Energy & Fuels 1988,2, 362-370
362
Art i d e s Treatment of Coal Devolatilization in Comprehensive Combustion Modeling? B. Scott Brewster,* Larry L. Baxter,* and L. Douglas Smoot Combustion Laboratory, Brigham Young University, Provo, Utah 84602 Received December 3, 1987. Revised Manuscript Received February 29, 1988
Comprehensive combustion codes typically use simple empirical models to predict weight loss associated with coal devolatilization. Individual evolved species are not taken into account nor are the individual products of heterogeneous char reaction. The effects of all particle reactions are lumped into a single overall rate of weight loss, and coal offgas composition and heating value are assumed constant. More detailed devolatilization models that consider the evolution of individual species and predict both rate and composition of the volatiles are now available. These models use general kinetic parameters for each coal constituent that are nearly independent of rank. Such models provide a basis for predicting composition and heating value of the volatiles as a function of burnout and reactor conditions for a wide range of coals. This paper presents a generalized theory based on the existing coal gas mixture fraction model, which allows the variation in offgas composition and heating value to be taken into account in comprehensive code predictions. Results are presented for a swirling combustion case. Results illustrating code sensitivity to several thermal parameters affecting devolatilization and to turbulent fluctuations are also presented.
Introduction Pulverized coal combustion is a complex interaction of several processes, including particle dispersion, gas mixing, particle heatup and mass transfer, gas and particle reaction, recirculating and swirling fluid mechanics, radiative heat transfer, phase transformation of mineral matter, and pollutant formation and destruction. Comprehensive models incorporating submodels for such processes have been developed by several investigators14 to predict local conditions inside pulverized coal combustors. Previously reported studies have demonstrated the importance of devolatilization in comprehensive codes. Smith et al.S performed an extensive parametric study of a twodimensional combustion model to investigate the effects of parametric uncertainty on code predictions. The effect of coal reaction parameters on burnout, pollutant formation, local gas temperature, and local equivalence ratio was dominant. In addition, Fletcher6 has shown that combustion efficiency, flame front location, and fluid dynamical structure are all sensitive to devolatilization rate over the range of published values. These studies imply a need for increased understanding of the devolatilization/oxidation mechanism and its treatment in modeling the overall combustion process. Comprehensive models that treat the interaction of chemistry and turbulence often assume the coal offgas to have constant elemental composition and heating value. These assumptions have been justified by the uncertainties
* Author t o whom correspondence should be addressed. 'Presented a t the Symposium on Coal Pyrolysis: Mechanisms and Modeling, 194th National Meeting of the American Chemical Society, New Orleans, LA, August 30-September 4, 1987. Current address: Sandia National Laboratories, Combustion Research Division 8361, 7011 East Avenue, Livermore, CA 94550.
*
in devolatilization and by data that indicate that the major elements (including carbon, hydrogen, nitrogen, and sulfur) all seem to be released in proportion to the total mass evolution except for hydrogen.l,'v8 If, to a first approximation, hydrogen is also assumed to evolve in proportion to the total mass evolution, the total offgas elemental composition is constant and the calculations are greatly simplified. The contribution of coal reaction to the local elemental gas composition in the reactor can then be modeled with a single progress variable (e.g. the coal gas mixture fraction). With the recent advances that have been made in devolatilization modelinggJOand the ever increasing availability of computer power, more detailed accounting of particle reactions in comprehensive codes is now practical. (1) Smoot, L. D.; Smith, P. J. Coal Combustion and Gasification; Plenum: New York, 1985. (2) Lockwood, F. C.; Abbas, A. S. Twenty-First Symposium (Znternational) on Combustion; The Combustion Institute: Pittsburgh, PA, 1986. (3) Boyd, R. K.; Kent, J. H. Twenty-First Symposium (International) o n Combustion; The Combustion Institute: Pittsburgh, PA, 1986. (4) Truelove, J. S. Twenty-First Symposium (International)on Combustion; The Combustion Institute: Pittsburgh, PA, 1986. (5) Smith, J. D.; Smith, P. J.; Hill, S. C., submitted for publication in Comput. Chem. Eng. (6) Fletcher, T. H. Report SAND85-8854;Sandia National Laboratories: Livermore, CA, 1985. (7) Solomon, P. R.; Colket, M. B. Seuenteenth Symposium (International) on Combustion; The Combustion Institute Pittsburgh, PA, 1979, 131-143. (8) Freihaut, J. D.; Seery, D. J.; Proscia, W. M. Presented at the 1987 Joint Symposium on Stationary Combustion NO, Control, New Orleans, LA, March 23-26. (9) Serio, M. A,; Hamblen, D. G.; Markham, J. R.; Solomon, P. R. Energy Fuels 1987, I , 138-152. (10) Solomon, P. R.; Hamblen, D. G.; Carangelo, R. M.; Serio, M. A.; Deshpande, G. V. Energy Fuels, this issue.
0S87-0624/~S/2502-0362~01.50/0 0 1988 American Chemical Society
Energy & Fuels, Vol. 2, No. 4, 1988 363
Treatment of Coal Devolatilization
Case A
This paper presents a generalized theory based on the existing coal gas mixture fraction model'Jl that allows variability in the offgas composition and heating value. Comprehensive code predictions illustrating the effects of such variability for a swirling combustion case are presented. It must be emphasized that allowing for varying offgas composition is extremely complex in comprehensive models treating chemistry/turbulence interactions, and this investigation is but a first step toward providing a comprehensive code framework suitable for incorporating detailed devolatilization models. Code predictions illustrating the effects of several important thermal parameters affecting the devolatilization process and the importance of accounting for chemistry/ turbulence interactions are also presented. The comprehensive code that was used in this study is PCGC-2 (pulverized coal gasification or comb~stion-2-dimensional).~J~ Volatiles Composition The variation of char and coal offgas composition with burnout has been correlated by both simple and complex reaction s ~ h e m e s . ~ J ~Accounting J~J~ for the variation is not difficult in the treatment of particles. However, dealing with a variable composition and its interplay with gas phase turbulent mixing and reactions is both complex and computationally expensive. The successful prediction of turbulent and mean flow properties is a difficult proposition in typical combustion environment^.'^ Although reasonable success has been achieved for some simple flows, the complexity of reacting, swirling, turbulent flows often exceeds the capability of even the most sophisticated turbulence models. The added complexity of chemical effects on these predictions and the effect of turbulence on the mean reaction rates compounds the problem. Indeed, combustion investigators have identified this area as one of the critical needs of combustion research.15 Several approaches to the problem have been proposed. Some of these were recently reviewed and compared with data by Smith and Fletcher.16 The approach used here is the statistical coal gas mixture fraction model.'J1 Applications of this model have been limited in the past to a single progress variable, or mixture fraction, for the coal offgas. The past approach is referred to here as the single solids progress variable (SSPV) method. The detailed theory and assumptions of the SSPV method are given eIsewhere.'J1 The method is generalized and extended here to allow for an arbitrary number of progress variables, assuming statistical independence of the variables. The extended approach is here referred to as the multiple solids progress variable (MSPV) method. Generalized Theory. The general theory for the MSPV method was developed as an extension of the SSPV approach, where a single progress variable is used to track the mixing of coal offgas with the total reactor inlet gas. This so-called coal gas mixture fraction is defined as the (11) Smoot, L. D., Smith, P. J., Brewster, B. S., Baxter, L. L., Eds. Revised User's Manual, Puluerized Coal Gasification or Combustion2-Dimensional (87-PCGC-2);Combustion Laboratory, Advanced Combustion Engineering Research Center, Brigham Young University Provo, UT, 1988. (12) Smoot, L. D., Hedman, P. 0.; Smith, P. 3. Final Report prepared for EPRI under Contract No. 364-1-3, 1979;; Vol. 11. (13) Niksa, S.;Kerstein, A. R. Combust. Flame 1986,66, 95-109. (14) Sloan, D.G.; Smith, P. J.; Smoot, L. D. F'rog. Energy Combust. SC~ 1986, . 12, 163-250. (15) Smoot, L. D.;Hill, S. C. Prog. Energy Combust. Sci. 1983, 9, 77-103. (16) Smith, P. J.; Fletcher, T. H. Combust. Sci. Technol. 1988,58(1-3), 59-76.
0
b
I
I
f,""
f,
'r
I
'
f,
f,
Figure 1. Shape of the probability density function and typical correapondi fluctuations for (A) no intermittency of component i, (B)parti3intermittency of component i (no i), (c)partial intermittency of component i (pure i), and (D) full intermittency of component i.
mass fraction of the local gas mixture that originated from the coal: mc
' = m, + m p + m,
(1)
where m,, 5,and m, represent the mass of gas originating from the coal, primary gas stream, and secondary gas stream, respectively. Transport equations are used to determine the local values of rl and g,,(variance of 9). If the primary and secondary gas streams differ in composition and/or temperature, another progress variable is needed to track the mixing of primary and secondary. This so-called inlet gas mixture fraction can be defined two ways, and both definitions are useful. The conserved mixture fraction definition is mP
fp
= m,
+ mp + m,
(2)
where fp represents the local mass fraction of the mixture that originated from the primary gas. Transport equations are also used to solve for f p and gr (variance of fJ. From the local values of 7 and fp, any conserved scalar (e.g. elemental composition) with equal diffusivity can be cal-
Brewster et al.
364 Energy & Fuels, Vol. 2, No. 4, 1988 culated with a linear mixing rule between the values for pure primary, pure secondary, and pure coal offgas. Average gas-phase properties can then be calculated by assuming gas-phase reactions are infinitely fast compared to the rate of mixing, so that the gas is in a state of local instantaneous equilibrium, and integrating the local instantaneous values over the joint probability density function (pdf) of q and f,,. The conserved mixture fraction definition is useful because its transport equation does not require a source term. However, because it includes m, in the denominator, it is not statistically independent of q , and the joint pdf cannot be assumed to be separable. However, if the inlet gas mixture fraction is redefined as (3)
i.e. the fraction of gas originating from the primary gas in the local mixture of primary plus secondary, then f and q may both range independently from zero to unity, and to a first approximation at least, f may be considered statistically independent of q. The joint pdf between f and q may then be considered separable. Obviously, f and fp are not independent for a given value of q , and one may be readily calculated from the other. Also, fp is not a true mixture fraction in the usual usage of the term, because it is not based on the entire mixture. However, the term “mixture fraction” will be used loosely here to refer to the partial mixture fraction of a component in a mixture where other components are not considered. The distinction between true mixture fractions and partial mixture fractions should be clear from the context. In a general mixture consisting of N + 1 components, N independent mixture fractions must be defined to specify the composition. The components may refer to gas from different inlet streams or to different fractions of gas originating from the coal or to any combination of both. The N mixture fractions may be defined by ml fl = mo + ml m, f 2 = mo + m; + m2
f
~
mo = + ml
mN
+ m2 + ... + mN
=- “ N
component i at a fixed point in space, and the right-hand side shows the value of the mixture fraction as a function of time. For purposes of this illustration, the mixture fraction is shown to fluctuate about the time-mean value in a regular sawtooth waveform between fixed maximum and minimum values, but in a real turbulent flow, the fluctuations are irregular. Case A shows a situation where there is no intermittency of component i. In this case, the mixture fraction of i fluctuates randomly with values always greater than zero and less than unity. Every eddy passing through a control volume around the fixed point in space contains some component i and some other components as well. The probability of fi taking on any value between fim“ and fi” is equal to the probability of fi taking on any other value between fiminand fim”. The area under the pdf is unity. If the fluid components are defined to coincide with streams entering the reactor in an unmixed state (e.g. pure primary, pure secondary, pure coal offgas), it is possible to have eddies of pure component i and eddies containing no component i that pass through the control volume. Case B shows a situation where some eddies contain no component i, but no eddies are pure i. Case C shows a situation where there are some eddies of pure i, but no eddies with no i. Case D shows a situation where there are both eddies of pure i and eddies with no i. There are two intermittency factors to take into account for each component except the zeroth component, as there is no intermittency or mixture fraction defined for a single component. For each mixture fraction i, there is an intermittency factor ai of the “pure i” gas and cyi, of the “i-free” gas. These are given by
where Fi and Gfi are implicitly given by the following two coupled equations (the average values are determined from transport equations):
(4)
C mi
i=O
where the components have been ordered and each mixture fraction neglects all higher-ordered components in its definition. In this way, each mixture fraction may vary independently between zero and unity and, to a first approximation, be considered statistically independent of the other mixture fractions. The subscript “0”will typically refer to the primary stream, “1”will typical refer to the secondary stream, “2” will typically refer to the first coal offgas component, “3” to the second, and so on. Alternatively, “2” could refer to an additional inlet stream, “3” to another additional inlet, and so forth. As described above, any combination of additional gas inlets and coal offgas components is also possible. Intermittency of streams entering the reactor must be taken into account. Intermittency is caused by eddies of unmixed gases passing through the sample volume. For each component, two types of intermittency are possible, resulting in four possible cases with regards to the intermittency of that component. These four cases are illustrated in Figure 1. The left-hand side shows the pdf for
The average values of fi and gfi are determined from transport equations, and typically, the Favre average is used. The intermittency factor ai corresponds to the fraction of time the mixture in the control volume is pure component i, and ai,corresponds to the fraction of time the mixture has no component i. The area under the Dirac A function in the pdfs at fi equal to zero is therefore ai,, and the area under the Dirac A function in the pdf at fi equal to unity is ai. The area under the continuous portion of the pdf is equal to the fraction of time that component i is nonintermittent. The average value of any dependent fluctuating gas property 0is calculated by convolving the instantaneous value over the joint pdf of the independent mixture fractions. For an arbitrary number of mixture fractions
Energy & Fuels, Vol. 2, No. 4, 1988 365
Treatment of Coal Devolatilization
Table I. Convolution of 9, over a Separable Triple-Probability Density Function
fl
no.
f3
fz
1 2 3
1 0 0 0
1 0 0
1 0
0
fi
4
5 6 7
8 9 10 11 12
13 14
15
0 0 0 0
fz fi
f2
fl
1
f3
0 0 0
f3 f3 f3 f3 f3
a383 a3‘aZ82
1 0
f3
fz fz fz
term
(Y~,LYZ,(Y~~~ CY~XX~,(Y~&-
~,az,S*(fi) 8(0, 0, fi) dfi a3,aiSA-g,(f2) 8(0, fz, 1) dfz ~ , ~ i ’ S & ~8LQ ( f zfz, ) 0) dfz a3’SAx(fZ) Si>(f,) 8(O, f2, fl) dfldfZ dAJ’(f3)
8U3, 1) df3
1 0
az~~iSV(f3) B(f3, 0,1) df3 az,ai,S&WJ 13U3, 0, 0) df3
fl
aZ’.f:-3(f3).f@(fl)
8(f37 O, fi) df1df3 dA~(f3)
[email protected]) fz, 1)dfZdf3 ai,S&P(f)lt>(f$ fz 0) dfZdf3 .fi7(f3.f:;p(fZ).f&f1) P(f3, f ~ f1) , dfldfZdf3
1 0 f1
Since the mixture fractions are assumed to be independent, the joint pdf is separable, i.e. for an arbitrary number of mixture fractions N
P U N , fN-1,
-3
fz,
ti) = i JJ PVi) = l
(10)
Equation 9 includes a term accounting for the contribution of each possible combination of fluid components, allowing for intermittency of each component. The total number of required terms is 4(2N-1)- 1. The necessary terms for three mixture fractions ( N = 3) are tabulated in Table I. In this case, 15 terms are required (4(2“’) - 1). With three mixture fractions, mixtures of four fluid components can be described. These are referenced by subscripts 0-3 and may be used to represent secondary gas, primary gas, and two components of coal offgas, respectively. The first term gives the contribution of pure fluid 3. In this case, f 3 is equal to unity. Since fluids 0-2 are intermittent, fl and f 2 are undefined for this term. The contribution due to pure fluid 3 is therefore equal to the fraction of the total time that the fluid is pure 3 multiplied by the property p of pure 3. The second term gives the contribution of pure fluid 2. In this case, fluids 0, 1, and 3 are intermittent. Since fluid 3 is intermittent, f 3 is equal to 0. Since 0 and 1 are intermittent, f2 is equal to 1 and fl is undefined. The contribution of pure fluid 2 is given by the product of a3,,the fraction of time that fluid 3 is totally absent, multiplied by a2,the fraction of time the fluid is pure component 2, multiplied by the value of p for pure component 2. The third and fourth terms similarly give the contributions of pure fluids 1 and 0. The fifth through 15th terms give the contributions of various mixtures of the four fluids. Where mixture fractions can take on values between 0 and 1, and the respective fluids are not intermittent, this is indicated by fl, f2, etc., in the appropriate column. The property /3 must then be integrated over the pdfs of the variable mixture fractions to calculate the contribution of that particular mixture. The 15th term gives the contribution of a mixture where there is no intermittency, i.e. when all mixture fractions are continuously variable over the range 0-1. The pattern for extending Table I to N mixture fractions is straightforward. First, a fluid intermittency matrix consisting of N columns and 4(2N-1)- 1 rows should be constructed. If the columns in the matrix are ordered from highest to lowest, as in Table I, the first N rows will correspond to pure fluids 1-N. These are indicated by a “1” in the column for the appropriate mixture fraction and a “0”for all higher order mixture fractions. Lower order mixture fractions are not meaningful in this case, since none of the lower order fluids are present. The N + 1row
description pure fluid 3 (intermittency of 0, 1, and 2) pure fluid 2 (intermittency of 0, 1, and 3) pure fluid 1 (intermittency of 0, 2, and 3) pure fluid 0 (intermittency of 1, 2, ahd 3) mixture of fluids 0 and 1 (intermittency of 2 and 3) mixture of fluids 1 and 2 (intermittency of 0 and 3) mixture of fluids 0 and 2 (intermittency of 1 and 3) mixture of fluids 0, 1, and 2 (intermittency of 3) mixture of fluids 2 and 3 (intermittency of 0 and 1); note that 8 is not a function of fl mixture of fluids 1 and 3 (intermittency of 0 and 2) mixture of fluids 0 and 3 (intermittency of 1 and 2) mixture of fluids 0, 1, and 3 (intermittency of 2) mixture of fluids 1, 2, and 3 (intermittency of 0) mixture of fluids 0, 2, and 3 (intermittency of 1) mixture of fluids 0, 1, 2, and 3 (no intermittency)
will correspond to pure fluid 0. This is indicated with a “0” in all N columns. The remaining rows correspond to mixtures where at least one fluid is nonintermittent. The final row corresponds to the mixture where all N 1fluids are nonintermittent. The sequence of rows and columns described above is arbitrary, but it provides a convenient procedure for writing down all the necessary terms. Each term will contain a contribution from each of the meaningful mixture fractions multiplied by the property p evaluated at the proper values of the mixture fractions. The contribution for each mixture fraction with a value of unity is the intermittency factor ai,representing the fraction of time i is present and all lower order components are absent. The contribution for each mixture fraction with a value of zero is the intermittency factor ai,, representing the fraction of time component i is absent. The contribution for each mixture fraction that is continuously variable is the integral over the pdf. Of course, if any of the meaningful mixture fractions are variable, p must be placed inside the integral(s). The MSPV method allows the coal offgas elemental composition to vary with extent of burnout. Hence, each element or group of elements can evolve at its own rate. Experimental evidence has shown that both hydrogen and nitrogen may evolve at rates different from the overall rate of weight l~ss.~’J*The evolution rate of nitrogen from coal is particularly important, because of its propensity to form nitrogen oxide in the presence of oxygen. Nitrogen evolved in fuel-rich regions of the reactor forms molecular nitrogen rather than nitrogen oxides. Hence, accurate prediction of the nitrogen evolution rate is prerequisite to accurate prediction of the nitrogen oxide level in the exit gas from the reactor. In the MSPV method, each element may be tracked independently or elements that evolve at similar rates may be lumped and tracked as a group. An additional progress variable is required for each additional independent element or group. The interaction of chemistry and turbulence is accounted for by integrating the instantaneous properties of the gas over the joint pdf of all mixture fractions as described above to calculate the average properties. Combustion Case. Calculations were performed for a slightly fuel-lean (6% excess air), swirling, diffusion-flame combustion case with the MSPV method used to separately track coal volatiles and char oxidation offgas. The coal composition was taken to be that of Wyoming subbituminous. The primary and secondary streams were
+
(17) Nichols, K. M.M.S.Thesis, Brigham Young University, 1985. (18)Wendt, J. 0. L. h o g . Energy Combust. Sei. 1980, 6, 201.
Brewster et al.
366 Energy & Fuels, Vol. 2, No. 4, 1988 a) SSPV method
CENTERLINE PREDICTION
b) MSPV method
'
CCD,,
'
1
RADIALLY INTEGRATED AXIAL PROFILE
.2
c) SSPV method
MSPV
-
0 Axial Distance (Normalized)
Figure d) MSPV method
..
A m i Distance (Normalizedl
Figure 2. Gas temperature isotherms and surface plots for SSPV and MSPV methods.
both air at 519 K. The single-step rate of Solomon and co-workerslg was used for devolatilization, and heat of devolatiliition was assumed to be negligible. The residual char was assumed to be pure carbon. Results are compared with those obtained with the SSPV method. Gas temperature for the combustion case is shown in Figure 2. Surface plots and isotherms are shown for both the SSPV and MSPV methods. Centerline gas temperature, total (radially integrated) burnout, and centerline concentrations of oxygen and carbon dioxide are shown in Figure 3. Differences between the predictions of the two methods can be seen to be substantial. The obvious effect of separately tracking coal volatiles and char oxidation offgas, where the char is assumed to be pure carbon and the volatile yield is fixed, is to decrease the carbon content of the early total offgas and increase the carbon content of the late total offgas. A more subtle effect is to alter the heating value, since total offgas enthalpy (calculated from a total reaction enthalpy balance) must remain constant. The differences in the predictions of the SSPV and MSPV methods can be explained in light of these two effects. The first major difference to be noted is the size and properties of the fuel-rich region behind the flame front. This region is caused by the rapid devolatilization of the coal particles and the finite rate of mixing between the primary and secondary streams. I t is characterized by a depression in the temperature surface surrounded by a high-temperature ridge where the fuel/oxidizer mixture is nearly stoichiometric. The fuel-rich region is much smaller and less extreme (more shallow) in the case of the MSPV method, as seen by comparing the two temperature (19)Solomon, P. R.; Serio, M. A.; Carangelo, R. M.; Markham, J. R. Fuel 1986,65,182-194.
surfaces in Figure 2. The explanation for this difference is 2-fold. First, the concentration of oxygen in the early total offgas is increased relative to carbon in the MSPV method, making the fuel-rich region smaller and less fuel-rich. Second, the heating value of the early offgas is apparently reduced by the composition change relative to the late offgas. This results in lower peak temperatures in the flame front, decreased volume expansion of gases, and, therefore, a smaller fuel-rich region. The lower peak temperature in the flame front and more shallow fuel-rich region for the MSPV method can also be seen in the centerline plots in Figure 3a. After passing through the stoichiometric peak at the aft edge of the fuel-rich region, the centerline temperature declines as secondary gases containing excess oxygen and nitrogen diluent mix with the primary. This decline can be seen to be steeper for the MSPV method, presumably because the early offgas has lower heating value relative to the late offgas. Further down the combustor, the temperature increases toward that of the SSPV method, as the offgas heating value increases. The higher temperature in the region immediately aft of the fuel-rich zone affects the burnout as shown in Figure 3b. The two methods are essentially indistinguishable until the point where the secondary and primary gases mix. At this point, the burnout of the SSPV method exceeds that of the MSPV method because of the higher gas temperature. Gas composition also differs significantly between the two methods. Centerline oxygen concentration (Figure 3c) drops quickly to zero at the flame front as the available oxygen in the primary is quickly consumed by reaction with volatiles and char. The drop is less steep for the MSPV method due to the increased content of oxygen in the early offgas relative to the late offgas. The oxygen level increases as the secondary gases mix into the center of the reactor. The increase is higher in the case of two mixture fractions because of the lower burnout. The centerline concentration of carbon dioxide (Figure 3d) rises sharply at the flame front due to reaction of oxygen with evolving carbon monoxide. It then drops in the fuel-rich region as the oxygen is depleted. The drop is less severe in the case of two mixture fractions because of the increased evolution of oxygen from the coal. The carbon dioxide concentration then increases as oxygen
Energy & Fuels, Vol. 2, No. 4, 1988 367
Treatment of Coal Deuolatilization
from the secondary mixes into the center of the combustor and reacts with the char. The increase is more rapid in the case of one mixture fraction because of the higher rate of burnout. The carbon dioxide profile is flat in the aft region of the reactor for the SSPV method, indicating that burnout at the centerline is egsentially complete. Burnout is not complete in the center of the reactor for the MSPV method, and the carbon dioxide concentration continues to increase. The increase in total burnout in the aft region of the reactor for the SSPV method (Figure 3b) must therefore be primarily due to reaction of particles near the wall. The effects of separately tracking coal volatiles and char oxidation offgas are particularly significant in this slightly fuel-lean, swirling combustion case, because of the fuel-rich zone where the particles devolatilize. In nonswirling or fuel-rich systems, the effects may not be so dramatic, although the trends are expected be similar.
Thermal Parameters Affecting Devolatilization/Oxidation Smith et ala5identified several kinetic parameters for coal devolatilization/oxidation as having a dominant effect on comprehensive code predictions. Not included in their analysis were several important thermal parameters that affect devolatilization/oxidation. Both single-particle and comprehensive code calculations were carried out to investigate these effects. Parameters that were investigated include particle heat capacity, particle emissivity, and volatiles heating value. Particle Heat Capacity. Merrick20 suggested the following function for coal heat capacity:
2400
(al
a I-
Ambient Gas
-
Constant C
.....
400-
2
--
These equations are recommended for both coal and char and predict a monotonic increase in c, with temperature. However, because composition varies with time, the increase in c, for a heating and reacting particle may not be monotonic due to changes in average atomic weight." The high-temperature limit for eq 11 is 3R/a. Using eq 11, Merrick obtained agreement between predicted and experimental values within about 10% over the temperature range of the available data (0-300 "C) for various coal ranks (15-35% volatile matter). Graphite and char heat capacities were correlated within 5% over the range 0-800 OC. Calculations were carried out for single particles of 40and 100-pm diameter and for coal-water slurry droplets to test the effect of variable heat capacity on particle temperature and devolatilization rate. Particle heat capacities were calculated as the weighted sum of the heat capacities for raw coal, char, and ash. Gas temperature was assumed constant at 2100 K. Constant heat capacity cases were calculated by using heat capacities calculated a t 350 and 525 K for the coal and char components, respectively. The two-equation model was used for devolatilization, with coefficients suggested by Ubhayakar et a1.21 The average atomic weights for the coal and char (20) Merrick, D. Fuel 1983, 62, 640-646.
Variable C
(bl 0.6
I
/..-.' 0
20
10
30
TIME (msl
Figure 4. Variations of (a) particle temperature and (b) mass loss when different particle heat capacity formulations are used. The variable cp case uses the correlation of Merrick.20
were assumed to be 8.18 and 12.0, respectively, with the latter corresponding to pure carbon. The heat capacity of ash was taken to be20 c, = 593.3
where g, is given by
I
P
+ 0.586T
(13)
The heat capacity of the particles at constant pressure was assumed to be equal to the heat capacity at constant volume. Radiative heat transfer and particle blowing were taken into account. However, oxidation was neglected to more clearly illustrate the effects of heat capacity. Profiles of temperature and devolatilization rate for the 100-pm particles are shown in Figure 4. Gas temperature is also shown for comparison. Calculations for the 40-pm coal particles and coal-water slurry droplets showed similar effects of variable heat capacity during particle heatup. The initial heatup rate for the 100-pm particles is approximately 1.6 X lo5 K/s for both constant and variable cp. As particle temperature increases, heatup of the particle with variable c is retarded by the increasing value of cp, as shown in dgure 4a, resulting in a temperature difference between the two particles of as much as 500 K. This temperature lag results in a 50% increase in the time required for the onset of pyrolysis and a slight decrease in the devolatilization rate, as shown in Figure 4b. The slower heatup rate during devolatilization allows a greater portion of the particle to devolatilize via the low-temperature reaction, thus giving an ultimate volatiles yield that is approximately 5% lower than for the particle with constant cp. As shown in Figure 4a, the heatup rate decreases markedly during devolatilization, due to the blowing effect. This effect was similarly predicted by Ubhayakar and co-workers.21 The asymptotic temperature of both particles is approximately 200 K less than the gas tempera~~~
(21) Ubhayakar, S. K.; Stickler, D. B.; von Rosenberg, C. W., Jr.; Gannon, R. E. Sixteenth Symposium (International) on Combustion; The Combustion Institute. Pittsburgh, PA, 1977; pp 427-436.
Brewster et al.
368 Energy & Fuels, Vol. 2, No. 4, 1988
RADIALLY INTEGRATEDAXIAL PROFILE
1.0
-g c
._
.3 '4
1.0
0.6
'0
E m
0.4
N
.
I
.
,
. , . ,
.
- cR =I225 Jkg-K,
-
-
- 5.6 x 105Jikg
Merrick cp
2
4
6
.8
10 12
1.4
16
Axial Distance (m)
0.2
b 0
-0
I
@ =87x106J/kg
-
2
1
.
l,--&J
0.8
J
p
. , . ,
0.2
0.4
0.6
0.8
1 .o
Normalized Axial Location
Figure 5. Contour plots of temperature for (a) constant particle heat capacity, (b)Merrick variable heat capacity, and (c) increased heat of formation of coal (hoc).
ture, due to radiative heat losses to the walls of the reador, which were assumed to have a temperature of 1000 K. Calculations were also performed with the comprehensive code (PCGC-2) for particles with constant and variable heat capacity. The same combustion case as used in the calculations of the MSPV method for tracking coal offgas was also used in these calculations, except that the primary and secondary streams were assumed to have temperatures of 300 and 589 K, respectively. Contour plots of temperature for the constant and variable cp cases are shown in parts a and b of Figure 5, respectively. The temperature fields are similar, except that the temperature is approximately 50 K lower in the variable case. This can be seen by noting that the isotherms in Figure 5b are generally shifted toward the exit and the centerline. The lower gas temperature was predominantly a result of the decrease in volatile yield from the coal. The delay in particle ignition caused by variable cp is also apparent in Figure 5b near the inlet. The effect of variable heat capacity on total burnout is shown in Figure 6. The curve for variable cp is shifted to the right, resulting in a decrease of approximately 3 % in particle burnout at the exit of the reactor. This effect is consistent with the delayed ignition and slightly slower devolatilization rate observed in the single-particle calculations. Interestingly, the decrease in burnout is approximately equal to the decrease in ultimate volatiles yield predicted for the single particles, even though particle oxidation was not ignored in the comprehensive predictions. The effects of variable heat capacity on the predictions shown in Figures 5b and 6 are fairly insignificant compared with all the other uncertainties that exist in the comprehensive code. The effects would be more important at higher solids loadings, e.g. in gasification. They are also expected to increase with decreasing rank, since low-rank coals have a lower average atomic weight and therefore a
cp
Figure 6. Effect of variable heat capacity and increased volatiles heating value on total particle burnout.
higher high-temperature asymptote for eq 11. As shown by Merrick,20the heat capacity increases with increasing temperature toward the high-temperature limit of eq 11 ( 3 R / a ) ,goes through a maximum and then decreases as devolatilization proceeds and the average atomic weight increases toward that of mature coke, and then increases again (after devolatilization is complete) toward the high-temperature limit given by eq 11 for coke. A t a heating rate of 3 K min-l, the maximum heat capacity for coal ranks varying from 15-35% volatile matter all occurred at approximately the same temperature, 500 "C. The maximum temperature increased with decreasing rank. Assuming the same trends hold true for heating rates typical of pulverized coal combustion, the lower rank coal would be expected to exhibit the widest variation in heat capacity and, therefore, the largest effects in comprehensive code predictions due to changing heat capacity. Particle Emissivity. Total emissivities for coal particles have been reported with large variation, as summarized by Solomon et al.19 Measurements by Brewster and KunitomoZ for micrometer-sizedparticles suggest that previous determinations of the imaginary part of the index of refraction for coal may be too high by an order of magnitude. If so, the calculated coal emissivity for these particles based on previous values may also be too high. The experimental work of Baxter et alqBindicates that the effective emissivity of 100-km coal particles of several ranks of coal at lower temperatures is probably not less than 0.7. Their values are in approximate agreement with those of Solomon et al.19 To investigate the sensitivity of devolatilization to coal emissivity, calculations were again performed both for single particles and for a laboratory-scale combustor using the previous combustion case and the comprehensive code. For the single particle cases, emissivity was varied between 0.9 and 0.1. In the comprehensive code calculations, emissivity was varied from 0.9 to 0.3. The wall temperature was 1250 K in the former and 1000 K in the latter. The effect of emissivity was negligible in both sets of calculations. The high gas temperature in the singleparticle calculations made convection/ conduction the principal mode of heat transfer. In the comprehensive code simulations, the secondary air was swirled (swirl no. = 2.0) and the flow field was recirculating. Thus the particles were heated primarily by contact with hot gases rather than by radiation. However, in large furnaces or (22) Brewster, M. Q.;Kunitomo, T.J. Heat Transfer 1984, 106, 678-683. (23) Baxter, L. D.;Fletcher, T.H.; Ottesen, D.K. Energy Fuels, this issue.
Energy & Fuels, Vol. 2, No. 4,1988 369
Treatment of Coal Devolatilization c 1.0
RADIALLY INTEGRATEDAXIAL PROFILE
TFMPFR TEMPERATURE (K)
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m
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1
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~
.
.
~
.
-
.
~
.
I
Taking q fluctua.8
06 Ignoring q llucluations
U
0.4 N
2 0.2 L
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Normalized Axial Location
Figure 7. Gas temperature isotherms predicted when fluctuations in coal gas mixture fraction are neglected.
in readors where the particles do not immediately contact hot gases, radiation may play a more significant role, resulting in greater sensitivity to the value of particle emissivity. Volatiles Heating Value. The heating value of the volatiles must be known in order to calculate the energy released by gas-phase reactions. This heating value is a function of volatiles composition, as discussed previously. The sensitivity of comprehensive code predictions to changing volatiles heating value with constant offgas composition was investigated by increasing the heat of formation of the coal. Since the volatiles enthalpy is calculated from an enthalpy balance and over 80% of the total particle mass loss was due to devolatilization, increasing the heat of formation of the coal effectively increased the volatiles heating value. A value was chosen such that the adiabatic flame temperature of the coal at a stoichiometric ratio of unity was increased by about 200 K. Since the simulations were performed for fuel-lean (combustion) conditions, the actual gas temperatures increased by 50-75 K. The results are shown in Figures 5c and 6. As shown in Figure 512,the gas temperatures are seen to be higher with the increased heat of formation. Otherwise the temperature fields are quite similar. The higher temperatures are due to a combination of higher heating value and greater volatiles yield. The latter effect dominates everywhere except in the near-burner region. The higher temperature significantly affects coal burnout, as shown in Figure 6, with a large portion of the impact coming from the volatile yield in the early regions of the reactor. The magnitude of the variation of the offgas heating value was arbitrary in this case but is regarded as representative of actual coals and is possibly conservative.
ChemistrylTurbulence Interactions In all of the comprehensive code calculations reported in this paper, turbulent fluctuations in the local gas-phase stoichiometry were taken into account by assuming local instaneous equilibrium and integrating all gas properties over the pdfs of the mixture fractions. The MSPV method, in particular, would be much simpler to implement if the effects of these fluctuations on the gas-phase chemistry could be ignored. A study of the importance of these fluctuations was therefore conducted. In this study, the fluctuations were either arbitrarily neglected or included, and the results of the comprehensive predictions under these assumptions were compared. Similar results have been shown by Smith and Fletcher.16 These results are an extension of their work, focusing on the effect of the coal offgas fluctuations. Figures 7-9 show the results of ignoring turbulent fluctuations in the coal gas mixture fraction on gas temperature, total particle burnout, and centerline NO, concentration. The coal gas mixture fraction (1)represents the degree of mixing between the coal volatiles and the inlet gas. Neglecting the fluctuations
0
.2 .4
.6 .8 1.0 1.2 1.4 1.6 Axial Distance (m)
Figure 8. Effect of neglecting fluctuations in coal gas mixture fraction on total particle burnout. NITROGEN OXIDE (PPMI
1.o
0.8 0.6 0
5
3
0.4
0.2
n
0
0.2
0.4 0.6 NormalizedAxial Location
0.8
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Figure 9. Predicted NO concentration (a) neglecting turbulent fluctuations of coal gas mixtwe fraction and (b)taking fluctuations into account. in inlet gas mixture fraction had little effect on the results, since both the primary and secondary streams were identical in composition (both were air) even though they differed in temperature (300 and 589 K, respectively). The effect of ignoring the fluctuations in 1on gas temperature can be seen by comparing Figures 5a and 7. Ignoring the fluctuations caused a high-temperature ridge at the location of mixing between the primary and secondary streams, as can be seen by the higher concentration of isotherms in Figure 7. Taking the fluctuations into account smoothed the high-temperature peaks. These observations are consistent with those reported by Smith and Fletcher,I6 where they ignored turbulent fluctuations in both mixture fractions simultaneously. Because the rate of mixing of fuel and oxidizer is reduced when turbulent fluctuations are ignored, the particle burnout is lowered as shown in Figure 8. The above results were obtained by assuming that mixing is rate-limiting. The kinetics of nitrogen oxide (NO) formation and destruction are of the same order of magnitude as the turbulent mixing rates. Therefore, both mixing and kinetic considerations must be made to predict NO concentrations. The model used to do so has been previously reported24and incorporated as a submodel in PCGC-2. Figure 9 shows the effect of the fluctuations on model predictions. In Figure 9a, turbulent fluctuations were ignored both in the calculation of major species and in the calculation of NO (the latter are decoupled from the former). In Figure 9b, turbulent fluctuations were taken into account for both calculations. As shown, the predicted NO levels are quite sensitive to rigorous accounting for the effects of turbulence on chemistry. When turbulent (24)Hill, S. C.; Smoot, L. D.; Smith, P. J. Turentieth Symposium (International) on Combustion;The Combustion Institute Pittsburgh, PA, 1984,pp 1391-1400.
370 Energy & Fuels, Vol. 2, No. 4, 1988
Brewster et al.
fluctuations are taken into account, oxygen from the secondary apparently mixes more rapidly with the primary, resulting in increased NO formation. Although experimental data were not available for comparing with this calculation, previously reported calculations have shown that solutions taking the turbulence into account agree more closely with data.24 These results are not thought to be typical for nonswirling cases, however. Nonswirling combustion does not typically produce a fuel-rich zone where the coal devolatilizes, and the role of mixing between primary and secondary streams in NO formation is not as significant.
Acknowledgment. This study was conducted principally under subcontract to Advanced Fuel Research, Inc., who was under contract to the Morgantown Energy Technology Center (Contract No. DE-AC21-86MC23075). Justin Beeson is the contract officer. Some of the single-particle calculations were performed by Dr. Larry Baxter while he was on leave at Sandia National Laboratories, Livermore, CA.
Conclusions Advanced models are available for coal devolatilization that predict the variability in volatiles composition and heating value. This variability can have a significant effect on comprehensive code predictions. Predictions for a slightly fuel-lean, swirling, diffusion flame case resulted in a smaller and less extreme fuel-rich region, lower temperature in the region aft of the fuel-rich region, and lower burnout, when volatiles and char oxidation offgas were tracked separately. These differences can be explained in terms of increased oxygen content and lower heating value in the early volatiles. Further research is needed to identify the elements (e.g. hydrogen or nitrogen) or groups of elements that should be tracked separately and to what extent they can be assumed to fluctuate independently in the turbulent flowfield. Variability in particle heat capacity and volatiles heating value was shown to have significant effects on particle burnout when a two-step devolatilization model was used, largely through increased volatiles yield. The effect of particle emissivity was negligible due to the insignificant role of radiation in this reactor. Turbulent fluctuations in a single progress variable tracking coal offgas (SSPV method) were shown to significantly affect burnout, temperature, and pollutant predictions, and turbulence/ chemistry interactions should not be neglected in future developments involving multiple progress variables tracking coal offgas.
g1
a cu
CP
f
Gf gf
m
PO
List of Symbols average atomic weight of coal or char, kg/ (kgmol) constant volume heat capacity, J/(kg K) constant pressure heat capacity, J/(kg K) function defined by eq 12 gas mixture fraction; inlet gas mixture fraction transformed variance mixture fraction variance mass, kg probability density function for mixture fraction f
I
R
universal gas constant, 8.314 J/(mol K) temperature, K parameter in eq 12
T 2
Greek variance arbitrary gas-phase property coal gas mixture fraction
a
B 17
Superscripts average value time-mean value
N
-
C
h 1
i’ P S V
0, 1, 2,
...,N
Subscripts coal char gas component i i-free gas primary; conserved mixture fraction secondary volatiles fluid components defined in mixture fraction approach
