208
Energy & Fuels 1993, 7, 208-214
Use of Equilibrium Calculations To Predict the Behavior of Coal Ash in Combustion Systems J. N. Harb,* C. L. Munson, and G . H. Richards Department of Chemical Engineering and Advanced Combustion Engineering Research Center, Brigham Young University, Provo, Utah 84602 Received June 10, 1992. Revised Manuscript Received January 4 , 1993
This paper examines the use of computer calculations to estimate the phase and species composition of silica-based systems which are important in slagging and high-temperature fouling deposita that form in pc-fired utility boilers. Advanced numerical techniques were used to minimize the free energy of the system in order to determine the equilibrium composition and phase distribution while avoiding the numerical problems often associated with such calculations. The equilibrium model, which assumed ideal solutions of complex species, adequately approximated the behavior of a variety of systems for which experimental phase diagrams were available. The model, however, performed poorly for certain silica-rich systems due to an inadequate representation of the silica activity. Comparison of calculated results for actual coal ashes with the experimentally observed behavior showed good agreement for systems which did not have SiOn(1)in the calculatedresulta. Calculations for ashes with high silica content predicted excessive amounts of liquid that were inconsistent with the experimental observations. The addition to the calculations of an empirical constraint on Si02(l), based on eutectic temperatures from ternary phase diagrams, yielded good agreement between the calculated results and the observed slagging behavior.
Introduction
These two studies suggest that equilibrium predictions are applicable in the analysis of slagging deposits in coalfired boilers. It is more difficult to assess the role of equilibrium in the prediction of fouling behavior where low-meltingsulfates play a role, since thermodynamic data for many of the complex sulfate systems are not readily available. Also, the time scales associated with fouling are often much longer than those associated with slagging due to reaction limitation^.^ Therefore, equilibrium is less likely to be reached. However, in instances where the appropriate data are available, equilibrium will always provide limiting information regarding species formation, even when other factors must be considered. Ideally, one would like to perform equilibrium predictions for systems of arbitrary complexity from a knowledge of the temperature, pressure, and elemental composition of the system, without the limitations and simplifications associated with the use of phase diagrams. This objective can be adequately met by computer calculation of equilibrium conditions which provides a quantitative measure of the amount of liquid (phase) and the chemical species present. The purpose of this paper is to examine the use of computer calculations to estimate the phase and species composition of silica-based systems which are important in slagging and high-temperature fouling deposits that form in pc-fired utility boilers.
One of the major factors limiting coal utilization is the presence of inorganic constituents (mineral matter) in the coal. Characterization of the chemical composition and phase of both ash particles and deposits is essential to the understanding and prediction of mineral-related problems. For example, the minimum temperature at which significant amounts of liquid are present has an important influence on both the capture of ash and the physical state of deposits on boiler walls. Equilibrium represents a natural limit to the mineral transformations which may occur. This paper examines the utility of equilibrium calculations for prediction of coal ash behavior in combustion systems. Previous studies have indicated that equilibrium phase diagrams can be used to predict coal ash species and phases. Sanyal and Williamson’ used high-temperature microscopy to observe the melting and crystallization behavior of “low-temperature” ashes prepared from two subbituminous coals. Observations of the crystallization behavior, which included identification of the principal crystalline species, were consistent with behavior expected from a phase diagram for the three principal components CaOAl203-SiO2. In a subsequent study, Kalmanovitch, Sanyal, and Williamson2 outlined a technique for predicting the liquidus temperature and crystallization behavior of coal ashes by plotting normalized ash compositions on equilibrium phase diagrams (ternary cuts at fixed FeO levels) for the CaO-FeO-Al203-SiO2 system. This information was then used to assess the slagging propensity of the coal. Good agreement was observed between the predicted slagging propensities and reported performance in actual boilers.
Calculation of the equilibrium phases and their composition was performed by minimizing the Gibbs free energy of the system. This method is well adapted to complex systems and has been used previously by a number
(1) Sanyal, A.; Williamson, J. J. Inst. Energy 1981,54, 158-162. (2)Kalmanovitch, D.P.; Sanyal, A.; Williamson, J. J. Inst. Energy 1986,59, 20-23.
(3) Benson, S. A.; Jones, M. L.;Harb, J. N. Ash Formation and Deposition. InFundamentalsof CoaECombllstionfor CleanandEfficient Use; Smoot, L. D., Ed.; Elsevier: New York, 1992; Chapter 4.
Equilibrium Model
0887-0624/93/2507-0208$04.00/00 1993 American Chemical Society
Coal Ash in Combustion Systems
Energy & Fuels, Vol. 7, No. 2, 1993 209
of investigator^.^^ The expression for the Gibbs free energy, g, to be minimized is NT
where p j and nj are the chemical potential and moles for species j , respectively, and NT is the total number of species. The chemical potentials are represented as p j = pjo
+ RT In ai
(2)
where pj0 is the standard-state chemical potential and aj is the activity of species j . The minimization is subject to a mass balance constraint for each element, i, NT
C a i j n j- pi = o i = I, ..., 1
(3)
j=l
where aij is the stoichiometric coefficient of element i in species j , & is the number of moles of element i in the overall system, and 1 is the total number of elements. Several assumptions were made in order to approximate the activities ( U j ) in eq 2. First, only pure solids were considered. A value of unity for the activity of pure solids gives the following expression for the chemical potential of a solid species: = P,' (4) Second, it was assumed that the behavior of gas-phase species can be adequately represented by the ideal gas law. The chemical potential of gas phase species can therefore be expressed as pj
pj
= p j o + RT In (nj/nTg) + RT In (P/Pref)
(5)
where (nj/nT,)is the mole fraction of species j in the gas phase and P is the system pressure. Finally, it was necessary to approximate the activity of liquid-phase species. There are two basic approaches to modeling the liquid phase activities, as discussed by Berman and Browns8 In the first approach, referred to as a speciation model, the Gibbs free energy of the system is based on the actual species present in the melt. There are many types of complex species which form in molten silicate s y ~ t e m s . ~ ~For ~ -example, l~ NazO and Si02 in the liquid phase may behave as NaZSiOa rather than the individual oxides. A speciation model explicitly accounts for the presence of such complex species (e.g., NazSiO3) in the calculations. Standard-stateproperties are needed for each of the complex species Considered. An advantage of this approach is that the activity coefficients of the complex species are often close to unity.12 However, the (4) Eriksson, G. Chem. Scr. 1975,8,100. (5)Gordon, S.;McBride, B. J. NASA Report NASA SP-273,1971. (6) Blander, M.; Pelton, A. D. Geochim. Cosmochim. Acta 1987,51, 85-95. (7)Ramanathan, M.; Kalmanovitch, D.; Ness, S. Preprints of Papers Presentedat the 197th ACS National Meeting: Dallas, Texas, April 9-14, 1989;Vol. 34,311-317. (8) Berman, R. G.; Brown, T. H. Reuiews, in Mineralogy, Volume 1 7 Thermodynamic Modeling of Geological Materials: Minerals, Fluids and Melt; Mineralogical Society of America: Washington, DC, 1987;pp 40.5-437. .- - - - . . (9)Stebbins, J. F.;Murdoch, J. B.; Schneider, E.; Carmichael, I. S. E.; Pines, A. Nature 1986,314, 25C-252. (10)Taylor, M.; Brown, G. E. Geochim. Cosmochim. Acta 1979,43, 61-75. (11)Taylor, M.; Brown, G . E. Geochim. Cosmochim. Acta 1979,44, 109-118. (12)Hastie, J. W.; Bonnell, D. W. High Temp. Sci. 1985,19,275-305.
development of speciation models is limited to some degree by the inherent complexityof molten silicate systems which makes it difficult to determine the actual species present in the melt. Therefore, the complex liquid species or components used in the speciation approach can be considered subphases that simulate the local associative order;12 these subphases do not necessarily represent independent molecular or ionic species present in the melt. The second type of approach is a stoichiometric model in which a minimum number of chemical species, equal to the number of components in the system, are considered (Le., minimum number of species needed to span the compositional space of interest). The stoichiometric approach does not require the chemical formula of any of the components to represent a species that is actually present in the melt. Therefore, the simple oxides are often chosen as the component species. Both the interaction of components to form complex species and nonideal mixing are taken into account through activity coefficients. It is necessary to calibrate the model by fitting several adjustable parameters to experimental data in order to obtain the required expressions for the activity coefficients. However, proper fitting or calibration of the model parameters does allow representation of the data to within experimental accuracy.8 Therefore, the stoichiometric approach provides an accurate method for interpolation of phase equilibrium data. Its use, however, is best suited to systems for which extensive experimental data are available. The quasichemical approach developed for silicate systems by Blander and Pelton6 is essentially a stoichiometric method which accounts for the structure of complex (ordered) species in the melt in order to generalize the procedure and minimize the number of adjustable parameters. This method was usedto fit phase equilibrium data from binary systems to within experimental accuracy. A strong point of this approach was that it was also possible to extrapolate to composition and temperatures other than those used to calibrate the model. For example, binary parameters were used with some simple mixing rules to predict the behavior of ternary systems containing a single acidic component (Si02).6 However, most practical coal ash systems contain A1203and perhaps other oxides which exhibit both network forming and network modifying characteristics. Prediction of these systems requires calibration of the stoichiometric model with ternary data in order to fit additional empirical parameters.I3 The present study uses a speciation model to calculate the equilibrium phases of coal ash systems. In addition, ideal liquid mixtures were assumed.I2 The expression for the chemical potential of the liquid-phase components is therefore p j = pjo
+ RT In (nj/nTJ
(6)
where n,/nTl is the mole fraction of species j in the melt. The present approach allows calculation of a wide variety of chemical systems which contain a relatively large number of components; it has been the basis of a number of popular equilibrium codes. The only data required are the free energy data for the complex species considered. Therefore, it is not necessary to calibrate the model for each system of interest. On the other hand, the approximate nature of this model is clearly recognized. In (13)Pelton, A. D., personal communication, 1991.
210 Energy &Fuels, Vol. 7,No. 2, 1993
Harb et al.
particular, a single set of complex species was chosen for use with all the chemical systems considered. In general, these species will not represent the actual species in solution for the total range of systems and compositions. Also, it is impossible to represent the immiscibility gap (found, for example, on the silica-rich side of the equilibrium phase diagrams) with the assumption of ideal solutions. A key question addressed in this paper is whether or not this method is sufficiently accurate for engineering purposes. Numerical Considerations. A disadvantage of the speciation approach is that a large number of species must be considered and the species which will be present in the final solution are not known a priori. Therefore, it is likely that the equilibrium concentration of several of the species considered will be zero or that phases assumed in the initial solution will not be present in the converged equilibrium solution. Because of this, minimization of the free energy calculationswhich include condensed phases are frequently plagued by numerical problems. One strategy for avoiding these problems has been to limit the number of condensed species according to the Gibbs phase rule, and then swap species until the most thermodynamically favorable ones (Le., the set which yields the lowest free energy) are identified. However,this procedure is somewhat awkward and difficult to converge. Numerical problems were avoided in the present study through the use of a sophisticated minimization algorithm developed at Brigham Young University.14 The algorithm is a hybrid of the generalized reduced gradient (grg) and sequential quadratic programming (sqp)algorithms;it has been tested on a wide variety of engineering design problems and is the basis for the general purpose optimization code OPTDES.15 The algorithm is coded to permit simultaneous consideration of the entire species set. It does not require that phases present in the initial solution be present in the final equilibrium solution. The algorithm also requires that intermediate solutions remain feasible as the optimum is approached. A tight convergencetolerance was necessary to prevent the calculations from stalling before reaching the minimum since the changes in the free energy were very small. Converged solutions containing more than one phase were also checked to make sure that phase equilibrium constraints had been satisfied. Specifically, multiphase systems at equilibrium should satisfy the following pja
= p.8 J = piy
(7)
where the superscripts a, 0, and y represent different phases. CalculationalStrategy. Inputs to the model included the elemental composition of the system of interest and the temperature(s1 at which the calculations were to be performed. Based on the elemental composition, the computer program selected all of the species in the database (solid, liquid, and gas) which contained one or more of the elements entered by the user. Species which contained elements other than those specified by the user were not considered. Although the numerical algorithm was capable of handling a large set of unknowns, it was desirable to reduce (14)Parkinson, A.; Wilson, M. Trans. ASME 1988,110, 308-315. (15)Parkinson, A.; Balling, R.; Free, J. OPTDESBYU User's Manual; Department of Mechanical Engineering, Brigham, Young University: Provo, UT 84602,1988.
the number of species considered in order to enhance computational efficiency. In order to accomplish this, the following strategy was used. First, the equilibrium problem was solved for pure species only (no activity corrections) as suggested by Ramanathan et al.' The equilibrium problem without the activity corrections is a linear problem which is relatively easy to solve. The solution to the linear problem was then used as a basis to reduce the number of species considered in the full nonlinear calculation.16 Finally, the minimization algorithm was used to obtain the solution to the nonlinear equilibrium problem which included mixing of species in the gas and liquid phases. ThermodynamicDatabase. Studies have shown that equilibrium computations are very sensitive to errors in thermodynamic data, as well as to the kinds and numbers of species considered in the ~alcu1ations.l~ Hence, the quality of data in the database and the species making up the database have a significant effect on results. A database of Gibbs free energies of formation was compiled for use in the calculations. The primary sources include the JANAF tables,l8 mineral thermodynamic data from a US. Geological Survey Bulletin,lg and Hastie et which lists thermodynamic data for complex oxides from the NBS phase equilibria data base. From these sources, data entries for about 125 solid and liquid mineral species and about 40 gas species have been selected. These are mineral and gas species of interest in high-temperature mineral equilibria; data for hydrocarbons, for example, are for the most part absent. Temperature ranges for the data extent in most cases from 298.15 to 3000 K. The data were fit to an expression of the following formI6
+
g(T) = ( A / T )+ B + CT O F + Er? + FT In T (8)' where A-F are numerical coefficients for each species for a given temperature range. The database itself contains speciesnames, stoichiometric information, and sets of these coefficients for 1-3 temperature ranges for each entry, as well as the source from which the data were taken. It was necessary to adjust the free energy values of some species in the database to ensure that the solid to liquid phase transition occurred at the proper temperature (melting point) for each species. Inaccurate prediction of melting points was believed to be attributable to experimental uncertainty in the data, imperfect curve fits, and inconsistency between data obtained from different sources. Although the magnitude of these adjustments typically varied between 0 and 0.17'% , adjustments of as much as 3-5 ?6 were necessary for a few solid-liquid species pairs, especially those where solid data and liquid data for the same species were taken from different sources. The data from the source considered less reliable (e.g., estimated data) was adjusted to correct the phase transition point of the pure species. Adjustments were made prior to performing the desired equilibrium calculations. (16)Munson, C. L. M.S. Thesis, Brigham Young University, Provo, UT 84602.1991. (17)Cakng;R. W.; Mar,R. W.; Nagelberg,A. S. SandiaReportSAND 82-8035,February, 1983. (18)Chase, M. W. Jr.; Davies, C. A.; Downey, J. R. Jr.; Frurip, D. J.; McDonald, R. A.; Syverud, A. N. JANAF Thermochemical Tables, 3rd edition; J. Phys. Chem. Ref. Data 1985,14. (19)Robie, R. A.; Hemingway,B. S.;Fisher, J.R. US.GeologicalSurvey Bulletin, 1452,US.Government Printing Office, Washington, DC, 1979. (20) Hastie, J. W.; Bonnell, D. W.; Plante, E. R. Paper No. 3 in R o c . 23rd SEAM 1985,(June). (21)Levin, E. M.;Robbins, C. R.; McMurdie, H. F. Phase Diagram for Ceramists; American Ceramic Society: Columbus, OH, 1964. (22)Pelton, A. D.;Thompson, W. T.; Bale, C. W.; Eriksson, G. High Temp. Sci. 1990,26,231-250.
Coal Ash in Combustion Systems
Energy & Fuels, Vol. 7, No. 2, 1993 211 Weight Percent
Weight Percent 20
40
60
20
80
I
60 I
I
I
I
40
Liquid
u^
> -2
l
Mullite+
h
1800
-
1800
L
a
n L
F
c
80
l
1400
’E
1600
1600
I
0 Si02
I
Silica+Mullite I
I
20
I
I 40
Aullite solid solution
I I 60
I 80
I
i
Mullite solid solution
1400
I
0
AI203
Si02
Mole Percent Ab03
All of the calculations which follow were performed under oxidizing conditions. Also, calculations of coal ash species and phases were based on the elemental composition of the ash and did not consider organic components.
-
Silica+Mullite
I
100
Figure 1. Experimental22and calculated phase diagrams of the Si02-Al203 system.
I
1468O I
I
I
I
20
40
I
I 80
I
60
100
A1203
Mole Percent Ab03
Figure 2. Experimental22and calculated phase diagrams of the Si02-Al203 system with adjusted mullite data. 1600
9
Experimental
-
1
1500
v
-f
1400
n
Results and Discussion Silica-Alumina Phase Diagram. One of the simplest systems that includes two of the key oxide components in coal ash is the silica-alumina binary system. An experimental phase diagram22of this system is given in Figure 1, upon which the calculated phase diagram has been superimposed in gray. As in all cases discussed in this paper, calculations were made from the free energy data alone. In addition, there was no arbitrary adjustment of the free energy data to fit the experimental data, and no a priori selection of specific complex species from the database to match the experimentally observed species. Note (Figure 1)that the proper phase regions, including solid, two-phase, and liquid regions, were almost all calculated with correct species as labeled on the diagram. The single exception, of course, was the region where the mullite solid solution was observed experimentally, as solid solutions were not considered in the present simulations. In general, the agreementwas good, although the predicted eutectic composition of the silica side of the diagram was at 15wt % alumina as opposed to the experimental value of about 7 wt %. The discrepancy in the eutectic composition reflects the approximate nature of the ideal solution model used for the liquid phase. In the case of the silica-alumina system, the complex species that appeared in the liquid phase were silica, Si02(l), and mullite, Al&i2013(1). Furthermore, it was assumed that these two species were components of an ideal liquid phase. However, it is unlikely that such a complex grouping of alumina and silica (represented by mullite) exists as the weight fraction of Si02 in the melt approaches unity. Therefore, the use of liquid mullite throughout a wide composition range is at least partly responsible for the improper slope of the liquidus line as the weight fraction of Si02 approaches one, and the discrepancy between the predicted and experimental eutectic compositions. The influence of the liquid-phase species is shown in Figure 2 where the silica-alumina diagram has been recalculated assuming a liquid species of Al3SiOs.5(1)
d
1300
G 1200
-
CaMgSizO6+ CaAlzSizOs I
1
I
I
1
1
1
I
I
instead of mullite. In this form, a fewer number of aluminum atoms (three)were required to form the complex species, as opposed to six for the original Al&i&. This changing of species is an approximate way of expressing the fact that the interaction between aluminum atoms in a complex species decreases as the concentration of aluminum decreases. Note that the slope of the liquidus line at the Si02 axis is much closer to the experimental slope. The predicted eutectic temperature, however, is lower than the experimental value making the overall predictions less satisfactory. It was generally observed that the choice of liquid species with a stoichiometry equal to that of the solid species (e.g. mullite(1) and mullite@)) gave the best approximation of experimental behavior. It is evident, however, that the use of a single set of complex species does not adequately track activity changes over a range of compositions. Other Systems. Figures 3-5 show binary subsets of systems which involve elements important in coal ash deposition. Binary diagrams such as these clearly show the phase of the system as a function of temperature. Prediction of the quantity and composition of the liquid phase is important in the determination of ash deposition behavior as it plays a role in sticking, sintering, strength development, and the thermal properties. The predictions shown in Figures 3-5 are of sufficient accuracyto be used as part of an engineeringmodel of coal ash behavior. In all, this study examined more than 50 systems. The accuracy of most of these predictions was similar to that shown above. However, there were several systemsfor which the predictions were poor. Investigation
212 Energy &Fuels, Vol. 7,No. 2, 1993 I . 2100
-Experimental
Harb et al. I
Liquid
u^
1600
1900
1500
w
A1203 + Liquid
+ Liquid
2
-
Calculated
2000
2 1800
1400
0
4
E 1700
-
G za
1300
1
Cristobalite +Liquid
F
1470'C
Liquid
1200
L
I
I
I
I
I
I
I
I
I
I
0
10
20
30
40
50
60
70
80
90
K2AISi208
1 100
Weight Percent AI203
A1203
1100
G 1000
Figure 4. Experimental22and calculated phase diagrams of the K2A12Si208-Al203 system. 1400
c
I
-
Exuerimental Calculated
I
900
I
800
700
Liquid
600
1200
0 w
10
20
30
Na20
2 1100
-
40
50
70
60
80
90
Weight Percent Si02
100
Si02
3
Figure 6. Experimental22and calculated phase diagrams of the NaaO-Si02 system.
7
k 1000
c
FeO + Liquid
900 800
r
700
n FeO
in
I
I
I
I
I
I
I
I
20
30
40
sn
60
70
80
90
Weight Percent NazSi2Os
1700
NazSizOs
Figure 5. Experimentalz2and calculated phase diagrams of the FeO-NaZSi205 system.
revealed two principal causes for the poor predictions. The first of these is inadequacieswith the thermodynamic database. Potential database problems include missing species and inaccurate free energy data. The second cause of poor predictions was inadequate treatment of liquid-phase Si02 in the model. As mentioned previously, it was recognized that the ideal solution model would not be able to predict the immiscibility gap often found in silica-rich systems. However, the extent to which the model would be able to approximate the amount of liquid present as a function of temperature was unknown. Unfortunately, the predictions were quite unsatisfactory as shown in Figure 6 for the Na2O-SiO2 system where the results indicate liquid at much lower temperatures than those observed experimentally on the silica side of the diagram. The predictions are even worse on the Si02 side of the CaO-Si02 system as shown in Figure 7. Note also that the failure to predict the eutectic near the middle of the NazO-SiOz diagram (Figure 6) was due to a lack of free energy data for liquid Nasi04 below the melting point of the solid. The prediction of liquid at low temperatures for Si02rich systems resulted from inaccurate representation of the silica activity in the liquid phase. The model assumes that the liquid-phase species is SiOZ(1)and that its activity is equal to its mole fraction. However, silica is known to polymerize in the liquid phase.6 Therefore, the liquid phase may contain a number of different complex silica species which are not accounted for in the model. Im-
k' 2 Liquids
1 100
1600
2
3
1400
a L
a
1300 b
1200
1100 1000 0
Si02
10
20
30
Weight Percent CaO
40
50 CaO
Figure 7. Experimental22and calculated phase diagrams of the Si02-Ca system.
proved agreement between experimental and calculated results was observed when calculations were performed with a single more complicated silica species in the liquid phase (e.g., Si204 or si408 instead of SiOn). However, the complex silica species needed to best represent the experimental system of interest varied from system to system. Also, the extent of silica polymerization varies with both temperature and silica concentration; hence, the choice of a single species would not be expected to work well over a range of conditions and systems. There-
Coal Ash in Combustion Systems
Energy & Fuels, Vol. 7, No. 2, 1993 213
Table I. Elemental Weight Percents (Expressed as Equivalent Oxides) of Two Coal Ashes8 ash Si02 A1203 CaO Fez03 MgO Ti02 NazO K20 MnO 4.4 1.5 0.2 0.6 0.1 highCaO 33.7 23.0 34.7 2.4 low CaO 43.0 27.7 17.3 5.1 3.8 1.9 0.7 0.3 0.02 See ref 1. 100
.-0a
80
U
1 E
60
Q
2 0) E
40
.-
U J
20
--.--
High CaO Ash (calc.) Low CaO Ash (cab) First Liquid, High CaO
A
First Liquid, Low CaO
0.
Temperature (OC)
Figure 8. Calculated weight percent liquid as a function of temperature for high and low CaO coal ashes. Experimental values for the temperature at which liquid was first observed are also shown.'
fore, in order to be consistent with the model assumption of an ideal solution and still provide reasonable results in the silica-rich region, one is forced to "fit" experimental data by choosing the best complex silica species to represent the liquid activity for a particular simulation. However, this method of fitting the data is limited in scope and somewhat awkward. Given that some sort of fitting or calibration is required to improve predictions in the silica rich region, it would seem more reasonable to develop an activity model for the silica in order to account for the nonideal behavior. In summary, we have seen that a variety of oxide systems of interest in coal ash deposition can be simulated with reasonable accuracy. These include systems containing combinations of elements such as Si, Al, Ca, Na, Mg, and Fe. Problems were observed, however, in the simulation of systems where the database did not contain the appropriate species or in silica-rich systems where the ideal solution assumption does not work well. Application to Coal Ash Systems. One of the principal objectives of this study was to determine if the equilibrium calculations could be used to distinguish between coal ashes which cause deposition problems and those which do not. The compositions of two coal ashes are given in Table I. Equilibrium calculations were performed for these ashes, and from the results, the percent liquid as a function of temperature is plotted in Figure 8. The behavior of these ashes was examined experimentally by Sanyal and Wi1liamson.l Although the experimental study did not include determination of percent liquid of the melted ashes, the temperatures at which liquid was first seen were determined (see Figure 8). The predicted temperature at which liquid was first expected to form was about 50 "C higher than the temperature where the first trace of liquid was observed experimentally for the low CaO ash (1020 "C); on the other hand, the prediction for the high CaO
ash was approximately 100 "C lower than the observed value of 1120"C. Note that the calculated results compare better with the experimental observations than do the eutectic temperatures corresponding to the normalized composition from the Ca-Al-Si ternary phase diagram of 1170 "C for the low-Ca ash and 1265 "C for the high-Ca ash. Therefore, a more conservative (safe) assessment of the deposition potential would result from the calculations which show liquid at significantly lower temperatures than those predicted from the ternary phase diagram eutectics. Another interesting point of agreement between the calculations and the experimental observations is the rapid increase in percent liquid calculated for the low CaO ash curve around 1350 "C, consistent with the experimental observation of a sudden increase of liquid at 1320 "C!while heating this ash. Also, the higher liquid content of the high CaO ash is in agreement with experimental ohservations for most of the temperature range. Finally, the primary crystalline fields for the two ashes were accurately predicted by the equilibrium calculations (gehlenite and anorthite for the high CaO and low CaO compositions, respectively). Calculations were also made for the coal ashes shown in Table I1 which were originally examined for Kalmanovitch, Sanyal, and Williamson.2 These ashes were classified as either slagging or non-slagging based on performance in actual units. Kalmanovitch et al. used equilibrium phase diagrams from the CaO-FeO-Al203-SiOZ system to approximate the slagging behavior of six ashes. They reported excellent agreement between the observed slagging behavior and qualitative predictions made from the equilibrium diagrams. Based on their success, it should be possible to use equilibrium calculations, as opposed to phase diagrams, to make the same type of slagging assessment from the coal ash composition. Equilibrium calculations were performed in 25-deg increments to determine the weight percent of liquid in the ash for temperatures from 875 to 1800 "C. The ash from a slagging coal should produce significant quantities of liquid at lower temperatures than the ash from a nonslagging coal. Results are shown in Table 111 which gives the observed slagging performance of the ashes and the temperature, Tlo, at which at least 10% liquid WRS present in the ash. Note that the calculated Tlo temperatures do not correlate well with the observed behavior. Also indicated in the table is whether or not SiOz(1) was present in the calculated results. The discrepancy between the calculations and the observed slagging performance was believed to be due to the presence of SiOz(1). In order to verify this, SiOz(1) was removed from the calculations at temperatures below the eutectic temperature of the dominant ternary system. For example, the dominant ternary system for ash 1 (mass basis) is Ca-Al-Si. The corresponding eutectic temperature based on the normalized ternary composition is 1345"C. Therefore, Si& (1) was not considered as a possible species at temperatures below that value. Note that this constraint did not preclude the formation of liquids which do not contain SiOp(1) at temperatures below the ternary eutectic temperature. Calculations with the SiOz(1) constraint were performed for all six of the ashes and the resulting Tlo* temperatures are shown in Table 111. These temperatures are in good agreement with the observed slagging performance. The constraint did not affect ashes 2 and 6 which did not contain SiOz(1) in the original calculation.
Harb et al.
214 Energy &Fuels, Vol. 7, No. 2, 1993 Table 11. Composition of Six Coal Ashes Expressed as Weight Percent Oxidee ash
unitlocation
unitcapacity(MW)
Si02
A1203
Fen03
CaO
MgO
NazO
K20
Ti02
1 2 3 4 5 6
Hong Kong South Africa Finland Holland UK Australia
350 600 113 190 399 200
59.6 39.6 47.2 48.1 41.1 20.0
21.3 26.8 20.1 21.8 22.1 15.9
2.5 5.4 10.2 15.1 28.0 12.2
4.7 17.6 7.0 5.2 4.5 17.3
1.1 3.4 3.9 1.5 1.5 5.4
0.2 0.8 0.8 0.5 0.4 10.5
0.7 0.6 2.4 2.7 1.4 0.1
1.3 1.6 1.0 0.9 0.9 1.0
See ref 2.
Table 111. Comparison of the Observed Slagging Behavior with the Temperature T10 at Which the Weight Percent Liquid Was 110% ashn 1 2 3 4 5 6
slagging obsd?b no no Yes yes Yes Yes
2'10
(OC)
950 1200 950 950 950 1000
SiOdl)?
Tlo* ( O C I c
yes no yes yes Yes no
1325 1200 1100 1100 1100 1000
See Table I1 for ash compositions. See ref 2. TKI*= 2'10 with empirical silica correction.
Note also that these two ashes contained the lowest weight fraction of silica. As seen from the above results, equilibrium can be used to provide a qualitative assessment of slagging behavior. Specifically, equilibrium provides information on the potential for liquid-phase formation. It is the liquid phase that plays a critical role in the formation and strengthening of coal ash deposit^.^ There are, however, limitations associated with the use equilibrium calculations or phase diagrams to predict deposition slaggingpropensity. First, equilibrium can only be used if the composition of the ash is known. Therefore, proper characterization of slagging deposits requires that the composition of the ash on the wall be known. This composition may be approximated by the average composition of the coal ash (e.g., low-temperature ash). However,the composition of the ash on the wall may differ significantly from the average ash composition. Second, both fly ash and deposits are heterogeneous in nature, as opposed to a homogeneous, isothermal mixture of elements. Deposits often form in layers which may vary in make-up from a combination of discrete particles to a molten slag. The temperature also changes by hundreds of degreesthrough the deposit. Clearly,more sophisticated models are needed to account for the heterogeneous nature of deposits. Conclusions Calculations have been performed to determine the equilibrium composition of chemical systems important in coal ash deposition. Advanced numerical techniques were applied to avoid numerical problems often associated with such calculations. The equilibrium model, which assumed ideal solutions of complex species, adequately approximated the behavior of a variety of systems for which experimental phase diagrams were available. The model, however, performed poorly for silica-rich systems due to an inadequate representation of the silica activity. Comparison of calculated results for actual coal ashes with experimentally observed behavior showed good agreement for systems which did not have SiOz(1) in the calculated
results. Calculations for ashes with higher silica content predicted excessive amounts of liquid that were inconsistent with the experimental observations. The addition to the calculations of an empirical constraint on SiOz(1) based on eutectic temperatures from ternary phase diagrams yielded good agreement between the calculated results and the observed slagging behavior. In order to improve the quality of the predictions in the silica-richregion without the use of an empirical correction factor, it would be necessary to abandon the ideal solution assumption and include activity coefficients. It would be possible to add activities to the present model, which is basically a speciation model. This, however, would require fitting data to determine the necessary thermodynamic parameters. Since fitting of data is required anyway to improve the predictions, use of a stoichiometric approach should be considered as an alternative to the above approach. As mentioned previously,stoichiometric methods use a simple species set and account for the formation of complex species and nonideal mixing with activity corrections determined from experimental data. The stoichiometric method has been used recently to model silicate systems of interest in ash deposition with promising results.22There are, however, several reasons why this approach has not been used more widely to date: (1) the model itself is inherently more complex, (2) a complicated procedure is required to fit the available data in order to determine the necessary thermodynamic parameters, (3) thermodynamic parameters have typically been determined for a limited number of systems only, and (4) experimental data are not available for all systems of interest. Parameters for a wider range of systems are now available and computer codes based on this approach are becoming available to a much wider audience.22 The ability of these models to predict the behavior of multicomponent systems for which phase equilibrium diagrams are not available needs to be evaluated. Therefore, it is recommended that results of calculations from models based on the stoichiometric approach be compared to both experimental results and predictions from other thermodynamic models such as that presented in this paper. Acknowledgment. The authors thank Dr. Murali Ramanathan of the EERC at the University of North Dakota and Dr. David Kalmanovitch of Riley Stoker for their valuable suggestions. We also thank Dr. Alan Parkinson for his help with the numerical methods. This work was sponsored by the Advanced Combustion Engineering Research Center. Funds for this Center are received from the National Science Foundation, the State of Utah, 29 industrial participants, and the U.S. Department of Energy.
