Measurements and Application of a Discrete Particle Model(DPM) to Simulate Combustion of a Packed Bed of

Individual Fuel Particles

B. PETERS*Research Centre Karlsruhe P.O. Box 3640, D-76021 Karlsruhe, Germany

The objective of this study is to investigate experimentally and numerically all the processes (i.e., heat-up,drying, pyrolysis, and combustion) experienced by coal or biomass in a packed bed moving on a forward actinggrate. As a novelty, the approach considers a packed bed to be composed of a finite number of individualparticles, which may have different properties or sizes. Each of these particles undergoes a sequence ofprocesses such as heat-up, drying, pyrolysis, or gasification and oxidation. The latter are described withsufficient accuracy by a set of one-dimensional and transient conservation equations for mass and energy. Thus,the sum of all these processes constitutes conversion of a packed bed. The ensemble of particles has a solidphase and a void space between them. Heat and mass transfer couples the flow within the void spaces to theparticles. The state of the gaseous phase is described by differential conservation equations for mass,momentum, and energy of a compressible reacting flow. The predictions of the numerical model are comparedto both experiments with single particles and measurements taken inside a combustion chamber close to thebed’s surface. The experiments with single particles validated the model for single particles. Good agreementwas achieved for the processes of drying, pyrolysis, and gasification for a range of both particle sizes andtemperatures. The computed concentrations and temperatures along the surface of the bed were compared tomeasurements and showed satisfactory agreement. © 2002 by The Combustion Institute

NOMENCLATURE

A surface m2

A pre-exponential factor dependingC Forchheimer constant 1/mc concentration kmol/m3

cp constant-pressure specific heat W/kgKcv constant-volume specific heat W/kgKcr reactive species kmol/m3

D diffusion coefficient m2/sd diameter mEa activation energy J/mole internal energy Jf correlation coefficient JFi3j view factor -Hm reaction enthalpy kJ/kgHevap. evaporation enthalpy kJ/kgK Forchheimer constant m2

k Arrhenius constant dependingk permeability m2

L characteristic length mM molecular weight kg/kmolm mass kgO inner surface area m2

P porosity of bed -

p pressure N/m2

q heat flux W/m2

q specific heat flux W/m3

r independent variable mR radius mRg gas constant J/molKS mass source kg/m3st time sT temperature KT� ambient temperature KTw wall temperature Kv� velocity m/sY mass fraction -

Greek Symbol

� heat transfer coefficient W/Km2

� mass transfer coefficient m/s� pore length m/s� heat loss/gain W� contact angle o� difference -� emissivity -� porosity -� dissipation rate m2/s3

� heat conductivity W/m2K� dynamic viscosity kg/m s*Corresponding author. E-mail: Bernhard.Peters@avl.com

COMBUSTION AND FLAME 131:132–146 (2002)0010-2180/02/$–see front matter © 2002 by The Combustion InstitutePII S0010-2180(02)00393-0 Published by Elsevier Science Inc.

� kinematic viscosity m2/s� stoichiometric coefficient - density kg/m3

Boltzmann constant J/K� time scale s� tortuosity -� temperature °C source term depends

Subscripts

B packed bedc charcond conductioneff effective valuesevap evaporationg gaseous phasei, j species0 reference valueP particlerad radiations solid phaseT Tar� ambient value

Superscripts

n geometry exponentma reaction order of species amb reaction order of species bmc reaction order of species co initial value

Surscripts

- dimensionless variable� time derivative

INTRODUCTION

Conversion of Particles

A numerical study by Veras et al. [1] showed therate of particle combustion to be independentof pressure for large bituminous coal particles(�300 �m) at moderate gas temperatures.However, the rate is strongly affected by a lowtotal pressure in a medium size range (�100�m) and inversely dependent on pressure forsmall particles (�20 �m). Veras et al. [2] con-cluded from their experiments that high concen-trations of oxygen permit the oxidiser to reach

the particle’s surface. Thus, combustion is al-ready initiated while pyrolysis takes place. Anumerical analysis, based on the parameters ofKobayashi’s model [3], provided further evi-dence of devolatilization and combustion over-lapping. Saastamoinen and Richard [4] ob-tained similar results from numerical andexperimental investigations, indicating that si-multaneous drying and pyrolysis do occur with asolid fuel. They also concluded that a realisticmodel of pyrolysis should use a temperature-dependent asymptotic yield. Applying the samemodel to the drying and pyrolysis of wet bio-mass particles [5] showed that drying startsmuch earlier than pyrolysis, but continues al-most to the end of the pyrolysis stage. Simmonsand Ragland [6] studied the effect of moistureon the combustion of wood particles (10 mm)suspended in a thermo-balance. They concludedthat drying and combustion occur simulta-neously. Jung and Stanmore [7] observed over-lapping drying and devolatilization of large coalparticles in a fluidized bed.

As regards various processes for waste mate-rial, Swithenbank et al. [8] assume sequentialprocesses without overlap. Weber et al. [9] alsoassumed sequential devolatilization and com-bustion when modeling a swirling flame ofpulverised coal. However, experimental resultsgive evidence of processes not occurring indistinct temperature regions. Saastamoinen etal. [10] found that simultaneous pyrolysis andchar oxidation do occur, when oxygen reaches aparticle’s surface in the devolatilization stage.Moreover, the overlap of homogeneous andheterogeneous combustion is favored by lowtemperatures, and by high concentrations ofoxygen and small particles.

While the investigations mentioned aboveconcentrated on a phenomenological descrip-tion of combustion, Loewenberg and Levendis[11] included the effects of diffusion in poresand the growth of pores, as well as inert mineralmatter and heat and mass transfer in the gasphase. Time-dependent, one-dimensional equa-tions for the particle’s temperature, radius, andthe ash layer thickness described the dynamicsof combustion. These equations were coupledwith conservation equations for gas-phase trans-port. The conversion of solid carbon into COwas accounted for by a one-step reaction with

133PACKED BED COAL COMBUSTION

oxygen. On the basis of experimental results,char was characterized in terms of particle size,morphology, density, and pore structure as partof the simulation. In conjunction with theseparameters, the intrinsic rate of reaction wasevaluated. Comparison with a simpler model[12] revealed that predicted intrinsic rates dif-fered by a factor of 5 to 8, because of gas phaseproperties and pore enlargement. The esti-mated rates were used to calculate temperatureprofiles, which were found to be in good agree-ment with measurements. A similar experimen-tal and modeling study of the combustion ofcellulosic char under laminar flow conditionswas carried out by Smith, Pendarvis, and Rice[13]. They tried to develop an integral reactormodel, which fitted the combustion rates mea-sured in a thermogravimetric furnace at 473 to1173 K with a mole fraction of oxygen of 0.03 to0.21. But unlike previous authors, who hadstated that reactions were chemically con-trolled, they developed a model for mass trans-fer control and hence assumed char to burninherently quickly. A one-dimensional unsteadytransport equation, with mass transfer charac-terised by the Sherwood number, gave results,which agreed with the experimental measure-ments to within 11%. From these results theauthors inferred that the reaction zone does notpenetrate into the porous char to any apprecia-ble extent.

Another study emphasising the importance ofthe kinetics of oxygen chemisorption on coaland char was conducted by Khan, Everitt, andLui [14]. The chemisorption of oxygen is impor-tant in evaluating auto-ignition and in investi-gating heterogeneous combustion. The chemi-sorption of oxygen on coal particles 24 �m indiameter was measured with a thermogravimet-ric analyzer at 100° to 225°C. For a betterunderstanding of the process, the validities ofvarious one-dimensional and unsteady modelsin predicting chemisorption rates were tested.One of them, the Elovich equation is commonlyused and describes the relationship between therate and the concentration of oxygen dcO2

/dt �a exp(��cO2

), where a and � are empiricalconstants. Comparison with the measurementsshowed that no fit could be achieved with asingle set of constants, a and �. Similar resultsof the model breaking down in distinct regions

were also reported by [15, 16]. The secondmodel with an Arrhenius equation revealed thatthe activation energy increased from 4- to 63kJ/mol with a rise in temperature. Additionally,the activation energy was found to depend onthe coverage of oxygen. With the shift of acti-vation energy taken into account it was pro-posed that chemisorption is influenced to alarge extent by diffusion. A shrinking-areamodel which allowed oxygen to access freelyavailable surface area without any limits ondiffusion also was incapable of predicting thetime-dependent uptake of oxygen. Finally, adiffusion model was tested [14] and showedgood agreement with the adsorption data. How-ever, errors in the early stage of chemisorptionmay be quite large. Therefore, the authors [14]concluded that in the early phases the Elovichequation represents a good approximation,whereas the latter stages are better representedby the parabolic diffusion law.

Man [17] et al. numerically solved the two-dimensional, unsteady, laminar conservationequations for mass, momentum, energy, andgas-phase species in the conversion of a singleparticle. The effects of particle entrainment,pre-exponential factor, initial relative velocity,the particle size and the free-stream oxygenconcentration on the combustion of a singleparticle were investigated. The burn-out timedecreased by 25% when the entrainment of theparticles was included. As the particle is en-trained by the surrounding steady flow in anearly stage of its combustion, a different freestream velocity has only minor effects on theburn-out times. An increasing particle diameteralso causes the burn-out time to increase. Vari-ation of surrounding conditions showed thatafter an initial stage of combustion the two-dimensional distributions shifted to one-dimen-sional profiles. Similar investigations enabledLee at al. [18] to solve the reacting flow field onand around the surface of an isolated carbonparticle using a fully transient formulation, withgas phase reactions and five heterogeneoussteps. Particles ranging from 10 to 2000 �mwere placed in various gaseous oxidising mediaat 1400 K and showed highly transient burningcharacteristics, which could deviate significantlyfrom those predicted by quasi-steady state as-sumptions. Furthermore, Lee et al. [18] stressed

134 B. PETERS

the fact that it is essential to apply intrinsic ratemodeling. Numerical simulations by Lee et al.[19] confirmed the transient behavior and werein sufficient agreement with the experiments.They assessed that progressing combustion islikely to affect the morphological structure of aparticle, for example, its porosity for which theyaccounted for by a constant factor.

It is common to all the above-mentionedstudies that they only assess the ideal case ofsurface reactions on a particle without temper-ature and species profiles inside the particle.However, the existence of different regimes hadalready been postulated by [20, 21]. A detailedstudy of reaction regimes of a packed bed canbe found in [22]. Some papers [23, 24] alsostressed modeling of intrinsic rate. Despite thedifficulty of developing an adequate model, itoffers the greatest potential for differentiationamong various rate-influencing parameters.One recommendation seems to be that intrinsicrate modeling cannot be circumvented, despitethe effort that must be invested.

Overall Conversion of the Bed

To describe the drying of a packed bed,Raubenstrauch [25] supplied the two-dimen-sional Phoenics code, solving the conservationequations for the gaseous and the solid phases,with material properties and source terms. Thesolid phase was considered to be a porouscontinuum with no detailed distribution of par-ticle sizes. Drying was approximated by a heter-ogeneous reaction, for which the rate constantsincluded the effects of pore diffusion as well asheat and mass transfer [26]. Based on a one-dimensional homogeneous model Fatehi andKaviany [27] predicted the propagation velocityof a conversion front through a fixed bed ofwood as a function of initial flow rate of air.Likewise Hartner [28] described a reacting fixedbed by a one-dimensional and transient conser-vation equation for the gaseous and the solidphases. Beckmann and Scholz [29, 30] approxi-mated the incineration of waste material on atraveling grate by a cascade of well-stirred reac-tors. The thermodynamic and chemical state ofeach reactor was predicted by a global mass andenergy balances. Therefore, each reactor re-quires empirical correlations, which are deter-

mined experimentally. To describe the inciner-ation of entire tree trunks on a grate, Brydenand Ragland [31] approximated the process by aconversion layer propagating through a trunk.Incineration was considered to be the rate-determining process, for which the rates ofdrying and pyrolysis were derived from empiri-cal correlations. To support the design of plantsincinerating wood, Kuo et al. [32, 33] developeda one-dimensional model in conjunction with aglobal energy balance to predict the conversionrate, the thermal load of a grate and the gasphase. The approach, however, requires exper-imental correlations to describe major charac-teristics of the process. Krull et al. [34] de-scribed the packed bed as a continuous porousmedium divided into two layers with mass andenergy balances for the solid and the gaseousphases. Their effort was aimed at determining therelease of species and energy from the packed bedwith a CFD-code as boundary conditions for thegas plenum above the packed bed.

Goh et al. [8] divided the packed bed abovethe grate into four layers representing fuel,drying, pyrolysis, and ash. Each layer was de-scribed by integral balance equations, with thetransport of energy only occurring normal to thegrate through convection and an effective con-ductivity. Empirical correlations were requiredto describe thermal conversion adequately.They had to be determined experimentally foreach fuel, which consisted of four main compo-nents: free moisture, volatiles, solid carbon, andbound ash. As the solid material was heated, themoisture is removed by evaporation at �373 K.The volatiles consist of carbon, hydrogen, andoxygen and are formed during pyrolysis. In theabsence of oxygen, the gaseous volatiles re-leased are assumed to be mainly hydrocarbons(CxHy), carbon-monoxide (CO), hydrogen (H2),and water (H2O). When the moisture and thevolatiles have been driven out, carbon andbound ash remain as solids. The carbon isassumed to react with the available oxygen andcarbon-monoxide to form carbon-dioxide even-tually. The bound ash is set free during oxida-tion. Saastamoinen et al. [35] studied the speedof the propagation of an ignition front down-wards against the air flow in a packed bed ofwood. They described the temperature withequations for energy conservation in the gas and

135PACKED BED COAL COMBUSTION

the solid phases, respectively, for which thespeed of propagation was introduced by a coor-dinate transformation. The effects of the flowrate of air, moisture, particle size, density, andspecies in the wood on the velocity of theignition front were investigated both experi-mentally and numerically. Moisture was foundto lower significantly the speed of the ignitionfront, whereas no influence of particle size wasnoticed. They also found that the front’s speedis inversely proportional to the specific heat ofthe wood and the density of the fuel bed. Shinand Choi [36] developed a one-dimensionalmodel to describe the incineration of wood for alaboratory scale furnace. They used macro-kinetic data to characterize conversion as afunction of the primary air supply and thecalorific value of wood.

The above-mentioned approaches have incommon the simplification, that a one-dimen-sional treatment of a packed bed as a continu-ous two-phase system represents a rough ap-proximation of all the conversion processes;consequently any information on individual par-ticles becomes irrelevant by this approach.Hence, such a model cannot predict thermalconversion very accurately and requires severalempirical correlations to compensate for thisloss of information. Therefore, this paper dealswith the development of a Discrete ParticleModel (DPM) to detail the thermal conversionof a packed bed by describing processes forindividual particles with sufficient accuracy.Thus, a model for a single particle is developed;it can be applied to each particle in a packedbed and represents the entire conversion of apacked bed as a sum of processes for singleparticles. The single particle model is based ona system of one-dimensional transient conserva-tion equations for mass and energy to predictmajor properties such as temperature and thedistribution of species inside a particle. Theparticles are coupled to the surrounding gas-eous phase by heat and mass transfer.

Products released during pyrolysis anddevolatilization are transferred into the gaseousphase of the void space in a packed bed. Fromthere they are transported into the gas plenumabove the packed bed, where the combustiblecomponents are burned by homogeneous com-bustion.

EXPERIMENTAL SET-UP

Single Particle Test Facility

Experiments were carried out to compare thepredictions of heating-up, drying, and pyrolysisof large wood particles with the measurements.For the investigations into the drying of spher-ical wood particles under defined heat transferconditions the experimental set-up shown inFig. 1 was used [37]. The drying chamber con-sisted of an insulated cylinder (d � 5 cm, h � 10cm), electrically heated to the desired temper-ature. The wooden sample was suspended fromscales to record the weight loss because ofdrying or decomposition. While the reactor washeated up, the sample was isolated from thechamber to avoid uncontrolled reactions. At thestart of the experiment, the sample was movedup into the reaction chamber, through whichnitrogen of constant temperature flowed. Thesamples consisted of spherical particles of beechwood (dp � 8 mm) [38] with an initial moisture-content of x � 67 wt%. A different value of x �33 wt% was achieved by a controlled pre-dryingprocess.

Packed Bed Test Facility

The experimental test facility TAMARA isshown in Fig. 2. Its thermal capacity was 0.5 kW;it was designed for a fuel charge of 150 to 300kg/h at a maximum volumetric flow rate of air of1000 Nm3/h. Because of variable roof elements,co-, center-, and counter-flow configurations

Fig. 1. Test facility for experiments with single particles.

136 B. PETERS

were all possible. The experiments for woodwere conducted with central flow. The grate’ssurface (length: 3.2 m, width: 0.8 m) was dividedinto four zones, for which the grate’s motionand the primary air supply may be adjustedseparately. Any secondary air was introduced atthe entrance of the first flue.

Temperature measurements of the flue gasleaving the bed were carried out at the fivesampling locations S1 to S5 along the grate andat the entrance of the first flue. Additionally, gaswas sampled at these locations �10 cm abovethe bed of fuel. The sampling was conductedwith cooled probes, with subsequent dust filtra-tion (carbon analysis of the dust) and watercondensation for the determination of vapourconcentration. To identify and quantify the ma-jor C-H-species off-line analyses by GC/MSusing filter, condensate and separate gas sam-ples. On-line-monitoring of the following com-ponents took place: Oxygen, carbon-dioxide,carbon-monoxide, hydrogen, sulfur, and organiccarbon, as described by Hunsinger et al. [39].Sampling was carried out for a period of 15 minat each position. This procedure was repeated 5to 6 times. The total duration of the experimentwas about 7 to 8 h. Measurements of concen-tration during the single runs of one experimentshowed good reproducibility [40].

NUMERICAL MODEL FOR THE PACKEDBED

Conversion of a Single Particle

To describe the phases of one particle beingheated up with the simultaneous evaporation ofwater, pyrolysis, and heterogeneous combustion[5, 4], a differential approach, including intrinsicmodelling, yields more accurate results thanpostulating a reacting or a shrinking core modein advance. It is not feasible to employ a three-dimensional model for each particle in a packedbed, as this would exceed currently availablecomputer sources. However, an unsteady, one-dimensional method for spherical particlescombines sufficient resolution of the particle’sproperties with a reasonable computation time.The assumption of one-dimensionality is alsosupported by Man [17], who detected a mainlyone dimensional behaviour when comparing hiscomputations with measurements. Further con-firmation comes from the experimental investi-gations of Senf [41], whose results indicate thatemissions of PM (particulate matter) and ratiosof volume to surface are not correlated.

The mechanism of gasification and oxidationis taken to involve adsorption, reaction anddesorption of gaseous molecules on the innersurface of the particle and is described by theLangmuir isotherm [42, 43]. Thus, the rate of aheterogeneous reaction can be written asdcs/dt � kcsci,g/�1 � Kci,g�, where k denotes afrequency factor and cs and ci,g are concentra-tions of the solid and gaseous phases. Thisequation represents the source term for thetransport equations, which determine the distri-bution of temperature, concentration of gases inthe pores, solid material, specific inner surfacearea, and porosity. The volume-averaged quan-tities � are derived from the phase-averaged�i quantities with the local value of the poros-ity [44]. Because of the general formulation ofthe conservation equation the geometrical do-main representing the particle’s shape can beconsidered as an infinite plate (n � 0), aninfinite cylinder (n � 1), or a sphere (n � 2).

The conservation of a component ci in the gasmixture depends on a chemical source term, adiffusive and a convective flux:

Fig. 2. Pilot test plant TAMARA.

137PACKED BED COAL COMBUSTION

�ci�

�t �1

rn

��r � rnDi

�ci�i

�r � rnv�ci�� � ci

(1)

Any contribution from Knudsen diffusion isneglected, because the pores [45, 46] have adiameter of �50.0 �m and the pressure is �1bar, so that only molecular diffusion occurs. Asa result of the averaging process and the influ-ence of tortuosity � on the diffusion, an effectivediffusion coefficient is derived as Di,eff �Di�p/�, where �P is the porosity of the particleand the molecular diffusion coefficients Di aretaken from the equivalent ones of the appropri-ate species in nitrogen [47, 48]. To treat heter-ogeneous reactions efficiently over a wide rangeof applications, a formal approach for the source

term in Eq. 1 is introduced as ci� k0 exp ��Ea

RT �ca

macbmbcc

mc and ci� k0 exp ��Ea

RT � camacb

mbOspmc.

In this way, a heterogeneous reaction can bedescribed by the concentration of the solidmaterial cc or the specific inner surface area Osp

representing the available active sites for ad-sorption and desorption. Although, a detaileddescription of adsorption and desorption isomitted, it is believed to offer a great flexibilityand moderate computation time. Thus, a de-scription of the transport of educts in conjunc-tion with the evolution of the inner surfacecovers the entire range of the particle’s reactionbetween the limiting cases of a reacting and ashrinking core model. Homogeneous reactionsof gaseous components in the pores of a particleare excluded, because the residence time insidethe particle is too short.

For the conservation of solid and liquid spe-cies, transport mechanisms are neglected, sothat their change in time is due to a reactionsource term �ci�/�t � ci

. Because kinetic con-trol and transport control are taken into ac-count by intrinsic rate modelling and equationsof transport, respectively, the current approachcovers all the modes of reaction between ashrinking and a reacting core. Depending on therate-limiting process, the depletion of solid ma-terial, therefore, results in either a decreasingparticle density or a reduction of particle size

[22, 49]. The latter causes a decreasing height ofa reacting bed.

The distribution of porosity � and specificinner surface area Osp is determined by thefollowing equations ��/�t � sMs/s� and �Osp/�t � s(1 � �o)/cs

o, where Ms, cs, s, and �denote the molecular weight, concentration ofsolid material, reaction rate of solid materialand characteristic pore length, respectively [49,50].

For convective transport, immediate outflowof the products is assumed. Therefore, a repre-sentative velocity in Eq. 1 is estimated by con-verting the sum of all reaction rates in a volumeelement Vi into an out-flowing flux at its bound-ary surface Ai according to

v� �Vi�k k

AiG�(2)

The density G� of the gas mixture is deter-mined by the equation of state. The outflow ofgases will prevent species surrounding the par-ticle from penetrating the particle. Thus, gas-eous species can only be transported to theparticle’s surface if the convective term due tothe gas production in the particle is smaller thanthe diffusive transport through the boundarylayer. This is accounted for by relating thesurface flux to a maximum diffusion rate.

ci

A�

D � c�

�� � � c� (3)

This approach estimates the time when speciesstart to penetrate the particle. It is believed todescribe the change from pyrolysis to the charcombustion regime with sufficient accuracy forthe case of a wood particle with high productionrates of gas during pyrolysis.

By assuming thermal equilibrium between thegas mixture phase, solid material and water, the

�cpT�

�t�

1rn

�

�r �rn��T�

�r� rnv�Gcp,GT���

(4)

The locally varying effective transport coeffi-cient �eff because of averaging is approximatedby the following expression �eff � �P�g ��wood (1��)�c �rad, which takes intoaccount heat transfer by conduction in the gas,

138 B. PETERS

solid, char, and radiation in the pore [46]. Thelatter is assumed to be significant at highertemperatures [51]. The convective term as afurther mechanism of transport is estimated bythe velocity of Eq. 2. The source term representsheat production or consumption caused by reac-tions weighted by their respective enthalpies.

Integral methods describing transfer by heatand mass transfer coefficients, respectively, willbe applied in this study. A wide range of exper-imental work has already been carried out inthis field and the appropriate laws in terms ofNusselt and Sherwood numbers are well estab-lished for different geometries and flow condi-tions.

The following boundary conditions for massand heat transfer of a particle are applied:

�Di,eff

�cG,i�i

�r�

R� �i�cGi,R�i � c�� (5)

��eff

�T�

�r�

R� ��TR� � T�� � qcond � qrad

(6)

where ci,�, T�, �, and � stand for the ambientgas concentration, temperature, mass, and heattransfer coefficients, respectively. As well asconvective heat transfer, a radiative heat fluxqrad on the particle’s surface and a conductiveflux qcond between particles in contact can betaken into account.

The conductive heat flux between two neigh-bouring particles in contact is estimated by

qcond � �1

1/�1 � 1/�2

�T�r

� �1

1/�1 � 1/�2

TS,1 � TS,2

�rS,1 � �rS,2(7)

where the temperature gradient between twoparticles is approximated by the temperaturedifference between the outer shell values of theparticles and its distance �rS,i from the outerparticle surface. The thermal conductivities �1

and �2 refer to the particles in contact, respec-tively. The contact area is assumed to be qua-dratic and determined by the contact angles �1

and �2 by Ac � 1/ 2 ((R1 tan �1)2 (R2 tan�2)2) as sketched in Fig. 3.

At higher temperatures, a particle i emits aradiative flux with its surface temperature (TS)and adsorbs a flux qrad,j from all neighbouringparticles j weighted by the respective view factorFi3 j. Thus, the total flux because of radiationis given by qrad � �j Fi3 j � qrad, j � �TA�4,where � and � denote the adsorbtion and emis-sion coefficient, respectively. The view factor isdetermined as the ratio of the surface of particlei to the sum of the surfaces of all neighbouringparticles j with Fi 3 j � Ai/�j Aj.

Because of the outflow of volatiles and steamfrom the particle the Stefan correction is intro-duced into the transfer coefficients, which areestimated as follows [52]:

� �mg/g

exp �mg/g�0� � 1(8)

� �mg cp,g

exp �mg cp,g/�0� � 1(9)

where �0 and �0 denote the transfer coefficientsfor a vanishing convective flux over the particlesurface.

In a packed bed, the mass and heat transferrates or the Nusselt and Sherwood numbers areaugmented by the tortuosity of the flow paths ascompared to a single particle [53]. According toSchlunder et al. [54] the appropriate Nusseltnumber NuB and Sherwood number ShB for apacked bed are derived from a single particle byNuB � f NuS and ShB � f ShS. The correlationcoefficient f is determined by the followingrelationship [55] f � 1 1.5(1 � �P) with �P

denoting the void fraction of the packed bed.

Model for the Void Space of a Packed Bed

The gas flow in the void space between theparticles of the bed is treated as a flow through

Fig. 3. Conduction between two neighboring particles.

139PACKED BED COAL COMBUSTION

porous media according to Darcy’s law with thefollowing assumptions.

● The packed bed consists of solid particles andvoid space

● Void space is distributed at random● No void space is sealed off● The spatial distribution of the void space

varies moderately● The porosity is not too high (i.e., � � 50%)● Diffusion (slip) phenomena are lacking

Under the assumptions outlined above the re-sulting set of coupled non-linear differentialequations for mass, momentum, energy, andspecies together with the equation of state issummarized below in Cartesian coordinates formass, momentum, species, and energy.

�g

�t� � � �gv�g� � Sg (10)

Here g and v�g are the gas density and velocityat a position and time t, respectively. The sourceterm Sg on the right hand side includes rates ofmass transfer between the solid and the gaseousphases because of processes of decompositionof the particle.

��gv�g�

�t� � � �gv�gv�g� � ��pg � F �v�g� (11)

where pg stands for the gas pressure. The func-tion F(v�g) accounts for different flow regimesdefined by Eq. 12. Experimental measurements[56] have shown that Darcy’s law is valid for aReynolds number based on �k smaller than�10 with k being the permeability. Above thisvalue inertia effects reminiscent of turbulentflow over a rough surface introduce a non-linearbehavior, which leads to Forchheimer’s equa-tion as a modification of Darcy’s law.

F�v�g� � � ��

kv�g

��

Kv�g � gCv�g�v�g�

if Re � 10 (Darcy)

if Re � 10 (Forchheimer)(12)

where K and C are constants of the form [57],[58] K � d2P3/150(1 � P)2 and C � 1.75(1 �P)/dP3.

��gYi,g�

�t� � � �gv�Yi,g� � SYi,g

� Yi,g(13)

where Yi,g are mass fractions (e.g., H2O, H2, CO,CO2). The source term SYi,g

takes into accountmass sources because of evaporation, devolatil-ization, pyrolysis, gasification, and oxidation ofparticles released into the gas phase. Becausethe species transferred into the gas phase arenon-premixed, additionally to a chemical timescale, a mixing time scale is taken into account[59]. Thus, the slowest of these processes deter-mines the overall rate of conversion of speciesin the gaseous void space. According to Rotta[60] a mixing time scale is defined as tm � ��/�,where � and � denote the viscosity and thedissipation rate, respectively. Applying Kolmog-oroff’s first law of similarity, which relates thedissipation rate to a velocity v and a character-istic length scale L with � � v�3/L, yields themixing time scale tm � 1/�m � Cm��L/v�3 with

Cm as an empirical constant. Hence, the rate ofconversion in the gas phase is determined by thelimiting value of the Arrhenius equation and ofthe rate of mixing as follows:

� Yi,g� min � �i,k�mYi,k, �

k

�i,kkkeEa,k

RTg� (14)

where k indicates the summation over all reac-tions involving a species i.

��geg�

�t� � � �gv�geg� � � � ��g�Tg�

� � � pgv�g � F�v�g�v�g � �

�k

Yi, g Hm, i (15)

Here � is the heat loss/gain of the gas at the wallsand the particles. The last term includes genera-tion of heat because of chemical reactions. e �cv,gTg is the specific internal energy, given by theproduct of constant-volume specific heat cv,g

weighted by mass fractions and gas temperatureTg. The emissive and adsorptive properties of thegas phase are negligible because of the short

140 B. PETERS

distances, rays travel, and low concentrations ofvapor, carbon-monoxide, and carbon-dioxide.

To treat numerically the differential conser-vation equations the conceptual and computa-tional design is best implemented in a modularscheme, which is favored by the object-orientedtechniques applied in TOSCA (Tools of Object-oriented Software for Continuum-MechanicsApplications) [61, 62]. The relevant informationsuch as material properties and kinetic data isstored in a data base, which allows an entireparticle process to be represented through acombination of different sub-processes.

DISCUSSION

Conversion Processes of a Single Particle

Drying

The process of drying of a spherical particle offir wood was predicted and compared to mea-surements. The relevant wood properties arelisted in Table 1.

A wall temperature of Theat � 743 K was setfor the experiment while immediate outflow ofvapor was assumed because of an increasinginner particle pressure. Mass transfer, for exam-ple, transfer of vapor was estimated by Eq. 9with vanishing concentrations of vapor in theparticle’s surroundings. The process of dryingwas described by two approaches: one approxi-mated the evaporation based on an energybalance in conjunction with a given evaporationtemperature of the form

cH2O � � �T � Tevap.�cp

Hevap. �t0

if T � Tevap.

if T � Tevap.

(16)

The second approach represents a heteroge-neous reaction between liquid water and vaporas proposed by Chan and Krieger [63, 64]. The

latter is represented by � cH2O � A � exp ��Ea

RT�cH2O for free and bound water with its kineticparameters A � 5.13 � 106 1/s, Ea,1 � 24 kJ/moland Ea,2 � 120 kJ/mol. The enthalpy of evapo-ration is Hevap � �48.6 kJ/mol.

Figure 4 depicts the comparison between thepredictions and experiments of spherical parti-cles of wet fir wood with a moisture content of33% and 67%. The constant evaporation tem-perature model agrees satisfactorily with bothexperiments and is supported by the findings ofHeidenreich et al. [65]. As mentioned above, heattransfer becomes the dominant and the rate lim-iting step for large particles. Therefore, it ismatched best by the constant evaporation temper-ature model. The heterogeneous reaction model,however, significantly under-estimates the rate ofdrying and thus, leads to extended drying times.Therefore, this approach is not suited to thepresent application of large wood particles. It isassumed that the kinetic parameters of this modelpartly reflect experimental parameters such asheat transfer and therefore, cannot be employedunder different conditions.

Pyrolysis

Experiments were carried out by Bruch [37] toinvestigate the influence of the sample diameterand heating temperatures in an inert atmo-sphere of nitrogen. The kinetic data of Balci[66] (A � 1.35 � 109 1/s, Ea � 123.1 kJ/mol, �h �

TABLE 1

Properties of fir wood [45, 46]

Particle radius R 4 mmDensity p 330 kg/m3

Porosity �P 0.6Pore diameter dp 50.0 � 10�6 mTortuosity � 1.0Diffusivity D 1.1 � 10�4 m2/sSpecific Heat cp 1733.0 J/kgKConductivity �wood 0.2 W/mKConductivity �c 0.1 W/mKConductivity �rad 0.0 W/mK

Fig. 4. Drying of a particle.

141PACKED BED COAL COMBUSTION

�4500 kJ/kg) were used to predict pyrolysis offir wood, with its properties listed in Table 1. Acomparison between different models of pyrol-ysis revealed, that this model among others wasin satisfactory agreement with the experimentaldata [67]. Because of its simplicity it was chosenfor the current study. Heat and mass transfer wereestimated by Eq. 9. Figure 5 depicts the mass lossdue to pyrolysis versus time for different particlesizes and surrounding gas temperatures.

The start of the pyrolysis indicated by anegligible mass loss of the sample depends onboth the sample size and temperature. After-wards, pyrolysis progresses with an almost con-stant rate, which decreases with larger diame-ters and lower heating temperatures. Propertiesand kinetic data taken from literature, withoutfurther empirical correlations, were sufficientlyaccurate to obtain a good agreement with themeasurements. Thus, application of the kineticdata derived from dust samples within the ki-netically controlled regime to larger particlesappears to be valid. Furthermore, the resolutionin time and space of the present model is wellsuited for the current application.

Combustion

Similar to the experiments of Schaffer [38],Bruch [37] carried out combustion experimentsfor spherical particles of char, 10 mm and 15mm in diameter and a temperature of thereactor wall of 773 K. For the first order reac-tion of char and oxygen to give carbon-monox-

ide, the kinetics of Kulasekaran et al. [68] (A �301 m/s, Ea � 149.38 kJ/mol, �H � �110kJ/mol) were used. Under these conditions goodagreement between measured and predicteddata was achieved as shown in Fig. 6.

The particle radius decreases linearly indicat-ing a shrinking core behavior. Although temper-atures are rather moderate, the high reactivityof char makes transfer of oxygen through theboundary layer the rate limiting step.

Conversion on a Forward Acting Grate

The process of conversion was predicted for thepacked bed of the pilot test plant TAMARA. It

Fig. 5. Comparison between measurements and predictions for pyrolysis of fir wood.

Fig. 6. Comparison between measurements and predictionsfor gasification [37].

142 B. PETERS

included all processes of heat-up, drying, pyrol-ysis, and combustion for fir wood with its prop-erties listed in Table 1. Its initial content ofmoisture was x � 45%. The porosity of the bedwas given with �B � 0.56, which corresponds toa bed height of approximately hB � 100 mm.Combustion air was supplied at T � 300 K.Through the grate zones I and IV streams a flowrate of 45 kg/h, whereas the distribution forgrate zones II and III was twice the amounts ofzones I and IV. A constant radiative flux of q �80 kW/m2 on the bed surface was employed.This flux heats the particle on the top layer ofthe bed and eventually leads to ignition.

The process of drying was simulated with theconstant evaporation temperature model. Be-cause of pyrolysis, modeled with the approachof Balci [66], the fuel particle decomposes intochar, carbon-monoxide and hydrogen. The massfraction of hydrogen is determined by the as-sumption of the products of decomposition [37]having the same enthalpy as fir wood. Of theseproducts char is considered to be carbon under-going gasification to carbon-monoxide accord-ing to the kinetics of Kulasekaran et al. [68].After carbon-monoxide and hydrogen havebeen transferred into the gas phase of the voidspace, they are oxidized to their products of

complete combustion. The reaction rate of hy-drogen is assumed to be infinitely fast. However,the oxidation of carbon-monoxide to carbon-dioxide is estimated by the following rate � cCO

� cCOcO2

0.5cH2O0.5 A exp ��Ea

RT � with the kinetic

parameters according to Howard et al. [69](A � 1.3 � 108 m2/mols, Ea � 125550 kJ/mol,�H � �283.0 kJ/mol).

Concerning the relevance of Boudard’s reac-tion and the gasification with vapor, only theoxidation of char appears to contribute signifi-cantly to its conversion. Sufficient vapour isavailable only in the drying zone of a packedbed, where the temperatures are not highenough to initiate a significant reaction rate.Although, zones of higher temperatures followthe drying zone, vanishing vapor concentrationsprevent further reactions. In analogy, the com-bustion air supplied, excluding exhaust gas re-circulation, does not contain sufficient carbondioxide to allow for comparable reaction rates.The predictions were compared to measure-ments taken above the packed bed. Figure 7depicts the concentrations of vapor, carbonmonoxide, carbon dioxide, and oxygen emittedfrom the void space of the packed bed.

The top figure of Fig. 7 depicts the profile of

Fig. 7. Concentrations versus grate length.

143PACKED BED COAL COMBUSTION

vapor because of drying of the wooden particles.Because of radiation the particles heat up andsubsequently water evaporates and is trans-ferred into the void space of the packed bed.From there it flows to the surface of the packedbed. The constant radiative flux cause the pro-cess of drying to start at a higher rate thanmeasured and therfore, to finish earlier as com-pared to the measurements.

The distributions of carbon-monoxide andcarbon-dioxide are to a large extent determinedby the processes of pyrolysis and combustion inconjunction with the oxidation of carbon mon-oxide in the gas phase of the void space of thepacked bed. During pyrolysis the wooden mate-rial decomposes into carbon-monoxide and car-bon-dioxide. The profile of carbon-dioxidetherefore, represents the overall effect of pyrol-ysis and oxidized carbon-monoxide and is insatisfactory agreement with the measurements.The over-estimated concentration of carbon-monoxide may be attributed to an access of air,for example, oxygen that is introduced into thecombustion chamber by a leakage through theporous walls. The surplus of oxygen might causean increased rate of oxidation, which accountsfor less carbon-monoxide.

For the subsequent zone of oxidation, whichis marked by a significant increase of carbon-dioxide, the profile of carbon-monoxide de-

clines. Carbon-monoxide, produced by oxida-tion of particles, is transferred into the gasphase of the void space, where further oxidationto carbon-dioxide takes place. Towards the end ofthe grate, carbon-dioxide concentrations decreasebecause of low temperatures, which preventfurther conversion of carbon-monoxide. There-fore, the latter concentration rises slightly.

The profile of oxygen shows a decreasingbehavior during heat-up, drying, and pyrolysisof the packed bed, which is a result of thediluting effect of the emitting concentrations ofvapour, carbon monoxide, and carbon dioxide.The deviation from the measurements in thisregion is because of air leaking through thewalls into the combustion chamber and thus, toan increasing amount of oxygen. As oxidationtakes place, large amounts of oxygen are used tooxidise carbon-monoxide. With a decreasingrate of combustion, less oxygen is used andtherefore, its amounts increase towards the endof the burn-out zone, for example, grate.

Figure 8 shows the distributions of tempera-ture above the packed bed and the evolution ofbed height versus dimensionless grate length. Inthe first zone the predicted gas temperaturerises faster than indicated by the measurements.This is attributed to the applied constant radia-tive flux, which most probably is larger than theemitted radiation of the combustion chamber

Fig. 8. Temperature and bed height versus grate length.

144 B. PETERS

onto this section of the bed surface. Because theglobal energy balance of the packed bed has tobe fulfilled, the fast rise of the temperature inthe beginning is compensated by lower maxi-mum values of the gas temperature. However,taking uncertainties of measurements and theirlocation into account, the total temperaturedistribution is in good agreement with the ex-perimental data.

Because of the shrinkage of particles mainlyduring combustion, the bed is reduced in height.In agreement with empirical experience, a re-duction of the packed bed takes place only afterapproximately half of the grate length. Theheight decreases almost linearly until the lastquarter of the grate, where particles shrinkmore slowly because of falling temperatures. Inconclusion, the predicted values of temperature,species and bed height allow further applicationto CFD-codes. For the latter, these profilesserve as input, for example, boundary condi-tions to describe the processes occurring in thegas phase as carried out by Peters et al. [40]

CONCLUSIONS

Within this study a novel DPM to stimulate theconversion of a packed bed was presented. Aseach particle in the combustion chamber con-tributes to the global process of a packed bed,application of the DPM to each particle of thepacked bed contributes likewise to the entireprocess of a packed bed. It takes into account allprocesses of particles (heat-up, drying, pyroly-sis, gasification, and combustion). The flow ofgas in the void space is coupled to the solidphase via heat and mass transfer. An interactionbetween the particles themselves is consideredby both a conductive and a radiative heat flux.

The above-mentioned model was applied topredict the thermal conversion process for botha single particle and a packed bed, whichyielded the following results:

● Ensembles of particles with coupling of heatand mass transfer represent an accurate ap-proach to describing the conversion of packedbeds

● A one-dimensional and transient approachfor each particle in a packed bed is sufficientlyaccurate in describing the conversion consist-

ing of heating, drying, pyrolysis, gasification,and combustion

● A differential approach covers the entirespectra of time/length scales between a react-ing and a shrinking core behavior

● In the present approach micro-kinetic dataare applied to a single particle and a packedbed without further empirical correlations

● The fluid and thermodynamic properties inthe void space of a packed bed are estimatedby a flow through a porous medium includingheat and mass transfer between the solid andgas phases

● The method provides properties of the gasphase above the packed bed as importantinput data to describe processes of conversionin the gas plenum of furnaces

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Received 18 July 2001; revised 15 April 2002; Accepted 30April 2000

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