A coal combustion model for circulating fluidized bed boilersL. Huilina,*, Z. Guangboa, B. Rushana, C. Yongjina, D. Gidaspowb

aDepartment of Power Engineering, Harbin Institute of Technology, Harbin 150001, Peoples Republic of ChinabDepartment of Chemical & Environmental Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA

Received 9 September 1998; received in revised form 15 February 1999; accepted 28 June 1999

Abstract

A steady state model of a coal-fired circulating fluidized-bed boiler, based on 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 inboth the axial and radial locations along the furnace including the bottom and upper portion. The model was validated against experimentaldata generated in a 35 t/h commercial boiler with low circulation ratio. q 1999 Elsevier Science Ltd. All rights reserved.

Keywords: Circulating fluidized-bed boiler; Modelling; Coal combustion

1. Introduction

Circulating fluidized bed combustors (CFBCs) areconsidered in some respects to be an improvement overthe traditional methods of coal combustion. Operation ofindustrial CFBCs has confirmed many advantages includingfuel flexibility, broad turn-down ratio, high combustionefficiency, low NOx emissions and high sulphur captureefficiency. These characteristics assure increasing commer-cialization of CFBC in power generation applications.Although CFBC technology is becoming more common,there are some significant uncertainties in predicting perfor-mance in large-scale systems.

Technical knowledge about design and operation of CFBCis widely available, but little has been done in the field ofmathematical modelling and simulation of combustion inCFBCs. This might be attributed to the fact that the combus-tion process occurring in a CFBC involves complex phenom-ena including chemical reaction, heat and mass transfer,particle size reduction due to combustion, fragmentationand other mechanisms, and gas and solid flow structure.Using a lumped-modelling approach, Weiss et al. [1] andArena et al. [2] introduced a CFBC model by dividing itinto several blocks, each corresponding to continuous stirredtank reactors for both gas and solid phase. Lee and Hyppaueu[3] presented a CFBC model that considered the riser as aplug flow reactor for the gas phase and a continuous stirredtank reactor for the solid phase. The model also considers thefeed particle size distribution and the attrition phenomena.

Weib et al. [4] and Maggio et al. [5] developed a model forcirculating bed reactors including the riser, cyclone, loop sealand external fluidized heat exchanger. Kudo et al. [6]proposed a computer program to simulate flow and heattransfer in a circulating fluidized bed boiler. Radiative heattransfer is modelled by using a Monte Carlo method.Sotudeh-Gharebaagh et al. [7] developed a CFBC modelbased on ASPEN, and predicted the performances of aCFBC in terms of combustion efficiency, emission levels.Park and Basu [8] and Wang et al. [9] introduced a combus-tion model for CFBCs to characterize the effect of the oper-ating conditions on CFB behaviour. Adanez et al. [10]proposed a mathematical model for a circulating fluidizedbed coal combustion process. The model considered thebed to have two regions: a dense zone of constant voidageand a dilute zone of core-annulus structure. However, most ofthe models do not completely take account of the perfor-mance of the dense zone. Generally speaking, the particlesize distribution of bed material in a CFB boiler is in avery wide range. A calculated average particle diameter isnot suitable to represent the behaviour of the total bed par-ticles. The particles will be segregated by their differentdiameters and densities. Only the fine particles can beentrained with flue gas passing through the furnace. Mostof large particles remain in the bottom of furnace. The parti-cle concentrations are much higher in the bottom than in theupper portion in the furnace. The fluidization regime in thebottom may be bubbling or turbulent fluidized bed. Leckneret al. [11] examined this zone and found that it could beexplained by the presence of bubble-like voids. They reportedthe height of the dense zone was about 1.0 m from the

Fuel 79 (2000) 165172

0016-2361/00/$ - see front matter q 1999 Elsevier Science Ltd. All rights reserved.PII: S0016-2361(99)00139-8

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* Corresponding author.

distributor in a 12 MW thermal CFB boiler. Montat et al. [12]also found that the dense zone was characterized by abubbling bed, and the bulk density was in the range of 7001000 kg/m3 in a 125 MWe CFB boiler. These results implythat the combustion of coal, particles mixing and heat transferin the dense zone dominate the performances of CFB boilers.

In the present work, a steady state mathematical model ofa coal fired CFB boiler has been developed, integrating thehydrodynamics, heat transfer and combustion which includethe dense zone and dilute region in the furnace. The modelpredicts the distributions of the gas concentration, chemicalspecies, temperature and heat flux along the furnace in boththe axial and radial locations. The model was validatedagainst experimental data generated in a 35 t/h CFB boilerof low circulation ratio with wide size distributions.

2. Modelling approaches

In a typical CFBC used for coal combustion, crushed coaltogether with limestone or dolomite and ash particles arefluidized by the combustion air entering at the bottom of thebed and at the secondary air injection points. Because coalcombustion in a CFBC is directly affected by its hydrody-namic parameters, both hydrodynamic and combustionmodels must be treated simultaneously to yield a predictivemodel for the CFBC.

2.1. Hydrodynamic model

For steady state conditions, the model considers that theCFBC is divided into two regions: a dense zone in thebottom and a dilute region with a decaying suspensiondensity in the upper portion of the furnace.

Dense zone: The dense zone is fluidized by the primaryair supply. Kunii and Levenspiel [13] and Sariava et al. [14]treated the dense zone using the models developed origin-ally for bubbling fluidized beds. This is inconsistent with thefact that the superficial gas velocity in this region is usuallyhigher than a critical value where the region becomes turbu-lent. At this condition, bubble diameter and particle velo-cities are quite different from the bubbling regime. It isassumed that the dense zone consists of the bubble phaseand emulsion phase. The emulsion phase voidage isconstant at the minimum fluidization. Portions of gas flowthrough 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 withbed height and is uniform across a given cross-sectionthroughout the bed. The gas concentration in the bubblephase Cb can be expressed along the height as [14]

Cb Cp 1 Co 2 Cpexp 2 Kbe1bzbug

!1

where Kbe is the mass transfer coefficient between thebubble and emulsion phases predicted by a correlationproposed by Sit and Grace [15]:

Kbe 2umf 1 12Dg1mfub=Db1=2

Db2

The bubble diameter and bubble velocity, Db and ub, maybe obtained using the correlations proposed by Mori andWen [16]. The fraction of flow within the bubbles, b , ispredicted by

b 1 2 umfkeuo1 2 1b 3

and the coefficient ke is given by Saraiva et al. [14]:

ke 1 1 0:25 ub1mfumf

1 2

1b 4

Dilute region: The dilute region is suspended both by thecombustion gases from the dense zone and the secondary air

L. Huilin et al. / Fuel 79 (2000) 165172166

NomenclatureA surface area (m)a decay coefficient (m21)b dimensionless coefficientCb gas concentration (mol)Cp concentration in particulate (mol)Db bubble diameter (m)Dg diffusion coefficient (m2 s21)d particle diameter (m)Gr solid flux (kg m22 s21)Gs net solid flux (kg m22 s21)H heating value (J kg21);h heat transfer coefficient (W m22 K21)kbe mass transfer coefficient (s21)kc kinetic rate (s21)km diffusion rate (s21)ke coefficient (s21)kr total reaction rate (g mol m22 s21)m particle mass (m3)r radial coordinateR reaction rate (g mol m22 s21)Rg universal gas constant (J mol K21)Tg temperature (K)tr residence time (s)tv devolatilization time (s)ub bubble velocity (m s21)ug superficial gas velocity (m s21)umf minimum fluidization velocityvb bubble volumez height (m)Greek letterse voidagee b voidage of bubble phaseemf voidage at minimum fluidizatiionf constantr density (kg m23)b fraction of fluxs StefanBoltzman constant (W m22 K24)

supply. Hydrodynamics models, as proposed in most CFBliterature regarding the dilute region, are classified into threegroups [17]: (1) those predicting the axial profile of solidsuspension density but failing to predict the radial varia-tions; (2) those assuming two regions considering core-annular flow structure to predict the radial variation; (3)those applying the fundamental equations of fluidmechanics to model gassolid flow. Type 1 and 2 models,which are lumped models, can be easily coupled with reac-tion and heat transfer models to simulate CFBC reactors. Onthe other hand, type 3 models rapidly become tedious whencoupled to reaction and heat transfer models because of thenumerical complexity.

For simulation purposes, the type 2 model was chosen topredict the axial and radial voidage profiles. The mean valueof voidage between height Zi21 and Zi can be calculatedusing the modified expression by Kunii and Levenspiel [13]:1 i 1p 2 1p 2 11exp20:5aZi21 1 Zi 5

Rhodes et al. [18] suggested a radial profile based on thereduced radial flux Gr=Gs expressed by the equation:GrGs a 1 2 r

R

5" #1 b 6

where Gs is the net solid flux. The dimensionless coeffi-cients, a and b, are considered as the adjustable parametersin the model. The particle velocity was estimated by thecomputed solid mass flux and concentration.

2.2. Reaction model

Dense zone: The reaction model allows for the determi-nation of the chemical changes and the heat released duringcombustion. Since coal combustion in the CFBC is quitecomplex, only the major steps of coal combustion areconsidered in the model. For the steady state condition, itis assumed that the coal, recirculated particles and limestoneare fed into the bottom of the bed at a uniform temperature.The evolution of coal particles is assumed to be in threesteps. In the first one, coal particles are dried (in this steptemperature is taken as 1008C) and heated to the devolati-lization temperature. The devolatilization time for a givenparticle class is obtained [19]:

tv 10 1048Tg

!dp;i 7

Since the time required for volatile combustion is very short,the devolatilization process is considered to take place in thedense zone, and distributes uniformly along bed height. Todescribe the combustion of char particles, the shrinking-coremodel was assumed, with mixed control by chemical reac-tion and gas film diffusion control, assuming that the ashseparates, once formed. The char particle diameter aftercombustion is calculated by [14]:

dp d3p;o 2 6pkrtr

dp;oCchar

!1=38

L. Huilin et al. / Fuel 79 (2000) 165172 167

Table 1Expressions of the overall reaction rate

dCEO2dz

1uo 2 ub1b 2

Xi

R1;ij 1 R21mf 2 2fO2

" #1 2 1b

21 kbeCBO2 2 CEO2 1b 2 CEO2

dVb 2 ub1bdz

( )

dCBO2dz

1Vb

212

R21b 2 kbeCBO2 2 CEO2 1b 1 CEO2 2 CBO2 dVbdz

dCECOdz

1uo 2 ub1b

Xi

R1;ij 2 R21mf 1 2X

iR3;ij 2 fCO

!1 2 1b1 kbeCBCO 2 CECO1b 2 CECO dVb 2 ub1bdz

" #

dCBCOdz

1Vb

2R21b 2 kbeCBCO 2 CECO1b 1 CECO 2 CBCO dVbdz

dCECO2dz

1uo 2 ub1b R21mf 2

Xi

R3;ij" #

1 2 1b1 kbeCBCO2 2 CECO2 1b 2 CECO2dVb 2 ub1b

dz

( )

dCBCO2dz

1Vb

R21b 2 kbeCBCO2 2 CECO2 1b 1 CECO2 2 CBCO2 dVbdz

C 1 12 O2 ! CO : R1; 1

1=Kc1 1 1=Km1CO2 RgTg; K

c1 0:667exp216000=RgTg; Km1 4D=dpRgTg

CO 1 12 O2 ! CO2 : R2; Kc2CH2O1=2 CCO CO2 1=2;Kc2 1:3 1014exp230000=RgTg; Kc3 4:1 1010RgTg21exp259200=RgTg

where kr and tr are the total reaction rate of char particles andthe residence time, respectively.

The concentrations of chemical species can be expressedas a function of the mass combustion rate. Table 1 shows thereaction model of the dense zone required for simulations[20].

Dilute region: The particles in the dilute region includeparticles coming from the dense zone and recirculated parti-cles from the separator. Only char combustion was consid-ered in the model. It is assumed that particles are sufficientlyseparated from each other that the single-particle combus-tion analysis is valid for each, the temperature of the particleis uniform, and the particle density remains constant. Theconcentrations of the chemical species are given as follows[14,20]:dCO2

dz tg12X

iR1;ij 2

12

R21 2 1s" #

9a

dCCOdz tg

Xi

R1;ij 1 2X

iR3j 2 R21 2 1s

" #9b

dCCO2dz tg

Xi

R3;ij 1 R21 2 1s" #

9c

SO2 absorption: During coal combustion, the sulphurcompounds are oxidized and the resultant sulphur dioxideis reduced by calcium oxide particles (produced by the lime-stone calcination), forming calcium sulfate according to thereaction:

SO2 1 CaO 1 12 O2 ! CaSO4The reaction rate of a limestone particle can be expressed as[21]:

kL p6 d3s kvLCSO2 10

where, kvL represents the overall volumetric reaction rateconstant and CSO2 is the SO2 concentration in the combustiongases. The overall volumetric reaction rate is calculated by:kvL 490 exp217500=RTsSgls 11where Sg is the specific surface area correlated with calcina-tion temperature given by [21]:Sg 2384Tg 1 5:6 104 Tg $ 1253 K 12a

Sg 35:9Tg 2 3:67 104 Tg , 1253 K 12band ls is the limestone reactivity which is a function of thefractional conversion of CaO, temperature and particlediameter.

2.3. Heat transfer modelDense zone: A 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:

CpfmfdTfdt Afmv;cHv;c 2 Qv1 AfhTg 2 Tf

1 Afs1fT4g 2 T4f 1 HH2OdmH2O

dt

13

where Qv represents the fraction of the particle heat ofcombustion, mv and mc are the mass flow rate for volatilecombustion and char combustion, respectively. The energyequation for inert particles is similar to Eq. (13) but withoutconsidering the combustion:

CpsmsdTsdt AshTg 2 Ts1 Ass1sT

4g 2 T4s 14

Dilute region: A typical energy balance for a cell near thewall in the dilute region can be written as follows:ddz m

zgCgTg 1 mzfCfTf 1 mzsCsTs1

ddr m

rgCgTg 1 mrf CfTf

1 mrsCsTs Qrel 1 Qrad 1 4hD Tw 2 Tg 15

where superscripts, z and r, represents axial and radial direc-tions, respectively. Qre and Qrad are energy released fromcombustion and radiative heat fluxes to the walls, and D isthe equivalent diameter of the furnace. The convection coef-ficient, h, is predicted according to the model of Mahalim-gam and Kolar [22] for circulating fluidized beds.

The most extensively used model to predict the radiativeproperties of spherical particles is the Mie theory. The parti-cles in a CFB combustor that may be assumed as spherespresent typical size parameters x (x pd=l, where d and lare the particle diameter and wavelength) that do not fallinto the Mie theory [23]. For the cases where particles havea size parameter x much larger than unity the scattering ismainly a reflection process and hence can be calculatedfrom relatively simple geometric reflection relations. Theoverall emissivity was computed considering the gasesand particles as a mixture of gray media. The radiativeheat flux to the walls is evaluated by the zone method.The gas and wall cells are assigned, and the temperatureis assumed to be constant within each cell. The energyequation for gas cell j is:X

iSiGjsT4w;i 1

Xi

GiGjsT4g;i 4KDVsT4g;j 2 qh;g;j 16

and for wall cell j:Xi

SiSjsT4w;i 1X

iGiSjsT4g;i 1jsT4w;j 2 qa;s;j 17

where qh and qa represent the heat generation by combustionin the gas cell and the net heat load of the wall cell. The totalexchange areas, GiGj, GiSj, SiGj and SiSj are a function ofonly the shape of the system, and can be predicted accordingto the method proposed by Hottel and Sarofim [24] forcombustors.

L. Huilin et al. / Fuel 79 (2000) 165172168

3. Numerical procedure

Coal particles are considered as a discrete number ofsizes. Each particle size is partially burned out in eachpassage in the furnace, and its diameter is thus reduced.The recirculating char particles are considered in the sizeclasses closer to the diameter at the end of previous passage.

The overall strategy applied to the model can be outlinedin four steps. (1) The solution of the hydrodynamic equa-tions of mass was first obtained by means of the hydrody-namic model. To calculate the size distribution of ash andlimestone in the dense region, it was initially assumed thatthe limestone in the dense region had the same distributionas that of the feed. The mean particle size present in thedense region was calculated and the hydrodynamic modelwas solved. Then, taking into account the distribution ofsolids in the recirculation stream, a new particle diameterin the dense region was determined and the hydrodynamicmodel was again solved. This process was iterated untilconvergence to the given condition. In the dilute region,plug flow of gas was assumed, and the particle concentra-tion, size and flow-rate of solids were obtained by means ofthe hydrodynamic model. (2) With the size distribution andconcentration values obtained in step 1, the devolatalizationof a coal particle and combustion of the char particle werecomputed by making use of the combustion model. The setof non-linear differential equations governing the combus-tion model are solved using the RungeKutta method [25].In the dense region, the oxygen concentration of the input

was given. At the inlet of dilute region, the secondary airmodified the oxygen concentration profiles, increasing itsvalue from the secondary air ports. The carbon combustionefficiency was predicted. (3) With the size distribution andgas species distribution along the furnace, the temperaturedistribution was computed by means of the heat transfermodel. (4) The solution of the hydrodynamic field wasrepeated with the updated values in steps (1) and (3), Newsize distribution in the dense region and particle concentra-tion profile along the dilute region can be obtained. Theprocess is iterated until convergence on the carbon concen-tration is reached.

4. Simulation results and discussion

The model described in the previous section was appliedto a typical circulating fluidized bed boiler [26]. The tech-nical parameters of the CFB boiler are steam capacity of35 t h21, superheated steam temperature and pressure of4008C and 2.45 MPa, respectively. The overall dimensionsare 9.3 m high and a cross-sectional area varying from 5.12(at the distributor) to 7.04 m2 (above). The combustion air issupplied through the distributor (primary air) and thesecondary air inlets, The secondary air ports are located at1.7 m from the distributor.

Most of the energy is released to the walls covered bywater tubes. It is assumed that the water-wall tubes have auniform temperature. In the present work, the temperature inthe dense zone was fixed at 1123 K. The design fuel for theboiler is a mixture of low grade coal and the cinder fromchain grade stoker boilers. Coal compositions used areshown in Table 2. The particle size distribution of thefeed coal is shown in Fig. 1. The average particle diameterof the feed coal is 1.96 mm.

Fig. 2 shows concentration profiles of CO2, CO, H2O andO2 along the height of the furnace. In the present model it isassumed that the reaction rate was directly proportional tothe reaction rate of coal combustion. The high concentrationof O2 and low levels of CO2 emissions show that thecombustion of coal in the dense zone is still significant inthe controlling coal combustion process. The resultant parti-cle size distribution in the dense zone is also shown in Fig. 1.The computed average particle diameter is 2.16 mm. Fig. 3shows the char concentration distribution in the dense zoneas a function of particle diameters. The computed averagechar concentration is 2.65 wt %. The content of watervapour is high in the flue gases due to the high moisturecontent in the coal considered.

The predicted gas temperature profiles along the furnaceare presented in Fig. 4. The inlet temperature of feed andrecirculated particles are about 293 and 773 K, respectively.The feed coal particles are dried and heated in the densezone leading to a slight decrease in the gas temperature untilthe coal particles ignite. The volatile gasses released fromthe coal particles were assumed to be instantaneously

L. Huilin et al. / Fuel 79 (2000) 165172 169

Table 2Ultimate analysis of the firing fuel (wt % as received)

Loading C H O N S Moisture Ash Qnet J/kg38.2 t/h 43.7 1.8 3.9 0.9 0.6 8.9 40.0 1602435.0 t/h 41.9 1.8 3.9 1.3 0.7 8.6 41.9 1568124.5 t/h 43.0 1.9 3.4 1.5 0.7 8.3 41.3 15773

Fig. 1. Particle size distribution.

burned and distributed uniformly in the dense zone. Forrecirculated particles, only char combustion is consideredsince devolatilizations are complete in the first passage inthe furnace. Due to these particles, the gas temperatureremains almost constant along the whole furnace, which istypical for CFBC. Computed results indicated the gastemperature near the wall was less than at the centre inthe dilute region. The trend of gas temperature along theradial direction depends mainly upon the solid mass fluxdistribution. Simulation results also indicated that the dryingtime is not negligible in the dense zone.

Heat flux distributions of radiative and convectivecomponents are shown in Fig. 5 along the furnace height.Convective heat transfer is almost constant, and radiativeheat flux decreases along the furnace height because of gastemperature. This leads to a slight decrease in the total wallheat flux. It can be seen that about 70% of the total heat fluxto the walls is by radiation transfer, while the other 30% is

transferred by convection. In this case, the gassolid is rela-tively dense and the convective heat transfer still plays animportant role in the transfer process. For low loadings,however, computed data showed that radiation transferdominates the whole heat transfer process, and the convec-tion component is negligible.

Fig. 6 shows the variations of heat flux with boiler loads.It can be seen that the heat flux decreases with decreasingboiler loads. The measured and computed boiler perfor-mances are shown in Table 3. The computed circulatingratio is 4.75, while the design value of the boiler was 3.32for 100% maximum continuous rating.

Fig. 7 shows the SO2 concentration profiles as a functionof the limestone mean particle size with furnace height. Thesmaller particles have higher reactivity than the larger parti-cles, this means a larger capability to absorb SO2 for largeparticles in the combustion gas, but their residence time islow. Considering recirculation, however, the residence time

L. Huilin et al. / Fuel 79 (2000) 165172170

Fig. 2. CO2, O2, CO and H2O concentrations along the furnace.

Fig. 3. Profile of char concentration in dense zone.

Fig. 4. Flue gas temperature profile along the furnace.

Fig. 5. Predicted heat fluxes along bed height.

of particles is similar for all particle sizes. Thereby, theretention of SO2 is higher for small limestone particlesdue to the higher reactivity for a given conversion fraction.Fig. 8 shows the SO2 emission profiles for various Ca/S

mole ratios at given particle size. It is clear that the reactivityof limestone does not remain the same throughout. Decreas-ing the calcium to sulphur ratio, the conversion of CaO toCaSO4 within the particles increases.

5. Conclusions

A numerical model to simulate two regions with combus-tion in the furnace of a circulating fluidized bed boiler oflow circulating ratio with wide size distribution was imple-mented. This model was coupled a model for the denseregion derived from turbulent bubbling bed theory with amodel for dilute region which was a core-annular flow struc-ture. Radiative heat transfer in the dilute region wasmodeled by using zone method.

The model allows for the calculation of gas concentra-tion, chemical species, temperature and heat flux along thefurnace. A model for SO2 retention was also included. Themodel can now be used to represent a CFBC unit in variousapplications but more experimental data are still required toconfirm the proposed CFBC model in order to make it morecomprehensive and reliable.

L. Huilin et al. / Fuel 79 (2000) 165172 171

Fig. 6. Profile of heat fluxes to the wall.

Fig. 7. SO2 emissions as a function of limestone particle size.

Fig. 8. SO2 emissions as a function of Ca/S mole ratio.

Table 3Test performance of the 35 t/h CFB boiler with low circulating ratio

Boiler load (t/h) Excess air ratio Heat lossdue tounburnedcarbon (%)

Heat lossdue tounburnedgases (%)

Boilercombustionefficiency (%)

110% MCR 38.2 0.37 10.16a/4.28b 5.74a/2.07b 84.1a/93.65b100% MCR 35.0 0.32 9.90a/5.61b 5.36a/2.13b 84.74a/92.26b75% MCR 24.5 0.93 11.09a/5.74b 7.70a/2.63b 81.21a/91.63b

a Experimental values.b Computed data.

Acknowledgements

This work is currently supported by The State KeyLaboratory of Clean Combustion of Coal in TsinghuaUniversity.

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