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Fuel 86 (2007) 722–734

Numerical simulation of the bubbling fluidized bed coal gasificationby the kinetic theory of granular flow (KTGF)

Liang Yu a,b, Jing Lu a,b, Xiangping Zhang a,*, Suojiang Zhang a,*

a Research Laboratory of Green Chemistry and Technology, Institute of Process Engineering, Chinese Academy of Sciences, 100080 Beijing, Chinab Graduate University of Chinese Academy of Sciences, 100049 Beijing, China

Received 8 May 2006; received in revised form 8 September 2006; accepted 13 September 2006Available online 10 October 2006

Abstract

A new numerical model based on the two-fluid model (TFM) including the kinetic theory of granular flow (KTGF) and complicatedreactions has been developed to simulate coal gasification in a bubbling fluidized bed gasifier (BFBG). The collision between particles isdescribed by KTGF. The coal gasification rates are determined by combining Arrhenius rate and diffusion rate for heterogeneous reac-tions or turbulent mixing rate for homogeneous reactions. The flow behaviors of gas and solid phases in the bed and freeboard can bepredicted, which are not easy to be measured through the experiments. The calculated exit values of gas composition are agreed well withthe experimental data. The relationship between gas composition profiles with the height of gasifier and the distributions of temperature,gas and solid velocity and solid volume fraction were discussed.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Bubbling fluidized bed coal gasifier; Two-fluid model; Kinetic theory of granular flow

1. Introduction

The oil crisis and global environmental problems havebecome critical challenge worldwide, therefore more andmore attentions have been paid to the clean coal technol-ogy, among which the coal gasification is one of the criticaltechnologies for the efficient utilization of coal. Comparingto the coal combustion, there is a lower reaction rate incoal gasification process. Therefore the bubbling fluidizedbed gasifier (BFBG) is one of widely applied technologies,because a longer residence time, uniform temperature dis-tribution, high mass and heat transfer rates could beachieved in such kind of reactor. However, it has been achallengeable problem to scale-up the fluidized bed coalprocess due to its complicated reaction and transfer mech-anism [1].

0016-2361/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.fuel.2006.09.008

* Corresponding authors. Tel./fax: +86 10 82627080.E-mail addresses: xpzhang@home.ipe.ac.cn (X. Zhang), sjzhang@

home.ipe.ac.cn (S. Zhang).

Since the two-phase model was firstly proposed by Too-mey and Johnstone [2], many improvements have beendeveloped to simulate the coal gasification process of thebubbling fluidized bed [3–7]. However, the inherentlyexisted drawbacks are impossible to be solved due to itsempirical nature in the description of gas and particle inmotions and interactions without solving the momentumbalance equations.

In recent years, mass conservation and momentum bal-ance for gas and solid have been applied to simulate thehydrodynamics of bubbling fluidized bed. Two approacheshave been proposed, one is based on molecular dynamics,called discrete element method (DEM), and another isbased on the assumption that the gas and particulatephases form two inter-penetrating continua, called two-fluid model (TFM) [8]. A characteristic feature of bubblingfluidized bed is the chaos motion of large numbers ofparticles in the bed. So the fundamental procedure is toclosure complex particle stresses resulted from multi-bodycollisions.

Nomenclature

A constantB constantCp,i heat capacity, J/kg KCd drag coefficientDm,i diffusion coefficient of the mixture, m2/sDi,j binary mass diffusion coefficient, m2/se coefficient of restitutiong gravity, m/s2

g0 radial distribution functionH specific enthalpy, J/kgHi enthalpy, J/kgDHf,i enthalpy of formation, J/kghgs heat transfer coefficient, W/m2 KJg,i diffusion flux, kg/m2 sKAr kinetic rate constantKEBU turbulent mixing rate constantKHom homogeneous rate constantks diffusion coefficient for granular energy, kg/m sNu Nusselt numberPk,g shear productionPr the continuous phase Prandtl numberp gas pressure, PaQ intensity of heat exchange between the gas and

solid phases, W/m2

R universal gas constant, J/kmol KRe Reynolds numberRg,i net rate of production of homogeneous species i

Rs,i the heterogeneous reaction rater volume fractionS source termSh Shawood numberSP,j associated stoichiometric coefficients of prod-

ucts.SR,i associated stoichiometric coefficients of reac-

tants

T gas mixture mean temperature, KT0 reference temperature, KU the instantaneous velocity, m/su the mean velocity, m/su 0 the fluctuating velocity, m/swi molecular weight, kg/kmolXi molar fractionYi the mass fraction

Greek symbolsa mixture thermal conductivity, W/m Kc dissipation of fluctuating energy, W/m3

e dissipation rate of turbulent kinetic energy,m�2 s�3

Hs granular temperature, (m/s)2

j turbulent kinetic energy, m2/s2

ks bulk viscosity, Pa sl viscosity, kg/m sq density, kg/m3

re turbulent Prandtl number for erj turbulent Prandtl number for jrY Schmidt numbers stress tensor, PaUgs drag, kg/m3 s

Subscriptsg gas phasei the ith speciesl laminar flowm mixtures solid phaset turbulent flow

L. Yu et al. / Fuel 86 (2007) 722–734 723

Based on DEM, the soft sphere simulation by means ofthe empirical coefficient of restitution and friction and thehard sphere simulation by means of empirical spring stiff-ness and a friction coefficient were performed to describeparticle collisions and to predict frequency of pressure fluc-tuations, bubble formation and particles segregation [9–12]. However, if one requires modeling complex industrialsystems like the BFBG with the millions of particles, manycomputational practices indicate that huge computationaltimes put DEM at a disadvantage [8,13]. On the contrary,TFM cannot only save computational time, but obtain themean particulate flow fields which are convenient to facili-tate quantifiable decisions for an engineering design. Com-putational simulations done by several group in manycountries have been shown it is feasible to compute theobserved bubbles and clusters and the flow regime usingTFM [14].

By analogy with the kinetic theory of gas molecules toimprove the description of particle collision, the kinetictheory of granular flow (KTGF) was introduced intoTFM [15]. Many people who participate in modelinggas–solid flows in fluidized beds and risers use kinetic the-ory of granular flow to predict and validate lots of flowphenomena in the systems of dilute phases and densephases, e.g., [16–18]. Applying KTGF into bubbling fluid-ized bed model, Enwald and Almstedt [19] comparednumerical solutions with experimental results using fourdifferent two-fluid model closures, and obtained the statis-tical consistency of bubble frequency, mean pierced bubblelength, mean bubble rise velocity and mean bubble volumefraction. According to this literature, our group carried outthe similar TFM to investigate fluid dynamics in a gas–solid bubbling fluidized bed [20], and concluded that it isa success for the simulation of bubble characteristics using

724 L. Yu et al. / Fuel 86 (2007) 722–734

Enwald’s method. Critical comparison of hydrodynamicmodels for jet bubbling fluidized beds and freely bubblingfluidized beds, Patil et al. [21,22] came to the conclusionthat the KTGF was in good agreement with the experimen-tal data and correlations from the literature compared tothe constant viscosity model (CVM) for the prediction ofbubble size distribution, bubble rise velocity, and visiblebubble flow rate. It is more importance that KTGF canbe applied into the wider variety of cases due to no assump-tion of solid phase viscosity.

Although KTGF based on TFM has given a reasonableflow description of dense gas–solid flows, it is difficult thatthe complicated chemical reactions are introduced to simu-late the bubbling fluidized gasification process due to com-plex mechanism of heat transfer and chemical reactionneed to be modeled. More careful consideration has to begiven on the solution of large numbers of energy and spe-cies transport equations and the nonlinear source term ofcomplicated chemical reactions. However, the scale-upand optimal design of industrial reactors cannot be carriedout without considering chemical reaction. Until now, notmuch effort has been devoted to couple multi-phase flowwith complex gasification in the bubbling fluidized bed.

In this work, TFM, which includes KTGF and chemicalreaction kinetics, is extended to simulate the bubblingfluidized bed coal gasification. Particles collision and fluc-tuation in the bed can be described by KTGF. The compli-cated coal gasification process includes a system of 15species and 11 chemical equations. The devolatalizationand drying can be considered as instantaneous process infeed zone, and the proportion of products distribution isderived from pyrolysis results in the experiment [23–25].Heterogeneous reaction rates are determined by kineticsand diffusion and the mass, momentum and heat exchangebetween gas and solid phases are caused by the reactions.Homogeneous reactions are controlled by the smaller oneof Arrhenius rate and eddy-dissipation rate presented byD.B. Spalding [26]. With proposed model, the exit simula-tion results are compared with experimental data [7] andthe relationship between composition profile with tempera-ture profile and coal volume fraction can be obtained.

2. Mathematical model

2.1. Main assumptions on coal gasification process

In order to decrease the impact of the strong nonlinearcharacteristic of the model and ensure the good conver-gence and acceptable computational time, the gas–solidhydrodynamic and coal gasification models are simplifiedas follows:

(1) The vertical section of BFBG is rectangular, whichcan be assumed as two-dimensional. The 2D flowbehavior has been verified by comparing the experi-mentation with CFD [27–29]. The frictional stressesmodels are not taken into account by TMF equations

in here and their actions on flow behavior will becompared in next work. Other interaction forces suchas lift force, thermophoretic force, Brownian forceand virtual mass force are neglected.

(2) The intensity of particles collision does not vary withtemperature, i.e., exothermic or endothermic reactionhas no impact on the fluctuation of solid velocity anddoes not have a rise in the temperature of granular.

(3) The coal gasification is an overall endothermic and itstemperature is lower than that of combustion. Theheat for gasification should be supplied. The solidphase is dense and continuous in the bed, and contactwith the wall, in which the mean free path of radia-tion is much smaller than the solid dimensions so asto limit the contribution of radiative heat transfer.The gas phase is also continuous in the freeboardand can be assumed as transparent so that the radia-tive energy is neither absorbed nor emitted [25]. Thebed temperature will be uniform rapidly due to strongagitation of particles. There is not much temperaturedifference to drive radiative heat transfer among theparticles. Thus it is reasonable to assume that theheat loss by radiation is negligible.

(4) Particle is isothermal. The particles are assumedinelastic, smooth and monodispersed spheres.

2.2. Gas–solid hydrodynamics

The general model of multiphase flow was derived fromEulerian–Eulerian approach, and developed to describe theflow behavior of the BFBG based on conservation equa-tions for mass and momentum for both gas and solidphase.

2.2.1. Continuity equations

The continuity equations for gas and solid phases aregiven by

o

otðrgqgÞ þ r � ðrgqgU gÞ ¼ Sgs ð1Þ

o

otðrsqsÞ þ r � ðrsqsU sÞ ¼ Ssg ð2Þ

where r, q and U are the volume fraction, the density andthe instantaneous velocity, respectively. In a laminar field,the entire field of values is either time-steady or changingsystematically. Thus the instantaneous velocity of particlesUs can be substituted by the solid mean velocity us. Thisform was also derived from the Boltzmann integral–differ-ential equation by Ding and Gidaspow [30]. Even for gasphase of continuity equation, ug can take the place of Ug

due to Reynolds averaging, which will be described indetail at Section 2.2.4. S on the right-hand side is the sourceterm and set to zero only in flow field [31,32]. When thecontinuity equations are used in heterogeneous reaction,there is the mass, momentum and heat exchange betweengas phase and solid phase. In the present work, coal reacts

L. Yu et al. / Fuel 86 (2007) 722–734 725

with oxygen, steam and carbon dioxide to change solidphase into gas phase, so mass source for the phases yield

Ssg ¼ wC

XcCRC ¼ �Sgs ð3Þ

For the gas phase density, a mixture of ideal gas wasassumed

qg ¼p

RTPn

i¼1Y iwi

ð4Þ

where p, T, Yi and wi are gas pressure, gas mixture meantemperature, mass fraction and the molecular weight forevery species, respectively. The solid phase density is as-sumed as constant.

2.2.2. Momentum equationsThe momentum equation for gas phase can be written as

o

otðrgqgU gÞ þ r � ðrgqgU gU gÞ

¼ �rgrp � UgsðU g � usÞ þ ðr � rgsgÞ þ rgqgg þ Sgsus

ð5Þ

where Ugs is the drag coefficient between the gas phase andsolid phase, and g is gravity. The stress tensor sg is given by

sg ¼ ll;gðrU g þrUTg Þ �

2

3ll;gr � U g ð6Þ

In the right hand of Eq. (5), the fifth term Sgsus describesthe momentum transfer of the coal. The momentum equa-tion for the solid phase should obtain the reverse sourceterm and can be expressed as

o

otðrsqsusÞ þr � ðrsqsususÞ ¼ �rsrp� ps�Ugsðus�U gÞ

þ ðr � rsssÞ þ rsqsgþ Ssgus ð7Þ

where the solid stress tensor ss is given by

ss ¼ ks �2

3ls

� �rus þ lsðrus þruT

s Þ ð8Þ

In the equation above, ks is bulk viscosity, which can beobtained as follow:

ks ¼4

3rsqsdsg0ð1� eÞ Hs

p

� �1=2

ð9Þ

and the equation of the solid shear viscosity ls is derivedfrom Gidaspow [18]

ls ¼4

5r2

s qsdsg0ð1þ eÞffiffiffiffiffiffiHs

p

r

þ 10qsds

ffiffiffiffiffiffiffiffiffipHs

p

96ð1þ eÞesg0

1þ 4

5g0rsð1þ eÞ

� �2

ð10Þ

The solid pressure ps is defined in analogy with ls and con-sists of a collision and a kinetic term

ps ¼ rsqsHs þ 2ð1þ eÞr2s g0qsHs ð11Þ

where Hs is granular temperature; e is the coefficient of res-titution for particle collisions; g0 is the radial distributionfunction.

For the restitution coefficient, the different values werepresented, from 0.8 to 1 in the literature [22,33,34]. In thiswork, a restitution coefficient value of 0.9 was used due tothe fact that the granular diameter of 0.62 mm is close tothat of 0.7 mm in the literature [35]. For the radial distribu-tion function of solid phase, g0 is expressed as [16]

g0 ¼3

51� rs

rs;max

� �13

" #�1

ð12Þ

The granular temperature Hs is a pseudo-temperaturewhich can be defined as

3

2Hs ¼

1

2hu0su0si ð13Þ

where u0s is the fluctuating velocity of the particles and canbe derived from

u0s ¼ U s � us ð14Þ

where Us is the instantaneous velocity of the particles. Thesolid mean velocity us is defined as

us ¼ hU s;ii ¼1

n

ZU s;if dU s ð15Þ

where f, n are single-particle velocity distribution functionand particle number density respectively.

The details can be obtained from Ding and Gidaspow’swork [30], where the derivation of the granular temperaturetransport equation has been reported.

2.2.3. Kinetic theory of granular flow (KTGF)

A transport equation which describes particles collideresulting in a random granular motion is defined for solidphase [21]

3

2

o

otðrsqsHsÞ þ r � ðrsqsHsusÞ

� �

¼ �ðpsI þ rs��ssÞ : r~us þr � ðksrHsÞ � c� 3UgsHs ð16Þ

The diffusion coefficient for granular energy ks is given by

ks ¼150qsds

ffiffiffiffiffiffiffiffiffiHspp

384ð1þ eÞg0

1þ 6

5rsg0ð1þ eÞ

� �2

þ 2qsr2s dsg0ð1þ eÞ

ffiffiffiffiffiffiHs

p

rð17Þ

The dissipation of fluctuating energy due to inelastic colli-sion takes the form

c ¼ 3ð1� e2Þr2s qsdsg0Hs

4

ds

ffiffiffiffiffiffiHs

p

r !�rus

" #ð18Þ

The remaining term which needs to be considered is theinterphase momentum transfer. It is thought for the dragbetween gas phase and solid phase to play important rolein the momentum exchange. If eg < 0.8, the well-known

726 L. Yu et al. / Fuel 86 (2007) 722–734

Ergun equation [36] is suitable for describing the denseregime

Ugs ¼ 150ð1� rgÞrslg

rgd2s

þ 1:75qgrsjug � usj

ds

ð19Þ

If eg > 0.8, the drag coefficient was given based on thework by Wen and Yu [31]

Ugs ¼3

4Cdjug � usj

ds

r�2:65g ð20Þ

where

Cd ¼24Re ð1þ 0:15Re0:687Þ Re 6 1000

0:44 Re > 1000

(ð21Þ

Re ¼jug � usjrgqgds

lg

ð22Þ

2.2.4. j–e turbulence models

Unlike the single-phase j–e models, there is no ‘indus-trial standard’ model for multiphase flow to perform rea-sonably well to engineering accuracy in a wide range ofapplication. To the bubbling fluidized bed, prediction willbe in good agreement with experimental data for laminargas phase and laminar solid phase [21,22]. In the presentwork, the competition between turbulent mixing rate andchemical kinetic rates will be considered in the homoge-neous reaction. So we assume that gas phase is in turbulentflow and solid phase is in laminar flow. When turbulentflows are taken into account, the interesting is in obtainingthe mean values of the independent variables of interest.Thus the process of Reynolds decomposition may beemployed. The instantaneous values of the independentvariables are represented by the sum of a time-mean valueand an instantaneous fluctuating value

U g ¼ ug þ u0g ð23ÞU ¼ �/þ /0 ð24Þ

Eq. (5) is averaged over a sufficiently long time andexpressed as [38]

o

otðrgqgugÞ þ r � ½rgqgðugug þ hu0gu0giÞ�

¼ �rgrp � Ugsðug � usÞ þ ðr � rgsgÞ þ rgqgg þ Sgsus

ð25Þ

where long-time average of u0g and p 0 are zero and �hu0gu0giis called Reynolds stress closed by

�qghu0gu0gi ¼ lt;g � ½rug þ ðrugÞT� �2

3ðlt;grug þ qgjÞ ð26Þ

lt,g is the turbulent viscosity and computed as a function ofj and e

lt;g ¼ qgClj2

eð27Þ

The transport equations for j and e only take the gas phaseform

o

otðrgqgjÞ þ r � ðrgqgugjÞ

¼ r � rg ll;g þlT;g

rjr � j

� �þ rgP j;g � rgqge ð28Þ

o

otðrgqgeÞ þ r � ðrgqgugeÞ

¼ r � rg ll;g þlT;g

rer � e

� �þ rge

jðCe;1P j;g � Ce;2qgeÞ

ð29ÞIn these equations, Pj,g is the shear production defined by

P j;g ¼ lt;grug � ½rug þ ðrugÞT� �2

3rugðlt;grug þ qgjÞ

ð30Þand rj, re is the turbulent Prandtl numbers for j and e.

Let the model constants take these values

Ce;1 ¼ 1:44; Ce;2 ¼ 1:92; Cl ¼ 0:09; rj ¼ 1:0;

re ¼ 1:3

2.3. Coal gasification reactions

As part of gasification models, the complicated pro-cesses of chemical reactions were simulated and set as thesource term of species transport equations when the reac-tants were consumed and the products were created. Theheat exchanged between gas phase and solid phase wastaken into account by energy equations.

2.3.1. Chemical reactions

In this work, only char belongs to solid phase, which isreleased by coal particles and the continue equation ofsolid phase can ensure the mass balance of char. So thereis no further species transport equation proposed for char.At the feed position, the drying process and the devolatal-ization reactions take place very quickly according toexperimental results [7], so it is assumed that the pyrolyticprocess of the raw coal is completed in this region. Theyield of each product is determined by the proximate anal-ysis of the raw coal. The sum of the mass fraction of prod-ucts is calculated to be unity in the raw coal

Y Char þ Y Volatile þ Y Water þ Y ash ¼ 1

Coal! Charþ VolatileþH2OþAshðR1Þ

The following chemical processes are included in thepresent model: (1) pyrolysis of the released volatile, (2) het-erogeneous char reactions, (3) homogeneous reactions ofgas phase.

There is no standard chemical stoichiometrically equa-tion for the pyrolysis of the volatile due to its complex com-position. For the sake of simplification it was assumed themolecular formula of the volatile is determined by the finalpyrolysates [23–25]. In the present work, the volatile matteris composed of several species as follow:

Volatile! m1CO2 þ m2COþ m3H2 þ m4CH4

þ m5C2H6 þ m6H2Sþ m7NH3 þ m8tar ðR2Þ

Table 1Homogeneous reaction and the kinetic equations

Chemical reactions Equations Units

CO + H2O M CO2 + H2 R6 ¼ K6 Y COY H2O �Y CO2

Y H2

K�6

h iR6 (kg m�3 s�1)

2CO + O2! 2CO2 R7 ¼ K6 Y COY 0:5O2

q1:5g

h iR7 (kg m�3 s�1)

2H2 + O2! 2H2O R8 ¼K7

T 1:5g

½Y 1:5H2

Y O2q2:5

g � R8 (kg m�3 s�1)

CH4 + 2O2! CO2 + 2H2O R9 ¼K9

T gY CH4

Y O2q2

g R9 (kg m�3 s�1)

2C2H6 + 7O2! 4CO2 + 6H2O R10 ¼K10

T gY C2H6

Y O2q2

g R10 (kg m�3 s�1)

4NH3 + 5O2! 4NO + 6H2O R11 ¼ K11Y 0:86NH3

Y 1:04O2

q1:9g R11 (kg m�3 s�1)

Table 2Arrhenius coefficients related to the R3–R11

Reaction Equations Units

R3 K3 = 17.9exp[�13,750/Ts] Pa�1 s�1

R4 K4 = 5.95 · 10�5 exp[�13,650/Ts] Pa�1 s�1

R5 K5 = 3.92exp[�26,927/Ts] Pa�1 s�1

R6 K6 = 2.78 · 103 exp[�1510/Tg] kmol�1 m3 s�1

R6* K�6 ¼ 0:0265 exp½3968=T g� —R7 K7 = 1.0 · 1015 exp[�16,000/Tg] kmol�0.75 m2.25 K1.5 s�1

R8 K8 = 5.159 · 1015 exp[�3430/Tg] kmol�1.5 m4.5 K1.5 s�1

R9 K9 = 3.552 · 1014 exp[�15,700/Tg] kmol�1 m3 K s�1

R10 K10 = 3.552 · 1014 exp[�15,700/Tg] kmol�1 m3 K s�1

R11 K11 = 9.78 · 1011 exp[�19,655/Tg] kmol�0.9 m2.7 s�1

L. Yu et al. / Fuel 86 (2007) 722–734 727

The composition of tar is usually regarded as condensed-nuclei aromatics, so it is reasonable to further proposeC6H6 instead of tar [24]. Combined the element analysisof coal with the final pyrolysates, the molecular formulaof the volatile can be determined as C24.2H46.2O8.5N1.1S.Although the drying and devolatalisation process is han-dled into two steps – pyrolysis of coal and volatile, it canbe considered as an instantaneous phenomenon that wecan calculate the kinetic coefficient from the mass balanceprinciple.

The heterogeneous reactions between char and gases(O2, H2O, CO2) can be described by different reactionmechanisms which are take account for possible diffusioneffect or further simplified by kinetic model. For example,Souza-Santos [25] and Chejne and Hernandez [7] used theunreacted core model to combine reaction with diffusionresistance. In Eaton and Smoot’s review [37], Reade et al.presented char oxidation model based on measured intrin-sic char kinetic rates and a pore diffusion model. Chen et al.[39] assumed that the oxygen, carbon dioxide and steamreact with char on the char particle surface and the valuefor reaction order was 0.5. In this study, we assumed charparticle is a spherical particle surrounded by a stagnantboundary layer through which gas species must diffusebefore they react with the char. The overall char reactionrate of a particle is controlled by the smaller of the ratesof diffusion and kinetic

3Cþ 2O2 ! CO2 þ 2CO ðR3ÞCþH2O! COþH2 ðR4ÞCþ CO2 ! 2CO ðR5Þ

The diffusion rate can be derived from the definition ofShawood number

KDif ¼ShDgswC

RT sds

ð31Þ

where Sh and R are Shawood number and the universal gasconstant, respectively. For the gas, Shawood number iswritten as

Sh ¼ 2:0þ 0:552Re1=2Pr1=3 ð32Þ

The char reaction rate is obtained as a mixture of kineticand diffusion controlled mass transfer rate

RC ¼6ðvolÞrs

ds

½ðKDifÞ�1 þ ðKArÞ�1��1pX i ð33Þ

The different expressions of homogeneous reactions canbe provided from several references, it is convenient tomake use of Souza-Santos [25] and Chejne’s works [7],which are summarized in Tables 1 and 2. The extendedwork is to consider that chemistry does not play any expli-cit role while turbulent motions control the overall reactionrate. So the chemical reaction rates are computed by

KHom ¼ minðKAr;KEBUÞ ð34Þwhere KHom is homogeneous rate constant and KAr iskinetic rate constant; KEBU is the turbulent mixing rateconstant and calculated with an Eddy Break-up model

KEBU ¼ Aej

minY R;i

SR;i;B

Y P;j

SP;j

� �ð35Þ

Here A and B are constants, SR,i and SP,j are the associatedstoichiometric coefficients of reactants and products.

2.3.2. Species transport equations

Gas phase is assumed as a mixture from 14 species, rep-resented by their mass fraction as follows: volatile, O2,CO2, H2O, NO, CH4, H2S, H2, C2H6, CO, NH3, Tar,Ash and N2. The conservation equations take the generalform as (36) for these chemical species but the N2, which

728 L. Yu et al. / Fuel 86 (2007) 722–734

is computed from the fact the sum of all mass fractions isequal to one in the gas phase

o

oTðqgrgY g;iÞ þ rðqgrgugY g;iÞ

¼ �r � rgJ g;i þ rgRg;i þ Rs;i ð36Þ

where Jg,i, Rg,i and Rs,i are the diffusion flux of species i ingas phase, the net rate of production of homogeneous spe-cies i and the heterogeneous reaction rate, respectively.

In the species transport equations of gas phase, mass dif-fusion coefficients are used to calculate the diffusion flux ofchemical species in turbulent flow using modified Fick’slaw

J g;i ¼ � qgDm;i þlt

rY

� �r � Y g;i ð37Þ

where rY is the Schmidt number, which is set as 0.7.The diffusion coefficient of the mixture, Dm,i is calcu-

lated from the binary mass diffusion coefficient Di,j asfollow:

Dm;i ¼1� X iP

j 6¼iX j

Di;j

ð38Þ

Fig. 1. Schematics of the reactor and simulation grid [40].

Table 3Coal analyses and properties [7]

Parameters Values

Proximate analysis (wt%)

Moisture 2.6Volatile matter 41.8Fixed carbon 54.1Ash 1.5

Ultimate analysis (wt%)

Carbon 75.3Hydrogen 5.4Nitrogen 1.8Oxygen 15.6Sulfur 0.4

Others

Mean particle size (mm) 0.62Density (kg m�3) 1250High heating value (kJ kg�1) 29, 695

2.3.3. Energy conservation equations

This section describes the heat transfer treatment formultiphase flow. In our work, although the compressibilityof gas phase and solid phase are taken into account, theflow at low Mach numbers (M� 0.3) makes some approx-imations valid. So the pressure work, kinetic terms and vis-cous heating are negligible. The energy transport equationsare solved for the specific enthalpy of gas phase and solidphase, which take the form

o

otðrgqgH gÞþr� ðrgqgugH gÞ¼rðagrT gÞþQgsþSgsH s

ð39Þo

otðrsqsH sÞþr� ðrsqsusH sÞ¼rðasrT sÞþQsgþ ssgH s ð40Þ

where H, a, Q are the specific enthalpy, the mixture thermalconductivity and the intensity of heat exchange between thegas and solid phases, respectively. The third term on theright hand is the heat transfer in that the solid phase chan-ged into gas phase.

The specific enthalpy is defined by

H ¼Xn

i¼1

Y iHi ð41Þ

where Hi is the enthalpy for each chemical species in themixture and considers both, thermal and chemical enthalpy

Hi ¼Z T

T 0

CP;i dT þ DH f;i ð42Þ

where the term T0, Cp,i and DHf,i are the reference temper-ature, the heat capacity at constant pressure for the ith spe-cies, and the enthalpy of formation for the ith species in thestandard state.

For the ideal gas, the mixture thermal conductivity iscomputed as

ag ¼X13

i¼1

X iaiPi6¼jX j/ij

ð43Þ

where /ij ¼1þ li

lj

� �1=2wjwið Þ

1=4

� �

8 1þwiwj

� �h i1=2 , Xi is the molar fraction of the

ith species.

The heat exchange between phases can be expressed as afunction of the temperature difference and conform to thelocal balance condition Qgs = �Qsg

Qgs ¼ hgsðT g � T sÞ ð44Þ

L. Yu et al. / Fuel 86 (2007) 722–734 729

where hgs is the heat transfer coefficient between the gasphase and the solid phase, and expressed in terms of ano-dimensional Nusselt number

Table 4Operating conditions and experimental results [7]

Exp. no. 1 2 3 4 5 6

Coal feed (kg h�1) 8.0 8.0 8.0 8.0 8.0 6.6Air supply (kg h�1) 21.9 17.0 19.4 21.9 28.4 14.8Steam supply

(kg h�1)4.6 4.6 4.6 4.6 4.6 4.0

Air and steamtemperature atentrance (�C)

420 413 422 435 368 336

Temperature ofreactor (�C)

855 812 841 866 826 829

Exp. result

H2 (%) 8.53 8.84 9.63 7.88 6.48 10.80CO2 (%) 19.31 18.38 14.40 15.60 14.86 21.59N2 (%) 60.37 61.10 64.62 64.52 71.54 56.60CH4 (%) 0.84 1.07 1.34 1.01 1.29 0.86CO (%) 10.94 10.59 9.97 10.94 5.80 10.14

Fig. 2. Comparisons between predictions a

hgs ¼Nu � ag � As

ds

¼ 6rs � Nu � ag

d2s

ð45Þ

In the case of fluidized beds, Gunn [36] proposed thefollowing empirical correlation:

Nu ¼ ð7� 10rg þ 5r2gÞð1þ 0:7Re0:2Pr

13Þ

þ ð1:33� 2:4rg þ 1:2r2gÞðRe0:7Pr

13Þ ð46Þ

where the continuous phase Prandtl number is defined by

Pr ¼lgCP;g

ag

ð47Þ

3. Numerical considerations

The simulated case is a bubble fluidized bed coal gasifierwhich was designed and built for studying the gasificationof Colombia coal [40]. A schematic view of the BFGB isshown in Fig. 1. The calculation domain is divided intostandard uniform grids (22 · 100 control volumes) accord-

nd experimental data in different cases.

730 L. Yu et al. / Fuel 86 (2007) 722–734

ing to the literature [19]. The air and steam flow into thebottom of the gasifier at uniform velocity so there is unes-sential to propose an air distributor model for the sake offully gas and solid mixing. Only gas phase is allowed tooutflow the reactor due to the assumption of particles inuniform size and ash in gas phase. The outlet pressure isfixed to atmosphere. The bed is initially filled particles witha 1.0 m high, where the total volume fraction of solids ispatched as 0.48 [7]. To prevent the spacing between parti-cles from decreasing to zero, the maximum particle packingis rs,max = 0.64 [19]. At the walls, a zero gradient conditionis used for the turbulent kinetic energy. The no-slip wallcondition is used for the gas phase and solid phase [30].The value of all the compositions into the gasifier can beobtained from Tables 3 and 4. The simulation was carriedout with the finite volume method (FVM), in which the

Fig. 3. Concentration distributions of H2, C

inter-phase slip algorithm (IPSA) of Spalding was used tosolve velocity–pressure coupled differential equations. Forthe evaluation of the convective terms, the second orderQUICK scheme was used. The time steps was set as1 · 10�4. The governing equations were discretized intoalgebraic equations that can be solved numerically.Gauss–Seidel method was applied to solve these equationswhich can be stable due to point by point iteration. Inorder to reduce the number of iteration and to acceleratethe convergence of solution, algebraic multigrid (AMG)scheme was also used to coarsen grids [41].

4. Results and discussion

The six different cases were calculated and their resultswere validated by the experimental data with Colombia

O2, N2, CH4 and CO in different cases.

-0.10 -0.05 0.00 0.05 0.10

0.0015

0.0016

0.0017

0.0018

0.0019

0.0020

Mol

ar C

once

ntra

tion

of O

xyge

n

(km

ol/m

3 )

Bed diameter (m)

0.002 m (Bed height) 0.004 m 0.006 m

Fig. 5. Radial profiles of oxygen concentration at the bottom of gasifier indifferent heights.

L. Yu et al. / Fuel 86 (2007) 722–734 731

coal. The simulation results of outlet molar fraction of gascomposition can be compared with experimental data bythe following form of area average:

X i ¼1

A

ZX i dA ð48Þ

Fig. 2 shows that the prediction results are well in agree-ment with the experimental data. It can be observed thatthe calculation errors of CO2 and N2 molar fraction are lessthan 5% and most of other results are within the 20%range. One or two calculation errors of CH4 molar fractionare more than 10% due to the fact that it only comes fromdevolatalisation but the reaction of char and H2 isneglected. The higher differences of these cases are pre-sented in the H2 and CO molar fraction due to the fact thatthe effect of limestone is ignored. According to the decom-position reactions of limestone in the work of Souza-Santos [25], CO2 can be produced. Through the impactof the equilibrium of water–gas shift reaction (R6), it willtake place for the phenomenon that the contents of H2

decrease and the contents of CO increase. This tendencycan contribute to improve the predicted exit value of H2

concentration and CO concentration. But it is reasonableto ignore the effect of limestone due to its lower contentsand higher decomposing temperature. The results of H2

concentration and CO concentration in lower calculationerror can verify this assumption.

Simulated distributions for gas compositions of thesecases are shown in Fig. 3. Observed from Fig. 3, the overalltrend of each composition profile is coincident in differentcases. For example, the concentrations of CO2 and COincrease along the height of the gasifier, while the contentsof H2 and CH4 go up at first then drop down to the top ofreactor due to the devolatalisation and the equilibrium ofwater–gas shift reaction. Although the water–gas shift reac-tion is exothermic and low temperature favors the forwardstep [42], the content of CO is so low that it is impossible tomove the water–gas shift reaction toward the backward

Fig. 4. Contours of the simulated gas temperature in different cases.

step. On the contrary, the contents of H2 and CO2 are highenough to move the water–gas shift reaction toward thebackward step. Although H2 and CO2 are depleted simul-taneously, the quantity of CO2 can be compensated bycombusting the methane. So the (R8) and the (R9) canbe used to explain why the contents of H2 and CH4 dropdown to the top of reactor. However, due to the existenceof water–gas exothermic reaction, on the top of gasifier, theradial profile of CO concentration is favored by high tem-perature and the radial profile of H2 concentration isfavored by low temperature. Besides the common rules,each case has its own characteristics which can be observedfrom the contour of molar fraction for each composition inFig. 3 due to different operating conditions, for example,the most evident difference of composition contour canbe shown at the top of gasifier between case 6 and others.Due to lower flow rate of air supply for case 6, the upwardsparabolic contour of molar fraction for each compositioncannot be formed at the exit and the content of N2 is lessthan that of other cases.

-0.10 -0.05 0.00 0.05 0.10

900

950

1000

1050

1100

1150

Gas

Tem

pera

ture

(K

)

Bed diameter (m)

0.002 m 0.004 m 0.006 m (Bed height)

Fig. 6. Radial profiles of gas temperature at the bottom of gasifier indifferent heights.

Fig. 7. Velocity vector distributions: (A) gas; (B) solid.

732 L. Yu et al. / Fuel 86 (2007) 722–734

4.1. Relationship between temperature and gas

composition profile

The composition distribution is strongly relative withthe temperature profile in reactor. In the gasifier, the pre-dicted temperature profile shown in Fig. 4 further illus-trates that the high temperature zone of the top sectioncontribute to increase the molar fraction of carbon monox-ide and decrease the molar fraction of Hydrogen. Thehigher wall temperature promotes the upward parabolicchange of radial temperature profile. Moreover, Fig. 4shows that there is a clear division in the upper of reactor.Above the division, the calculated zone can be consideredas a pure gas phase region while the gas phase and solidphase existed in the low regime of gasifier. The heatexchange of gas–solid mixture is different from that ofthe pure gas phase. It leads to the evidently different tem-perature distribution between the up regime of pure gasphase and the low regime of gas–solid mixture.

At the feed point, the temperature dropped down rap-idly at first due to the devolatalisation and drying thenwent up gradually. The methane is released from the vola-tile at the feed region and reduced along the height of gas-ifier due to oxidization reaction. At the gas inlet, theoxygen is supplied into the gasifier and was depleted alongthe gasifier height due to the gasification reaction. The heatof combustion is released and the temperature of the reac-tor bottom was elevated rapidly.

From Figs. 5 and 6, the relationship between oxygenconcentration and gas temperature can be revealed clearly.The similar radial profile of oxygen concentration and gastemperature but reversed trend further illustrate that theheat of combustion is the key reason of elevating the tem-perature of gasifier. When the oxygen is depleted, the tem-perature of gasifier will decrease due to the fact that theoverall gasification is an endothermal reaction.

Fig. 8. Relationship between coal vo

Fig. 7 gives gas and solid velocity vector distribution tofurther illustrate the effect of flow behavior on the heattransfer. The coal bed was agitated by the gas up-flowand vortex field is formed due to the unbalanced forcesof drag and gravity. It is the internal circulation of coalbed that promotes the bed temperature uniform. However,in the freeboard of the gasifier, there exists a strong up-flowwhich will keep from the occurrence of backmixing. Thenthe radial profile of freeboard temperature is formed dueto thermal diffusion. So the gasifier can be divided into hightemperature zone and low temperature zone by the cleardivision that is different from the circulating fluidized bed[43].

lume fraction and reaction rates.

L. Yu et al. / Fuel 86 (2007) 722–734 733

4.2. Relationship between coal volume fraction and gas

composition profile

Fig. 8 shows the calculated distributions of coal volumefraction and heterogeneous reaction rates. It is noted thatthe contents of CO, CO2 and H2 increase subsequently atthe bottom of gasifier due to coal combustion, char-CO2

and Char-H2O gasifications in all cases, while significantdifference of these heterogeneous reaction rates are shownin Fig. 8. The predicted result is consistent with that of areview on char oxidization mechanisms [44]. Accordingto this review, the first product which was observed nearthe gas inlet is CO whether two-step or three-step reactionmechanism were proposed. Fig. 3 gives the distributions ofCO, CO2 and H2 concentration that are released along thebed height subsequently in the low regime of gasifier. Dueto the fact that there is few coal particles in the bubblephase, the heterogeneous reaction rates is lower than thatof emulsion phase which can be verified by contrastingthe heterogeneous reaction rates with coal volume fractionin Fig. 8.

5. Conclusion

A comprehensive model based on TFM includingKTGF and complicated reactions was developed to simu-late BFBG numerically which can be used to predict andanalyze the impact of flow behavior on chemical reaction.The simulation results would give much more exact predic-tions of the distributions of pressure, temperature, velocity,volume fraction of the phases and gas composition alongthe reactor which cannot be described by two-phase orthree-phase model. The calculated exit gas compositionsare in well agreement with the experiment data which isavailable from Colombia coal. From these results, a rea-sonable interpretation of the change trend of gas composi-tion profile along the gasifier with the distributions oftemperature, gas and coal velocity and coal volume frac-tion can be obtained.

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