Ind. Eng. Chem. Res. 1995,34,3129-3138
3129
Modeling of Carbon Combustion Efficiency in Circulating Fluidized Bed Combustors. 1. Selection of Submodels and Sensitivity Analysis Juan AdBnez* and Luis F. de Diego Znstituto de Carboquimica (CSZC), P.O. Box 589, 50080 Zaragoza, Spain
The application of a specific model to coal combustion in circulating fluidized beds presents the initial difficulty of having to choose between the different submodels proposed in the literature, where some important discrepancies exist. Therefore, in this work a sensitivity analysis of the carbon combustion efficiency predictions to the different hypotheses, equations, and parameters defining the different submodels has been carried out. Thus, it has been found t h a t the hypotheses related to the radial and axial solid distributions and the possible combustion of the descending char particles in the annulus exercise a n important effect on the predictions when low-reactivity coals were considered, its importance being lower with high-reactivity coals. The same occurs when modifying parameters or equations referring to the reactivity of the char or t o the mass transfer around particles. However, those corresponding to the devolatilization type have no significant effect on the efficiency predictions. On the other hand, however, it has been found t h a t the hypotheses of the type of gas flow in the dense region has a medium sensitivity on the carbon combustion efficiencies.
Introduction Coal combustion in circulating fluidized beds is a developed technology for a great variety of fuels and installation scales. This technology has some advantages over bubbling fluidized beds, such as higher combustion effciencies and better control of SO2 and NO, emissions. Some models have already been proposed for circulating fluidized bed combustors (CFBCs). A classification of these models is shown in Table 1. As can be seen in this table, there are important differences between their different submodels, especially referring to CFB hydrodynamics. Thus, for the axial solid distribution in the bed, different assumptions are considered: a mean voidage in all of the bed, two or three regions of different voidage, or voidage existing a t each bed position as it is in the three-dimensional models. The radial solid distribution can be considered as uniform, with a core-annulus structure, or with a three-dimensional model. Another important difference is the dense region structure. There are models which assume that this region behaves as a bubbling fluidized bed, that the solids are completely dispersed in a continuous gas phase, and that there are clusters of solids suspended in a continuous gas phase. For the gas flow, the most common assumption is plug flow in the whole bed, even though some models assume perfect mixing of gas in each bed region and plug flow between regions. Other models assume plug flow in the dilute region and perfect mixing in the dense region. For the solids flow there are different assumptions: perfect mixing of solids in compartments with plug flow between them, perfect mixing of solids in each region with plug flow between them, or perfect mixing in the dense region and plug flow in the dilute region. The char combustion is usually modeled as a shrinking particle with mixed control by chemical reaction and gas film diffusion, even though in some cases only chemical reaction control is considered. The coal devolatilization can be considered as uniform in the dense region, instantaneous in the feed plane, or dependent on the coal type, particle size, and heating rate.
In this work, different versions of a global model, which are capable of predicting the carbon combustion efficiencies in a circulating fluidized bed combustor, are suggested and solved. With these versions, a sensitivity analysis has been carried out showing the submodels and critical parameters in the carbon combustion efficiency prediction. Furthermore, other submodels and parameters which, although formally more correct, complicate the model too much without improving the quality of the predictions have been found.
Combustor Modeling Bed Hydrodynamics. To calculate the hydrodynamic properties of the bed, mean particle size and density of solids in the bed (partially sulfated limestone, coal, and ashes) were used. Initially, it was assumed that the ashes had the same size distribution as the coal particles fed in the boiler, and then a fraction of them, P b r , had a breakage giving fines with a function of size distributions P t ( r ) l a s h experimentally determined. In this case the distribution of ashes generated in the combustion was calculated by the following expression:
The mean particle size (Sauter mean diameter) and density of the solids were calculated iteratively by solving the hydrodymanic model and taking into account the efficiency of recovery of solids by the cyclone. The ash fraction in the bed was used as convergence criterion through the following expression: k Xash,bed
k+l
- Xash,bed
< 10-5
Studies on solids distribution have demonstrated that, in general, the CFB can be divided into two zones, a dense region at the bottom and a dilute region at the top of the riser (Kwauk et al., 1986; Schnitzlein and Weinstein, 1988; Kat0 et al., 1989; Zhang H. et al., 1991). The dilute region had a core-annulus structure with solids rising through the core in a dilute suspension
0888-588519512634-3129$Q9.QQlQ 0 1995 American Chemical Society
3130 Ind. Eng. Chem. Res., Vol. 34, No. 9, 1995 Table 1. Models for Coal Combustion in CFB and Their Description a. Models author A l A 2 A 3 B C D E F 2 5 1 2 Basu et al. (1987) 3 1 4 1 5 1 4 1 2 1 Weiss et al. (1987) 2 4 3 Lee and Hyppanen(1989) 1 1 1 1 2 1 2 2 2 1 Bernardi et al. (1991) Zhang L. et al. (1991) 2 1 2 3 3 1 3 2 2 3 SenguptaandBasu(1991) 1 2 1 2 6 4 3 Hyppanen et al. (1991) 4 3 3 5 2 1 3 4 4 2 Mori et al. (1991) Arena et al. (1991) 1 1 3 1 4,5 5 2,3 1 Senior andBrereton(1992) 1 2 1 1 1 2 3 2 1 Wang et al. (1994) 2 1 1 1 b. Description Al. Hydrodynamic submodel. Axial solid distribution. 1.The bed is divided into three regions: dense, transition, and dilute. 2. The bed is divided into two regions: dense and dilute. 3. Uniform voidage in all of the bed. 4. Experimentally measured, with variations in the space and the time (three-dimensionalmodel). 5 . Experimentally measured. A2. Hydrodynamic submodel. Radial solid distribution. 1.There is no radial solid distribution. 2. There is no radial solid distribution in the dense region. core-annulus structure in the rest of the bed. 3. Experimentally measured (three-dimensionalmodel). A3. Separation between the dense and the transition and/or dilute regions. 1. In the secondary air injection. 2. By application of a hydrodynamic model. 3. Experimentally measured. 4. Not considered. B. Gas flow pattern in the bed. 1.Plug flow in all the bed. 2. Mixed flow in the dense region and plug flow in the rest of the bed. 3. Bed divided into compartments in mixed flow, but the dense region is a bubbling fluidized bed. 4. Mixed flow in each region. 5. Three-dimensional model. C. Model of solid flow. 1. Mixed flow in the dense region and plug flow with dispersion between the core and the annulus in the rest of the bed. 2. Bed divided into compartments in mixed flow. 3. The same as 2, but the dense region is only a compartment. 4. Mixed flow in each region. 5. Mixed flow in each region, but in the dense region the solids are in clusters. 6 . Three-dimensional model. D. Devolatilization of the feed coal. 1. Instantaneous devolatilization across the feed plane. Instantaneous combustion of volatiles. 2. Uniform devolatilization in the dense region. Instantaneous combustion of volatiles. 3. Instantaneous devolatilization across the feed plane. Uniform combustion of volatiles in all of the bed. 4. Devolatilization depending on rank coal, particle size, heating rate, and mixing solid rate. 5. Not considered. E. Kinetics of char combustion. 1. Chemical reaction control. 2. Control by chemical reaction and mass transfer in the gas film. 3. Control by chemical reaction, mass transfer in the gas film and difusion into the clusters. F. Heat balance around char particle. 1. Considered. 2. Consider a constant char particle temperature higher than the bed. 3. Not considered.
and solids descending near the walls in a suspension with higher solids concentration (Horio et al., 1988; Rhodes, 1990; Herb et al., 1992). Moreover, the rising
solid flux in the core and the descending solid flux in the annulus decreased when the height was increased, indicating the existence of a net solid transfer from the core to the annulus (Bolton and Davidson, 1989; Herb et al., 1992). However, in the mathematical modeling of CFBCs different hypotheses to calculate the axial and radial solid distributions in the bed were considered (Table 1). In this work, for the sensitivity analysis, three hypotheses are considered: (a) The radial and axial solid distribution in the dilute region of the bed are considered with a core-annulus structure. (b) The axial solid distribution is considered, assuming uniform radial distribution at each height. (c) The radial and axial solid distribution are considered uniform in all the bed. In the more complex case, hypothesis a, the model considers the bed as divided into two regions: a dense region at the bottom of the bed with a constant solid voidage of 0.82 (Ouyang and Potter, 1993; de Diego, 1994) and a dilute region in the upper part in which the solid fraction decreases exponentially with the bed height and was determined with the exponential decay model of Kunii and Levenspiel (1990) modified by Adlnez et al. (19941, by the following equations:
(1- E ) = [(l- E * )
W = Hd(l- Ed) 4
+ (E*
- cRo)exp(-ah,)l
-K
(3)
+ HA1 - E ) =
6
The K constant was calculated (Adanez et al., 1994) using expression 6, the solid fraction at the exit of the bed with expression 7, and the value of the solid fraction (1 - E * ) or the solid circulation flux above the transport disengaging height TDH (G*) with the equations proposed by Wen and Chen (1982).
K=
G, - G*
(6)
@SUP
(7) The principal parameter in this model is the decay constant a , defined at complete reflux, and the following equation to calculate its value was used (Adanez et al., 1994): a(uo - U J ~ D O . ~= 0.88 - 420d,
(8)
The dilute region was characterized by a coreannulus structure with the solids rising through the core with a voidage cc and descending through the annulus at a velocity of 1 m/s (Horio et al., 1988; Grace, 1990; Wang et al., 1993) in a denser suspension. It was assumed that the gas rises only through the core. To calculate the flow rate of solids rising through the core and descending through the annulus the Rhodes (1990) model was used. In this model the flow rate of solids transferred from the core to the annulus is proportional to the solid concentration present in the core and to the interface surface. The solid dispersion constant was calculated by the following equation which was deter-
Ind. Eng. Chem. Res., Vol. 34,No. 9, 1995 3131 ticles has the following system of equations:
P3(ri)Ari=
-- Wcl F3Ari
+ Wclr(ri)+ 3 Wclr(ri)Ari/ri Pi = Foi + Fli + F2i
A r
I
ttt Air
Figure 1. Density char size distribution functions and solid streams in a circulating fluidized bed combustor.
mined experimentally (de Diego et al., 1995):
k=- 0 14 uo - Ut The flow rate of entrained solids fkom the dense region was calculated by the following equation (de Diego et al., 1995):
Solid flow patterns in the dense region are complex and difficult to characterize. However, taking into account the incoming and outgoing solids flow rates of this region, perfect mixing of solids was considered. In the dilute region plug flow with dispersion of solids to the annulus was considered. In case b, the same equations to calculate the axial solid distribution as in case a were used. But in this case no distinction between core and annulus in the dilute region was made. Char Population Balances in the Bed. To make mass balances and determine carbon combustion efficiencies in a circulating fluidized bed with shrinking particles it is necessary to develop population balances of char particles in the dense region and in the dilute region. A circulating fluidized bed system as shown in Figure 1was considered for developing the population balances. The carbon streams in the reactor are the carbon in the coal feed FO(kg/s)which has a function of density of particle size Po(r), the carbon in the recirculation stream F1 (kg/s), with a density size distribution function Pl(r),and carbon in the solids descending near the wall F2 (kg/s) which has a density size distribution function P2(r). In the dense region there is a broad char particle size distribution with different reaction rates for each size. For the calculation of the overall char reaction rate in this region it is necessary to know the density function of char particles in the bed P3(r). For discrete particle size distributions, the population balance of char par-
when r(rJ corresponds to the shrinking rate of char particles of ri size. This system of equations was solved iteratively by working on the total carbon weight in the dense region, Wcl,and calculating values for Wcli a t each size interval until the convergence condition given by eq 12 was reached. In the first step P l ( r ) = Pz(7-1 = P3(r) was assumed to start the calculations.
Knowing P3(r) in the dense region the flow rates of carbon F1 and F2 were calculated for each char population. This was done by solving the population balances in the dilute region and taking into account the efficiency of solids recovery by the cyclone. To do this, the dilute region was divided into '100 compartments in series. In each compartment it was assumed that the solids were in perfect mixing with plug flow between compartments. An overall mass balance in each compartment gives the following expression:
+ T3j + C reacted to CO, F2j = FZj+,+ T3j- C,reacted to CO,
F3j-1= F3j
(13)
(14)
The flow rate of transmitted carbon from the core to the annulus, T3j, has the same particle size distribution as those present in thejth compartment of the core and was calculated with the following expression taking into account the hydrodynamic model considered. The population balance of char particles burning in each compartment j has the following expressions for the core and the annulus:
F323 P3j(ri)Ari= -= F3j
'
F%j P2j(ri)Ari= -F2j
The solution of population balances in each compartm e n t j allowed calculation of the carbon flow rate from the bed F4, which corresponds to the outlet of the last compartment, and the carbon flow rate coming into the dense region F2, which corresponds to the outlet of the first compartment of the annulus. With these values and knowing the solid recovery efficiency in the cyclone, the flow rate of streams F5 and F6 and their density size'
3132 Ind. Eng. Chem. Res., Vol. 34, No. 9, 1995
distribution functions P d r ) and P d r ) were calculated. The streams F5, F1, and F7 had the same density size function, because it was assumed that there was no combustion in the auxiliary bed (Weiss et al., 1987)due to the low temperature in this bed.
F5 = F , iF,
(18)
Moreover, the following mass balances, considering the rate of C combustion (kgh) in the bed, must be fulfilled:
F, = F6 4-F ,
+ C reacted
(19)
With Fo, F1, and F2 and their density distribution functions Po(r),Pl(r),and Pz(r) the population balance in the dense region was solved without the assumptions Pl(r)= P d r ) = P3(r). In this way an improved P3(r)was obtained and, therefore, new Pl(r) and P2(r). The process was repeated iteratively until convergence on the carbon concentration in the dense region was reached. The convergence condition was the following: k k + l < 10-6 (20) Xcl - XC1 The solution of population balances in the dense and dilute regions allowed calculation of the carbon flow rates in all the process streams. The carbon combustion efficiency was calculated with the following expression:
E, =
Fo - F6 - F , FO
x
100
+
(22)
The term Co2* indicates the effective oxygen concentration seen by the coal particles burning in the bed. This concentration depends directly on the hypotheses, on type of gas flow in the bed, and on devolatilization and volatile combustion considered. Therefore, the application of equations to solve the population balances was not direct, and these balances were solved at the same time as the oxygen profiles in the bed. Moreover, the secondary air modified the oxygen concentration profiles in the bed, increasing its value from the secondary air ports. The mass-transfer coefficient around a particle, k, = ShD,/d,, in the core of the dilute region was calculated from the Sh number using the equation proposed by Chakraborty and Howard (1981):
+
S h = 2~ 0.69(Re,/~)”~Sc’/~ (23) where Re, was calculated with the equation proposed by Basu et al. (1989):
Re, = egdp(ug- u J p
k,
= ShDJd,
In the first assumption the Sh number was calculated with the equation proposed by Chakraborty and Howard (1981) (eq 231, where
ug = U
= G d ~ , (l ~
d )
(26)
d , = d , (char particle diameter)
(27)
~ C ;U ,
and In the second assumption, two equations to calculate the S h number were proposed. Arena et al. (19911, assuming that the gas was stagnant in the clusters, used the following equation:
S h = 2c (28) and, in this case, dpj was the characteristic diffusional length which was calculated as the logaritmic mean between the average radius of char particles and the size of the lump of solids, whose radius was taken to be equal to the riser radius. On the other hand, from a study made in turbulent fluidized beds, Halder et al. (1993) assumed that the clusters were continuosly forming and destroying and then the char particles were in contact both with the clusters and the main gas stream, and proposed the following equation:
(21)
Shrinking Rates. Assuming the shrinking unreacted core model, with a mixed control by chemical reaction and mass transfer in the gas film and with a first-order reaction, the shrinking rates of char particles are given by the following expression: 12CO2* dr, = r ( rI ) = - dt e, j,( l l k , d,/ShDg)
particle was calculated with the following expression:
(24) and ug and us values were determined by solving the hydrodynamics submodel. In the dense region two assumptions were analyzed: one considers that the solids are completely dispersed on the gas stream, and the other that the solids are forming spherical clusters which entrap char particles. In this region the mass-transfer coefficient around a
where: D, = DglE,the clusters voidage, cclu,was taken as 0.5, and dpj = d,. In the assumption of char combustion in the annulus it was supposed that the oxygen went into the annulus by diffusion, with an infinite diffusion coefficient. In this condition S h = 2c was assumed. The kinetic constants referring to the external surface area were determined in a previous work (Adanez et al., 1993) and were obtained with the following expression:
k , = koTS1I2exp(-E,IRT,) (30) Although the bed is isothermal, the char particle temperature is higher than that of the bed. Therefore, the surface temperature which appears in the kinetic constant was calculated by simultaneously solving th’e heat balance for a particle which transfers heat to the medium by both convection and radiation, together with the reaction rate. Oxygen Concentration Profiles (Co,*). The oxygen concentration profile in the bed depends on the type of gas flow. In addition, the way in which the devolatilization and combustion of the volatiles take place will also affect the 0 2 concentration profile in the bed. Some authors (Helmrich et al., 1986; Bader et al., 1988; Martin et al., 1992) have found that the type of gas flow in circulating fluidized beds was plug flow. Therefore, in this work, this assumption will be used. However, and as seen in Table 1, different hypotheses for the type of gas flow were assumed in the models. For this, a comparison between model predictions using different hypotheses for the type of gas flow in the dense region of the combustor will be made. Futhermore, different hypotheses on devolatilization will be analyzed. Cyclone Solids Recovery Efficiency. The efficiency of solids recovery in the cyclone depends on its design. In this work the recovery efficiency standard
Ind. Eng. Chem. Res., Vol. 34, No. 9, 1995 3133 Table 2. Input Data Used in Sensitivity Analysis Analysis of Coals (wt %) moisture ash volatiles fixed C
Andorra
Lucia
12.4 32.9 22.8 31.9
1.3 18.8 10.6 69.3
C H N S
Andorra
Lucia
35.6 2.9 0.4 5.8
71.4 3.0 1.5 2.2
Feed Size Distribution (mm, wt %)
