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Modeling of sulfur retention by limestone in coal briquette
FUEL PROCESSING TECHNOLOGY ELSEVIER
Fuel Processing
Technology
53 (1997) 49-67
Modeling of sulfur retention by limestone in coal briquette Caixia Chen, Toshinori Kojima
*
Department of Industrial Chemistry, Faculty of Engineering Seikei Uniuersity, Kichijojikitamachi, Musashino-shi, Tokyo 180, Japan Received 9 September
1996; accepted 3 June 1997
Abstract A detailed simulation model was developed for sulfur retention by limestone in a coal briquette. Four submodels, i.e., coal briquette combustion, volatile and sulfur evolution, H,S retention, and SO, retention, were included in the simulation. In the model, the coal briquette combustion was divided into two successive stages: volatile ignition and char burnout. The temperature profile and its time variation, sulfur release and retention behavior within the burning coal briquette for the two stages were simulated separately. In the stage of volatile evolution and ignition, a part of coal sulfur is released as H,S, and reacted with the calcined limestone in the area near the particle surface, where the local temperature is increased along with the volatile ignition, and the limestone in the coal briquette is partially calcined. H,S retention in the coal briquette was thus simulated as a result of the competition among its transportation by the bulk flow of evolved volatile, its molecular diffusion due to the concentration gradient within the coal briquette, and its capture by the calcined limestone. In the stage of char burnout, the remaining part of coal sulfur is released as SO, with char burning which is simulated by the shrinking core model. SO, release rate is assumed to be proportional to the char burning rate and controlled by oxygen diffusion in the ash layer. The sulfate formation occurs in the ash layer within which oxygen exists. SO, retention was thus simulated as a result of the competition among the sulfate formation with the calcined limestone, SO, diffusion in the ash layer and its emission from the briquette surface. The sulfur retention by limestone in a spherical centimeter sized coal briquette was simulated by the model. The effects of heating rate, briquette size, calcium to sulfur ratio (Ca/S), and volatile matter of coal on the sulfur retention were predicted. The simulation results showed that rapid heating condition was good for both the H,S retention in the volatile and the SO, retention in the combustion gas. The simulation also predicted a higher SO, retention for a
’ Corresponding
author. Tel.: + 81-0422-37-3750:
fax: + 81-0422-37-3871
037%3820/97/$17.OO 0 1997 Elsevier Science B.V. All rights reserved PII SO378-3820(97)00036-2
50
C. Chen, T. Kojima/ Fuel Processing Technology 53 (1997) 49-67
larger sized coal briquette. The coals of higher rank and lower organic sulfur contents also showed a higher sulfur retention.
0 1997 Elsevier Science B.V.
Keywords: Coal briquette combustion; Sulfur retention; Numerical model
1. Introduction Limestone is a well-known and commonly used sorbent either for SO, removal from combustion gases or for H,S removal from fuel gas of coal grassfires. In the recent years, researches using limestone as a sorbent in coal briquettes have also been carried out to reduce the sulfur release from domestic and small scale use of coal in developing countries. It is of significant interest to study the combustion and the sulfur retention behavior in a centimeter sized spherical coal briquette mixed with limestone and binder, because such sized coal particles are widely used in fixed bed furnaces and rotary kilns, in which the coal briquettes are generally combusted in a hot air stream. At the first stage of coal conversion, the volatile is evolved and ignited in the gas boundary film around the particle, while the coal sulfur is also evolved as species of the volatile. On the other side, the limestone, if mixed in the coal briquette, is partially calcined with the briquette temperature increase and volatile ignition. Most of the coal sulfur is found to be released below 800°C while the main component of limestone, calcium carbonate, undergoes rapid calcination to calcium oxide above 800°C [I]. Therefore, the volatile sulfur (mostly abundant in H,S) retention by limestone within the coal briquette is a result of the competition among the carrying by the bulk flow of evolved volatile, H,S diffusion due to the concentration gradient within the briquette, the calcination of limestone and the reaction of H,S with the calcined limestone. In our previous experimental research [2,3], the pulverized Illinois No. 6 coal sample (smaller than 0.125 mm) was granulated to a 18-20 mm coal briquette, and combusted experimentally. The experimental apparatus consists of a horizontal electrically-heated reaction tube furnace, a gas supplier, and the gas product analysis system. In the experiment, the coal briquette sample was put on a ceramic boat and combusted in an air stream at a rate of 10 cm’/s (room temperature base). Two types of experimental procedures, abbreviated to rapid heating and constant-rate heating, were used in the experiments. In the case of rapid heating, the sample was moved quickly to the preheated hot reactor at the temperature of 1073 K, and cornbusted. In the constant heating rate condition, however, the sample was put into the reactor at room temperature, heated at the constant rate of 10 K/min, and cornbusted. The sulfur retention behavior of the limestone mixed high sulfur Illinois No. 6 coal briquette was studied. It was found that the sulfur retention was affected by the surrounding gas temperature, heating rate of the briquette, and calcium to sulfur ratio (Ca/S). The experimental results showed that the rapid heating rate of coal briquette led to a relatively high sulfur retention, and the sulfur retention was not improved by the further addition of limestone beyond Ca/S of 2. To explain the experimental results, in the present research, the combustion and sulfur retention process in a 8-16 mm spherical coal briquette mixed with limestone is
C. Chen, T. Kojima / Fuel Processing Technology 53 (1997) 49-67
numerically simulated corresponding to some of the typical experimental time-temperature profile and the temperature distribution within the calculated by the model. The evolution behavior of H,S and SO,, calcination and the limestone conversion to sulfate within the coal evaluated. The effects of heating rate, briquette size, Ca/S ratio, volatile sulfur release behavior on the sulfur retention efficiency are discussed.
51
results. The briquette are the limestone briquette are evolution and
2. Modeling methods
2.1. Overall description Four submodels, i.e., the coal briquette combustion, volatile and sulfur evolution, H,S retention and SO, retention, are included in the simulation. In the model, the combustion of coal briquette is divided into two successive stages of volatile ignition and char burnout. The time-temperature profile and its distribution within the burning coal briquette for the two stages are calculated by solving the energy equations. The volatile evolution and sulfur release are predicted by a volume reaction model by Sugawara et al. [4,5], taking the temperature change and its distribution in the coal briquette into account. H 2 S retention in the volatile evolution stage and SO, retention in the char burnout stage are simulated by solving the mass equation in the porous coal briquette or the ash layer, coupled with the limestone calcination, sulfide and sulfate formation rate expressions. 2.2. Coal briquette combustion In the past years, considerable efforts were spent investigating the time-temperature history and the temperature distribution in a centimeter sized burning char particle [6- 101. The available information on the behavior of centimeter sized coal particle, however, is very little, because a quantitative treatment of the effect of coal volatile combustion on the particle temperature is difficult to be established. Gururajan et al. [ 111 predicted the combustion of evolved volatile matter in the vicinity of pulverized coal particle, and found that the volatile burnt too distant from the particle to feed back energy from the volatile flame when devolatilization rate was high. It is thought that the volatile flows rapidly outward the particle, and the volatile reactions with air do not occur on the particle surface. Therefore, the direct effects of the volatile evolution behavior on the coal particle temperature are not strong. The indirect effects, however, can be very strong, because the volatile matter, devolatilization rate, flammability of the volatile and its transport from the particle determine whether ignition of an isolated coal particle occurs heterogeneously or homogeneously, and affect the coal particle temperature significantly [ 12,131. For millimeter- and centimeter sized particles there is generally a convective flow, and a flame is established around the particle, especially in the wake. In this case, the effects of volatile combustion on the particle temperature is more complicated.
52
C. Chen, T. Kojim/
Fuel Processing Technology 53 (1997) 49-67
In our previous experiment [2,3], the transient time-temperature profile was measured by a thin CA thermocouple inserted into the coal briquette center. The temperature distribution within the coal briquette, being difficult to be measured in the experiment, is calculated by a simplified model as follows. At the stage of volatile evolution and ignition, the time-temperature history and its distribution within the coal briquette is determined by the heat balance of a spherical coal particle combustion in a hot air steam. The unsteady energy equation of a spherical coal particle is: aT 1 a pcCPx = 7%
aT Ar2~
- wAH (1) i i The volatile release rate is calculated by w = p,dV/dt, (kg/m3 s>, and the devolatilization reaction heat AH is 300 kJ/kg [ 121. It is assumed that the volatile is ignited in the boundary gas film nearby the briquette surface, and only a fraction of combustion heat is used to heat the briquette itself. The heat from the volatile flame, the convection from the hot gas and the radiation from the reactor wall reaches to the surface of the briquette and the heat propagates toward the sphere center through heat conduction. Thus the boundary conditions of Eq. (1) are: aT r=O,--0 ar
where, cp is an adjustable factor from 0 to 1, and determined by fitting the numerical temperature variation of particle center to the experimental one. The volatile combustion heat 4, is 30 MJ/kg [ 121, and w, is the cumulative volatile release rate per unit particle surface area, i.e.: ” @=zFo
1
R /
dV 4n=r&;dr
At the char combustion stage, it is assumed that the residual char combustion starts when 80% of the volatile is released for the rapid heating condition, and 30 min for the constant-rate heating condition, when the briquette temperature increases sharply and roughly 80% of the volatile is released which was observed experimentally. A traditional unreacted shrinking core model [14] and the quasi-steady state assumption of temperature in ash layer were used to simulate the residual char combustion of the briquette. The time dependent variables of the unreacted core size R,, the unreacted core temperature c, the briquette surface temperature T, were calculated by the same method described previously [lo] with the initial conditions: t = ti, r = R, T, = T,. The temperature distribution in the ash layer for a given time is then calculated by the steady state energy equation: At-‘: =0 ( 1 with the boundary conditions: r = R, , T = T,, and r = R, T = T,. $i
(5)
C. Chen, T. Kojima / Fuel Processing Technology 53 ( 1997149-67
The solution
53
is:
&’ r
T=T,+
c
i
I
T-T, 1
(6)
1
---
2.3. Volatile and sulfur evolution It is well known that the devolatilization of large coal particle highly depends on the large temperature gradients within the particle and its time-temperature history, which in turn, depends on the external heat transfer to the particle. Much effort has been focused on the kinetics, mechanisms and product distribution in the devolatilization of small coal particles. However, relatively few studies on the devolatilization of the large particles ( > 10 mm) exist in the literature [ 151. In this paper, the volatile evolution from the coal briquette is assumed to be one single reaction step. The devolatilization rate is expressed by [ 161: dV -=K,(V* dt
-V)
(7)
where, V * denotes total volatile mass, which is adopted from the value of ASTM volatile matter of daf basis. K, is defined by Arrhenius relation: K, = K,,exp(
- E,/RT)
(8)
where, T is the local temperature in the coal briquette, and calculated by Eq. (1). The sulfur release is estimated based on the volume reaction model by Sugawara et al. [4,5]. In this model, the coal sulfur is divided into organic sulfur (A) and pyrite (E). When coal is heated, the organic sulfur is decomposed to release H,S (D) and organic sulfur in tar (C) or remains in coal as sulfur in Char (B). The pyrite sulfur (E) is decomposed to release H,S, and produces ferrous sulfide sulfur (F). The model can be expressed as follows [5]:
9
The material
dCA
-= dt
C Sulfur in Tar
balance for each sulfur form is given by the following -(K,+K,+K,)C,
Eqs. (4,5):
54
C. Chen, T. Kojim / Fuel Processing Technology 53 (1997) 49-67
-
dt
= K,C,
- K,C;
dCc -=KK,CA-C, dt dCD -
dt
dG
-
(11)
K3CA i- ; K,C;.’ i- K,C;
=
-K
4
- K,C,
Co.5
( 14)
cc
(15)
=F
where, Ki is expressed K, = K,,exp
(12) (13)
E
1 = ZK4C;.5
dCcci dt
(10)
TC
=
dt dC, dt
+ K,C,
by the Arrhenius
equation:
(16)
- 2 i
i
A part of sulfur in tar (Cc, ) is assumed to be emitted as one of the gaseous species of the volatile from the briquette surface at the rate of volatile evolution. The fate of the remaining part of tar sulfur is assumed to be combusted with char as same as sulfur in char. The residence time of gaseous tar sulfur in the briquette is:
(17) The kinetic parameters proposed by Sugawara et al. [5] were used. It was noted that the organic sulfur decomposition rate constant (K, + K, + K3), and the rate constants for the other reaction steps are independent on the heating condition in Ref. [5]. Therefore, one set of parameters is used for the two heating conditions in the present analysis. In Sugawara’s model [5], no effects of coal rank were included. However, in the recent experimental research of Garcia-Labiano et al. [17], very different sulfur yields were found for different coals, depending on both the sulfur content and the coal rank. It was found that the fraction of sulfur passing into the tar was 30-40% for all kinds of coal, and the percentage of sulfur released with the volatile matter was in line with the volatile matter of the coal. Based on the above facts, the kinetic parameters used in the present research are improved as follows: K,=(l-0.3-V*)K,,, K, = 0.3 Korg K3=V*Korg where, Korg is the summation
of K,, K, and K, in Ref. [5].
C. Chen. T. Kojima/ Fuel Processing Technology 53 (1997149-67
55
In the calculation, the coal sphere was divided into N shells. The overall weight loss, volatile evolution rate and sulfur species of the coal briquette were calculated by summation over the shells. 2.4. The retention of H2S in volatile evolution
stage
At the stage of volatile evolution, the evolved volatile matter serves as reaction medium to produce gaseous tar sulfur and H,S within the coal briquette. The gaseous tar sulfur and H, S, in turn, are carried by volatile matter through the porous coal particle and diffuse through the pores due to the concentration gradient existed in the briquette. At the same time, H,S reacts with the calcined limestone by the reaction CaO + Hz S + CaS + H,O when atmosphere within the coal briquette is reducing. The flow velocity of the bulk volatile within the coal briquette V, is calculated by the continuous equation:
(18) where &r is the porosity of particle, p is the volatile gas density at averaged temperature, and o is the volatile release rate per unit coal volume. The mass balance of H,S in the briquette is then expressed as:
with the boundary
particle
condition
dY r=O,z=O
(20)
r=R,-D&,urY=K,Y
(2’)
where, Y is the mass fraction of H, S in volatile, D, is H,S diffusivity in volatile and . w, is H, S evolution rate per unit coal particle volume, and calcu-
K, = Ns,D,\/D, lated by:
dCn
0 I = PCdt
(22)
o2 is the H,S retention d[CaO] wz=--
dt
M
rate with limestone,
H2S
and calculated
as follows: (23)
(24)
C. Chen, T. Kojima / Fuel Processing Technology 53 (1997) 49-67
56
The reaction K u,s i
rate constant
is (M. Horio, 1996, private communication):
= 0.94 exp( - 20,00O/RT)
T> 1073K
= 238.0exp(
T < 1073 K
-69,00O/RT)
The initial molar concentration
of limestone
(25)
[CaO], in the coal briquette
is calculated
by: [CaO],
= Ca/Sp,[
s]/32
(26)
where the Ca/S ratio is calculated from the weight of the coal sample and limestone, and the initial sulfur concentration in the coal sample [sl (40 mg S/g coal (daf)). During the heating process, the limestone in the particle is partially calcined. The calcination rate is calculated by [ 181: df
6Mcaco,
ii=
P,s4,
c co 2sq- Go,,, 1 K+m
(27) d,,{(l
-f)-1’3
- 1} + Rcaco,(l
-f)-2’3 RTk,
20,
where, the diffusion resistance in the bulk film, being much smaller than that within the coal briquette, is neglected in the calculation, i.e.: 1 K,-
-0
(28)
The calculation
equations
of the parameters
2.5. The retention of SO, in char combustion
in Eq. (27) are listed in Table 1. stage
The sulfur in char (Schar), including FeS, CaS, the organic sulfur (B) and the remaining sulfur in tar (C) are combusted with char. It is assumed that CaS transforms to CaSO, directly and quickly, and the release rate of SO, is proportional to the combustion rate of coal char, which is controlled by oxygen diffusion in the ash layer. According to the shrinking core mode, the char briquette is divided into two zones: unreacted core and ash layer. The following reactions are thus assumed to occur along a sharp interface between the ash layer and the unreacted char core: c + 0, + co, S char
+
‘2
4
“2
CaS + 20, --f CaSO, The shrinking core thus the produced SO, O,, CO,, and SO,) (SO, + l/20, + CaO as:
model also implies that there is no oxygen in the unreacted core, is carried to the briquette surface by the combustion gases (N,, through ash layer and reacts with limestone in the ash layer -+ CaSO,). The mass equation of SO, in the ash layer is written
C. Chen, T. Kojima / Fuel Processing Technology 53 (1997) 49-67
with the boundary
51
conditions:
dY
r=O,--0
(30)
ar
r = R,De;i,
= K,Y
where, Y is the mass fraction N,, and K,, = N,,D,/D,SO,
(3’) of SO, in the combustion gases, D, is SO, diffusivity retention rate by limestone is [20]:
in
dX o4 =
Ka%~~sO,
(32)
dX = K&l-X)Y+ dt
so2
(33)
where, X is the conversion of limestone to CaSO, and D is the maximum value of X. which was assumed to be 0.7 according to Ref. [20]. The reaction rate constant is calculated by the Arrhenius expression [21] with the frequency A of 403.7 (mol SOJmol gas)-‘s‘: K SO?= Aexp( -6750/T)
(34)
3. Results 3. I. The burning coal particle temperature The time-temperature profile and the temperature distribution of the burning coal briquette were calculated by solving the Eqs. (l)-(6). The operation conditions, same as those in the previous experiments, were used in the calculation. The parameters, and the physical and chemical properties are listed in Table 1. Fig. 1 shows the calculated and experimental time-temperature profiles in a 16-mm coal briquette burned under the rapid heating condition. The initial part of the profile (O-54 s, volatile ignition stage) was best fitted by using the adjustable factor cp of 1.75 X 1Om3, while the remaining part of the profile (after 54 s, char combustion stage) was fitted by selecting a set of adjustable model parameters as described in the previous paper [ 101. Fig. 2 shows the results under the constant-rate heating condition. The time-temperature profile of the volatile evolution stage was best fitted by using the adjustable factor cp of 0.095. The temperature profile in the char combustion stage, however, was very difficult to be fitted because two serial stages are assumed, thus the char was ignited at a surrounding gas temperature above 673 K, accompanied with a sharp particle temperature increase in the modeling calculation. A lowest difference between the calculated peak temperature and the experiment data was obtained by assuming the char combustion started at 30 min when the surrounding gas temperature reached 573 K.
C. Chen, T. Kojim / Fuel Processing Technology 53 (1997) 49-67
58 Table 1 Kinetic parameters,
coal properties
Density of coal briquette: Diameter of coal briquette: Heat of combustion: carbon volatile ASTM analysis of coal (dry basis)
Sulfur content
and other data 1015 kg/m’ 16, 12, 8 mm 32.819 MJ/kg 30 MJ/kg %VM = 40.45 %F.C = 47.53 %Ash = 12.02 %S = 4.0 (daf)
Deuolafilization Frequency factor: Activation energy: Heat of devolatilization: Adjustable factor
rapid heating 2250 l/s 64 kJ/mol (Ref. [19]) 300 kJ/kg (coal) 1.75x 10-3
constant-rate heating 33 l/s 50 kJ/mol (Ref. [5]) 0.095
Sulfur evolution Frequency factor: (Ref. 151) KIO + Kzo + K,o K40 K,o K60
Activation
15.0X lo6 l/min 2 X 10” (mg S)“,s/min 1 X IO9 g mg S/min lX106 l/min
energy: (Ref. [5])
E,> E2. Ex E4 E5 E6 Organic sulfur Char combustion (Ref. [lo]) Diffusivity of ash layer: Emissivity of the surface: heat conductivity: ash layer char Frequency factor: Activation energy: The calculation equations of the parameters in Eq. (27): (Ref. [ 181)
92.0 kJ/mol(22.0 kcal/mol) 175.8 kJ/mol(42.1 kcal/mol) 234.8 kJ/mol (56.1 kcal/mol) 134 kJ/mol(32.0 kcal/mol) 80% of total sulfur
1.0 cm2/s 0.6 0.7 J/s m2 K 1.1 J/s m* K 8.0~ lOa l/s 188 kJ/mol (45 kcal/mol) D, = DE, 5. 5 = &,“-“‘, D= 2.23x 10-6Ts’ 78, E, = 0.702, cP +0.298, gp = 0.3, LogKc,,oz = - 8920/ Tp + 8.54, k, = 9.12 X 10-4exp( - 167,OOO/RT,), C coz.eq = (Gxo, x 273)/(0.0103 X 22.4 X lo- 3 X T)
The time-temperature profiles of various sizes of 16-, 12- and g-mm briquettes combusted under the rapid heating condition were calculated by using the same operation conditions and parameters as those for Fig. 1. As shown in Fig. 3, smaller briquette combusts quickly with a higher peak temperature, which is consistent with the
C. Chen, T. Kojima / Fuel Processing Technology 53 (1997) 49-67
59
1473 1273 -
873
673
-
473
-
modelling
---
modelling
-
furnace
.
Tc Ts Te Tc
experimental
273 0
20
40 time
Fig. I. Calculated condition.
and experimental
time-temperature
-
-
- ______
1073
-
873
-
80
(min)
profile of coal briquette combusted
modelling
1273
60
Tc
-
furnace experimental
0
20
40 time
Fig. 2. Calculated heating condition.
and experimental
time-temperature
273.
’ 0
10
’ 20
time Fig. 3. Calculated heating.
time-temperature
60
Te Tc
80
100
(min)
profile of coal briquette combusted
’ 30
under rapid heating
40
50
60
’ 70
under constant-rate
80
(min)
profile at center of different
sized coal briquette
combusted
under rapid
60
C. Chen, T. Kojim / Fuel Processing Technology 53 (1997) 49-67
12mm
115 mm
A-/:/
-----_.
10
”
1,
0,
20
30
time Fig. 4. Calculated time-temperature under rapid heating condition.
r=o a
1
40
60
50
(s)
profile at the volatile combustion
stage of different
sized coal briquette
previous simulation results [9]. The temperature distributions of the three sizes were also predicted and shown in Fig. 4. It is found that smaller coal briquette is heated more quickly than larger coal briquette, with lower temperature difference between the center and the surface. The maximum temperature difference of the 16-cm coal briquette is 180 K, but lower than 60 K for a g-mm coal briquette.
3.2. Sulfur and volatile evolution
behavior
The volatile and sulfur evolution behavior was predicted by solving Eqs. (7)-(17). The fraction of volatile and H,S released against the center temperature of the coal briquette are shown in Fig. 5. An activation energy of 64 kJ/mol, suitable to large coal briquette devolatilization at 1073 K in nitrogen, proposed by Fu et al. [19], was used for the calculation of rapid heating condition. For the constant-rate heating condition, a
0.4 10 K/min 0.3
: : /’ / ,’ I’
0.2
/
0.1
,
I’
I’ rapid
1.: o-$OO~;:O
600
h;::““,,O
Tc WI Fig. 5. Calculated
400
500
600
700
Tc WI
time variation curve of volatile and H,S evolution.
600
61
C. Chen, T. Kojima / Fuel Processing Technology 53 f 1997) 49-67
(I)
0.4
1 .
:
-
1
1
0 .
1
rapid heating 75.9%
0.0
0.2
0.4
0.6
0.8
1 .o
1.2
r/R and owd
Fig. 6. Calculated radial profile of limestone conversion (sorbent: Ca(OH)2),
sulfur retention
(values in W).
value of 50 kJ/mol in Ref. [51 was adopted. The frequency factors were selected to be 2250 l/s for rapid heating and 33 l/s for constant-rate heating, in order to obtain 80% of total volatile evolution before the defined char ignition time in consistence with the coal briquette combustion model.
3.3. Sulfur retention behavior
3.3.1. Effects of heating rate In order to study the effects of heating rate on the sulfur retention efficiency, two extreme conditions were simulated for a coal briquette of 16 mm size and Ca/S of 2.8 (standard condition). One of the simulation calculations was done by using a sorbent of Ca(OH),, which is decomposed quickly above 150°C. Therefore the influence of limestone decomposition rate attributed to the heating conditions was excluded in the
,0.3
1’
c 0
tJ
1
8
rapid heating
----__
1OK/min
z E
1’
-
r
51.29%
0.2-
u0 : ‘;;
0.1 -
; > : u
0.0
0.0
0.2
0.4
0.6
0.8
1 .o
1.2
r/R Fig. 7. Calculated
radial profile of limestone conversion
(sorbent: &CO,,
Pco2: 5%).
62
C. Chen, T. Kojima / Fuel Processing Technology 53 (1997) 49-67
+I
.
8mm
‘U 0.0 -
m Fig. 8. Calculated 0.03%).
calcined
’
0.2
0.0
”
32s
’
0.4
0.6
0.8
1.0
1.2
r/R
fraction
of limestone
in different
sized coal briquettes
(sorbent:
CaCO,,
PcO,:
calculation. As can be found in Fig. 6, a higher efficiency of sulfur retention is obtained both in the stage of volatile combustion stage and in the overall processes of coal briquette combustion for the rapid heating condition. At the stage of volatile combustion, the sulfur retention efficiency of rapid heating condition is 23.9%, which is about twice that of constant-rate heating condition. Another numerical calculation was performed by assuming the sorbent of limestone, with CO, concentration in the coal pores as high as 5%, at which the limestone remained to be uncalcined until the char ignition occurred. Although the sulfur retention at the volatile combustion stage is zero both for tbe rapid heating and for the constant-rate heating conditions, it is found in Fig. 7 that higher sulfur retention is obtained for the rapid heating condition. In other words, higher sulfur retention efficiency can be obtained for the rapid heating condition at the stage of char combustion stage, too.
L
-
16mm
60.35%
7.5%
,Zmm
55,7&
10.1%
--__-.
6mm
52.51%
11.0%
0.2
0.4
0.6
0.3 -
E
IC
.
vol. comb.
overall
cl
-
b 0
0.2 -
0’ ‘Gj b 0.1 z 8 0.0 0.0
0.8
1 .o
1.2
r/R Fig. 9. Calculated radial profile of limestone conversion briquette (values in %).
(sorbent: CaCO,,
P,,*:
0 03%) in different sized coal
C. Chen, T Kojima / Fuel Processing Technology 53 (1997149-67
63
Ca/S ratio (-) Fig. 10. Sulfur retention vs. Ca/S
ratio under rapid heating condition.
3.3.2. Effects of briquette size The radial profile of calcined fraction of limestone with various briquette sizes under the rapid heating condition, when the organic sulfur in the coal is decomposed completely (54, 44 and 32 s corresponding to the size of 16, 12, and 8 mm, separately), is calculated and shown in Fig. 8. It is thought that CO, concentration in the briquette is in the range between 5% and 0.03% (in atmosphere). The numerical results show that the retention efficiency of H,S in volatile is lower than 20% even when Ca/S is as high as 3.68 and CO, concentration is as low as 0.03% for the rapid heating condition, because the volatile sulfur release rate was faster than that of calcination or sulfide reaction of limestone. As the extreme case, all of the following calculations were performed by assuming CO, concentration of 0.03%. The radial conversion distribution and the sulfur retention (in %) of the three sizes are shown in Fig. 9. The overall sulfur retention decreases with decreasing particle size. The results can be explained by that SO, undergoes longer residence time in the coal briquette for larger sizes, and has more chance to be absorbed by limestone than that of smaller sizes. 3.3.3. Effects of Ca/S ratio Fig. 10 shows the effects of Ca/S ratio on the sulfur retention under rapid heating condition. The sulfur retention efficiency increases quickly with an increase in Ca/S
Ii Fig.
0.0
0.1 0.2 0.3 0.4 VM of daf coal (-)
11.Sulfur retention vs. volatile matter under rapid heating condition
64
C. Chen, T. Kojima / Fuel Processing
0
1
2
Technology53 (1997) 49-67
3
4
5
orghnorg (-) Fig. 12. Sulfur retention vs. organic to inorganic
sulfur ratio.
ratio when Ca/S is lower than 2, but increases very little with further Ca/S increase. The calculation is consistent qualitatively with the experimental results published previously [2,3]. 3.3.4. Esfects of volatile ana’sulfur evolution behavior The effect of volatile matter, and the ratio of organic to inorganic sulfur on the sulfur retention was simulated. Fig. 11 shows the predicted sulfur retention for coal briquettes with various volatile matter under the rapid heating condition, and Fig. 12 shows the predicted sulfur retention curve of various organic sulfur to inorganic sulfur ratios (total sulfur content of 4%, daf basis). It is found that the overall sulfur retention decreases by increasing the volatile matter and the organic sulfur content.
4. Discussions As can be found in Figs. 1 and 4, the coal briquette burns with a higher average temperature history and larger temperature gradient within the coal briquette, due to the higher surrounding gas temperature under the rapid heating condition. Under the constant-rate heating condition as shown in Fig. 2, however, the briquette surface temperature and the average temperature history are relatively lower, and the briquette temperature is nearly uniform. To predict the effects of heating rate on the sulfur retention efficiency, the conversion of limestone is calculated under the calculated time-temperature profiles. Although the calculated sulfur retention efficiency might be overestimated by the unsatisfactory fitting with two peaks under the constant-rate heating case, the calculated conversion of limestone within the coal briquette is much lower than that of the rapid heating conditions (Figs. 6 and 7). At the volatile ignition stage, H,S is released at higher particle temperature (Fig. 5) due to the rapid heating condition, and a higher limestone conversion is obtained in the area nearby the particle surface due to the larger temperature gradient within the briquette (Fig. 6). At the char combustion stage, the higher conversion of limestone under rapid heating condition (Fig. 7) is obtained mainly due to the higher briquette temperature level, fast char burning and sulfur releasing, which are thought to be accompanied by a relatively higher concentration level and a faster sulfate formation.
C. Chen, T. Kojim / Fuel Processing Technology 53 (1997149-67
6.5
The rapid particle heating rate also leads to fast calcination of limestone. As shown in Figs. 8 and 9, the limestone in smaller sized coal briquette is calcined more quickly than that in larger sized one, because of the higher heating rate and small temperature difference in the smaller sized briquette. As a direct effect of the increase in the calcined limestone, the conversion of limestone increases with a decrease in particle size at the volatile combustion stage. In Fig. 11, the sulfur retention increases slightly with an increase in volatile matter since the absolute amount of released H,S is increased with volatile matter. However, the overall sulfur retention is found to decrease rapidly with an increase in volatile matter due to the low retention efficiency of H,S in volatile matter. In addition to this, the overall sulfur retention decreases with an increase in organic sulfur content, both for the rapid heating condition and for the constant-rate heating condition (Fig. 12). When the organic sulfur is high, more H,S is released at very low particle temperature, which is far below the limestone calcination temperature. The prediction showed that the amount of sulfur remaining in char increased with an increase in pyrite sulfur, and the retention efficiency of sulfur in the char was higher than 90% when Ca/S was higher than 2 for the rapid heating condition. In other words, the lower volatile sulfur retention, leading to a limited sulfur retention efficiency for the overall process, is a critical point in coal briquette desulfurization by limestone.
5. Conclusion The time-temperature profile and the radial temperature distribution in a burning spherical coal briquette were calculated by a simple two stage model. The evolution of H,S, and SO, in the coal particle was predicted. The limestone conversion was evaluated. The following conclusions can be drawn from the results. (1) The coal briquette bums with a higher average particle temperature under the rapid heating condition than that under the constant-rate heating condition. (2) The volatile and sulfur are evolved at higher particle temperature under the rapid heating condition. (31 The rapid heating condition is better for both the sulfur retention in volatile and the sulfur retention in combustion gas. (4) The large sized coal briquette provides a longer residence time of SO, in the particle, and more chance for SO, retention. (5) A sulfur retention limit exists in the coal briquette desulfurization, because the volatile sulfur retention efficiency is very low. The model predicts that higher rank and lower organic sulfur contained coal are suitable for briquette combustion for the sense of sulfur retention.
6. Nomenclature
[CaOl Ca/S Ci(i = A - F)
molar concentration of CaO, mol/m3(coal volume) molar ratio of calcium to sulfur concentration of each sulfur form, mg S/g (coal)
66
C. Chew T. Kojima / Fuel Processing Technology 53 (1997) 49-67
c CG
concentration of gaseous tar sulfur oxygen concentration, mol/m3 carbon concentration, mol/m3 CO, concentration in bulk flow, mol/m3 equilibrium concentration of limestone decomposition, mol/m3 heat capacity of unreacted core, J/kg K volumetric heat capacity of ash layer, J/m3 K effective diffusivity of H,S in coal particle, m*/s effective diffusivity of H,S in ash layer, m2/s molecular diffusivity, m*/s diameter of limestone particle, mm diameter of coal particle, mm activation energy of char reaction rate constant, kJ/mol activation energy of devolatilization rate constant, kJ/mol fraction of calcined limestone convective heat transfer coefficient, J/s m2 K radiation heat transfer coefficient, J/s m* K4 heat of reaction, J/mol reaction constant of sulfide reaction, l/(mol/mol) s reaction constant of sulfate reaction, l/(mol/mol) s frequency factor of char reaction rate constant, l/s equilibrium constant of CaCO, decomposition, MPa effective heat conductivity in ash layer, J/s m K reaction constant of sulfur release reactions, l/s reaction constant of devolatilization, 1/s frequency factor of devolatilization rate constant, l/s mass transfer coefficient of oxygen in gas film, m/s surface reaction rate constant, l/s molecular weight of H 2 S molecular weight of CaCO, Nusselt number for convective heat transfer Sherwood number distance from center of sphere, mm radius of unreacted core, mm particle radius, mm gas constant, kJ/mol K initial sulfur concentration in coal, mg S/g coal time, s temperature, T, at unreacted core surface, T, gas temperature, Tp coal particle temperature, T, at particle surface, To in bulk gas, T, at reactor wall, K ultimate volatile matter fraction, g volatile/g daf coal volatile move velocity, m/s conversion rate of limestone mass fraction of H,S in volatile, or SO, in combustion gas
CA0 CSO CCO,3
cCO,,eq
CP CP”
De
D eA QA
4s
DP E
f” h
hr
AH K H2S K SO2 KO K CaC03
Ke
K,(i = l-6) K” K VO K mA 4 M M
H2S cacoj
N NU Nsb
r
Rc RO
2l t
T
V*
v,
X Y
C. Chen, T. Kojima / Fuel Processing Technology 53 (1997) 49-67
Greek symbols 6 ‘ash &Q
; A
P PC P&r PIS Pash cp w
“”
rc
61
emissivity of particle surface porosity of ash layer porosity of limestone phase porosity of calcined lime phase tortuousity of calcined lime phase heat conductivity of char particle, J/s m* K density of gas, kg/m3 density of coal particle, kg/m3 density of unreacted core, kg/m3 density of limestone, kg/m3 density of ash layer, kg/m3 fraction of volatile combustion heat used to heat the particle reaction rate, w, H,S evolution rate, o2 H,S retention rate, w3 SO, evolution rate, w4 SO, retention rate, kg/m3 s volatile evolution rate of unit surface, kg/m* s residence time of tar sulfur in coal briquette, s
References [I] A. Attar, Fuel 57 (4) (1978) 201. [2] S. Uemiya, K. Itoh, T. Kojima, Coal Sci. Technol. Vol. 24, Elsevier Science B.V., 1995. [3] S. Uemiya, K. Itoh, T. Kojima, in: J.A. Pajares, J.M.D. Tascon (Eds.), Coal Science, Vol. 2, Elsevier Science, pp. 1835-1838. [4] T. Sugawara, K. Sugawara, Y. Nishiyama, M.A. Sholes, Fuel 70 (1991) 1091-1097. [5] K. Sugawara, Y. Tozuka, T. Sugawara, Y. Nishiyama, Fuel Processing Technol. 37 (1994) 73-85. [6] S.C. Wang, C.Y. Wen, AIChE. J. 31 (1972) 1231. [7] C.Y. Wen, S.C. Wang, Ind. Eng. Chem. 62 (1970) 30. [8] R.W. Froberg, R. Essenhigh, 17th symposium (international) on Combustion, The Combustion Institute, Pittsburgh, PA, 1978, p. 179. [9] C. Chen, S. Uemiya, T. Kojima, J. Japan Inst. Energy 74 (10) (1995) 882. [lo] C. Chen, T. Kojima, Fuel Processing Technol. 47 (1996) 215. [11] V.S. Gururajan, T.F. Wall, J.S. Truelove, Combust. Flame 72 (1988) 1. [12] V.S. Gururajan, T.F. Wall, R.P. Gupta, J.S. Truelove, Combust. Flame 81 (1990) 119-132. 1131 X. Du, K. Annamala, Combust. Flame 97 (19941 339. [ 141 0. Levenspiel, Chemical Reaction Engineering, 2nd edn., Wiley, 1972. [15] B.A. Adesanya, H.N. Pham, Fuel 74 (6) (1995) 896. [ 161 D.B. Anthony, J.B. Howard, H.C. Hottel, H.P. Meissner, 15th symposium (international) on Combustion, The Combustion institute, Pittsburgh, 1975, pp. 1303-1317. [17] F. Garcia-Labiano, E. Hampartsoumian, A. Williams, Fuel 74 (7) (1995) 1072-1079. [18] J. Yagi, K. Tamura, I. Muchi, Nippon Kinzoku Gakukai Shi 31 (2) (1967) [19] W. Fu, Y. Zhang, H. Han, Y. Duan, Combust. Flame (1987) 253-266. [20] T. Kojima, K. Take, D. Kunii, T. Furusawa, J. Chem. Eng. Japan 18 (5) (1985) 432-438. [21] S.K. Bhatia, D.D. Perlmutter, AIChE J. 27 (1981) 226.
Fuel Processing
Technology
53 (1997) 49-67
Modeling of sulfur retention by limestone in coal briquette Caixia Chen, Toshinori Kojima
*
Department of Industrial Chemistry, Faculty of Engineering Seikei Uniuersity, Kichijojikitamachi, Musashino-shi, Tokyo 180, Japan Received 9 September
1996; accepted 3 June 1997
Abstract A detailed simulation model was developed for sulfur retention by limestone in a coal briquette. Four submodels, i.e., coal briquette combustion, volatile and sulfur evolution, H,S retention, and SO, retention, were included in the simulation. In the model, the coal briquette combustion was divided into two successive stages: volatile ignition and char burnout. The temperature profile and its time variation, sulfur release and retention behavior within the burning coal briquette for the two stages were simulated separately. In the stage of volatile evolution and ignition, a part of coal sulfur is released as H,S, and reacted with the calcined limestone in the area near the particle surface, where the local temperature is increased along with the volatile ignition, and the limestone in the coal briquette is partially calcined. H,S retention in the coal briquette was thus simulated as a result of the competition among its transportation by the bulk flow of evolved volatile, its molecular diffusion due to the concentration gradient within the coal briquette, and its capture by the calcined limestone. In the stage of char burnout, the remaining part of coal sulfur is released as SO, with char burning which is simulated by the shrinking core model. SO, release rate is assumed to be proportional to the char burning rate and controlled by oxygen diffusion in the ash layer. The sulfate formation occurs in the ash layer within which oxygen exists. SO, retention was thus simulated as a result of the competition among the sulfate formation with the calcined limestone, SO, diffusion in the ash layer and its emission from the briquette surface. The sulfur retention by limestone in a spherical centimeter sized coal briquette was simulated by the model. The effects of heating rate, briquette size, calcium to sulfur ratio (Ca/S), and volatile matter of coal on the sulfur retention were predicted. The simulation results showed that rapid heating condition was good for both the H,S retention in the volatile and the SO, retention in the combustion gas. The simulation also predicted a higher SO, retention for a
’ Corresponding
author. Tel.: + 81-0422-37-3750:
fax: + 81-0422-37-3871
037%3820/97/$17.OO 0 1997 Elsevier Science B.V. All rights reserved PII SO378-3820(97)00036-2
50
C. Chen, T. Kojima/ Fuel Processing Technology 53 (1997) 49-67
larger sized coal briquette. The coals of higher rank and lower organic sulfur contents also showed a higher sulfur retention.
0 1997 Elsevier Science B.V.
Keywords: Coal briquette combustion; Sulfur retention; Numerical model
1. Introduction Limestone is a well-known and commonly used sorbent either for SO, removal from combustion gases or for H,S removal from fuel gas of coal grassfires. In the recent years, researches using limestone as a sorbent in coal briquettes have also been carried out to reduce the sulfur release from domestic and small scale use of coal in developing countries. It is of significant interest to study the combustion and the sulfur retention behavior in a centimeter sized spherical coal briquette mixed with limestone and binder, because such sized coal particles are widely used in fixed bed furnaces and rotary kilns, in which the coal briquettes are generally combusted in a hot air stream. At the first stage of coal conversion, the volatile is evolved and ignited in the gas boundary film around the particle, while the coal sulfur is also evolved as species of the volatile. On the other side, the limestone, if mixed in the coal briquette, is partially calcined with the briquette temperature increase and volatile ignition. Most of the coal sulfur is found to be released below 800°C while the main component of limestone, calcium carbonate, undergoes rapid calcination to calcium oxide above 800°C [I]. Therefore, the volatile sulfur (mostly abundant in H,S) retention by limestone within the coal briquette is a result of the competition among the carrying by the bulk flow of evolved volatile, H,S diffusion due to the concentration gradient within the briquette, the calcination of limestone and the reaction of H,S with the calcined limestone. In our previous experimental research [2,3], the pulverized Illinois No. 6 coal sample (smaller than 0.125 mm) was granulated to a 18-20 mm coal briquette, and combusted experimentally. The experimental apparatus consists of a horizontal electrically-heated reaction tube furnace, a gas supplier, and the gas product analysis system. In the experiment, the coal briquette sample was put on a ceramic boat and combusted in an air stream at a rate of 10 cm’/s (room temperature base). Two types of experimental procedures, abbreviated to rapid heating and constant-rate heating, were used in the experiments. In the case of rapid heating, the sample was moved quickly to the preheated hot reactor at the temperature of 1073 K, and cornbusted. In the constant heating rate condition, however, the sample was put into the reactor at room temperature, heated at the constant rate of 10 K/min, and cornbusted. The sulfur retention behavior of the limestone mixed high sulfur Illinois No. 6 coal briquette was studied. It was found that the sulfur retention was affected by the surrounding gas temperature, heating rate of the briquette, and calcium to sulfur ratio (Ca/S). The experimental results showed that the rapid heating rate of coal briquette led to a relatively high sulfur retention, and the sulfur retention was not improved by the further addition of limestone beyond Ca/S of 2. To explain the experimental results, in the present research, the combustion and sulfur retention process in a 8-16 mm spherical coal briquette mixed with limestone is
C. Chen, T. Kojima / Fuel Processing Technology 53 (1997) 49-67
numerically simulated corresponding to some of the typical experimental time-temperature profile and the temperature distribution within the calculated by the model. The evolution behavior of H,S and SO,, calcination and the limestone conversion to sulfate within the coal evaluated. The effects of heating rate, briquette size, Ca/S ratio, volatile sulfur release behavior on the sulfur retention efficiency are discussed.
51
results. The briquette are the limestone briquette are evolution and
2. Modeling methods
2.1. Overall description Four submodels, i.e., the coal briquette combustion, volatile and sulfur evolution, H,S retention and SO, retention, are included in the simulation. In the model, the combustion of coal briquette is divided into two successive stages of volatile ignition and char burnout. The time-temperature profile and its distribution within the burning coal briquette for the two stages are calculated by solving the energy equations. The volatile evolution and sulfur release are predicted by a volume reaction model by Sugawara et al. [4,5], taking the temperature change and its distribution in the coal briquette into account. H 2 S retention in the volatile evolution stage and SO, retention in the char burnout stage are simulated by solving the mass equation in the porous coal briquette or the ash layer, coupled with the limestone calcination, sulfide and sulfate formation rate expressions. 2.2. Coal briquette combustion In the past years, considerable efforts were spent investigating the time-temperature history and the temperature distribution in a centimeter sized burning char particle [6- 101. The available information on the behavior of centimeter sized coal particle, however, is very little, because a quantitative treatment of the effect of coal volatile combustion on the particle temperature is difficult to be established. Gururajan et al. [ 111 predicted the combustion of evolved volatile matter in the vicinity of pulverized coal particle, and found that the volatile burnt too distant from the particle to feed back energy from the volatile flame when devolatilization rate was high. It is thought that the volatile flows rapidly outward the particle, and the volatile reactions with air do not occur on the particle surface. Therefore, the direct effects of the volatile evolution behavior on the coal particle temperature are not strong. The indirect effects, however, can be very strong, because the volatile matter, devolatilization rate, flammability of the volatile and its transport from the particle determine whether ignition of an isolated coal particle occurs heterogeneously or homogeneously, and affect the coal particle temperature significantly [ 12,131. For millimeter- and centimeter sized particles there is generally a convective flow, and a flame is established around the particle, especially in the wake. In this case, the effects of volatile combustion on the particle temperature is more complicated.
52
C. Chen, T. Kojim/
Fuel Processing Technology 53 (1997) 49-67
In our previous experiment [2,3], the transient time-temperature profile was measured by a thin CA thermocouple inserted into the coal briquette center. The temperature distribution within the coal briquette, being difficult to be measured in the experiment, is calculated by a simplified model as follows. At the stage of volatile evolution and ignition, the time-temperature history and its distribution within the coal briquette is determined by the heat balance of a spherical coal particle combustion in a hot air steam. The unsteady energy equation of a spherical coal particle is: aT 1 a pcCPx = 7%
aT Ar2~
- wAH (1) i i The volatile release rate is calculated by w = p,dV/dt, (kg/m3 s>, and the devolatilization reaction heat AH is 300 kJ/kg [ 121. It is assumed that the volatile is ignited in the boundary gas film nearby the briquette surface, and only a fraction of combustion heat is used to heat the briquette itself. The heat from the volatile flame, the convection from the hot gas and the radiation from the reactor wall reaches to the surface of the briquette and the heat propagates toward the sphere center through heat conduction. Thus the boundary conditions of Eq. (1) are: aT r=O,--0 ar
where, cp is an adjustable factor from 0 to 1, and determined by fitting the numerical temperature variation of particle center to the experimental one. The volatile combustion heat 4, is 30 MJ/kg [ 121, and w, is the cumulative volatile release rate per unit particle surface area, i.e.: ” @=zFo
1
R /
dV 4n=r&;dr
At the char combustion stage, it is assumed that the residual char combustion starts when 80% of the volatile is released for the rapid heating condition, and 30 min for the constant-rate heating condition, when the briquette temperature increases sharply and roughly 80% of the volatile is released which was observed experimentally. A traditional unreacted shrinking core model [14] and the quasi-steady state assumption of temperature in ash layer were used to simulate the residual char combustion of the briquette. The time dependent variables of the unreacted core size R,, the unreacted core temperature c, the briquette surface temperature T, were calculated by the same method described previously [lo] with the initial conditions: t = ti, r = R, T, = T,. The temperature distribution in the ash layer for a given time is then calculated by the steady state energy equation: At-‘: =0 ( 1 with the boundary conditions: r = R, , T = T,, and r = R, T = T,. $i
(5)
C. Chen, T. Kojima / Fuel Processing Technology 53 ( 1997149-67
The solution
53
is:
&’ r
T=T,+
c
i
I
T-T, 1
(6)
1
---
2.3. Volatile and sulfur evolution It is well known that the devolatilization of large coal particle highly depends on the large temperature gradients within the particle and its time-temperature history, which in turn, depends on the external heat transfer to the particle. Much effort has been focused on the kinetics, mechanisms and product distribution in the devolatilization of small coal particles. However, relatively few studies on the devolatilization of the large particles ( > 10 mm) exist in the literature [ 151. In this paper, the volatile evolution from the coal briquette is assumed to be one single reaction step. The devolatilization rate is expressed by [ 161: dV -=K,(V* dt
-V)
(7)
where, V * denotes total volatile mass, which is adopted from the value of ASTM volatile matter of daf basis. K, is defined by Arrhenius relation: K, = K,,exp(
- E,/RT)
(8)
where, T is the local temperature in the coal briquette, and calculated by Eq. (1). The sulfur release is estimated based on the volume reaction model by Sugawara et al. [4,5]. In this model, the coal sulfur is divided into organic sulfur (A) and pyrite (E). When coal is heated, the organic sulfur is decomposed to release H,S (D) and organic sulfur in tar (C) or remains in coal as sulfur in Char (B). The pyrite sulfur (E) is decomposed to release H,S, and produces ferrous sulfide sulfur (F). The model can be expressed as follows [5]:
9
The material
dCA
-= dt
C Sulfur in Tar
balance for each sulfur form is given by the following -(K,+K,+K,)C,
Eqs. (4,5):
54
C. Chen, T. Kojim / Fuel Processing Technology 53 (1997) 49-67
-
dt
= K,C,
- K,C;
dCc -=KK,CA-C, dt dCD -
dt
dG
-
(11)
K3CA i- ; K,C;.’ i- K,C;
=
-K
4
- K,C,
Co.5
( 14)
cc
(15)
=F
where, Ki is expressed K, = K,,exp
(12) (13)
E
1 = ZK4C;.5
dCcci dt
(10)
TC
=
dt dC, dt
+ K,C,
by the Arrhenius
equation:
(16)
- 2 i
i
A part of sulfur in tar (Cc, ) is assumed to be emitted as one of the gaseous species of the volatile from the briquette surface at the rate of volatile evolution. The fate of the remaining part of tar sulfur is assumed to be combusted with char as same as sulfur in char. The residence time of gaseous tar sulfur in the briquette is:
(17) The kinetic parameters proposed by Sugawara et al. [5] were used. It was noted that the organic sulfur decomposition rate constant (K, + K, + K3), and the rate constants for the other reaction steps are independent on the heating condition in Ref. [5]. Therefore, one set of parameters is used for the two heating conditions in the present analysis. In Sugawara’s model [5], no effects of coal rank were included. However, in the recent experimental research of Garcia-Labiano et al. [17], very different sulfur yields were found for different coals, depending on both the sulfur content and the coal rank. It was found that the fraction of sulfur passing into the tar was 30-40% for all kinds of coal, and the percentage of sulfur released with the volatile matter was in line with the volatile matter of the coal. Based on the above facts, the kinetic parameters used in the present research are improved as follows: K,=(l-0.3-V*)K,,, K, = 0.3 Korg K3=V*Korg where, Korg is the summation
of K,, K, and K, in Ref. [5].
C. Chen. T. Kojima/ Fuel Processing Technology 53 (1997149-67
55
In the calculation, the coal sphere was divided into N shells. The overall weight loss, volatile evolution rate and sulfur species of the coal briquette were calculated by summation over the shells. 2.4. The retention of H2S in volatile evolution
stage
At the stage of volatile evolution, the evolved volatile matter serves as reaction medium to produce gaseous tar sulfur and H,S within the coal briquette. The gaseous tar sulfur and H, S, in turn, are carried by volatile matter through the porous coal particle and diffuse through the pores due to the concentration gradient existed in the briquette. At the same time, H,S reacts with the calcined limestone by the reaction CaO + Hz S + CaS + H,O when atmosphere within the coal briquette is reducing. The flow velocity of the bulk volatile within the coal briquette V, is calculated by the continuous equation:
(18) where &r is the porosity of particle, p is the volatile gas density at averaged temperature, and o is the volatile release rate per unit coal volume. The mass balance of H,S in the briquette is then expressed as:
with the boundary
particle
condition
dY r=O,z=O
(20)
r=R,-D&,urY=K,Y
(2’)
where, Y is the mass fraction of H, S in volatile, D, is H,S diffusivity in volatile and . w, is H, S evolution rate per unit coal particle volume, and calcu-
K, = Ns,D,\/D, lated by:
dCn
0 I = PCdt
(22)
o2 is the H,S retention d[CaO] wz=--
dt
M
rate with limestone,
H2S
and calculated
as follows: (23)
(24)
C. Chen, T. Kojima / Fuel Processing Technology 53 (1997) 49-67
56
The reaction K u,s i
rate constant
is (M. Horio, 1996, private communication):
= 0.94 exp( - 20,00O/RT)
T> 1073K
= 238.0exp(
T < 1073 K
-69,00O/RT)
The initial molar concentration
of limestone
(25)
[CaO], in the coal briquette
is calculated
by: [CaO],
= Ca/Sp,[
s]/32
(26)
where the Ca/S ratio is calculated from the weight of the coal sample and limestone, and the initial sulfur concentration in the coal sample [sl (40 mg S/g coal (daf)). During the heating process, the limestone in the particle is partially calcined. The calcination rate is calculated by [ 181: df
6Mcaco,
ii=
P,s4,
c co 2sq- Go,,, 1 K+m
(27) d,,{(l
-f)-1’3
- 1} + Rcaco,(l
-f)-2’3 RTk,
20,
where, the diffusion resistance in the bulk film, being much smaller than that within the coal briquette, is neglected in the calculation, i.e.: 1 K,-
-0
(28)
The calculation
equations
of the parameters
2.5. The retention of SO, in char combustion
in Eq. (27) are listed in Table 1. stage
The sulfur in char (Schar), including FeS, CaS, the organic sulfur (B) and the remaining sulfur in tar (C) are combusted with char. It is assumed that CaS transforms to CaSO, directly and quickly, and the release rate of SO, is proportional to the combustion rate of coal char, which is controlled by oxygen diffusion in the ash layer. According to the shrinking core mode, the char briquette is divided into two zones: unreacted core and ash layer. The following reactions are thus assumed to occur along a sharp interface between the ash layer and the unreacted char core: c + 0, + co, S char
+
‘2
4
“2
CaS + 20, --f CaSO, The shrinking core thus the produced SO, O,, CO,, and SO,) (SO, + l/20, + CaO as:
model also implies that there is no oxygen in the unreacted core, is carried to the briquette surface by the combustion gases (N,, through ash layer and reacts with limestone in the ash layer -+ CaSO,). The mass equation of SO, in the ash layer is written
C. Chen, T. Kojima / Fuel Processing Technology 53 (1997) 49-67
with the boundary
51
conditions:
dY
r=O,--0
(30)
ar
r = R,De;i,
= K,Y
where, Y is the mass fraction N,, and K,, = N,,D,/D,SO,
(3’) of SO, in the combustion gases, D, is SO, diffusivity retention rate by limestone is [20]:
in
dX o4 =
Ka%~~sO,
(32)
dX = K&l-X)Y+ dt
so2
(33)
where, X is the conversion of limestone to CaSO, and D is the maximum value of X. which was assumed to be 0.7 according to Ref. [20]. The reaction rate constant is calculated by the Arrhenius expression [21] with the frequency A of 403.7 (mol SOJmol gas)-‘s‘: K SO?= Aexp( -6750/T)
(34)
3. Results 3. I. The burning coal particle temperature The time-temperature profile and the temperature distribution of the burning coal briquette were calculated by solving the Eqs. (l)-(6). The operation conditions, same as those in the previous experiments, were used in the calculation. The parameters, and the physical and chemical properties are listed in Table 1. Fig. 1 shows the calculated and experimental time-temperature profiles in a 16-mm coal briquette burned under the rapid heating condition. The initial part of the profile (O-54 s, volatile ignition stage) was best fitted by using the adjustable factor cp of 1.75 X 1Om3, while the remaining part of the profile (after 54 s, char combustion stage) was fitted by selecting a set of adjustable model parameters as described in the previous paper [ 101. Fig. 2 shows the results under the constant-rate heating condition. The time-temperature profile of the volatile evolution stage was best fitted by using the adjustable factor cp of 0.095. The temperature profile in the char combustion stage, however, was very difficult to be fitted because two serial stages are assumed, thus the char was ignited at a surrounding gas temperature above 673 K, accompanied with a sharp particle temperature increase in the modeling calculation. A lowest difference between the calculated peak temperature and the experiment data was obtained by assuming the char combustion started at 30 min when the surrounding gas temperature reached 573 K.
C. Chen, T. Kojim / Fuel Processing Technology 53 (1997) 49-67
58 Table 1 Kinetic parameters,
coal properties
Density of coal briquette: Diameter of coal briquette: Heat of combustion: carbon volatile ASTM analysis of coal (dry basis)
Sulfur content
and other data 1015 kg/m’ 16, 12, 8 mm 32.819 MJ/kg 30 MJ/kg %VM = 40.45 %F.C = 47.53 %Ash = 12.02 %S = 4.0 (daf)
Deuolafilization Frequency factor: Activation energy: Heat of devolatilization: Adjustable factor
rapid heating 2250 l/s 64 kJ/mol (Ref. [19]) 300 kJ/kg (coal) 1.75x 10-3
constant-rate heating 33 l/s 50 kJ/mol (Ref. [5]) 0.095
Sulfur evolution Frequency factor: (Ref. 151) KIO + Kzo + K,o K40 K,o K60
Activation
15.0X lo6 l/min 2 X 10” (mg S)“,s/min 1 X IO9 g mg S/min lX106 l/min
energy: (Ref. [5])
E,> E2. Ex E4 E5 E6 Organic sulfur Char combustion (Ref. [lo]) Diffusivity of ash layer: Emissivity of the surface: heat conductivity: ash layer char Frequency factor: Activation energy: The calculation equations of the parameters in Eq. (27): (Ref. [ 181)
92.0 kJ/mol(22.0 kcal/mol) 175.8 kJ/mol(42.1 kcal/mol) 234.8 kJ/mol (56.1 kcal/mol) 134 kJ/mol(32.0 kcal/mol) 80% of total sulfur
1.0 cm2/s 0.6 0.7 J/s m2 K 1.1 J/s m* K 8.0~ lOa l/s 188 kJ/mol (45 kcal/mol) D, = DE, 5. 5 = &,“-“‘, D= 2.23x 10-6Ts’ 78, E, = 0.702, cP +0.298, gp = 0.3, LogKc,,oz = - 8920/ Tp + 8.54, k, = 9.12 X 10-4exp( - 167,OOO/RT,), C coz.eq = (Gxo, x 273)/(0.0103 X 22.4 X lo- 3 X T)
The time-temperature profiles of various sizes of 16-, 12- and g-mm briquettes combusted under the rapid heating condition were calculated by using the same operation conditions and parameters as those for Fig. 1. As shown in Fig. 3, smaller briquette combusts quickly with a higher peak temperature, which is consistent with the
C. Chen, T. Kojima / Fuel Processing Technology 53 (1997) 49-67
59
1473 1273 -
873
673
-
473
-
modelling
---
modelling
-
furnace
.
Tc Ts Te Tc
experimental
273 0
20
40 time
Fig. I. Calculated condition.
and experimental
time-temperature
-
-
- ______
1073
-
873
-
80
(min)
profile of coal briquette combusted
modelling
1273
60
Tc
-
furnace experimental
0
20
40 time
Fig. 2. Calculated heating condition.
and experimental
time-temperature
273.
’ 0
10
’ 20
time Fig. 3. Calculated heating.
time-temperature
60
Te Tc
80
100
(min)
profile of coal briquette combusted
’ 30
under rapid heating
40
50
60
’ 70
under constant-rate
80
(min)
profile at center of different
sized coal briquette
combusted
under rapid
60
C. Chen, T. Kojim / Fuel Processing Technology 53 (1997) 49-67
12mm
115 mm
A-/:/
-----_.
10
”
1,
0,
20
30
time Fig. 4. Calculated time-temperature under rapid heating condition.
r=o a
1
40
60
50
(s)
profile at the volatile combustion
stage of different
sized coal briquette
previous simulation results [9]. The temperature distributions of the three sizes were also predicted and shown in Fig. 4. It is found that smaller coal briquette is heated more quickly than larger coal briquette, with lower temperature difference between the center and the surface. The maximum temperature difference of the 16-cm coal briquette is 180 K, but lower than 60 K for a g-mm coal briquette.
3.2. Sulfur and volatile evolution
behavior
The volatile and sulfur evolution behavior was predicted by solving Eqs. (7)-(17). The fraction of volatile and H,S released against the center temperature of the coal briquette are shown in Fig. 5. An activation energy of 64 kJ/mol, suitable to large coal briquette devolatilization at 1073 K in nitrogen, proposed by Fu et al. [19], was used for the calculation of rapid heating condition. For the constant-rate heating condition, a
0.4 10 K/min 0.3
: : /’ / ,’ I’
0.2
/
0.1
,
I’
I’ rapid
1.: o-$OO~;:O
600
h;::““,,O
Tc WI Fig. 5. Calculated
400
500
600
700
Tc WI
time variation curve of volatile and H,S evolution.
600
61
C. Chen, T. Kojima / Fuel Processing Technology 53 f 1997) 49-67
(I)
0.4
1 .
:
-
1
1
0 .
1
rapid heating 75.9%
0.0
0.2
0.4
0.6
0.8
1 .o
1.2
r/R and owd
Fig. 6. Calculated radial profile of limestone conversion (sorbent: Ca(OH)2),
sulfur retention
(values in W).
value of 50 kJ/mol in Ref. [51 was adopted. The frequency factors were selected to be 2250 l/s for rapid heating and 33 l/s for constant-rate heating, in order to obtain 80% of total volatile evolution before the defined char ignition time in consistence with the coal briquette combustion model.
3.3. Sulfur retention behavior
3.3.1. Effects of heating rate In order to study the effects of heating rate on the sulfur retention efficiency, two extreme conditions were simulated for a coal briquette of 16 mm size and Ca/S of 2.8 (standard condition). One of the simulation calculations was done by using a sorbent of Ca(OH),, which is decomposed quickly above 150°C. Therefore the influence of limestone decomposition rate attributed to the heating conditions was excluded in the
,0.3
1’
c 0
tJ
1
8
rapid heating
----__
1OK/min
z E
1’
-
r
51.29%
0.2-
u0 : ‘;;
0.1 -
; > : u
0.0
0.0
0.2
0.4
0.6
0.8
1 .o
1.2
r/R Fig. 7. Calculated
radial profile of limestone conversion
(sorbent: &CO,,
Pco2: 5%).
62
C. Chen, T. Kojima / Fuel Processing Technology 53 (1997) 49-67
+I
.
8mm
‘U 0.0 -
m Fig. 8. Calculated 0.03%).
calcined
’
0.2
0.0
”
32s
’
0.4
0.6
0.8
1.0
1.2
r/R
fraction
of limestone
in different
sized coal briquettes
(sorbent:
CaCO,,
PcO,:
calculation. As can be found in Fig. 6, a higher efficiency of sulfur retention is obtained both in the stage of volatile combustion stage and in the overall processes of coal briquette combustion for the rapid heating condition. At the stage of volatile combustion, the sulfur retention efficiency of rapid heating condition is 23.9%, which is about twice that of constant-rate heating condition. Another numerical calculation was performed by assuming the sorbent of limestone, with CO, concentration in the coal pores as high as 5%, at which the limestone remained to be uncalcined until the char ignition occurred. Although the sulfur retention at the volatile combustion stage is zero both for tbe rapid heating and for the constant-rate heating conditions, it is found in Fig. 7 that higher sulfur retention is obtained for the rapid heating condition. In other words, higher sulfur retention efficiency can be obtained for the rapid heating condition at the stage of char combustion stage, too.
L
-
16mm
60.35%
7.5%
,Zmm
55,7&
10.1%
--__-.
6mm
52.51%
11.0%
0.2
0.4
0.6
0.3 -
E
IC
.
vol. comb.
overall
cl
-
b 0
0.2 -
0’ ‘Gj b 0.1 z 8 0.0 0.0
0.8
1 .o
1.2
r/R Fig. 9. Calculated radial profile of limestone conversion briquette (values in %).
(sorbent: CaCO,,
P,,*:
0 03%) in different sized coal
C. Chen, T Kojima / Fuel Processing Technology 53 (1997149-67
63
Ca/S ratio (-) Fig. 10. Sulfur retention vs. Ca/S
ratio under rapid heating condition.
3.3.2. Effects of briquette size The radial profile of calcined fraction of limestone with various briquette sizes under the rapid heating condition, when the organic sulfur in the coal is decomposed completely (54, 44 and 32 s corresponding to the size of 16, 12, and 8 mm, separately), is calculated and shown in Fig. 8. It is thought that CO, concentration in the briquette is in the range between 5% and 0.03% (in atmosphere). The numerical results show that the retention efficiency of H,S in volatile is lower than 20% even when Ca/S is as high as 3.68 and CO, concentration is as low as 0.03% for the rapid heating condition, because the volatile sulfur release rate was faster than that of calcination or sulfide reaction of limestone. As the extreme case, all of the following calculations were performed by assuming CO, concentration of 0.03%. The radial conversion distribution and the sulfur retention (in %) of the three sizes are shown in Fig. 9. The overall sulfur retention decreases with decreasing particle size. The results can be explained by that SO, undergoes longer residence time in the coal briquette for larger sizes, and has more chance to be absorbed by limestone than that of smaller sizes. 3.3.3. Effects of Ca/S ratio Fig. 10 shows the effects of Ca/S ratio on the sulfur retention under rapid heating condition. The sulfur retention efficiency increases quickly with an increase in Ca/S
Ii Fig.
0.0
0.1 0.2 0.3 0.4 VM of daf coal (-)
11.Sulfur retention vs. volatile matter under rapid heating condition
64
C. Chen, T. Kojima / Fuel Processing
0
1
2
Technology53 (1997) 49-67
3
4
5
orghnorg (-) Fig. 12. Sulfur retention vs. organic to inorganic
sulfur ratio.
ratio when Ca/S is lower than 2, but increases very little with further Ca/S increase. The calculation is consistent qualitatively with the experimental results published previously [2,3]. 3.3.4. Esfects of volatile ana’sulfur evolution behavior The effect of volatile matter, and the ratio of organic to inorganic sulfur on the sulfur retention was simulated. Fig. 11 shows the predicted sulfur retention for coal briquettes with various volatile matter under the rapid heating condition, and Fig. 12 shows the predicted sulfur retention curve of various organic sulfur to inorganic sulfur ratios (total sulfur content of 4%, daf basis). It is found that the overall sulfur retention decreases by increasing the volatile matter and the organic sulfur content.
4. Discussions As can be found in Figs. 1 and 4, the coal briquette burns with a higher average temperature history and larger temperature gradient within the coal briquette, due to the higher surrounding gas temperature under the rapid heating condition. Under the constant-rate heating condition as shown in Fig. 2, however, the briquette surface temperature and the average temperature history are relatively lower, and the briquette temperature is nearly uniform. To predict the effects of heating rate on the sulfur retention efficiency, the conversion of limestone is calculated under the calculated time-temperature profiles. Although the calculated sulfur retention efficiency might be overestimated by the unsatisfactory fitting with two peaks under the constant-rate heating case, the calculated conversion of limestone within the coal briquette is much lower than that of the rapid heating conditions (Figs. 6 and 7). At the volatile ignition stage, H,S is released at higher particle temperature (Fig. 5) due to the rapid heating condition, and a higher limestone conversion is obtained in the area nearby the particle surface due to the larger temperature gradient within the briquette (Fig. 6). At the char combustion stage, the higher conversion of limestone under rapid heating condition (Fig. 7) is obtained mainly due to the higher briquette temperature level, fast char burning and sulfur releasing, which are thought to be accompanied by a relatively higher concentration level and a faster sulfate formation.
C. Chen, T. Kojim / Fuel Processing Technology 53 (1997149-67
6.5
The rapid particle heating rate also leads to fast calcination of limestone. As shown in Figs. 8 and 9, the limestone in smaller sized coal briquette is calcined more quickly than that in larger sized one, because of the higher heating rate and small temperature difference in the smaller sized briquette. As a direct effect of the increase in the calcined limestone, the conversion of limestone increases with a decrease in particle size at the volatile combustion stage. In Fig. 11, the sulfur retention increases slightly with an increase in volatile matter since the absolute amount of released H,S is increased with volatile matter. However, the overall sulfur retention is found to decrease rapidly with an increase in volatile matter due to the low retention efficiency of H,S in volatile matter. In addition to this, the overall sulfur retention decreases with an increase in organic sulfur content, both for the rapid heating condition and for the constant-rate heating condition (Fig. 12). When the organic sulfur is high, more H,S is released at very low particle temperature, which is far below the limestone calcination temperature. The prediction showed that the amount of sulfur remaining in char increased with an increase in pyrite sulfur, and the retention efficiency of sulfur in the char was higher than 90% when Ca/S was higher than 2 for the rapid heating condition. In other words, the lower volatile sulfur retention, leading to a limited sulfur retention efficiency for the overall process, is a critical point in coal briquette desulfurization by limestone.
5. Conclusion The time-temperature profile and the radial temperature distribution in a burning spherical coal briquette were calculated by a simple two stage model. The evolution of H,S, and SO, in the coal particle was predicted. The limestone conversion was evaluated. The following conclusions can be drawn from the results. (1) The coal briquette bums with a higher average particle temperature under the rapid heating condition than that under the constant-rate heating condition. (2) The volatile and sulfur are evolved at higher particle temperature under the rapid heating condition. (31 The rapid heating condition is better for both the sulfur retention in volatile and the sulfur retention in combustion gas. (4) The large sized coal briquette provides a longer residence time of SO, in the particle, and more chance for SO, retention. (5) A sulfur retention limit exists in the coal briquette desulfurization, because the volatile sulfur retention efficiency is very low. The model predicts that higher rank and lower organic sulfur contained coal are suitable for briquette combustion for the sense of sulfur retention.
6. Nomenclature
[CaOl Ca/S Ci(i = A - F)
molar concentration of CaO, mol/m3(coal volume) molar ratio of calcium to sulfur concentration of each sulfur form, mg S/g (coal)
66
C. Chew T. Kojima / Fuel Processing Technology 53 (1997) 49-67
c CG
concentration of gaseous tar sulfur oxygen concentration, mol/m3 carbon concentration, mol/m3 CO, concentration in bulk flow, mol/m3 equilibrium concentration of limestone decomposition, mol/m3 heat capacity of unreacted core, J/kg K volumetric heat capacity of ash layer, J/m3 K effective diffusivity of H,S in coal particle, m*/s effective diffusivity of H,S in ash layer, m2/s molecular diffusivity, m*/s diameter of limestone particle, mm diameter of coal particle, mm activation energy of char reaction rate constant, kJ/mol activation energy of devolatilization rate constant, kJ/mol fraction of calcined limestone convective heat transfer coefficient, J/s m2 K radiation heat transfer coefficient, J/s m* K4 heat of reaction, J/mol reaction constant of sulfide reaction, l/(mol/mol) s reaction constant of sulfate reaction, l/(mol/mol) s frequency factor of char reaction rate constant, l/s equilibrium constant of CaCO, decomposition, MPa effective heat conductivity in ash layer, J/s m K reaction constant of sulfur release reactions, l/s reaction constant of devolatilization, 1/s frequency factor of devolatilization rate constant, l/s mass transfer coefficient of oxygen in gas film, m/s surface reaction rate constant, l/s molecular weight of H 2 S molecular weight of CaCO, Nusselt number for convective heat transfer Sherwood number distance from center of sphere, mm radius of unreacted core, mm particle radius, mm gas constant, kJ/mol K initial sulfur concentration in coal, mg S/g coal time, s temperature, T, at unreacted core surface, T, gas temperature, Tp coal particle temperature, T, at particle surface, To in bulk gas, T, at reactor wall, K ultimate volatile matter fraction, g volatile/g daf coal volatile move velocity, m/s conversion rate of limestone mass fraction of H,S in volatile, or SO, in combustion gas
CA0 CSO CCO,3
cCO,,eq
CP CP”
De
D eA QA
4s
DP E
f” h
hr
AH K H2S K SO2 KO K CaC03
Ke
K,(i = l-6) K” K VO K mA 4 M M
H2S cacoj
N NU Nsb
r
Rc RO
2l t
T
V*
v,
X Y
C. Chen, T. Kojima / Fuel Processing Technology 53 (1997) 49-67
Greek symbols 6 ‘ash &Q
; A
P PC P&r PIS Pash cp w
“”
rc
61
emissivity of particle surface porosity of ash layer porosity of limestone phase porosity of calcined lime phase tortuousity of calcined lime phase heat conductivity of char particle, J/s m* K density of gas, kg/m3 density of coal particle, kg/m3 density of unreacted core, kg/m3 density of limestone, kg/m3 density of ash layer, kg/m3 fraction of volatile combustion heat used to heat the particle reaction rate, w, H,S evolution rate, o2 H,S retention rate, w3 SO, evolution rate, w4 SO, retention rate, kg/m3 s volatile evolution rate of unit surface, kg/m* s residence time of tar sulfur in coal briquette, s
References [I] A. Attar, Fuel 57 (4) (1978) 201. [2] S. Uemiya, K. Itoh, T. Kojima, Coal Sci. Technol. Vol. 24, Elsevier Science B.V., 1995. [3] S. Uemiya, K. Itoh, T. Kojima, in: J.A. Pajares, J.M.D. Tascon (Eds.), Coal Science, Vol. 2, Elsevier Science, pp. 1835-1838. [4] T. Sugawara, K. Sugawara, Y. Nishiyama, M.A. Sholes, Fuel 70 (1991) 1091-1097. [5] K. Sugawara, Y. Tozuka, T. Sugawara, Y. Nishiyama, Fuel Processing Technol. 37 (1994) 73-85. [6] S.C. Wang, C.Y. Wen, AIChE. J. 31 (1972) 1231. [7] C.Y. Wen, S.C. Wang, Ind. Eng. Chem. 62 (1970) 30. [8] R.W. Froberg, R. Essenhigh, 17th symposium (international) on Combustion, The Combustion Institute, Pittsburgh, PA, 1978, p. 179. [9] C. Chen, S. Uemiya, T. Kojima, J. Japan Inst. Energy 74 (10) (1995) 882. [lo] C. Chen, T. Kojima, Fuel Processing Technol. 47 (1996) 215. [11] V.S. Gururajan, T.F. Wall, J.S. Truelove, Combust. Flame 72 (1988) 1. [12] V.S. Gururajan, T.F. Wall, R.P. Gupta, J.S. Truelove, Combust. Flame 81 (1990) 119-132. 1131 X. Du, K. Annamala, Combust. Flame 97 (19941 339. [ 141 0. Levenspiel, Chemical Reaction Engineering, 2nd edn., Wiley, 1972. [15] B.A. Adesanya, H.N. Pham, Fuel 74 (6) (1995) 896. [ 161 D.B. Anthony, J.B. Howard, H.C. Hottel, H.P. Meissner, 15th symposium (international) on Combustion, The Combustion institute, Pittsburgh, 1975, pp. 1303-1317. [17] F. Garcia-Labiano, E. Hampartsoumian, A. Williams, Fuel 74 (7) (1995) 1072-1079. [18] J. Yagi, K. Tamura, I. Muchi, Nippon Kinzoku Gakukai Shi 31 (2) (1967) [19] W. Fu, Y. Zhang, H. Han, Y. Duan, Combust. Flame (1987) 253-266. [20] T. Kojima, K. Take, D. Kunii, T. Furusawa, J. Chem. Eng. Japan 18 (5) (1985) 432-438. [21] S.K. Bhatia, D.D. Perlmutter, AIChE J. 27 (1981) 226.