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Fluidized bed char combustion kinetic models
Chemical Enbwint Science Printed in Great Brilain.
Vol. 31. No. I, PP. 17-25,
1982
W9-25CW32/01Ctl1740$02.~W/0 PErgarm” Press Lid.
FLUIDIZED BED CHAR COMBUSTION KINETIC MODELS DRAGOMIR BUKURt and NEAL R. AMUNDSON* Department of Chemical Engineering, University of Houston, Houston, TX 77004, U.S.A (Received 1I September 1980; accepfed 25 March 1981) Abstract-The effect of the kinetics of the heterogeneous reaction between the char and oxygen, and the importance of the subsequent homogeneous oxidation of carbon mo?oxide on the performance of an atmospheric Ruidized bed combustor have been examined by a comparative analysis of three models. Numerical calculations illustrating the effect of operating variables such as bed temperature, fuel and sorbent particle Feed size and excess air were performed For values of the parameters which are pertinent to the design of large scale utility boilers. It is found that the kinetic models predict existence of multiple steady states over a wide range of operating conditions and values of model parameters. The model predictions of combustion efficiency, carbon loading and CO concentrations are in qualitative agreement with experinental data reported in the literature. INTRODUCTION
where C,, is the oxygen concentration at the particle surface, El’ = El/R, = l7,976(“K) and koI = 535.3(m/s). This expression is based on the external particle surface area which is consistent with our assumption that the shrinking core model is applicable for combustion of relatively large char particles. The heterogeneous reaction between the char and carbon dioxide is not taken into account in our model for two reasons. Firstly, the rate expression (1) of Field et al. [Z] is believed to give the overall rate of carbon consumption by all reactions, and secondly the rate of reaction between the carbon and COz is too slow to compete with the carbon oxidation by O2 under the conditions prevailing in fluidized bed combustors. This conclusion is based on the kinetic rate expression of Dutta et al.[6] and others (e.g. see Laurendeau [5]) for the C + COr reaction. As discussed in Ref.[I], it is fairly well established that carbon monoxide is the primary product of reaction between the carbon and O2 for temperatures which are typical for fluidized bed combustors, but it is rather uncertain where the subsequent CO oxidation takes place. The assumption that the homogeneous reaction between CO and 02 is instantaneous and that no oxygen reaches the particle surface, which is known as the double film theory of particle combustion, was shown not to be valid for conditions prevailing in fluidized bed combustors (Zabrodsky[7], Basu et al.[8], Bukur and Amundson[l]). Basu et al.[81 modified the double film theory by assuming that oxygen reacts instantaneously with CO, but that it also reaches the particle surface where it reacts with the carbon. However, the proposed combustion mechanism appears to be inconsistent to us. Caram and Amundson[9] and Mon and Amundson[lO] studied the problem of singIe carbon particle combustion with a finite reaction rate for CO oxidation inside the boundary layer under conditions which are typical for pulverized fuel combustion and/or combustion of single particles in the air or in pure oxygen. They found that the CO may be completely or only partially burnt inside the boundary layer. The extent of CO combustion is dete:mined by particle size, ambient temperature, and oxygen concentration, Sundaresan [ 1I] studied the same problem but using values of parameters which are typical for
In our recent paper [l] two models for fluid&d bed combustors based on the single film and the double film theory of char particle combustion were analyzed by assuming that the rate of the reactions are controlled by the rate of mass transport of reactant from the gas phase
to the particle. On the basis of predicted values of the char particle temperature it was found that the double film combustion mechanism must be discarded and that the reaction kinetic resistance is not negligible. The purpose of this study is to examine the effect of the kinetics of the heterogeneous char oxidation reaction on fluidized bed combustor performance for values of the parameters which are relevant to the design of large scale utility boilers. The carbon monoxide which is produced at the particle surface can be oxidized immediately at the particle surface or inside the stagnant gas boundary layer surrounding each particle or in the interstitial volume. In this study the two limiting cases, CO oxidation at the particle surface and CO oxidation in the interstitial volume, are analyzed, which enables one to test the model sensitivity with respect to the assumption of where the CO oxidation takes place. KINETICS
In spite of intensive research on the heterogeneous reaction between carbon and oxygen, the kinetics of this reaction is still subject to a great deal of uncertainty (e.g. Field et a1[2], Mulcahy and Smith[3], Smith[4] and Laurendeau[5]). The reported orders of reaction with respect to oxygen are between zero and one, and the values of activation energy are in the range between 62 and 335 kJ/gmol. In the present study the rate expression of Field et al.[2], which was obtained on the basis of analysis of experimental data by several investigators, has been used in numerical calculations, i.e. RI = k,C,, = k,,T, exp(-E,‘/TC)C3,
(ky$C)
(1)
*Author to whom correspondence should be addressed. Wesent address: Department of Chemical Engineering, Texas A & M University College Station, TX 77843, U.S.A. CES Vol. 37. No. I--B
17
D. BIJKUR and N. R.
18
fluidized bed combustors, and his results show that most of the CO leaves the boundary layer unreacted. From the above discussion it is obvious that in the rigorous analysis one should allow for a finite rate of CO oxidation both inside and outside the boundary layer, but this would considerably increase the complexity of the problem. In order to estimate the effect of CO oxidation on the FBC performance, we have chosen to study the following two limiting cases: (I) the CO burns at the particle surface, or (2) CO oxidation takes place outside the boundary layer. The overall reaction rate expression of Howard et af.[12] for homogeneous oxidation of CO has been used in all numerical calculations:
AMUNDSON
obtained as a solution of eqns (3) and (6b)
The integration constant is determined from the boundary condition (6a), giving
K13 =D,k,R,‘+*;jd,Rc
and the oxygen mole fraction at the particle surface is then given by
R4 = kaCcoC~~C~~o = k04exp(-E41/Tb)CCOC~~C~~~ (2) where Ed’ = EAR, = 15,098(X) 1.3 x 10”(m3/kmol). CO COMBUSTION
and
x3, =
X3d
x3(&) =
(8)
kw= The value of oxygen concentration at the particle surface is greatly affected by the dimensionless ratio of diffusion and kinetic resistances, i.e.
AT THE PARTICLE SURFACE (KM11
The model to be considered represents an extension of the diffusion limited single film model @FM) which was analyzed in our previous paper [ I] by taking into account the effect of the finite kinetic resistance at the particle surface, Thus, the mass balance equations for the solids and the gaseous species in the bubble and dense phase derived in [l] can be used directly by substituting the appropriate expression for the rate of particle combustion which will be derived next. By assuming that the CO produced is immediately oxidized at the particle surface, the overall reaction rate is C+OZ=COZ;
(7)
- l/b)
R _ kl(T,)R, _ diffusional resistance D kinetic resistance This ratio is a strong function of particle temperature and particle size. For kinetically controlled reaction (i.e. low temperatures and/or small particles) R +O and ~3~+x3d while for a reaction which is controlled by the rate of mass transfer (i.e. high temperatures and/or large particles) R + m and xlS +O. Rate
of particle combustion
(shrinkage)
From the stoichiometry of the overall reaction at the particle surface it follows that
R,=k,Cq,.
Notation used in [I] is retained here, and only the new symbols will be explicitly defined. Mass conservation equations for gaseous species and the energy balance for the gas inside the boundary layer which were derived in [ 11will be restated for convenience.
After differentiation and rearrangement one obtains the following expression for the rate of particle shrinkage R(“)=dt=
dd,
D
rt+ I
d
B&d
(
1-k
(9)
>
and with d, = d,, at f = 0 where B =20X4&p,. In terms of the dimensionless particle size the above equation becomes
where iv, = -cD(ax,ia<).
(5)
These equations are subject to the following set of boundary conditions at .$= R, NY= -R, = -k,Cx,,,
N, = -AN,, T, = Tc
(6a)
and at 5 = b x, = X,d;
x3 = .x3,3;
T, = Tb.
(10) where K(T,) = kl(Tc)do,/2D. We note that when the rate of chemical reaction is much faster than the rate of mass transfer (i.e. K(T,) + I), the last expression reduces to the one for the diffusion limited reaction (see eqn (23) of Ref. [l]).
(6b)
The oxygen concentration profile in the boundary layer is
Energy balance for the char particle The energy balance for the particle which is at uniform
Fluidized
temperature is o~(Tb4-T~4)t+-AH,)k,Cx,,
19
bed char combustion-kinetic models
differential equations for a single particle in each iteration, while in the case of diffusion limited models these equations were integrated only once.
I 1 (11)
+k aT, g 8% .$=Rc
CO COhlBUSTION
OUTSIDE THE BOUNDARY
and T, = T,” at f = 0. The expression for the heat flux at the particle surface obtained by solving eqn (4) is of the form
as the KM2 model, it is assumed that oxygen reacts with carbon producing carbon monoxide which in turn diffuses away and reacts with oxygen in the dense and the bubble phase. Thus, at the particle surface we have the heterogeneous reaction (-AH31 Ct;O2-CO;
In numerical calculations this expression has been approximated with an error which can be shown to be less than 1% by the following
From eqns (10) and (11) one can obtain the following expression for the rate of change of temperature with particle size
F
+
b,(T_
_
Tb)
a
IIK(Tc)+ r(l - rip) r’(l - rip)
(13)
where b3 = 3k,y,ICDM,&_+
R,=k,C,,
(16)
and outside the boundary layer homogeneous oxidation of CO which is catalyzed by water vapor, i.e. Ct)+$O*Z
~=p,[~+(l-$)](T~-TV)-
LAYER (KMZ)
In this model, which will subsequently be referred to
COz; Rq = k&,C::C& (17)
Single particle equations If one neglects the bulk flowof gaseous species arising
from unequal molar counter-diffusion, the mass balance equations are the same as in the previous model (eqns (3) and (5)). This can be done without aily appreciable error since the system is diluted by an inert componentnitrogen. The boundary conditions at the particle surface need to be modified according to the stoichiometry of reaction (16)giving at f = R,
The culculation procedure The general procedure for generating a solution for this model is similar to the one described in detail for diffusion limited models in Ref.[l], so that only the essential features will be described here. As shown in [l] the solution of the solids and gaseous species mass balances reduces to finding a solution of the following system of two nonlinear equations
The oxygen mole fraction at the particle surface obtained as the solution of eqns {3), (5), (6b) and (IS) is given by
(14)
Rate of particle combusfion From the stoichiometry of the heterogeneous reaction at the particle surface (16). the following expression is obtained for the rate of change of particle size
gzcf. hi)
= X3”-
X3d *
‘
I
N,=-;R,,
T, = T,
Nz=-2N3,
x,.=x,(%-R=)=
6r d,‘l(d,,d,,)dd, = 0 mud 0 US)
where in the present case R(d,) is given by eqn (9) and is a function of particle temperature and size. The calculation procedure is as follows. First, one assumes values for fs and xla and then integrates eqn (13) to obtain the particle temperature and the rate of particle combusion as a function of particle size. When the rate of particle combustion is known one can find a solution of the system of eqns (14) and (IS). The entire procedure is repeated until convergence is obtained. Wifh the correct values of f. and xjd one can calculate all the desired quantities as described in [l]. The computational procedure for this model requires numerical integration of
(18)
(19)
or in terms of the dimensionless particle size dr
;
r(O)= I
(20~
Energy balance for the particle The energy balance for the particle is of the same form as in the KM1 model (eqn (11)). If one approximates the heat flux at the particle surface by eqn (12), one obtains the
D. BUKURand N.
20
following expression for the rate of change of particle temperature with size.
with T, = T,” at r = 1 and where b2 = 3y, (-A&)i~J&. Mass balance equations for gaseous species
The mass balance equations for the solids derived in [l] can be used in the present case as well by inserting the expression for the rate of particle combustion (19) where required. However, the mass balance equations for gaseous species need to be modified by taking into account the homogeneous oxidation of CO in the bubble and the dense phase. The change in total number of moles can be neglected, because of the large amount of diluent in the system, as well as due to the fact that most of the CO produced is converted into CO?. Since there are two independent reactions in the system it is sufficient to consider the mass balance equations for two species only (02 and CO), while the concentration of the third species (COZ) can be determined from the stoichiometry of eqns (16) and (17). The mass balance equations for OJ = 3) and CO(j = 2) in a dimensionless form are as follows. Bubble phase: +
= X(XZI - XZb)- X4bXZbX :;*; X%(O)= 0
F =X(XJI
- X3b)- y
(22)
xuJ:62;x3*(0) = X3” (23)
Dense phase: do‘ XzO- XZd+ (0 - 1)X(& - XZd)- KI - piL,x,,x:z
d:l(dc,d,c)ddc
I0
= 0
(24) dot
x3O-
X3d +
(/3- 1)X(.& - XU) - $
d,21(d,, d,, )ddr
I0
- ; KIdXZdX :‘,’ = 0
(25)
where K4b = (H -H,,)k,(Tb)Cx&IU
- U,,
8& = H,,~,,,,k,(TXx&lU
KI = 3ycF,cP/McdZcNt”; 8=LlUm,;
fib =
I I
xi(s)
ds
(26)
XI0 = x*O = 0. o
The mole fraction of COZ in the dense or in the bubble phase is calculated as x,*
=x,"t x3” -
x*O- X2k 2
X3r t -
(k = b or d). (27)
R. AMUNDSON The calculation
procedure
The numerical solution of equations describing this model requires more computer time than the previous models (DLM and K&U), but the general calculation procedure is similar for all models. The computational procedure is initiated by assuming initial values for the three unknowns fs, x2d and x,d. Then, the differential equations (22) and (23) for the bubble phase are solved numerically in order to obtain the concentration profiles +(s) (j = 2,3), which are needed for calculation of .Zjb by numerical quadrature. The differential equations for a single particle (20) and (21) are also integrated numerically, and the calculated values of I?(&) are substituted into eqns (14),(24) and (25). The solution of the resulting system of these nonlinear algebraic equations is obtained by the Newton-Raphson method and the whole procedure is repeated with the new values for the unknowns until convergence is obtained. The inlet gas feed temperature which corresponds to the given bed temperature is calculated from eqn (34) of Ref. [I], and the combustion efficiency is given by
where
PREDICTION
OF COMJWSOR
PERFORMANCE
Numerical values of parameters and the correlations used in computations are taken from Ref. [l] (Tables l-8). In the case of CO combustion outside the boundary layer (KM2) the molar flow rates of COZ and CO leaving the combustor given in Table 5 of [l] are modified by taking into account the stoichiometry of the reactions (see eqns (27) and (29)). In all calculations the standard values of model parameters (Table 8 of [l]) were used unless indicated otherwise. Preliminary calculations have indicated the importance of the kinetic resistance for a reaction between oxygen and carbon at the temperatures which are typical for fluidized bed combustors (i.e. I’,,= 1050-l 150°K). Under these conditions the kinetic resistance is greater than the diffusional resistance, and only at temperatures above 1200°K the latter becomes dominant. This has the important implication that the thickness of the boundary layer b does not have a significant effect on the rate of particle combustion. Hence, in all calculations the dimensionless parameter p was evaluated as p = 6 X 10m3/&,,,where d,, is given in meters. A change of particle emissivity E, in the range of 0.6-1.0, was found to have only a minor effect on the model predictions of combustion efficiency, and thus a value of unity is used in all calculations reported in this paper. A change in particle emissivity affects the difference in temperature between the particle surface and the bed to some extent but this temperature difference is not nearly as large as the one predicted by the diffusion limited model (SFM). (The largest tem-
Fluidired bed char combustion-kinetic
21
models
perature differences (AT,,, = T,,,, - i”,) predicted by the KM1 model is 54.S”K, while if one uses the heat of reaction corresponding to CO production this difference is even smaller, i.e. AT,., = 10.2%. The quoted values were obtained for e = 0.60, X = 100 and d,,, = I mm.) Hence, as a first approximation one may assume that the particle temperature is equal to the bed temperature. This assumption was used to generate the approximate values for the unknowns f., xjd and xZd, but the final values for these unknowns were obtained by solving the appropriate differential equations for the rate of change of particle temperature with size. Influence of the interphase mass transfer rate The model predictions of combustion efficiency and carbon loading as a function of mass transfer parameter are shown in Fig. 1. The single film diffusion limited model (DLM) predicts the highest combustion efficiency and the lowest carbon loading as expected on the basis of the previous discussion on the relative roles of kinetic and diffusional resistances. The carbon loading predicted by the KM2 model is lower than the one predicted by the KM1 model for all values of X, because more char is being consumed in the former than in the latter. However, this does not imply that the combustion efficiency predicted by the KM2 model will always be greater than the one predicted by the KMI model since in this case the unburnt CO leaving the combustor lowers the combustion efficiency. The predicted values of Q obtained using the KM2 model are greater for smaller values of X, while for larger values of X (i.e. X > 1.8) the KM1 predicts higher values for the combustion efficiency than the KM2 model. These predictions can be explained by analyzing the expressions for the rates of particle combustion for these two models-eqns (10) and (20). Although they are of similar form it should be noted that the lirst term in the denominator does not have the same value, since the particle temperature history is not the same for these two models. As the oxygen concentration in the dense phase increases with the increase of the interphase mass trans-
LOO-
T
yo.90 -
Fig. I. Influenceof interphasemass transfer rate.
I 003
co
IO
1.0
2.0
3D
XC-)
Fig. 2. Effect of mass transfer parameter on concentrations of oxygen and carbon monoxide.
fer rate (see Fig. 2), the particle temperature increases more rapidly in case of CO2 production than in the case of CO production at the particle surface. As a result of the rise in particle temperature the kinetic resistance decreases and the rate of particle combustion, and hence the combustion efficiency, predicted by the KM1 model becomes greater than the one predicted by the KM2 model, despite the fact that the oxygen concentration in the dense phase is greater for the latter model than for the former one (Fig. 2). The oxygen concentration at the top of the bed (xoz in Fig. 2) is related to combustion efficiency, i.e. lower oxygen concentration implies higher combustion efficiency. Tt is interesting to note that while the CO concentration in the dense phase decreases, the exit CO concentration slightly increases with increase of X. The latter fact has an adverse effect on combustion efficiency, as can be seen in Fig. 1 where the t),vs X curve passes through a maximum (albeit rather flat) as X increases. This somewhat surprising result is characteristic for the particular kinetics in the study (i.e. COW secutive reactions in which the CO is an intermediate product). A similar problem has been studied earlier by Jones and Pyle [13], but these authors were concerned with the problem of maximizing the yield of an intermediate product, while in the present case the intermediate product is an undesirable one. influence of bed temperature The effect of bed temperature on the predicted values of combustion efficiency which were obtained using the DLM model and the two kinetic models is illustrated in Fig. 3. The values of combustion efficiency predicted by kinetic models decrease significantly at lower bed temperatures, while the DLM model predicts a slight in-
22
D. BUKURand N. R. AMUNDSON
600 P t t’ 500
300 900
1000
1100
1200
Tb (‘K)
Fig. 4. Multiplicity of steady states. T,,(‘K)
Fig. 3. Jnhence of bed temperature.
crease in combustion efficiency. The reasons for the latter behavior were discussed in Ref. [l]. The relative sensitivity of model predictions to changes in bed temperature clearly demonstrates the ;mportance of the kinetic resistance at the particle surface. It is obvious that the DLM model cannot be used for prediction of an AFBC performance for values of bed temperature of practical interest. Another difference between the diffusion limited models and the kinetically limited models is that the former do not predict the existence of multiple steady states (Fig. 4) while the kinetic models do over a wide range of parameters which are relevant to the design of large scale utility boilers. The results obtained using the KM1 model are shown only in Fig. 4. (The curves obtained using the KM2 model are only slightly displaced from the ones shown for the KM1 model.) Only two branches corresponding to an ignited and an intermediate steady state are shown in Fig. 4 while the third branch corresponding to an unignited steady state is not shown. The intermediate steady states are probably unstable, but nevertheless the existence of multiple steady states still has an important bearing on the design of AFBC since the proper start up procedure must be maintained to assure that an ignited steady state will be achieved. Influence of excess air Combustion efliciency increases with the increase of excess air, the rate of increase being the greatest for the DLM model and the smallest for the KM2 model (Fig. 5). The curves obtained using the DLM model overpredict the combustion efficiency, and the relative position of the curves obtained from the kinetic models can be explained in terms of oxygen concentration in the dense
phase as it was done when discussing the influence of X (The increase in the rate of interphase mass transfer at a constant level of excess air has the same effect as the increase of excess air for a fixed value of X, i.e. both tend to increase the oxygen concentration in the dense phase and thus the rate of combustion.) Injtuence of particle feed size The importance of particle feed size (both fuel and sorbent) is illustrated in Figs. 6 and 7. In general, the combustion efficiency increases with an increase in char particle feed size, but in some cases there may be an optimal particle feed size which gives the highest combustion efficiency (DLM and KM1 models for X = 1.4 in Fig. 6). The curves for the kinetic models also pass through a minimum at a very small particle feed size, but
Fig. 5. Influence of excess air.
Fluidized bed char combustion-kinetic
0.20
7
2 0. IO
2.0
1.0
3.0
d&d Fig. 6. Influence of char particle feed size (d,, = 1.5 mm).
o.e5
0.10
0.75
0.05
065
2.0 d,,hm)
Fig. 7. Influenceof char particle feed size (d,, = 1mm).
this is not shown in the figures. The reasons for existence of a maximum and a mimimum have been discussed in [l]. According to the kinetic model predictions the design value of combustion efficiency of 90% (Combustion Engineering (141) for a commercial size unit of dimensions similar to the ones used in our numerical calculations (Table 6 of [l]), wouldbe obtainedfor X = 2 and mean char particle feed sizes in the range l-2 mm (Fig. 6). This value of the mass transfer parameter is more
models
23
reasonable than the value X = 1.2, which was deduced on the basis of DLM model predictions in Ref. [I]. The predictions of carbon loading are very sensitive to char particle feed size, and for particle sizes in the range of l-2 mm these predictions are reasonable, but still somewhat higher than expected (particularly in the case of the KM1 model). The curves shown in Fig. 7 were obtained for a smaller sorbent particle feed size (i.e. d,, = I mm) and this results in a considerable reduction of combustion efficiency, as can be seen by comparing the values of qc in Figs. 6 and 7 which correspond to the same values of X and d,,. It is obvious that at such a high superficial gas velocity (i.e. U -3.4 m/s) one must use larger sorbent particles in the feed in order to achieve a reasonably high combustion efficiency. However, the use of large sorbent particles in the bed which operates at high gas velocity will have an adverse effect on SO1 capture, and this imposes certain restrictions on design of AFBC units. Influence of operating conditions on CO emission from the bed The purpose of this section is to illustrate the influence of selected operating conditions on CO emissions from the bed, and to compare KM2 model predictions with existing experimental data. As in the case of model predictions of combustion efficiency and carbon loading this comparison will be only a qualitative one, i.e. no attempt is made to simulate any particular set of experimental data. The calculations were performed using the standard values of mode1 parameters (Table 8 of Ref. [ll) and the kinetic rate expressions (1) and (2) unless otherwise indicated. In most of the experimental studies only the CO concentration in the flue gas is reported (e.g. Skinner[l5], Campbell and Davidson[l6], Walters[17]) and this is not sufficient for a meaningful comparison of model predictions and experimental data to be made. Only the experimental studies of Gibbs and Beer[lSl, Gibbs et al. [19] and Gibbs and Hedley [20] provide information on CO concentration profiles inside the bed, and the CO concentration above the bed surface in the freeboard region as well as in flue gas, thus enabling one to test the model predictions. It was found in these experimental studies that the CO concentration in the flue gas increases with decrease in bed temperature, while it decreases with increase of excess air. The model predictions of CO concentrations at the bed exit are shown in Figs. 8 and 9. The CO concentration passes through a maximum as the bed temperature decreases (full line curves in Fig. 8). This qualitative behavior is to be expected, since at very low bed temperatures there will be no CO production at all, and at high bed temperatures all CO produced will be completely burnt. However, it should be realized that the bed temperature at which the CO concentration reaches a maximum as well as the magnitude of this maximum concentration are strong functions of the relative rates of the heterogeneous char oxidation reaction and the homogeneous CO oxidation reaction, which govern the rate of production and consumption of CO respectively.
24
D. BUKUR and N. R. AMUNDS~N
5.07
o.ol 900
1000
1100
1200
T,(“K)
Fig. 8. Effect of bed exit (-
temperature on CO Ei = 17976, ----
concentration at the bed Ei = WOO).
5.0
40
0.10
0.20
0.30
et-1
Fig. 9. Effect of excess air on the exit concentrations of carbon monoxide and oxygen. In order to illustrate this point calculations were performed by arbitrarily reducing the activation energy for the heterogeneous char oxidation reaction by a factor of two approximately (i.e. E’ = 9OOO),and by determining the corresponding value of the preexponential factor in the kinetic rate expression (1) from a condition that the values of modified rate constant and the original one are equal at 1100°K. The effect of this modification is to increase the rate of production of CO at lower bed
temperatures, aad this gives higher values for the CO concentration leaving the bed (see the broken line curves in Fig. 8). The presence of volatiles in coal is expected to have the same effect, because the rate of devolatilization is high even at low bed temperatures. The experimental results of Gibbs et a[.[191 clearly support the latter conclusion, as they show that CO emissions from a bed burning relatively low volatile char are significantly lower than the ones resulting from combustion of coal with a greater content of volatile matter. Various investigators, [8], [ 15-171, have reported different values for the temperatures (9%1050°K) at which the concentration of CO starts to increase rapidly. This may be explained, in light of the previous discussion, in terms of differences in fuel reactivities and their volatile matter content. The influence of excess air on CO concentrations leaving the top surface of the bed is shown in Fig. 9. The CO concentration is not significantly affected by the change in excess air, and it may slightly decrease (X = 30) or increase (X = 1.4) with an increase in the excess air depending on the interphase mass transfer rate. A possible explanation for a minor effect which the excess air has on the CO concentration inside the bed is that the oxygen concentration increases with an increase of excess air, and this tends to increase both the rate of CO consumption and the rate of CO production. The net result of these two opposing factors is that the CO concentration does not change significantly. The experimental results of investigators, 1181and [ 191, who have sampled the gas below the bed surface show that the CO concentration is essentially independent of the excess air level in the bed, which is in a qualitative agreement with the model predictions. The importance of excess air is to provide a sufficient amount of oxygen (see Fig. 8) to burn CO in the freeboard region and thus to reduce the CO concentration leaving the combustor to an acceptable level. This was clearly demonstrated by Gibbs and Beer and their associates in a series of carefully planned experiments carried out in a pilot plant coal combustor at She%eld[l8-201. Their measurements show that the CO concentration in the freeboard region and in the off-gas decreases with an increase of excess air. In order to further reduce CO emissions from tluidized bed combusters these authors have proposed the introduction of secondary air above the bed surface. The bed temperature also has a strong influence on the extent of CO oxidation in the freeboard region (Gibbs et a!.[ 19]), and Sarofim and Beer[21] have tackled this problem theoretically. A detailed investigation of reactions in the freeboard region is necessary in order to predict the emissions of major gaseous pollutants from an atmospheric fluidized bed combustor, but this problem is beyond the scope of present study. CONCLUSIONS
The kinetic resistance for the heterogeneous char oxidation reaction is greater than the resistance due to mass transport of oxygen from the gas to the particle surface at temperatures which are typical for atmospheric
25
Fluidized bed char combustion-kinetic models fluidized bed combustors (i.e. Tb= 1050-l 150°K). The predicted values of combustion efficiency and carbon loading obtained using two kinetic models, which differ with respect to the position of CO burnout, are not the same in general. The differences in model predictions of combustion efficiency are in the range of l-3%. The kinetic model in which it is assumed that CO burns outside the boundary layer (KM2) is recommended for use in Auidized bed combustor simulation studies, because of its capability of predicting CO emissions. The kinetic models correctly predici the effects of changing bed temperature, fuel and sorbent particle feed size and excess air. The model predictions of carbon loading are reasonable for small particles in the feed, but the models tend to overpredict it for relatively large char particles, This is attributed to large particle breakage and attrition upon entering the bed, which are not taken into account in the present models. The models predict that the combustion efficiency can be improved by using large char particles in the feed in order to reduce the ellutriation loss. Higher combustion efficiencies are also obtained for larger sorbent particles in the feed, but it is realized that this may have an adverse effect on SOz capture. Both kinetic models predict the existence of multiple steady states for values of parameters which are relevant to design of a large scale utility boilers, and this is important for start up procedures. The model predictions of CO concentrations at the top of the bed are also in a qualitative agreement with the existing experimental data. CO emissions from the bed are very sensitive to changes in the kinetics of char oxidation and for homogeneous CO oxidation reactions, and reliable reaction rate expressions are needed for quantitative predictions. It is shown that the bed temperature at which the rapid increase in CO concentration occurs, is a function of fuel reactivity and its volatile matter content. Acknowledgment-This work was supported by the Department of Energy Grant ET-78-G-01-3020and by the University of Houston. NOTATION
Symbols appearing in the text, but which are not listed below are defined in Ref.[l]. B constant defined after eqn (9) bz dimensionless constant defined after eqn (21) b, dimensionless constant defined after eqn (13) El activation energy for heterogeneous reaction between the carbon and oxygen E4 activation energy for homogeneous CO oxidation reaction dimensionless group defined after eqn (10) integration constant defined by eqn (7)
dimensionless group defined by eqn (26) reaction rate constant for C t 02 reaction preexponential factor for C + 02 reaction reaction rate constant for CO + 40, reaction preexponential factor for CO t ;O, reaction ratio of diffusional kinetic resistance for C t OZ reaction universal gas constant reaction rate for C t O2reaction reaction rate for CO+ :O, reaction mean value of mole fraction of jth species in the bubble phase mole fraction of jth species at the particle surface ratio of superficial gas velocity and minimum fluidization velocity
REFERENCES
1. Bukur D. B. and AmundsonN. R., Chew. Engng Sci. 198136 1239. 2. Field. M. A., Gill. D. W., Morean, B. B. and Hawkslev, P. G. W., Comhu&on ‘of Pulverizes Coal, BCURA Leatherhead, Cherev and Sons. Ltd., Banburv, England (1967). 3. Mulcahy M. F. R. and Smith I. W.,-Rev. Pure Appl. Chem. 196919 81. 4. Smith I. W., Fuel 197858 409. 5. Laurendean N. M., Frog. EnergyCambust. Sci. I9784 221. 6. Dutta S.. Wen C. Y. and Belt J. R.. Ind. Eww __ Chem. Proc. Des. De;. 1977I6 20. 7. Zabrodskv S. S. and Parnas S. S.. Institute of Fuel, Sump. Ser. No. 1, Paper B5, London (1975). 8. Basu P., Broughton J. and Elliot D. E., Institute of Fuel, Symp. Ser. No. 1, Paper A3, London (1975). 9. Caram H. S. and AmundsonN. R., Ind. Engng Chem.Fundls, 197716 171. 10. Mon E. and AmundsonN. R., Ind. Engng Chem. Fundls 1978 17 313. 11.Sundaresan S., Personal communication, University of Houston (1980). 12. Howard J. B., Williams G. C. and Fine D. H., Proc. 14th Symp. (Znt.on Combustion, p. 975, The CombustionInstitute, Pittsburgh (1973). 13. Jones B. R. E. and Pyle D. L., Chem. Engng Sci. 1970 25 859. 14. Combustion Engineering, Preliminary design study for a fluidized bed demonstration unit. TID-28598,Final Rep. (Zune 1978). 1.5.Skinner D. G., Fluidized Combustion of Coal. Millsand Boon MonographNo. CE/3, London (1974). 16. Campbell E. K. and Davidson J. F., Institute of Fuel, Symp. Ser. No. 1, Paper A2, London (1975). 17. Walters P. L., Institute of Fuel, Symp. Ser. No. I, Paper C6, London (1975). 18. Gibbs B: M. and Beer J. M., Proc. of Combustion Instif. EuroDean Znstifute, p. 627. Academic Press, London (1973). 19. Gibbs B. M., Pereira F. J. and Beer I. M., Institute of Fuel, Symp. Series No. 1, Paper D6, London 1975. 20. Gibbs B. M. and Hedley A. B., Proc. 17fh Symp. (Znt.) on Combusfion, p. 21I. The Combustion Institute, Pittsburgh ( 1979). 21. Sarofim A. F. and Beer J. M., Proc. 17th Symg. (fnt.) on Comb&on, p. 189. The Combustion Institute, Pittsburgh (1979).
Vol. 31. No. I, PP. 17-25,
1982
W9-25CW32/01Ctl1740$02.~W/0 PErgarm” Press Lid.
FLUIDIZED BED CHAR COMBUSTION KINETIC MODELS DRAGOMIR BUKURt and NEAL R. AMUNDSON* Department of Chemical Engineering, University of Houston, Houston, TX 77004, U.S.A (Received 1I September 1980; accepfed 25 March 1981) Abstract-The effect of the kinetics of the heterogeneous reaction between the char and oxygen, and the importance of the subsequent homogeneous oxidation of carbon mo?oxide on the performance of an atmospheric Ruidized bed combustor have been examined by a comparative analysis of three models. Numerical calculations illustrating the effect of operating variables such as bed temperature, fuel and sorbent particle Feed size and excess air were performed For values of the parameters which are pertinent to the design of large scale utility boilers. It is found that the kinetic models predict existence of multiple steady states over a wide range of operating conditions and values of model parameters. The model predictions of combustion efficiency, carbon loading and CO concentrations are in qualitative agreement with experinental data reported in the literature. INTRODUCTION
where C,, is the oxygen concentration at the particle surface, El’ = El/R, = l7,976(“K) and koI = 535.3(m/s). This expression is based on the external particle surface area which is consistent with our assumption that the shrinking core model is applicable for combustion of relatively large char particles. The heterogeneous reaction between the char and carbon dioxide is not taken into account in our model for two reasons. Firstly, the rate expression (1) of Field et al. [Z] is believed to give the overall rate of carbon consumption by all reactions, and secondly the rate of reaction between the carbon and COz is too slow to compete with the carbon oxidation by O2 under the conditions prevailing in fluidized bed combustors. This conclusion is based on the kinetic rate expression of Dutta et al.[6] and others (e.g. see Laurendeau [5]) for the C + COr reaction. As discussed in Ref.[I], it is fairly well established that carbon monoxide is the primary product of reaction between the carbon and O2 for temperatures which are typical for fluidized bed combustors, but it is rather uncertain where the subsequent CO oxidation takes place. The assumption that the homogeneous reaction between CO and 02 is instantaneous and that no oxygen reaches the particle surface, which is known as the double film theory of particle combustion, was shown not to be valid for conditions prevailing in fluidized bed combustors (Zabrodsky[7], Basu et al.[8], Bukur and Amundson[l]). Basu et al.[81 modified the double film theory by assuming that oxygen reacts instantaneously with CO, but that it also reaches the particle surface where it reacts with the carbon. However, the proposed combustion mechanism appears to be inconsistent to us. Caram and Amundson[9] and Mon and Amundson[lO] studied the problem of singIe carbon particle combustion with a finite reaction rate for CO oxidation inside the boundary layer under conditions which are typical for pulverized fuel combustion and/or combustion of single particles in the air or in pure oxygen. They found that the CO may be completely or only partially burnt inside the boundary layer. The extent of CO combustion is dete:mined by particle size, ambient temperature, and oxygen concentration, Sundaresan [ 1I] studied the same problem but using values of parameters which are typical for
In our recent paper [l] two models for fluid&d bed combustors based on the single film and the double film theory of char particle combustion were analyzed by assuming that the rate of the reactions are controlled by the rate of mass transport of reactant from the gas phase
to the particle. On the basis of predicted values of the char particle temperature it was found that the double film combustion mechanism must be discarded and that the reaction kinetic resistance is not negligible. The purpose of this study is to examine the effect of the kinetics of the heterogeneous char oxidation reaction on fluidized bed combustor performance for values of the parameters which are relevant to the design of large scale utility boilers. The carbon monoxide which is produced at the particle surface can be oxidized immediately at the particle surface or inside the stagnant gas boundary layer surrounding each particle or in the interstitial volume. In this study the two limiting cases, CO oxidation at the particle surface and CO oxidation in the interstitial volume, are analyzed, which enables one to test the model sensitivity with respect to the assumption of where the CO oxidation takes place. KINETICS
In spite of intensive research on the heterogeneous reaction between carbon and oxygen, the kinetics of this reaction is still subject to a great deal of uncertainty (e.g. Field et a1[2], Mulcahy and Smith[3], Smith[4] and Laurendeau[5]). The reported orders of reaction with respect to oxygen are between zero and one, and the values of activation energy are in the range between 62 and 335 kJ/gmol. In the present study the rate expression of Field et al.[2], which was obtained on the basis of analysis of experimental data by several investigators, has been used in numerical calculations, i.e. RI = k,C,, = k,,T, exp(-E,‘/TC)C3,
(ky$C)
(1)
*Author to whom correspondence should be addressed. Wesent address: Department of Chemical Engineering, Texas A & M University College Station, TX 77843, U.S.A. CES Vol. 37. No. I--B
17
D. BIJKUR and N. R.
18
fluidized bed combustors, and his results show that most of the CO leaves the boundary layer unreacted. From the above discussion it is obvious that in the rigorous analysis one should allow for a finite rate of CO oxidation both inside and outside the boundary layer, but this would considerably increase the complexity of the problem. In order to estimate the effect of CO oxidation on the FBC performance, we have chosen to study the following two limiting cases: (I) the CO burns at the particle surface, or (2) CO oxidation takes place outside the boundary layer. The overall reaction rate expression of Howard et af.[12] for homogeneous oxidation of CO has been used in all numerical calculations:
AMUNDSON
obtained as a solution of eqns (3) and (6b)
The integration constant is determined from the boundary condition (6a), giving
K13 =D,k,R,‘+*;jd,Rc
and the oxygen mole fraction at the particle surface is then given by
R4 = kaCcoC~~C~~o = k04exp(-E41/Tb)CCOC~~C~~~ (2) where Ed’ = EAR, = 15,098(X) 1.3 x 10”(m3/kmol). CO COMBUSTION
and
x3, =
X3d
x3(&) =
(8)
kw= The value of oxygen concentration at the particle surface is greatly affected by the dimensionless ratio of diffusion and kinetic resistances, i.e.
AT THE PARTICLE SURFACE (KM11
The model to be considered represents an extension of the diffusion limited single film model @FM) which was analyzed in our previous paper [ I] by taking into account the effect of the finite kinetic resistance at the particle surface, Thus, the mass balance equations for the solids and the gaseous species in the bubble and dense phase derived in [l] can be used directly by substituting the appropriate expression for the rate of particle combustion which will be derived next. By assuming that the CO produced is immediately oxidized at the particle surface, the overall reaction rate is C+OZ=COZ;
(7)
- l/b)
R _ kl(T,)R, _ diffusional resistance D kinetic resistance This ratio is a strong function of particle temperature and particle size. For kinetically controlled reaction (i.e. low temperatures and/or small particles) R +O and ~3~+x3d while for a reaction which is controlled by the rate of mass transfer (i.e. high temperatures and/or large particles) R + m and xlS +O. Rate
of particle combustion
(shrinkage)
From the stoichiometry of the overall reaction at the particle surface it follows that
R,=k,Cq,.
Notation used in [I] is retained here, and only the new symbols will be explicitly defined. Mass conservation equations for gaseous species and the energy balance for the gas inside the boundary layer which were derived in [ 11will be restated for convenience.
After differentiation and rearrangement one obtains the following expression for the rate of particle shrinkage R(“)=dt=
dd,
D
rt+ I
d
B&d
(
1-k
(9)
>
and with d, = d,, at f = 0 where B =20X4&p,. In terms of the dimensionless particle size the above equation becomes
where iv, = -cD(ax,ia<).
(5)
These equations are subject to the following set of boundary conditions at .$= R, NY= -R, = -k,Cx,,,
N, = -AN,, T, = Tc
(6a)
and at 5 = b x, = X,d;
x3 = .x3,3;
T, = Tb.
(10) where K(T,) = kl(Tc)do,/2D. We note that when the rate of chemical reaction is much faster than the rate of mass transfer (i.e. K(T,) + I), the last expression reduces to the one for the diffusion limited reaction (see eqn (23) of Ref. [l]).
(6b)
The oxygen concentration profile in the boundary layer is
Energy balance for the char particle The energy balance for the particle which is at uniform
Fluidized
temperature is o~(Tb4-T~4)t+-AH,)k,Cx,,
19
bed char combustion-kinetic models
differential equations for a single particle in each iteration, while in the case of diffusion limited models these equations were integrated only once.
I 1 (11)
+k aT, g 8% .$=Rc
CO COhlBUSTION
OUTSIDE THE BOUNDARY
and T, = T,” at f = 0. The expression for the heat flux at the particle surface obtained by solving eqn (4) is of the form
as the KM2 model, it is assumed that oxygen reacts with carbon producing carbon monoxide which in turn diffuses away and reacts with oxygen in the dense and the bubble phase. Thus, at the particle surface we have the heterogeneous reaction (-AH31 Ct;O2-CO;
In numerical calculations this expression has been approximated with an error which can be shown to be less than 1% by the following
From eqns (10) and (11) one can obtain the following expression for the rate of change of temperature with particle size
F
+
b,(T_
_
Tb)
a
IIK(Tc)+ r(l - rip) r’(l - rip)
(13)
where b3 = 3k,y,ICDM,&_+
R,=k,C,,
(16)
and outside the boundary layer homogeneous oxidation of CO which is catalyzed by water vapor, i.e. Ct)+$O*Z
~=p,[~+(l-$)](T~-TV)-
LAYER (KMZ)
In this model, which will subsequently be referred to
COz; Rq = k&,C::C& (17)
Single particle equations If one neglects the bulk flowof gaseous species arising
from unequal molar counter-diffusion, the mass balance equations are the same as in the previous model (eqns (3) and (5)). This can be done without aily appreciable error since the system is diluted by an inert componentnitrogen. The boundary conditions at the particle surface need to be modified according to the stoichiometry of reaction (16)giving at f = R,
The culculation procedure The general procedure for generating a solution for this model is similar to the one described in detail for diffusion limited models in Ref.[l], so that only the essential features will be described here. As shown in [l] the solution of the solids and gaseous species mass balances reduces to finding a solution of the following system of two nonlinear equations
The oxygen mole fraction at the particle surface obtained as the solution of eqns {3), (5), (6b) and (IS) is given by
(14)
Rate of particle combusfion From the stoichiometry of the heterogeneous reaction at the particle surface (16). the following expression is obtained for the rate of change of particle size
gzcf. hi)
= X3”-
X3d *
‘
I
N,=-;R,,
T, = T,
Nz=-2N3,
x,.=x,(%-R=)=
6r d,‘l(d,,d,,)dd, = 0 mud 0 US)
where in the present case R(d,) is given by eqn (9) and is a function of particle temperature and size. The calculation procedure is as follows. First, one assumes values for fs and xla and then integrates eqn (13) to obtain the particle temperature and the rate of particle combusion as a function of particle size. When the rate of particle combustion is known one can find a solution of the system of eqns (14) and (IS). The entire procedure is repeated until convergence is obtained. Wifh the correct values of f. and xjd one can calculate all the desired quantities as described in [l]. The computational procedure for this model requires numerical integration of
(18)
(19)
or in terms of the dimensionless particle size dr
;
r(O)= I
(20~
Energy balance for the particle The energy balance for the particle is of the same form as in the KM1 model (eqn (11)). If one approximates the heat flux at the particle surface by eqn (12), one obtains the
D. BUKURand N.
20
following expression for the rate of change of particle temperature with size.
with T, = T,” at r = 1 and where b2 = 3y, (-A&)i~J&. Mass balance equations for gaseous species
The mass balance equations for the solids derived in [l] can be used in the present case as well by inserting the expression for the rate of particle combustion (19) where required. However, the mass balance equations for gaseous species need to be modified by taking into account the homogeneous oxidation of CO in the bubble and the dense phase. The change in total number of moles can be neglected, because of the large amount of diluent in the system, as well as due to the fact that most of the CO produced is converted into CO?. Since there are two independent reactions in the system it is sufficient to consider the mass balance equations for two species only (02 and CO), while the concentration of the third species (COZ) can be determined from the stoichiometry of eqns (16) and (17). The mass balance equations for OJ = 3) and CO(j = 2) in a dimensionless form are as follows. Bubble phase: +
= X(XZI - XZb)- X4bXZbX :;*; X%(O)= 0
F =X(XJI
- X3b)- y
(22)
xuJ:62;x3*(0) = X3” (23)
Dense phase: do‘ XzO- XZd+ (0 - 1)X(& - XZd)- KI - piL,x,,x:z
d:l(dc,d,c)ddc
I0
= 0
(24) dot
x3O-
X3d +
(/3- 1)X(.& - XU) - $
d,21(d,, d,, )ddr
I0
- ; KIdXZdX :‘,’ = 0
(25)
where K4b = (H -H,,)k,(Tb)Cx&IU
- U,,
8& = H,,~,,,,k,(TXx&lU
KI = 3ycF,cP/McdZcNt”; 8=LlUm,;
fib =
I I
xi(s)
ds
(26)
XI0 = x*O = 0. o
The mole fraction of COZ in the dense or in the bubble phase is calculated as x,*
=x,"t x3” -
x*O- X2k 2
X3r t -
(k = b or d). (27)
R. AMUNDSON The calculation
procedure
The numerical solution of equations describing this model requires more computer time than the previous models (DLM and K&U), but the general calculation procedure is similar for all models. The computational procedure is initiated by assuming initial values for the three unknowns fs, x2d and x,d. Then, the differential equations (22) and (23) for the bubble phase are solved numerically in order to obtain the concentration profiles +(s) (j = 2,3), which are needed for calculation of .Zjb by numerical quadrature. The differential equations for a single particle (20) and (21) are also integrated numerically, and the calculated values of I?(&) are substituted into eqns (14),(24) and (25). The solution of the resulting system of these nonlinear algebraic equations is obtained by the Newton-Raphson method and the whole procedure is repeated with the new values for the unknowns until convergence is obtained. The inlet gas feed temperature which corresponds to the given bed temperature is calculated from eqn (34) of Ref. [I], and the combustion efficiency is given by
where
PREDICTION
OF COMJWSOR
PERFORMANCE
Numerical values of parameters and the correlations used in computations are taken from Ref. [l] (Tables l-8). In the case of CO combustion outside the boundary layer (KM2) the molar flow rates of COZ and CO leaving the combustor given in Table 5 of [l] are modified by taking into account the stoichiometry of the reactions (see eqns (27) and (29)). In all calculations the standard values of model parameters (Table 8 of [l]) were used unless indicated otherwise. Preliminary calculations have indicated the importance of the kinetic resistance for a reaction between oxygen and carbon at the temperatures which are typical for fluidized bed combustors (i.e. I’,,= 1050-l 150°K). Under these conditions the kinetic resistance is greater than the diffusional resistance, and only at temperatures above 1200°K the latter becomes dominant. This has the important implication that the thickness of the boundary layer b does not have a significant effect on the rate of particle combustion. Hence, in all calculations the dimensionless parameter p was evaluated as p = 6 X 10m3/&,,,where d,, is given in meters. A change of particle emissivity E, in the range of 0.6-1.0, was found to have only a minor effect on the model predictions of combustion efficiency, and thus a value of unity is used in all calculations reported in this paper. A change in particle emissivity affects the difference in temperature between the particle surface and the bed to some extent but this temperature difference is not nearly as large as the one predicted by the diffusion limited model (SFM). (The largest tem-
Fluidired bed char combustion-kinetic
21
models
perature differences (AT,,, = T,,,, - i”,) predicted by the KM1 model is 54.S”K, while if one uses the heat of reaction corresponding to CO production this difference is even smaller, i.e. AT,., = 10.2%. The quoted values were obtained for e = 0.60, X = 100 and d,,, = I mm.) Hence, as a first approximation one may assume that the particle temperature is equal to the bed temperature. This assumption was used to generate the approximate values for the unknowns f., xjd and xZd, but the final values for these unknowns were obtained by solving the appropriate differential equations for the rate of change of particle temperature with size. Influence of the interphase mass transfer rate The model predictions of combustion efficiency and carbon loading as a function of mass transfer parameter are shown in Fig. 1. The single film diffusion limited model (DLM) predicts the highest combustion efficiency and the lowest carbon loading as expected on the basis of the previous discussion on the relative roles of kinetic and diffusional resistances. The carbon loading predicted by the KM2 model is lower than the one predicted by the KM1 model for all values of X, because more char is being consumed in the former than in the latter. However, this does not imply that the combustion efficiency predicted by the KM2 model will always be greater than the one predicted by the KMI model since in this case the unburnt CO leaving the combustor lowers the combustion efficiency. The predicted values of Q obtained using the KM2 model are greater for smaller values of X, while for larger values of X (i.e. X > 1.8) the KM1 predicts higher values for the combustion efficiency than the KM2 model. These predictions can be explained by analyzing the expressions for the rates of particle combustion for these two models-eqns (10) and (20). Although they are of similar form it should be noted that the lirst term in the denominator does not have the same value, since the particle temperature history is not the same for these two models. As the oxygen concentration in the dense phase increases with the increase of the interphase mass trans-
LOO-
T
yo.90 -
Fig. I. Influenceof interphasemass transfer rate.
I 003
co
IO
1.0
2.0
3D
XC-)
Fig. 2. Effect of mass transfer parameter on concentrations of oxygen and carbon monoxide.
fer rate (see Fig. 2), the particle temperature increases more rapidly in case of CO2 production than in the case of CO production at the particle surface. As a result of the rise in particle temperature the kinetic resistance decreases and the rate of particle combustion, and hence the combustion efficiency, predicted by the KM1 model becomes greater than the one predicted by the KM2 model, despite the fact that the oxygen concentration in the dense phase is greater for the latter model than for the former one (Fig. 2). The oxygen concentration at the top of the bed (xoz in Fig. 2) is related to combustion efficiency, i.e. lower oxygen concentration implies higher combustion efficiency. Tt is interesting to note that while the CO concentration in the dense phase decreases, the exit CO concentration slightly increases with increase of X. The latter fact has an adverse effect on combustion efficiency, as can be seen in Fig. 1 where the t),vs X curve passes through a maximum (albeit rather flat) as X increases. This somewhat surprising result is characteristic for the particular kinetics in the study (i.e. COW secutive reactions in which the CO is an intermediate product). A similar problem has been studied earlier by Jones and Pyle [13], but these authors were concerned with the problem of maximizing the yield of an intermediate product, while in the present case the intermediate product is an undesirable one. influence of bed temperature The effect of bed temperature on the predicted values of combustion efficiency which were obtained using the DLM model and the two kinetic models is illustrated in Fig. 3. The values of combustion efficiency predicted by kinetic models decrease significantly at lower bed temperatures, while the DLM model predicts a slight in-
22
D. BUKURand N. R. AMUNDSON
600 P t t’ 500
300 900
1000
1100
1200
Tb (‘K)
Fig. 4. Multiplicity of steady states. T,,(‘K)
Fig. 3. Jnhence of bed temperature.
crease in combustion efficiency. The reasons for the latter behavior were discussed in Ref. [l]. The relative sensitivity of model predictions to changes in bed temperature clearly demonstrates the ;mportance of the kinetic resistance at the particle surface. It is obvious that the DLM model cannot be used for prediction of an AFBC performance for values of bed temperature of practical interest. Another difference between the diffusion limited models and the kinetically limited models is that the former do not predict the existence of multiple steady states (Fig. 4) while the kinetic models do over a wide range of parameters which are relevant to the design of large scale utility boilers. The results obtained using the KM1 model are shown only in Fig. 4. (The curves obtained using the KM2 model are only slightly displaced from the ones shown for the KM1 model.) Only two branches corresponding to an ignited and an intermediate steady state are shown in Fig. 4 while the third branch corresponding to an unignited steady state is not shown. The intermediate steady states are probably unstable, but nevertheless the existence of multiple steady states still has an important bearing on the design of AFBC since the proper start up procedure must be maintained to assure that an ignited steady state will be achieved. Influence of excess air Combustion efliciency increases with the increase of excess air, the rate of increase being the greatest for the DLM model and the smallest for the KM2 model (Fig. 5). The curves obtained using the DLM model overpredict the combustion efficiency, and the relative position of the curves obtained from the kinetic models can be explained in terms of oxygen concentration in the dense
phase as it was done when discussing the influence of X (The increase in the rate of interphase mass transfer at a constant level of excess air has the same effect as the increase of excess air for a fixed value of X, i.e. both tend to increase the oxygen concentration in the dense phase and thus the rate of combustion.) Injtuence of particle feed size The importance of particle feed size (both fuel and sorbent) is illustrated in Figs. 6 and 7. In general, the combustion efficiency increases with an increase in char particle feed size, but in some cases there may be an optimal particle feed size which gives the highest combustion efficiency (DLM and KM1 models for X = 1.4 in Fig. 6). The curves for the kinetic models also pass through a minimum at a very small particle feed size, but
Fig. 5. Influence of excess air.
Fluidized bed char combustion-kinetic
0.20
7
2 0. IO
2.0
1.0
3.0
d&d Fig. 6. Influence of char particle feed size (d,, = 1.5 mm).
o.e5
0.10
0.75
0.05
065
2.0 d,,hm)
Fig. 7. Influenceof char particle feed size (d,, = 1mm).
this is not shown in the figures. The reasons for existence of a maximum and a mimimum have been discussed in [l]. According to the kinetic model predictions the design value of combustion efficiency of 90% (Combustion Engineering (141) for a commercial size unit of dimensions similar to the ones used in our numerical calculations (Table 6 of [l]), wouldbe obtainedfor X = 2 and mean char particle feed sizes in the range l-2 mm (Fig. 6). This value of the mass transfer parameter is more
models
23
reasonable than the value X = 1.2, which was deduced on the basis of DLM model predictions in Ref. [I]. The predictions of carbon loading are very sensitive to char particle feed size, and for particle sizes in the range of l-2 mm these predictions are reasonable, but still somewhat higher than expected (particularly in the case of the KM1 model). The curves shown in Fig. 7 were obtained for a smaller sorbent particle feed size (i.e. d,, = I mm) and this results in a considerable reduction of combustion efficiency, as can be seen by comparing the values of qc in Figs. 6 and 7 which correspond to the same values of X and d,,. It is obvious that at such a high superficial gas velocity (i.e. U -3.4 m/s) one must use larger sorbent particles in the feed in order to achieve a reasonably high combustion efficiency. However, the use of large sorbent particles in the bed which operates at high gas velocity will have an adverse effect on SO1 capture, and this imposes certain restrictions on design of AFBC units. Influence of operating conditions on CO emission from the bed The purpose of this section is to illustrate the influence of selected operating conditions on CO emissions from the bed, and to compare KM2 model predictions with existing experimental data. As in the case of model predictions of combustion efficiency and carbon loading this comparison will be only a qualitative one, i.e. no attempt is made to simulate any particular set of experimental data. The calculations were performed using the standard values of mode1 parameters (Table 8 of Ref. [ll) and the kinetic rate expressions (1) and (2) unless otherwise indicated. In most of the experimental studies only the CO concentration in the flue gas is reported (e.g. Skinner[l5], Campbell and Davidson[l6], Walters[17]) and this is not sufficient for a meaningful comparison of model predictions and experimental data to be made. Only the experimental studies of Gibbs and Beer[lSl, Gibbs et al. [19] and Gibbs and Hedley [20] provide information on CO concentration profiles inside the bed, and the CO concentration above the bed surface in the freeboard region as well as in flue gas, thus enabling one to test the model predictions. It was found in these experimental studies that the CO concentration in the flue gas increases with decrease in bed temperature, while it decreases with increase of excess air. The model predictions of CO concentrations at the bed exit are shown in Figs. 8 and 9. The CO concentration passes through a maximum as the bed temperature decreases (full line curves in Fig. 8). This qualitative behavior is to be expected, since at very low bed temperatures there will be no CO production at all, and at high bed temperatures all CO produced will be completely burnt. However, it should be realized that the bed temperature at which the CO concentration reaches a maximum as well as the magnitude of this maximum concentration are strong functions of the relative rates of the heterogeneous char oxidation reaction and the homogeneous CO oxidation reaction, which govern the rate of production and consumption of CO respectively.
24
D. BUKUR and N. R. AMUNDS~N
5.07
o.ol 900
1000
1100
1200
T,(“K)
Fig. 8. Effect of bed exit (-
temperature on CO Ei = 17976, ----
concentration at the bed Ei = WOO).
5.0
40
0.10
0.20
0.30
et-1
Fig. 9. Effect of excess air on the exit concentrations of carbon monoxide and oxygen. In order to illustrate this point calculations were performed by arbitrarily reducing the activation energy for the heterogeneous char oxidation reaction by a factor of two approximately (i.e. E’ = 9OOO),and by determining the corresponding value of the preexponential factor in the kinetic rate expression (1) from a condition that the values of modified rate constant and the original one are equal at 1100°K. The effect of this modification is to increase the rate of production of CO at lower bed
temperatures, aad this gives higher values for the CO concentration leaving the bed (see the broken line curves in Fig. 8). The presence of volatiles in coal is expected to have the same effect, because the rate of devolatilization is high even at low bed temperatures. The experimental results of Gibbs et a[.[191 clearly support the latter conclusion, as they show that CO emissions from a bed burning relatively low volatile char are significantly lower than the ones resulting from combustion of coal with a greater content of volatile matter. Various investigators, [8], [ 15-171, have reported different values for the temperatures (9%1050°K) at which the concentration of CO starts to increase rapidly. This may be explained, in light of the previous discussion, in terms of differences in fuel reactivities and their volatile matter content. The influence of excess air on CO concentrations leaving the top surface of the bed is shown in Fig. 9. The CO concentration is not significantly affected by the change in excess air, and it may slightly decrease (X = 30) or increase (X = 1.4) with an increase in the excess air depending on the interphase mass transfer rate. A possible explanation for a minor effect which the excess air has on the CO concentration inside the bed is that the oxygen concentration increases with an increase of excess air, and this tends to increase both the rate of CO consumption and the rate of CO production. The net result of these two opposing factors is that the CO concentration does not change significantly. The experimental results of investigators, 1181and [ 191, who have sampled the gas below the bed surface show that the CO concentration is essentially independent of the excess air level in the bed, which is in a qualitative agreement with the model predictions. The importance of excess air is to provide a sufficient amount of oxygen (see Fig. 8) to burn CO in the freeboard region and thus to reduce the CO concentration leaving the combustor to an acceptable level. This was clearly demonstrated by Gibbs and Beer and their associates in a series of carefully planned experiments carried out in a pilot plant coal combustor at She%eld[l8-201. Their measurements show that the CO concentration in the freeboard region and in the off-gas decreases with an increase of excess air. In order to further reduce CO emissions from tluidized bed combusters these authors have proposed the introduction of secondary air above the bed surface. The bed temperature also has a strong influence on the extent of CO oxidation in the freeboard region (Gibbs et a!.[ 19]), and Sarofim and Beer[21] have tackled this problem theoretically. A detailed investigation of reactions in the freeboard region is necessary in order to predict the emissions of major gaseous pollutants from an atmospheric fluidized bed combustor, but this problem is beyond the scope of present study. CONCLUSIONS
The kinetic resistance for the heterogeneous char oxidation reaction is greater than the resistance due to mass transport of oxygen from the gas to the particle surface at temperatures which are typical for atmospheric
25
Fluidized bed char combustion-kinetic models fluidized bed combustors (i.e. Tb= 1050-l 150°K). The predicted values of combustion efficiency and carbon loading obtained using two kinetic models, which differ with respect to the position of CO burnout, are not the same in general. The differences in model predictions of combustion efficiency are in the range of l-3%. The kinetic model in which it is assumed that CO burns outside the boundary layer (KM2) is recommended for use in Auidized bed combustor simulation studies, because of its capability of predicting CO emissions. The kinetic models correctly predici the effects of changing bed temperature, fuel and sorbent particle feed size and excess air. The model predictions of carbon loading are reasonable for small particles in the feed, but the models tend to overpredict it for relatively large char particles, This is attributed to large particle breakage and attrition upon entering the bed, which are not taken into account in the present models. The models predict that the combustion efficiency can be improved by using large char particles in the feed in order to reduce the ellutriation loss. Higher combustion efficiencies are also obtained for larger sorbent particles in the feed, but it is realized that this may have an adverse effect on SOz capture. Both kinetic models predict the existence of multiple steady states for values of parameters which are relevant to design of a large scale utility boilers, and this is important for start up procedures. The model predictions of CO concentrations at the top of the bed are also in a qualitative agreement with the existing experimental data. CO emissions from the bed are very sensitive to changes in the kinetics of char oxidation and for homogeneous CO oxidation reactions, and reliable reaction rate expressions are needed for quantitative predictions. It is shown that the bed temperature at which the rapid increase in CO concentration occurs, is a function of fuel reactivity and its volatile matter content. Acknowledgment-This work was supported by the Department of Energy Grant ET-78-G-01-3020and by the University of Houston. NOTATION
Symbols appearing in the text, but which are not listed below are defined in Ref.[l]. B constant defined after eqn (9) bz dimensionless constant defined after eqn (21) b, dimensionless constant defined after eqn (13) El activation energy for heterogeneous reaction between the carbon and oxygen E4 activation energy for homogeneous CO oxidation reaction dimensionless group defined after eqn (10) integration constant defined by eqn (7)
dimensionless group defined by eqn (26) reaction rate constant for C t 02 reaction preexponential factor for C + 02 reaction reaction rate constant for CO + 40, reaction preexponential factor for CO t ;O, reaction ratio of diffusional kinetic resistance for C t OZ reaction universal gas constant reaction rate for C t O2reaction reaction rate for CO+ :O, reaction mean value of mole fraction of jth species in the bubble phase mole fraction of jth species at the particle surface ratio of superficial gas velocity and minimum fluidization velocity
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