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___________________________________________________________________________________ www.paper.edu.cn Energy 24 (1999) 633–653 www.elsevier.com/locate/energy A mathematical model for a circulating fluidized bed (CFB) boiler Qinhui Wang*, Zhongyang Luo, Xuantian Li, Mengxiang Fang, Mingjiang Ni, Kefa Cen Institute for Thermal Power Engineering, Zhejiang University, Hangzhou, 310027, People’s Republic of China Received 3 November 1997 Abstract In developing a mathematical model for a CFB boiler we use earlier work. Our model includes mathematical descriptions of the underlying physical and chemical processes. It has been applied to simulation of a 12 MW CFB boiler. The calculations agree well with test results. 1999 Elsevier Science Ltd. All rights reserved. Nomenclature A Ci CO2,⬁ Dac Dca Dh Dl Dspi Dt f F F0 Fd1 Cross-sectional area, m2 Concentration of particles of size i, kg/m3 Oxygen concentration in the bed, kg/m3 Dispersion coefficient from the annulus to the core, m/s Dispersion coefficient from the core to the annulus, m/s Diffusion coefficient of oxygen in the ash shell, m2/s Axial dispersion coefficient, m2/s Axial dispersion coefficient in the cyclone, m/s Furnace equivalent diameter, m Mass fraction of solid particle Interface between the core and the annulus Mass flow rate of feed, kg/s Bed material drain rate, kg/s * Corresponding author. Fax: ⫹ 86-571-795-1616; e-mail: ccctasun.zju.edu.cn 0360-5442/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 3 6 0 - 5 4 4 2 ( 9 9 ) 0 0 0 0 8 - 0 ___________________________________________________________________________________ 中国科技论文在线 www.paper.edu.cn 634 Q. Wang et al. / Energy 24 (1999) 633–653 Fd2 Mass flow rate of back down the dense bed from the dilute region, kg/s Total heat transfer coefficient ht Chemical reaction rate constant, m/s kc Specific combustion rate of char particle, kg/m3/s Ks Fragmentation constant kt l Length of the spiral in the cyclone, m Bed material inventory in the dense bed, kg M1 Particle distribution function P(R, ) Particle distribution function of feed mass P0(R,) Pd1(R,) Particle distribution function of drained bed material Pd2(R,) Particle distribution function of mass flow that back down the dense bed Natural size distribution Pf(R) Particle distribution function of recycle solids Pin(R,) Pnew(dp,new) Size distribution after fragmentation Pold(dp,new) Size distribution before fragmentation Pu1(R,) Particle distribution function of mass flow that elutriated into dilute region Fin Recycle solids rate, kg/s ith mass component flowing into the cell, kg/s Fin,i ith mass component flowing out of the cell, kg/s Fout,i Ratio of weight consumption of char to that of oxygen fs Mass flow rate of elutriated into the dilute region, kg/s Fu1 Generating rate of i particle in the annulus, kg/s Gai Generating rate of i particle in the core, kg/s Gci Net solids circulation rate, kg/m2/s Gs Generating rate of particle group i in the cyclone, kg/s Gspi H Furnace height, m h Height above the distributor, m Convective heat transfer coefficient for the cluster, W/m2s hc Convective heat transfer coefficient for the dispersed phase, W/m2s hd Radiative heat transfer coefficient for the cluster, W/m2s Hrc Radiative heat transfer coefficient for the dispersed phase, W/m2s hrd Heat coming from other regions, kJ/s Qin Heat going to other regions, kJ/s Qout Heat produced in the cell, kJ/s Qrelease R Particle diameter, m Maximum particle diameter, m Rmax r Fine particle diameter, m Radius of char particle, m; R1 Re Renault number Upper size limit of the fines, m Rfi U Gas velocity, m/s Superficial gas velocity, m/s U0 V Particle velocity, m/s Particle velocity; m/s Vpi ___________________________________________________________________________________ 中国科技论文在线 www.paper.edu.cn Q. Wang et al. / Energy 24 (1999) 633–653 W Z dmi d ⌬Ri 635 Downward solids flux, kg/m2/s Height, m Variation rate of i component in the cell, kg/s i component generated or consumed in the cell, kg/s Greek symbols ␦ 0 Suspension density or particle density, kg/m3 Time, s Thickness of annulus Thickness of the ash shell, m Mass transfer coefficient, m/s Subscripts i c a Particle size increment Core Annulus 1. Introduction The CFB represents an improvement over traditional systems used for coal combustion and is widely applied in industry. Previous studies may be found in Refs [1–6]. Although published models have a similar structure, significant differences are found in the sub-models. Our model includes following constraints: (i) The physical and chemical processes occurring in the boiler are described but include empirical models for poorly understood processes. (ii) The model should be applicable to different applications of CFB boilers. (iii) The computer code should be modular to allow users to update component modules easily as new findings become available. The model is shown schematically in Fig. 1. 2. Brief description of main sub-models This paper only gives a brief description of the sub-models. For more detailed information readers may refer to Ref. [7]. 2.1. Particle properties The bed material in the furnace consists of fuel particles (burned or burning), inert particles and sulfur sorbent, such as limestone. Fuel particles’ behavior during gas–solid reactions is assumed to be described in terms of three limiting types: (i) shrinking core with attriting shell i.e. the dual shrinking-core model, (ii) shrinking core with non-attriting shell i.e. the single shrinking-core ___________________________________________________________________________________ 中国科技论文在线 www.paper.edu.cn 636 Q. Wang et al. / Energy 24 (1999) 633–653 Fig. 1. Structure of the mathematical model for CFB boilers. model and (iii) uniform reaction. These three reaction modes may occur within a CFB boiler, and different particles may be in different modes. Hence, the particle population should be described by particle size and/or density. The two dimensional particle distribution functions may be given as P(R,). Here, R is the particle diameter and is the particle density. 2.2. Hydrodynamics model Fig. 2 shows the hydrodynamic structure in CFB boilers with a square cross-section furnace. In this paper, on the basis of previous researches [8–11], a model is suggested to describe the core–annulus flow structure in a CFB boiler furnace with a bed material of wide size distribution. ___________________________________________________________________________________ 中国科技论文在线 www.paper.edu.cn Q. Wang et al. / Energy 24 (1999) 633–653 Fig. 2. 637 Gas–solid flow structure in the CFB boiler and overall balance of gas and solid. The principal assumptions are: (i) the furnace is characterized by two flow regimes: a dense phase at the bottom and a dilute phase above the solid entry or secondary air inlet. The dense phase operates in turbulent fluidized bed regime while in dilute phase core–annulus solids flow structure is established. Particles travel upward in the core and downward in the annulus. (ii) Both the thickness of the annulus and the suspension density vary with the furnace height. (iii) Within the core and the annulus there are no radial suspension density gradients, while the lateral dispersion between the core and the annulus is considered. (iv) The flow pattern in the furnace is assumed to be symmetric. (v) While moving in the boiler, the char particle burns and undergoes attrition, and the gases participate in homogeneous reactions; (vi) The gas phase is modeled as only flowing upward, backmixing of gas is neglected. The model used in this paper to determine the voidage in the dense bed is suggested by Hannes et al. [1]. Bed materials may be divided into size groups. For every solid particle group i in the core or annulus of the dilute region, a one-dimensional axial dispersion model is used to characterize solid behavior. For the core, ___________________________________________________________________________________ 中国科技论文在线 www.paper.edu.cn 638 Q. Wang et al. / Energy 24 (1999) 633–653 冋 册 (1) 冋 册 (2) d(VcicfciAc) d d(cfci) ⫽ AcDlci ⫹ (Daci·afai ⫺ Dcaicfci)F ⫹ Gci. dZ dZ dZ For the annulus, d d(afai) d(VaiafaiAa) ⫽ AaDla ⫹ (Dcaicfci ⫺ Daci·afai)F ⫹ Gai, dZ dZ dZ where V is the particle velocity, the suspension density in the furnace, f the mass fraction of size i particle, F the interface between core and annulus, Dl the axial dispersion coefficient, Dac the dispersion coefficient from annulus to core, and A stands for cross-section area, Gci and Gai are the generating rate of i particle in the core and the annulus, to be calculated by the attrition and the reactions of solid particles. Subscript c stands for the core, a for the annulus, and i for particle group. The thickness of annulus ␦ is given by Werther [12] as 冉冊 冉 冊 ␦ H ⫽ 0.55Re−0.22 Dt Dt 0.21 H⫺h H 0.73 , (3) where Dt is the furnace equivalent diameter, H the furnace height and h the height above the distributor. The downward solids velocity in the annulus maintains constant, about 1.2–1.5 m/s [13,14]. The upward solids velocity in the dilute core can be taken as: Vci ⫽ Ugc ⫺ Vti, (4) where Vti is the terminal velocity of particle group i, the gas velocity in the core, Ugc, is given by Bai et al. [15]. The dispersion coefficients Dlci, Dlai, Daci, Dcai can be obtained from previous literature [15–18]. Similarly, the balance equations for the gas phases can be given [7]. 2.3. Particle population model for the dense bed Fig. 3 shows the solid balance in the dense bed. In this paper, a particle population model has been developed by properly accounting for the attrition and reaction, in which the particle size distribution is divided into two size range, one is from 0 to Rfi (the upper size limit of fines) for fines, and the other one from Rfi to the maximal size of feed particles Rmax for mother particles. By considering the population of a given solid particle group (R,), the solid mass balance for mother particles is given as F0·P0(R,) ⫺ Fd1Pd1(R,) ⫺ Fu1Pu1(R,) ⫹ Fd2·Pd2(R,) ⫹ FinPin(R,) ⫹ M1· 冉 冊 (5) ∂P1(R,) dR ∂P1(R,) d 3 dR 1 d ⫹ M1· ⫺ M1·P1(R·) ⫹ ⫽ 0, ∂R dt ∂p dt R dt dt where F0, Fd1, Fu1, Fd2 and Fin are mass flow rates of feed, bed material drain, elutriated into dilute region, back down the dense bed from the dilute region and recycle solids, respectively. ___________________________________________________________________________________ 中国科技论文在线 www.paper.edu.cn Q. Wang et al. / Energy 24 (1999) 633–653 Fig. 3. 639 Flow chart of the numerical solution. The fines generated will react further but not subject to further attrition, and it is assumed that the fines have a known size distribution (natural grain size) Pf(r). So, for the fine particle (Rfi > r > 0), the following item should be added to the population equation, i.e.: dR R max 3·P(R,) latt dt dR·Pf(r). (6) R 冕冤 Rfi 冥 ___________________________________________________________________________________ 中国科技论文在线 www.paper.edu.cn 640 Q. Wang et al. / Energy 24 (1999) 633–653 In addition, the normalization of the distribution function requires, R 冕 冕 max 0 max P1(R,)ddR ⫽ 1. (7) min 2.4. Coal combustion model The combustion of coal particles may be modeled as: (i) devolatilization and volatiles combustion, (ii) primary fragmentation, (iii) char combustion with attrition and (iv) homogeneous gas reaction. 2.4.1. Devolatilization and volatile combustion Because of the rapid mixing in CFB furnace, the volatile fraction of coal is completely and instantaneously released in the gas phase in the dense bed. To simplify the volatiles combustion model, the hydrocarbons in the volatiles may be treated as one gas species, and its molecular formula may be written as CnHm. So the overall chemical reaction of volatile with oxygen can be assumed to be C n Hm ⫹ 1 1 nO2→ mH2 ⫹ nCO. 2 2 (8) The nitrogen and sulfur in the volatiles are considered in the models of NO and N2O formation and sulfur retention. 2.4.2. Fragmentation Fragmentation can be treated as happening immediately at feed port. An empirical model has been proposed by Bellgardt et al. [19] as 1/3 Pnew(dp,new) ⫽ Pold(dp,new·K 1/3 f )K f , (9) where Kf is the fragmentation constant. 2.4.3. Char combustion The main assumptions for char combustion are: (i) both CO and CO2 are primary products; (ii) CO burns after leaving the char particle surface; (iii) coal particles with high ash content burn according to the dual shrinking-core model, but for those with low ash content the single shrinking-core model is applied, and for fine particle the uniform reaction model should be employed. (iv) The combustion rate of the char particle is determined by reaction kinetics, gaseous and intraparietal diffusion resistance. So, the specific combustion rate of char particle Ks may be given as ___________________________________________________________________________________ 中国科技论文在线 www.paper.edu.cn Q. Wang et al. / Energy 24 (1999) 633–653 fsCO2,⬁ 冉冊 Ks ⫽ 1 1 R ⫹ kc 0 R1 2 R ⫹ Dh R 1 , 641 (10) where fs is the ratio of weight consumption of char to that of oxygen, ranging from 0.375 to 0.75, R1 is the radius of the char particle, represents the thickness of the ash shell, ⫽ R ⫺ R1, kc the chemical reaction rate constant, Dh diffusion coefficient of oxygen in ash shell, m2/s. 2.4.4. Homogeneous gas reaction The main homogeneous reactions for combustible gases are given below: 1 O →CO2; 2 2 (11) 1 O →H2O; 2 2 (12) CO ⫹ H2 ⫹ CO ⫹ H2O ⫽ CO2 ⫹ H2. (13) 2.5. Particle attrition For each bed material having its own attrition characteristics, different empirical models for the attrition rate of the individual components should be applied. The particle material may be divided into two types: one is coal/char particles with low ash content, and the other one includes coal/char particles with high ash content and limestone particles. 2.6. Heat transfer Based on the special hydrodynamics of the CFB boiler, the cluster renewal model of the bed to membrane wall heat transfer process has been described in the literature [20]. The dilute phase comprises of a continuous upflowing gas phase with thinly dispersed solids (dispersed phased) and relatively denser cluster moving downward along the wall. Any part of the wall comes in alternate contact with the cluster and the dispersed phase. If ␦c is the average fraction of the wall area covered by the clusters, the time-averaged overall heat transfer coefficient, ht, may be written as the sum of the convective and radiative heat transfer coefficients, ht ⫽ ␦chc ⫹ (1 ⫺ ␦c)hd ⫹ ␦chrc ⫹ (1 ⫺ ␦c)hrd, (14) where hc and hd stand for the convective heat transfer coefficient for the cluster or the dispersed phase respectively, hrc and hrd for the radiative heat transfer coefficient for the cluster or the dispersed phase respectively. ___________________________________________________________________________________ 中国科技论文在线 www.paper.edu.cn 642 Q. Wang et al. / Energy 24 (1999) 633–653 2.7. Emission An improved model for evaluating the performance of sulfur retention by limestone in the CFB boiler is established based on the model developed by Li et al. [21]. Meanwhile, a simplified kinetic model for the formation and reduction of NO and N2O is developed on the basis of the previous research works [22–25]. 2.8. Boiler components A simplified model is established to simulate the gas–solid flow structure in the cyclone. The basic assumptions are: (i) gas and solid move together in plug flow around a helical path in the cyclone body. (ii) The cross-sectional area of the spiral is the same as that of the cross-sectional area at the entry point of the cyclone, and the gas–solid slip velocity entering the cyclone also depends on the entry area of the cyclone. (iii) Gas–solid separation takes place only at the end of the spiral. (iv) The combustion of char and combustible gases also takes place in the cyclone due to the rapid mixing between gas and solid. So, the balance equation for every solid particle group i may be described as d 2C i d(VpiCi) ⫽ Dspi 2 ⫹ Gspi, dl dl (15) where Ci is the concentration of particles of size i, Vpi the particle velocity, Dspi the axial dispersion coefficient, Gspi the generating rate of particle group i in the cyclone; l the length of the spiral. Because there is no suitable model for the cyclone of CFB boiler, traditional calculation models of grade separation efficiency, overall separation efficiency and the pressure drop are used. In addition, the models of other CFB boiler components such as inertial separator, external heat exchanger, recycle device valves and heat transfer surfaces are developed. 3. Numerical results The CFB boiler may be divided into cells along gas and solid flow path for solving the model. The cells are treated as balance sections (control volumes), and mass balance and enthalpy balance are drawn up. While the dense bed is treated as the first cell, the dilute region is divided into a number of cells. Each cell of the dilute region is divided horizontally into two parts: core and annulus, and each part is treated as one balance section. Cyclone, external heat exchanger, recycle device and each type of heating surfaces in the back-pass are treated as one cell, respectively. In each balance section, the balance equation for one component of gases or solids may be written as dmi ⫽ Fin,i ⫺ Fout,i ⫹ ⌬Ri, d (16) where Fin,i is the ith mass component flowing into the cell, including that coming from other regions and the external; Fout,i the ith mass component flowing out of the cell, including going ___________________________________________________________________________________ 中国科技论文在线 www.paper.edu.cn Q. Wang et al. / Energy 24 (1999) 633–653 643 to other regions and the external; ⌬Ri the i component generated or consumed in the cell by dmi physical and chemical processes; the variation rate of i component in the cell, and it is zero d under steady state. The balance equation of energy for one balance section may be given as dHi ⫽ Qin ⫹ Qrelease ⫺ Qout, d (17) where Qin is the heat coming from section outside, Qout the heat going to section outside, Qrelease the heat released in the cell. dHi ⫽ 0. The enthalpy of gas and ash is invariant with time under steady state. So, d According to the balance equations for each balance section, the flow chart of the numerical solution of the model is given in Fig. 3. 4. Simulation results and model validation 4.1. Introduction of a 12 MW CFB boiler Fig. 4 shows the scheme of a 12 MW bituminous-fired CFB boiler which has an external heat exchanger. The furnace is 21.0 m high and has a square cross-section measuring 5.45 ⫻ 2.45 m in the water-wall region and 1.5 ⫻ 5.45 m in the bottom refractory-lined section. It is equipped with two cyclones. Part of the solids separated by the cyclones is cooled by the external heat exchanger, and the rest is recycled into the furnace by a pair of recycle devices [7,26]. Our model is applied to the simulation of the 12 MW CFB boiler, and the simulation results are compared with the detailed performance test results. 4.2. Simulation results and comparison with the test results The particles in the furnace are divided into 70 classes, i.e. 10 size classes from 0 to 8 mm and seven density classes from 1100 to 2400 kg/m3. The furnace is divided into 30 cells, i.e. one for dense bed and 29 cells for the dilute region. The model input data shown in Table 1 are obtained from the operation parameters of the boiler. The temperature of feed water dropped to 105°C from the designed temperature, 150°C, and no limestone is fed. Tables 2 and 3 show the ultimate analysis and the size distribution of the test coal respectively. The feed coal is mixed with the fly ash of a stoker boiler. The stoker fly ash is very fine with high carbon content but almost no volatility. 4.2.1. Main performance parameters Table 4 shows the predictions and the measurements of main performance parameters. Table 4 shows that, in general, the predictions of main performance parameters except the carbon content in fly ash are in good agreement with the tested results. Because the blending of fly ash of the ___________________________________________________________________________________ 中国科技论文在线 www.paper.edu.cn 644 Q. Wang et al. / Energy 24 (1999) 633–653 Fig. 4. The scheme of the 12 MW CFB boiler. stoker boiler is not considered in the model, the prediction of residual carbon content is much lower than measurement and the calculated boiler efficiency is slightly higher. 4.2.2. Temperature profile Fig. 5 shows that close agreement is observed between the predicted and measured temperature profile throughout boiler system. In Fig. 6 the predicted temperature profile and the measured ___________________________________________________________________________________ 中国科技论文在线 www.paper.edu.cn Q. Wang et al. / Energy 24 (1999) 633–653 645 Table 1 The model input data Item Parameter Item Parameter Rated capacity Main steam pressure Main steam temperature Feed water temperature 73 t/h 3.82 MPa 450°C 105°C Air temperature Combustion air flow rate Primary air flow rate Primary air ratio 25°C 苲 70 500 Nm3/h 苲 42 000 Nm3/h 苲 60% Ultimate analysis, air dry Test coal Table 2 The ultimate analysis of the test coal Ultimate analysis, air dry Mt,ar, moisture, as-received, wt% Cad, carbon, wt% Had, hydrogen, wt% Oad, oxygen, wt% Nad, nitrogen, wt% Test coal 5.72 Sad, sulfur, wt% 63.01 3.59 6.23 1.15 0.85 Aad, ash, wt% Mad, moisture, wt% Vad, volatile, wt% Qad, heating value, MJ/kg 23.74 1.43 24.035 24.45 Table 3 The size distribution of the test coal Diameter 0–0.1 (mm) Mass 0.5 fraction (%) 0.1–0.3 0.3–0.5 0.5–1 1–1.5 1.5–2.0 2.0–3.5 3.5–5.0 5–6.5 6.5–8 2 6 16 9 10 13 18 12 13.5 Table 4 Comparison between prediction and test of the main performance parameters Item Unit Prediction Measurement Boiler efficiency Carbon content in fly ash Fraction of fly ash in total ash Solids recycle rate Stack gas temperature Carbon content in the bottom ash % % % kg/s °C % 89.6 4.8 73 47.5 154 1.8 88.3 11 74.6 苲 50 159.6 1.4 ___________________________________________________________________________________ 中国科技论文在线 www.paper.edu.cn 646 Q. Wang et al. / Energy 24 (1999) 633–653 Fig. 5. Profile of gas temperature in the boiler system; (•) measurement; the solid line is the calculation. Fig. 6. Temperature profile in the furnace; (䊏) measurement; the thick line is the calculated temperature profile in the core and the thin line is that in the annulus. temperature in the core region are given. The model predictions show that the temperature in the core is clearly higher than that in the annulus, and the temperature in the annulus decreases along the furnace height but increases slightly near the furnace exit. The reasons for this are that most of the heat transferring to the membrane wall is from the annulus region and the combustion reactions in the thin annulus are much lower than that in the core. Fig. 6 also shows model predictions are in agreement with that measured in the core. ___________________________________________________________________________________ 中国科技论文在线 www.paper.edu.cn Q. Wang et al. / Energy 24 (1999) 633–653 647 4.2.3. Profile of solid particle flux Fig. 7 shows the predictions and measurement results of the solid particle flux in the core and annulus. The particle flux in the annulus is much higher than that in the core. The particle flux decreases along the furnace height both in the core region and in the annulus region, but the particle flux in the annulus increases slightly near the furnace exit. It is caused by the solids backmixing at the tee and downward flow in the thin annulus region. In this region, the net solids exchange between the core and the annulus is towards the core. Fig. 7 also shows the close agreement observed between predicted and measured results at 13 m above the distributor. 4.2.4. Particle population As seen in Fig. 8, the mean size of solid particles decreases along the vertical position in the furnace in both core and annulus, and decreases slower in the upper furnace. The model predictions are in agreement with that measured in the furnace. The particle population varies with height in the furnace. Here only the particle population of the core region at the middle part of the furnace (above 13 m the distributor) is given in Fig. 9, which shows most of the bed material particles are the ash particles with low carbon content from 0.3 to 1.0 mm. In Fig. 10 a comparison between the predicted size distribution and the measurements in the core region at the same place are given. In general, the model predictions of particles population are reasonable and in good agreement with the measurement results. 4.2.5. Profile of carbon content Here, only the comparison between the measured residual carbon content in particles in the core region at the middle part of the furnace (13 m above the distributor) and those predicted by the models are given in Fig. 11, which shows the model predictions for carbon content in small Fig. 7. Profile of the particle flux in the furnace; (䊐) and (•) are the average measured particle flux in the core and annulus respectively; the thick line and thin line represent the calculation of the particle flux in the core and annulus respectively. ___________________________________________________________________________________ 中国科技论文在线 www.paper.edu.cn 648 Q. Wang et al. / Energy 24 (1999) 633–653 Fig. 8. Profile of the particle mean diameter in the furnace; (䊏) and (䊐) are the average measured particle mean diameter in the core and annulus respectively; the thick line and thin line denote the calculation of the particle mean diameter in the core and annulus respectively. Fig. 9. Population of particles at 13 m above the distributor (in the core region). ___________________________________________________________________________________ 中国科技论文在线 www.paper.edu.cn Q. Wang et al. / Energy 24 (1999) 633–653 649 Fig. 10. The size distribution of particles collected at 13 m above the distributor (in the core region);(䊏) the measurement; the solid line is the calculation. Fig. 11. Residual carbon content in particles sampled at 13 m above the distributor in the furnace (in the core region); (䊏) the measurement; the solid line is the calculation. particle (0 苲 1 mm) agree well with the measurement data, whereas there exists great deviation for coarse particles ( > 1 mm). This difference may be attributed to the model assumptions that large particles are less likely to be entrained to the upper part of the furnace and to the effects of particle sampling in the test as well. However, because of the low occurrence of coarse particles ( > 1 mm) in the dilute region, the influences of the deviation may be ignored. ___________________________________________________________________________________ 中国科技论文在线 www.paper.edu.cn 650 Q. Wang et al. / Energy 24 (1999) 633–653 As seen in Fig. 12, the carbon content decreases slightly along the furnace height and is slightly lower in the annulus region. This indicates that the combustion of char particles takes place throughout the height of the furnace. There exists a sharp peak above the dense bed (around 1.5 m). This may be explained as the following: due to the higher density, the elutriated char particles return more easily back down to the dense bed at the bottom of the dilute region. So the mass fraction of char particles is higher in this region. The model predictions of carbon content profile do not fit very well to the measurement data. The calculated carbon content in the bottom bed material is higher than the measurement data. This can be due to the fact that the measured carbon content in the bottom material is the residual carbon content in the drained bed material. In fact, the residual carbon content in drained bed material is lower than the average carbon content in the bottom material in this CFB boiler. This may be explained by the following two reasons: (i) two draining ports are arranged in the rear of the furnace and far away from the feeding ports. (ii) There exists slight segregation in the dense bed, i.e. the mass fraction of coarse particles is higher near the distributor. 4.2.6. Profile of O2, SO2, NO and N2O concentration Here, the profiles of several gas species in the furnace are given. Fig. 13 shows the calculated and measured profiles of O2 concentration both in the core region and in the annulus region. The model predictions of O2 concentration are slightly higher than the experimental data. Due to the secondary air injection, the O2 concentration changes rapidly in the secondary air inlet region (about 2 m), and forms a peak. The profiles of SO2, NO and N2O in the furnace and the average tested concentrations of SO2 and NO at gas exit are given in Figs. 14 and 15. In general, model predictions are in agreement with measurement data. Because the violent char combustion formats a great deal of NO and the dilution of secondary air is not considered in the code, the NO Fig. 12. Profile of residual carbon content in particles along the furnace height; (䊏) and (䊐) are the average measured residual carbon content in particles in the core and annulus respectively; the thick line and thin line represent the calculation of residual carbon content in particles in the core and annulus respectively. ___________________________________________________________________________________ 中国科技论文在线 www.paper.edu.cn Q. Wang et al. / Energy 24 (1999) 633–653 651 Fig. 13. Profile of O2 concentration; (䊏) measured O2 concentration; the thick line and thin line represent the calculation of O2 concentration in the core and annulus respectively. Fig. 14. Profile of SO2 concentration; (䊏) is the measured SO2 concentration at the gas exit; the thick line and thin line represent the calculation of SO2 concentration in the core and annulus respectively. concentration in the annulus near the secondary air inlet is very high. But it decreases rapidly owing to the NO reduction along the furnace height. It should be noted that, because of the small area fraction of annulus and low gas velocity, the gas flux in the annulus region is very low and accounts for only a small fraction of total crosssection gas flux in the furnace. ___________________________________________________________________________________ 中国科技论文在线 www.paper.edu.cn 652 Q. Wang et al. / Energy 24 (1999) 633–653 Fig. 15. Profile of NO and N2O concentration along the furnace height; (䊏) is the measured NOx concentration at the gas exit of the boiler; Lines 1 and 2 denote the calculation of NO and N2O concentration in the core respectively; lines 3 and 4 represent the calculation of NO and N2O concentration in the annulus respectively. 4.2.7. Heat transfer coefficient Fig. 16 shows a comparison between the predicted overall heat transfer coefficient and the measurement result together with the profiles of convective and radiative heat transfer coefficients in the furnace. The range of the calculated heat transfer coefficient is from 160 to 190 W/m2/°C, and decreases along with the furnace height. The average heat transfer coefficient measured is 168 W/m2/°C and is in agreement with the model prediction. Fig. 16. Profile of heat transfer coefficient in the furnace. Line 1 is the calculation of heat transfer coefficient in the furnace; line 2 refers to the tested heat transfer coefficient; lines 3 and 4 represent the calculation of radiative heat transfer coefficient and convetive heat transfer coefficient respectively. ___________________________________________________________________________________ 中国科技论文在线 www.paper.edu.cn Q. Wang et al. / Energy 24 (1999) 633–653 653 5. Conclusions A mathematical model for a CFB boiler including the mathematical descriptions of the underlying physical and chemical processes has been developed. These processes are hydrodynamics, coal combustion, particle attrition, heat transfer, formation and reduction of NO and N2O, sulfur retention and operation of boiler components such as gas–solid separator, external heat exchanger, non-mechanical valves and heat transfer surfaces. 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