Ind. Eng. Chem. Res. 1990,29,669-675
\
669
peratures, further shortening of separation times are expected. However, in this case, darkening of the sulfonated products might be a considerable drawback. Separation times higher than 6 h may be undesirable from the industrial point of view. The sulfonation product produced under the conditions described in this work has the following composition and properties: sulfonic acid, 60.8%; spindle oil, 32.9%; p dialkylbenzene, 2.6%; inorganic acid, 4.2%; MWAv= 470, and yield, 86.9%.
\
Registry No. Oleum, 8014-95-7.
Literature Cited
1
2
3
4 Time,hrs
-
5
6
Figure 3. Effects of the amounts of sulfonic acids and the phase separation time on the amount of inorganic acids (I, 49.2%; 11, 49.4%; 111, 56.2%;IV, 63.8%).
2. In process I, the recipe (formulation) of run 4 is preferred due to the low oleum consumption and high sulfonation yield. 3. For phase separation, 6-h reaction time at 70 "C is preferred. If reactions were carried out at higher tem-
Besergil, B.; Baysal, B. M. Determination of the Composition of Post Dodecyl Benzene by IR Spectroscopy. J . Appl. Polym. Sci. 1989, in press. Gilbert, E.; Veldhius, B. Sulfation with Sulfur Trioxide. Znd. Eng. Chen. 1958,50,997-1000. Holtzman, S.; Mildwidsky, B. M. SOs Sulphonation of Heavy Alkylates. Soap Chem. Spec. 1965, 4 1 , 64-67. Kirk, J. C.; Shadan, A. Chemicals from Petrol. Prepr., Am. Chem. SOC.Diu. Pet. Chem. 1956, 2, 49-55. Lavigne, J. B.; Huges, M. F. (to Chevron Research Co.) U.S. Patent 3470097, 1969. Sweeney, W. J.; Hudson, B. E. Sulphonation of Petroleum Products. Sci. pet. 1955, 5 , 329. William, M.; Le Suer, T. (to the Lubrizol Co.) U.S. Patent 2760970, 1956. Received for review January 27, 1989 Accepted October 12, 1989
Radiative Heat-Transfer Model in the Interior of a Pulverized Coal Furnace L. Cafiadas,* L. Salvador, and P. Ollero Departamento de Zngenieria Quimica y Ambiental, Escuela Superior de Zngenieros Industriales, 41012 Sevilla, Spain
A practical mathematical model simulating radiative heat transfer in the furnace of a pulverized coal boiler is presented. The model is based on an adaptation of the zone method, and it has been originally developed as an essential part of an overall pulverized coal combustion model. The model includes calculation of the internal exchanges between coal particles and also the exchanges between the two phases, gas and solid particles, and furnace walls, for which the gas-phase participating character is taken into account. T h e inclusion of this model in a pulverized coal combustion model allows for testing its validity and its sensitivity to furnace walls and particle emissivity values, by comparison with measurements in a 550-MW power plant boiler. One of the greatest difficulties in constructing a model that simulates pulverized coal combustion in the furnace of an industrial boiler lies in determining the radiative heat exchanges established in the interior of the coal cloud and between the cloud and the bounding walls. This is a complex problem because of the consequence of the great heterogeneity of this system, since the coal cloud is a biphasic medium, composed of a particle suspension at different temperatures and size distributions in each furnace point and a gas phase with important contents of C 0 2 and water vapor, where strong temperature and composition gradients exist. This medium is confined in a prismatic enclosure with a rectangular base and walls covered by a layer of slag with radiative properties that are difficult to determine. From a global perspective, the solution techniques for a radiation problem with complex geometry like the one approached here can be grouped into two large categories,
flux methods and zone methods (Heap et al., 1986), apart from the radiation diffusion methods applicable to optically dense systems. Without entering into a detailed discussion of these, the flux methods, based on evaluating the radiant intensity in a determined direction (usually coinciding with the coordinate's axis) from the integration of the corresponding intensity flux equations, are designed to be solved with finite difference techniques, with special application to coupled models where the radiative exchange is solved simultaneously with the momentum, matter, and energy balances. These types of techniques are only approximate, and the results obtained with different versions of these models differ considerably from each other (Richter and Bauersfeld, 1974). An example of these would be the Richter (1978) two-flux model and the Lockwood and Shah (1976) six-flux model. Zone methods allow for a more accurate simulation of
0888-5885190f 2629-0669$02.50/0 0 1990 American Chemical Society
670 Ind. Eng. Chem. Res.. Vol. 29, No. 4,1990
the radiative transport directional dependency at the expense of a considerable increase in computational effort. They are based on the subdivision of the nonhomogeneous system into a sufficiently high number of zones so as to be able to consider each one of them as substantially homogeneous, that is to say, isothermal and with constant properties. An energy balance is established for each one of these divisions so that the energy exchange can be known. This technique, extensively commented on by Hottel and Sarofim (19671, although not elegant in a formal mathematical sense, is practical and powerful for the treatment of radiation in nonhomogeneous enclosures. Some specific applications and extensions of the zone method are due to Hottel and Cohen (19581, who applied it to multidimensional problems, and to Steward and Guruz (1974), who combined the technique with a Monte Carlo method for the analysis of an oil-fired power plant boiler. In this model, the zone method philosophy is used, developing a specific application for the exchanges occurring in the interior of a pulverized coal furnace.
General Statement of the Radiation Model The radiation model presented here was included in a pulverized coal combustion model which is particularized for bituminous fuels burned in a tangentially fired furnace (Caiiadas, 1988). This combustion model is mainly composed of four submodels simulating the flow field in the furnace, coal devolatilization, char combustion, and radiant heat transfer. The flow model results from a strong simplification of the actual flow field, based in the furnace technological configuration. Flow is assumed to be one-dimensional, and the furnace geometry is divided in two sections with different ideal flow patterns: burner zone, where induced turbulence deals in a completely mixed flow, and furnace upper section, where plug flow is assumed. Coal combustion is composed of two successive stages: coal devolatilization and char combustion. The coal devolatilization model includes moisture evaporation, pyrolisis, and volatile matter combustion, and it is based on the experimental results of Neoh and Gannon (1984) and Kobayashi et al. (1977). Pyrolysis is the only rate-limiting step, and the volatile matter evolved depends on the pyrolysis temperature. The volatile composition is estimated according to the ultimate analysis of coal. The char combustion model is adapted from the Mon and Amundson (1978) reaction model assuming spherical char particles, composed of carbon and ash, which change in particle diameter during the reaction, according to the apparent kinetics of the carbon heterogeneous oxidation with O2 and COz. These two reactions yield CO as the product, which later is oxidized homogeneously to COz. Heterogeneous reaction kinetics are taken from the Mulcahy and Smith (1969) review and the Dobner (1976) results, while homogeneous oxidation kinetics of CO is taken from Howard et al. (1973). The rate of molecular diffusion to/from the particle surface is calculated from integration of Stefan-Maxwell multicomponent transport equations. The combustion model is applied to each one of feed coal particle sizes, evaluating the size dependence on the reaction and diffusion rates. The radiation model takes into account that the system is a participating medium in two senses: there are solid particles in suspension, and the gas itself is also participating due to its content in COz and water vapor. In this manner, an overlying sequence of radiation emission, absorption, and scattering between gas, particles, and walls is produced. For simplicity. the model only considers the
t
ph.’
a
n
,
L
I
L ,
Figure 1. Scheme of global zone energy balances.
radiation emission and absorption processes without taking the scattering phenomena into account, and all surfaces and media have been considered as gray bodies. A double treatment was made for the gas phase, assuming it to be transparent for radiation exchanges between different sections of the particle cloud, where the effect of particles is predominant and taking its participating character into account by making it capable of radiating energy to furnace walls. The first two hypotheses, not to consider scattering and to assume gray bodies, are shared by other high-level models of radiation in pulverized coal clouds (Smith et al., 1982; Smoot et al., 19841, whereas the double consideration made for the gas phase is a necessary contribution to avoid the relative adiabatic character that these models confer to the gas phase. By the one-dimensional approximation for the combustion process in the furnace, there will only be axial gradients, so the heat exchange between the different media portions is established between elementary transversal sections of differential height that form the zones of this system. Total radiative transfer in each of these zones can be divided into three independent heat flows: (1)heat flow received by the particles in one zone coming from all other particles within the furnace; (2) heat flow exchanged between particles and furnace walls; (3) heat flow radiated from the gas to the walls. Global energy balances governing one zone where char combustion is produced are represented in Figure 1. The energy balance for particles of generic size j’ is described by P],k+lHp(T],k+l) - pj,kHp(T,,k) = Qrad,,k - Qradpwj,k - Qconvpjb (1) Qpart,,k where Qpart includes the energy release rate by heterogeneous char oxidation reactions and QcOnv represents the convective heat transfer between particles and the gas phase. In the same way, the energy balance for the gas phase is depicted by G ~ + I H G ( T G-~ + GkHG(TG,) ,) = Qgasa + Qconvp,k - QradGw,k - Qconv,b (2)
Ind. Eng. Chem. Res., Vol. 29, No. 4, 1990 671
but for an absorbing medium, the value of i, is given by the Bouger-Lambert law
i, = ipo exp(-Jsa(s) I
a)
bl
&-
Figure 2. Basic outline of the radiative transfer model zone division and the exchange between particles.
where Q, is the rate of heat generation by homogeneous reaction means. Sucessive resolution of matter and energy balances of each individual zone deals in predicted furnace temperature and composition profiles, but the temperature and properties of the whole coal cloud should be known to evaluate the radiant heat transferred to the zones. So an iterative technique must be used, starting with an initial distribution for temperature, size, and particle density in the furnace, calculating the resulting radiant heat transfer, and then solving the constitutive equations with the given radiative transfer as input. The assumed profiles are then updated, and the procedure is repeated until a specified convergence level is achieved. The convergence criterion is defined as the root mean square of the temperature differences of each particle type in each zone between two consecutive iterations. A convergence limit of 5 K was imposed in this particular work.
Exchange between Particles To calculate the heat that particles in one zone receive from radiation, an integral analysis of exchanges needs to be done, including all individual surfaces that are emitting and absorbing energy in the whole system. In this case, each zone has a particle size distribution that can be considered by dividing the particle cloud into different types, each of which corresponds to one of the existing particle size cuts. Each particle type is defined by its size, temperature, and number density (number of particles per furnace unit volume), quantities that are conditioned by pulverized coal characteristics and combustion process evolution. To calculate the net rate of radiant energy received by particles in a zone coming from the rest of the particles in the furnace, two arbitrary zones, k and p, consisting of two elementary furnace transversal sections separated by a distance S (Figure 2a), will be considered. Since the zones are sufficiently narrow, we will suppose that no particle is hidden from view by another within the zone, and for geometrical effects, we will consider that all particles are on the middle plane of the zone and are homogeneously distributed throughout. Thus, there is a surface portion occupied by solid particles, dAk, in every middle plane differential element, dAkt, that exchanges radiative heat with the surface elements occupied by solids in the opposite zone, in the way indicated in Figure 2b. The classical treatment of radiation problems (Siege1 and Howell, 1972) states that the radiant energy rate received by a differential element in zone k coming from another element in zone p is dAk COS @k d2Q,k = i p dAp cos PP (3) spkZ
If the medium separating both zones were not absorbing, the radiant intensity would be
ds)
(5)
where the exponential term represents the medium transmittance and the function a(s) is the radiation attenuation linear coefficient as a function of the intermediate position between the two zones. On the other hand, taking into account that not all of the zone is occupied by particles, it can be written that dAp = f p dA,t
(6)
dAp = f k dAkt
(7)
where f represents the surface fraction occupied by particles. By substituting eqs 4-7 in eq 3, we obtain d2QDk=
and using the definition of the view factor between both middle planes, Fpk,we obtain
1
COS b p COS P k
FpkApt
=
dApt (9)
PSpkz
The expression that gives the radiant energy rate received in zone k coming from zone p is
where the existence of the particle cloud intermediate to both zones has been taken into account, together with the fact that not all of the section in each zone is able to emit or receive radiation. By defining the local emission coefficient of the particles in zone p as lr
up = tpnpqdp2
and by evaluating the total area occupied by solids in the zone middle plane as
eq 10 can be written as
Up to this point, we have only considered the existence of a single type of particle in the zones. Considering that there exists j types of particles emitting radiant energy a t different temperatures in zone p, we can extend the analysis with the formula
that represents the radiative power emitted by the j t h particles in zone p that reach zone k. Obviously, the total radiative power received in zone k from zone p is obtained by summing up the above quantities for aU types of particles existing in the emitting zone:
672 Ind. Eng. Chem. Res., Vol. 29, No. 4, 1990
which, when expanded, is equivalent to In light of eq 15, it is still necessary to analyze the term corresponding to radiation attenuation on its way through the solid particles suspension. Pulverized coal and char particles have a typical size in the range 10-200 pm, and the furnace volume fraction occupied by solids represents an amount lower than 10-5th of the furnace volume. Therefore, we are facing a low concentration suspension of particles of large size as compared to the radiation wavelength, for which the radiation absorption coefficient is proportional to the area intercepted by particles (Gray and Muller, 1974). In this way, where neglecting possible radiation scattering, the attenuation coefficient in an arbitrary position s will be given by 4 s ) = CY(s)n(s)%(s)2
4
(16)
According to Kirchoffs law, c = CY for a gray body, so the attenuation coefficient is equivalent to the local emission coefficient defined in (11): a(s) = t(s)n(s)%(s)2
4
(17)
By making use of furnace division into zones, a discrete representation of the integral extended to the distance that separates both zones can be made:
where subindex q indicates every intermediate zone between p and k . On the other hand, the term a4 includes the sum of all the attenuation coefficients corresponding to the j particle types:
Substituting eqs 17-19 in eq 15 yields
an expression that allows us to evaluate the rate of radiant energy received in zone k coming from particles in zone p as a function of furnace geometrical parameters and the particle’s radiative properties, size distribution, number density, and temperature along the furnace axis. The total radiant power received in zone k coming from all the particle cloud is obtained by summing up every individual zone contribution:
Only part of this energy is absorbed by particles in zone k , so the radiant power absorbed by the j t h particles is given by
Before calculating the rest of the radiative exchanges, it is convenient to make a brief comment on the meaning of term Fpkin the expression above, which represents the view factor between zones p and k in the furnace. Since zone geometry corresponds to that of transversal furnace sections of differential height, i.e., prismatic volumes of rectangular base coincident with the transversal section of the furnace, this view factor can be adequately approximated by the one corresponding to two rectangular, parallel, facing, plane plates of the dimensions of this transversal section and separated a distance equivalent to that separating the middle planes of the considered zones, the expression of which can be found in many radiation treatises (Le., Siege1 and Howell, 1972).
Exchange between Particles and Walls Hottel (1954) provides a simple, approximate procedure to estimate the radiative exchange between an absorbing medium and the enclosure boundary, applicable when the cooled walls are black and are at a temperature where they emit appreciable radiation. The total energy received by the walls is such that the net heat flux directed toward them is the medium emission minus the emission from the walls that is absorbed by the medium. Taking into account that, in the case we are considering, the medium is composed of a distribution of j particle types, for each one of them we can write
where and am,& represent the emittance and the absorptance of the particle suspension existing in the zone. Assuming gray medium, then t, = CY,, with the value given by cmj,h = - exp(-aj,kleqk) (27) where the mean beam length for radiation from the entire volume can be estimated with Leqk = O*gDhyd (2.8) Substituting these relations in expression 26, we get - Awku(T/,k4 - T w k 4 ) [ 1 - exp(-a,,k(O*gD,yd))] (29)
Qrad,,,k
which represents the net radiant energy rate emitted from the j t h particles in zone k to the walls when these are considered black bodies. Taking into account the consideration of gray bodies made for the walls, expression 29 can be modified according to Qrad,,,i
--
As particles absorb radiant energy, they emit it to the rest of the furnace in an amount given by Qemj.k
=
a j r k VelemkgTj,k4
(23)
In this way, the net rate of radiant energy received by the j t h particles coming from the rest of the particles in suspension is given by
which estimates the net radiant power emitted from the particles toward the furnace walls in each zone, when the wall emissivity has a value greater than 0.7. Although a more complex analysis is required if t, is lower than 0.7, for simplicity, expression 30 will be used without restriction
Ind. Eng. Chem. Res., Vol. 29, No. 4, 1990 673 in the whole range of usual wall emissivity values.
Exchange between Gas and Walls Evaluation of the radiant power emitted from the gas in one zone to the walls is treated in a similar way to the scheme followed for solid particles. An expression for calculating it is a modification of eq 26, which becomes
where t G and CYG are the gas emittance and absorptance, respectively. Expression 31 also takes into account the gray character of the furnace walls. Evaluation of terms t G and CYG is carried out from the emittance of radiating constituents present in the gas phase, C 0 2 and H20, in agreement with the scheme proposed by Hottel (1954):
+ f H 2 0 - 6t aG = a C 0 2 + a H 2 0 - 6a tG
=
tCO,
2000
,
where it has been considered that the system under analysis is at atmospheric pressure. From these two expressions, it is possible to obtain the according to equations values of parameters aC02 and aHZO (36) (37) where tCO * and tHzO*represent the emittances of these compounds evaluated according to eqs 34 and 35 a t T, with parameters Pco2Leq(TW/ TG) and PH,o.Leq(TW/TG), respectively.
Results and Model Sensibility with Respect to Radiative Properties of Particles and Walls This radiation model uses as data the particle temperature, size, and number density evolution and the temperature and composition profiles of the gases in the furnace, which are results of the whole coal combustion process. Also, the model uses char particles and furnace wall emissivities as direct parameters. There are very limited data available on spectral output of chars and coals at combustion temperatures. However, it has been suggested that char particles are relatively gray (Folsom et al., 1986), as it has been considered in this model, and their emissivity is approximately 1, although its correct value cannot be stated precisely and neither can its dependency on temperature. Mon and Amundson (1978) propose a typical char emissivity a t combustion temperatures of 0.93.
,
0
(33)
0.15 + 0.0328(PH20.Leq- 0.1524) 12.6 x 10-5vG - 1111) (35)
aco2 = t c o , * ( T ~ / T ~ ) ~ . ~ ~
"S = South Africa; B
(32)
where the gas total emittance and absorptance are the sum of C 0 2 and H 2 0 when considered isolated minus an adjusting term that accounts for the reduction resulting from spectral overlap of the absorption bands of both compounds. These parameters are complicated functions of gas composition, pressure, temperature; wall temperature, and system meam beam length. Using regression techniques, we get the following approximate expressions, applicable to evaluate the abovementioned parameters in the range of typical conditions for pulverized coal combustion: tco2 = - 5.4 X 1 0 - 5 ( T ~ 1111) (34) ~ H , O=
Table I. Operating Conditions of the Contrast Cases case 1 2 3 operating load, MW 510 425 330 coal typea S/B S S coal flow, tons/h 184 149 105 elem coal anal. 7.1 5.9 5.9 moisture, % wt 13.2 12.5 14.3 ash, 70wt, d.b.* 73.8 73.6 72.2 carbon, 70 wt, d.b. 4.0 4.3 4.2 hydrogen, % wt, d.b. nitrogen, % wt, d.b. 1.9 1.7 1.7 sulfur, 70 wt, d.b. 0.7 0.6 0.5 equiv mean diam, wm 70 101 74 total air flow, tons/h 1938 1590 1136 O2at boiler exit 3.4 3.3 3.7 6.9 1.4 fly ash unburned C content, % wt, d.b. 2.6
1000
5
,
,
4 230 SIB 84 6.7 15.1 72.0 4.0 1.6 0.6 94 912 4.4 2.7
= Bierzo (Spain). bd.b. = dry basis.
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
NO REPRESENTATIVE TEMPERATURE MEASUREMENTS REPRESENTATIVE TEMPERATURE MEASUREMENTS
i
-1
1600
w
1400
B I
2!
1200
1000
0
5
10 FURNACE HEIGHT
15
20
(ml
Figure 3. Predicted temperature profiles and temperature measurements for contrast case l.
On the other hand, furnace wall emissivity depends on the emissivity of ash deposits that cover the walls as a continuous film. Ash deposit emissivity measurements reviewed by Becker (1982) indicate that its value moves in a wide range with a strong dependency on temperature. Measured emissivities at wall temperatures range from 0.5 to 0.95, whereas most measurements of wall emissivities are approximately 0.7. Radiation model validation was made by comparison between global coal combustion model predictions and measurements in an industrial boiler taken along the tracking program of a 550-MWe power plant (Cariadas, 1988). To present the results, four experimental contrasting cases will be used, whose basic operating conditions can be found in Table I. These four cases have been selected so as to cover the entire spectrum of boiler operating loads, from 230 to 510 MW,, and they include favorable, medium, and unfavorable combustion conditions. Different validation tests were performed including experimental and theoretical temperature profile comparisons, experimental and predicted unburned carbon content in fly ash concordance, and others based on unburned particles distribution and expected fly ash morphology and crystallography. Figure 3 presents predicted temperature profiles for contrast case 1and temperature measurements within the furnace, where continuous lines represent temperature evolutions of different particle types and gas phase. Unfortunately, relative location of furnace measurement openings, with respect to burners and secondary air nozzles
674 Ind. Eng. Chem. Res., Vol. 29, No. 4, 1990 7.5
'
Unburned Carbon Conimt ( 2 u l ) w o
5
3 0
0
,
'
a
CASE' CASE CASE CASE
\
1516 MW)
NO. 2 NO 3 NO 4
( 4 2 5 MW) 1330 MWI (230 MW)
NO.
'
I
?
5k 4r
/
I
-1
-
0
c
=
3-
0
'CASE N O . ' 1
( 5 1 0 MW)
2
( 4 2 5 MW)
CASE N O .
1
g
-31l
I
-1
I
I
l
1
,
I
,
1
/
1
1
1
1
0 . 4 0 0.50 0 . 6 0 0 . 7 0 0 . 8 0 0 . 9 0 1.00
FURNACE WALL
EMISSIVITY
Figure 6. Model sensitivity with furnace wall radiative properties.
raowc I
U
> c i
w w o o x
t
-2,
-
t
-
-3-
0 BO
0 a5
0 90
0 95
I 00
PARTICLE EMISSIVITY
Figure 5. Model sensitivity with particle radiative properties
discharge points, make several of the measurements locally not representative to the actual combustion temperatures, so comparison must be restricted to a few temperature values which agree with model predictions. Concordance between the predicted carbon content in fly ash and that experimentally determined is the strongest validation test, since the unburned content is extremely sensitive to any modification in the combustion conditions (temperature evolution) due to its particular physical significance (final quantity of unconsumed feeding carbon expressed in weight percentage over the fly ash produced), which implies that, for the considered coal types, the absolute value of its fluctuations are amplified with respect to the feed currents by a factor of 7 . Figure 4 shows the comparison between the experimental unburned content values and the combustion model predictions, in the four contrast cases, using as reference emissivities 0.93 for char particles and 0.7 for walls. Absolute deviations of 0.54, 0.69, 0.44, and 0.06 points, respectively, are found, representing an average deviation of 16% of the mean unburned carbon content. Model sensitivity, varying the char emissivity value from 0.8 to 1in the four selected contrast cases, yields the results of Figure 5. This figure indicates the practical insensitivity of radiation model with respect to the particle emissivity, with a parallel evolution of results within a deviations range in the predicted fly ash unburned carbon content lower than 170. The same does not happen with the furnace wall emissivity, where a modification around its reference value produces a substantial alteration in the model results, a change being observed in its overall tendency, as indicated in Figure 6. Thus, a wall emissivity value of 0 . 4 4 5 makes
the unburned carbon content predicted by the model always be lower than the experimental content, whereas, at the other extreme, the value of 0.9-1.0 leads to theoretical value contents much higher than the actual ones. Logically, unburned carbon content is directly related to particle temperature evolution. A lower content means a higher temperature of the solids and, therefore, their faster combustion velocity. Using a wall emissivity lower than the real one implies a lower radiant energy transfer to the walls, thus maintaining a higher temperature inside the furnace. The inverse phenomenon is produced when using a higher wall emissivity value. The sensitivity analysis in Figure 6 indicates that, for the four cases used, the wall emissivity value that produces the best adjustments is between 0.55 and 0.80, perfectly centered above the reference value of 0.7.
Summary and Conclusions The radiation model developed permits an acceptable heat-exchange simulation in the furnace of a utility boiler, as verified by the overall results arrived at with a pulverized coal combustion model that incorporates it as one of its primary parts. Division of the exchange set into three independent heat flows allows for model mathematical simplification without diminishing representativity. Use of the zone method gives versatility in the treatment of the considered complex geometry and in the incorporation of the char particle size distribution in the model. Different from other radiation models previously published, the consideration usually used for the gas phase to be transparent to the radiation has been substituted by a double consideration of this, which lessens the complexity of calculating internal exchanges into the particle cloud, maintaining the cooling effect suffered by the gases due to radiative transfer to the furnace walls. The radiation model is found to give quite accurate results with good stability when several real operating conditions of a 550-MWepower plant boiler are simulated by the overall combustion model. Use of the reported solid particles and furnace wall emisjivity values leads to an acceptable concordance between predictions and measurements. Practical model insensitivity with respect to the solid particles' emissivity value and its strong depen-
Ind. Eng. Chem. Res., Vol. 29, No. 4, 1990 675
on the furnace walls’ emissivity are shown. A reference wall emissivity of 0.7, a typical experimentally measured value, is suitable for our specific contrast application. dency
Acknowledgment
The power plant tracking program was performed under PIE P r o j e c t 34.27, Activity 1. We acknowledge the Direcci6n General de Desarrollo of Compaiiia Sevillana de Electricidad, S.A., and ASINEL for their financial support and also the assistance of the Los Barrios Power Plant staff. Nomenclature a = attenuation coefficient or local emission coefficient, m-l
Ak = projected area of t h e particles in zone k over their mean plane, m 2
Akt = total mean plane surface of zone k , m 2 A , = furnace wall surface, m2 d = particle diameter, m = hydraulic diameter of t h e furnace, m f k = surface fraction of t h e zone k mean plane occupied by Dhrd
t h e solid particles’ projected area - view factor between zones p a n d k &k=gas-phase molar flow, kmol/s HG = gas-phase enthalpy, k J / k m o l Hp= char particles’ enthalpy, k J / k g ip = radiation intensity considering t h e attenuation of t h e medium, kW/ (m2.sr) ipo = radiation intensity without considering attenuation k W / (m2.sr) Le, = mean beam length for radiation, m nj,k= particle number density, particles/m3 P = particles’ mass flow, kg/s Qk= total radiant power received by zone k from all remaining zones, kW Q,,,, = convective h e a t transfer between particles a n d gas, kve Q,,,, = convective h e a t transfer between gas and furnace walls, kW Qgas = homogeneous combustion energy release rate, kW Qp& = heterogeneous char oxidation energy release rate, kW Q p k = radiant power received by zone k coming from zone p , kW Qaba= radiant power absorbed by t h e particles, kW Q,, = radiant power emitted by the particles, kW Qrad = n e t radiant power emitted by t h e gases t o t h e walls, k@ Qrad, = n e t radiant power received by t h e particles from t h e rest of t h e particles, kW Qrad = n e t power radiated t o t h e walls from t h e particles, km S = distance between the mean planes of two arbitrary furnace zones, m s p k = distance between two differential elements of the mean plane of two arbitrary zones, m T.,k= temperature of t h e particles, K = wall temperature, K Velem= volume of one zone, m3
F
T,
Greek Symbols = particle absorptivity cy, = particle suspension absorptance cyG = gas absorptance a C O , = COPabsorptance aHZ0= H 2 0 absorptance (3 = angle with respect t o t h e normal, rad 6a = overlying factor of t h e spectral absorption bands 6 t = overlying factor of t h e spectral emission bands 6 x , = height of zone q , m cy
t t,
= particle emissivity = particle suspension emittance
= gas emittance = COz emittance tHzO= HzO emittance t, = furnace wall emissivity u = Stefan-Boltzmann constant, kW/(mZ.K4) tG
tC0,
Subscripts
j = particle type k = furnace zone p = second furnace zone ( p # k ) q = furnace zones situated between p a n d k
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