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Transcript of CFBC fuel flexibility: Added value of advanced process optimization n3 2014 pp 48-61.pdf ·...
CFBC fuel flexibility: Added value of advanced process optimization
M. Weng, A. Omer Aixprocess GmbH, Aachen, Germany
Keywords: CFB, fuel flexibility, process optimization, plant audit, CFD simulation
Abstract—A major advantage of circulating fluidized bed combustors (CFBC) is the high flexibility according to fuel type, composition and specific properties like particle size, moisture and morphology. On the other hand, flow and transport characteristics of large scale fluidized beds are far from ideal mixing conditions. Hence, fuel flexibility design for new or existing plants is a multi-parameter optimization problem with numerous aspects from storage and feeding equipment over optimum feeding location to the effect on fuel burn-out, emissions and wear. The combination of plant audits, specific measurements (e.g. primary air nozzle pressure drop as a measure for flow distribution and bed flow pattern) and the application of advanced computational fluid dynamics are presented in this contribution. Specific fuel flexibility challenges and solutions considering
• air staging,• wear reduction and• limestone injection for direct desulphurization
are shown for 3 selected German and Polish CFB plants (150–490 MWth) and fuel compositions varying between
• coal/RDF mixture,• up to 40% substitution of coal with wood pellets and/or wood chips and• 100% biomass with different fuel specifications.
The examples demonstrate the added value of a joint process optimization approach for an efficient analysis of the complex coupling flow and transport mechanisms in CFBs. The increased insight and understanding is a major support for finding proper design and operation conditions for the application of flexible fuel compositions.
INTRODUCTION A major advantage of circulating fluidized bed combustors (CFBC) is the high flexibility according to fuel type, composition and specific properties like particle size, moisture and morphology. However, flow and transport characteristics of large scale fluidized beds are far from ideal mixing conditions. Due to the loop mode of a CFB, multiple time-scales exist from short-term pressure and velocity fluctuations to long-term shifting of bed inventory particle size distribution and miscellaneous accumulation processes. Time-scale issues are even enhanced if plant operation is not stationary due to fuel inhomogeneity or load changes as required by economic reasons.
As a consequence, fuel flexibility design for new or existing plants is a multi-parameter optimization problem with numerous aspects from storage and feeding equipment over optimum feeding location to the effect on fuel burn-out, emissions and wear.
The combination of plant audits, specific measurements (e.g. primary air nozzle pressure drop as a measure for flow distribution and bed flow pattern) and the application of advanced computational fluid dynamics (CFD) for reacting dense particle flows is presented in this contribution.
South African Journal of Chemical Engineering, vol. 19, 2014, no. 3, pp 48-61 48
PlanThe banalydata for edistrinormattritiwith conteinvenCFB pheninformcyclo
WespecFor insealinexcesheat e
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nt audit basic step o
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n addition, tanger duringibutor nozzleher subject lly accompliation. Typicainspection osingle secon
zle measurod conditionan optimal fe internal asppropriate mmation abou
measurementmetric flow r
of any procetional data fre base for inf the operat
D). Whilst thn, bed invens emission aexibility andd and filterd, the analy
n chamber al models orut the solidst. ed mass andtime excess vrt-term tempal pot with and increase
ection. the on-site ig a downtime wear, wallof inspectionished by hanally, on-line mof flap positidary air line
rements n of the air fluidization osh circulationmeasuring deut the inner dt equipment rate ramp is s
Figure
ess optimizatrom the proc
ntegral fuel, ational state he latter shontory is subjand cannot bd multiple lor ash withdysis of tempe
taken fromr simulated ds inventory w
d heat balanvalues and sperature deca
multiple sued dust outta
investigationme provides u
l or cyclone n during a nd flaps dumeasuremenion sometimgives insigh
distributor nof the bed. An in the comevice, which degree of weis connected
supplied and
e 1. Equipmen
METHODS
tion is a cocess control air/flue gas of a FBC isould be knoject to long-
be easily meaoad changes
drawal does erature and
m the procedata for momwithin the w
nce of a CFspikes can gay within the
ubsequent prake from the
n of the innuseful informerosion andplant audit
uring commints of each sin
mes in combiht in the actu
nozzles is a Also even dismbustion cha
measures thear or even bd to each sind the pressur
nt for on-site n
S
mprehensivesystem in coand heat ba
s the bed inown from r-term procesasured. Espes, solids bala
not characpressure prss control
mentum andwhole circle
FB furnace igive helpful he cyclone canrocess issues
cyclone with
ner conditionmation accordd solids depo
is the trimmissioning andngle secondaination withal secondary
prerequisitestribution of amber depenhe pressure dblockages (Figngle nozzle ore drop chara
nozzle measur
e plant audiomparison toalances. Evennventory andegular sampsses like accecially in theancing by coterize the inofiles along system in
d heat transfeand its loca
s yet difficuhints for pron display inss like incomph wear and/
n of boiler, ding to operosition in theming of secod may be reary air nozzle
pressure dry air distribut
for even airbed materia
nds on propedrop over theg. 1). In a staf the distribuacteristic is m
rement
it. Obviouslo the boiler den more impd its particlple taking dcumulation, e case of opeomparing funstantaneouthe height
comparison er provides uation in the
ult to accomocess malfunsufficient pre
mplete combu/or slugging
cyclone andrational issuee flue gas seondary air te-adjusted de are not instrop calculati
ution.
r distributioal and fuel, aer air distribe nozzle, proandard proceutor grid. A
measured.
y, the design ortant e size
during solids ration el ash s bed of the
with useful riser,
mplish, nction. essure ustion,
in the
d heat es like ection. that is during talled. ion of
n and as well bution. ovides edure, given
South African Journal of Chemical Engineering, vol. 19, 2014, no. 3, pp 48-61 49
NUMERICAL SIMULATION IN FLUIDIZED BEDS AND DENSE PARTICLE FLOWS The CFD simulations make use of the Multiphase Particle-in-Cell (MP-PIC) method.3 The CPFD method solves the fluid and particle momentum equations in three dimensions. The fluid is described by the Navier-Stokes equation in bi-directional coupling with the discrete particles. The MP-PIC numerical scheme is a Lagrangian description of particle motion described by ordinary differential equations with back-coupling to the fluid. This Computational Particle Fluid Dynamics (CPFD) solution as applied in the commercially available software Barracuda VR® is aimed at solving industrial problems, which are generally physically large systems. In the CPFD scheme, a numerical particle is defined where particles are grouped with the same properties (species, size, density, etc.). The numerical particle is an approximation similar to the numerical finite control volume where a spatial region has a single fluid property. Using numerical particles, large commercial systems containing billions of particles can be analyzed using only millions of numerical particles. The simulation is strictly transient, thus accounting for the inherently fluctuating character of flows with high solid volume fractions.
Governing equations The volume average two-phase continuity equation for the fluid (here written without interphase mass transfer) is + ∇ ∙ = 0 (1)
with fluid velocity uf and fluid volume fraction θf. The volume average two-phase incompressible momentum equation for the fluid is + ∇ ∙ = − ∇ − + + ∇ ∙ (2)
where ρf is fluid density, p fluid pressure, τ the macroscopic fluid stress tensor, and g the gravitational acceleration. F is the rate of momentum exchange per volume between the fluid and particles phases.
The particle acceleration is = − − ∇ + − ∇ ∙ (3)
where up the particle velocity, ρp particle density and τp particle normal stress. The terms represent acceleration due to drag, pressure gradient, gravity and inter-particle normal stress gradient. Particle properties are mapped to and from the Eulerian grid. The interpolation operator is the product of interpolation operators in the three orthogonal directions.
The interphase drag coefficient is = (4)
where µf is the fluid viscosity, r is the particle radius and Cd , and the drag correlation from Wen and Yu.6
Particle-to-particle collisions are modeled by a particle normal stress expression. The particle stress is derived from the particle volume fraction which is in turn calculated from particle volume mapped to the grid. The particle normal stress model used here is
= , (8)
where Ps is a material parameter, β a model parameter in the recommended range of 2 ≤ β ≤ 51, is particle close pack volume fraction and ε is a small number of the order of 10-7 to remove
the singularity. The close-pack limit is somewhat arbitrary and depends on size, shape and
South African Journal of Chemical Engineering, vol. 19, 2014, no. 3, pp 48-61 50
ordering of the particles. Therefore the solution method allows the particle volume fraction, at times, to slightly exceed close-pack which is physically possible considering that shifting or rearranging of granular materials may occur. The particle normal stress is mapped to discrete particles. Because particles have sub-grid (no grid) behavior, the application of the normal stress gradient to a discrete particle accounts for the particle properties and whether the particle is moving with or against the stress gradient.
The gas phase turbulence is taken into account by a Large Eddy model with a Smagorinsky model based on a coarse sub-grid allowing for time steps in a millisecond order of magnitude. However, there are currently no validated turbulence models for dense particle flow. Large density and size particles act as large eddies of momentum transfer while gas flow around close pack particles produces small sub-grid eddies and dissipation.4
Modeling of coal and secondary fuel combustion The homogeneous and heterogeneous fuel reactions are represented by a reduced mechanism (see Table 1). The equilibrium reactions are split into single equations for forward and backward reactions. All kinetic reactions rates are taken from approved references.2,5,7 Simplifying the complex heat and mass transfer in partially porous particles, moisture and volatile fuel contents are assumed as gaseous inlet streams at the same positions as the solid fuel feed. The model error is considered to be small since drying and volatiles evaporation are very fast at fluidized bed conditions with relatively small fuel particles. Variation simulations with modeling of a distinct volatiles release rate from solid particles showed a low sensitivity for small fuel particles.
Table 1. Stoichiometric equations for the reduced combustion mechanism
Steam gasification C(s) + H2O ↔ CO + H2
CO2 gasification C(s) + CO2 ↔ 2CO
Combustion λC(s) + O2 → 2(λ-1)CO + (2-λ)CO2
Water gas shift CO + H2O ↔ CO2 + H2
Volatile combustion CxHyOz + αO2 → βCO2 + γH2
CO combustion 2CO + O2 → 2CO2
Circulating fluidized bed plant model A full CFB loop model including combustion chamber, cyclone, sealpot, fluidized bed cooler and solids recycle line can principally be modeled by transient MP-PIC simulation, but for large models, a combined CFD and process model may be more economic. For the given examples with focus on combustion and wear phenomena in the combustion chamber, CFD was performed for the CFB riser only. Fractional cyclone separation and heat withdrawal in the fluidized bed cooler were calculated by zero-dimensional balancing models and coupled to the boundary conditions of the combustion chamber outlet (exit to cyclones) and recycle line inlets.
SELECTED EXAMPLES FOR PROCESS OPTIMIZATION
CFB Wuppertal-Elberfeld, Germany The Elberfeld plant consists of 2×137 MWth CFB boilers (Fig. 2) manufactured by L+C Steinmüller and was commissioned in 1991. Actual data is given in Table 2. The operational mode depends on the district steam and heat demand for industrial and communal use and the market price for electricity. Due to the German power market regulations for renewable energies, the plant undergoes daily load alternations between 60–100% load with an actual ratio of partial to full load of 3:1. The specific requirement is a high plant flexibility and fast load change velocities.
South African Journal of Chemical Engineering, vol. 19, 2014, no. 3, pp 48-61 51
Mdamaboilerdeforveloc
Thheighchamdistri“S2”.operatube
Ongrid rturbufor comeasfront presswith
Firing Steam generaFuel
Thermal outpSteam param
Feed water teOperation hoAnnual opera
Main motivatage causing r roof in dirermations sugcities. he damages ht from norm
mber (“high ibution had The operati
ations of 102damages coune root causreleasing a m
ulent, it is weomplete mixisurement for
wall indicatsure drop) ina rather unif
ator
put meters
emperature ours -XII/2013ation hours
tion for a coan unplann
ect line abovggest the im
occurred afmal operatio
bed”) to Δbeen adopte
ional trials w%. As a supeuld not be eae assumptio
massive primell known thing of any m
r the Elberfelting some pan the sectionform distribu
Table 2. E
AtmospheOnce throuHard coal,input after2×137 MWHP 2×47,2LP 2×42,8 260°C
3 149,108 (B~ 4,500–7,0
Figure 2
omprehensivned shut-dowve the RDF fumpact of lar
fter a series on characteriΔp=150 mbaed from the were superimerposition ofasily identifien for the loc
mary air streahat lateral di
mal-distributild plant. Theartial blockin
of RDF inleution and a c
Elberfeld CFB
eric circulatingugh (system B, residuals derr retrofit
W 2 kg/s, 535°C,
kg/s, 535°C, 4
31), 139,824 (B000
2. Elberfeld C
ve process awn, revealingfuel inlet locarge particles
of former ized by Δp =ar (“low bed
original casmposed by df a set of opeed from operally restricte
ak into the fuispersion in ion or streakere is a regiong, but no noet. Generallycentral orient
plant data
g fluidized bedBenson) rived fuel (RD
201 bar 46 bar
B32), ~ 80% fu
FB plant
nalysis of thg a very speated in the bs being shot
operational = 175 mbar d”). In anotse “S1” to a daily load cherational conrational obseed roof wear urnace. Altholarge scale f
k. Fig. 4 showon of high nooticeable wea
y the measurtation across
d (system LUR
DF) up to 25% t
ll load
he Elberfeldecific wear p
bottom left cot against th
trials with cthroughout ther trial, thnearly equaanges with editions, the m
ervations. was a partly
ough the fluiluidized bed
ws the result ozzle pressuar (as indicaements showthe distribu
RGI)
thermal
d CFB was apattern undorner (Fig. 3
he roof with
changing ththe fluidize
the secondaralized distribeventual ovemain cause f
y worn distridization is hds is not suffof the nozzl
ure drop alonated by low nw a pressure
utor grid.
a tube er the
3). The h high
he bed d bed ry air bution erload for the
ibutor highly ficient le grid ng the nozzle e drop
South African Journal of Chemical Engineering, vol. 19, 2014, no. 3, pp 48-61 52
CFair diflue gfluctu
Ththe quppeload simila
FD simulatioistribution, bgas speed (riuations, enabhe wear evalqualitative trer right edge
(b), whereasar tendency
Fig
ons were perboiler load). ight). Singlebling big parluation (Fig.
rend of diffeas observeds a simple lbut with low
gure 3. Elberfe
Figure 4. G
rformed for Figure 5 shoparticles are
ticles to be tr6) is based
erent scenarid from the realowering of wer efficienc
eld plant: spec
Grid nozzle me
different opows instantae acceleratedransported thon time- and
ios. The normal plant. Thethe bed hei
cy can be ach
ific tube dama
easurement
peration condaneous valued well abovehroughout thd area-relatemal case (a)e wear is furtight reduceshieved by sec
ages
ditions (bed es for particle 10 m/s by he fluidized ed particle im reveals the ther increase
the wear sicondary air t
height, secole speed (left the local flubed chambe
mpacts and se wear spot ed by an enhignificantly trimming (d
ndary t) andue gas er. shows in the
hanced (c). A
d). The
South African Journal of Chemical Engineering, vol. 19, 2014, no. 3, pp 48-61 53
seconsecon
Figu
Figur
ndary air trimndary fuel in
ure 5. Instantan
re 6. Wear scen
mming is limnlet in order t
neous values o
nario simulati
mited by theto burn out th
of particle spe
ions: plot of w
e high requihe high amo
eed (left, max.value 25 m/s
wall/roof wear
irement of oount of volati
value 10 m/s)
r intensity and
oxygen aboviles released
s) and flue gas
d normalized v
ve the asymmby RDF.
s speed (right,
values for roo
metric
max.
f wear
South African Journal of Chemical Engineering, vol. 19, 2014, no. 3, pp 48-61 54
Asmaximobser
GDFThe Pcomm
FS
FT
S
Figu
Ththe fudifferto gedistrivirtuaemiss
Fichamin a m
s a result omum load erved.
F Suez CFBPołaniec pla
missioned 20
Firing Steam generat
Fuel Thermal outp
Steam parame
ure 7. Polaniec
he CFB has 3urnace via 8 rent moisturet insights inibution to pral plant for psion or mainigure 8 displ
mber. The quamid-region a
of the studyvents was re
BC Połaniecant is a 489012. Actual da
tor
ut
eters
c CFB plant (©
3 parallel cycports. A sere, wood pelln general asredict emissiprediction of
ntenance issulays flue gasality of lateraccording to h
y, the bed ieduced. In th
c (Poland)9 MWth CFBata is given i
Table 4. P
AtmosphericOnce-throug
100% bioma489 MW
535/535°C, 1
© Foster Wheelcyclon
clones on theies of operatlets), secondspects as diion and erosf actual and fes and for evs temperatural distributioheight indica
inventory whe meantime
B boiler main Table 3.
Polaniec CFB
c circulating fgh Foster Whe
ass: Wood chip
128/20 bar
ler); 1 wind bone, 5 heat exch
e right hand tional modes
dary air distristribution osion charactefuture fuels’valuation of rre distributioon is significating a suffic
was slightly e, no more sp
anufactured
plant data
fluidized bed eeler AFBC tec
ps, wood pelle
ox, 2 INTREX hanger
side of the fus under variaribution and of velocities, eristics. The influence onrespective opon on the ceantly good, m
cient burn-ou
reduced andpecific roof d
by Foster W
chnology
ets and palm k
cooler, 3 comb
urnace (Fig. ation of fuel load were stemperaturoperator us
n plant perfoperational menter plane omaximum te
ut of volatiles
nd the numbdamages cou
Wheeler and
kernel shells
bustion chamb
7). The fuel (wood chips
simulated in re, solids anses the modeormance, pot
modes. of the combuemperatures s.
ber of uld be
d was
ber, 4
enters s with order
nd gas el as a tential
ustion occur
South African Journal of Chemical Engineering, vol. 19, 2014, no. 3, pp 48-61 55
Fig
Figu
Fitempfrom meanpushiseconfurna
Asflow
Lonot presideoperafluctu
gure 8. Time a
ure 9. Time ave
iring of wooperatures (~3
symmetrican furnace teming the low
ndary air porace. ssuming lowrates resultinow primary properly mixence times sation is noncuations are o
averaged flue gwood pelle
eraged flue gapellets
od chips with0°) when the
al (A) to non-mperature inwer bed and
rtion on that
wer velocitiesng from evapair flow whexed above tso that burncritical in ter
observed from
gas temperatuets with non-s
as velocity distwith non-sym
h high moiste fuel mass fl-symmetricalcreases. Mai
d the suspent side suppor
s due to lowporation of wen operatingthe distributn-out is securms of velocm the simula
ure distributiosymmetrical se
tribution (m/smmetrical seco
ture contentlow is kept cl conditions
in reason is tnded fuel prts volatile a
wer temperatuwood chips mg in partial mtor nozzles ured and prcities, tempeation.
on (°C): A wooecondary air d
s): A wood pendary air dist
t (B) results constant. Wh(C, 75% seco
the high momarticles to t
and coke bur
ures (B) is mmoisture (seemode leads t(see Fig. 10
redicted emieratures, emi
od pellets, B wdistribution
ellets, B wet wribution
in significanhen the seconondary air frmentum fromthe back sidrn-out in the
misleading due Fig. 9). to low fluidiz0). Low veloissions are lissions and e
wet wood chip
wood chips, C w
ntly lower fundary air is srom rear sidem the recyclede. Increasine lower part
ue to high vo
zation. The focities allowlow. Partial erosion, no e
s, C
wood
urnace shifted e), the ed ash ng the of the
olume
fuel is w long
mode excess
South African Journal of Chemical Engineering, vol. 19, 2014, no. 3, pp 48-61 56
BerliThe Bwas c
FSFTR
T
Casystemshoul
in-Moabit, Berlin-Moabicommissione
Firing Steam generatFuel Thermal outpuRatio partial/f
Typical operat
alculations om for co-firld be predic
Figure
Germany it plant is a 2ed in 1990. A
tor
ut full load
tional mode
F
of the Moabing of biom
cted for full
10. Operation
242 MWth CFActual data is
Table 5.
AtmospheOnce throHard coal242 MW 2/1 Operation60–100%
Figure 11. Mo
it CFBC accmass up to 40
and partial
n in partial loa
FB boiler mas given in Tab
Moabit CFB p
eric circulatingough (system Bl, biomass up t
n-control by di
abit CFB plan
companied a0% of the toload, differe
d (50%): wood
nufactured bble 5 and pla
plant data
g fluidized beBenson) to 40% therma
istrict heat dem
nt (© Vattenfal
a revamp wiotal enthalpyent fuels an
d pellets
by Lurgi-Lenant overview
d (system LUR
al input after r
mand
l)
ith an additiy input. Boid feeding po
ntjes-Babcockw in Figure 11
RGI)
retrofit
ional fuel feiler characteositions. Dif
k and 1.
eeding eristics fferent
South African Journal of Chemical Engineering, vol. 19, 2014, no. 3, pp 48-61 57
biomrecirc
Fusignifdisplbiom
Althe cythe fu
mass feeding culated ash c
uel parametficantly diffeayed colored
mass particles
lthough volayclones is beurnace result
locations wechute, mixing
ters differ verent dryingd by volatile about 10 sec
Figur
atilization ofeneath 5%. Tting in high r
ere assessed g scenarios).
Figure 12. F
very clearly g and volatilis content. Coconds or clea
re 13. Fuel par
f biomass is The very largrates of coke
(100% mixin
Fuel Composit
in composization behaoal particles arly over 30 s
rticles colored
considerablyge biomass p
combustion
ng with fresh
tion and Size
sition and savior. In Figuvolatilizatio
seconds depe
by volatiles co
y slower, thearticles lead
n (Fig. 14).
h coal, 100%
size (see Figure 13, only n occurs witending on fe
ontent
e amount of to long resid
% injection in
g.12) resultiy fuel particlthin 5 second
eeding point.
f unburned fdence time w
nto the
ing in es are ds, for
fuel in within
South African Journal of Chemical Engineering, vol. 19, 2014, no. 3, pp 48-61 58
Thunfavdistriheatinbest v
Drcombuppeover-
he analysis vorable one-ibution issueng value, revalues were f
rying the mobustion to theer furnace ne- temperature
Figu
of the as-is -sided oxygee is to adjustsulting a mofound when
oist biomasse upper furnearby the traes in the cycl
ure 14. Fuel p
situation wen distributiot biomass feeore even oxyfeeding 30%
Figu
s leads to lownace area. As ansition to thlones known
articles colore
with 100% coon. An obvioeding on theygen distribu
% biomass at
ure 15. Oxygen
w temperatu shown in Fihe cyclones. n from curren
ed by coke con
oal firing fedous and conve both sides ution. Consifeeding poin
n distribution
ures in the loigure 16, highHowever, t
nt operation
ntent
d on one sidvenient wayto meet air dering operants II as show
n
ower furnacehest temperahe values arcombusting
de had showy to overcom
requirementational limit
wn in Figure
e shifting voatures occur re still well b100% coal.
wn an me this
ts and ations 15.
olatiles in the below
South African Journal of Chemical Engineering, vol. 19, 2014, no. 3, pp 48-61 59
A otherpeaks
Biemissconce
major concer hand, the is and therefoiomass co-firsions and entration do
ern of biomasimproved fuore lower eroring proves terosion. Slnot lead to u
Figure 16. F
ss co-firing isuel distributiosion at the fto be beneficiightly high
unfavorable b
Fi
Flue gas tempe
s higher erosion allows ffurnace roof ial in aspects
her temperabehavior.
igure 17. Erosi
eratures (°C)
sion due to hfor better flo(Fig. 17). s of combustature gradie
ion
higher flue gaow uniformit
tion rates, oxents due to
as volume. Oity, lower ve
xygen distribo local vo
On the elocity
bution, olatiles
South African Journal of Chemical Engineering, vol. 19, 2014, no. 3, pp 48-61 60
CONCLUSION The examples demonstrate the added value of a joint process optimization approach for an efficient analysis of the complex coupling flow and transport mechanisms in CFB’s. The increased insight and understanding is a major support for finding proper design and operation conditions for the application of flexible fuel compositions. Although CFB simulation is now an established and central tool for understanding the complex interactions of gas/solids kinematics, heat transfer and combustion reactions, plant audit and verification of the actual plant state are crucial procedures for process evaluation and optimization. Analysis of distribution grid nozzle wear as the primary indicator for fluidization quality and instantaneous and averaged values from the process control system are required for plant balancing, definition of any model boundary conditions and interpretation of both measured values and simulation result.
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S., Ciocco, M. V., Morreale, B. D., Chattopadhyay, S. and Shi, S. 2004. AIChE J., 50:1028–41.3. O’Rourke, P.J., Zhao, P., Snider, D.M. 2009. Chemical Engineering Science, 64.4. Snider, D. M. 2001. Journal of Computational Physics, 170:523-49.5. Syamlal, M., Bissett, L.A. 1992. DOE/METC--92/4108, DE92 001111.6. Wen, C.Y. Yu, Y.H. 1996. Chem. Eng. Progr. Symp., Ser., 62:100-1107. Yoon, H., Wei, J. & Denn, M.M. 1978. AIChE J., 24:5
South African Journal of Chemical Engineering, vol. 19, 2014, no. 3, pp 48-61 61