J. Phys. Chem. 1980, 84, 1644-1649
1644
by the present investigation. The size distribution, shown in Figure 3, can be interpreted as the nucleation mode. References a n d Notes (1) G. M. Hidy, J . Air Poilut. Control Assoc., 25, 1106 (1975). (2) K. T. Whitby, W. E. Clark, V. A. Marple, G. M. Sverdrup, G. J. Sem,
K. Willeke, B. Y. H. Liu, and D. Y. Pui, A f m s . Environ.,9, 463 (1975). (3) G. M. Sverdrup, Ph.D. Thesis, University of Minnesota, Minneapolls, Minn., 1977. (4) K. T. Whitby, R. B. Husar, and B. Y. H. Liu, J . CoiioMInterface Scl., 39, 177 (1972). (5) P. E. Wagner and F. G. Pohl, Staub-Reinhalt. Luft 38, 72 (1978). (6) K. T. Whitby, Atmos. Environ., 12, 135 (1978).
Coal Combustion Fly Ash Characterization. Rates of Adsorption and Desorption of Water S. J. Rothenberg" and Y. S. Cheng Inhalation Toxicology Research Institute, Lovelace Biomedical and Environmental Research Institute, Albuquerque, New Mexico 871 15 (Received September 24, 1979) Publication costs assisted by fhe Unlted States Department of Energy
Rates of adsorption and desorption of water by cod combustion fly ash have been measured over the temperature range 0-300 "C. Adsorption isotherms and specific surface areas are summarized. Models for adsorption by fly ash and the assumptions underlying each model are reviewed. The change of rates with temperature and pressure predicted by each model is compared with experimentally determined values of half-times, tl/z. The predicted values of t1lz,obtained by using the model of Natusch and Tomkins, change by five orders of magnitude over the temperature range &300 "C. The measured change is approximately two orders of magnitude. Measured values of tl for adsorption of water vapor at 0 "C (1-4 torr) range from less than 1 min to 1 h. The rate data can be expiained by either of the hypotheses that (1) fly ash is porous and mass transfer processes are rate controlling at some temperatures and pressures or (2) adsorption causes reversible changes (flexure) in the structure of fly ash.
Introduction Fly ash particles are emitted to the atmosphere by coal combustors used in the generation of electric power. Total fly ash emissions to the environment in 1968 were estimated at 36 X 10l2g (4 X lo7ton).l Fly ash particles may adsorb gases or vapors, some of which are potentially toxic, in the exhaust stack and plume.2 If the environmental effects of fly ash are to be adequately assessed, adsorption and desorption of sulfur dioxide, polycyclic aromatic hydrocarbons (PAH), and other vapors present in the stack must be characterized. Measurement of adsorption rates for all vapors present in the stack is not feasible; therefore, models must be used to generalize those conclusions made from available data. Water vapor, chosen for this initial study, is readily adsorbed by fly ash and is present at a higher concentration than any other vapor which is present in the stack ( - 4 % by eight).^ Adsorption isotherms for the small polar water molecule show certain pe~uliarities,~-~ but some general conclusions have been drawn from the rate data presented in this paper. The primary emphasis of this paper is the comparison between experimental data for the interaction of water with fly ash and those predictions derived from models. Because of dilution, some vapor phase materials are present in high concentrations in the stack and are at significantly lower concentrations in the ambient air. Such materials may be adsorbed by particles in the stack and may subsequently be desorbed to ambient air. Therefore, sorption rate data must be measured and compared to contact times which are within the range 1-40 s in the stack8 and 1 h to several weeks in the plume.' Adsorbed water may prevent adsorption of other mole c u l e ~ . ~The , ~ moisture load of fly ash is, therefore, of 0022-3654/80/2084-1644$0 1.OO/O
environmental interest, and some preliminary estimates have been made from the data presented herein. Models and Method of Data Analysis Different treatments of the kinetics of adsorption, each with different basic assumptions, have been reviewed in standard t e ~ t s . ~ J The ~ J l treatment given by Natusch and Tomkins2which explicitly treats adsorption of vapors by fly ash in the stack and plume is discussed in detail. The mathematical approach used by Natusch and Tomkins would appear adaptable to other adsorption models (BET, Freundlich, Temkin, etc.)I0and other adsorbates. Specific parameters used were selected to be appropriate for polycyclic aromatic hydrocarbons (PAH).2 Natusch and Tomkins use a Langmuir modeP modified to include activation energies for both adsorption and desorption.13 They used three simplifying assumptions: (A) activation energies for adsorption, E,, and desorption, Ed, are independent of temperature; (B) the sticking coefficient, c, is independent of temperature and extent of reaction; and (C) mass transfer process at the air-solid interface can be disregarded. Three additional assumptions implicit in the treatment given by Natusch and Tomkins are (D)the solid surface contains a fixed number of sites, each of which can hold one adsorbed molecule; (E) activation energies E,, Ed are independent of degree of reaction which implies that the surface is uniform and no sorbate-sorbate interaction nor strong sorbate-sorbent chemical interaction occur; (F) available surface area per particle is 4rd2,that is the particles are spherical and have ratio of actual to geometric surface area (roughness factor) equal to one. Assumptions A-E are widely used in treatments of adsorption and desorption rates and equilibria. Available surface area data suggest that assumption 0 1980 American
Chemical Society
The Journal of Physical Chemistry, Vol. 84, No. 12, 1980 1645
Coal Combustion Fly Ash Characterization
-
TABLE I: Adsorption for Coal-Fired Fly Ash BET sample no.
combustor type conventional
2b
sample weight, mg
coal type several
Standard Sample 214.1
Bag House Samples 53.9 Colorado 49.2 western 47.6 Montana rosebud 35.4 Texas lignite Filter Samples 9C experimental FBC Montana rosebud 23.5 13c experimental FBC Texas lignite 26.7 a Blank corrections (Rothenberg, 1980) have been applied to these data. from adsorption curve, no data obtained at P < 1 torr. 4c 5c 7c 8c
stoker fed conventional experimental FBC experimental FBC
400r
I
weight N,, PP
specific surface area, mz g-'
water adsorbed,a pg 0.5 torr 3 torr
129
2.1
130
200
550 75 70 207
35.5 5.3 5.1 20.3
350 70 50 140
1700 9 20 620 815
22 3.2 (200)d 1000 120 15.7 110 385 Data at 20 C. Data at 0 "C. Estimate
experimental data with arbitrary changes in xi. A set of curves, all having different intercepts and the same slope, b , was obtained. Natusch and Tomkins used estimates of the parameters E,,Ed,and c to predict values for k,, kd, and tl 2. Predictions made are very sensitive to the value o E, employed. For physical adsorption, E, is assumed to be zerolo and Edequal to the heat of adsorption AH. Natusch and Tomkins use a value of 10 kcal/mol for E, for adsorption of PAH which is appropriate to the dissociative chemisorption of organic compounds on metaldo and may possibly be correct for activated migration (or diffusion) in m i c r o p ~ r e s . ~ JPredicted ~J~ values of tl12vary continuously and monotonically from lo6 s ( e 2 week) at 0 "C to less than 1 s at temperatures above 200 "C. Thomas and Thomasll treated adsorption by porous catalysts for which assumptions C and F are not valid. They concluded: "on gradually raising the temperature (of the sample), there will be a smooth transition from a true chemical rate to a rate determined by diffusion". Recent work on diffusion-controlled adsorption has been reviewed by Debelek and Wright.lsJg Over the range 0-300 "C, the rate of a reaction controlled by diffusion will increase by -50%. The heat of adsorption varies with surface coverage and temperat~re.~ Models ? ~ ~ treating changes in AH are discussed by Hayward and TrapnelllO whose discussion is limited to pure sorbents and is not generalized to heterogenous materials such as fly ash. The models discussed all treat the adsorbent as a fixed structure with an unchanging number of adsorption sites. In the discussion of Findenegg's paper,21 Adamson emphasized the need to consider changes in both adsorbent and adsorbate. Fuller22has studied several systems in which both the equilibria and kinetics could not be adequately treated without considering changes in the adsorbent. The applicability of these concepts to the fly ash/water system is discussed.
i
200
P=2 Torr
P = 3 Torr
--__________ 3
4
TIME IN MINUTES
Figure 1. Microbalance chart recorder trace following admission of water vapor (s,[imple8, 0 "C).
F is not correct for fly ash particles14 and electron microscopy studies have shown that the morphology of fly ash does not correspond to smooth spherical particles for conventional combustors14J5 or for an experimental fluidized-bedl combustor (FBC).14J6The third assumption is not normally employed when treating porous adsorbents.ll First-order kinetics may be expressed as In [(x, - x)/(x, - xi)I = -bt ( 1) where x, is the weight of water adsorbed at equilibrium and at vapor pressure P, x is the weight adsorbed at time t , xi is the initial weight, and b is a constant. The time, tl q , required to adsorb a fraction l / q of the total amount oi water adsorbed, x, - xi, is readily measured (Figure 1). If first-order kinetics are obeyed, then tl/, = -1n (1 - l / d / b
(2)
which is a generalized form of the equation used by Natusch and Tomkins to predict values for t l p Langmuir's theory is a particular case of first-order kinetics for which
b = k,P + k d
(3) where k, and kd are rate constants for adsorption and desorption and P is adsorbate pressure. Values of b may be predicted theoretically from Langmuir's theory if assumptions A--E are made. Values may also be empirically determined. The values of b which are presented herein are empirically determined from the slopes of log-linear data plots (eq 1). The value of xi is subject to considerable uncertainty, as discussed below. However, to a first approximation, the value of b is independent of xi. This has been confirmed by differentiating eq 1and by plotting the
Experimental Section The apparatus used, a vacuum microbalance (Cahn RG 2000) and Edwards pumping assembly, the experimental procedures, the samples examined, and their chemical composition have been described previ0us1y.l~Adsorption data are summarized in Table I. A typical trace from the microbalance chart recorder which follows admission of water vapor is shown (Figure 1). The sample adsorbed water vapor and increased in weight until it reached a new constant (equilibrium) weight. The time required to reach equilibrium is of significance. Chart recorder traces were used to obtain rate
1646
The Journal of Physical Chemistry, Vol. 84,
No. 12, 1980
Rothenberg and Cheng
TABLE 11: Rate Data for Adsorption of Moisture from Mixtures of Nitrogen and Water Vapor for Fly Ash from an Experimental FBC Burning Texas Lignite sample no. 9
sample weight, mg 23.5
temp, " C
torr
PI 9
p* torr
0 0
2.6 3.5
3.5 4.2
9
weight change, pg 800 2080
tl I?, min
tl!,, rnin
150 540
360 1440
t3/4,
min 840 2760
TABLE 111: Data for Fly Ash from an Experimental FBC Burning Montana Rosebud (Sample 7 ) sample weight, mg 47.6
p ,9 torr
temp, 'C 0 0 0
1
50'"
3 3 3 2 2 2
100a 150a 200a 250a 300a
3
10-3 x x 10-5
x 10-5 x 10-5
p2 torr 9
2 4 3x 3x 4x 3x 2x 2x
weight change, b g t 55 t 1505
10-5 10-5 10-5 10-5
- 80
- 20 - 60 -50 -125 - 230 - 90
t l 1.49
tl(2,
ty4,
min 1
min
min
1.5 48 120 8 4 4 50 30
2.5 72 530 25 14 7
6 34 4 2 2 6 18 5
10-5 b x 10-5 10-5 45 x 10-5 z x 10-5 9 24 a Data obtained on raising sample temperature from that recorded immediately above (e.g., 0 -+ 50 "C). Room thermostat failed during night, leading to large uncertainties in readings. The balance requires a constant temperature environment to give reliable readings.
data. Rates of adsorption and desorption of water vapor at 0 "C were measured over the pressure ranges 0.1-4 torr (adsorption) and 4-104 torr (desorption). Rates of adsorption or desorption of water were measured at higher temperatures for some samples. Measurements for one sample were carried out by using a mixture of water vapor (1-4 torr) diluted by nitrogen (Matheson Research Grade) at 500 torr. This experiment was carried out to determine whether the presence of an inert gas (or air) changed the rate of adsorption of water vapor. Nitrogen was bubbled through a saturated calcium chloride solution and water vapor pressure was controlled by regulating the temperature in the bubbler train. Temperature control was fl "C. The corresponding uncertainty in the water vapor pressures is -20%. Treatment of Data. Values of tll, are readily determined (Figure 1) and may be compared with values predicted by Natusch and Tomkins,2as well as with residence times in the stack and plume. Therefore, tll, was selected as one of the most reliable and useful measurements which could be derived from the data. Rates of change of weight (dx/dt at time tllq) were also calculated. Precision. Normal weighing precision was fl pg. At sample temperatures of more than 50 O C corrections for thermomolecular flow forces (TMF) are significant. The TMF at 200 " C varied between 10 and 50 pg over the pressure range 3-15 torr. When the system was pumped down the TMF correction passed through a sharp maximum of 400 pg at - 5 X torr, and became less than 5 bg at pressures less than lo4 torr.14 Desorption data were normally obtained at pressures for which the TMF correction was less than 10 pg, however, this was not possible for adsorption data. The sample is blown from the balance pan (aerosolized) if adsorbate is admitted too rapidly to the balance. Initial rate measurements were not attempted. The uncertainty in tl/ caused by admitting vapor slowly is approximately half h e time of vapor admission (normally -5 s).
Results and Discussion Adsorption equilibrium was attained rapidly even at 0 OC at low pressures (less than 0.5 torr water vapor). Times taken to reach adsorption equilibrium at pressures over 2 torr were several hours in some cases. In the presence of 500 torr of nitrogen as diluent values of tllz exceeded 1 day (Table 11). Times taken to reach desorption equilibrium exceeded 1 min at all temperatures and
pressures studied, and often exceeded 1 h. When a small quantity of water vapor was admitted to the vacuum bottle to create a pressure less than 0.5 torr, the sample weight increased rapidly and then decreased as water vapor pressure decreased. A similar decrease in pressure was observed during blank runs and was probably the result of adsorption of water vapor on the glass walls of the apparatus. The lag time between the peak in the pressure curve and the peak in the sample weight curve ranged from 10 to 50 s which is indicative of the speed at which equilibrium was attained. However, detailed kinetic analysis was not attempted. Changes in water vapor pressure subsequent to vapor admission were small (less than 0.2 torr) at pressures above 1 torr, presumably because the glass was now covered by a complete monolayer of water and further adsorption was small. The glass appears to have acted as a buffering reservoir,of water vapor, since the adsorption determined for some samples exceeded 1.5 mg, which is sufficient to cause a change in pressure of 0.4 torr in a constant volume system of 4-L capacity. Values of tlis were measured at pressures greater than 1 torr. Data were obtained for samples of National Bureau of Standards Reference Material No. 1633 (NBS fly ash) and fly ash from a Stoker fed power plant, a conventional pulverized coal-fired power plant, and an experimental FBC burning either Montana rosebud or Texas lignite. Data for one sample are shown in Table 111; data for other samples are available as supplementary material (see paragraph at end of text regarding supplementary material). Despite the range of temperatures, pressures, combustor types, and coal types investigated, the range of values obtained for tllz was small. No values of tl over 120 min were observed. Typical values appeare to be between 5 and 30 min which are long compared to stack residence times but are short compared to plume residence times. Thus, equilibrium adsorption isotherms may be used to estimate the moisture load of fly ash in the plume but not in the stack. The change of tl12 with temperature determined experimentally for desorption (Table 111)was much less than that predicted by Natusch and Tomkins for PAH,' corresponding to smaller mean values of the activation energies of adsorption and desorption (Ea,Ed) for the interaction of fly ash and water vapor, 0-300 OC. The plot of rates against temperature (Figure 2) suggests that assumptions A and E are not valid for the desorption of
d
Coal Combusticin Fly Ash Characterization
The Journal of Physical Chemistry, Vol. 84, No. 12, 1980 4
3.7 Torr
1647
r E
2007 -\-
0.4 0.2
o
r
I
'
10
-&--do
'
20 30 TIME (minutes)
Figure 4. Adsorption data, variation of sample weight with time at different adsorbate pressures, 0 OC (filter sample of fly ash taken at stack exit, Texas Lignite, FBC, sample 13).
Figure 2. Desorption data, variation of I/Uxdx/dt with temperature (sample 7).
,
O.Ol0
2
6
4
8
TIME (minutes)
Figure 5. Comparison of adsorption rate data with eq 1, plots of log [ ( q - l ) / q ] vs. t (sample 8). TIME (minutes)
Figure 3. Adsorption data, variation of sample weight with time at different adsorbate pressures, 0 "C (baghouse fly ash, Texas Lignite, FBC, sample El).
water vapor by fly ash. A peak can be observed at a furnace temperature of -125 "C, and an upward trend above 250 "IC. Similar desorption curves have been obtained by F~hredi-Milhofer~~ for hydroxylapatite and by Peri7 and h4atsushima6 for alumina. The first peak is caused by desorption of physically adsorbed water molecules. The trend above 250 "C is the result of the onset of desorption of strongly bound water6v7pZ3 probably resulting from desorption of chemisorbed water and water formed by condensation of hydroxyl group^.^^' Fly ash includes several components which can react chemically with water.14 An estimate of the heat of adsorption at 0 "C may be made from adsorption data by the method of Keattch and Dollimore which is based on BET theory.24 Monolayer completion occurred at pressures between 0.01 and 0.2 torr,14corresponding to heats of adsorption between 1and 5 kcal greater than the latent heat of vaporization of water. If first-order kinetics are obeyed, the ratio t1/4:t1/2:t3/4 should be 0.42:1.0:2.0 (eq 2). For the data analyzed, the were mean values) and standard deviation of t1/4:t1/2:t3/4 (0.46 f 0.16]1:1.0:(2.26f 0.75). A third of the ratio values obtained agreed within estimated experimental error (*lo% ) with the values predicted for first-order kinetics. Adsorption of water at 0 "C by samples of fly ash from an FBC burining Texas lignite (samples 8 and 13, respectively) is plotted as a function of time in Figures 3 and 4.
I
0.01 0
,\
I
I
I
I
3
6
9
12
15
TIME (minutes)
Figure 6. Comparison of adsorption rate data with eq 1, plots of log [ ( q - l ) / q ] vs. t (sample 13).
Four pressures were chosen for each sample to demonstrate the kinetics characteristic at different positions of the adsorption isotherms. Figures 5 and 6 are curves fitted to eq 1. There is a rapid initial adsorption stage for sample 8 where as much as 30% of adsorption takes place within 10 s. The data follow eq 1quite well following rapid initial adsorption. There is considerable uncertainty in the value of xi which should be inserted in eq 1because of the shape of the adsorption curve (Figure 1). If the value of x i is adjusted to x ( (Figure l),plots which are linear for more
Rothenberg and Cheng
7.
M of llbagalnst
P. show@
adsorpaOn data fasamples
8 and 13. 50
40
1 ' I 30 E
F
I
E
P
P
e
20
IO
0 P
npua 8.
P TORR
P
Hysteresis loops obtained wim water (adsorption (0); deswptlon (m)).
P
vapor as adsorbate
than 90% of the mass change are obtained and it appears that within experimental error the adsorption obeys first-order kinetics throughout the adsorption. As discussed above, the value of b obtained (eq 1)is not altered by more than 5%. Plots based on xi. not x ( . have been used, since these show clearly that the adsorption consists of a t least two components, a fast initial phase followed by a slow first-order adsorption. When the constant l l b is plotted as a function of equilibrium pressure (Figure 7),data for the two samples of Texas Lignite fly ash fall onto a single curve. The constant increases with pressure contrary to the Langmuirt2or Natusch and T o m k i d models, however, their models were intended for nonporous materials and monolayer adsorption. Rate data and irreversibility in the isotherms (Figure 8) suggest that fly ash particles from both conventional combustors and the FBC may be porous. Holes in the shells of conventional fly ash particles may he discerned in SEM pictures (Figure 9). The increase in the time constant may be the result of mass transport processes in the pores. Adapting the methods given by
h
A
Flour. 8.
SEM 01 broken shells of conventional combustcf fly ash particles. showing holes in shells: pictures by Sturm and Carpenter.
Crank% (Chapter 8). we can show that, if the diffusion process is of importance, then the effective diffusion coefficient will decrease as P increases and the constant l l b will increase. The increase in values of tl12with increasing P obtained for other samples studied, the increase in values of tl12caused by 500 torr of nitrogen as diluent, and the values o f t , in excess of 1min obtained at temperature of 200 and above may also be tentatively explained by diffusion control. FulleP has suggested that the fast phase of adsorption (Figure 1) is the result of adsorption on the exterior of the particle, while the slow phase is penetration of water into the interior of the particles.
"d
Coal Combusticin Fly Ash Characterization
The phenomenon of adsorption is caused by presence of unsaturated surface forces. Therefore, sorption must change the surface and the sorbent. The models discussed do not considler changes in the sorbent. Our rate data are very similar to data obtained by Fuller (Figure 9 of ref 22) for adsorption of nitrogen by a pelleted silica-alumina catalyst. Fuller22explains his data by considering “flexure” within the adsorbent,. As the interstices of the system are filled, the sorbent is modified by the capillary forces of the sorbate. Welll-known examples are clays and coals which swell markedly during ad~orption.~’For more rigid adsorbents, such as burnt clay and fly ash, both resistance to adsorption and values of tIl2may increase as adsorption proceeds. Future study comparing predictions from diffusion and flexure models is planned. Concentrations of water vapor in the stack of an experimental fluidized-bed combustor (FBC) may be estimated as 4 f 1% wt/wt from published coal analysis data, coal/air feed ratios,16*28 and the stoichiometric equations for combustion of coal. Rate data for adsorption of water vapor at 0 “C!and pressures less than 0.5 torr suggest that monolayer completion probably occurs in times comparable to stack residence times. The initial rate of adsorption of water for the 1.8 torr of H20/500 torr of nitrogen mixture also suggests this. ‘rimes taken for multilayer formaition and pore filling were much longer than stack residence times, and these slow processes are probably not significant in the stack.
Conclusions Monolayer formation by physical adsorption is usually rapid, but micropores fill and empty slowly over a wide range of temperature^,^ with half-times which usually exceed 1 min and may exceed 1 day. Rate data presented here suggest that vapors adsorbed in the stack and plume may be retained for long periods. Mass transfer processes may be rate determining in adsorption and desorption of vapors by fly ash. There is probably no activation energy for adsorption of water by fly ash and tlhis may be true for most vapors. Adsorption isotherms may be used to estimate the moisture load of fly ash in the plume, but may lead to overestimates of the moisture load in the stack since the time of residence in the stack is an order to magnitude smaller than the half-time for adsorption. Acknowledgment. This research was supported by the National Institute of Environmental Health Sciences and the U S . Deplartment of Energy under Contract No. EY76-C-04-1013. We thank our colleagues, especially R. Pfleger and 13. Mokler, for many helpful suggestions and for review of the manuscript, and A. Ferris for editing; also F. Williams (University of New Mexico), D. Natusch and E. L. Fuller for discussion and access to material in press,
The Journal of Pbysical Chemistry, Vol. 84, No. 12, 1980
1649
Hugh McDonald for data on C.E.G.B. power plants, T. Thoem (EPA) for data on EPA Region 8 power plants, and an anonymous reviewer for his comments.
Supplementary Material Available: Tables IV-VI containing additional data for fly ash from various coal samples (3 pages). Ordering information is available on any current masthead page. References and Notes (1) J. H. Seinfeld, “Air Pollution: Physical and Chemical Fundamentals”, McGraw-Hill, New York, 1975. (2) D. F. S. Natusch and B. A. Tomkins, “Carcinogenesis-A Comprehensive Survey”, Vol. 3, P. W. Jones and R. I.Freudenthal, Ed., Raven Press, New York, 1978, pp 145-153. (3) Estimate made from publlshed data for coal/air feed ratios, see ref 16 and 26. (4) S. J. &egg and K. S. Sing, “Adsorption, Surface Area and Porostty”, Academic Press, New York, 1967. (5) M. A. F. Pyman and A. M. Posner, J. C O W Interface Sci., 88, 85-93 (1978). (6) T. Matsushima and J. M. White, J . Catal., 44, 183-196 (1976). (7) J. 8. Peri, J. Pbys. Cbem., 89, 211-219 (1965). (8) Estimates made from publlshed flow rates and dlmenslons for a large modern conventional power station (Klngsnorth Power Station, Central Electricity Generating Board, Bankside House, London, 1975), and for over 50 stations in EPA region 8 (G. E. Parker and G. Boulter, Region 8, 1977 Power Plant Summary, EPA-908/4-78-002, 1978). (9) R. B. Gammage, E. L. Fuller, and H. F. Holmes, J. Colloid Interface Sci., 38, 91-96 (1972). (10) D. 0. Hayward and B. M. W. Trapnell, “Chemisorption”, 2nd ed, Butterworths, Washington, D.C., 1964. (11) J. M. Thomas and W. J. Thomas, “Introduction to the Principles of Heterogeneous Catalysis”, Academic Press, New York, 1967. (12) I.Langmulr, J. Am. Cbern. SOC.,38, 2221-2295 (1916). (13) H. S. Taylor, J. Am. Cbem. Soc., 53,578-597 (1931); Cbem. Rev., 9, 1-47 (1931). (14) S. J. Rothenberg, Atmos. Envlron., accepted for publication. (15) G. L. Fshar, D. P. Y. Chang, and M. Brummer, Sclence, 192,553-555 (1976). (16) M. H. Mazza, D. A. Green, M. W. Paris, and G. J. Newton, “Mineral Characterization of Fluidized-Bed Combustion Aerosol Ash-Montana Rosebud Sub-Bituminous Coal”, MERC/TPR 78/1, 1978. (17) V. M. Bulashev, V. K. Popov, L. A. Kogan, and L. 0. Ol’shanetskil, Cherniya Tverdogo Topliva, 10, 5, 75-80 (1976). (18) A. L. Wright, A. S. Berman, and S. Prager, J. Pbys. Cbem., 82, 2131-2135 (1978). (19) K. A. Debelak and J. T. Schrodt, J. ColbidInterface Scl., 70, 67-73 (1979). (20) B. A. Hendrikson, D. R. Pearce, and R. Rudham, J. Catal.,24, 82-87 (1972). (21) G. H. Flndenegg and W. V. Rybinski, presented at 53rd Colloid and Surface Science Symposium, Rolla, 1979. (22) E. L. Fuller, Jr., “Microgravimetrlc Studies of Catalysts and Catalytic Processes” In “Mlcroweighing in Vacuum and Controlled Environments”, A. W. Czanderna, Ed., Elsevier, New York, 1979. (23) H. Fijrdi-Milhofer, V. Hhdy, F. S. Baker, R. A. Beebe, N. W. Wikholm, and J. S. Kittelberger, J. Colloid Interface Sci., 70, 1-9 (1979). (24) C. J. Keattch and D. Dollimore, “An Introduction to Thermogravimetry”, 2nd ed, Heyden, London, 1975. (25) J. Crank, “The Mathematics of Diffusion”, 2nd ed, Oxford University Press, London, 1975. (26) E. L. Fuller, personal communlcatlon. (27) E. L. Fuller, presented at 53rd Colbd and Surface Sclence Symposium, Rolla, 1979. (28) J. S. Mei, U. Grimm, and J. S. Halow, “Fluidized Bed Combustion Test of Low-Quality Fuels-Texas Lignite and Lignite Refuse”, MERC/RI-78/3, 1978.
