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A model of coal devolatilization and combustion in fluidized beds
C O M BUS T I ON A N D F L A M E 61: 1-16 (1985)
1
A Model of Coal Devolatilization and Combustion in Fluidized Beds GIORGIO BORGHI, ADEL F. SAROFIM, and JANOS M. BEI~R Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
A mathematical model of the combustion of coal particles under conditions prevailing in fluidized combustors has been developed. Allowance is made for the evolution and burning of volatiles in addition to the combustion of the residual char. The relative significance of the various steps in the oxidation process of the char, such as external diffusion, pore diffusion, and chemical kinetics of the reactions at the surface, is evaluated for the ranges of particle size, temperature, and partial pressure of the oxidant of interest in fluidized coal combustion.
I. I N T R O D U C T I O N When coal is heated to temperatures in excess of about 620K it undergoes a rapid thermal decomposition during which a fraction of the coal, in the range of 30-50% for high volatile bituminous coals, can be released in the form of volatiles. The composition of these volatiles varies with the type of coal. In general, the major constituents are methane, carbon dioxide, carbon monoxide, chemical water, hydrogen, ethane, and higher hydrocarbons. The relative amounts of these constituents vary during the devolatilization process; the chemical water and carbon oxides are released mainly in the early stages of the decomposition, while the hydrocarbons and hydrogen are retained for a longer period [1]. The release of the volatiles influences many of the parameters critical to fluidized bed combustion of coal. Pilot plant studies [2] have shown that the volatiles contribute to a major fraction of the CO emission from fluidized beds, and a large extant body of experimental work [3, 4] indicates that most of the NO formed is due to the oxidation of nitrogenous groups present in the volatiles. The oxygen and temperature profiles in the bed are also affected by the volatile release, since a strong evolution in some particular section of the bed would Copyright © 1985 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc. 52 Vanderbilt Avenue, New York, NY 10017
deplete the oxygen there, and possibly cause hot spots. Finally, due to their low ignition temperature, the volatiles effectively extend the stable range of operation of fluidized beds to lower temperatures. A predictive model for the evolution and combustion of the volatiles is essential if one wants to understand the behavior of the bed near the extinction limit. The traditional approach to fluidized bed combustion modeling and experiments with small beds has been either to neglect the volatiles altogether and deal with devolatilized char or coke instead, or to assume that the v01atiles are instantaneously released at the feed point, effectively lowering the inlet oxygen concentration. The model presented in this paper combines a mechanistic approach to the combustion of the coal particles with a kinetic model for its simultaneous devolatilization.
II. PRESENT MODEL A. Devolatilization Kinetics A number of researchers [5-9] have been successful in fitting their devolatilization data to rate expressions based on assumed mechanisms of volatile evolution. Of these the one obtained from the model derived by Anthony, e t al. [9]
0010-2180/85/$03.30
2
GIORGIO BORGHI ET AL.
has demonstrated a wide range of applicability and was therefore chosen for the purpose of this study. The model is an extension of that formulated by Pitt [8] and is based on the assumption that thermal decomposition occurs as a result of a large number of simultaneous, independent, and irreversible first order reactions by which the different organic species present in coal are converted into volatiles. Each reaction rate expression takes the form
dVi dt
= kl(V/*--Vi),
(1)
where Vi is the mass of volatiles per mass of original coal evolved up to time and II,.* is the value of Vi at t = oo. ki is a reaction rate constant of the Arrhenius form
ki=ko e x p [ - E J R T ] .
(2)
Integrating Eq. (1) and allowing for a variation of T with time gives
It is assumed that all reaction rate constants have the same frequency factor /Co, and that a large enough number of reactions occur to enable one to express the fraction of V* evolved due to reactions having a particular activation energy, E, as a continuous function f ( E ) . One can then write for the amount of volatiles released by reactions having an activation energy lying between E and E + dE
dV* = V*f(E) dE
(4)
with
integrate Eq. (3) to obtain
V*- V_
I
i=
× ex (- o I'o (E-EoV so 2 I dE.
(6)
Replacing the limits of integration with E0 + 20 includes 95.5 % of the value of the integral and makes it amenable to numerical evaluation. The parameters /Co, E0, and a must in general be fitted to experimental data and the value of V* may vary for different coals as well as for different temperatures and heating rates. In this study, the values of E0, k0, and o used were those obtained by Anthony et al. [9] for a Montana lignite with a volatile content of about 37 %. The value of V* was determined from the volatile yields versus temperature obtained by Suuberg et al. [10] for the same coal. It is recognized that the composition of the volatiles released varies between coals and for a given coal varies with time. Detailed composition of the volatiles and the time dependence of their release are becoming increasingly available [1, 11] and have been used to determine the variation with time of their heat of combustion [12]. Allowance for temperature gradients within the coal particle resulted in a reduced rate of evolution of volatiles at early times but the cumulative volatile yields obtained from an isothermal model were found to be in good agreement with those obtained from the nonisothermal model for the cases of volatile yields exceeding 50% of the asymptotic value for a 1.0 m m diameter particle [13]; internal conduction within the particle becomes a dominant factor for larger particles [14].
ao
S f(E) dE = 1. 0
(5)
Taking f ( E ) to be Gaussian with mean activation energy E0 and standard deviation ~, one can
B. Residue Burning Burning of the residual char and trapped volatiles occurs mainly due to a carbon/oxygen reaction yielding varying amounts of CO and
FLUID BED COAL DEVOLATILIZATION/COMBUSTION CO2. Under conditions of external diffusion control of the combustion process, it has been maintained [15-17] that it is possible for the rate of the reaction 2CO + 02 ~2CO2 to be fast enough to consume all the oxygen before it reaches the carbon surface, the CO then being supplied by the reaction CO2 + C ~ 2CO. Field et al. [18] argue correctly that this is particularly unlikely to be the case for particles below 100 /~m, since mass transfer rates to small particles are high, and would therefore require a rate of supply of CO that exceeds that attainable by the CO2 + C reactions. As reaction kinetics become controlling, the atmosphere surrounding the particle will be approximately uniform and CO2 and 02 will have equal opportunity to reach the surface. Under these conditions, kinetic data [18-20] show that the C + CO2 reaction is too slow to compete with the oxidation by oxygen. Even for particle sizes of interest for FBC measurements, burning rates reported by Gray and Kimber [21] and Golovina et al. [22] show that the CO2 + C reaction is too slow to account for the observed combustion rates, and thus support the view that oxygen attacks the particles directly. Another factor that point toward an oxidation by oxygen is the observed temperature of the particles; since the C + CO2 reaction is endothermic while the reaction C + 02 is highly exothermic, particle surface temperatures will be expected to fall below or exceed bed temperature for these two respective reactions. Temperature readings of burning particles obtained by two wavelength radiation pyrometry [23, 24] give surface temperatures which are substantially higher than the bed temperatures, indicating oxidation by oxygen. These results were shown to be in agreement with the predictions based on a simple energy balance on a particle assuming the heat of reaction equal to that for carbon oxidation by oxygen to CO. Although the empirical equation derived by Arthur [20] indicates that at temperature relevant to fluidized bed combustion the main product of this reaction is CO, the subsequent oxidation of CO by oxygen is assumed to occur fast enough to convert most of the CO to CO2
3
within the boundary layer of the particles, so that for the purpose of oxygen balance the reaction C + 02 --' CO2 can be considered to occur. Detailed calculations of the CO reactions in the boundary layer have been performed as a function of bed temperature, particle size, and partial pressure of water vapor which show that the CO oxidation may under certain conditions such as very small particle size, low temperature, and low oxygen or OH concentrations occur far removed from the particle s~urface [25]. This limitation of the model should be kept in mind when comparing experimental and computed burning times in the complementary experimental program. The oxygen flux computed on the basis of complete combustion to CO2 is assumed to be depleted by reactions partially on the external surface of the particles and partially on the interior surface areaslaccessible by pore diffusion. The reaction rate expression used in this model is that obtained by Smith and Tyler [26] in their studies with !brown coal. It is an intrinsic reaction rate expression determined by assuming a zero order reaction. In spite of much research conducted in this area, researchers are still debating as to what the true order of this reaction is. Tyler et al. [27] claim that it lies between 0.2 and 0.6 for temperatures between 950 and 1050K at 350 Torr Po2. Duval et al. [28, 29] found the order varying fro m 0.48 to 0.54 for similar conditions. Lewis et al. [30] obtained values between 0.5 and 0.8, and Essenhigh and Froberg [31] a value of zero. The Langmuir-Hinshelwood kinetics proposed by Howard and Essenhigh [32] or its extension to more than one type of reaction site by Strickland-Constable [33] suggests that the order must depend on temperature and Oxygen partial pressure, with low temperatures favoring zero order kinetics and low partial pressure favoring a first order process. Due to this uncertainty, and the computational advantage of using a first order rate expression, it was decided to adapt Smith's expression to a first order reaction occurring at the surface. Reaction rate constants kn of order n were fitted to Smith and Tyler's zero order r a t e k0 by equating k0 to kn at the average o x y g e n partial
4
GIORGIO BORGHI ET AL.
pressure used in their experiments. The first order rate so derived is Po2 moles C R = 9 . 1 6 3 Tp e x p [ - 16, 400/Tp) - - c m2 s " (7)
C. Coal Structure Having selected an intrinsic reaction rate expression, the question arises as to what pore geometry should be assumed. It seems at present an exceedingly complicated task to model accurately the structural changes which take place in the coal particle during combustion. The wide spread in pore size distribution, the tortuosity of the pores, and the complexity of the intersecting passages in the coal matrix, varying swelling and softening behavior of different coals when heated, are factors that need to be better understood before a predictive structural model can be developed. The more detailed mathematical models, such as that of Hashimoto and Silveston [34], are computationally involved and introduce a large number of parameters which must either be determined experimentally or by regression analysis of experimental data. For the purpose of this paper, i.e., to determine the burning histories of the particles, two parameters are sufficient, namely, the oxygen concentration at the surface and oxygen flux into the pores. An oxygen balance can then be constructed around the particle by equating the flux to the particle with the total oxygen consumption due to combustion, given by the sum of the oxygen reacting on the external surface of the particle, the flux of oxygen into the pores, and the oxygen needed to burn the volatiles evolved. For an nth order reaction at the surface this balance takes the form 47rR 2 DG Sh (C~ - Cs) _ 4rR2(1 _ ot)knCs" 2Rp +FporJCs, geom, n) + Fo2 vow,
(8)
where Rp
= particle radius,
C~
= 02 concentration in bulk phase,
Cs
= 02 concentration at particle surface,
DG
= gas diffusion coefficient in bulk phase,
kn
= rate expression for nth order reaction,
Fo2 Vol
= oxygen flow needed for combustion of volatiles,
a
= void surface fraction,
Sh
= Sherwood number to burning particle,
Fpore
=
oxygen flux into pores.
The term FOE vol is calculated from Eq. (1) with the assumption that the elemental composition of the volatiles is the same as that of the parent coal and that they undergo complete combustion. The flux into the pores depends as indicated on the surface concentrations and the reaction order assumed, as well as on geometrical factors such as pore radius and pore shape. If an expression for this flux as a function of Cs can be found, Eq. (8) can be solved for the surface concentration either directly or numerically, depending on the complexity of the dependence of the expression for Fpore o n U s. The simplification introduced in this model is that of a single average pore size and a conical pore shape. The initial pore radius is calculated from the coal porosity, specific surface area, and density. For oxygen flux into conical pores analytical solutions can be obtained [35]. Equation (8) can then be solved directly for Cs for the case of a first or a zero order reaction, and by a simple Newton-Raphson iterative procedure for nonintegral order. Physical intuition suggests that regardless of the initial pore geometry, as long as the dimensions of the pore are small compared with the volume of solid coal surrounding it, the shape of the pore will change until a geometry is reached for which the pore walls recede at the same rate regardless of the local radius. The pore shape
FLUID BED COAL DEVOLATILIZATION/COMBUSTION will then be self-preserving. From heat transfer and solid mechanics analogues (fin of minimum weight for given heat transfer, column of minimum weight for given load) it can be shown that the self-preserving shape will be obtained when all cross sections of the pore will be uniformly utilized; that is, when the flux of oxidant per unit area remains constant with depth
dc D--=K.f(x). dx
(9)
5
equating the flux into a pore with the amount of oxidant reacting on the pore walls. The limits of integration for the reaction term go from Rp to the values of x corresponding to 1 = 0 in Eq. (12). For coal combustion Knudsen diffusion prevails in the pores, with a consequent complication of the problem by the dependence of diffusivity on pore radius. An implicit re!ationship between pore radius and particle radius can still be obtained, however, in the form m
Combining this relation with the following differential mass balance for a pore, for a reaction of nth order between oxygen and carbon
d 12D dc = 21kC n, dx dx gives
d (dl)
l/n
kt/nK O-l/n) -
(10)
D
as the equation relating the pore radius I to the particle radius x. For the case of a constant diffusivity, Eq. (10) can be integrated directly to yield
-(n+ l)q(lo-l)= -~n+l +("[+qx)n+l,
(11)
where k l/nK(l
q=
- l/n)
D ll k'~ iln
= otz. )
,
"y = qRp + 13, and l0 is the radius of the pore at x = Rp. For the particular case of n = 1, Eq. (11) becomes /32 = 2q(10 - / ) + (7 + qx)2,
(12)
which can be seen to correspond to the equation of a circle of radius ~ around the point x0 = "Y/q, Yo = 1o. The values of x0 and/3 depend on K, which can be calculated by a mass balance
2k "t R - r ) ~ l
1
fto [(k/2)(Co/Kd)2+ln
(l/lo)] 1/2 dl,
(13)
where d is the proportionality constant in the relationship between D and 1. In spite of the valid physical concept of a selfpreserving pore shape, use of such a model would cause uncertainty in the interpretation of a uniform particle porosity before combustion. The results shown in this paper were obtained with the assumption of conical pores of selfpreserving geometry but progressively increasing solid angle, which has the virtue of mathematical tractability for the case of a first order reaction without causing blatant inconsistencies with the more obvious physical facts. Since the initial development of this model [13] several refined models of pore treatment have been published [36-40]. These !models differ in their treatment of pore shape, size distribution, and evolution with time. The shapes of the pores proposed include spheres [36], spherical vesicules interconnected with cylinders [37], cylindrical pores of random size [38], and orientation [39] and a pore tree [40]. Allowance is made for pore size distribution and for pore overlap. Since the intrinsic reactivity of the carbon is an adjustable parameter one cannot differentiate between the merits of the different models on the basis of burnout times. The models are differentiated in their ease ofiuse and their ability to match the correct pore evolution with time. In the absence of extensive data for
6
GIORGIO BORGHI ET AL.
the detailed pore evolution we have not seen the need in this paper to modify the computed results while recognizing the merits of more recent analyses. Differences between models become important in calculating variables such as internal pressure during devolatilization which are not of concern in this paper.
Changes in Physical Properties During Combustion The effect of combustion on the physical properties of the coal can be conveniently taken into account if one assumes that the oxygen burning on the outside surface of the particle and a fraction of that penetrating the pores cause particle shrinkage, while the remaining fraction of the oxygen penetrating the pores causes an increase in particle porosity. In deciding how much of the oxygen expressed by the term Fpore in Eq. (8) should be considered to burn in depth and how much near the surface it is useful to consider the depth of penetration of the oxidant into the pore, defined as the distance from the surface at which oxygen concentration reaches 1/100th of its surface value. Depending on the magnitude of the depth of penetration a coal particle may appear to burn as a shrinking sphere at constant density or with an increase in porosity at constant diameter. The ratio Z/Rp of penetration depth to particle radius can be taken to be a measure of the importance of internal combustion, and a fraction of Fpore, Z/Rp, was therefore utilized for the calculation of the extent of internal combustion, while the flux Fpore(l -
Z/Rp) + 4rR2(1 - ot)k,,C/'
was used to determine the shrinkage of the particle.
Pore Overlap Another problem that must be addressed is that of pore collapse during combustion. Data on specific surface area of coals clearly show that a maximum in the value of the specific area occurs at about 25 % burnout. This is believed to be due to an initial pore widening process followed by progressively more extensive overlap and col-
lapse between adjacent pores. This causes a decrease in the number of pores and prevents the specific surface area from increasing throughout the combustion process, as would be the case if no collapse took place. In the absence of a valid pore collapse model, a semiempirical expression based on a qualitative understanding of the process must be introduced which accounts for the effect described. A measure of the probability of overlap due to an increase of porosity A0 can be given as P=(1-
A0 0-~la) 6'
(14)
which approaches 1 as 0 ~ 1. The value of/~ should lie between 1 and 2 if we assume the concentration of pores to be proportional to the particle porosity and we take the pore overlap process to be of first to second order. The value of specific surface area calculated by use of the model was therefore corrected by multiplication with the factor (1 - p). A value oft5 of 2 gives a maximum in specific surface area at about 40 % burnoff, which is acceptably close to the range of experimentally observed values. The Sherwood number for the burning particles was calculated from the Frossling correlation for flow past a single sphere, modified to allow for the effect of bed particles on the effective diffusivity [3]. Since the carbon loading in a fluidized bed is typically around 2 % of the total bed weight, interaction between coal particles can be neglected and this approach should be valid. The diffusivity of oxygen in the gas surrounding the particles and the viscosity and thermal conductivity of the gas were estimated from the Chapman-Enskog correlations.
D. Combined Model of Particle Devolatilization and Volatile and Residual Char Combustion The model follows the history of a particle originally at ambient temperature from the time of introduction into the dense phase of a fluidized bed in which both the temperature and oxygen concentrations are known. The tempera-
FLUID BED COAL DEVOLATILIZATION/COMBUSTION ture of the particle rises and volatiles begin to be released at a high rate, the latter being computed using Eq. (6). In the initial stages of devolatilization, the oxygen diffusing to the surface is less than the amount required for complete combustion of the volatiles. It is assumed that during this period the volatiles diffuse from the surface and react with oxygen. The volatiles are assumed to react with oxygen in a spherical diffusion flame surrounding the particle. The existance of a diffusion flame surrounding the particles is known from visual observation of large coal particles injected into a heated fluidized sand bed. The radius of the flame front is determined by solving the transient problem which considers a uniform volatile evolution from the particle surface during the time interval of interest, which tends to increase the volume of the volatile shell that surrounds the particle, while simultaneously oxygen diffuses to the volatile shell from the bulk and burns the volatiles, thus causing the volatile front to recede. Assuming the reaction between oxygen and volatiles to be infinitely fast, so that the concentration at the volatile front is equal to zero and the flame is infinitely thin, leads to the following differential equation which describes the movement of the reaction front with time, dry Fvo~" 82.057 • T 1 dt
4~
rf 2
Cr,DGT. 82.057 1 0 2 PGV " MWv
(15)
re
where rf is the radius of the volatile shell, Fvot is the volatile mole flux per unit area, calculated from Eq. (6), MWv is the mean molecular weight of the volatiles, and 02 POV is the molar oxygen requirement for complete combustion of 1 g of volatiles, which can be calculated assuming that the composition of the volatiles is the same as that of the parent coal. In the derivation of Eq. (15) the simplifying assumption was made that the volatiles inside the flame front were not diluted by combustion products. Equation (15) can be integrated nu-
7
merically together with the energy balance that will be presented shortly. As time progresses, the rate of devolatilization decreases and the radius of the flame front diminishes until it attaches to the particle. From then on, the oxygen flux to the particle exceeds the oxygen requirements of the volatiles being evolved. The excess oxygen attacks the particle directly, burning the char and the residual volatiles as discussed earlier. Since the ratio h R / k (where h is the heat transfer coefficient to a particle, R is the radius of the particle, and k is its thermal conductivity) is small for particles of the size range of interest to fluidized b e d combustion when the Nusselt number is taken to be of the order o f 2, the particles can be treated to a good approximation as isothermal spheres. Energy balance has been formulated to allow for the temperature variation of the particles with time. The balance takes the form
437rR3pCpdrp --~=
471"R20rB(TB4 -- Tp4)
+ 41rR2h(TB - Tp) + Fo2( - z~r--/rx) -- Fvol(Z~g'~dev),
(16) where Tp, R , p, and Cp are the temperature, radius, density, and heat capacity of the coal, respectively; Fvol and Foz are the fluxes of volatiles and oxygen with their associated molar enthalpies of reaction AHd~v and AHrx; Ta is the bed temperature; aB is Boltzmann's cOnstant; and h is the heat transfer coefficient to the particle. The value of h was estimated from the Frossling correlation. The molar change in enthalpy due to evolution of the volatiles is small relative to the combustion term and was set to zero in the absence of reliable data. In the presence of the flame front, one must allow for heat conduction from the flame to the particle, while the radiative exchange between the particle and the bed can be assumed to be unaffected by the existence of the flame due to the low values of its emissivity and abso~'ptivity. There is no oxygen flux to the surface and a
8
G I O R G I O B O R G H I ET AL. TABLE 1 Input to Program
Physical Properties of Coal:
Initial density Initial porosity Initial internal surface area Initial radius Thermal conductivity Heat capacity
0.92 g/cm 3 0.25 140 m2/g varied 0.0075-0.15 cm 0.003 cal/s cm 0.25 cal/g K
Characteristics of Bed:
Bed temperature Void fraction of dense phase Minimum fluidization velocity Oxygen fraction in dense phase
varied 1023-1323K 0.45 4.6 cm/s varied 1-8%
Coal Composition, d.a.f.:
C H O S N
Parameters Needed for Eq. (6):
V* computed from coal composition and bed temperature 32.7% at 1023K 36.7% at 1173K 40.6% at 1323K E0 48720 cal/g mole a 9380 cal/g mole k0 1.07 × 101°s -I
Other Parameters Needed:
AHr, = -28,080 cal/gmole AHdev = 0 cal/gmole Reaction rate expression C + 02 ~ CO or CO2 [see Eq. (7)] TAF 2200K Cpv 7.5 cal/gmole K
70% 6% 22.2% 1.0% 0.8%
b o u n d a r y c o n d i t i o n TgaslR = Tp at the surface o f the particle can be f o r m u l a t e d since the volatiles e v o l v e d are at the same t e m p e r a t u r e as the particles. The balance then b e c o m e s
4 3
=
IrR3pCp dTp
dt = 47rR 20rB(TB4 -- Tp4) [ dTgas 1 +47rR2kg L---~-r j R -Fvol(AHdev) ,
(17)
w h e r e kg is the thermal c o n d u c t i v i t y o f the gas s u r r o u n d i n g the particles. F r o m a balance on the gas between a particle and the flame front
dTgas I = dr [R
where TAF is the adiabatic flame t e m p e r a t u r e o f the flame, taken to be 2200K, rf is its radius, and is defined as
r / ( T g F - Tp)
1
R2
exp[r/(1/R- 1/rf)]- 1 ' (18)
Fvol Cpv M W v
4rkg
(19)
in which Cpv and M W v are the m o l a r heat c a p a c i t y and m o l e c u l a r weight o f the volatiles. A value o f 30 was a s s u m e d for the a v e r a g e m o l e c u l a r weight o f the volatiles species and a value o f 7.5 c a l / g m o l K for their a v e r a g e heat capacity. III. RESULTS OF COMPUTATION DISCUSSION
AND
Table 1 lists the input p a r a m e t e r s o f the c o m p u tational p r o g r a m . F i g u r e s 1-3 show the results obtained for a particle 3 m m in d i a m e t e r and an o x y g e n fraction o f 8% in the s u r r o u n d i n g gas.
FLUID BED COAL DEVOLATILIZATION/COMBUSTION
9
10-09
\ 0.8-
\
0,7 o
.....
06 t
......
1
(15
>
\
\
1
0.4
'.
\ \ \
V--- (1323K) W-~- - ~ p Vo WO
O.3
\
\ ~ - - - v ( 1 0 2 3 K ) - -w - -
'\ Vo
0.2
Wo •
\
O.1
"
\
\
\
\
O.U_ O1
1
5
10
,
4
50
100
i
•
200
500 1000
TIME ( SEC ] Fig. l. B u r n o u t and devolati]ization histories o f particles with a radius o f 1.5 mm f o r bed temperatures of 1023 and 1323K and Yo2 = 0.08.
,o
\
R:l.5 ram, T = 1 3 2 3 " K Density
Q,. 6
Porosity [ i
,2
(a)
1"6 L
z/~'~lO
oh. ,I
'
'
"3 Particle
'IF,
~
i
J
i
Temperature (K)
~
J
l
l
(b) .y.u~nD 1 . -r~ w ,6 bJ < ._J
6
~ Radius (¢m)
a,-.--Flame
Q5 10 2£]
50
10.0 TIME
50.0
100 0
5000
( SEC )
(c) Fig. 2. Combustion history for R = 1.5 ram, Yoz = 0.08, T = 1323K: (a) density and porosity of particle; (b) particle temperature and ratio of oxygen concentrations at surface and in ambient; (c) flame or particle radius.
10
GIORGIO BORGHI ET AL. R= 1.5mrn , T=1023*K 1
.
0
~
_
(g/crn 3
:
,
Porosity~ i ; I
o~ (D
.b[
.2h,;
(a)
8 .6F
ollll
i
I
I
I
i
T"
J
I
X/
II I
'
'/
I
I
1
I
(b) E u
.9 0
8 ~ w
.4 5
<
t
J
i
01 05 1 2
5
10
L
l
20 50 TIME (SEC)
100 200
500
I000
(c) Fig. 3. Combustion history for R = 1.5 mm, Yo2 = 0.08, T = 1023K: (a) density and porosity of particle; (b) particle temperature and ratio of oxygen concentrations at surface and in ambient; (c) flame or particle radius.
The curves in Fig. 1 depict the total fractional weight loss and the fractional weight loss due to volatile evolution alone of the particle at 1323 and 1023K. Notice the use of a nonlinear time scale [ln(t + 1)] to allow one to follow closely events near zero time in the early stages of combustion. After an initial short time during which the particles are still cold and the values of I1"/Vo and W~ I4/o do not change, a period of fast devolatilization sets in as the flame front is ignited. As devolatilization slows down, the flame front attaches to the particle surface and burning of the residue begins. Devolatilization is complete after about 7 s at 1323K and after about 11 s at 1023K, while the final burning times are 285 and 817 s, respectively. These devolatilization times are of the same order as the mixing times for particles in fluidized beds, which are typically in the range of 2-20 s. Therefore, the assumptions of either an instantaneous release of volatiles at the feed point or a uniform release of volatiles throughout the bed
appear to be inadequate representations of the volatile release process for particles in the millimeter size range. Figure 2 shows some of the details of the process for the case of a bed temperature of 1323K. The curves of Fig. 2a illustrate the variation with time of the density and porosity of the particles. In spite of the fact that most of the combustion occurs in the pores, the depth of penetration is short compared with the radius of the particle, causing it to burn as a shrinking sphere without a change in porosity and density. The initial drop in density is due to the evolution of the volatiles. In Fig. 2b the temperature and the oxygen concentration at the surface as a fraction of the oxygen concentration at infinity are plotted versus time. The oxygen fraction at the surface is a direct measure of the relative importance of observed kinetic and diffusional resistance. The observed kinetic resistance includes both the resistance due to chemical kinetics and that due to pore diffusion. As the particle is introduced into the bed, the
FLUID BED COAL DEVOLATILIZATION/COMBUSTION
11
ment of the flame, and the oxygen concentration at the surface increases steadily until burnout occurs since the particle is shrinking and the mass transfer rate is enhanced, while the particle temperature decreases and levels off at about 27K above the bed temperature. The oxygen fraction at the surface has an average value of about 0.25 during the burning of the residue, showing the process to be mainly diffus~onally controlled. Figure 3 is analogous to Fig. 2, but pertains to a bed temperature of 1023K. At this temperature, the particles heat up more slowly and devolatilize at a lower rate. As the flame front approaches the surface, the volatile content of the particle is still high enough to ~espond to the rise in temperature with an enhanced volatile flux which drives the flame front back. The oxygen fraction at the surface is higher than in the previous case, showing the process to be more kinetically controlled. Figures 4-6 are analogous to Figs. 1-3, but were obtained for a 150 #m particle. Without discussing these figures in detail, it is nOteworthy that the devolatilization step is now complete after a few hundredths of a second and the particle temperature overshoots the bed temper-
temperature begins to rise. Devolatilization is slow and therefore no flame front is produced, while the reaction rate at the surface is also slow and thus the process is kinetically controlled, the oxygen fraction being close to unity. As the temperature rises, the rate of devolatilization increases and eventually the flame front develops, shielding the particle from the oxygen diffusing towards it (02 FRS = 0) and causing a further increase in the temperature of the particle. After about 7 s, the bulk of the devolatilization is completed and the flame front attaches. Notice that just as the flame front is about to attach, its proximity to the particle causes the particle temperature to reach a sharp maximum. The radius of the flame front is somewhat larger than observed in practice, since the treatment of the volatile combustion neglects the effects of natural and forced convection on the shape and dimensions of the volatile shell. It appears that much of the volatiles which cannot be reached by oxygen immediately following evolution will be carried away by the airstream flowing by the particles. The radius of the flame front is equal to the radius of the particle from the time of attach-
,o i 0.9 0.8 0.7 :~
0.6 0.5-
o :~
0.40,30.20.1 0
l .05
0.5
1
2 TIME
5
10
15
(SEC)
F i g . 4. B u r n o u t a n d d e v o l a t i l i z a t i o n h i s t o r i e s o f p a r t i c l e s f o r b e d t e m p e r a t u r e s o f 1023 a n d 1 3 2 3 K , Yo2 = 0 . 0 8 , R = 75 /~m.
12
GIORGIO BORGHI ET AL. 1.0~-
R : 7.5 Hm , T=1323*K .
o~ .6 t ~
I~'D~nsity(g/cm3) ~
©
,~- Porosity (crn3/cm~) i-i I (a)
.2
.
~8
~
"i
~Particl=
'" o
u E
lJ
~
~
l
"-
~mp=rature ('K}
Cs,C=J I
I
I (b)
Ilhr~mam= Radius (cm)
<~ '°251[III zw 5
[ Particle Radius
oi11T T
I
i
l
I
.05 Q2
Q5
1.0
2.0
~O
TIME (SEC) (c) Fig. 5. Combustion history for R = 75/zm, Yo2 = 0.08, T = 1323K: (a) density and porosity of particle; (b) particle temperature and ratio of oxygen concentrations at surface and in ambient; (c) flame or particle radius.
ature considerably, reaching a value close to the temperature of the flame front. Also, the particles tend to burn at constant size over much of the combustion period, as indicated by the roughly constant value of the char particle radius and by the curves pertaining to the density and porosity of the particles. Figure 7 presents a series of curves of burning times versus oxygen mole fraction in the particulate phase for different sizes and temperatures. These curves are applicable to fluidized bed combustion after the oxygen concentration in the particulate phase is obtained by means of an overall oxygen balance on the bed. Two questions that have aroused great interest in relation to fluidized bed combustion are that of whether the combustion process is kinetically or mass transfer controlled, and the related one of whether a shrinking core or a constant size combustion model, respectively, applies. Figures 8 and 9 summarize the answers of the model described to these questions. In Fig. 8, the average fractional kinetic resistance (taken
as the oxygen concentration at the surface over the oxygen concentration at infinity at the time of 50% burnout) is plotted versus particle size for different temperatures. It is apparent that there is a shift from almost complete kinetic control at low temperatures and small sizes to a predominantly mass transfer determined burning rate for large particles and high temperatures. Giving reference to an earlier presentation of our results, Ross and Davidson [35] report remarkably good agreement between these theoretically calculated values of the fractional chemical resistance and those determined from their theory. Figure 9 addresses the question of in-depth burning of the coal particles. Two extreme cases are plotted. Under conditions of kinetically controlled burning, combustion occurs in-depth and the particles do not shrink significantly while the density decreases. When combustion is diffusion limited, the shrinking core model applies, the density remaining constant over
FLUID BED COAL DEVOLATILIZATION/COMBUSTION
13
R=75~Jm , T=1023K 1.0~r- ~'/ Density (g/cm ! ) .5 L
I~ P°r°sity !cm31cm3~
0
~__i
__L
(a)
ip/-Particle Temperature (*K) 81.0~ ~"
tic
/ I
I
10
15
(b) E u
~ 017pl u_
Flame Radius (cm) ParticleRadius
OIkk"I
I
I
.02 .2
•5
1
I
I
2 TIME (SEC)
5
(c) Fig. 6. Combustion history for R = 75 #m, Yo2 = 0.08, T = 1023K: (a) density and porosity of particle; (b) particle temperature and ratio of oxygen concentrations at surface and in ambient; (c) flame or particle radius.
most of the burnout period. The initial drop in density is due to the release of volatiles. Note the difference in volatile contents at the two different temperatures (see Table 1). In presenting this model, we are aware of the fact that the structure of coal is complicated enough and physical and chemical differences between coals so great as to make a universally valid combustion model a practical impossibility. Moreover, uncertainties in many of the parameters involved, such as the reaction rate expression and the Sherwood number for burning particles in fluidized beds, as well as the inability to model accurately the structural changes occurring in the coal during combustion, must have an adverse effect on the predictions of the model. Nevertheless, this model reflects the current state of the art in fluidized bed combustion, and appears to reproduce many of the features observed in the complementary experimental study.
IV. C O N C L U S I O N S A mechanistic model has been presented that enables the burning and devolatilization histories of particles in fluidized beds to be predicted. The application of the model toi conditions prevailing in fluidized coal combustors indicates that . The devolatilization times for average size particles are commensurable with the mixing times, making the assumption of an instantaneous release of volatiles at the point of introduction of the coal feed unrealistic. . The combustion rate can be contro!led by either external mass transfer or the combined processes of pore diffusion and surfaee reaction depending upon the particle size and the temperature of the coal. For coal chat particles in the size range of 1000-3000 ~m and temperature of 1023-1323K none iof the kinetic processes of diffusion and Surface
6°I
14
GIORGIO BORGHI ET AL. 1.01
50
75 ~rrl Z i,i a
4O 30
1173K
.J <
0,8 R=1.5 mrn
13
10
I
I
I
z
t
0.6
U 9 0 0 r-
75or
n< h 0
R=o.5 mm
600r
0.4 T=lO23°K-
~
0.2 1
I
I
I
r
4500 F 3000r3750~-- ~
Z W Q
L 02
I J I 04 0.6 08 TIME / BURNOUT TIME
~ 10
Fig. 9, Density change of particles during combustion for Yo2 = 0.04 and (i) R = 1.5 mm, T = 1323K; (ii) R = 75 /zm, T = 1023K.
R=l.Smm
225011500 r 750 r 2
4
PERCENT OXYGEN
6
8
IN DENSE PHASE
Fig. 7. Burnout times forR = 75 t~m, 0.5 mm, and 1.5 mm char particles.
1.0 02=4
°/.
0.9 w
U z v~ w
O.8
1023 " K 0,7~ 0.6
U IZ
0.5-0.4--
z 0
0.3--
=< 0.2-0.1 --
~ i
0 IO0
200
i
i
~ i i
400 800 RADIUS, p m
i i 1500
J 3000
Fig. 8. D e p e n d e n c e o f f r a c t i o n o f total r e s i s t a n c e attributed to c h e m i c a l k i n e t i c s as a f u n c t i o n o f bed t e m p e r a t u r e and p a r t i c l e d i a m e t e r , for Yo2 = 0.04.
reaction can be neglected; they all have to be taken into account in the calculation of the overall rate o f char burning. . The model can predict variation in particle size and density with time that is consistent with the expectation that the particles burn in the shrinking core mode when external mass transfer dominates, and burn internally without change in size when the rate o f combustion is controlled by that o f the surface reaction. . Several assumptions in the model that may restrict the range o f its applicability are that the coal is noncaking, ash released during combustion does not provide a major resistance to diffusion, and no significant particle fragmentation occurs during combustion. Recent experiments in our laboratory on the combustion o f particles of a noncaking coal in a fluidized bed have yielded results on volatile flame formation and on the rate of the combustion o f the residual char that are in remarkably good agreement with values calculated by the model, and are presented in a companion paper. NOMENCLATURE heat capacity o f coal particle
FLUID BED COAL DEVOLATILIZATION/COMBUSTION
c~ C~ D Dc E, E0
Fpore
oxygen concentration at particle surface oxygen concentration in dense phase (ambient) pore diffusivity for oxygen gas phase diffusivity for oxygen energy of activation and mean energy activation of thermal decomposition reactions oxygen flux into pores
Fo2
Fo2 Vol Fvol
h
AHdev A~x ki, ko kg
k. K l MWv n
02 PGV
0 2 FRS
P
,002 q rf
R Rc Sh t
TAF TB Tgas
oxygen flux needed for the complete combustion of the volatiles flux of volatiles heat transfer coefficient to a particle specific enthalpy change of devolatilization specific enthalpy change of carbon/ oxygen reaction rate constants for devolatilization reactions gas phase thermal conductivity rate constant for nth order carbon/ oxygen reaction flux density of oxygen diffusing in pore pore radius molecular weight of volatiles order of carbon/oxygen reaction molar oxygen requirement for complete combustion of unit mass of volatiles oxygen concentration at surface divided by oxygen concentration in dense phase probability of overlap of pores due to an increase A0 in porosity oxygen partial pressure at particle surface parameter defined after Eq. (11) flame radius particle radius rate of carbon consumption per unit surface area Sherwood number time temperature at flame front bed temperature gas temperature
Tp Vi Vi* Z c~ ~7 0 X p o OB
15 particle temperature weight of volatiles released up to time t per weight of original coal asymptotic weight of volatiles released at long times depth of penetration of oxygen into pores fraction of surface occupied by pores transpiration parameter defined by Eq. (19) porosity of particle thermal conductivity of coal particle particle density standard deviation of Gaussian distribution of activation energy Stefan-Boltzmann constant
The authors are grateful for support received under DOE contract No. E(49-18)2295. REFERENCES 1.
2. 3. 4.
5. 6. 7. 8. 9.
10.
11.
12. 13. 14.
Howard, J. B., in Chemistry of Coal Utilization Second Supplementary Volume (M. A. Elliot, Ed.), Wiley, New York, 1981, pp. 665-784. Gibbs, B. M., and Be6r, J. M., 1. Chem. E. Symposium Series No. 43, 1975, pp. 1-11. Be6r, J. M., and Martin, G. B., AIChE 691h Annual Meeting, Chicago, Nov. 28-Dec. 2, 1976. Pohl, J. H., and Sarofim, A. F., Sixteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1976. Badzioch, S., and Hawkesly, P. G. W., Ind. Eng. Chem. Process Design Develop. 9:521 (1970). Wiser, W. H., Hill, G. R., and Kertamus, N. J., Ind. Eng. Chem. Process Design Develop. 6:133 (1967). Skylar, M. G., Shustikov, V. I., and Virozub, I. V., Intern. Chem. Eng. 9:595 (1969). Pitt, G. J., Fuel41:267 (1962). Anthony, D. B., Howard, J. B., Hottel, H. C., and Meissner, H. P., Fifteenth Symposium ~(lnternational) on Combustion, The Combustion Institute, Pittsburgh, 1975, p. 1303. Suuberg, E. M., Peters, W. A., and Howard J. B., 173rd National A CS Meeting, Division of Fuel Chemistry, Vol. 22, No. 1, 1977, p. 112. Solomon, P. R., and Colket, M. B., Seventeenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1979, PPi 131-142. Suuberg, E. M., Peters, W. A., and Howard, J. B., Ibid., pp. 117-128. Borghi, G. G., S. M. Thesis, M.I.T., Cambridge, MA, 1976. Agarwal, P. K., Genetti, W. E., and Lee, Y. Y., Fuel 63:1157 (1984).
16 15. 16.
17. 18.
19. 20. 21. 22.
23.
24. 25. 26. 27.
GIORGIO BORGHI ET AL. de Graft, J. G. A., Brennst.-Warme-Kraft 17:227 (1965). Burke, S. P., and Schuman, T. E. W., Proc. 3rd International Conf. on Bituminous Coal 2:485 (1931). Van der Held, E. F. M., Chem. Eng. Sci. 14:300 (1961). Field, M. A., Gill, D. W., Morgan, B. B., and Hawksley, P. G. W., Combustion o f Pulverized Coal, BCURA, Leatherhead, 1967. Rossberg, M., and Wicke, E., Chemie-lng.-Tech. 28:181 (1956). Arthur, J. R., Trans. Faraday Soc. 47:164 (1951). Gray, M. O., and Kimber, G. M., Nature (London) 214:797 (1967). Golovina, E. S., and Khaustovich, G. P., Eighth Symposium (International) on Combustion, The Combustion Institute, 1962, p. 784. Ayling, A. B., Mulcahy, M. F. R., and Smith, I. W., Proc. Second Members" Conf., International Flame Research Foundation, 1971, Chapter 1. Smith, I. W., CSIRO Div. Min. Chem. Invest. Rept. 86, Dec. 1970. Sundaresan, S., and Amundson, N. R., Ind. Eng. Chem. Fundam., 19:351-357 (1980). Smith, I. W., and Tyler, R. J., Combustion Science and Technology 9:87 (1974). Tyler, R. J., Wouterlood, M. J., and Mulcahy, M. F. R., Carbon, 14:271 (1976).
28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40.
Amariglio, H., and Duval, X., J. Chim. Physique 64:916 (1967). Magne, P., and Duval, X., Bull. Soc. Chim. 5:1585 (1971). Lewis, J. B., Connor, P., and Murdoch, R., Carbon 2:311 (1964). Howard, J. B., and Essenhigh, R. H., Combust. Flame 9:337 (1965). Nagle, J., and Strickland-Constable, R. F., Carbon 1:333-338 (1964). Hashimoto, K., and Silveston, P. L., A I C h E Journal 19:259-277 (March 1973). Thomas, W. J.,Carbon 3:435 (1966). Ross, I. B., and Davidson, J. F., Trans. I Chem. E. 57:215 (1979). Beshty, B. S., Combust. Flame 32:295-311 (1978). Zygourakis, K., Ani, L., and Amandson, R., Ind. Eng. Chem. Fundam. 21:1-12 (1982). Bhatta, S. K., and Perlmutter, D. D., A . I . C h . E . J . 27:247 (1981). Gavalas, G. R., Combustion Science and Technology 24:197-210 (1981). Simons, G. A., Nineteenth Symposium (InternationaO on Combustion, The Combustion Institute, Pittsburgh, 1983, pp. 1067-1084.
Received 23 February 1983; revised 19 December 1984
1
A Model of Coal Devolatilization and Combustion in Fluidized Beds GIORGIO BORGHI, ADEL F. SAROFIM, and JANOS M. BEI~R Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
A mathematical model of the combustion of coal particles under conditions prevailing in fluidized combustors has been developed. Allowance is made for the evolution and burning of volatiles in addition to the combustion of the residual char. The relative significance of the various steps in the oxidation process of the char, such as external diffusion, pore diffusion, and chemical kinetics of the reactions at the surface, is evaluated for the ranges of particle size, temperature, and partial pressure of the oxidant of interest in fluidized coal combustion.
I. I N T R O D U C T I O N When coal is heated to temperatures in excess of about 620K it undergoes a rapid thermal decomposition during which a fraction of the coal, in the range of 30-50% for high volatile bituminous coals, can be released in the form of volatiles. The composition of these volatiles varies with the type of coal. In general, the major constituents are methane, carbon dioxide, carbon monoxide, chemical water, hydrogen, ethane, and higher hydrocarbons. The relative amounts of these constituents vary during the devolatilization process; the chemical water and carbon oxides are released mainly in the early stages of the decomposition, while the hydrocarbons and hydrogen are retained for a longer period [1]. The release of the volatiles influences many of the parameters critical to fluidized bed combustion of coal. Pilot plant studies [2] have shown that the volatiles contribute to a major fraction of the CO emission from fluidized beds, and a large extant body of experimental work [3, 4] indicates that most of the NO formed is due to the oxidation of nitrogenous groups present in the volatiles. The oxygen and temperature profiles in the bed are also affected by the volatile release, since a strong evolution in some particular section of the bed would Copyright © 1985 by The Combustion Institute Published by Elsevier Science Publishing Co., Inc. 52 Vanderbilt Avenue, New York, NY 10017
deplete the oxygen there, and possibly cause hot spots. Finally, due to their low ignition temperature, the volatiles effectively extend the stable range of operation of fluidized beds to lower temperatures. A predictive model for the evolution and combustion of the volatiles is essential if one wants to understand the behavior of the bed near the extinction limit. The traditional approach to fluidized bed combustion modeling and experiments with small beds has been either to neglect the volatiles altogether and deal with devolatilized char or coke instead, or to assume that the v01atiles are instantaneously released at the feed point, effectively lowering the inlet oxygen concentration. The model presented in this paper combines a mechanistic approach to the combustion of the coal particles with a kinetic model for its simultaneous devolatilization.
II. PRESENT MODEL A. Devolatilization Kinetics A number of researchers [5-9] have been successful in fitting their devolatilization data to rate expressions based on assumed mechanisms of volatile evolution. Of these the one obtained from the model derived by Anthony, e t al. [9]
0010-2180/85/$03.30
2
GIORGIO BORGHI ET AL.
has demonstrated a wide range of applicability and was therefore chosen for the purpose of this study. The model is an extension of that formulated by Pitt [8] and is based on the assumption that thermal decomposition occurs as a result of a large number of simultaneous, independent, and irreversible first order reactions by which the different organic species present in coal are converted into volatiles. Each reaction rate expression takes the form
dVi dt
= kl(V/*--Vi),
(1)
where Vi is the mass of volatiles per mass of original coal evolved up to time and II,.* is the value of Vi at t = oo. ki is a reaction rate constant of the Arrhenius form
ki=ko e x p [ - E J R T ] .
(2)
Integrating Eq. (1) and allowing for a variation of T with time gives
It is assumed that all reaction rate constants have the same frequency factor /Co, and that a large enough number of reactions occur to enable one to express the fraction of V* evolved due to reactions having a particular activation energy, E, as a continuous function f ( E ) . One can then write for the amount of volatiles released by reactions having an activation energy lying between E and E + dE
dV* = V*f(E) dE
(4)
with
integrate Eq. (3) to obtain
V*- V_
I
i=
× ex (- o I'o (E-EoV so 2 I dE.
(6)
Replacing the limits of integration with E0 + 20 includes 95.5 % of the value of the integral and makes it amenable to numerical evaluation. The parameters /Co, E0, and a must in general be fitted to experimental data and the value of V* may vary for different coals as well as for different temperatures and heating rates. In this study, the values of E0, k0, and o used were those obtained by Anthony et al. [9] for a Montana lignite with a volatile content of about 37 %. The value of V* was determined from the volatile yields versus temperature obtained by Suuberg et al. [10] for the same coal. It is recognized that the composition of the volatiles released varies between coals and for a given coal varies with time. Detailed composition of the volatiles and the time dependence of their release are becoming increasingly available [1, 11] and have been used to determine the variation with time of their heat of combustion [12]. Allowance for temperature gradients within the coal particle resulted in a reduced rate of evolution of volatiles at early times but the cumulative volatile yields obtained from an isothermal model were found to be in good agreement with those obtained from the nonisothermal model for the cases of volatile yields exceeding 50% of the asymptotic value for a 1.0 m m diameter particle [13]; internal conduction within the particle becomes a dominant factor for larger particles [14].
ao
S f(E) dE = 1. 0
(5)
Taking f ( E ) to be Gaussian with mean activation energy E0 and standard deviation ~, one can
B. Residue Burning Burning of the residual char and trapped volatiles occurs mainly due to a carbon/oxygen reaction yielding varying amounts of CO and
FLUID BED COAL DEVOLATILIZATION/COMBUSTION CO2. Under conditions of external diffusion control of the combustion process, it has been maintained [15-17] that it is possible for the rate of the reaction 2CO + 02 ~2CO2 to be fast enough to consume all the oxygen before it reaches the carbon surface, the CO then being supplied by the reaction CO2 + C ~ 2CO. Field et al. [18] argue correctly that this is particularly unlikely to be the case for particles below 100 /~m, since mass transfer rates to small particles are high, and would therefore require a rate of supply of CO that exceeds that attainable by the CO2 + C reactions. As reaction kinetics become controlling, the atmosphere surrounding the particle will be approximately uniform and CO2 and 02 will have equal opportunity to reach the surface. Under these conditions, kinetic data [18-20] show that the C + CO2 reaction is too slow to compete with the oxidation by oxygen. Even for particle sizes of interest for FBC measurements, burning rates reported by Gray and Kimber [21] and Golovina et al. [22] show that the CO2 + C reaction is too slow to account for the observed combustion rates, and thus support the view that oxygen attacks the particles directly. Another factor that point toward an oxidation by oxygen is the observed temperature of the particles; since the C + CO2 reaction is endothermic while the reaction C + 02 is highly exothermic, particle surface temperatures will be expected to fall below or exceed bed temperature for these two respective reactions. Temperature readings of burning particles obtained by two wavelength radiation pyrometry [23, 24] give surface temperatures which are substantially higher than the bed temperatures, indicating oxidation by oxygen. These results were shown to be in agreement with the predictions based on a simple energy balance on a particle assuming the heat of reaction equal to that for carbon oxidation by oxygen to CO. Although the empirical equation derived by Arthur [20] indicates that at temperature relevant to fluidized bed combustion the main product of this reaction is CO, the subsequent oxidation of CO by oxygen is assumed to occur fast enough to convert most of the CO to CO2
3
within the boundary layer of the particles, so that for the purpose of oxygen balance the reaction C + 02 --' CO2 can be considered to occur. Detailed calculations of the CO reactions in the boundary layer have been performed as a function of bed temperature, particle size, and partial pressure of water vapor which show that the CO oxidation may under certain conditions such as very small particle size, low temperature, and low oxygen or OH concentrations occur far removed from the particle s~urface [25]. This limitation of the model should be kept in mind when comparing experimental and computed burning times in the complementary experimental program. The oxygen flux computed on the basis of complete combustion to CO2 is assumed to be depleted by reactions partially on the external surface of the particles and partially on the interior surface areaslaccessible by pore diffusion. The reaction rate expression used in this model is that obtained by Smith and Tyler [26] in their studies with !brown coal. It is an intrinsic reaction rate expression determined by assuming a zero order reaction. In spite of much research conducted in this area, researchers are still debating as to what the true order of this reaction is. Tyler et al. [27] claim that it lies between 0.2 and 0.6 for temperatures between 950 and 1050K at 350 Torr Po2. Duval et al. [28, 29] found the order varying fro m 0.48 to 0.54 for similar conditions. Lewis et al. [30] obtained values between 0.5 and 0.8, and Essenhigh and Froberg [31] a value of zero. The Langmuir-Hinshelwood kinetics proposed by Howard and Essenhigh [32] or its extension to more than one type of reaction site by Strickland-Constable [33] suggests that the order must depend on temperature and Oxygen partial pressure, with low temperatures favoring zero order kinetics and low partial pressure favoring a first order process. Due to this uncertainty, and the computational advantage of using a first order rate expression, it was decided to adapt Smith's expression to a first order reaction occurring at the surface. Reaction rate constants kn of order n were fitted to Smith and Tyler's zero order r a t e k0 by equating k0 to kn at the average o x y g e n partial
4
GIORGIO BORGHI ET AL.
pressure used in their experiments. The first order rate so derived is Po2 moles C R = 9 . 1 6 3 Tp e x p [ - 16, 400/Tp) - - c m2 s " (7)
C. Coal Structure Having selected an intrinsic reaction rate expression, the question arises as to what pore geometry should be assumed. It seems at present an exceedingly complicated task to model accurately the structural changes which take place in the coal particle during combustion. The wide spread in pore size distribution, the tortuosity of the pores, and the complexity of the intersecting passages in the coal matrix, varying swelling and softening behavior of different coals when heated, are factors that need to be better understood before a predictive structural model can be developed. The more detailed mathematical models, such as that of Hashimoto and Silveston [34], are computationally involved and introduce a large number of parameters which must either be determined experimentally or by regression analysis of experimental data. For the purpose of this paper, i.e., to determine the burning histories of the particles, two parameters are sufficient, namely, the oxygen concentration at the surface and oxygen flux into the pores. An oxygen balance can then be constructed around the particle by equating the flux to the particle with the total oxygen consumption due to combustion, given by the sum of the oxygen reacting on the external surface of the particle, the flux of oxygen into the pores, and the oxygen needed to burn the volatiles evolved. For an nth order reaction at the surface this balance takes the form 47rR 2 DG Sh (C~ - Cs) _ 4rR2(1 _ ot)knCs" 2Rp +FporJCs, geom, n) + Fo2 vow,
(8)
where Rp
= particle radius,
C~
= 02 concentration in bulk phase,
Cs
= 02 concentration at particle surface,
DG
= gas diffusion coefficient in bulk phase,
kn
= rate expression for nth order reaction,
Fo2 Vol
= oxygen flow needed for combustion of volatiles,
a
= void surface fraction,
Sh
= Sherwood number to burning particle,
Fpore
=
oxygen flux into pores.
The term FOE vol is calculated from Eq. (1) with the assumption that the elemental composition of the volatiles is the same as that of the parent coal and that they undergo complete combustion. The flux into the pores depends as indicated on the surface concentrations and the reaction order assumed, as well as on geometrical factors such as pore radius and pore shape. If an expression for this flux as a function of Cs can be found, Eq. (8) can be solved for the surface concentration either directly or numerically, depending on the complexity of the dependence of the expression for Fpore o n U s. The simplification introduced in this model is that of a single average pore size and a conical pore shape. The initial pore radius is calculated from the coal porosity, specific surface area, and density. For oxygen flux into conical pores analytical solutions can be obtained [35]. Equation (8) can then be solved directly for Cs for the case of a first or a zero order reaction, and by a simple Newton-Raphson iterative procedure for nonintegral order. Physical intuition suggests that regardless of the initial pore geometry, as long as the dimensions of the pore are small compared with the volume of solid coal surrounding it, the shape of the pore will change until a geometry is reached for which the pore walls recede at the same rate regardless of the local radius. The pore shape
FLUID BED COAL DEVOLATILIZATION/COMBUSTION will then be self-preserving. From heat transfer and solid mechanics analogues (fin of minimum weight for given heat transfer, column of minimum weight for given load) it can be shown that the self-preserving shape will be obtained when all cross sections of the pore will be uniformly utilized; that is, when the flux of oxidant per unit area remains constant with depth
dc D--=K.f(x). dx
(9)
5
equating the flux into a pore with the amount of oxidant reacting on the pore walls. The limits of integration for the reaction term go from Rp to the values of x corresponding to 1 = 0 in Eq. (12). For coal combustion Knudsen diffusion prevails in the pores, with a consequent complication of the problem by the dependence of diffusivity on pore radius. An implicit re!ationship between pore radius and particle radius can still be obtained, however, in the form m
Combining this relation with the following differential mass balance for a pore, for a reaction of nth order between oxygen and carbon
d 12D dc = 21kC n, dx dx gives
d (dl)
l/n
kt/nK O-l/n) -
(10)
D
as the equation relating the pore radius I to the particle radius x. For the case of a constant diffusivity, Eq. (10) can be integrated directly to yield
-(n+ l)q(lo-l)= -~n+l +("[+qx)n+l,
(11)
where k l/nK(l
q=
- l/n)
D ll k'~ iln
= otz. )
,
"y = qRp + 13, and l0 is the radius of the pore at x = Rp. For the particular case of n = 1, Eq. (11) becomes /32 = 2q(10 - / ) + (7 + qx)2,
(12)
which can be seen to correspond to the equation of a circle of radius ~ around the point x0 = "Y/q, Yo = 1o. The values of x0 and/3 depend on K, which can be calculated by a mass balance
2k "t R - r ) ~ l
1
fto [(k/2)(Co/Kd)2+ln
(l/lo)] 1/2 dl,
(13)
where d is the proportionality constant in the relationship between D and 1. In spite of the valid physical concept of a selfpreserving pore shape, use of such a model would cause uncertainty in the interpretation of a uniform particle porosity before combustion. The results shown in this paper were obtained with the assumption of conical pores of selfpreserving geometry but progressively increasing solid angle, which has the virtue of mathematical tractability for the case of a first order reaction without causing blatant inconsistencies with the more obvious physical facts. Since the initial development of this model [13] several refined models of pore treatment have been published [36-40]. These !models differ in their treatment of pore shape, size distribution, and evolution with time. The shapes of the pores proposed include spheres [36], spherical vesicules interconnected with cylinders [37], cylindrical pores of random size [38], and orientation [39] and a pore tree [40]. Allowance is made for pore size distribution and for pore overlap. Since the intrinsic reactivity of the carbon is an adjustable parameter one cannot differentiate between the merits of the different models on the basis of burnout times. The models are differentiated in their ease ofiuse and their ability to match the correct pore evolution with time. In the absence of extensive data for
6
GIORGIO BORGHI ET AL.
the detailed pore evolution we have not seen the need in this paper to modify the computed results while recognizing the merits of more recent analyses. Differences between models become important in calculating variables such as internal pressure during devolatilization which are not of concern in this paper.
Changes in Physical Properties During Combustion The effect of combustion on the physical properties of the coal can be conveniently taken into account if one assumes that the oxygen burning on the outside surface of the particle and a fraction of that penetrating the pores cause particle shrinkage, while the remaining fraction of the oxygen penetrating the pores causes an increase in particle porosity. In deciding how much of the oxygen expressed by the term Fpore in Eq. (8) should be considered to burn in depth and how much near the surface it is useful to consider the depth of penetration of the oxidant into the pore, defined as the distance from the surface at which oxygen concentration reaches 1/100th of its surface value. Depending on the magnitude of the depth of penetration a coal particle may appear to burn as a shrinking sphere at constant density or with an increase in porosity at constant diameter. The ratio Z/Rp of penetration depth to particle radius can be taken to be a measure of the importance of internal combustion, and a fraction of Fpore, Z/Rp, was therefore utilized for the calculation of the extent of internal combustion, while the flux Fpore(l -
Z/Rp) + 4rR2(1 - ot)k,,C/'
was used to determine the shrinkage of the particle.
Pore Overlap Another problem that must be addressed is that of pore collapse during combustion. Data on specific surface area of coals clearly show that a maximum in the value of the specific area occurs at about 25 % burnout. This is believed to be due to an initial pore widening process followed by progressively more extensive overlap and col-
lapse between adjacent pores. This causes a decrease in the number of pores and prevents the specific surface area from increasing throughout the combustion process, as would be the case if no collapse took place. In the absence of a valid pore collapse model, a semiempirical expression based on a qualitative understanding of the process must be introduced which accounts for the effect described. A measure of the probability of overlap due to an increase of porosity A0 can be given as P=(1-
A0 0-~la) 6'
(14)
which approaches 1 as 0 ~ 1. The value of/~ should lie between 1 and 2 if we assume the concentration of pores to be proportional to the particle porosity and we take the pore overlap process to be of first to second order. The value of specific surface area calculated by use of the model was therefore corrected by multiplication with the factor (1 - p). A value oft5 of 2 gives a maximum in specific surface area at about 40 % burnoff, which is acceptably close to the range of experimentally observed values. The Sherwood number for the burning particles was calculated from the Frossling correlation for flow past a single sphere, modified to allow for the effect of bed particles on the effective diffusivity [3]. Since the carbon loading in a fluidized bed is typically around 2 % of the total bed weight, interaction between coal particles can be neglected and this approach should be valid. The diffusivity of oxygen in the gas surrounding the particles and the viscosity and thermal conductivity of the gas were estimated from the Chapman-Enskog correlations.
D. Combined Model of Particle Devolatilization and Volatile and Residual Char Combustion The model follows the history of a particle originally at ambient temperature from the time of introduction into the dense phase of a fluidized bed in which both the temperature and oxygen concentrations are known. The tempera-
FLUID BED COAL DEVOLATILIZATION/COMBUSTION ture of the particle rises and volatiles begin to be released at a high rate, the latter being computed using Eq. (6). In the initial stages of devolatilization, the oxygen diffusing to the surface is less than the amount required for complete combustion of the volatiles. It is assumed that during this period the volatiles diffuse from the surface and react with oxygen. The volatiles are assumed to react with oxygen in a spherical diffusion flame surrounding the particle. The existance of a diffusion flame surrounding the particles is known from visual observation of large coal particles injected into a heated fluidized sand bed. The radius of the flame front is determined by solving the transient problem which considers a uniform volatile evolution from the particle surface during the time interval of interest, which tends to increase the volume of the volatile shell that surrounds the particle, while simultaneously oxygen diffuses to the volatile shell from the bulk and burns the volatiles, thus causing the volatile front to recede. Assuming the reaction between oxygen and volatiles to be infinitely fast, so that the concentration at the volatile front is equal to zero and the flame is infinitely thin, leads to the following differential equation which describes the movement of the reaction front with time, dry Fvo~" 82.057 • T 1 dt
4~
rf 2
Cr,DGT. 82.057 1 0 2 PGV " MWv
(15)
re
where rf is the radius of the volatile shell, Fvot is the volatile mole flux per unit area, calculated from Eq. (6), MWv is the mean molecular weight of the volatiles, and 02 POV is the molar oxygen requirement for complete combustion of 1 g of volatiles, which can be calculated assuming that the composition of the volatiles is the same as that of the parent coal. In the derivation of Eq. (15) the simplifying assumption was made that the volatiles inside the flame front were not diluted by combustion products. Equation (15) can be integrated nu-
7
merically together with the energy balance that will be presented shortly. As time progresses, the rate of devolatilization decreases and the radius of the flame front diminishes until it attaches to the particle. From then on, the oxygen flux to the particle exceeds the oxygen requirements of the volatiles being evolved. The excess oxygen attacks the particle directly, burning the char and the residual volatiles as discussed earlier. Since the ratio h R / k (where h is the heat transfer coefficient to a particle, R is the radius of the particle, and k is its thermal conductivity) is small for particles of the size range of interest to fluidized b e d combustion when the Nusselt number is taken to be of the order o f 2, the particles can be treated to a good approximation as isothermal spheres. Energy balance has been formulated to allow for the temperature variation of the particles with time. The balance takes the form
437rR3pCpdrp --~=
471"R20rB(TB4 -- Tp4)
+ 41rR2h(TB - Tp) + Fo2( - z~r--/rx) -- Fvol(Z~g'~dev),
(16) where Tp, R , p, and Cp are the temperature, radius, density, and heat capacity of the coal, respectively; Fvol and Foz are the fluxes of volatiles and oxygen with their associated molar enthalpies of reaction AHd~v and AHrx; Ta is the bed temperature; aB is Boltzmann's cOnstant; and h is the heat transfer coefficient to the particle. The value of h was estimated from the Frossling correlation. The molar change in enthalpy due to evolution of the volatiles is small relative to the combustion term and was set to zero in the absence of reliable data. In the presence of the flame front, one must allow for heat conduction from the flame to the particle, while the radiative exchange between the particle and the bed can be assumed to be unaffected by the existence of the flame due to the low values of its emissivity and abso~'ptivity. There is no oxygen flux to the surface and a
8
G I O R G I O B O R G H I ET AL. TABLE 1 Input to Program
Physical Properties of Coal:
Initial density Initial porosity Initial internal surface area Initial radius Thermal conductivity Heat capacity
0.92 g/cm 3 0.25 140 m2/g varied 0.0075-0.15 cm 0.003 cal/s cm 0.25 cal/g K
Characteristics of Bed:
Bed temperature Void fraction of dense phase Minimum fluidization velocity Oxygen fraction in dense phase
varied 1023-1323K 0.45 4.6 cm/s varied 1-8%
Coal Composition, d.a.f.:
C H O S N
Parameters Needed for Eq. (6):
V* computed from coal composition and bed temperature 32.7% at 1023K 36.7% at 1173K 40.6% at 1323K E0 48720 cal/g mole a 9380 cal/g mole k0 1.07 × 101°s -I
Other Parameters Needed:
AHr, = -28,080 cal/gmole AHdev = 0 cal/gmole Reaction rate expression C + 02 ~ CO or CO2 [see Eq. (7)] TAF 2200K Cpv 7.5 cal/gmole K
70% 6% 22.2% 1.0% 0.8%
b o u n d a r y c o n d i t i o n TgaslR = Tp at the surface o f the particle can be f o r m u l a t e d since the volatiles e v o l v e d are at the same t e m p e r a t u r e as the particles. The balance then b e c o m e s
4 3
=
IrR3pCp dTp
dt = 47rR 20rB(TB4 -- Tp4) [ dTgas 1 +47rR2kg L---~-r j R -Fvol(AHdev) ,
(17)
w h e r e kg is the thermal c o n d u c t i v i t y o f the gas s u r r o u n d i n g the particles. F r o m a balance on the gas between a particle and the flame front
dTgas I = dr [R
where TAF is the adiabatic flame t e m p e r a t u r e o f the flame, taken to be 2200K, rf is its radius, and is defined as
r / ( T g F - Tp)
1
R2
exp[r/(1/R- 1/rf)]- 1 ' (18)
Fvol Cpv M W v
4rkg
(19)
in which Cpv and M W v are the m o l a r heat c a p a c i t y and m o l e c u l a r weight o f the volatiles. A value o f 30 was a s s u m e d for the a v e r a g e m o l e c u l a r weight o f the volatiles species and a value o f 7.5 c a l / g m o l K for their a v e r a g e heat capacity. III. RESULTS OF COMPUTATION DISCUSSION
AND
Table 1 lists the input p a r a m e t e r s o f the c o m p u tational p r o g r a m . F i g u r e s 1-3 show the results obtained for a particle 3 m m in d i a m e t e r and an o x y g e n fraction o f 8% in the s u r r o u n d i n g gas.
FLUID BED COAL DEVOLATILIZATION/COMBUSTION
9
10-09
\ 0.8-
\
0,7 o
.....
06 t
......
1
(15
>
\
\
1
0.4
'.
\ \ \
V--- (1323K) W-~- - ~ p Vo WO
O.3
\
\ ~ - - - v ( 1 0 2 3 K ) - -w - -
'\ Vo
0.2
Wo •
\
O.1
"
\
\
\
\
O.U_ O1
1
5
10
,
4
50
100
i
•
200
500 1000
TIME ( SEC ] Fig. l. B u r n o u t and devolati]ization histories o f particles with a radius o f 1.5 mm f o r bed temperatures of 1023 and 1323K and Yo2 = 0.08.
,o
\
R:l.5 ram, T = 1 3 2 3 " K Density
Q,. 6
Porosity [ i
,2
(a)
1"6 L
z/~'~lO
oh. ,I
'
'
"3 Particle
'IF,
~
i
J
i
Temperature (K)
~
J
l
l
(b) .y.u~nD 1 . -r~ w ,6 bJ < ._J
6
~ Radius (¢m)
a,-.--Flame
Q5 10 2£]
50
10.0 TIME
50.0
100 0
5000
( SEC )
(c) Fig. 2. Combustion history for R = 1.5 ram, Yoz = 0.08, T = 1323K: (a) density and porosity of particle; (b) particle temperature and ratio of oxygen concentrations at surface and in ambient; (c) flame or particle radius.
10
GIORGIO BORGHI ET AL. R= 1.5mrn , T=1023*K 1
.
0
~
_
(g/crn 3
:
,
Porosity~ i ; I
o~ (D
.b[
.2h,;
(a)
8 .6F
ollll
i
I
I
I
i
T"
J
I
X/
II I
'
'/
I
I
1
I
(b) E u
.9 0
8 ~ w
.4 5
<
t
J
i
01 05 1 2
5
10
L
l
20 50 TIME (SEC)
100 200
500
I000
(c) Fig. 3. Combustion history for R = 1.5 mm, Yo2 = 0.08, T = 1023K: (a) density and porosity of particle; (b) particle temperature and ratio of oxygen concentrations at surface and in ambient; (c) flame or particle radius.
The curves in Fig. 1 depict the total fractional weight loss and the fractional weight loss due to volatile evolution alone of the particle at 1323 and 1023K. Notice the use of a nonlinear time scale [ln(t + 1)] to allow one to follow closely events near zero time in the early stages of combustion. After an initial short time during which the particles are still cold and the values of I1"/Vo and W~ I4/o do not change, a period of fast devolatilization sets in as the flame front is ignited. As devolatilization slows down, the flame front attaches to the particle surface and burning of the residue begins. Devolatilization is complete after about 7 s at 1323K and after about 11 s at 1023K, while the final burning times are 285 and 817 s, respectively. These devolatilization times are of the same order as the mixing times for particles in fluidized beds, which are typically in the range of 2-20 s. Therefore, the assumptions of either an instantaneous release of volatiles at the feed point or a uniform release of volatiles throughout the bed
appear to be inadequate representations of the volatile release process for particles in the millimeter size range. Figure 2 shows some of the details of the process for the case of a bed temperature of 1323K. The curves of Fig. 2a illustrate the variation with time of the density and porosity of the particles. In spite of the fact that most of the combustion occurs in the pores, the depth of penetration is short compared with the radius of the particle, causing it to burn as a shrinking sphere without a change in porosity and density. The initial drop in density is due to the evolution of the volatiles. In Fig. 2b the temperature and the oxygen concentration at the surface as a fraction of the oxygen concentration at infinity are plotted versus time. The oxygen fraction at the surface is a direct measure of the relative importance of observed kinetic and diffusional resistance. The observed kinetic resistance includes both the resistance due to chemical kinetics and that due to pore diffusion. As the particle is introduced into the bed, the
FLUID BED COAL DEVOLATILIZATION/COMBUSTION
11
ment of the flame, and the oxygen concentration at the surface increases steadily until burnout occurs since the particle is shrinking and the mass transfer rate is enhanced, while the particle temperature decreases and levels off at about 27K above the bed temperature. The oxygen fraction at the surface has an average value of about 0.25 during the burning of the residue, showing the process to be mainly diffus~onally controlled. Figure 3 is analogous to Fig. 2, but pertains to a bed temperature of 1023K. At this temperature, the particles heat up more slowly and devolatilize at a lower rate. As the flame front approaches the surface, the volatile content of the particle is still high enough to ~espond to the rise in temperature with an enhanced volatile flux which drives the flame front back. The oxygen fraction at the surface is higher than in the previous case, showing the process to be more kinetically controlled. Figures 4-6 are analogous to Figs. 1-3, but were obtained for a 150 #m particle. Without discussing these figures in detail, it is nOteworthy that the devolatilization step is now complete after a few hundredths of a second and the particle temperature overshoots the bed temper-
temperature begins to rise. Devolatilization is slow and therefore no flame front is produced, while the reaction rate at the surface is also slow and thus the process is kinetically controlled, the oxygen fraction being close to unity. As the temperature rises, the rate of devolatilization increases and eventually the flame front develops, shielding the particle from the oxygen diffusing towards it (02 FRS = 0) and causing a further increase in the temperature of the particle. After about 7 s, the bulk of the devolatilization is completed and the flame front attaches. Notice that just as the flame front is about to attach, its proximity to the particle causes the particle temperature to reach a sharp maximum. The radius of the flame front is somewhat larger than observed in practice, since the treatment of the volatile combustion neglects the effects of natural and forced convection on the shape and dimensions of the volatile shell. It appears that much of the volatiles which cannot be reached by oxygen immediately following evolution will be carried away by the airstream flowing by the particles. The radius of the flame front is equal to the radius of the particle from the time of attach-
,o i 0.9 0.8 0.7 :~
0.6 0.5-
o :~
0.40,30.20.1 0
l .05
0.5
1
2 TIME
5
10
15
(SEC)
F i g . 4. B u r n o u t a n d d e v o l a t i l i z a t i o n h i s t o r i e s o f p a r t i c l e s f o r b e d t e m p e r a t u r e s o f 1023 a n d 1 3 2 3 K , Yo2 = 0 . 0 8 , R = 75 /~m.
12
GIORGIO BORGHI ET AL. 1.0~-
R : 7.5 Hm , T=1323*K .
o~ .6 t ~
I~'D~nsity(g/cm3) ~
©
,~- Porosity (crn3/cm~) i-i I (a)
.2
.
~8
~
"i
~Particl=
'" o
u E
lJ
~
~
l
"-
~mp=rature ('K}
Cs,C=J I
I
I (b)
Ilhr~mam= Radius (cm)
<~ '°251[III zw 5
[ Particle Radius
oi11T T
I
i
l
I
.05 Q2
Q5
1.0
2.0
~O
TIME (SEC) (c) Fig. 5. Combustion history for R = 75/zm, Yo2 = 0.08, T = 1323K: (a) density and porosity of particle; (b) particle temperature and ratio of oxygen concentrations at surface and in ambient; (c) flame or particle radius.
ature considerably, reaching a value close to the temperature of the flame front. Also, the particles tend to burn at constant size over much of the combustion period, as indicated by the roughly constant value of the char particle radius and by the curves pertaining to the density and porosity of the particles. Figure 7 presents a series of curves of burning times versus oxygen mole fraction in the particulate phase for different sizes and temperatures. These curves are applicable to fluidized bed combustion after the oxygen concentration in the particulate phase is obtained by means of an overall oxygen balance on the bed. Two questions that have aroused great interest in relation to fluidized bed combustion are that of whether the combustion process is kinetically or mass transfer controlled, and the related one of whether a shrinking core or a constant size combustion model, respectively, applies. Figures 8 and 9 summarize the answers of the model described to these questions. In Fig. 8, the average fractional kinetic resistance (taken
as the oxygen concentration at the surface over the oxygen concentration at infinity at the time of 50% burnout) is plotted versus particle size for different temperatures. It is apparent that there is a shift from almost complete kinetic control at low temperatures and small sizes to a predominantly mass transfer determined burning rate for large particles and high temperatures. Giving reference to an earlier presentation of our results, Ross and Davidson [35] report remarkably good agreement between these theoretically calculated values of the fractional chemical resistance and those determined from their theory. Figure 9 addresses the question of in-depth burning of the coal particles. Two extreme cases are plotted. Under conditions of kinetically controlled burning, combustion occurs in-depth and the particles do not shrink significantly while the density decreases. When combustion is diffusion limited, the shrinking core model applies, the density remaining constant over
FLUID BED COAL DEVOLATILIZATION/COMBUSTION
13
R=75~Jm , T=1023K 1.0~r- ~'/ Density (g/cm ! ) .5 L
I~ P°r°sity !cm31cm3~
0
~__i
__L
(a)
ip/-Particle Temperature (*K) 81.0~ ~"
tic
/ I
I
10
15
(b) E u
~ 017pl u_
Flame Radius (cm) ParticleRadius
OIkk"I
I
I
.02 .2
•5
1
I
I
2 TIME (SEC)
5
(c) Fig. 6. Combustion history for R = 75 #m, Yo2 = 0.08, T = 1023K: (a) density and porosity of particle; (b) particle temperature and ratio of oxygen concentrations at surface and in ambient; (c) flame or particle radius.
most of the burnout period. The initial drop in density is due to the release of volatiles. Note the difference in volatile contents at the two different temperatures (see Table 1). In presenting this model, we are aware of the fact that the structure of coal is complicated enough and physical and chemical differences between coals so great as to make a universally valid combustion model a practical impossibility. Moreover, uncertainties in many of the parameters involved, such as the reaction rate expression and the Sherwood number for burning particles in fluidized beds, as well as the inability to model accurately the structural changes occurring in the coal during combustion, must have an adverse effect on the predictions of the model. Nevertheless, this model reflects the current state of the art in fluidized bed combustion, and appears to reproduce many of the features observed in the complementary experimental study.
IV. C O N C L U S I O N S A mechanistic model has been presented that enables the burning and devolatilization histories of particles in fluidized beds to be predicted. The application of the model toi conditions prevailing in fluidized coal combustors indicates that . The devolatilization times for average size particles are commensurable with the mixing times, making the assumption of an instantaneous release of volatiles at the point of introduction of the coal feed unrealistic. . The combustion rate can be contro!led by either external mass transfer or the combined processes of pore diffusion and surfaee reaction depending upon the particle size and the temperature of the coal. For coal chat particles in the size range of 1000-3000 ~m and temperature of 1023-1323K none iof the kinetic processes of diffusion and Surface
6°I
14
GIORGIO BORGHI ET AL. 1.01
50
75 ~rrl Z i,i a
4O 30
1173K
.J <
0,8 R=1.5 mrn
13
10
I
I
I
z
t
0.6
U 9 0 0 r-
75or
n< h 0
R=o.5 mm
600r
0.4 T=lO23°K-
~
0.2 1
I
I
I
r
4500 F 3000r3750~-- ~
Z W Q
L 02
I J I 04 0.6 08 TIME / BURNOUT TIME
~ 10
Fig. 9, Density change of particles during combustion for Yo2 = 0.04 and (i) R = 1.5 mm, T = 1323K; (ii) R = 75 /zm, T = 1023K.
R=l.Smm
225011500 r 750 r 2
4
PERCENT OXYGEN
6
8
IN DENSE PHASE
Fig. 7. Burnout times forR = 75 t~m, 0.5 mm, and 1.5 mm char particles.
1.0 02=4
°/.
0.9 w
U z v~ w
O.8
1023 " K 0,7~ 0.6
U IZ
0.5-0.4--
z 0
0.3--
=< 0.2-0.1 --
~ i
0 IO0
200
i
i
~ i i
400 800 RADIUS, p m
i i 1500
J 3000
Fig. 8. D e p e n d e n c e o f f r a c t i o n o f total r e s i s t a n c e attributed to c h e m i c a l k i n e t i c s as a f u n c t i o n o f bed t e m p e r a t u r e and p a r t i c l e d i a m e t e r , for Yo2 = 0.04.
reaction can be neglected; they all have to be taken into account in the calculation of the overall rate o f char burning. . The model can predict variation in particle size and density with time that is consistent with the expectation that the particles burn in the shrinking core mode when external mass transfer dominates, and burn internally without change in size when the rate o f combustion is controlled by that o f the surface reaction. . Several assumptions in the model that may restrict the range o f its applicability are that the coal is noncaking, ash released during combustion does not provide a major resistance to diffusion, and no significant particle fragmentation occurs during combustion. Recent experiments in our laboratory on the combustion o f particles of a noncaking coal in a fluidized bed have yielded results on volatile flame formation and on the rate of the combustion o f the residual char that are in remarkably good agreement with values calculated by the model, and are presented in a companion paper. NOMENCLATURE heat capacity o f coal particle
FLUID BED COAL DEVOLATILIZATION/COMBUSTION
c~ C~ D Dc E, E0
Fpore
oxygen concentration at particle surface oxygen concentration in dense phase (ambient) pore diffusivity for oxygen gas phase diffusivity for oxygen energy of activation and mean energy activation of thermal decomposition reactions oxygen flux into pores
Fo2
Fo2 Vol Fvol
h
AHdev A~x ki, ko kg
k. K l MWv n
02 PGV
0 2 FRS
P
,002 q rf
R Rc Sh t
TAF TB Tgas
oxygen flux needed for the complete combustion of the volatiles flux of volatiles heat transfer coefficient to a particle specific enthalpy change of devolatilization specific enthalpy change of carbon/ oxygen reaction rate constants for devolatilization reactions gas phase thermal conductivity rate constant for nth order carbon/ oxygen reaction flux density of oxygen diffusing in pore pore radius molecular weight of volatiles order of carbon/oxygen reaction molar oxygen requirement for complete combustion of unit mass of volatiles oxygen concentration at surface divided by oxygen concentration in dense phase probability of overlap of pores due to an increase A0 in porosity oxygen partial pressure at particle surface parameter defined after Eq. (11) flame radius particle radius rate of carbon consumption per unit surface area Sherwood number time temperature at flame front bed temperature gas temperature
Tp Vi Vi* Z c~ ~7 0 X p o OB
15 particle temperature weight of volatiles released up to time t per weight of original coal asymptotic weight of volatiles released at long times depth of penetration of oxygen into pores fraction of surface occupied by pores transpiration parameter defined by Eq. (19) porosity of particle thermal conductivity of coal particle particle density standard deviation of Gaussian distribution of activation energy Stefan-Boltzmann constant
The authors are grateful for support received under DOE contract No. E(49-18)2295. REFERENCES 1.
2. 3. 4.
5. 6. 7. 8. 9.
10.
11.
12. 13. 14.
Howard, J. B., in Chemistry of Coal Utilization Second Supplementary Volume (M. A. Elliot, Ed.), Wiley, New York, 1981, pp. 665-784. Gibbs, B. M., and Be6r, J. M., 1. Chem. E. Symposium Series No. 43, 1975, pp. 1-11. Be6r, J. M., and Martin, G. B., AIChE 691h Annual Meeting, Chicago, Nov. 28-Dec. 2, 1976. Pohl, J. H., and Sarofim, A. F., Sixteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1976. Badzioch, S., and Hawkesly, P. G. W., Ind. Eng. Chem. Process Design Develop. 9:521 (1970). Wiser, W. H., Hill, G. R., and Kertamus, N. J., Ind. Eng. Chem. Process Design Develop. 6:133 (1967). Skylar, M. G., Shustikov, V. I., and Virozub, I. V., Intern. Chem. Eng. 9:595 (1969). Pitt, G. J., Fuel41:267 (1962). Anthony, D. B., Howard, J. B., Hottel, H. C., and Meissner, H. P., Fifteenth Symposium ~(lnternational) on Combustion, The Combustion Institute, Pittsburgh, 1975, p. 1303. Suuberg, E. M., Peters, W. A., and Howard J. B., 173rd National A CS Meeting, Division of Fuel Chemistry, Vol. 22, No. 1, 1977, p. 112. Solomon, P. R., and Colket, M. B., Seventeenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1979, PPi 131-142. Suuberg, E. M., Peters, W. A., and Howard, J. B., Ibid., pp. 117-128. Borghi, G. G., S. M. Thesis, M.I.T., Cambridge, MA, 1976. Agarwal, P. K., Genetti, W. E., and Lee, Y. Y., Fuel 63:1157 (1984).
16 15. 16.
17. 18.
19. 20. 21. 22.
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Received 23 February 1983; revised 19 December 1984