Simplified modeling of circulating flow of solids between a fluidized bed and a vertical pneumatic transport tube reactor connected by orifices

1
Simplified modeling of circulating flow of solids
between a fluidized bed and a vertical pneumatic
transport tube reactor connected by orifices
1Karel Svoboda, 2David Baxter, 3Francesco Miccio,
2Sylwester Kalisz, 1Michael Pohorelý
1 Institute of Chem. Process Fundam., Academy of
Sciences of Czech Republic, Rozvojová 135 ,
165 02 Praha 6 Suchdol 2 , Czech Republic
Tel. [phone] E-mail
svoboda_at_icpf.cas.cz 2 Institute for Energy,
Joint Research Centre of EC, 1755 ZG Petten ,
The Netherlands E-mail david.baxter_at_jrc.nl 3
Istituto di Ricerche sulla Combustione, Consiglio
Nazionale delle Ricerche, Napoli, Italy,
E-mail miccio_at_irc.cnr.it
2
CAS Campus Prague 6

• Our team was
• First group (name)
• Second group (name)
• Third group (name)

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Concept of interconnected fluidized bed
technology Two different reacting gases
Application in gasification or gas cleaning with
regeneration of a sorbent
(Syngas without N2)
Gasification
Combustion of char
Biomass
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Model for circulating flow of fluidized particles
through an opening to PT-column and return to
the FB
Mass flux GFB of solids from a FB to a
PT-column GFB CD(?u)2.35 (Sorif/SFB)
2 ?s(1- ?mf ) ?Porif
0.5
Flue gas
Impactor for circulation of solids (sand)
Syngas
Steady state conditions Mass flow of solids ms
(kg/s) is constant GFBSFB Gorif Sorif GPT
SPT ms
PT-column
Auxiliary gas for L-valve
Orifices
Fluidized bed of sand, height LFB
Pressure drop at the orifice ?Porif
?PFB - ?PPT ?PFB LFB(1- ?mf)?sg ? mFBg/
SFB
Gas distributor
Steam (gas) for gasification
Air for combustion of char
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General model for circulating flow of solidswith
expression for pressure drop in PT-column
?Porif
(GFB)2 0.5 (?u)4.7 (Sorif/SFB)2 ?s (1-
?mf ) LFB(1 - ?mf)?s g - ?PPT
For ?PPT the general equation contains terms for
static and dynamic (due to particle acceleration)
pressure drop, gas-wall and particle-wall
friction losses ?PPT LPT (1- ?)?s
g 0.5 (1 - ?)?s (UP)2 LPT Ffw
LPTFpw Gas-wall friction factor can be
neglected and particle-wall friction force can be
expressed for lower concentrations of particles
(approx. below 6 vol. ) as
Fpw 0.057 GPT(g/D)0.5
Particle velocity UP in PT-column is needed for
computation of circulating flux of solids GPT or
GFB 3 simplified models for estimation of UP
considered
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UP is computed by means of particle terminal
velocitySlip velocity (gas velocity - particle
velocity) UT
UP1 Uf /? - UT Uf / 1 GPT/(?s UP1)
UT ( for ? gt 0.95 ) where ? was expressed
from equation for flux of solids GPT (1 - ?)
?s UP1
After rearrangement (UP1)2 UP1(Uf UT
GPT/?s ) GPT UT/?s 0 and UP1
0.5 ( Uf UT GPT/?s ) (( Uf UT
GPT/?s )2 4 GPTUT/?s )0.5
Pressure drop (?PPT)1 as a function of GPT and
UP1(GPT, UT) (?PPT)1 LPT(GPT/UP1) g
0.5 GPT UP1 LPT 0.057 GPT (g/D)0.5
And final non-linear equation for mass flux in
PT- column ( GPT ) GPTSPT2/(SFB)2 0.5
(?u)4.7 (Sorif/SFB)2 ?s (1- ?mf ) LFB(1- ?mf)
?s g (?PPT)1
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UP is computed by means of a slip factor ? and
empirical correlation for ?
? gas velocity/particle velocity (Uf
/?)/UP2 (for ? ? 0.9)
? is expressed from equation for flux of solids
GPT (1 - ?) ?s UP1 UP2 GPT/?s Uf / ?
Where slip factor ? is correlated with UT , Uf
and riser diameter D ? 1 5.6 (g
D)0.5/Uf 0.47 UT /(gD)0.50.41
Pressure drop (?PPT)1 as a function of GPT and
UP2(GPT, UT) (?PPT)2 LPT(GPT/UP2) g
0.5 GPT UP2 LPT 0.057 GPT (g/D)0.5
Final equation for GPT GPTSPT2/(SFB)2 0.5
(?u)4.7 (Sorif/SFB)2 ?s (1- ?mf ) LFB(1- ?mf)
?s g (?PPT)2
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UP is computed by means of a correlation for
relative slip velocity Uslip/UT
Relative slip velocity Uslip/UT ( for dP ?
0.7 and D ? 0.1 m )
Uslip/UT A1 (1 - ? )B1 where
A1 93.67/(ReP)0.994 (dp/D)1.014(?s /?f
)0.706 B1 1.075/(ReP)0.445
(dP/D)0.476 (?s /?f )0.313
Non-linear (implicit) equation for UP3 (GPT,
UT) UP3 Uf /1 GPT/(?s UP3) -
A1GPT/(?s UP3)B1 UT Non-linear equation
for GPT GPTSPT2/(SFB)2 0.5 (?u)4.7
(Sorif/SFB)2 ?s (1- ?mf ) LFB(1- ?mf) ?s g
(?PPT)3 Necessity to solve the set of two
non-linear equations for UP3 and GPT
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Model assumptions and comparison with reality in
particle concentration profiles in a CFB
The models with UP1, UP2, UP3 assume a constant
value of GPT along the height of the PT-column
and immediate acceleration of solid particles
from zero to the final velocity it means (1- e)
is constant along the height
In reality only for sufficiently low GPT and high
GPT the axial particle concentration profiles are
flat
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Validation of the models for dilute solids flow
conditions in PT-column, experimental arrangement
3 7
Free segment for particle flow
Impactor
Particle feed ring
Particle feed ring with suction effect of gas
Collecting cylinder for solids mass flow
measurement
PT-column ID 4.4 cm H 200 cm
PT-column
Orifice ? 10 mm
Fluidized bed of sand, height LFB
4 Orifices
Gas distributor for the FB
Air for fluidization in annulus
Gas distributor
Air for vertical transport
Air for vertical transport
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Validation of the models comparison of model
GPT with experimental data (quartz sand dP 0.2
- 0.4 mm), dependence on gas velocity Uf
Data for models ?mf 0.53 ?u ? (computed
from GPT) no gas leakage Discharge coefficient
CD 0.25 dP(aver.) 0.3 mm HFB 11 cm
Differences between experiments and models About
50 of sand particles with diameter dP below 0.3
mm and about 50 of particles with dP gt 0.3 mm
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Validation of the models comparison of model GPT
with experimental data (quartz sand dP 0.2 -
0.4 mm), dependence on FB height HFB
Data for models ?mf 0.53 ?u ?
(computed from GPT) Discharge coefficient CD
0.25 dP(aver.) 0.3 mm Uf 2.74m/s
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Validation of the models for dense suspension
flow comparison of model GFB with experimental
data of Ahn (quartz sand dP 0.3 mm), dependence
on Uf at FB height HFB 0.86 m
Experimental data PT(draft) tube ID 0.1 m,
length 0.9 m , 4 orifices ? 3 cm Model assump.
CD 0.5 dP(aver.) 0.3 mm emf 0.5
GFB SFB GPT SPT
GPT 7.88GFB
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Validation of the models for dense suspension
flow comparison of model GFB with experimental
data of Kim (sand dP 0.29 mm), Ua/Umf 1, HFB
0.86 m, dependence on Uf effect of CD
Experimental data PT(draft) tube ID 0.1 m,
length 0.9 m , 4 orifices ? 3 cm Model assump.
dP(aver.) 0.29 mm emf 0.5 GFB SFB
GPT SPT
Due to gas leakage from the annulus, the annular
bed is only partly fluidized
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Model predictions of various effect on
circulating flux of solids GPT for chosen
standard conditions
Table Standard conditions used for computations
of circulation mass flux in riser
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Model predictions of dependence of mass flux of
solids GPT on particle size for chosen standard
conditions
Uf 2.5 m/s HFB 0.5 m Length of PT-column
2.5 m t 20 oC
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Model predictions of temperature effect on
circulating flux of solids GPT for chosen
standard conditions
Uf 2.5 m/s HFB 0.5 m Length of PT-column
2.5 m t 20 and 800 oC
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Estimation of effects of pressure drop in
cycloneimpactor and effect of gas bypassing
(leakage from annulus to PT-column) on GPT for
chosen standard conditions, Uf 2.5 m/s , model
with Uslip UT
?Pcycl 33.33 (Uf)2 ?Pimpactor 10 (Uf)2
(1 0.1 GPT) (Vf)bypass ? 0.07 (Vf)FB
HFB/ 0.25 Sorif/SFB/0.01
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Regime constraints for stable pneumatic
transport choking and saturation carrying
capacity of gas
Comparison of model forecasts (with Uslip UT )
of mass flux GPT for standard conditions and for
reduced (lower) parameters ( HFB 0.25 m and
Sorif/SFB 0.01), dP 0.2 mm
Conditions for choking
Stable, smooth transport
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Conclusions
Effect of smaller particles on circulating flux
of bigger particles have not been taken into
consideration in modeling. Normally bigger
particles are pushed by smaller particles. The
models are able to predict qualitatively effects
of operating conditions and geometrical factors
on circulating flux The absolute values of model
forecasts of particle mass fluxes GPT are unsure,
because of uncertainty in several parameters (
emf , eu , exponent at eu, discharge coefficient
CD , particlewall friction factor). The models
have been validated for GPT ? 40 kg/m2/s) and for
GPT gt 190 kg/m2/s. Unfortunately for the region
of GPT between those values we have not found for
such arrangement experimental data for validation
of the models. For GPT ? 40 kg/m2/s values and
Uf gt UT the model assuming Uslip UT is able
to fit reasonably well experimental data. For GPT
gt 200 kg/m2/s, broader particle size
distribution and broader range of Uf the model
with empirical slip factor ? proved to be the
most suitable. GPT values (for a given dP)
increase with increasing Uf, HFB and Sorif .
Limiting factor is choking in riser (
PT-column).
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Thank you for your attention !