handbook of combustion (online) || modeling moving and fixed bed combustion

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7 Modeling Moving and Fixed Bed Combustion Bernhard Peters and Harald Raupenstrauch 7.1 Introduction Generally, any reaction process is governed by reactants available and their conver- sion rate. The availability of a reactant depends on the transport rate, either diffusive or convective. Thus, both transport and reaction rate determine the time scales of the overall process, whereby the slowest rate determines the rate of the entire process. If both rates differ signicantly, a transport or kinetic controlled reaction regime is distinguished, which may prevail for a single particle and a xed or moving bed. 7.1.1 Combustion Characteristics of an Individual Particle Based on the statements mentioned above, the conservation equation for a species Y i of a particle undergoing a mono-molecular reaction under the absence of convective transport writes in a dimensionless form as follows: 1 Fo qY i q t ¼ 1 r n q q r r n qY i q r Th Y i ð7:1Þ where the dimensionless variables Fo and Th denote the Fourier number ðt P D P =l 2 P Þ and Thiele modulus ðkl 2 P =D P Þ, respectively. The exponent n allows us to specify rectangular (n ¼ 0), cylindrical (n ¼ 1), and spherical (n ¼ 2) geometries [1]. The time- standard t P refers to a characteristic transport time scale in the regime of transport- control and to a characteristic reaction time scale in the kinetically controlled regime. A large Thiele modulus, that is, a high reaction rate limits the conversion process to a rather small spatial region at the outer surface of a particle. Hence, large parts of the interior domain of a particle remain unreacted, and therefore, this is labeled the shrinking core mode. The conversion rate may be signicantly improved by increasing the transport rate through increased mass transfer. A measure often applied is to enlarge the outer surface of the particulate material by grinding it. Handbook of Combustion Vol. 4: Solid Fuels Edited by Maximilian Lackner, Franz Winter, and Avinash K. Agarwal Copyright Ó 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-32449-1 j 257

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Page 1: Handbook of Combustion (Online) || Modeling Moving and Fixed Bed Combustion

7Modeling Moving and Fixed Bed CombustionBernhard Peters and Harald Raupenstrauch

7.1Introduction

Generally, any reaction process is governed by reactants available and their conver-sion rate. The availability of a reactant depends on the transport rate, eitherdiffusive or convective. Thus, both transport and reaction rate determine the timescales of the overall process, whereby the slowest rate determines the rate of theentire process. If both rates differ significantly, a transport or kinetic controlledreaction regime is distinguished, whichmay prevail for a single particle and afixed ormoving bed.

7.1.1Combustion Characteristics of an Individual Particle

Based on the statementsmentioned above, the conservation equation for a species Yi

of a particle undergoing a mono-molecular reaction under the absence of convectivetransport writes in a dimensionless form as follows:

1Fo

qYi

q�t¼ 1�rn

qq�r

�rnqYi

q�r

� ��Th Yi ð7:1Þ

where the dimensionless variables Fo and Th denote the Fourier number ðtPDP=l2PÞand Thiele modulus ðkl2P=DPÞ, respectively. The exponent n allows us to specifyrectangular (n¼ 0), cylindrical (n¼ 1), and spherical (n¼ 2) geometries [1]. The time-standard tP refers to a characteristic transport time scale in the regime of transport-control and to a characteristic reaction time scale in the kinetically controlled regime.

A large Thiele modulus, that is, a high reaction rate limits the conversion processto a rather small spatial region at the outer surface of a particle. Hence, large partsof the interior domain of a particle remain unreacted, and therefore, this is labeledthe shrinking core mode. The conversion rate may be significantly improved byincreasing the transport rate through increased mass transfer. A measure oftenapplied is to enlarge the outer surface of the particulate material by grinding it.

Handbook of Combustion Vol. 4: Solid FuelsEdited by Maximilian Lackner, Franz Winter, and Avinash K. AgarwalCopyright � 2010 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimISBN: 978-3-527-32449-1

j257

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For a small Thiele modulus the transport rate is dominant so that reactive speciesare available within the entire particle volume where, likewise, a conversion processtakes place. This is consequently referred to as reacting coremode because no regioninside the particle is excluded from the reaction process. Thus, a very efficientreaction process is initiated that includes the entire reactant available. However, ashrinking core mode makes use of only a fraction of available reactants and, thus,leads to a poor efficiency. Under steady-state conditions, this behavior is representedby the well-known Thiele diagram.

7.1.2Combustion Characteristics of a Fixed or Moving Bed

The same principles of kinetic or transport control apply likewise to the entirefixed ormoving bed consisting of a finite number of individual particles. Additionally to thetransport process due to diffusion, the overall transport may be enhanced byconvection due to the flow of primary air through the voids of a packed bed. Thus,since transport of species depends on both diffusive and convective transportmechanisms, the P�eclet number ðPe ¼ lv=DÞ, with l as a characteristic length ofthe flow domain, v as the velocity, and D as the diffusion coefficient for species,distinguishes between them and leads to the following form of the conservationequation for a gaseous species Yi,g in the voids of a packed bed:

Pe� 1:

1Tho

qðrgYi;gÞq�t

þr � rg~vg~v0

Yi;g

� �¼ Da1;i ð7:2Þ

Pe� 1:

1Fo

qðrgYi;gÞq�t

¼ r � Di;g

D0;grYi;g

� �þDa2;i ð7:3Þ

The dimensionless quantities Tho ¼ tB~v0=lB and Fo ¼ tBD0=l2B denote theThompson and Fourier numbers, respectively, with a characteristic time scale tBof the process, whereas the dimensionless numbers Da1 ¼ SYi;g lB=v0 andDa2 ¼ SYi;g l

2B=D0 denote Damk€ohler�s first and second numbers, respectively. The

velocity v0 represents a reference velocity. However, independently of the contribu-tion of the diffusive or convective flux to the net-transport, a high conversion rate ofparticles consumes almost completely a gaseous reactant, for example, oxygensupplied by the flow of primary air. Hence, the reaction process is again limitedto a small region of several particle layers and, thus, represents a conversion frontpropagating through the packed bed.

For a low reaction rate, the flow through the voids of a packed bed is able todistribute a reactant almost homogeneously over the entire fixed or moving bed.Consequently, each particle is provided with sufficient amounts of a reactant, forexample, oxygen and, thus, takes place in the conversion process. This behavior iscomparable to a well-stirred reactor.

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7.1.3Conversion Regimes

Based on the above-mentioned analysis, the different conversion regimes of a particleand a packed bed may be grouped into a single diagram as shown in Figure 7.1.

At first, considering the entire packed bed, a unity Damk€ohler number separatesthe reaction regime into awell-stirred reactor and that of a propagating reaction front.However, the conversion process of an individual particle, in either packed bedregime, may follow the shrinking or reacting core mode separated by the line onwhich the Thiele number is unity. Hence, four reaction regimes with their individualconversion characteristics appear in Figure 7.1.

These distinctions already highlight principal approaches to model fixed ormoving bed combustion: Only in combustion regimes, where internal gradients ofparticles almost vanish, may a continuum approach for a packed bed be permitted.However, for non-vanishing gradients within the interior of a particle, internalparticle processes such as spatial distributions of species and temperature need to betaken into account. During the time span of complete particle conversion, usually,transitions between reacting and shrinking core behavior occur, so that no reactionmode can be assigned to a particle a priori. Therefore, a discrete approach takinginternal processes of a particle into account is the most promising path to follow ascompared to the continuum approach.

Figure 7.1 Combustion regimes for a packed bed of a reacting solid.

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7.1.4Classification of Model Approaches

Based on the findings of the previous section the length scale is an appropriatemeasure to distinguish model approaches. The length scale spans a range from thespatial extensions of the pore space of a particle to the global dimensions of thepacked bed. This classification is also supported by Froment and Bishoff [2] whoconsider the entire packed bed as the �macroscale� and the �microscale,� whichcomprise particle processes. The latter includes a detailed description of the chemicalreactions inside a particle in conjunction with conservation equations for mass andenergy. Typical macroscale modeling includes the flow through the voids of a packedbed described by overall conservation equations for mass, momentum, and energy.Similarly, G€orner [3] considers fluid flow, heat transfer, and chemical reactions as themajor physical regimes for a modeling approach. Each of these regimes may berefined dependent on the required degree of accuracy.

A third classification by Hobbs [4] corresponds also to macro- and microscale thatrefer to the packed bed and intra-particle effects, respectively. The solid and gaseousphase of a packed bedmay be treated either pseudo-homogeneous or heterogeneous,meaning that thermal equilibrium of both phases is assumed or each phasetemperature is solved for by a an individual energy balance. Consequently, bothenergy balances for the solid phase and the fluid flow are coupled via heat transfer.The second distinctive feature is the spatial resolution of the approach. Apriori thereis no limitation on the dimensionality imposed; however, most applications werecarried out in a one- or two-dimensionalmodeling. Apseudo-homogeneous and one-dimensional approach is employed by Merrick [5], van der Lans et al. [6] andVortmeyer and Sch€afer [7], whereas the heterogeneous and one-dimensional ap-proach is represented by Liu andAmundson [8], Stillman [9], Eigenberger [10], Smithand Smoot [11], Hobbs et al. [12], Bryden and Ragland [13], Shin and Choi [14],Cooper and Halet [15], Di Blasi [16], Hartner [17], Raupenstrauch et al. [18], Saas-tamoinen et al. [19], and Thunmann and Leckner [20]. Two-dimensional models havebeen developed by Finlayson [21], Kaviany and Fatehi [22], Giese et al. [23], Bey andEigenberger [24], Tsotsas [25],Hein [26], Liang andKozinski [27], Raupenstrauch [28],Akun and Essenhigh [29], Jiang et al. [30], and Logtenberg [31]. For more details thereader is referred to Peters [32].

To achieve higher accuracy concerning the solid phase, a particle model may becoupled to the overall packed bed model as applied by Chejne et al. [33]. The authorstreated both the packed bed of coal and the particle by one-dimensional heteroge-neous conservation equations. Each node in the discretized packed bed was repre-sented by a particle and, therefore, the approach is labeled 1d þ 1d. The importanceof particle processes is also emphasized by the authors. Owing to the averagingprocess, a continuum approach of a packed bed dismisses significant data such asindividual material properties of particles, their sizes and shapes that need to becompensated for by empirical correlations. The latter are usually extracted bycomparison between measurements and predictions. Furthermore, transport pro-cesses of moving beds on, for example, a forward or backward acting grate are not

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taken into account. To balance these disadvantages the Discrete Particle Method(DPM) was developed by Peters [32]. Figure 7.2 depicts its modeling approach.

Contrary to the continuum mechanics approach, the DPM considers a fixed ormoving bed composed of a finite number of individual particles. Each of theseparticles may have a distinctive material property, size, and shape. For technicalapplications particles of similar characteristics such as material or shape may begrouped into piles of particles. All particles belonging to a fixed or moving bed aresubject to thermal conversion and transport as indicated in Figure 7.2 by �particlemotion� and �particle conversion�. Conversion includes the description of processessuch as heat-up, drying, pyrolysis, devolatilization, gasification, and combustion,whereas transport refers to the trajectories of each particle described in a Lagrangianframe of reference. Thus, in accordance with reality, the sum of all particle processesincluding conversion and motion represents the entire bed process:

S particle processes ¼ total bed process ð7:4ÞThe spatial arrangement of particles in a packed bed forms the voids between the

particles that are occupied by the fluid flow of the gaseous phase. Both phases, solidand gas, are coupled through mass and heat transfer. This affects both gas temper-ature and the particle surface temperature and accounts for the transport of reactantssuch as oxygen from the gas phase to the particle surface and the transfer of productsdue to thermal decomposition of the particle to the gas phase. The components in thegas phase undergo mixing and further reactions dependent on the composition andtemperature of the gas phase. Thus, theDPMconsists of the threemajor processes ofparticle conversion andmotion in conjunction with the reactive fluid flow in the voidspace of a packed bed. The next section describes the modeling approach for thesemajor processes.

Figure 7.2 Major processes during solid fuel combustion.

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7.2Modeling Approach

7.2.1Conversion

During thermal conversion of a fixed or moving bed fuel particles are undergoingvarious processes, major among which are heating up, drying, devolatilization,pyrolysis, gasification, and combustion. Each of these processes is characterized byits kinetics and is dependent on ambient conditions, for example, the compositionand temperature of the primary air in the proximity of the particle�s surface. Todescribe these conversion processes for an individual particle with sufficient accu-racy transient and one-dimensional conservation equations for mass and energy areemployed to each particle. Thus, the sum of individual particle processes in a packedbed leads to the overall conversion of the packed bed. The one-dimensional approachis supported byMan and Byeong [34], whereas the transient character is emphasizedby Lee et al. [35, 36]. Chapman [37] states that in general elaboratemodels are requiredto gain a deeper insight into the complexity of solid fuel conversion [1, 38, 39], asemployed in the current study to describe particle processes. Hence, the DPM wasdeveloped to meet these requirements. It offers a high degree of flexibility anddetailed information and, therefore, is assumed to omit empirical correlations. Thefollowing assumptions are made:

. one-dimensional and transient behavior,

. intrinsic rate modeling,

. particle geometry represented by slab, cylinder, or sphere,

. thermal equilibrium between gaseous and solid phases inside the particle.

The differential conservation equations for energy and species Yi are applied todescribe particle conversion:

qðrcpTÞqt

¼ 1rn

qqr

rnleffqTqr

� �þ

Xl

k¼1

_vkHk ð7:5Þ

qYi

qtþ 1

rnqqr

ðrn~vYiÞ ¼ 1rn

qqr

rnDiqYi

qr

� �þ

Xl

k¼1

_vk;i ð7:6Þ

where n defines the geometry of a slab (n ¼ 0), cylinder (n ¼ 1), or sphere (n ¼ 2).The locally varying conductivity (leff) is evaluated as [40]:

leff ¼ ePlg þ glparticle þð1�gÞlc þ lrad ð7:7Þ

which takes into account heat transfer by conduction in the gas, solid and char andradiation in the pore. The source term on the right-hand side represents heat releaseor consumption due to chemical reactions. The velocity~v represents a convectiveflux,whereas an effective diffusion coefficientDi;eff ¼ DieP=twith eP and t being porosityand tortuosity is employed to describe the diffusive transport [41, 42].

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The following boundary conditions for mass and heat transfer of a particle areapplied:

�leffqTqr

jR ¼ aðTR�T1Þþ _qrad þ _qcond ð7:8Þ

�Di;effqciqr

jR ¼ biðci;R�ci;1Þ ð7:9Þ

where T1, ci,1, a, and b denote ambient gas temperature, concentration of species i,and heat and mass transfer coefficients, respectively. Additionally, a radiative heatflux _qrad and a conductive flux _qcond between particles in contact are taken intoaccount. Representative approaches to model different stages of particle conversionare exemplified in the following sections.

7.2.1.1 DryingSince most solid fuels contain a significant amount of water, the drying processaffects the entire conversion process through energy and time consumption.Apart from treating the drying process by an Arrhenius-like equation as employedby Chan et al. [43] and Krieger-Brockett and Glaister [44], a thermal model thatbalances the energy available for evaporation may offer a more universal approach,because it is independent of chemical properties. The latter approach can beexpressed as follows:

_vcH2O¼

ðT�TevapÞrcpHevapdt

T � Tevap

0 T < Tevap

8><>: ð7:10Þ

where T, Tevap,Hevap, r, and cp denote local particle temperature, evaporation temper-ature, evaporation enthalpy, density, and specific heat of the particle, respectively.

7.2.1.2 Pyrolysis and DevolatilizationWhen a fuel particle is heated up the processes drying, pyrolysis and devolatilization,gasification and combustion take place in amore or less overlappingmanner. Duringpyrolysis the volatile matter of the fuel is released from the fuel particles, which isespecially important in thecaseofbiomasssince itmayhavecontentsofvolatilematterof up to 85% of the dry matter. Pyrolysis is a very complex phenomena in whichhundreds of components are generated and released. In the past few years severalmathematical models have been developed; a literature survey can be found inWurzenberger [45].DiBlasi [46] classifies theavailablemodels into threemaingroups:

. One-stage global models: these describe the pyrolysis by one single reaction ofthe type:

wood�!k a � gasesþ b � tarsþ c � char ð7:11Þwhere k is the chemical reaction rate constant and a, b, and c are stoichiometricconstants. These models do not distinguish between primary degradation andsecondary reactions such as tar cracking.

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. One-stage multi-reaction models: in these models not only the mass loss duringpyrolysis is calculated but also the yield of the main products like CO, CO2, H2O,H2, CH4, and tar are simulated with reactions of the type:

wood�!k productj¼½H2OðgÞ;COðgÞ;CO2ðgÞ;H2ðgÞ;CH4ðgÞ;tarðgÞ;charðsÞ� ð7:12Þ. Two-stage semi-global models: these models consider both primary and second-

ary pyrolysis reactions. For example, and intermediate product is formed first (k1)which decomposes into gases and tars (k2) as well as into char (k3):

wood�!k1 intermediate ð7:13Þ

intermediate�!k2 gasesþ tars ð7:14Þ

intermediate�!k3 char ð7:15ÞOwing to the complexity of modeling packed/moving bed reactors, a not too

complex mathematical model may be advantageous. Therefore, a one-stage multi-reaction model is used by Wurzenberger [45] in his 1d þ 1d packed bed model. Thereaction rates are calculated by:

_rpyro;j ¼ k0;je�EfRTswsrs ð7:16Þ

where

k0,j are the frequency factorsEj are the activation energiesR is the gas constantTs is the temperature of the solid phasewsrs describes the current amount of non-volatized pyrolysis gases left in thesolid phase.

The kinetic parameters for the calculation of the reaction rates can be obtained byThermogravimetric Analysis (TGA) experiments. Numerous kinetic data for varioussolid fuels at various conditions (atmosphere, pressure, heating rate, temperature,etc.) are available in the literature. Most of the data published were obtained fromexperiments at conditions without oxygen. In an oxidative environment the gasesleaving the fuel particle during pyrolysis are combusted in the surrounding of theparticle. The heat of reaction increases the ambient temperature and furthermore theheating rate of the particle. Therefore, the kinetic parameters obtained in the presenceand in the absence of oxygen may differ remarkably. As an example the kineticparameters for beech are presented in Table 7.1. More parameters may be found inSeebauer [47].

As mentioned above, tar is formed during pyrolysis. The tar components mayundergo further reactions like cracking or polymerization, which is referred to assecondary pyrolysis or tar cracking. Wurzenberger [45] used in his 1d þ 1d packedbed model a reaction scheme for tar cracking published by Boroson [48]:

tar!nCOCOðgÞþnCO2CO2ðgÞþnCH4CH2ðgÞþnH2H2ðgÞþntarinert tarinert ð7:17Þ

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with a kinetic approach for the reaction rate:

_rj;crack¼nj104:98e

�93:37RTg wg;tarrg ð7:18Þ

According to Rath and Staudinger [49] about 78% of the initial tars are cracked andonly 22% remain unchanged.

7.2.1.3 Gasification and CombustionWith the term �gasification� the chemical reactions between solid phase and gasphase species are summarized, whereby the term �combustion� includes thechemical reactions of the occurring species with oxygen. Gasification reactions arealways heterogeneous, combustion reactionmay beheterogeneous or homogeneous.The main, thermal relevant reactions to be considered in a mathematical model forthe thermal conversion of solid fuels in packed/moving beds are:

. Homogeneous reactions:(1) homogeneous water gas-shift reaction:

CO þH2O�!k1 CO2 þH2 ð7:19Þ(2) oxidation of CO:

2CO þO2 �!k2 2CO2 ð7:20Þ(3) oxidation of H2:

2H2 �!k3 H2O ð7:21Þ(4) oxidation of CH4:

CH4 þ 2O2 �!k4 CO2 þ 2H2O ð7:22Þ. Heterogeneous reactions:

(5) oxidation of char:

C þ 1=2O2 �!k5 CO ð7:23Þ

Table 7.1 Primary pyrolysis kinetics of beech according to Seebauer [47]; TGA experiments withparticles of 1mmdiameter, atmospheric conditions, heating rate 5 Kmin�1,maximum temperature900 �C.

Component k0, j (s�1) Ef (kJmol�1) ws,max,j (kg kg

�1) (dry basis)

H2O 3.68� 1013 149.5 0.0480CO 9.00� 109 110.0 0.0506CO2 5.23� 109 105.0 0.0724H2 4.73� 104 92.5 0.060CH4 1.09� 105 71.3 0.0106tar 2.09� 1010 112.7 0.6340

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(6) Boudouard reaction:

C þCO2 �!k6 2CO ð7:24Þ(7) heterogeneous water-gas reaction:

C þH2O�!k7 CO þH2 ð7:25Þ(8) Hydrogenation:

C þ 2H2 �!k8 CH4 ð7:26ÞA comprehensive literature survey on kinetic parameters for the heterogeneous

and homogeneous reactions taking place during thermal conversion of solid fuelscan be found in Raupenstrauch [50]. Wurzenberger [45] used in his 1d þ 1d modelthe parameters summarized in Tables 7.2 and 7.3.

7.2.2Transport of Fuel Particles

As mentioned above, a moving bed is viewed as a conglomeration of discrete solid,macroscopicparticles thatoffers thehighestpotential todescribe the transportprocessin a furnace. Each particle is assumed to have a different shape, sizes andmechanical

Table 7.2 Chemical kinetics for the homogeneous reactions.

Equation Reference

_r1 ¼ 2:78� 10�3 e�1510Tg yCOyH2O� yCOyH2O

KEQc2mol de Souza-Santos [51]

_r2 ¼ 3:98� 1014 e�20119

Tg yCOy0:25O2y0:5H2Oc

0:75mol Groppi et al. [52]

_r3 ¼ 2:19� 1012 e�13127

Tg yH2 yO2 c2mol Groppi et al. [52]

_r4 ¼ 1:58� 1013 e�24343

Tg y0:7CH4y0:8O2

c1:5mol Groppi et al. [52]

Table 7.3 Chemical kinetics for the heterogeneous reactions.

Equation Units Reference

_r5 ¼ 1:5� 106 e�13078

Ts pO2 ð1�XCÞ1:2 s�1 Di Blasi et al. [53]

g ¼ 3:0� 108 e�30178

Ts — Monson et al. [54]

_r6 ¼ 4364 e�29884

Ts CCO2 molm�3 s�1 Biggs and Agarwal [55]

_r7 ¼ k7pH2O

1þ k6pH2O þ k7pH2s�1 M€uhlen et al. [56]

_r7 ¼ 2:96� 105 e�18522

Ts bar�1min�1

_r8 ¼ 1:11� 101 e�3548Ts bar�1

_r8 ¼ 1:53� 10�9 eþ 25161

Ts bar�1

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properties. Thus, themotion of particles is characterized by themotion of a rigid bodythrough six degrees of freedom for translation and rotation in three directions. Bydescribing these degrees of freedom for each particle of a moving bed its motion isentirely determined. Newton�s Second Law for conservation of linear and angularmomentum describes the position and orientation of a particle as follows:

md~vdt

¼ S~Fi ð7:27Þ

Id~vdt

¼ S~Mi ð7:28Þ

wherem,~v,~Fi, I,~v, and ~Mi denote, respectively,mass, linear velocity, forces acting ona particle, inertia tensor, angular velocity, andmoments acting on a particle due to theforces. The latter include external forces due to moving grate bars, fluid forces, andcontact forces between the particles in contact. The contact forces consist of all forcesas a result of material contacts between a particle and its neighbors. In a compu-tational approach, the deformation of twoparticles in contactmaybe approximatedbya representative overlap h [57] as depicted in Figure 7.3.

The resulting force ~Fij due to contact may be decomposed into its normal andtangential components:

~Fij ¼ ~Fn;ij þ~Ft;ij ð7:29Þ

where the components additionally depend on displacements and velocities normaland tangential to the point of impact between the particles. In a simple approach theanalogy to a spring for an ideal elastic impact serves to determine the contact force as~Fij ¼ kij~hij. However, for more sophisticated applications additional influences suchas nonlinearity, dissipation, or hysteresis need to be taken into a count. For a detaileddiscussion of inter-particle forces the reader is referred to Peters [58].

7.2.3Gas Flow

The turbulent flow in the void space between the particles of a packed bed may betreated by available CFD-methods [59]. Commonly, the flow through the packed bed is

Figure 7.3 Overlap between two particles in contact.

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approximated as a flow through a porousmedia, for which the porosity is given by thepacking density of the bed. Both phases are coupled through heat and mass transferbetween the particles and the surrounding gas phase. After the flow has passed thepacked bed it will enter the gas plenum above the packed bed, where the flow is ahomogeneous phase and undergoing a further combustion process due to chemicalreactionof volatiles andgasificationproductswith secondary air. For further details thereader is referred to relevant CFD-literature [60].

7.3Applications

7.3.1Conversion

7.3.1.1 DryingFigure 7.4 depicts a comparison between two fundamentally different approaches todescribe the drying process of a particle. According to Raupenstrauch [61], Shei-kholeslami andWatkinson [62], andDiamond et al. [63], particles in a particular woodundergo a drying process starting at external parts of a particle. This suggests that theevaporation rate is dependent on the heat available or transferred and evaporationonly takes place at temperatures above the evaporation temperature. Alternatively, anapproach treating the process of evaporation as a heterogeneous reaction based on anArrhenius equation is also presented in Figure 7.4.

Figure 7.4 Drying of a fir wood particle.

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The constant-evaporation-temperature model agrees well with the experimentalmeasurements whereas the Arrhenius approach of Chan et al. [43] and Krieger-Brockett and Glaister[44] overpredict the drying time by a factor of2. Similarly, thedrying rate shown in Figure 7.4 of the constant-evaporation-temperature modelmatches the experimentalfindings satisfactorily, takingmeasuring uncertainties intoaccount.However, the drying rate of theArrheniusmodel differs significantly in bothmagnitude and gradient from the experiment. Equally satisfactory results wereobtained by applying the constant-evaporation-temperature model to a packed bedof beech wood during the drying process (Figure 7.5).

7.3.1.2 Pyrolysis and DevolatilizationAs an example of the behavior of a single fuel particle under pyrolysis conditionsFigure 7.6 shows the particle mass as well as the temperatures at the particle surfaceand the particle center versus time. It can be seen that the computer simulationperformed with the model described above shows good agreement with the exper-imental data. However, the calculated data differ from the experimental results.There can be numerical reasons (due to the geometrical conditions in the center), butalso the exact position of the thermo-element can be responsible for the deviation.

During pyrolysis, particles also experience changes in their morphology. Thesemay include an increase in size due to swelling and a change in porosity due to theformation of primary products of pyrolysis. The increasing volume may depend onthe particle geometry, which is exemplified for a cylindrical and spherical particleshape during time of pyrolysis in Figure 7.7.

Figure 7.5 Drying of a packed bed of beech wood.

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A spherical particle does not prefer any spatial direction of extension, whereas theradial direction is favored over the longitudinal one for a cylindrical geometry and,thus, an extension in two directions only occurs. However, in the current applicationtwo particles of equal mass and radial extensions, different geometries whereconsidered. Both beech wood particles where exposed to a radiative flux of_q ¼ 20 kWm�2 and a convective heat transfer to the ambient of a temperature ofTamb ¼ 773 K and a constant heat transfer coefficient of a¼ 10Wm�2 K�1. Hence,

Figure 7.6 Particle mass and temperaturedistributions of a beech particle as a function oftime – comparison of computer simulations(Raupenstrauch et al. [64]) with the

experimental results of Hochegger [65] (particlediameter 20mm, moisture content 25% d.b.,constant ambient temperature of 1098 K,atmosphere: nitrogen).

Figure 7.7 Swelling during pyrolysis.

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for a cylindrical particle the radius increases by 4%, whereas the spherical particleexperiences an increase of its radius by 2.5% only. Consequently, this behavioraffects positively, but to different extents, heat and mass transfer of the particlegeometries. Similarly, the total volume of a packed or moving bed will increase, thusaltering the flow conditions inside the void volume of the bed.

Owing to the formation of char in the current application, a change of porosityfrombeechwood to char takes placewhile the particle undergoes pyrolysis. Figure 7.8depicts the evolution of porosity for cylindrical and spherical particle geometries.

For both cases, the porosity changes from an initial value of beech wood(ewood ¼ 0:63) to a final value of that of char (ewood¼ 0.84). However, the evolutionin space and time differs for the cylindrical and spherical shape. Since the sphericalparticle has no preferred direction, the charring process occurs at a faster rate, andthus changes in pyrolysis will take place at a faster rate as compared to the cylindricalgeometry.

7.3.1.3 Gasification and CombustionAs an example of the modeling of the thermal conversion of a solid fuel with themodel described above, Figure 7.9 shows themass loss of a single fuel particle versustime during thermal conversion in nitrogen, carbon dioxide, and air.

The predicted results are in good agreement with the experimental data. Figure 7.9demonstrates the influence of oxygen on the pyrolysis rate as mentioned above.However, the acceleration of pyrolysis takes place only after a certain period of time(in this example after about 80 s). The reason for such behavior is that at thebeginning the pyrolysis rate is very high, which leads to high velocities of thepyrolysis gases. Therefore, the gases are combusted with the oxygen of the surround-ing atmosphere at a distance from the fuel particle. When the velocity of the gasesleaving the particle decreases, the gases are combusted near the particle, which leadsto an increase of heat transfer to the particle and furthermore to higher rates ofpyrolysis.

Figure 7.8 Evolution of porosity for spherical (a) and cylindrical (b) particles.

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7.3.1.3.1 Grate: Optimal Conditions for Fuel Ignition and Optimal Primary Air LoadAccording to Raupenstrauch [28] and Hartner [17] a quick ignition of the fuel iscrucial for an optimal operation of a furnace concerning:

. efficiency,

. percentage of burnable materials in the residues,

. flue gas composition with respect to emissions,

. part load performance.

The ignition characteristics of a fuel depend in addition to the fuel propertiesmainly on:

. radiative heat transfer to the fuel;

. convective heat transfer due to the primary air flow, flue gas recirculation, and soon;

. heat transfer inside the fuel bed;

. oxygen supply to the fuel by primary air;

. fuel mixing.

These parameters are influenced by both the furnace geometry and the operationalconditions. To demonstrate how the velocity of the reaction front depends on theprimary air supply the penetration depth of the reaction front as a function of timehasbeen investigated, as demonstrated in Figure 7.10 for a non-mixed fuel bed.

A slab of the fuel bed on a grate is considered throughwhich primary airflows fromthe bottom and radiative heat transfer from the arch takes place at the top of the bed.Since a �reaction front� does not exist in reality – it is more a reaction zone – thereaction front is defined as the location atwhich the temperature of 1073K is reached;hF is the penetration depth of the reaction front at a certain time with respect locationon the grate. (Note: with the feed rate of the grate and the time of reaction the locationof the slab on the grate can be determined.)

Figure 7.9 Particle mass of a beech particleversus time – comparison of simulations(Raupenstrauch et al. [64]) with theexperimental results of Petek [66]

(particle diameter 20mm, moisture content8% d.b., constant ambient temperature of1223 K, atmosphere: air, nitrogen, andcarbon dioxide).

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Figure 7.11 depicts the reaction front penetration from the fuel bed surfacetowards the grate at a certain primary air supply.

If the primary air is increased the thermal conversion is intensified, the reactionrate increases, and as a consequence the penetration depth of the reaction frontincreases as well. These calculations can be performed for various primary air flowrates with respect to air velocities at different times with respect to grate locations.The calculations lead to a diagram such that as presented in Figure 7.12.

If, for example, the primary air supply is increased at a defined grate location (and,thereby, time) the penetration depth of the reaction front increases, as mentionedabove. However, at a certain point it can be observed that the penetration depthdecreases again, whichmeans that there is an optimumprimary air supply at each gratelocation (and time). By connecting these optimums of each line a line of optimal air

Figure 7.10 Temperature profile in a non-mixed bed of solid fuel on a combustion grate (accordingto Hartner et al. [67]).

Figure 7.11 Reaction front penetration as a function of reaction time and superficial primary airvelocity (according to Hartner et al. [67]).

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supply can be drawn. If the primary air supply is too high, the penetration depthbecomes equal to zero, which means that the fire is blown out.

Similar results were obtained by Bruch [68], who also identified amaximum of theconversion rate dependent on the primary air flow. Based on the same reasoning asabove, the conversion rate decreases for a lower or higher air flow rate with respect tothe air flow rate at maximum conversion rate (Figure 7.13).

Figure 7.12 Penetration depth of the reaction front as a function of reaction time and superficialprimary air velocity (according to Hartner et al. [67]).

Figure 7.13 Conversion rate dependence on primary air flow.

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In this context it is necessary to point out the change of the characteristics of thelines at high reaction times and, thereby, downstream locations (Figure 7.14).

Such behavior arises due to the ash generated layer radiation from the arch can nolonger reach the reaction front. Therefore, an increase of primary air will lead tocooling of the reaction, zonewhichmay leadunder extreme conditions to blowing outthe fire. As a consequence there can be defined a maximum primary air velocity inaddition to the optimum air supply.

As a conclusion, the primary air supply as a function of the position on the grate canbe defined as shown in Figure 7.15.

Grates ofwaste incineration plants usually have a grate for the ignition of the fuel inaddition to the combustion grate. After ignition the fuel falls downon the combustion

Figure 7.14 Influence of radiation shielding by ash on the ignition behavior (according toHartner et al. [67]).

Figure 7.15 Primary air distribution as a function of grate position (according toHartner et al. [67]).

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grate and undergoes the phenomena explained above. The questions arising in thiscontext are:

. Which type of a grate is recommendable for optimal ignition (mixing versus non-mixing)?

. Which is the better direction of primary air supply (from the bottom via the grateor from above)?

. What is the optimal time to supply the ignited fuel to the combustion grate?

For a qualitative investigation the ignition temperature of the fuel is defined as inthe previous examples as 1073 Kwith the enthalpyH1073. The fuel is ignited at the bedsurface due to radiation from the arch and the reaction front penetrates from the topto the bottom. By supplying the partly ignited fuel to the combustion grate the fuelgets mixed; the fuel mixture has then the enthalpy H(t). If the enthalpy aftersupplyingH(t) is lower thanH1073 the ignited fuel will be extinguished – this meansthat the fuel was dumped to early. Therefore, the criterion for the optimal time forsupplying the fuel to the combustion grate is that the enthalpyH(t) after supplying isto equal or larger than the enthalpy at the ignition temperature (H1073). Fordemonstration three different cases are compared:

. Case 1: non-mixed bed; primary air is supplied from the bottom (through thegrate).

. Case 2: ideal mixing of the solid fuel; primary air is supplied from the bottom(through the grate).

. Case 3: non-mixed bed; primary air is applied from above.

Figure 7.16 Enthalpy profile of a slab of thepacked bed as a function of time for threedifferent cases (according to Hartneret al. [67]). Case 1: non-mixed bed, withprimary air is supplied from the bottom

(through the grate); case 2: ideal mixing ofthe solid fuel, with primary air is suppliedfrom the bottom (through the grate); andcase 3: non-mixed bed, with primary air isapplied from above.

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Figure 7.16 summarizes the simulation results.It can be seen that the fuel on a non-mixed fuel bed with a primary air supply

through the grate (case 1) takes the longest time to reach ignition conditions.In case 2, which corresponds to an ideallymixing grate with air supply through the

grate, the ignition of the fuel ismuch faster.However, the time taken to reach ignitionconditions depends strongly on the moisture content, which is represented by thehorizontal part of line 2. Case 3 (non-mixing grate, primary air from above)represents the ideal conditions for igniting the fuel since ignition conditions canbe reached faster than the other model cases.

7.3.2Transport on a Grate and in a Rotary Kiln

Owing to the discrete approach of the DPM-method, the motion of individualparticles with their interactions constitutes the overall motion of the moving bed.Thus, detailed data on particle�s velocities and paths are available, in particular theresidence time of each individual particle. Statistical methods such as averaging orclassification based on particle sizesmay be employed to extract characteristics and tocompare to experimental data.

7.3.2.1 GrateThe motion of particles on a forward acting grate of a length of l¼ 3.2 m and a widthw¼ 0.8 m has been predicted by the Discrete-Particle-Method. Spherical particleswere used with their diameters classified between Dmin¼ 5mm and Dmax¼ 40mmaccording to experiments. Figure 7.17 shows a comparison between experimentalmeasurements and predictions.

The residence time behavior was divided into five classes and good agreement isachieved between the experimental and mean residence time evaluated by theDiscrete-Particle-Method. Additional profiles representing minimum and maximumresidence time were extracted from the predicted results. The minimum residencetime is almost constant, whereas themaximum residence time declines by a factor of2 versus particle size. Hence, the residence time depends strongly on the particlesize and emphasizes the largely varying transport properties on a forward acting grate.The latter is due to vertical segregation along the grate, as depicted in Figure 7.18.

For this purpose, particles were separated into two classes and their verticalposition above the grate, for example, height within the bed, was traced over thesimulation period. Figure 7.18 shows clearly that small particles gather preferably inthe lower part of the bed, whereas larger particles occupy the upper region of amoving bed. Thus, a layer of small particles is formed in the neighborhood ofthe grate over which the large particlesmove with rather elevated transport velocities.This behavior might indicate that large particles experience a lower degree ofburnout due to reduced residence times. Similarly, small particles therefore,may retain a relatively high amount of heavy metals because, due to reducedtemperatures within the lower part of the moving bed, evaporation of heavy metalstends to be incomplete.

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Figure 7.17 Residence time versus particle size.

Figure 7.18 Segregation on a forward moving grate.

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7.3.2.2 Rotary KilnTransport and motion in a rotary kiln is an often encountered technical application.Similar to the transport on a forward acting grate, segregation in a rotary kiln mayaggravate transport characteristics. Owing to a larger kinetic energy of large particles,these particles emerging on the bed surface on the right-hand side of Figure 7.19will roll down the slope of the packed bed until they reach the opposite wall of thekiln. However, smaller particle with less kinetic energy will lose theirmomentumdueto friction and impact already before arriving at the oppositewall. This behavior causessegregation, because smaller particles are trapped in an inner loop while largerparticles from an outer loop, as indicated by the sketched trajectories in Figure 7.19.

7.4Outlook

The results presented indicate that models, in particular with a discrete character ascompared to continuum approaches, developed to predict the thermal conversionprocess of solid fuel particles have already reached a high degree of maturity. Hence,the models are readily applicable to assess major characteristics and aspects of bothpacked andmoving bed conversion. Themain aspects of solid fuel conversion consistmainly of chemical reaction processes of particles, their motion for example,transport, and the reacting flow of primary air through the void space of a packedbed. Presently, these methods still lack a close coupling between each other to someextent. Therefore, future efforts ought to be directed towards amore intense coupling

Figure 7.19 Velocity pattern in a rotary kiln.

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of all these aspects. Since all the methods as individual entities addressed in thischapter yield predictions of sufficient accuracy, it would be desirable to develop a toolthat encompasses those aspects of bed conversion so that it may be applied to thedesign and layout of various technical applications. Thus, such an approach givesmost detailed results that are not accessible even through experiments.

A further advancement would consider the emissions formed during thermalconversion of various fuels. In particular, the alkali components may form acidicenvironments that lead to corrosion and reduced heat transfer. Therefore, it would beadvantageous to assess the emission level in advance, so that both primary andsecondary measures could be chosen to lessen pollutants.

7.5Summary

Modeling approaches to describe the various aspects of solid fuel conversion havebeen presented and applied to predict thermal conversion of both single particles andfixed/moving beds. Conversion andmotion of fuel particles in conjunctionwith theircoupling to the gas phase of the void space between them through heat and masstransfer have been identified as major processes. The latter govern the thermalconversion of fixed andmoving beds to a large extent. The conversion characteristicsof both a packed bed and a single particle depend on a balance between the reactionrate and reactants available. Thus, thermal conversion of a particle spans the rangebetween a reacting and a shrinking core mode. Similarly, conversion of the entirepacked bed is bound by a well-stirred reactor approach or a conversion frontpropagating through the bed.

These reaction modes may affect all major processes during thermal conversion,including drying, pyrolysis, devolatilization, gasification, and combustion. Describingthese processes by a discrete approach on a particle-resolving level leads to predictionswith sufficient accuracy. Furthermore, the transport of particles on grates or in rotarykiln described by theDiscrete ParticleMethod (DPM) shows good agreement betweenexperimental results and predictions. The latter emphasize the segregation processestaking place on a forward acting grate and in a rotary kiln dependent on particle size orshape. Thus, a discrete approach is to be favored over the continuum mechanicsapproach. The latter lacks important features, such as the individual size and shape ofa particle, and therefore it usually does not predict relevant characteristics such asinner particle processes or segregation without additional empirical correlations.

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