mg, SO2 Pso,, S, Ox ionic imbalance
Pso,,
s, ox
'
log (so;-)
ox
constant
K1 K2 K3 K4 K5 Kw KSP
Hso2 pH ionic imbalance
- (SO:-)]+ (H+) + (MgOH+) - (HSO,)
- (OH-)
=
0
(12)
Activity coefficients: log ,y* =
-4(A 1
+ C+)11'2 + "p
log y 2 =
-4(A 1
+ C2)11" +p P 2
(13)
where A is the limiting Debye-Huckel slope, p is a constant related to the distance of closest approach of ions in solution, and C* and C2 are empirical constants. The coefficients of four in Equations 13 and 15 represent cation times anion unit charge for the 2-2 electrolyte MgS04, and squared magnesium ion unit charge, respectively. The ionic strength, I , of the solution is defined by:
I = 112 C m,z,2
A P
ci C2
where the total concentrations of Mg, SOP,and SO3 are the molalities of total dissolved magnesium, sulfite and sulfate species, respectively. The mass balances are written in the above form for computational convenience. Electroneutrality equation: 2[(Mg2+)- (SO:-)
Table II. Constants in Aqueous Solutions at 25 "C, at Infinite Dilution
(16)
I
where m, is the molality of any species, i, in the solution, and z, is the unit charge on species i. The constants Ci and C2 in Equations 13 and 15 are a deviation from traditional extensions of Debye-Huckel theory. However, such traditional extensions, while excellent for nearly all other salts, do not adequately explain observed mean activity coefficients for bivalent metal sulfates (19), including MgS04. The mean activity coefficients for MgS04 solutions are explained over the molality range of 0.01-1.2 by inclusion of the constant Ci in Equation 13. An additive BI term ( B = constant) in Equation 14 for log y 1 was considered; however, this did not improve the overall fit to experimental data. Such a BI term is usually the most effective first-order correction for the activity coefficient of a single-charged ion (19).
Constants The constants a t 25 "C for the thermodynamic equilibria,
value
ref
6.24X 1.30X lo-* 1.20x 10-3 5.6x 10-3 2.60x 10-3 1.01 X 5.46x 10-5 0.813 0.511 1 .o -0.089 -0.25
Tartar and Garretson (20) Johnstone and Leppla (27) Lowell et al. (22) Nair and Nancollas (23) Stock and Davies (24) Harned and Owen (25) Derived from Hagisawa (8) Johnstone and Leppla (27) Lewis, et al. (26) Bromley (79) Derived from Pitzer (27) Derived from Semishin et al. ( 7 7)
Equations 1-8, and for the activity coefficient relationships, Equations 13-15, are presented in Table 11. The thermodynamic constants in Equations 1-7 and the activity coefficient parameters A and p are available in the literature as indicated by Table 11. The effect of temperature on these constants has been summarized by Lowell et al. (22). The solubility product for MgS03.6H20 over the temperature range of 15-62.5 "C was obtained from the saturation concentrations of pure hexahydrate crystals (8) by plotting the logarithm of the calculated activity product of Mg2+and SO:- against inverse temperature (K). The standard deviation of the data points from the best straight-line correlation was only 4% saturation. The value for C+ a t 25 "C was obtained from the activity coefficient data of Pitzer ( 2 7 )for aqueous MgS04 solutions. These data are for the mean salt activity coefficient assuming complete dissociation, y+. Values of y+ are converted to corresponding values of yi by correction for partial association of Mg2+ and SO:- ions as MgSOf. This correction is expressed by yi = y+ m/(Mgi+),where m is the molality of the MgS04 solution, and (Mg*+)is the actual concentration of dissociated Mg2+ ion. Over the MgS04 molality range of 0.01-1.2, Equation 13 matches the data of Pitzer to within a standard error in log ,y+ of 0.0043; this corresponds to a standard relative error in y* of only 1%. The value of C+ was assumed to be independent of temperature. Note that C+ must be equal to zero a t infinite dilution in order to match the Debye-Huckel limiting slope. However, magnesia-based SO2 wet scrubbing systems always operate at magnesium molalities higher than 0.01, the lowest molality for which Ci was correlated. The value of Cp, also assumed to be independent of temperature, was estimated by using C2 to improve the fit of the model to the pH data of Semishin et al. (111. The calculated pH for the Semishin data was found to be particularly sensitive to C Lcompared to other constants in the model. Computational Procedure A Fortran IV computer program has been written to implement the model with a total usage of about 0.3 slcase. The iterative procedure that solves Equations 1-15 consists of three computational loops: Outer loop to calculate activity coefficients from ionic strength by Equations 13-15 Middle loop to calculate either pH, log (SO:-) or fraction oxidation, depending upon the input mode (see Table I), by use of the electmneutrality relation, Equation 12 Inner loop to calculate the other unknowns by use of Equations 1-11. The mass balances, Equations 9-11, are solved first, for (Mg2+),(SO:-) and (SO!-), respectively, in the manner described by Kester and Pytkowicz (28). Volume 12,Number 10,October 1978
1159
3
4
5
6
MEASURED pH
Figure 1. Comparison of measured and predicted values of liquor
PH
( 0 )Kuzminykhand Babushkina ( IO),(0) Semishin et al. ( I I), (A)Pinaev ( IZ),
and (V)Markant et al. ( 14)
covered by Figure 1. However, the model is not in good agreement with a few measured pH values obtained by Semishin et al. (11) in the high p H range of 7.0-8.2. The model predicts pH values of only about 6.0-6.6 for these cases. Additional data for the pH range of 6.5-8.0 are needed to determine whether the model is valid in this range, or if modifications are required. The model agrees with the few available pH data (15)over the range 8.3-9.5 to within a standard error of 0.34 pH unit; these data are for solutions of nearly pure MgSO3. The model predicts that the solubility of MgS03-6H20 is nearly independent of liquid composition in the sulfite-bisulfite range (mole ratio of dissolved SO2 to active magnesium between 1.0 and 2.0); solubility increases only with increasing temperature. This prediction is both qualitatively and quantitatively in good agreement with data for solubility of M g S 0 ~ 6 H 2 0in water (8,13,15,17),with the data of Semishin et al. (11) for solubility of MgS03 in solutions containing Mg(HS03)2 and 10 wt % MgS04, with the data of Pinaev(l2) for sulfite-bisulfite-sulfate, and with the data of Kuzminykh and Babushkina (IO) for sulfite-bisulfite a t 25 "C. However, the data of Semishin et al. (11) without MgS04 indicate a slight decrease in sulfite solubility with increasing bisulfite, so that the model predicts 60-100% saturation for these cases that were 100% saturated experimentally. Also, a few data obtained by Pinaev (13) indicate that sulfite solubility in MgS04 solutions increases with increasing MgS04 concentration. These apparent disagreements among experimental solubilities of MgSO3 in Mg(HS03)z and MgS04 solutions should be resolved by further study.
Equations Derived from the Model The chemical model was used to correlate equilibrium SO2 partial pressures and compositions for solutions saturated with MgS03-6H20 in the sulfite-bisulfite range (mole ratio of dissolved SO2 to active magnesium between 1.0 and 2.0) a t known temperature, pH, and oxidation. The resulting correlations, Equations 17-21, used with the mass balances, Equations 22-25, are useful for chemistry-related aspects of the design of magnesia-based slurry scrubbing processes. Correlations: log Pso2 = 14.0 0.45 log (1 - OX) - 1.58pH - 3000/T (17)
+
MEASURED P s o E , atm
log MgS03 = 3.1 - 1300/T
(18)
log F = O.55pH - 3.58
(20)
Figure 2. Comparison of measured and predicted values of equilibrium
SOn partial pressure (0)Smith and Parkhurst (0, (0) Conrad and Brice (9), (0)Kuzminykhand Babushkina ( IO),(A)Pinaev ( 73,and (V)Markant et al. ( 14)
For the slurry process design mode of input/output, solution of Equations 1-11 is noniterative. For the overspecified operation mode, solution of Equation 12 for the ionic imbalance is noniterative.
Model Verification The model has been verified by comparing its predictions with experimental data (7-15) in the ranges: SO2 partial pressure = to 1atm, pH = 3.0-6.5, fraction magnesium sulfite saturation = 0-1:0, MgS04 molality = 0-1.0, and Mg(HSO& molality = 0-4.0. Figures 1 and 2 show measured vs. predicted values of pH and equilibrium SO2 partial pressure, respectively. For the 114 pH data points, the model explains 83% of the variation (correlation coefficient of 0.91) with a standard error of estimate of 0.31 pH unit. For the 148 experimental values for log Pso2,the model explains 97% of the variation with a standard error of 0.24. The model agrees well with pH data in the range, 3.0-6.5, 1160
Environmental Science & Technology
G
=1
+ 0.70 log (1-1Ox) ~
where the active magnesium is the molality of MgS03 plus Mg(HS03)z (or total Mg minus MgS04), T is the absolute temperature in K, Ox is the fraction of sulfur oxidized, and F and G are functions of pH and oxidation, respectively, as indicated in Equations 20-21. Mass balances: Total Bisulfite = 2(Active Mg - MgS03) Total SO2 = MgS03
+ Total Bisulfite ox
Total SO3 = Total SO2 1 - ox Total Mg = Active Mg Total SO3
+
(22)
(23) (24) (25)
Equations 17-25 were tested against the chemical model for the ranges: temperature = 15-60 "C, pH = 3.5-6.0,,and oxidation = 0-80%. The equations correlated with the
7 9
a pH correction factor given in Table 111. The correction factor should be interpolated geometrically. Figure 4 shows the effects of dissolved sulfite oxidation and magnesium sulfite saturation on equilibrium SO2 partial pressure a t a pH of 5.0. Correction of SO2 partial pressure for p H is by the same method as for Figure 3, although the correction factors are different (see Table 111). Figure 5 shows the effects of p H and dissolved sulfite oxidation on the ratio of total dissolved sulfur to magnesium. The sulfur-to-magnesium ratio is essentially independent of magnesium molality a t pH values below 5.5; the stronger dependence on magnesium molality a t a p H of 6.0 is shown in the figure. The variable (1/1 Ox) was chosen for the abscissa because this variable is linear with the sulfur-to-magnesium ratio. As an example of the use of Figures 3-5, suppose that a laboratory sample of effluent liquor from an operating magnesia-SO2 scrubber is found to have a pH of 5.3, a dissolved magnesium molality of 0.70, and a dissolved total sulfur molality of 0.80. Figures 5,3, and 4 are used, respectively, to de-
3
+
1
0.5
I
I
I
I
90
80
70
60
I
, '
I
,
40
'
,
I
I
'
/
20
0 I
PERCENT OXIDATION
Figure 3. Effect of dissolved sulfite oxidation and dissolved magnesium concentration on equilibrium SO2 partial pressure at pH of 5.0
chemical model to within a standard relative error of 8%for total dissolved Mg, total dissolved SO2, and SO2 partial pressure. The equations constitute a simpler, noniterative model suitable for hand calculation. The following observations can be made from the forms of Equations 17-21: SO2 pressure over saturated MgS03.6H20 solutions is a strong negative function of pH and a strong positive function of temperature, increasing by a factor of about 40 for a pH drop of one unit, and by a factor of two for a temperature rise of 10 "C. The dissolved concentration of MgSO, in equilibrium with hexahydrate solid is independent of liquor composition and increases with temperature. The ratio of active magnesium to MgS03 is independent of temperature and only slightly dependent on oxidation, but strongly increases with decreasing pH, corresponding to increased bisulfite.
Parametric Plots Deriued from t h e Model The chemical model has also been used to prepare parametric plots, Figures %5, for a typical scrubbing temperature of 50 O C . These plots can be used to solve the design and operation problems summarized in Table I. Figure 3 shows the effects of dissolved sulfite oxidation and dissolved magnesium concentration on equilibrium SO2 partial pressure a t a pH of 5.0. T o obtain the equilibrium SO2 partial pressure for a different p H value, the SOn partial pressure determined from Figure 3 should be multiplied by
I
I
70
60
'
I
7
I
I
'
)
A
6
5
2 x
4
E
+ m
z
N
a
3
1.5
90
80
40
20
0
PERCENT OXIDATION
Figure 4. Effect of dissolved sulfite oxidation and magnesium sulfite saturation on equilibrium SO2 partial pressure at pH of 5.0
Table 111. Correction Factors for SO2 Partial Pressure in Figures 3 and 4
Correction factor = SO2 partial pressure at specified pH/S02 partial pressure at a pH of 5.0 specllled PH
4.0 4.5 5.0 5.5 6.0
Flgure 3
Figure 4
12.0 3.5
... 6.3 1.o
1.o 0.2 0.04
0.15
0.021
1. 0
0.9 0.8 0.7 0.6 (IllQx), Ox =FRACTION OXIDATION
0.5
Figure 5. Effectof dissolved sulfite oxidation and liquor pH on ratio of total dissolved sulfur to magnesium
Volume 12, Number 10, October 1978
1161
termine dissolved sulfite oxidation, equilibrium SO2 partial pressure, and magnesium sulfite saturation. Figure 5 indicates that, for the measured pH of 5.3, a sulfur-to-magnesium ratio of 0.80/0.70 or 1.14, and a dissolved magnesium concentration greater than 0.4 molal, the value of (1/1 Ox) is about 0.62. This corresponds to 61% oxidation. Figure 3 has a reference pH of 5.0. For this reference pH and 61% oxidation, linear interpolation of magnesium and SO2 pressure values gives an SO2 partial pressure of 3.3 X 10-4 atm for the measured magnesium molality of 0.70. The pH correction factor given in Table I11 for a pH of 5.5 is 0.2; therefore, the correction factor for a pH of 5.3 is 0.2 to the power of (5.3 - 5.0)/(5.5 - 5.0) = (0.2)0.6= 0.38. The equilibrium SO2 partial pressure for the liquor sample is (3.3 X 10-4)(0.38) = 1.25 x atm. To determine sulfite saturation from Figure 4, the SO2 partial pressure must be corrected to a pH of 5.0 as indicated in Table 111. The correction factor for a pH of 5.5 is 0.15; therefore, the factor for the measured pH of 5.3 is (0.15)0.6= 0.32. The SO2 partial pressure to be used in Figure 4 is (1.25 X 10-4)/0.32 = 3.9 X atm. By linear interpolation the sulfite saturation is found to be 80%for the sulfite oxidation of 61%. By comparison with these graphical values of 61% oxidation, 1.25 X atm SO2 partial pressure, and 80% magnesium sulfite saturation, the chemical model gives calculated values atm S02, and 78% saturation. of 63% oxidation, 1.24 X
+
Acknowledgment This paper was prepared while working on the EPA-funded Shawnee wet scrubbing Test Program, with the support and encouragement of John E. Williams, Project Officer. We appreciate the helpful comments of Harlan N. Head, Nancy E. Bell, and Kenneth A. Strom of Bechtel National, 1nc.k Air Quality Group, and also those of Gary T. Rochelle of the University of Texas at Austin. We are grateful for the assistance of Eleanor L. Tape1 and Jackson Hing. Literature Cited (1) Quig, R. H., “Chemic0 Experience for SO1 Emission Control on
Coal-Fired Boilers”, Coal and the Environment Tech. Conf., Louisville, Ky., Oct. 1974. (2) Quigley, C. P., Burns, J. A., “Assessment of Prototype Operation and Future Expansion Study-Magnesia Scrubbing a t Mystic
Generating Station, Boston, Massachusetts”,EPA Symp. on Flue Gas Desulfurization, Atlanta, Ga., Nov. 1974. (3) Clement, J. L., Tappi, 49 (8),127A-34A (1966). (4) Cronkright, W. A., Leddy, W. J., Enuiron. Sci. Technol., 10 (6), 569-72 (1976). (5) Head, H. N., Bechtel Corp., “EPA Alkali Scrubbing Test Facility: Advanced Program-Third Progress Report”, EPA Rep. 600/777-105, 1977. (6) Rochelle, G. T., PhD thesis, University of California, Berkeley, Calif., 1976. (7) Smith, W. T., Parkhurst, R. B., J . Am. Chem. SOC.,44,1918-27 (1922). (8)Hagisawa, H., Bull. Inst. Phys. Chem. Res. (Tokyo), 12,976-83 (1933). (9) Conrad, F. H., Brice, D. B., Tappi, 70,2179-82 (1948). (10) Kuzminykh, I. N., Babushkina, M. D., J. Appl. Chem. USSR, 30,495-8 (1957). (11) Semishin, V. I., Abramov, I. I., Vorotnitskaya, L. T., Khim. Khim. Tekhnol., 2,834-9 (1959). (12) Pinaev, V. A., J . Appl. Chem. U S S R , 36 ( l o ) , 2049-53 (1963). (13) Pinaev, V. A., ibid., 37 (61, 1353-5 (1964). (14) Markant, H. P., McIlroy, R. A., Matty, R. E., Tappi, 45 (11), 849-54 (1962). (15) Pyle, R. E., “Experimental Results for the Equilibrium Stidies on MgSO, Hydrates”, Radian Corp. Tech. Note 200-045-36-04, 1976. (16) Robinson, R. A., Stokes, R. H., “Electrolytic Solutions”, 2nd ed., London, England, 1965. (17) Markant, H. P., Phillips, N. D., Shah, I. S., TAPPI= 4- (ll), 648-53 (1965). (18) Rabe, A. E., Harris, J. F., J . Chern. Eng. Data, 8, 333-6 (1963). (19) Bromley, L. A., AICHE J., 19 (2), 313-20 (1973). (20) Tartar, H. V., Garretson, H. H., J . Am. Chem. Soc., 63,808-16 (1941). (21) Johnstone, H. F., Leppla, D. W., ibid., 56, 2233-8 (1934). (22) Lowell, P. S., Ottmers, D. M., Strange, T. I., Schwitzgebel, K., De Berry, D. W., “A Theoretical Description of the Limestone Injection-Wet Scrubbing Process”, Final Rep. for EPA Contract No. CPA-22-69-138with Radian Corp., 1970. (23) Nair, V.S.K., Nancollas, G. H., J . Chem. Soc. (London), 1958, pp 3706-10. (24) Stock, D. I., Davies, C. W., Trans. Faraday SOC.,44, 856-9 (1948). (25) Harned, H. S., Owen, R.B., “The Physical Chemistry of Electrolytic Solutions”, 3rd ed., Reinhold, New York, N.Y., 1958. (26) Lewis, G. N., Randall, M., Pitzer, K. S., Brewer, L., “Thermodynamics”, 2nd ed., McGraw-Hill, New York, N.Y., 1961. (27) Pitzer, K. S., J . Chem. Soc. Faraday Trans. I I , 68, 101-13 (1972). (28) Kester, D. R., Pytkowicz, R. M., Lirnnol. Oceanogr., 14,686-91 (1969). Receiued for review February 10, 1978. Accepted April 28, 1978.
A General Method for Fitting Size Distributions to Multicomponent Aerosol Data Using Weighted Least-Squares Otto 0. Raabe Radiobiology Laboratory and Department of Radiological Sciences, School of Veterinary Medicine, University of California, Davis, Calif. 95616
This information is directed to investigators using multistage and other multicomponent aerosol samplers for studies of aerosol size distribution. A general and straightforward approach is described for fitting a chosen size distribution (probability densityj function to the grouped data collected with such samplers as cascade impactors, cascade centripeters, horizontal elutriators, aerosol centrifuges, multiple cyclone samplers, and other devices that fractionate aerosol samples into several components or collect samples representing several different size ranges. The actual collection efficiencies with respect to particle size of each component or stage are 1162
Environmental Science & Technology
used to fit the size distribution function by weighted nonlinear least-squares regression analysis with each datum weighted by the reciprocal of its estimated variance. Particle size may be geometric, aerodynamic, or whatever size convention is measured by the sampling device. Estimates are made of the confidence limits of the fitted parameters, and the correlation coefficient and chi-square values are used to test the acceptability of the resulting size distributions. Illustrative examples are given for fitting log-normal functions to data collected with a cascade impactor, with a spiral-duct aerosol centrifuge, and with a diffusion battery.
0013-936X/78/0912-1 162$01.00/0
@
1978 American
Chemical Society
