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Radial gas mixing in a fast fluidized bed
POWDER TECHNOLOGY ELSEV|ER
Powder Technology 94 ( 1997 ) !(~3-171
Radial gas mixing in a fast fluidized bed P. Gayfin, L~F. de Diego, J. Adfinez * ln.s'titulo ~h" Carbnquhni~'a (CSICh PO Bor 589. 5(1015 Suragos.~'a. 3"ptdn Received I I October 1995: revised 30 May 1997
Abstract A steady-state dispersion model was used to determine the radial gas mixing coefficients I), in the dilute region of a cold fast l|uidized bed. 0. I m i.d. and 4 m high. CO2 used as tracer was injected into the centre of the bed from a point source. Radial concentration profiles of tracer gas were measured in two planes downstream of the injection point for a broad range of air velocities and solid fluxes, using two sizes of sand panicles of 710 and 380 p,m. A systematic experiment was carried out to find out the main variables acting on the radial gas mixing in the dilute region of a last tluidized bed. An analytical solution derived by Towle and Sherwood for the description of radial gas mixing in turbulent single-phase flow was applied to determine the radial dispersion coefficients, which were found to be dependent on the superficial gas velocity and solid circulating flux. The D~ values were well correlated with an apparent suspension Reynolds number ( Re ) by an equation of the type D~ = a R e ~'. The proposed equation allows the radial gas coefficient to be predicted as a function of the air velocity and external solid flux present in the riser. This equation, with it.,;corresponding parameters, is applied to the results of other authors and an acceptable fit was found. The high Pe numbers (5(10--2000) obtained in the dilute region of the fast fluidized bed indicate that the flow of the gas in the dilute region approximates to plug flow. ~) 1997 Elsevier Science S.A. Kevwords: Fluidized beds: Circulating beds; Gas lit}w: Mixing
1. Introduction The effectiveness of a circulating Iluidized bed (CFB} combustor depends on its ability to mix adequately the incoming flows of reactants: fuel, sorbent and air. Emissions and combustion efficiency are strongly related to the mixing process. Incomplete mixing of secondary air into a bulk gas stream might, for example, result in an increase of hydrocarbon emissions from substoichiometric zones as well as to NO, emissions from overstoichiometric areas. In an empty column, the gas is in plug flow owing to the high air velocities used, but the solids can modify this type of flow, which will be characterized by the values of the gas dispersion coefficients with respect to ideal flow. To characterize the gas mixing it is necessary to know three coefficients: the axial dispersion coefficienk ~he radial dispersion coefficient and the baci~ iiiiniii~, coeflicient. The number of investigations related to gas mixing in CFB~ is fairly small compared with others dealing with hydrodynamic solid properties. Moreover, there is no certainty about the behaviour pf the gas in this type of reactor owing to the great variety of results and methods used. Table I, from Patience and Chaouki I I I, summarizes the conditions of the * Corresponding author. Tel.: + 34 976 73 3977; fax: + 34 976 73 3318. 11{)32-5911)/97/$17.11t) c~ 1997 Elsevier Science S.A. All rights reserved PII S 0 0 3 2 - 5 9 10 ( 9 7 11)3322-6
investigations carried out by different authors, the L.,eometry of the reactor used :md the experimental and theoretical methods employed. Most of the data available on gas mixing have been obtained with particles of group A of the Geldart classilication at low gas velocities. Characterization of the gas mixing in fluidized beds can be done in steady or non steady-state conditions as shown in Table i. In the latter, the gas concentrations have to be measured within a few seconds, because the mean residence time.,, of the gas in last fluidized beds are ! or 2 s. This lhct can cause important er ~rs when using some systems of measurement. in additio~!, the results obtained can be analysed by two different models, such as the two-phase model and the dispersion model. In fast fluidized bed:, the dispersion model is the most widely used 12-7] although the two-phase model is also used I 1,8-111. applied to the ga~ exeh~mge between the core and the annulus of the dilute region of a fast fluidized bed. From their back-mixing measurements in a column of 0. i 5 m i.d. with FCC solids, Cankurt and Yerushalmi I 121 have Iound that back-mixing of gas diminishes when the gas velocity increases and pointed out that, in a CFB, back-mixing is negligible compared with the convective fow. The same conclusion was obtained by other authors 12,13 I. On the other
164
P. Gav6n ,'t al. / Powth,r Techm,iogy 94 ¢ 19'171 163-171
Table I Tracer techniques used in studies of gas flow hydrodynamics I I I Study
van Zoonen I 181 ~,'an Zoonen 1181 Cankurt and Yerushahni I 121 Yang et al. I 151 Dry 191 Adams 141 Bader et al. 121 Brereton et al. 181 White and Dry 1251 Dry and White 1261 Li and Weinstein I 141 Weinstein et al. 1271 Jiang et al. [ 28 ] Kagawa et al. I I01 Li and Wu 131 ~,'erther et al. 121 I Baiet al. 1291 White et al. 1301 White et al. 1301 Martin et al. 151 Martin et al. 151 Zethraeus et al. 171 Amos et al. 1161 P~itiencc and Chaouki I I I Win el al. 1171
Particle properties Tracer
Injection
dp( I.tm )
p. I k g / m ~)
Solids
D, I m )
Model
H2 H_, CH.~ He hot air CH~ He He Ar Ar He He ozone ozone H_, CO., organic Ar Ar Kr Hc CH.~ SF,, Ar-40 CO,
continuous pulse continuous continuous pulse continuous continuous step pulse pulse continuous continuous continuous continuous continuous/pulse continuous pulse pulse pulse pulse continuous continuous continuous pulse continuous
56 56 55 220 71 250 76 148 71 7i 59 59 65 46 58 130 I tXl 71 140 62 62 2110 71 277 100
II00 I I00 I I00 710 1370 2600 17 I0 2650 1370 1370 1450 14511 15110 2300 1575 261111 710 1370 16511 1560 15611 2800 2450 2630 25011
FCC FCC FCC silica FCC sand FCC sand FCC FCC FCC FCC FCC FCC FCC sand silica FCC sand FCC FCC sand FCC sand glass
0.05 0.115 O. 152 O. I 15 0.09 0.3 x 0.4 0.3115 O. 152 0.09 11.119 0.152 0.152 O. 1 1 1 2 O. I 0.09 11.4 O. 14 0.119 0.09 0.93 0.19 11.3 × 0.4 0.305 0.083 0.05
radial dispersion axial dispersion plug flow radial dispersion contact efficiency radial dispersion radial dispersion core-annulus core-'mnulus axial dispersion core-annulus disp. back-mixing at core back-mixing at wall core-annulus axial dispersion core-annulus disp. axial dispersion core-annulus core-annulus axial disper.;ion radial dispersion core-annulus core-annulus disp. core-annulus radial dispersion
h,'md, measurements of gas residence time distributions by Brereton et al. 181 have shown that the CFB as a whole exhibits a considerable amount o1' back-mixing in the gas phase. However t,i and Weinstein I 141 pointed out that this contradiction is due to the existence of different flow pattern regions inside the CFB, such as perfect mixing in the dense region or plug flow in the dilute region. Recently, Li and Wu 131 have shown that the extent of axial gas dispersion depends on average voidage, which is influenced by the gas velocity and the solid circulation flux. Concerning lateral mixing in the dilute region Yang et al. 1151 found that the radial gas dispersion coefficient decreased when the gas velocity increased and the solids flow rate decreased. On the contrary, Adams 141 indicated an increase in the horizontal dispersion when the gas velocity increased and solids flow rate decreased. From the work of Bader et al. 121 no relationship between the radial mixing and solids flow rate or gas velocity was obtained because both were changed simultaneously. Martin et al. 151 determined the radial dispersion coefficients which showed'a sligh! increase when the solids flow rate increased, whereas the influence of gas velocity was not studied. On the other hand, Werther et al. 161 suggested a constant value of the radial Peclet number for all situations. Recently, Amos et al. ! 161 applied a plug flow model with dispersion in a bed of 30.5 cm i.d. under a wide range of operating conditions, They tbund an increase in the radial coefficient when the solid, flow rate decreased and a slight
effect of the gas velocity, working with the same value of solids volume fraction. Also, Win et al. 117] carried ou.', a study of the radi,'d dispersion only in the bottom part of a CFB. They found a large increase in Dr after a dense bed was formed in the bottom part of the unit, that is, when the solids circulation flux was very high. These scattered and contradictory results might be due not only to the difficulties of the experimental measurements, but also to the different experimental units and operating conditions used. In summary, with respect to the above results lbr back-mixing measurements and axial dispersion studies 12,5,12,13,15,18,191, it can be considered that in fast fluidized beds these coefficients are negligible by comparison with the convective gas flow. However, the experimental values of the radial gas dispersion coefficients range from 0.0002 to 0.50 m2/s. Thus, it is clear that from these available data the relative importance of the radial dispersion in CFBs cannot be determined. Therelore the aim of this work was to determine the radial gas mixing in a fast fluidized bed and its variation with the operating conditions. Systematic experimental work was carried out to measure the value of Dr and to develop an equation to predict it as a function of the operating conditions. 2. Experimental
The experimental apparatus used in this work is shown in Fig. ! and was previously described by the authors ! 201. The
P. Gav6n et al. /Powder Techm, logy 94 ¢Iq97j 16.t-171
Cyclones
PIO Pressure taps m
Diverting solid reservoir
Feed hopper
Fast bed ~'Auxthary
bed
Fluidization air Rotameters Fig. I. Installation set-up.
CFB system consists of a 3.9 m tall riser which is 0. I m in diameter. Sand with two different mean diameters of 710 I.tm ( 630-800 ~rn) and 380 lxm ( 300-500 I.tm ) and a density of 2600 kg/m ~ were used in all experiments. The gas velocity was varied between 5 and 8 m / s and the solids circulation llux from 0 to 115 kg/m-" s. CO_, was used as gas tracer. To determine the dispersion coefficient in the dilute region. the tracer gas was injected at a constant rate in the centre of
165
the column at 2.5 m above the distributor plate. The gas injector consisted of a pipe o1"6 mm i.d. in which the gas flow rate was controlled with a valve and a rotameter. The tracer gas velocity was fixed equal to the mean gas ~e!ocity in the column, because its value did not affect the measured values at velocities higher than the fluidization velocity. Before starting a gas mixing experiment, the solids circulation flux was determined at each air velocity by the method shown elsewhere 1201. Also. axial mean solids fraction proliles were calcuh.,ted from the pressure drop measurements. For the ranee of o?erating conditions used in this work. the axial voidage profile was S-shaped and the point of tracer injection always remained in the upper dilute zone of the riser. As the concentration profile changes with height, the sampling was performed along the riser diameter at two different distances from the injection point, located at 3 and 3.5 m from the bottom of the column. The sampling probes of 4 mm i.d. had a wire mesh to prevent solids penetrating into the gas measurement system. A Siemens Llltramat 22P non-dispersive infrared gas analyser was used to detect ti~e tracer gas concentration. The sampling rate was set to 2 I/rain. due to detector limitations. This corre:,ponds to a velocity in the probe of 2.3 m/s: however, preliminary experiments gave no indication of any effect of this low velocity. All measured concentration profiles were checked by integration of the tracer concentration. The injection point was traversed across the diameter in order to conlin'n the existence of an interface between the core and the an|talus, as was indicated by Werther et al. 121 I. Due to the characteristics of the fast bed. there are two different regions in the column: the dense region, with a high .~olids concentration, and the dilute region, with a core-annulus structure. For this reason, besides determination of the radial gas dispersion coefficients in the dilute region, some tracer injections were made into the dense region in order to verily the gas mixing characteristics of this region (backmixing and radial mixing). To determine the significance of the radial gas dispersion and the gas back-mixing in the dense region, other experiments were performed. Tracer was injected into the centre of the riser at 0.5 m fi'om the bottom t the height of the dense region was I m) and the radial gas concentration profiles were measured downstream at I m from the bottom and at 3 and 10 cm upstream of the injection point. The profiles measured at ! m were flat under all the different c~mditions. ,~o the radial dispersion in this dense region is very large due to the vig¢~rous motion of the solids. This solids movement can cause some gas back-mixing in the dense region. However. the experiments performed to measure it I concentration profiles upstream of the injection point ) did not reveal any appreciable gas tracer concentration at any radial position, working in the same range of velocities and solids circulation fluxes as in dilute region experiments.
P. Gaydn et ,!. / Powder Tc+'hm,h,gy 04 ~1997~ 163-171
! 66
olnj.
3.Scm
i
12
•lnj.
m Inj.
2,5 c m z = 3 . 5 m I
I0
•
2.5 cm
mluj. 5cm z=3 m o i n j . 4era z = 3 . 5 m "Intl. 4cm z=3m
ln.i.
z=3m z=3
m
/
8 ""
8
m
6
•
o
""
5era z = 3 . 5 m
0,
[]
4
?0
=
II!
•
,
+
e
?
,
0
•
m
m
,•
n
,
o
u,
~, $91-In'i-~m.-.•o1~-,~l;. IP.. a,~,~zlmt4¢In, l P m ~ - . , : t .
,
,
, ....D , ~ , t ~ W D , , -
.,.
"I~ ~
o
.
,
n
.".qu*0.~
r (era)
$
4)
.
9~..ot~.:~cwl'tOgm.~mlD.
r
~S¢',dr~m:"
,. p.,P~q~ll, ~.-41*~ P,~.,
(era)
Fig. 2. T r a c e r gas concentration proliles with the injection point decentred and different heights ( u = 5.9 un/s. G. = 57 k g / m : s and d,, = 7 I0 p.m ).
These results confirmed those obtained by other authors 12,12.131, and it can be said that back-mixing in the dense region can be considered to be negligible.
,z-3 m ] a z=3.5 mJ "--'
la
3 m
m
R
3. Gas dispersion in the dilute region
2
As has been pointed out. to characterize the gas th)w in the dilute region of a circulating fluidized bed, some authors I 1,5,6.151 have defined a gas exchange coefficient between core and annulus, in a similar way to that between the bubble and emulsion phase in bubbling fluidized beds. This type of model assumes that the gas concentrations in each region are equal at all radii and the wall causes ,', resistance to the gas diffusion. Werther et al. I III further proposed a gas exchange coefficient between core and annulus and a radial dispersion coefficient in the core. in order to check the validity of that ,'tssumption, tracer gas was injected at 2.5 m from the bottom at ntdii of 2.5, 3.5, 4 and 5 cm. The concentration protiles were measured at 0.5 and I m from the injection point. Fig. 2 shows the tracer gas concentration profiles when the injection probe was located at different radii trom the centre axis ( 2.5, 3.5, 4 and 5 cm ), i.e. situated both in the core and in the annulus. This figure also shows the extent of the annulus zone, calculated from measurements of internal solids circulation fluxes 122 I. As can be seen in the figure, the existence of a discontinuity between the core and the annulus can be neglected. So, a gas exchange coefficient between the core and the annulus does not seem justified. Besides, it can be inferred l'rom the analyses of these profiles that the gas flow in the whole dilute region can be characterized using only one radial gas coefficient ( dependent on the operating conditions). The remainder of the paper concerns the value of the radial gas coefticient in the dilute region and its dependence on the operating conditions. The influence of three diffe,'ent variables (fluidizing air velocity, solids circulation flux and particle size) was analysed. Fig. 3 shows the effect of the sampling height on the tracer concentration profiles, working at 6 m/s and 51) kg/m-' s of solids circulation flux with a particle diameter of 710 I,tm. The sampling probes were located at 0.5 and I m from the injection point. As can be seen, the profiles become flatter
1
a
[]
m
m
0
m
m -5
-4
-3
[] -2
-I
0
I
2
3
4
5
r (cm) l:ig. 3. Tracer ga.,, concentration proliles m e a s u r e d al Iwo different heights ( tl = 5.9 in/s and G, = 50 k g / m - ' s ).
6
l
5.9 mls I
•
5
m 8mls
4 o
nl•nl
3 ")
.
m
m
l .
t , •
• •i ,
0 -5
-4
-3
,&
-2
i!•41 , •
!
•
-1
I
t
0 r
I
1
,
,d~
2
,
•
3
I
|
n
4
(cm)
Fig. 4. T r a c e r gas concenlralion prolile~, m e a s u r e d wilh two gas velocities ( (i, = 50 k g / m - ' s and : = 3.5 m ).
when the distance from lhe injection pc~i,l !o the sarnplirtg point increases, due to the radial diffusion of the tracer from the centre to the walls of the column. Tile effect of the gas velocity on the gas concentration profiles is shown in Fig. 4. It can be seen that the dispersion of tracer gas increases when the air velocity decreases because the gas flow behaves more like plug flow as the air velocity is increased. Fig. 5 shows the concentration profiles obtained when using three different solids circulation fluxes (0. 23 and 59 kg/m z s) at the same air velocity (6.5 m/s) and with a particle size of 710 p.m. The profiles become smoother as the solids circulation fluxes increase. A change in the solids flux
167
P. Gavdnet al. I Pnwth, r Techmdogy 94 ¢199 71 163-171
10
• 59 kglm~ s 023 kg/m~- s B 0 kg/m" s
0 0
Sampling point
Tracer gas injection point
4
o
o
t
BKI BBKI BKi
2
-5
-4
-3
-2
-1
0
1
2
3
4
Gas flow Fig. 7. Delinifionof.~and - parametcrs.
5
r (ctn) Fig. 5. Tracer gas concentration
profiles
measured with threc solidsp
ac a-'c I a(ac) u i ~ z = D" , ~ + D , - - -,.a,- r 7,.j
(I)
-
circulation Iluxes I t, = 6.5 m/s ard z = 3 m 1.
6
m 380 lure [ * 7101am I
5
@ B
m
4
e,D¢
3 m
[]
1 @E I 0
,
I
'
-5
-4
,.,,,I~ u, --
-3
-2
,
m@ I
-I
,
I
~
0
I
l
,
,.h_ --
2
I
3
•
I
4
,
5
r (cm) Fig. 6. Tracer gas COlleerdralitnl prolilcs measured with lwo particle sizes
lit
= 5.5 II1/s. (;. =
where z denotes the distance between the injection plane and the sample planes, and r is the radial distance from the axis of the column, as shown in Fig. 7. The assumption of a uniform axial velocity profile was based on the work of Martin et al. [ 5 ] which showed that in the range of operating conditions of our work ( u = 5-8 m/s and G~ = 0-115 kg/m 2 s). the n values in the equation to calculate the radial velocity profile were less than 0. i. and so the velocity profile can be assumed flat. Assuming that the axial dispersion can be neglected and without back-mixing in the dilute region, the equation is transformed: ac
I;~ [ ac)
{2)
"7. = n,-,. t";
31) kglm: s and - = .~ m }.
with the followip.g houndary conditions: and therefore in the solids concentration in the two-phase flow has ;111inlporlant inlluence on the gas dispersion. This figure also shows the concentration profile obtained when there is only air in the column, i! was found that the radial dispersion was greater without any particles in the column. This filet is in agreement with the results of Adams 141. Amos el al. 1161 concluded that at high enough mean solids volume fi'actions the solids do not displace the gas towards the core. but modify the gas flow in such way that the dispersir,n coefficients become smaller than the respective values for air alone• Finally, the effect of the solid particle size on the tracer gas profiles at 5.5 m/s and 30 kg/m-" s. working with particle diameters of 7 I0 and 380 p,m, is showr! in Fig. 6. As can he seen, a weak effect of the particle size was found.
4. A n a l y s i s of results
The results obtained in this work were analysed using a dispersi.on model. A mass balance on a differential volume element ( 2zrr dr d:) of the column in the steady-state and at constant velocity leads to the Iollowing equation:
r = R.
;),.//it=()
==0 and r=O.
c=c.
- = 0 and r ~ 0 .
c=0
W il~;on's equation for heat conduction, modilied hy Tow le and Sherwood l ..231to apply to radial diffusion when the ratio :./r is quite large, was used as an approximate solution of Eq. (2):
c q" cxp c,, 4~'sD,
(u(s--))
13 }
2D,
where the tracer concentration, c. depends on the constant Ilow rate of the tracer introduced, q,,. and the radial diffusion D,. A plot of Inisc/c,,} against { s - : . ) will give a straight line of slope - (u/2D,) and hence the r:;dial diffusion coef ficient can be found. Fig. 8 shows a typical plot of this kind. The radial dispersion coefficients obtained in this way in the dilute region of a fast fluidized bed were small, showing that they are of negligible magnitude. The radial gas diffusion coefficients calculated from the measurements of the probes located at heights of 3.0 and
P. Gaydn (,t al, / P o w d e r Teclmolo,ey +:4 ( lqq7~ 163-171
168
2~ In (s c1¢o) F 1
u=5,9 m/s ~ C,s=50 z=3 m
1-
x ~r)~I¢~t~,....= O~ - f
kg/m- s
~
(qo/4
coefficient when the solids circulation flux increases is due to the higher solids concentration present in the column, and therefore higher dispersion of the solids from the core to the annulus, which favours the gas dispersion. Once D~ values had been calculated for a variety of air velocities and solids fluxes, the mathematical expressions tested using our experimental data in order to find the most satisfactory. I~ott, n f the* tl,r~rlzt ,.~hntt! o*)t R n t t , n r o n o c ¢ , f . c l t t , l l i n r t ~ t o
0
0,0l
0,02
0,03
0,04
0,05
(s-z) (cm) Fig. 8. Plot o f In( .w/('.. ) as a function o f (s - z ) to determine D,. 10
="'710 pm]
calculate the radial dispersion coefficients in the dilute region of the fast bed. Thus, Yang et al. [ 151, working with a bed of I 1.5 cm in diameter and 8 m height, obtained values for the radial dispersion coefficients from 2 to 8 cm2/s, which were fitted as a function of the operating conditions to the following equation:
• 380 p m
D~ = 0.7 + 4.34
u
! - e
u l e - G , Ip,
•
(4 )
6
More recently, Amos et al. [ 161 proposed the Ibllowing equation to calculate the radial dispersion coefficient:
m e~""
4
•
•
m
il
Pc' = 3.23Re,~, ~2"7
(5 )
where Re,,, and Pc' are defined as 0
t 3
•
4
I
•
5
t
I
I
6
7
,
I 8
t 9
U (m/s) Fig. t). F.ffecl tDl' ga.,, velocity on the radial dispersion coel'licient for t w o panicle s! ~...s ( (;, = 30 k g l m ; ~ ).
3.5 m were practically equal. This confirms the assumption ot" a constant radi:d dispersion coeflicient with height. Having calcuhtted the radial gas dispersion coel'licients, the effect of the operating variables on the value of the coeflicient was analysed. Thus, the effect of the air velocity is shown in Fig, 9 for the two particle sizes used in this work. As was expected, the dispersion coefficient decreases when the air velocity increases. Fig. IO shows the effect of the solids circulation flux on D, t'or both particle sizes. The increase in the radial dispersion
Pc'= (u/e)(D,/2)/D~
The values of the radial coefficients found in their experimental unit of 30.5 cm i.d. and 6.6 m height were larger than those found in this work. Initially. to analyse the results obtained, the above equalions were used and the experimental and predicted radial dispersion coel'licients were compared. Figs. I I and 12 show a comparison between the experimental and predicted values c~l"the radial dispersion coel'licients I'ronl Eq. (4) [15] and Eq. (5) 116], respectively. As can be seen in Figs. I I and 12, the experimental results are in poor agreement with these equations. As none of the proposed equations was good enough to predict D, under a variety of conditions, an improved mathematical expression was developed in this work. The new expression determines
l0
7
:710pro
.
A
6.
380 p m
8
and
Re,,,= (G, +upv.)Dt/tl
,
•
i +ii 4
E
2
V_ ~t
0
1
0
0
2o
•
40
60 Gs
80
10o
1,.0
(kg/m2s)
Fig. I0. Effect o f solids circulation flux on the radial dispersion coefticient liar two partide sizes (u = 6,5 m / s l .
,
0
I
l
,
I
2
,
I
=
3
Calculated D r
I
,
4
I
5
,
I
6
,
7
(c m 2 / s )
Fi B. I I. C o m p a r i s o n betv,een experimental radial di,,pc'r,4on cool'lh.'iCl+l,, ;ind
those predicted by Eq. ( 4 ). alter Yang el al. I 15 I.
169
!'. Gavdn el al. / Powth'r l'et'hm,h,g.v 94 ¢ 1997) 163-171
40
-
35
j
@@
30
5
v
~'-
25
"~
20
oo
4 .
=
vx ' e•e e / e
•
15
/
5
":"--~-
I
Or.,. ' , ; ,"-;'-"~ .~'~ 0 5 I0 15 20
25
30
35
i ?I/"" 0
40
0
Calculated Dr (e~2/s)
-9
•@
i-ll
-
l
-13 It
I
i
12
I
13
f
l
.
l
,
2
I
.
3
I
4
,
I
5
.
I
6
.
I
I
7
Fig. 1 4 . Comparison between experimental radial dispersion coefficients and those predicted by Eq. (6).
it can therefore be concluded that more factors are important than just those accounted for in Eq. (6). However. this equation provides a good fit to the radial gas dispersion coeflicients found by each author using a different pair of parameters c, and c_~ for each work. Fig. ! 5 shows some plots of In( D,/G. + I ) versus In(Re,,,) obtained for data of different authors. Similar results were found tor all the works considered. For this reason an attempt was made to improve Eq. (6) by adding other factors such as bed diameter, solids density and particle size. The following equation with four parameters was used for this litting:
@@
-12
•
Calculated D r (cm2/s)
Fig. 12. Comparison between experimental radial dispersion coeflicienl.,, and tho.,,e predicted by Eq. ( 5 ), after Amos el al. 1161.
-I0
Lf
,
14
in Rein Fig. 13. Plot of In(I), IG, + I I v~,. In( Re,,, ) from the experimental rc.,,uils.
D, as a function of the air velocity, the external solids Ilux and the riser diameter and needs two parameters. The following exponential equation was proposed for the lilting of the radial dispersion coel'licient~< D, = c,R, ,,, ( G, + I )
(6 )
where Re,,, = ( G, + .p~ ) D, I It. Parameters c, and c2 in Eq. (6) were calculated through a plot of I n ( D , / G . + I ) versus InlRe,.). Fig. 13 shows the experiment:d results compared with this new expression with all the experimental coefficients determined in the experimental work. From this plot the following values tor the parameters were calculated: c, =0.55. c . = - 0 . 9 . Fig. 14 shows a comparison between the experimental radial dispersion coefficients and those predicted by Eq. (6). As can be seen. the lit is now adequate. Based on the above results, the capacity of Eq. (6) to predict the values of the radial dispersion coefficients obtained by other authors 12.4.5. I I. 15.181 was tested, taking into account their different installations and experimental conditions. Very important diff'erences between the experimental data and the predictions of Eq. ( 6 ) were found. These differences could be attributed to many different causes, such as colu,nn geometry and solids properties which cannot be taken into account in Eq. (6).
(7)
I), = ,'tRe,;,'-( G, + I ) ( d,,/p, )' 'D,"
The values of the radial dispersion coeflicienls obtained in this work and by other authors were lifted to this equation using the Nelder and Mead searching method 1241 to calculate the four parameters. The best values found are the following:
cl=l.4xl()
", c : = - 1 . 1 4 ,
c~=-1.3,
c.,=1.85
Fig. 16 shows a comparison between tile predicted D,. and the experimental ones. As can be observed, in spite of using four parameters, some of the coefficients are underestimated. It has to be pointed out that the values of the radial dispersion coefficient have been obtained in very different installations, which makes their extrapolation difficult. The coefficients obtained in small installations (diameter < 30 cm ) show the best lits. On the contrary, the results found by Adams [41 were the worst predicted, probably due to the square geometry of the column used. Eq. (7) predicts the radial gas diffusion coefficient as a function of the operating conditions ( u. G,) and the characteristics of the riser (d 0. D,). Seven different works ( including this one) were used to determine its parameter values. Thus. this equation summarizes the previous works on radial gas mixing in CFBs and provides a method to estimate the importance of the radial gas mixing, whatever the conditions used or the riser diameter.
170
P. Gaytin el aL /Powder "l'~'chn.l.,~y ~4 ¢1997J
163-171
0
• Martin et al. [5] o Werther et al. [6] n van Zoonen [18] ra Adams [4]
-2 -4
A
i
-6 i -8
=
-10 -12 -14 -16
,
9
I
,
I
10
i
II
I
i
12
13
.
i
.
14
15
In Rem Fig. 15. Plot of In(DJG, + I ) vs. In( Re,,, ) l'romthe J'c.~ultsof other authors.
01 "Jl 50
~
i
40
~
~o 0
i ~
0
I
.
l0
I
20
.
I
30
.
I
•
40
I
50
,
I
.
~
• • n • n •
Adams [4] Bader et ~'=. [2] Martin e t a i . [5] van Zoonen [18] Werther et al. [6] Yang et al. [15] This work
I
70
Calculated D r (cm2/s)
Fig. 16, Comparison helWeCllexperimental rad!al dispersion coel'licicnts and Ihose predicted by Eq. ( 7 ). However, it was particularly interesting that all ot" the D, values obtained gave high Peclet numbers (from 500 to 2000), denoting the slight significance of the radial gas diffusion in the dilute region of this type of reactor, in such way that the radial gas diffusion can be neglected by comparison with the convective flow of gas [ 31 ]. Therefore the gas flow can be taken as plug flow.
results published in seven works on radial gas mixing in CFBs. The radial dispersion coefficients in the dilute region obtained in this work lead to Peclet numbers from 500 to 2000, so that radial gas diffusion can be neglected.
6. List o f s y m b o l s $. Conclusions CI, C2
The systematic experimental work carried out in this study to determine the radial gas mixing in the dilute region of a fast bed shows that Dr is small and dependent mainly on the gas velocity and solids circulation flux. On the contrary, in the dense region, radial gas dispersion is very high due to the vigorous motion of the solids in this part of the reactor. An equation (Eq. (6)) has been proposed to calculate Dr as a function of the operating conditions, on account of the fact that previously published equations showed bad fits to our experimental data. Also, this equation was improved (Eq. (7) ) to allow D~ to be predicted tbr a wide range of operating conditions, solids used and riser diameters. The final expression was determined taking into account the experimental
('3, C4 C
Co C-I.
D. Dr Dt G, Pe Pe' q.
parameters of Eqs. (6) and ( 7 ) parameters of Eq. ( 7 ) tracer gas concentration ( m o l / m ~) gas tracer concentration at injection point ( m o l / m ~) tracer gas concentration at z = :I,, ( n,.oi'~~m ~) particle diameter ( m ) axial gas diffusion coefficient (m2/s) radial gas diffusion coei'ficient (m2/s) bed diameter ( m ) external solids circulation flux ( kg/m ~ s) Peclet number, Pe = u D J Dr Peclet number defined as Pe' = ( u/ e) ( DI/2 ) ~Dr tracer gas flow rate (m-~/s)
P. Ga vdo et al. / Powder Tec'imohJgy 94 ( ! 997) 163-171
R
Re,,, s
radial distance from vertical axis to sampling point (m) bed radius I m) Reynolds number detined in Eq. (6) -, direct distance from injection point to sampling point (m) gas velocity (m/s) distance along vertical axis from injection point to sampling plane ( m )
Greek h'tters E
/z P~
/9,
bed voidage gas viscosity ( kg/m s) gas density ( kg/m ~) solid particle density ( kg/m ~)
Acknowledgements The authors wish to thank the DGICYT (AMB92-0888C02-01 ) for funding the project of which this study is a part. Also. P. Gay~in wishes to thank the Spanish Ministry of Education for the FPI grant.
References J I I G. Patience and J. Chaouki, Chem. [-ng. Sci.. 48 1181 11993 ) 3195. 121 R. Bader. J. Findhty and M. Knowllon. in P. Basu and J.F. Large ( eds. ~. Circulating Fluidized Bed Technology II, Pel'gamon, ()xfbrd. 1988. p. 123. 131 V. l,i and P. Wtl. ill P. I|astl, M. Hol'io illld H. I|asalani (eds.), (.'ircuhlting I:luidized lied 'rcchn~d~,~ Iii. tL'rgalnon. ()xli~rd. 1991. p. 581. 141 ('. Adalns, ill P. I]asu and J.F. Large I etls. I. Circtllaling Fluidi,~cd Bed Technology Ii, Pergalnon. Oxl'~rd. 1988, p. 299. 151 M.P. Martin. P. Turlier. J.R. Bernard and G. Wild, Powder Tcchnol.. 71) I 19921 249. 161 J. Werther, E.U. Harlge and M. Kruse, P~wder Technol., 71) ( 1992 293. 171 B. Zethraeus, C. Adams and N. Berge. Powder Technol.. 69 I 1992 I II)l.
! 71
181 C.M.H. Brerettm, J.R. Grace and J. Yu, in P. Basu and J.F. Large I eds. I, Circulating Fluidized Bed Technology !!, Pergamon, Oxlbrd. 1988, p. 307. 191 R.J. Dry, Powder Technol.. 49 I 1986 ) 37. I I01 H. Kagawa, H. Mineo, R. Yamakazi and K. Yoshida. in P. Basu, M. Horio and H. Hasatani ( eds. I. Circulating Fluidized Bed Technology !11, Pergamon, Oxford. 1991, p, 551. I I I I J. Werther. E.U. Hartge and M. Kruse. in O.E. Potter and D.J. Nicklin reds. I. Fiuidization Vil, Engineering Foundation, New York, 1992, p. 257. 1121 N.T. Cankurt and J. Yerushalmi. in J.F. Davidson and D.L. Keairns leds. I. Fluidization, Cambridge University Press, London, 1978, p. 387. I 131 H. Helmrich, K. Schiigerl and K. Janssen, in P. Basu ~eds. I. Circulating Fluidtzed Bed Technology. Pergamon, Oxfi)rd, ! 986. p. i 6 I. 1141J. Li and H. Weinstein, Chem. Eng. Sci., 44 { 19891 1697. 115J G. Yang. Z. Huang and L. Zhao, in D. Kunii and R. Toei (eds. I. Fluidization IV. Engineering Foundation. New York, 1984, p. 145. 161 G. Amos. M.J. Rhodes and H. Mineo, Chem. Eng. Sci., 48 ( 5 ) ( 1993 943. 171 K.Win, W. Nowak, H. Matsuda, M. Hasatani, M. Kruse and J.J. Werther. Cllem. Eng. Jpn., 27 ( 5 ~ I 1994 ) 696. 181 D. van Zoonen, Proc. Conf. Interaction Between Fluids and Particles. Institution of Chemical Engineers, London, 1962, p. 66. 191 J. Yerushalmi and A. Avidan, in J.F.Davidson. R. Cliff and D. Harrison l eds. 1, Fluidization, Academic Press. London, 2nd edn.. 1985. p. 225. 201 J. Ad:inez, P. Gay~in, F. Garcia-Labiano and L.F. de Diego. Powder Technol., 81 131 t 19941 259. 211 J. Werther. E.U. Hartge. M. Kruse and W. Nowak, in P. Basu, M. Horio and H. Hasatani teds. ). Circulating Fluidized Bed Technology Iil. Pergamon, Oxford, 1991, p. 593. 1221 L.F. tie Diego. P. Gay;in and J. Ad~inez, Powder Technol.. 85 t 1995 19. 1231 W.L. Towle and T.K. Sher~,,od. Ind. Eng. Chem., 31 14 ) ( 19391 457. 1241 J.A. Nelder and R. Mead, Comput. J.. 7 ~ 1964) 3(18. ! 251 C.C. While and R.J. Dry. Powder Technol.. 57 119891 89. 1261 R.J. Dry and C.( ?. White. Powder Technol., 58 11989) 17. 1271 H. Weinslein, J. l,i, E. Bandlamudi, tt.J. Feindt and R.A. Graff. in J.R. Grace, I,.W. Shemilt :n|d M.A. Bergougnou l eds. ], Fluidization VI. Engineering Ft~tlnthttion. New York. 1989. p. 57. 1281 I'. Jiang, K. Inokuchi, R. Jean. H. Bi and 1,. Fan. in P. Basu. M. Htu'io and H. Has:ttani t eds. l. Circulating Fluidi/.ed Bed Technolog) III. I)t.'rganlon. Oxli~rd. 1991, p. 557. 1291 D.R. Bat. J. Yi. Y. Jin and Z.Q. Yu. in O.E. Ih,tter and D.J. Nicklin l eds.), Fluidization VII. Engineering F~mndation, New York. 1992. p. 195. 13111 C.C. White, R.J. Dry and O.E. Poner, in O.E. Poner and D J. Nicklin l eds. I. Fluidization Vii. Engineering Foundation. New York. 1992. p. 265. 1311 C.Y. Wen and L.T. Fan. Models Ibr Flow Systems and Chemical Reaclt~rs. Marcel Dekker. New York. 1975.
Powder Technology 94 ( 1997 ) !(~3-171
Radial gas mixing in a fast fluidized bed P. Gayfin, L~F. de Diego, J. Adfinez * ln.s'titulo ~h" Carbnquhni~'a (CSICh PO Bor 589. 5(1015 Suragos.~'a. 3"ptdn Received I I October 1995: revised 30 May 1997
Abstract A steady-state dispersion model was used to determine the radial gas mixing coefficients I), in the dilute region of a cold fast l|uidized bed. 0. I m i.d. and 4 m high. CO2 used as tracer was injected into the centre of the bed from a point source. Radial concentration profiles of tracer gas were measured in two planes downstream of the injection point for a broad range of air velocities and solid fluxes, using two sizes of sand panicles of 710 and 380 p,m. A systematic experiment was carried out to find out the main variables acting on the radial gas mixing in the dilute region of a last tluidized bed. An analytical solution derived by Towle and Sherwood for the description of radial gas mixing in turbulent single-phase flow was applied to determine the radial dispersion coefficients, which were found to be dependent on the superficial gas velocity and solid circulating flux. The D~ values were well correlated with an apparent suspension Reynolds number ( Re ) by an equation of the type D~ = a R e ~'. The proposed equation allows the radial gas coefficient to be predicted as a function of the air velocity and external solid flux present in the riser. This equation, with it.,;corresponding parameters, is applied to the results of other authors and an acceptable fit was found. The high Pe numbers (5(10--2000) obtained in the dilute region of the fast fluidized bed indicate that the flow of the gas in the dilute region approximates to plug flow. ~) 1997 Elsevier Science S.A. Kevwords: Fluidized beds: Circulating beds; Gas lit}w: Mixing
1. Introduction The effectiveness of a circulating Iluidized bed (CFB} combustor depends on its ability to mix adequately the incoming flows of reactants: fuel, sorbent and air. Emissions and combustion efficiency are strongly related to the mixing process. Incomplete mixing of secondary air into a bulk gas stream might, for example, result in an increase of hydrocarbon emissions from substoichiometric zones as well as to NO, emissions from overstoichiometric areas. In an empty column, the gas is in plug flow owing to the high air velocities used, but the solids can modify this type of flow, which will be characterized by the values of the gas dispersion coefficients with respect to ideal flow. To characterize the gas mixing it is necessary to know three coefficients: the axial dispersion coefficienk ~he radial dispersion coefficient and the baci~ iiiiniii~, coeflicient. The number of investigations related to gas mixing in CFB~ is fairly small compared with others dealing with hydrodynamic solid properties. Moreover, there is no certainty about the behaviour pf the gas in this type of reactor owing to the great variety of results and methods used. Table I, from Patience and Chaouki I I I, summarizes the conditions of the * Corresponding author. Tel.: + 34 976 73 3977; fax: + 34 976 73 3318. 11{)32-5911)/97/$17.11t) c~ 1997 Elsevier Science S.A. All rights reserved PII S 0 0 3 2 - 5 9 10 ( 9 7 11)3322-6
investigations carried out by different authors, the L.,eometry of the reactor used :md the experimental and theoretical methods employed. Most of the data available on gas mixing have been obtained with particles of group A of the Geldart classilication at low gas velocities. Characterization of the gas mixing in fluidized beds can be done in steady or non steady-state conditions as shown in Table i. In the latter, the gas concentrations have to be measured within a few seconds, because the mean residence time.,, of the gas in last fluidized beds are ! or 2 s. This lhct can cause important er ~rs when using some systems of measurement. in additio~!, the results obtained can be analysed by two different models, such as the two-phase model and the dispersion model. In fast fluidized bed:, the dispersion model is the most widely used 12-7] although the two-phase model is also used I 1,8-111. applied to the ga~ exeh~mge between the core and the annulus of the dilute region of a fast fluidized bed. From their back-mixing measurements in a column of 0. i 5 m i.d. with FCC solids, Cankurt and Yerushalmi I 121 have Iound that back-mixing of gas diminishes when the gas velocity increases and pointed out that, in a CFB, back-mixing is negligible compared with the convective fow. The same conclusion was obtained by other authors 12,13 I. On the other
164
P. Gav6n ,'t al. / Powth,r Techm,iogy 94 ¢ 19'171 163-171
Table I Tracer techniques used in studies of gas flow hydrodynamics I I I Study
van Zoonen I 181 ~,'an Zoonen 1181 Cankurt and Yerushahni I 121 Yang et al. I 151 Dry 191 Adams 141 Bader et al. 121 Brereton et al. 181 White and Dry 1251 Dry and White 1261 Li and Weinstein I 141 Weinstein et al. 1271 Jiang et al. [ 28 ] Kagawa et al. I I01 Li and Wu 131 ~,'erther et al. 121 I Baiet al. 1291 White et al. 1301 White et al. 1301 Martin et al. 151 Martin et al. 151 Zethraeus et al. 171 Amos et al. 1161 P~itiencc and Chaouki I I I Win el al. 1171
Particle properties Tracer
Injection
dp( I.tm )
p. I k g / m ~)
Solids
D, I m )
Model
H2 H_, CH.~ He hot air CH~ He He Ar Ar He He ozone ozone H_, CO., organic Ar Ar Kr Hc CH.~ SF,, Ar-40 CO,
continuous pulse continuous continuous pulse continuous continuous step pulse pulse continuous continuous continuous continuous continuous/pulse continuous pulse pulse pulse pulse continuous continuous continuous pulse continuous
56 56 55 220 71 250 76 148 71 7i 59 59 65 46 58 130 I tXl 71 140 62 62 2110 71 277 100
II00 I I00 I I00 710 1370 2600 17 I0 2650 1370 1370 1450 14511 15110 2300 1575 261111 710 1370 16511 1560 15611 2800 2450 2630 25011
FCC FCC FCC silica FCC sand FCC sand FCC FCC FCC FCC FCC FCC FCC sand silica FCC sand FCC FCC sand FCC sand glass
0.05 0.115 O. 152 O. I 15 0.09 0.3 x 0.4 0.3115 O. 152 0.09 11.119 0.152 0.152 O. 1 1 1 2 O. I 0.09 11.4 O. 14 0.119 0.09 0.93 0.19 11.3 × 0.4 0.305 0.083 0.05
radial dispersion axial dispersion plug flow radial dispersion contact efficiency radial dispersion radial dispersion core-annulus core-'mnulus axial dispersion core-annulus disp. back-mixing at core back-mixing at wall core-annulus axial dispersion core-annulus disp. axial dispersion core-annulus core-annulus axial disper.;ion radial dispersion core-annulus core-annulus disp. core-annulus radial dispersion
h,'md, measurements of gas residence time distributions by Brereton et al. 181 have shown that the CFB as a whole exhibits a considerable amount o1' back-mixing in the gas phase. However t,i and Weinstein I 141 pointed out that this contradiction is due to the existence of different flow pattern regions inside the CFB, such as perfect mixing in the dense region or plug flow in the dilute region. Recently, Li and Wu 131 have shown that the extent of axial gas dispersion depends on average voidage, which is influenced by the gas velocity and the solid circulation flux. Concerning lateral mixing in the dilute region Yang et al. 1151 found that the radial gas dispersion coefficient decreased when the gas velocity increased and the solids flow rate decreased. On the contrary, Adams 141 indicated an increase in the horizontal dispersion when the gas velocity increased and solids flow rate decreased. From the work of Bader et al. 121 no relationship between the radial mixing and solids flow rate or gas velocity was obtained because both were changed simultaneously. Martin et al. 151 determined the radial dispersion coefficients which showed'a sligh! increase when the solids flow rate increased, whereas the influence of gas velocity was not studied. On the other hand, Werther et al. 161 suggested a constant value of the radial Peclet number for all situations. Recently, Amos et al. ! 161 applied a plug flow model with dispersion in a bed of 30.5 cm i.d. under a wide range of operating conditions, They tbund an increase in the radial coefficient when the solid, flow rate decreased and a slight
effect of the gas velocity, working with the same value of solids volume fraction. Also, Win et al. 117] carried ou.', a study of the radi,'d dispersion only in the bottom part of a CFB. They found a large increase in Dr after a dense bed was formed in the bottom part of the unit, that is, when the solids circulation flux was very high. These scattered and contradictory results might be due not only to the difficulties of the experimental measurements, but also to the different experimental units and operating conditions used. In summary, with respect to the above results lbr back-mixing measurements and axial dispersion studies 12,5,12,13,15,18,191, it can be considered that in fast fluidized beds these coefficients are negligible by comparison with the convective gas flow. However, the experimental values of the radial gas dispersion coefficients range from 0.0002 to 0.50 m2/s. Thus, it is clear that from these available data the relative importance of the radial dispersion in CFBs cannot be determined. Therelore the aim of this work was to determine the radial gas mixing in a fast fluidized bed and its variation with the operating conditions. Systematic experimental work was carried out to measure the value of Dr and to develop an equation to predict it as a function of the operating conditions. 2. Experimental
The experimental apparatus used in this work is shown in Fig. ! and was previously described by the authors ! 201. The
P. Gav6n et al. /Powder Techm, logy 94 ¢Iq97j 16.t-171
Cyclones
PIO Pressure taps m
Diverting solid reservoir
Feed hopper
Fast bed ~'Auxthary
bed
Fluidization air Rotameters Fig. I. Installation set-up.
CFB system consists of a 3.9 m tall riser which is 0. I m in diameter. Sand with two different mean diameters of 710 I.tm ( 630-800 ~rn) and 380 lxm ( 300-500 I.tm ) and a density of 2600 kg/m ~ were used in all experiments. The gas velocity was varied between 5 and 8 m / s and the solids circulation llux from 0 to 115 kg/m-" s. CO_, was used as gas tracer. To determine the dispersion coefficient in the dilute region. the tracer gas was injected at a constant rate in the centre of
165
the column at 2.5 m above the distributor plate. The gas injector consisted of a pipe o1"6 mm i.d. in which the gas flow rate was controlled with a valve and a rotameter. The tracer gas velocity was fixed equal to the mean gas ~e!ocity in the column, because its value did not affect the measured values at velocities higher than the fluidization velocity. Before starting a gas mixing experiment, the solids circulation flux was determined at each air velocity by the method shown elsewhere 1201. Also. axial mean solids fraction proliles were calcuh.,ted from the pressure drop measurements. For the ranee of o?erating conditions used in this work. the axial voidage profile was S-shaped and the point of tracer injection always remained in the upper dilute zone of the riser. As the concentration profile changes with height, the sampling was performed along the riser diameter at two different distances from the injection point, located at 3 and 3.5 m from the bottom of the column. The sampling probes of 4 mm i.d. had a wire mesh to prevent solids penetrating into the gas measurement system. A Siemens Llltramat 22P non-dispersive infrared gas analyser was used to detect ti~e tracer gas concentration. The sampling rate was set to 2 I/rain. due to detector limitations. This corre:,ponds to a velocity in the probe of 2.3 m/s: however, preliminary experiments gave no indication of any effect of this low velocity. All measured concentration profiles were checked by integration of the tracer concentration. The injection point was traversed across the diameter in order to conlin'n the existence of an interface between the core and the an|talus, as was indicated by Werther et al. 121 I. Due to the characteristics of the fast bed. there are two different regions in the column: the dense region, with a high .~olids concentration, and the dilute region, with a core-annulus structure. For this reason, besides determination of the radial gas dispersion coefficients in the dilute region, some tracer injections were made into the dense region in order to verily the gas mixing characteristics of this region (backmixing and radial mixing). To determine the significance of the radial gas dispersion and the gas back-mixing in the dense region, other experiments were performed. Tracer was injected into the centre of the riser at 0.5 m fi'om the bottom t the height of the dense region was I m) and the radial gas concentration profiles were measured downstream at I m from the bottom and at 3 and 10 cm upstream of the injection point. The profiles measured at ! m were flat under all the different c~mditions. ,~o the radial dispersion in this dense region is very large due to the vig¢~rous motion of the solids. This solids movement can cause some gas back-mixing in the dense region. However. the experiments performed to measure it I concentration profiles upstream of the injection point ) did not reveal any appreciable gas tracer concentration at any radial position, working in the same range of velocities and solids circulation fluxes as in dilute region experiments.
P. Gaydn et ,!. / Powder Tc+'hm,h,gy 04 ~1997~ 163-171
! 66
olnj.
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Fig. 2. T r a c e r gas concentration proliles with the injection point decentred and different heights ( u = 5.9 un/s. G. = 57 k g / m : s and d,, = 7 I0 p.m ).
These results confirmed those obtained by other authors 12,12.131, and it can be said that back-mixing in the dense region can be considered to be negligible.
,z-3 m ] a z=3.5 mJ "--'
la
3 m
m
R
3. Gas dispersion in the dilute region
2
As has been pointed out. to characterize the gas th)w in the dilute region of a circulating fluidized bed, some authors I 1,5,6.151 have defined a gas exchange coefficient between core and annulus, in a similar way to that between the bubble and emulsion phase in bubbling fluidized beds. This type of model assumes that the gas concentrations in each region are equal at all radii and the wall causes ,', resistance to the gas diffusion. Werther et al. I III further proposed a gas exchange coefficient between core and annulus and a radial dispersion coefficient in the core. in order to check the validity of that ,'tssumption, tracer gas was injected at 2.5 m from the bottom at ntdii of 2.5, 3.5, 4 and 5 cm. The concentration protiles were measured at 0.5 and I m from the injection point. Fig. 2 shows the tracer gas concentration profiles when the injection probe was located at different radii trom the centre axis ( 2.5, 3.5, 4 and 5 cm ), i.e. situated both in the core and in the annulus. This figure also shows the extent of the annulus zone, calculated from measurements of internal solids circulation fluxes 122 I. As can be seen in the figure, the existence of a discontinuity between the core and the annulus can be neglected. So, a gas exchange coefficient between the core and the annulus does not seem justified. Besides, it can be inferred l'rom the analyses of these profiles that the gas flow in the whole dilute region can be characterized using only one radial gas coefficient ( dependent on the operating conditions). The remainder of the paper concerns the value of the radial gas coefticient in the dilute region and its dependence on the operating conditions. The influence of three diffe,'ent variables (fluidizing air velocity, solids circulation flux and particle size) was analysed. Fig. 3 shows the effect of the sampling height on the tracer concentration profiles, working at 6 m/s and 51) kg/m-' s of solids circulation flux with a particle diameter of 710 I,tm. The sampling probes were located at 0.5 and I m from the injection point. As can be seen, the profiles become flatter
1
a
[]
m
m
0
m
m -5
-4
-3
[] -2
-I
0
I
2
3
4
5
r (cm) l:ig. 3. Tracer ga.,, concentration proliles m e a s u r e d al Iwo different heights ( tl = 5.9 in/s and G, = 50 k g / m - ' s ).
6
l
5.9 mls I
•
5
m 8mls
4 o
nl•nl
3 ")
.
m
m
l .
t , •
• •i ,
0 -5
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!
•
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I
t
0 r
I
1
,
,d~
2
,
•
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n
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Fig. 4. T r a c e r gas concenlralion prolile~, m e a s u r e d wilh two gas velocities ( (i, = 50 k g / m - ' s and : = 3.5 m ).
when the distance from lhe injection pc~i,l !o the sarnplirtg point increases, due to the radial diffusion of the tracer from the centre to the walls of the column. Tile effect of the gas velocity on the gas concentration profiles is shown in Fig. 4. It can be seen that the dispersion of tracer gas increases when the air velocity decreases because the gas flow behaves more like plug flow as the air velocity is increased. Fig. 5 shows the concentration profiles obtained when using three different solids circulation fluxes (0. 23 and 59 kg/m z s) at the same air velocity (6.5 m/s) and with a particle size of 710 p.m. The profiles become smoother as the solids circulation fluxes increase. A change in the solids flux
167
P. Gavdnet al. I Pnwth, r Techmdogy 94 ¢199 71 163-171
10
• 59 kglm~ s 023 kg/m~- s B 0 kg/m" s
0 0
Sampling point
Tracer gas injection point
4
o
o
t
BKI BBKI BKi
2
-5
-4
-3
-2
-1
0
1
2
3
4
Gas flow Fig. 7. Delinifionof.~and - parametcrs.
5
r (ctn) Fig. 5. Tracer gas concentration
profiles
measured with threc solidsp
ac a-'c I a(ac) u i ~ z = D" , ~ + D , - - -,.a,- r 7,.j
(I)
-
circulation Iluxes I t, = 6.5 m/s ard z = 3 m 1.
6
m 380 lure [ * 7101am I
5
@ B
m
4
e,D¢
3 m
[]
1 @E I 0
,
I
'
-5
-4
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-3
-2
,
m@ I
-I
,
I
~
0
I
l
,
,.h_ --
2
I
3
•
I
4
,
5
r (cm) Fig. 6. Tracer gas COlleerdralitnl prolilcs measured with lwo particle sizes
lit
= 5.5 II1/s. (;. =
where z denotes the distance between the injection plane and the sample planes, and r is the radial distance from the axis of the column, as shown in Fig. 7. The assumption of a uniform axial velocity profile was based on the work of Martin et al. [ 5 ] which showed that in the range of operating conditions of our work ( u = 5-8 m/s and G~ = 0-115 kg/m 2 s). the n values in the equation to calculate the radial velocity profile were less than 0. i. and so the velocity profile can be assumed flat. Assuming that the axial dispersion can be neglected and without back-mixing in the dilute region, the equation is transformed: ac
I;~ [ ac)
{2)
"7. = n,-,. t";
31) kglm: s and - = .~ m }.
with the followip.g houndary conditions: and therefore in the solids concentration in the two-phase flow has ;111inlporlant inlluence on the gas dispersion. This figure also shows the concentration profile obtained when there is only air in the column, i! was found that the radial dispersion was greater without any particles in the column. This filet is in agreement with the results of Adams 141. Amos el al. 1161 concluded that at high enough mean solids volume fi'actions the solids do not displace the gas towards the core. but modify the gas flow in such way that the dispersir,n coefficients become smaller than the respective values for air alone• Finally, the effect of the solid particle size on the tracer gas profiles at 5.5 m/s and 30 kg/m-" s. working with particle diameters of 7 I0 and 380 p,m, is showr! in Fig. 6. As can he seen, a weak effect of the particle size was found.
4. A n a l y s i s of results
The results obtained in this work were analysed using a dispersi.on model. A mass balance on a differential volume element ( 2zrr dr d:) of the column in the steady-state and at constant velocity leads to the Iollowing equation:
r = R.
;),.//it=()
==0 and r=O.
c=c.
- = 0 and r ~ 0 .
c=0
W il~;on's equation for heat conduction, modilied hy Tow le and Sherwood l ..231to apply to radial diffusion when the ratio :./r is quite large, was used as an approximate solution of Eq. (2):
c q" cxp c,, 4~'sD,
(u(s--))
13 }
2D,
where the tracer concentration, c. depends on the constant Ilow rate of the tracer introduced, q,,. and the radial diffusion D,. A plot of Inisc/c,,} against { s - : . ) will give a straight line of slope - (u/2D,) and hence the r:;dial diffusion coef ficient can be found. Fig. 8 shows a typical plot of this kind. The radial dispersion coefficients obtained in this way in the dilute region of a fast fluidized bed were small, showing that they are of negligible magnitude. The radial gas diffusion coefficients calculated from the measurements of the probes located at heights of 3.0 and
P. Gaydn (,t al, / P o w d e r Teclmolo,ey +:4 ( lqq7~ 163-171
168
2~ In (s c1¢o) F 1
u=5,9 m/s ~ C,s=50 z=3 m
1-
x ~r)~I¢~t~,....= O~ - f
kg/m- s
~
(qo/4
coefficient when the solids circulation flux increases is due to the higher solids concentration present in the column, and therefore higher dispersion of the solids from the core to the annulus, which favours the gas dispersion. Once D~ values had been calculated for a variety of air velocities and solids fluxes, the mathematical expressions tested using our experimental data in order to find the most satisfactory. I~ott, n f the* tl,r~rlzt ,.~hntt! o*)t R n t t , n r o n o c ¢ , f . c l t t , l l i n r t ~ t o
0
0,0l
0,02
0,03
0,04
0,05
(s-z) (cm) Fig. 8. Plot o f In( .w/('.. ) as a function o f (s - z ) to determine D,. 10
="'710 pm]
calculate the radial dispersion coefficients in the dilute region of the fast bed. Thus, Yang et al. [ 151, working with a bed of I 1.5 cm in diameter and 8 m height, obtained values for the radial dispersion coefficients from 2 to 8 cm2/s, which were fitted as a function of the operating conditions to the following equation:
• 380 p m
D~ = 0.7 + 4.34
u
! - e
u l e - G , Ip,
•
(4 )
6
More recently, Amos et al. [ 161 proposed the Ibllowing equation to calculate the radial dispersion coefficient:
m e~""
4
•
•
m
il
Pc' = 3.23Re,~, ~2"7
(5 )
where Re,,, and Pc' are defined as 0
t 3
•
4
I
•
5
t
I
I
6
7
,
I 8
t 9
U (m/s) Fig. t). F.ffecl tDl' ga.,, velocity on the radial dispersion coel'licient for t w o panicle s! ~...s ( (;, = 30 k g l m ; ~ ).
3.5 m were practically equal. This confirms the assumption ot" a constant radi:d dispersion coeflicient with height. Having calcuhtted the radial gas dispersion coel'licients, the effect of the operating variables on the value of the coeflicient was analysed. Thus, the effect of the air velocity is shown in Fig, 9 for the two particle sizes used in this work. As was expected, the dispersion coefficient decreases when the air velocity increases. Fig. IO shows the effect of the solids circulation flux on D, t'or both particle sizes. The increase in the radial dispersion
Pc'= (u/e)(D,/2)/D~
The values of the radial coefficients found in their experimental unit of 30.5 cm i.d. and 6.6 m height were larger than those found in this work. Initially. to analyse the results obtained, the above equalions were used and the experimental and predicted radial dispersion coel'licients were compared. Figs. I I and 12 show a comparison between the experimental and predicted values c~l"the radial dispersion coel'licients I'ronl Eq. (4) [15] and Eq. (5) 116], respectively. As can be seen in Figs. I I and 12, the experimental results are in poor agreement with these equations. As none of the proposed equations was good enough to predict D, under a variety of conditions, an improved mathematical expression was developed in this work. The new expression determines
l0
7
:710pro
.
A
6.
380 p m
8
and
Re,,,= (G, +upv.)Dt/tl
,
•
i +ii 4
E
2
V_ ~t
0
1
0
0
2o
•
40
60 Gs
80
10o
1,.0
(kg/m2s)
Fig. I0. Effect o f solids circulation flux on the radial dispersion coefticient liar two partide sizes (u = 6,5 m / s l .
,
0
I
l
,
I
2
,
I
=
3
Calculated D r
I
,
4
I
5
,
I
6
,
7
(c m 2 / s )
Fi B. I I. C o m p a r i s o n betv,een experimental radial di,,pc'r,4on cool'lh.'iCl+l,, ;ind
those predicted by Eq. ( 4 ). alter Yang el al. I 15 I.
169
!'. Gavdn el al. / Powth'r l'et'hm,h,g.v 94 ¢ 1997) 163-171
40
-
35
j
@@
30
5
v
~'-
25
"~
20
oo
4 .
=
vx ' e•e e / e
•
15
/
5
":"--~-
I
Or.,. ' , ; ,"-;'-"~ .~'~ 0 5 I0 15 20
25
30
35
i ?I/"" 0
40
0
Calculated Dr (e~2/s)
-9
•@
i-ll
-
l
-13 It
I
i
12
I
13
f
l
.
l
,
2
I
.
3
I
4
,
I
5
.
I
6
.
I
I
7
Fig. 1 4 . Comparison between experimental radial dispersion coefficients and those predicted by Eq. (6).
it can therefore be concluded that more factors are important than just those accounted for in Eq. (6). However. this equation provides a good fit to the radial gas dispersion coeflicients found by each author using a different pair of parameters c, and c_~ for each work. Fig. ! 5 shows some plots of In( D,/G. + I ) versus In(Re,,,) obtained for data of different authors. Similar results were found tor all the works considered. For this reason an attempt was made to improve Eq. (6) by adding other factors such as bed diameter, solids density and particle size. The following equation with four parameters was used for this litting:
@@
-12
•
Calculated D r (cm2/s)
Fig. 12. Comparison between experimental radial dispersion coeflicienl.,, and tho.,,e predicted by Eq. ( 5 ), after Amos el al. 1161.
-I0
Lf
,
14
in Rein Fig. 13. Plot of In(I), IG, + I I v~,. In( Re,,, ) from the experimental rc.,,uils.
D, as a function of the air velocity, the external solids Ilux and the riser diameter and needs two parameters. The following exponential equation was proposed for the lilting of the radial dispersion coel'licient~< D, = c,R, ,,, ( G, + I )
(6 )
where Re,,, = ( G, + .p~ ) D, I It. Parameters c, and c2 in Eq. (6) were calculated through a plot of I n ( D , / G . + I ) versus InlRe,.). Fig. 13 shows the experiment:d results compared with this new expression with all the experimental coefficients determined in the experimental work. From this plot the following values tor the parameters were calculated: c, =0.55. c . = - 0 . 9 . Fig. 14 shows a comparison between the experimental radial dispersion coefficients and those predicted by Eq. (6). As can be seen. the lit is now adequate. Based on the above results, the capacity of Eq. (6) to predict the values of the radial dispersion coefficients obtained by other authors 12.4.5. I I. 15.181 was tested, taking into account their different installations and experimental conditions. Very important diff'erences between the experimental data and the predictions of Eq. ( 6 ) were found. These differences could be attributed to many different causes, such as colu,nn geometry and solids properties which cannot be taken into account in Eq. (6).
(7)
I), = ,'tRe,;,'-( G, + I ) ( d,,/p, )' 'D,"
The values of the radial dispersion coeflicienls obtained in this work and by other authors were lifted to this equation using the Nelder and Mead searching method 1241 to calculate the four parameters. The best values found are the following:
cl=l.4xl()
", c : = - 1 . 1 4 ,
c~=-1.3,
c.,=1.85
Fig. 16 shows a comparison between tile predicted D,. and the experimental ones. As can be observed, in spite of using four parameters, some of the coefficients are underestimated. It has to be pointed out that the values of the radial dispersion coefficient have been obtained in very different installations, which makes their extrapolation difficult. The coefficients obtained in small installations (diameter < 30 cm ) show the best lits. On the contrary, the results found by Adams [41 were the worst predicted, probably due to the square geometry of the column used. Eq. (7) predicts the radial gas diffusion coefficient as a function of the operating conditions ( u. G,) and the characteristics of the riser (d 0. D,). Seven different works ( including this one) were used to determine its parameter values. Thus. this equation summarizes the previous works on radial gas mixing in CFBs and provides a method to estimate the importance of the radial gas mixing, whatever the conditions used or the riser diameter.
170
P. Gaytin el aL /Powder "l'~'chn.l.,~y ~4 ¢1997J
163-171
0
• Martin et al. [5] o Werther et al. [6] n van Zoonen [18] ra Adams [4]
-2 -4
A
i
-6 i -8
=
-10 -12 -14 -16
,
9
I
,
I
10
i
II
I
i
12
13
.
i
.
14
15
In Rem Fig. 15. Plot of In(DJG, + I ) vs. In( Re,,, ) l'romthe J'c.~ultsof other authors.
01 "Jl 50
~
i
40
~
~o 0
i ~
0
I
.
l0
I
20
.
I
30
.
I
•
40
I
50
,
I
.
~
• • n • n •
Adams [4] Bader et ~'=. [2] Martin e t a i . [5] van Zoonen [18] Werther et al. [6] Yang et al. [15] This work
I
70
Calculated D r (cm2/s)
Fig. 16, Comparison helWeCllexperimental rad!al dispersion coel'licicnts and Ihose predicted by Eq. ( 7 ). However, it was particularly interesting that all ot" the D, values obtained gave high Peclet numbers (from 500 to 2000), denoting the slight significance of the radial gas diffusion in the dilute region of this type of reactor, in such way that the radial gas diffusion can be neglected by comparison with the convective flow of gas [ 31 ]. Therefore the gas flow can be taken as plug flow.
results published in seven works on radial gas mixing in CFBs. The radial dispersion coefficients in the dilute region obtained in this work lead to Peclet numbers from 500 to 2000, so that radial gas diffusion can be neglected.
6. List o f s y m b o l s $. Conclusions CI, C2
The systematic experimental work carried out in this study to determine the radial gas mixing in the dilute region of a fast bed shows that Dr is small and dependent mainly on the gas velocity and solids circulation flux. On the contrary, in the dense region, radial gas dispersion is very high due to the vigorous motion of the solids in this part of the reactor. An equation (Eq. (6)) has been proposed to calculate Dr as a function of the operating conditions, on account of the fact that previously published equations showed bad fits to our experimental data. Also, this equation was improved (Eq. (7) ) to allow D~ to be predicted tbr a wide range of operating conditions, solids used and riser diameters. The final expression was determined taking into account the experimental
('3, C4 C
Co C-I.
D. Dr Dt G, Pe Pe' q.
parameters of Eqs. (6) and ( 7 ) parameters of Eq. ( 7 ) tracer gas concentration ( m o l / m ~) gas tracer concentration at injection point ( m o l / m ~) tracer gas concentration at z = :I,, ( n,.oi'~~m ~) particle diameter ( m ) axial gas diffusion coefficient (m2/s) radial gas diffusion coei'ficient (m2/s) bed diameter ( m ) external solids circulation flux ( kg/m ~ s) Peclet number, Pe = u D J Dr Peclet number defined as Pe' = ( u/ e) ( DI/2 ) ~Dr tracer gas flow rate (m-~/s)
P. Ga vdo et al. / Powder Tec'imohJgy 94 ( ! 997) 163-171
R
Re,,, s
radial distance from vertical axis to sampling point (m) bed radius I m) Reynolds number detined in Eq. (6) -, direct distance from injection point to sampling point (m) gas velocity (m/s) distance along vertical axis from injection point to sampling plane ( m )
Greek h'tters E
/z P~
/9,
bed voidage gas viscosity ( kg/m s) gas density ( kg/m ~) solid particle density ( kg/m ~)
Acknowledgements The authors wish to thank the DGICYT (AMB92-0888C02-01 ) for funding the project of which this study is a part. Also. P. Gay~in wishes to thank the Spanish Ministry of Education for the FPI grant.
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