Computations of a Circulating Fluidized-Bed Boiler with Wide Particle

A steady-state model of a coal-fired circulating fluidized-bed (CFB) boiler considering the hydrodynamics, heat transfer, and combustion is presented...
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Ind. Eng. Chem. Res. 2000, 39, 3212-3220

Computations of a Circulating Fluidized-Bed Boiler with Wide Particle Size Distributions Lu Huilin,* Bie Rushan, Liu Wenti, Li Binxi, and Yang Lidan Department of Power Engineering, Harbin Institute of Technology, 150001, China

A steady-state model of a coal-fired circulating fluidized-bed (CFB) boiler considering the hydrodynamics, heat transfer, and combustion is presented. This model predicts the flue gas temperature, the chemical gas species (O2, H2O, CO, CO2, and SO2), and char concentration distributions in both the axial and radial location along the furnace including the bottom and upper portion. The model of the gas-solid flow in the dilute regime calculates solid volume concentrations and local solid velocity. The model was validated against experimental data generated in a 35 t/h commercial CFB boiler with a low circulation ratio. Introduction Circulating fluidized-bed combustors (CFBCs) are considered as an improvement over the traditional methods associated with coal combustion. Operation of CFBCs at industrial levels has confirmed many advantages that include fuel flexibility, high combustion efficiency, low NOx emissions, and high sulfur capture efficiency. These characteristics ensure an ever-increasing number of successful commercializations of CFBC in power generation applications. Although CFBC technology is becoming more common from these commercial applications, there are some significant uncertainties in predicting their performances in large-scale systems. Technical knowledge about design and operation of a CFBC is widely available for designers and operators. However, little has been done in the field of mathematical modeling and simulation of combustion in CFBCs. This might be attributed to the fact that the combustion process occurring in a CFBC involves complex phenomena including chemical reaction, heat and mass transfer, particle size reduction due to combustion, fragmentation and other mechanisms, and gas and solid flow structure. Using a lumped-modeling approach, Weiss et al.1 and Arena et al.2 introduced a CFBC model by dividing it into several blocks, each corresponding to CSTR reactors for both the gas and solid phase. Lee and Hyppaueu3 presented a CFBC model that considered the riser as a plug flow reactor for the gas phase and a CSTR for the solid phase. The model also considers the feed particle size distribution and the attrition phenomena. Weiss et al.4 and Maggio et al.5 developed a model for circulating bed reactors including the riser, cyclone, loop seal, and external fluidized heat exchanger. Kudo et al.6 proposed a computer program to simulate flow and heat transfer in a circulating fluidized-bed boiler. Radiative heat transfer is modeled by using a Monte Carlo method. Das and Bhattacharya7 assumed the core-annular flow structure in the dilute regime and computed the char distributions in the CFB boilers. However, their model ignored the char combustion in the annular. Haider and Linzer8 considered the coal combustion, heat transfer, and particle distributions in the furnace and analyzed * To whom correspondence should be addressed. E-mail: [email protected]. Fax: +86-0451-3222.

the combustion and pollution emissions in the CFB boilers. Hannes et al.9 proposed a model considering the coal combustion and heat transfer and predicted the performance of CFB boilers. Sotudeh-Gharebeagh et al.10 developed a CFBC model based on ASPEN and predicted the performance of a CFBC in terms of combustion efficiency and emission levels. Hartge et al.11 proposed a three-dimensional model that was concerned with the effects of gas and particle mixing on the distribution of gaseous and solid species in the CFB boilers. However, most of the models mentioned above do not completely consider the performances of dense zone, and no special treatments are given in the dense zone. Generally speaking, the particle size distribution of bed material in a CFB boiler is in a very wide range. A calculated average particle diameter is not suitable for representing the behavior of the total bed particles. The particles will be segregated by the difference in diameters and densities. Only fine particles can be entrained with flue gas passing through the furnace. Most large particles remain in the bottom of the furnace. The particle concentrations are much higher in the bottom than in the upper portion of the furnace. The fluidization regime in the bottom may be a bubbling or turbulent fluidized bed. Leckner et al.12 and Svensson et al.13 examined this zone and found that it could be explained by the presence of bubble-like voids. They reported the height of the dense zone was about 1.0 m from the distributor in a 12 MW CFB boiler. Montat and Maggio14 also found that the dense zone is characterized by a bubbling bed, and the bulk density was in the range of 700-1000 kg/m3 in a 125 MW CFB boiler. These mean the combustion of coal, particles mixing, and heat transfer in the dense zone dominate the performances of CFB boilers. This paper attempts to predict the performances of a CFB boiler with the steady-state mathematical model considering the detailed hydrodynamics, heat transfer, and combustion, which include the dense zone and dilute region in the furnace. The model predicts the distributions of the gas concentration, chemical species, temperature, and heat flux along the furnace in both the axial and radial locations. The model was validated against experimental data generated in a 35 t/h CFB boiler of low circulation ratio and wide size distributions.

10.1021/ie9808054 CCC: $19.00 © 2000 American Chemical Society Published on Web 08/18/2000

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Modeling Approaches In the typical CFBC used for coal combustion, crushed coal together with limestone or dolomite and ash particles are fluidized by the combustion air entering at the bottom of the bed and at the secondary air injection points. The dense zone is assumed to operate in either the bubbling or the turbulent mode. The dilute region operates in the fast fluidized conditions, and the cross-sectional averaged solid concentration decreases along the height of the furnace. Because coal combustion and heat transfer in a CFBC is directly affected by its hydrodynamic parameters, both the hydrodynamic, heat transfer, and combustion model must be treated simultaneously to yield a predictive model for the CFBC. 1. Hydrodynamic Model. For steady-state conditions, the model considers that the CFBC is divided into two regions: a dense zone in the bottom and a dilute region in the upper portion of the furnace with a suspension density decaying with height. Dense Zone. The dense zone is fluidized by the primary air supply. Kunii and Levenspiel15 and Saraiva et al.16 treated the dense zone using the models developed originally for bubbling fluidized beds. This is inconsistent with the fact that the superficial gas velocity in this region is usually higher than the critical value where the region becomes turbulent. At this condition, bubble diameter and particle velocities are quite different from the bubbling regime. We assume that the dense zone consists of the bubble phase and emulsion phase. The emulsion phase voidage is constant at the minimum fluidization. Portions of gas flow through the emulsion phase at umf, and the rest of the gas, which is in excess of the minimum fluidization velocity, passes through the bed as bubbles. Bubble size varies with bed height and is assumed to be uniform across a given cross section throughout the bed. The gas concentration in the bubble phase, Cb, can be expressed along the height as

(

Cb ) Cp + (C0 - Cp) exp -

)

Kbebz βug

(1)

where Kbe is the mass-transfer coefficient between the bubble and emulsion phases predicted by a correlation proposed by Sit and Grace:17

Kbe )

2umf + 12(Dgmfub/Db)1/2 Db

(2)

The bubble diameter and bubble velocity, Db and ub, may be obtained using the correlation proposed by Mori and Wen.18 The fraction of flow within the bubbles, β, is predicted by

β)1-

umfke (1 - b) u0

(3)

and the coefficient ke is given by Saraiva et al.:16

(

ke ) 1 + 0.25

)

ubmf + 2 b umf

(4)

Dilute Region. The dilute region is suspended both by the combustion gases from the dense zone and by the secondary air supply. Hydrodynamic models, as proposed in most CFB literature regarding the dilute

region, are classified into three broad groups:19 (1) those predicting the axial profile of solid suspension density but failing to predict the radial variations; (2) those assuming two regions considering a core-annular flow structure to predict the radial variation; (3) those applying the fundamental equations of fluid mechanics to model gas-solid flow. Types 1 and 2 models, which are lumped models, can be easily coupled with reaction and heat-transfer models to simulation CFBC reactors. On the other hand, type 3 models become rapidly tedious when coupled to reaction and heat-transfer models because of the numerical complexity. For simulation purposes, we chose to apply a type 2 model to predict the axial and radial voidage profiles. The mean value of voidage between height Zi-1 and Zi can be calculated using the expression by Kunii and Levenspiel:15

ji ) / - (/ - 1) exp[-0.5a(Zi-1 + Zi)]

(5)

Data reported by Zhang et al.20 showed that the normalized radial void fraction was a unique function of radial distance. According to the expression suggested by Zhang et al., the center-line void fraction was approximated by cen ) av0.191. This value, however, appears to underestimate the actual void fraction inasmuch as it poorly accounts for the observed trends in solid mass flux. Solid mass flux is the product of the local density and local particle velocity. The local particle velocity is the highest at the center. For this reason, Patience et al. 21 recorrelated Zhang’s data with mass flux data and developed the relationship

0.4 - r 0.4



-

(Rr )

)4

6

(6)

where r is the local void fraction and  is the average void fraction that can be computed from eq 5. The local particle velocity can be predicted by the equation proposed by Godfroy et al.,22

[ ( )]

us,r ) (ug,c - ut) 1 -

r Rω0.5

R

(7)

where ω is the fraction of the cross-sectional area in which particles ascend and ug,c and ut are the gas velocity at the center and particle terminal velocity, respectively. The radial profile of gas velocity is assumed continuous and can be approximated by a power law type expression, similar to that proposed by Martin et al.23 It assumed the no slip boundary condition at the wall and that the gas velocity is maximum at the center. The local gas velocity can be calculated by the expression

ug,r )

ug,av γ[1 - (r/R)R]

(8)

where ug,av is the average gas velocity. The value of R varies between 1 and 7, where 1 approximates a triangular profile, 2 is parabolic, and 7 approximates a turbulent profile of gas velocity. The values of R, γ, and ω can be obtained using the correlations proposed by Godfroy et al.22 2. Reaction Model. Dense Zone. The reaction model allows for the determination of the chemical changes and the heat released during combustion. Since

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Table 1. Expressions of the Overall Reaction Rate E dCO 2

dz dCECO

-[

(u0 - ubb)

dz B dCO 2

{

1

)

)

[

∑R

(1 - b)

1,iξ

+ R2mf - 2φO2]

i

2

B E E - CO )b - CO + kbe(CO 2 2 2

}

d(Vb - ubb) dz

]

dVb 1 1 B E E B - R2b - kbe(CO - CO )b + (CO - CO ) 2 2 2 2 Vb 2 dz

[

1

)

(u0 - ubb)

dz

∑R

(

1,iξ

- R2mf + 2

i

∑R

3,iξ

- φCO)(1 - b) + kbe(CBCO - CECO)b - CECO

dz

i

[

]

d(Vb - ubb)

]

dVb dCBCO 1 -R2b - kbe(CBCO - CECO)b + (CECO - CBCO) ) dz Vb dz E dCCO 2

(u0 - ubb)

dz B dCCO 2

dz

1

)

)

{

[R2mf -

∑R

3,iξ](1

B E E - b) + kbe(CCO - CCO )b - CCO 2 2 2

dz

i

[

}

d(Vb - ubb)

]

dVb 1 B E E B R  - kbe(CCO - CCO )b + (CCO - CCO ) 2 2 2 2 Vb 2 b dz

C + 1/2O2 f CO:

R1 )

1 CO2RgTg 1/Kc1 + 1/Km 1

Kc1 ) 0.667 exp(-16 000/RgTg), CO + 1/2O2 f CO2: CO2 + C f 2CO:

R2 ) Kc2(CH2O)1/2(CCO)(CO2)1/2, R3 )

1 CCO2RgTg, 1/Kc3 + 1/Km 3

Km 1 ) 4D/(dpRgTg) Kc2 ) 1.3 × 1014 exp(-30 000/RgTg)

Km 3 ) 2D/(dpRgTg)

Kc3 ) 4.1 × 1010(RgTg)-1 exp(-59 200/RgTg)

coal combustion in the CFBC is quite complex, only the major steps of coal combustion are considered in the model. For steady-state conditions, we assumed that the coal, circulating particles, and limestone are fed into the bottom of the bed. The evolution of coal particles is assumed to be in three steps. In the first one, coal particles are dried (in this step temperature is given and equal to 100 °C) and heated until the devolatilization temperature is reached. The devolatilization time for a given particle class is obtained:24

( )

tv ) 10

1048 dp,i Tg

(9)

Since the time required for volatile combustion is very short, the devolatilization process is considered to take place at the dense zone and uniform distribution along the bed height. Char particle combustion is assumed to be controlled by surface reaction and gas diffusion. The char particle diameter after the combustion process is calculated by

(

dp,i ) dp,i,0

3

krtr 6 π dp,i,0Cchar

)

assumed to be equal to the bed temperature in the simulations. Dilute Region. The particles in the dilute region include particles coming from the dense zone and circulating particles from the separator. Only char combustion was considered in the model. We assumed that particles are sufficiently separated from each other that the single-particle combustion analysis is valid for each, the temperature is uniform in the inside of the particles, and the particle density remains constant. The concentrations of the chemical species are given as follows:16,25,26

dCO2

dz

)

1

[ ug

(10)

where kr and tr are the total reaction rate of char particles and the residence time, respectively. The concentrations of chemical species can be expressed as a function of the mass combustion rate. Table 1 shows the reaction model of the dense zone required for simulations,25,26 where the sum is for all particle sizes. The reaction rate expressions of the species are also summarized in the table. The gas temperature is

1

1

]

(11a)

∑i R1ξ + 2∑i R3ξ - R2(1 - s)]

(11b)

-

ug

dCCO2

1/3

[

∑R1ξ - 2R2(1 - s) 2 i

dz dCCO

1

)

dz

)

1 ug

∑i R3ξ + R2(1 - s)]

[

(11c)

where the reaction rates R1, R2, and R3 are calculated from Table 1 and the gas temperature is predicted from the energy equation in the heat-transfer model. SO2 Absorption. During coal combustion, the sulfur compounds are oxidized and the resultant sulfur dioxide is reduced by calcium oxide particles (produced by the limestone calcination), forming calcium sulfate according to the following reaction:

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1 SO2 + CaO + O2 f CaSO4 2 The reaction rate of a limestone particle can be expressed as16

π kL ) ds3kvLCSO2 6

(12)

We assumed that particles obeyed the “geometrical optics theory”, and the overall emissivity is computed considering the gases and particles as a mixture of gray media. The radiative heat fluxes to the walls is evaluated by the zone method. The gas and wall cells are assigned, and the temperature is assumed to be constant within each cell. The energy equation for gas cell j is

where kvL represents the overall volumetric reaction rate constant and CSO2 is the SO2 concentration in the combustion gases. The overall volumetric reaction rate is calculated by

∑i SiGjσTw,i4 + ∑i GiGjσTg,i4 ) 4K∆VσTg,j4 - qh,g,j

kvL ) 490 exp(-17500/RTs)Sgλs

where K is the absorption coefficient of the media and ∆V is the volume of the cell. For wall cell j, the energy equation is

(13)

where Sg is the specific surface area correlated with calcination temperature given by28

Sg ) -384Tg + 5.6 × 104 Tg g 1253 K (14a) Sg ) 35.9Tg - 3.67 × 104 Tg < 1253 K (14b) and λs is the limestone reactivity that is a function of the fractional conversion of CaO, temperature, and particle diameter. 3. Heat-Transfer Model. Dense Zone. The constant gas temperature is assumed in the dense zone. The energy equation for a coal particle is based on mass and energy balances and can be written as

Cpfmf

dTf ) Afmv,c(Hv,c - Qv) + Afh(Tg - Tf) + dt dmH2O Afσf(Tg4 - Tf4) + HH2O (15) dt

where f is the emissivity of coal particles, Qv represents the fraction of the particle heat of combustion, mv and mc are the mass flow rates for volatile and char combustion, respectively, and mH2O is the mass of evaporated water in the heating process of coal particles. The energy equation for inert particles is similar to eq 15 but without considering the combustion,

C sm s

dTs ) Ash(Tg - Ts) + Asσs(Tg4 - Ts4) dt

(16)

where s is the emissivity of the inert particles and Ts represents the inert particle temperature. Dilute Region. An energy balance for a cell in the dilute region can be written as

∂ z (m C T + mfzCfTf + mzsCsTs) + ∂z g g g ∂ r (m C T + mrf CfTf + mrsCsTs) ) ∂r g g g 4h Qrel + Qrad + (Tw - Tg) (17) D0 where superscripts “z” and “r” represent axial and radial direction, respectively. Qrel and Qrad are energy released from combustion and radiative heat fluxes to the walls, which are computed from the reaction model and by a “zone” method. D0 is the equivalent diameter of the furnace. The convection coefficient, h, is predicted according to the model of Mahalimgam and Kolar for circulating fluidized beds.28

(18)

∑i SiSjσTw,i4 + ∑i GiSjσTg,i4 ) w,jσTw,j4 - qa,s,j

(19)

where w is the wall emissivity and qh and qa represent the heat generation by combustion in the gas cell and net heat load of the wall cell. The total exchange area, GiGj, GiSj, SiGj, and SiSj, is the function of only the shape of the system and can be predicted according to the method proposed by Hottel and Sarofirm for combustors.29 4. Numerical Procedure. Coal particles are considered as a discrete number of sizes. Each particle size is partially burned out in each passage through the furnace, and its diameter is thus reduced. A constant diameter of the circulating char particles, however, is considered in the present numerical simulations. The overall strategy applied to the model can be outlined in four steps: (1) The solution of the hydrodynamic equations of mass was first obtained by means of the hydrodynamic model. To calculate the size distribution of ash and limestone in the dense region, it was initially assumed that the limestone in the dense region had the same distribution as that of the feed. The mean particle size present in the dense region was calculated and the hydrodynamic model was solved. Then, taking into account the distribution of solids in the circulation stream, a new particle diameter in the dense region was determined and the hydrodynamic model was again solved. This process was iterated until convergence to the given condition was obtained. In the dilute region, the particle concentration, size, and flow rate of solids were obtained by means of the hydrodynamic model. (2) With the size distribution and concentration values obtained in step 1, the devolatilization of a coal particle and combustion of the char particle were computed by making use of the combustion model. The set of nonlinear differential equations governing the combustion model was solved using the Runge-Kutta method. In the dense region, the oxygen concentration of the input was given. At the inlet of the dilute region, the secondary air modified the oxygen concentration, increasing its value. The carbon combustion efficiency was predicted. (3) With the size distribution and gas species distribution along the furnace, the temperature distribution was computed by means of the heattransfer model. (4) The solution of the hydrodynamic field was repeated with the updated values in steps (1) and (3). A new size distribution in the dense region and particle concentration profile along the dilute region

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Table 2. Numerical Values of Model Parameters Used in the Computations parameter

parameter

a ) 1.6 (1/m) Cf ) Cs ) 840 (J/(kg °C)) D ) 0.054 (m2/s) ds ) 150 (µm) Tw ) 557 (K)

f ) S ) 0.8 w ) 0.72 mf ) 0.5 Fchar ) 1700 (kg/m3) FS ) 1400 (kg/m3)

Table 3. Ultimate Analysis of the Firing Fuel Car %

Har %

Oar %

Nar %

Sar %

War %

Aar %

Qnet (J/kg)

110% MCR 43.74 1.83 3.94 0.95 0.65 8.90 39.99 16 024 100% MCR 41.85 1.76 3.93 1.30 0.66 8.57 41.93 15 681 75% MCR 43.03 1.91 3.41 1.47 0.65 8.28 41.25 15 773

Figure 2. Predicted CO2, O2, CO, and H2O concentrations along the furnace at the 100% MCR.

Figure 1. Particle size distributions at the 100% MCR.

were then obtained. The process is iterated until the carbon concentration converged. Simulation Results and Discussion The model described in the previous section was applied to a typical circulating fluidized-bed boiler. This CFB boiler is designed for the Linhe sugar mill of the Inner Mongolia Autonomous region. The steam capacity of the CFB boiler is 35 t/h, and the superheated steam temperature and pressure are 400 °C and 2.45 MPa, respectively. The CFB boiler has a total height of 9.3 m and a width varying from 2.4 m at the distributor to 3.2 m in the dilute regime, and the cross-sectional area varies from 7.12 to 11.4 m2. The combustion air is supplied through the distributor (primary air) and the secondary air inlets. The fluidized velocity was about 4.1 m/s at the bed temperature of 910 °C. The dense zone is designed to be 1.05 m in height. The secondary air inlets are located 1.7 m above the distributor. The ratio of the secondary air to the primary air is 20:80. The equivalent diameter and exit speed of a secondary air port is designed to be 150 mm and 30.5 m/s, respectively. The secondary stream is tangentially injected into the dilute regime and it formed an artificial circle of diameter 350 mm. The circulating particles return to the dense zone from the rear wall using a modified H-valve. The fraction of circulating particles is 1.2, which means the circulation mass flux of ash particles is 4.4 t/h. The average diameter of the circulating particles is assumed to be 150 µm. The values of

Figure 3. Predicted profile of char concentration in dense zone at the 100% MCR.

the main parameters used in the computations are listed in Table 2. Most of the energy is released to the walls covered by water tubes. It is assumed that the water-wall tubes have a uniform temperature. In the present work, the temperature in the dense zone was fixed at 1183 K. The fuel for the boiler is a mixture of low-grade coal and cinder from chain-grate stoker boilers. Coal compositions are shown in Table 3. The particle size distribution of the feed coal is shown in Figure 1. The average particle diameter of the feed coal is 1.96 mm. Figure 2 shows the computed average concentration distributions of CO2, CO, H2O, and O2 along the height of the furnace at the 100% MCR (maximum continuous rating). In the present model it is assumed that the reaction rate is directly proportional to the reaction rate of coal combustion. The high concentration of O2 and low levels of CO2 emission show that the combustion of coal in the dense zone is still significant in controlling coal combustion processes. The calculated resultant particle size distribution in the dense zone is also shown in Figure 1. It can be seen that most particles in the dense zone are in the range of 2.0-6.0 mm in size.

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Figure 4. Predicted gas temperature distributions as a function of boiler loading: (a) 110% MCR; (b) 100% MCR; (c) 75% MCR.

Figure 5. Computed results of heat flux distributions at the 100% MCR.

Because of combustion, the fraction of large particles decreases in the dense zone. The computed average particle diameter of the resultant particles is 2.16 mm. Figure 3 shows the computed char concentration distribution of the resultants in the dense zone as a function of particle diameter. The computed average char concentration is 2.65%. The content of water vapor is high in the flue gases because of the high moisture content in the coal considered. Figure 4a-c shows the predicted distributions of the flue gas temperature in the dilute regime at the boiler loadings of 38.2, 35.4, and 24.5 ton/hour, respectively. The temperature of the dense zone is assumed to be 910 °C. The inlet temperature of the feed and circulating particles are about 293 and 773 K, respectively. The feed coal particles are dried and heated in the dense zone. The volatiles released from the coal particles were assumed to be instantaneously burned and uniformly distributed in the dense zone. For circulating particles, only char combustion is considered because devolatilization is complete in the first passage in the furnace. From Figure 4, it can be seen that the distributions of the flue gas temperature decrease along both the radial and the vertical directions in the dilute regime. Computed results indicate that the gas temperature near

Figure 6. Predicted profile of heat fluxes to the wall.

the wall is less than that at the center in the dilute region. The trends of gas temperature along the radial direction depend mainly upon the solid mass flux distribution. The simulations show that the averaged flue gas temperature remains almost constant along the furnace at the higher rate of recirculating solid mass fluxes, which is typical for a CFBC. For the coal of higher moisture, the simulation results also implied that the drying time of coal particles is not negligible in the combustion simulation of the dense zone. Heat flux distributions of radiative and convective components are shown in Figure 5 along the furnace height. Gas convective heat transfer drops gradually along the bed height, and radiative heat flux decreases because of the gas temperature. This leads to the total wall heat flux slight decrease along the bed height. Figure 6 shows the variations of averaged heat fluxes with boiler loads. It can be seen that the heat flux decreases with decreasing boiler load. From the simulation results, the heat losses due to the unburned-out char particles and gases can be calculated. The measured and predicted boiler performances were shown in Table 4. Combustion efficiency of a boiler was determined from the computed heat losses due to unburned carbon particles and unburned combustible gases. It can

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Table 4. Computed and Tested Performance of the 35 t/h CFB Boiler

110% MCR 100% MCR 75% MCR a

boiler load (t/h)

heat loss due to unburned carbon (%)

heat loss due to unburned gases (%)

boiler combustion efficiency (%)

38.23 35.37 24.54

10.16a/6.82b 9.90a/6.26b 11.09a/7.17b

5.74a/2.92b 5.36a/2.54b 7.70a/2.82b

84.1a/90.26b 84.74a/91.20b 81.21a/90.01b

Experimental values. b Computed date.

Figure 8. Computed SO2 emissions as a function of Ca/S ratio at the 100% MCR.

Figure 7. Predicted SO2 emissions as a function of particle diameter at the 100% MCR.

be seen that the predicted combustion efficiency is higher than the experimental data. The main reasons may be due to the fact that the actual mass flux of circulation particles is less than the simulations. Simulation results indicated that the combustion efficiency decreased with decreasing mass flux of circulation particles. Figure 7 shows the averaged SO2 concentration profiles as a function of limestone diameters with furnace height. The smaller particles have higher reactivates than the larger particles, which means a larger capability to absorb SO2 in the combustion gas, but their residence time is low. Considering the circulation of the particles, however, the residence time is similar for all particle sizes. Thereby, the retention of SO2 is higher for small limestone particles because of the higher reactivity for a given conversion fraction. Figure 8 shows the averaged SO2 emission profiles for various Ca/S ratios at given particle sizes. It is clear that the reactivity of limestone does not remain similar along the height. When the calcium-to-sulfur ratio is decreased, the conversion of CaO to CaSO4 within the particles is increased. The model has also been applied to the 12 MW CFB combustor at the Chalmers University in Gothenburg, Sweden.30 A detailed description of the unit can be found in Amand and Leckner.31 The boiler has a width of 1.6 m and a total height of 13.5 m.11 Fuel is injected from one side into the bed and the externally recycled solids are returned to the boiler from the opposite side without limestone addition. The gas velocity and solid flow rate are about 6.3 m/s and 31.9 kg/m2s in the simulations, respectively. All the calculations have been done with primary air only. The flue gas temperature was 850 °C in the dense zone. The ultimate analysis of the bitumi-

Figure 9. Predicted profile of oxygen concentration at a constant ug ) 6.3 m/s.

nous coal has been taken from Johnsson et al.30 The exit of the furnace is assumed to be at the top in the simulations. Since no information was available for the particle size distribution and the height of the dense zone, it was assumed that the average particle diameter of coal and the height of the dense zone are equal to 1.5 mm and 1.0 m in the simulations. The distribution of oxygen concentration is shown in Figure 9 along the height of the furnace. Near the wall a minimum oxygen concentration can be observed. The minimum near the wall is mainly due to the strong consumption of oxygen by the combustion of char. The lower oxygen concentrations may be critical for the total performance of the combustor because it may lead to emissions of CO. Figure 10 shows the profiles of the cross-sectional averaged char mass flux along the height of the furnace. The curve shows that the char content decreases with height. It is also seen that the char mass flux decreases with increasing gas velocity. This is due to the greater oxygen fraction for the combustion of char particles. Figure 11 shows the distribution of the crosssectional averaged carbon monoxide concentration along the height of the furnace. It can be seen that the CO

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Conclusions

Figure 10. Predicted cross-sectional averaged char mass flux.

A numerical model has been implemented to simulate two regions with combustion in the furnace of a circulating fluidized-bed boiler of low circulating ratio and wide size distribution. This model coupled a model for the dense zone derived from turbulent bubbling bed theory with a model for the dilute region based on a core-annular flow structure. Radiative heat transfer in the dilute region is modeled using a zone method. The model allows for the calculation of gas concentration, chemical species, temperature, and heat flux along the furnace. A model for SO2 retention was also included. The agreement between the model prediction and experimental data is satisfactory, but more experimental data are still required to validate the proposed CFBC model to make it more comprehensive and reliable. Nomenclature

Figure 11. Predicted profile of cross-sectional averaged CO concentration.

Figure 12. Computed gas temperature distributions at a constant ug ) 6.3 m/s.

concentrations in the dense zone are much higher. Figure 12 shows the computed distributions of the flue gas temperature. The wall temperature and the temperature of recirculating particles are assumed to be 460 and 1073 K in the simulations. It can be seen that the flue gas temperature is lower at the wall than that at the center of the furnace. The flue gas temperature decreases with increasing height. The above predictions demonstrate that the flue gas temperature, gaseous species, and char contents change across the crosssectional area of the furnace.

Af ) coal particle surface area (m2) As ) inert particle surface area (m2) a ) decay coefficient (m-1) C ) concentration of species (mol) Cb ) gas concentration (mol) Cg ) gas specific heat capacity (J kg-1 K-1) Cf ) particle specific heat capacity (J kg-1 K-1) Cs ) inert particle specific heat capacity (J kg-1 K-1) D ) equivalent diameter (m) Db ) bubble diameter (m) Dg ) diffusion coefficient (m2 s-1) d ) particle diameter (m) Hv ) heating value of volatiles (J kg-1) Hc ) heating value of char (J kg-1) HH2O ) evaporating heat of water (J kg-1) h ) heat-transfer coefficient (W m-2 K-1) kbe ) mass-transfer coefficient (s-1) kc ) kinetic rate (s-1) km ) diffusion rate (s-1) ke ) coefficient (s-1) kr ) total reaction rate (gmol m-2 s-1) K ) absorption coefficient (m-1) ms ) particle mass flow (kg s-1) mg ) gas mass flow (kg s-1) Qrad ) radiative heat flux (W m-3) Qrel ) released heat of combustion (W m-3) qh,g ) heat flux in gas cell (W m-2) qa,s ) net heat flux in wall cell (W m-2) R ) radius (m), reaction rate (gmol m-2 s-1) r ) radial coordinate Rg ) universal gas constant (J mol K-1) Tg ) gas temperature (K) Tf ) coal particle temperature (K) Ts ) inert particle temperature (K) Tw ) wall temperature (K) tr ) residence time (s) t ) time (s) tv ) devolatilization time (s) ub ) bubble velocity (m s-1) u0 ) superficial gas velocity (m s-1) ug ) gas velocity (m s-1) ug,av ) average gas velocity (m s-1) ug,r ) local gas velocity (m s-1) ug,c ) center-line gas velocity (m s-1) umf ) minimum fluidization velocity (m s-1) vb ) bubble volume (m3) ∆V ) cell volume (m3) z ) height (m)

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Greek Letters  ) voidage b ) voidage of bubble phase s ) particle concentration, emissivity mf ) voidage at minimum fluidization w ) wall emissivity φ ) constant F ) density (kg m-3) β ) fraction of flux ξ ) specific surface area of char particles σ ) Stefan Boltzman constant (W m-2 K-4)

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Received for review February 1, 2000 Revised manuscript received May 17, 2000 Accepted June 7, 2000 IE9808054