Table Of ContentAppendix 1
Characteristics of Solid Particles
A particle may be defined as a small object having a precise physical boundary in all directions.
Theparticleischaracterizedbyitsvolumeandinterfacialsurfaceincontactwiththeenvironment.
A1.1 SOLID PARTICLES
Solidparticlesarerigidandhaveadefiniteshape.Asphereisanaturalchoicetodefineaparticle,
thoughmostnaturalparticlesarenotspherical.Hence,naturalparticlesarecharacterizedbytheir
degree ofdeviation fromspherical shape, sphericity,and an equivalent diameter.
A1.1.1 EQUIVALENTDIAMETERS
Let us take a nonspherical particle having a surface area S, and a volume V. Several types of
equivalentdiameteroftheparticlecanbedefinedtodescribetheparticle,asshowninFigureA1.1.
Four morefrequently useddefinitionsare:
A1.1.1.1 Volume Diameter (d )
v
Volume diameter isthe diameter ofa sphere thathas the same volume asthe particle:
(cid:4)(cid:2) 6(cid:3) (cid:5)13 (cid:4)(cid:2)6V(cid:3)(cid:5)13
d ¼ £volumeof particle ¼ ðA1:1Þ
v p p
A1.1.1.2 Surface Diameter (d)
s
Surfacediameteristhediameterofaspherethathasthesameexternalsurfaceareaastheparticle.
Thus,
(cid:4)surfaceareaof particle(cid:5)12 (cid:4)S (cid:5)12
d ¼ ¼ : ðA1:2Þ
s p p
A1.1.1.3 SieveSize (d )
p
Sievesizeisthewidthoftheminimumsquareapertureofthesievethroughwhichtheparticlewill
pass.
A1.1.1.4 Surface-VolumeDiameter (d )
sv
Surface-volumediameteristhediameterofaspherehavingthesamesurfacetovolumeratioasthat
ofthe particle:
6pd2 S
sv ¼
pd3 V
sv ðA1:3Þ
V
d ¼6
sv S
439
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440 CombustionandGasificationinFluidizedBeds
ds dsv
Equivalent sphere with same Equivalent sphere with same
external surface area as the ratio of surface to volume as
original particle the original particle
Original Particle Equivalent sphere passing
through same aperture as
does the original particle
Equivalent sphere with same
volume as the original particle
d d
d p p
v Screen
Aperture
FIGUREA1.1 Differentrepresentationsofanonregularshapedparticle.
A1.1.2 SPHERICITY(f)
Sphericitydescribesthedepartureoftheparticlefromasphericalshape.Forexample,aspherical
particle hasa sphericityof 1.0:
Surfaceareaofaspherewiththevolumesameastheparticle pd2
SphericityðfÞ¼ ¼ v: ðA1:4Þ
Actualsurfaceareaoftheparticle S
Eliminating S and V fromEquationA1.1, Equation A1.3, and Equation A1.4, one gets:
d ¼fd : ðA1:5Þ
sv v
The relationship between the above sizes and the sieve size d can be derived through
p
experiments for irregular particles and through calculations for geometrically shaped particles.
An approximate relation for crushed quartz of sphericity 0.8 was given as (Abrahamsen and
Geldart,1980):
d <1:13d ; d <0:773d ; d <0:87d ; d <1:28d
v p sv v sv p s p
Thesphericityisusuallymeasured.Typicalvaluesofsomecommonlyusedparticlesaregiven
in Table A1.1. Biomass particles often have very low sphericity. Characteristics of some typical
particlesare shown inTable A1.2.
A1.1.3 MEANPARTICLESIZEANDITSMEASUREMENT
Millionsofsmallparticlesaresimultaneouslyhandledinanindustryforthepurposesofreactions,
heat and mass transfer, or homogeneity. In such a particulate mass, generally particles are not
uniform in sizeand are characterizedby particle size distribution.
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Appendix1:CharacteristicsofSolidParticles 441
TABLE A1.1
Sphericityof SomeGranular Solids
Particle Sphericity
Sand(Ottawa) 0.95
Sand(flint,jagged) 0.65
Sand(averageofalltypes) 0.75
Limestone 0.45
Gypsum 0.40
Coal(crushed) 0.65
Coal(pulverized) 0.73
Alumina 0.3–0.8
Catalysts 0.4–0.9
Crushedglass 0.65
FCCcatalyst 0.58
Source: CoalConversionSystemData Handbook.Table IVB10.1,DOE/FE/
05157-2,1982.
There are several characteristic properties that define aparticulate mass:
† Number ofparticles
† Total surface area
† Total volume
Itisdifficulttoprovideindividualattentiontotheseproperties,andhenceitisnecessarytodefine
some average properties. Therefore, one finds it convenient to imagine an equivalent particulate
massofparticlesofuniformsizethatmatchesthepropertiesoftheactualparticulatemass.However,
itispossibletomatchonlytwopropertiesbetweentheactualandtheequivalent.Influidizationand
in most chemical engineering applications, total volume and surface area are the two chosen
properties.Theserepresentthematerialcontentandinterfacialareaacrosswhichtransferprocesses
occur.Forapressuredropthroughthebed,thesurfaceareaismostimportant.Themeanparticlesize
isthusdefinedinsuchawaythatitequalstheaveragesurfaceareaofparticlesofsizesinthebed.
TABLE A1.2
Sphericityand Densityof Some Biomass Fuels and Ash Producedfrom
Them
VoidageatMinimum
Particle ParticleDensity(kg/m3) Fluidization Sphericity
Biomass
Sawdust 430 0.586 0.95
Ricehusk 500 0.795 0.65
Ash
Sawdustash 380 0.603 0.75
Ricehullash 410 0.678 0.45
Source:Chenetal.,CirculatingFluidizedBedTechnologyV,Kefa,C.ed.,InternationalAcademic
Publishers,Beijing,p.508,2005.
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442 CombustionandGasificationinFluidizedBeds
Sieving is the most commonly used technique for the measurement of the surface area of
granular solid particles. Particles of size greater than 44 microns are measured by using a set of
standardtestsieveswithsquareapertureopenings.Thetestsievesarestackedwiththeonewiththe
largestapertureonthetop.Thelowersievesareselectedsuchthattheaperturesaresmaller.After
vibratingandshakingthestackusingasieveshakerforaperiodof20to30minutes,theparticles
collectedoneachsieveare weighedandassigned asizebytakingthe arithmeticalaverage ofthe
aperture size of the sieve through which the material just passed and the sieve on which it is
retained:
1
d ¼ ; ðA1:6Þ
m (cid:2)x (cid:3)
P i
d
i
whered isthearithmeticmeanoftheaperture(opening)oftwoadjacentsieves,andx istheweight
i i
fractionofsamplescollectedbetweenthesetwosieves.Theaboveequationwillmatchthesurface/
volume ratio of the actual poly-size particles. For nonspherical particles, all having the same
sphericity,f, the mean size d , would then be fd . Equation A1.6 is, however, not valid for a
m m
discontinuousparticle size.
Inindustriestheparticlesizedistributionissometimesdescribedbyd ,whichisasizebelow
50
whichlies50%ofthesamplebyweight.TherelativesizerangeR,isanothercharacteristicusedto
describethe spread ofthe size distribution.It isdefined as
d 2d
R¼ 84 16: ðA1:7Þ
2d
m
whered andd arethediametercorrespondingtosizebelowwhichparticlesconstitute84%and
84 16
16%, respectively,by weight.
A1.2 PACKING CHARACTERISTICS
Inaparticulatemass,particlesrestoneachotherduetotheforceofgravitytoformapackedbed.
Depending on the shape of particles and packing characteristics, a certain volume of space in
between the particles remains unoccupied. Such space is called a void volume and is specified as
voidageor porosity, defined as
voidvolume
Voidage; 1¼porosity¼ : ðA1:8Þ
volumeof ðparticlesþvoidsÞ
Themeasurementofparticlevolumeissimple,buttheprecisemeasurementofitssurfacearea
isverydifficult.Thisproblemcompoundswhenoneattemptstodefinethesphericityofamassofa
large number of dissimilar particles. The packing characteristics of particles are important
parameters that depend on the particle’s shape and mode of packing. In some special situations,
such as in the vicinity of a sphere or a plane wall, the distribution of local voidage becomes
important. Unlike bulk voidage, it is not uniform or monotonically varying. It follows a damped
oscillatorypattern.
A1.3 PARTICLE CLASSIFICATION
Inthelightoffluidizationexperience,Geldart(1972)classifiedsolidsbroadlyunderfourgroups,A,
B, C, and D as shown in Figure A1.2. The particle’s classification is plotted against the density
differencebetweenthesolidandthefluidizinggas.Thisclassificationisimportantinunderstanding
thefluidizationbehaviourofsolidparticles,becauseundersimilaroperatingconditionsparticlesof
different groups may behave entirelydifferently.
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Appendix1:CharacteristicsofSolidParticles 443
7
6
5
4
B D
3
Sand-Like Spoutable
2 A
rp – rf (g/cm3) Aeratable
1
0.5 C
Cohesive
20 50 100 200 500
Dp (mm)
FIGUREA1.2 PowderclassificationdevelopedbyGeldart.
A1.3.1 GROUPC
These particles are very fine and are typically smaller than 30mm (r ¼2500kg/m3). The inter-
p
particle forces are comparable to the gravitational force on these particles. So, these particles are
verydifficulttofluidize.Anattemptatfluidizationoftenresultsinchannelling.Specialtechniques
are required tofluidize these particles.
A1.3.2 GROUPA
These particles are typically in the range of 30 to 100mm (r ¼2500kg/m3). These particles
r
fluidize well, but expand considerably after exceeding the minimum fluidization velocity and
before bubbles start appearing. Many circulating fluidized bed systemsuse Group Aparticles.
TABLE A1.3
Distinguishing Featureof Four Groupsof Particles
Group C A B D
Particlesizefor ,20mm 20–90mm 90–650mm .650mm
r ¼2500kg/m3
r
Channeling Severe Little Negligible Negligible
Spoutability None None Shallowbed Readily
Expansion Low High Medium Medium
Minimumbubbling Nobubble .U ¼U ¼U
mf mf mf
velocity,U
mb
Bubbleshape Onlychannel Flatbase Roundedwith Rounded
sphericalcap smallindentation
Solidmixing Verylow High Medium Low
Gasback-mixing Verylow High Medium Low
Sluggingmode Flatrainingplugs Axisymmetric Mostlyaxisymmetric Mostlywallslugs
Effectofparticlesize Unknown Appreciable Minor Unknown
onhydrodynamics
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444 CombustionandGasificationinFluidizedBeds
A1.3.3 GROUPB
Theseparticlesarenormallyintherangeof100to500mm(ifr ¼2500kg/m3)size.Theyfluidize
p
well,andbubblesappearassoonastheminimumfluidizationvelocityisexceeded.Themajorityof
the fluidized bed boilers usethis group ofparticles.
A1.3.4 GROUPD
These are the coarsest of all particles (.500mm) (for r ¼2500kg/m3). They require a much
p
higher velocity to fluidize these solids. Spouted beds and some bubbling fluidized bed boilers
generallyoperate on thissize ofsolids.
Acomparison ofproperties ofparticles ofdifferent groups isgivenin Table A1.3.
NOMENCLATURE
a, b: constantsin Equation A1.9
C : coefficientof drag ina particle
D
d: mean openingof successivesieves, (d þd )/2
i pi piþ1
d : mean diameter ofa particulate mass with varying sizes, m
m
d : sieve size (diameter), m
p
d: surface diameter,m
s
d : volume diameter,m
v
d : surface volume diameter, m
sv
d , , : diameterscorrespondingtocumulativeweightsof84%,50%,and16%,respectively
84 50 16
F : drag forcein aparticle, N
D
m : mass ofparticle, kg
p
R: relative size range defined in Equation A1.6
S: actual surface ofthe particle,m2
U : minimum fluidizationvelocity, m/sec
m
U: superficial gas velocity, m/sec
V: actual volume of the particle,m3
x: weight fractionof particlescollected betweensievei andiþ1
i
f: sphericity
e: voidage
r: density ofgas, kg/m3
g
r: density ofsolids, kg/m3
p
m: viscosityof gas, kg/sq.m
Ar: Archimedes number, ðgd3(r2r))/m2
p p g
Re: Reynolds number, ðUd r)/m
v g
REFERENCES
Abrahamsen,A.R.andGeldart,D.,PowderTechnol.,26,p.35,1980.
Chenetal.,CirculatingFluidizedBedTechnologyV,KefaC.,ed.,InternationalAcademicPublishers,Beijing,
p.508,2005.
Geldart,D.,Theeffectofparticlesizeandsizedistributiononthebehaviourofgas-fluidizedbeds,Powder
Technol.,6,201–215,1972.
InstituteofGasTechnology,CoalConversionSystemDataHandbook,DOE/FE/05157-2,TableIVB10.1,1982.
q2006byTaylor&FrancisGroup,LLC
Appendix 2
Stoichiometric Calculations
Stoichiometric calculations (also known as combustion calculations) provide much of the basic
informationnecessaryforthedesignofaboilerplant.Theyhelpfindtheamountoffueltobefed
for the required thermal output of the plant. The specifications offans and blowers are based on
the air required for burning or gasifying that quantity offuel. Combustion calculations also give
theamountoflimestonerequiredtoachieveacertainamountofsulfurcapture.Finallythesolidand
gaseouspollutantsproducedfromthecombustionarecomputedfromthis.Mostofthecalculations
are based on overallchemical reactions.
A2.1 CHEMICAL REACTIONS
Some boiler furnaces burning high-sulfur coal are required to retain the sulfur released from the
coal during combustion in solid form such that it is not emitted into the atmosphere. Thus,
stoichiometriccalculationsoftheseboilersrequirespecialconsiderations.Theoverallcombustion
reactions for this type offurnace can be writtenas follows:
CþO ¼CO þ32;790kJ=kgof carbon ðA2:1Þ
2 2
(cid:2) m(cid:3) m
C H þ nþ O ¼nCO þ H Oþheat ðA2:2Þ
n m 4 2 2 2 2
SþO ¼SO þ9260kJ=kgof sulfur ðA2:3Þ
2 2
where mand nare stoichiometric coefficients of EquationA2.2.
ForabsorptionoftheSO ,limestoneisfedintothefurnace.LimestoneisfirstcalcinedtoCaO
2
through the followingreaction:
CaCO ¼CaOþCO 21830kJ=kgofCaCO ðA2:4Þ
3 2 3
Ifthe sorbentcontainsmagnesium carbonate, an additional reactionoccurs:
MgCO ¼MgOþCO 21183kJ=kgofMgCO ðA2:5Þ
3 2 3
Calcium oxide, from either limestone or coal ash, absorbs a fraction of the sulfur dioxide
releasedfrom the coal during combustion. Thereactionis:
CaOþSO þ 1O ¼CaSO þ15;141kJ=kgofsulfur ðA2:6Þ
2 2 2 4
The above equations show that oxygen is required for both the combustion and the sulfation
reactions.Sinceinanygas–solidprocessthecontactbetweenthegasandsolidislessthanperfect,
an excess amount of oxygen is needed for complete combustion. The extra air that provides this
oxygeniscalledexcessair.Thisexcessairisabout20%forthecombustionandsulfationreactions
combined.
445
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446 CombustionandGasificationinFluidizedBeds
A2.2 AIR REQUIRED
Notingthatdryaircontains23.16%oxygen,76.8%nitrogenand0.04%inertgasesbyweight,the
dryair required for complete combustionofa unit weight ofcoal M , is givenby:
da
M ¼½11:53Cþ34:34ðH2O=8Þþ4:34SþA·S(cid:2)kg=kgcoal ðA2:7Þ
da
where C, H, O, and S are weight fractions offuel constituents known from the ultimate analysis.
For each unit mass of sulfur converted to calcium sulfate, an additional amount of dry air A, is
required(seeReactionA2.6).SotheextraairforaunitweightofcoalisA·S,whereAis2.16for
sulfur capture and is zero when no sulfur is captured as calcium sulfate.
For efficient combustion, a certain amount of air, in excess of what is required theoretically,
isprovided.Togetthetotalaironemustmultiplythetheoreticalairbytheexcessaircoefficient,
EAC. The total dry air T , is the sum of the theoretical requirement and whatever excess air is
a
allowed tocomplete the combustion.
T ¼EAC·M kg=kgburned ðA2:8Þ
da da
TheexcessaircoefficientEAC,isdefinedinsuchawaythatEAC¼1.2wouldmean20%excess
air.Airusuallycontainssomemoisture.InstandardairthisweightfractionofmoistureX ,isabout
m
0.013kg/kgair,andX istheweightfractionofmoistureintheair.Thus,M ,thetotalwetairis:
m wa
M ¼T ð1þX Þ ðA2:9Þ
wa da m
A2.3 SORBENT REQUIREMENT
Ifthecoalashcontainsanegligibleamountofcalciumoxide,thesorbentrequiredL ,toretainthe
q
sulfur in aunit weight offuelis found from the following equation:
100S
L ¼ XR ðA2:10Þ
q 32X
CaCO3
whereSistheweightfractionofsulfurincoal,andX istheweightfractionofCaCO inthe
CaCO 3
3
sorbent.Risdefinedasthecalciumtosulfurmolarratiointhefeedofsorbentandcoalrespectively.
Sometimesthecoalashcontainsanappreciableamountofcalciumoxide,whichremovesapart
ofthesulfurreleasedfromthecoal.IfX istheweightofcalciumoxideperunitweightoffuel
CaO
fed, theinherentCa/Sratio is32X /56S.Thereforethe limestone requiredfor removal ofsame
CaO
amount of sulfur (E S) will be reduced by the above amount. Thus, R is to be replaced by R0 in
sor
EquationA2.10and elsewhere asbelow:
(cid:4) 32X (cid:5)
R0 ¼ R2 CaO ðA2:11Þ
56S
A2.4 SOLIDWASTE PRODUCED
From Reaction A2.4 to Reaction A2.5 we find that the sorbent decomposes into MgO and CaO.
OutofthisapartoftheCaOisconvertedintoCaSO .ThespentsorbentwouldthuscontainCaSO ,
4 4
unconverted CaO, unconverted MgO, and inert components of the sorbent. The weight of spent
sorbentproducedperunitweightofcoalburnedL ,isthesumofCaSO ,CaO,MgO,andinerts.
w 4
Spentsorbents¼calciumsulfateþcalciumoxideþmagnesiumoxideþinert
S (cid:2)L X SE (cid:3) 40L X
L ¼136 E þ56 q CaCO3 2 sor þ q MgCO3 þL X ðA2:12Þ
w 32 sor 100 32 84 q inert
where L is the sorbent fed per unit weight of coal burned and is given by Equation A2.10.
q
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Appendix2:StoichiometricCalculations 447
Thetotalsolidwastecontains,inadditiontothespentsorbentL ,coalashASH,andunburned
w
carbon ð12E Þ;lessthe CaO content X ,ofcoal converted toCaSO andincludedinL .The
c CaO 4 w
solid waste producedper unitweight offuel burned is thus:
W ¼½L þASHþð12E Þ2X (cid:2) ðA2:13Þ
a w c CaO
where E is the combustionefficiency expressedas afraction.
c
A2.5 GASEOUS WASTE PRODUCTS
Theweightoffluegasduetothecombustionreaction,W isthesumofcarbondioxide,watervapor,
c
nitrogen, oxygen, sulfur dioxide, and fly ash. These individual constituents of a flue gas can be
found as follows.
A2.5.1 CARBONDIOXIDE
Carbondioxideproducedfromfixedcarbonincoal¼3:66C ðA2:14Þ
In addition to the CO produced from the fixed carbon, an extra amount of carbon dioxide is
2
generatedduetocalcinationofCaCO andMgCO inthesorbentmaterial,seeEquationA2.4and
3 3
EquationA2.5.This amount W , may be calculatedas:
CO
2
! !
44SR 100X 1:19X
W ¼ 1þ MgCO3 ¼1:375SR 1þ MgCO3 ðA2:15Þ
CO2 32 84X X
CaCO3 CaCO3
where R is the calcium/sulfur molar ratio.
ExampleA2.1
The following table gives an analysis of a coal. Calculate the amount of CO produced
2
per kilogram of the coal burned. Assume that a calcium/sulfur molar ratio of 2.5 is used for
sulfur capture. The limestone contains 88%CaCO by weight and 10%MgCO byweight.
3 3
C H O N S ASH Moisture
Ultimateanalysisofcoal(%) 72.8 4.8 6.2 1.5 2.2 9.0 3.5
Solution
CO produced from coal combustionEquationA2.14¼3.66£0.728.
2
¼2:66kg=kg coalduetocombustion:
CO produced from calcinationEquationA2.15¼1.375£0.022£2.5 (1þ1.19£0.1/0.88)
2
¼0:0858kg=kg fuel:
Total carbon dioxide produced¼2.66þ0.0858.
¼2:745kg=kg of coal burned:
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448 CombustionandGasificationinFluidizedBeds
A2.5.2 WATERVAPOR
Waterinthefluegascomesfromthecombustionofhydrogeninthecoalandthemoisturepresentin
thecombustionair,coal,andlimestone.Thewaterinthefluegasperunitweightofcoalburnedis:
9HþEAC·M X þM þL X ðA2:16Þ
da m f q ml
A2.5.3 NITROGEN
Nitrogen inthe fluegas comes fromthe coal as well asthe combustion air
Nitrogenfromfuelandair¼Nþ0:768M EAC ðA2:17Þ
da
A2.5.4 OXYGEN
Theoxygeninthefluegascomesfromoxygeninthecoal,excessoxygeninthecombustionair,and
theoxygenleftinthefluegasforincompletecaptureofsulfur.WerecallfromEquationA2.6that
for each moleof unconvertedsulfur, 1/2mol of oxygen is saved. Thus:
Oxygeninfluegas¼Oþ0:2315M ðEAC21Þþð12E ÞS=2 ðA2:18Þ
da sor
A2.5.5 SULFURDIOXIDE
If only E fraction ofthe sulfur is converted toCaSO , the SO present inthe fluegas is:
sor 4 2
2Sð12E Þ ðA2:19Þ
sor
A2.5.6 FLYASH
The flue gas may carry a part of the coal ash or sorbents. Though it is very small in amount and
iseventuallycollectedinthedustcollector,itcarriesthroughtheconvectivesectionoftheboilera
fractionofthesensibleheatthatmaynotbenegligible.Thefluegasisapproximatedonthebasisof:
Unitweightof coalburned¼a ASH ðA2:20Þ
c
where a is the fraction ofthe ash incoal asit appearsas fly ash ð<0:120:5Þ:
c
Thetotalweightofthefluegascanbefoundbyaddinguptheabovecomponents.Simplifying
them, the total weight of the flue gas per unit weight of coal burnedis:
W ¼M 20:2315M þ3:66Cþ9HþL X þNþOþ2:5Sð12E Þ
c wa da q ml sor
!
1:19X
þ1:375SR 1þ MgCO3 þa ASHkg=kgburned ðA2:21Þ
X c
CaCO3
A2.6 HEATING VALUE OF FUELS
Theapproximatehigherheatingvalue,HHV,ofasolidfuelmaybecalculatedfromtheDulongand
Petit formula:
HHV¼33;823Cþ144;249ðH2O=8Þþ9418SkJ=kg ðA2:22Þ
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