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Heat transfer behaviour and temepratures of freely moving burning carbonaceous particles in fluidized beds
Twenty-Third Symposium (International) on Combustion/The Combustion Institute, 1990/pp. 917-925
HEAT T R A N S F E R BEHAVIOUR A N D T E M P E R A T U R E S OF FREELY MOVING B U R N I N G C A R B O N A C E O U S PARTICLES IN F L U I D I Z E D B E D S TEMI M. LINJEWILE AND PRADEEP K. AGARWAL Department of Chemical Engineering University of Adelaide GPO Box 498, SA 5001 Australia
In fluidized bed combustion, relatively few large coal particles are fluidized along with more dense and smaller sulphur-sorbent bed particles. Predictions for drying, ignition and devolatilization, as well as particle temperatures during char combustion, require knowledge of external heat transfer coefficients. Several studies have dealt with mass transfer for freely moving large particles in fluidized beds; heat transfer to immobile tubes has also received wide research attention. Very few studies have dealt with heat transfer to freely moving large particles in fluidized beds and the correlations available are, at best, semi-empirical. In this paper a mechanistie model for heat transfer is proposed which takes into account the movement of the active particle within the bed. The average heat transfer coefficients predicted by the model are in good agreement with direct measurements reported in the literature. The average heat transfer coefficients are then used, in conjunction with a shrinking core formulation, to predict the temperature histories of burning coke and char particles. The model predicts that the coke and char particles experience rapidly changing external heat transfer conditions. In the case of the char particles the presence or absence of the ash layer will infuence the temperature history. The implication of these variations on the temperature histories in batch/continuous operation and for drying, ignition and devolatilization require further consideration, Introduction
few studies have considered heat transfer to a freely moving sphere in a fluidized bed. The empirical and semi-empirical correlations in the literature, Table I, attempt to predict only the maximum average heat transfer coefficient, hmax; neglecting the effect of superficial velocity on the average heat transfer coefficient, h. Further, the verification of most of these correlations has been indirect, that is, from measurements (with substantial scatter) of the temperatures of burning carbon particles. Clearly, such comparisons would necessitate assumptions regarding the CO/CO2 product ratio, chemical kinetics and mass transfer behaviour. In this paper, a mechanistic model for heat transfer to mobile spheres, including details Of active particle motion based on experimental observations of Nienow et al., 16 is proposed. The model predictions are compared with direct measurements of average heat transfer coefficients. 2 Using the mass transfer formulation reported at the previous Symposium, s CO/C02 product ratio from recent experimental evidence of Prins z and half-order kinetics17A8 for the carbon oxygen reaction, simplified mass and energy conservation equations are solved numerically to predict the temperature of
In fluidized bed combustion (FBC), relatively few coal particles are fluidized with denser and smaller sulphur-sorbent bed particles. The temperature of burning particles exceeds that of the bed. Prediction of the excess temperature is important not only for modelling FBC behaviour of the carbonaceous particles1"2 but also for assessing ash fusion. 3 Mathematical models for the combustion of carbonaceous particles, employing the shrinking unreacted core formulation, a are abundant in the literature. Major factors that influence particle temperature are refleeted in the estimation of the relevant heat and mass transfer coefficients, CO/CO2 product ratio and the kinetics of the carbon reaction. However, literature review reveals that existing FBC models have employed conflicting assumptions regarding Sherwood and Nusselt numbers and the CO/CO2 product ratios. 5 Several studies have now been reported on the external mass transfer behaviour for large freely moving "active' particles in fluidized beds. ~8 Heat transfer to tubes immersed in fluidized beds has also received wide research attention. 9-n However, very 917
918
FLUIDIZED BED COMBUSTION TABLE I Correlations for heat transfer to large mobile 3articles in fluidized beds Ref.
Correlation
Remarks
12
(hda)/k, = (k~d~)/(DA~f)
based on the argument that bed particles hinder mass transfer but assist heat transfer
13
(hdo)/k , = 5Ar ~176 ( d J d 2 ~
the equations apply for 1.4 x 103 < Ar < 4 x 10'; 2.3 < (d~/do) < 14
14
/~,,,~ = (kJd,){O.41ArO3 (d,/d,)O.2 (pp/po)-o.oT}
the equations apply for 1.55 x 10s < Ar < 2.2 x 10 7, 0.074 < dr/ d= < 1.21, 0.44 < Po/Pa < 2.07; for non-spherical 'active' particles, a sphericity correction factor has to be employed
15
= h, + (h2 -
h,) exp{-d,/(4do)}
h, = (kg/dp)(O.S5Ar ~
+ O.O06Ar~ Pr '/a)
the equations apply for (d,/do) > 1; additional equations were proposed for (do/do) < 1
hz = (kg/d,){lO + 0.23(ArPr) '/3} h~
= ( k J do)(3.539Ar" f r)(dJ do) -~
the equations apply for 10 < Ar < 20000 and 3 < (da/dp) < 200
n = O.105(da/do) ~176 f r = 0.844 + 0,0756(Tb/273)
freely moving carbonaceous (coke or char) particles in bubbling fluidized beds. Other implications of the heat transfer model on FBC of coal are discussed qualitatively.
Heat Transfer to a Mobile Sphere
The experimental observations of Nienow et ai.16 indicate that when flotsam (coal) particles are present in low concentrations and consist of a few large pieces, a circulation pattern is set up due to the slow sinking of the particles in the downward motion in the dense phase and a jerky upward movement provided by short rides in passing bubbles. The average contact time between the emulsion and the mobile particle during its ascent will then be different in comparison with that during its descent in the bed. Consider an 'active' particle of diameter da and density Pa moving freely in a fluidized bed of particles of diameter dp and density pp. The probability that the 'active' particle resides in the emulsion phase during one whole circulation is denoted as p; and that it is in the emulsion during its rise within the bed is denoted as p'. Then,
Emulsion Phase Residence Probabilities: The average rise velocity of the mobile particle is denoted as UR. When associated with the bubble phase, the active particle is assumed to travel upwards at the height averaged bubble velocity Us. When associated with the emulsion phase, the active particle sinks with the emulsion at a velocity Uo (Fig. 1 in Ref. 7). If there are m captures and sheddings of the active particle during its rise to the top, then m(tiUn - tzUo) = X = Un(mtl + mt2)
where X is the penetration depth of the active particle; tl and t2 are the times spent by the particle moving up with the bubble phase during each capture and moving down after being shed, respectively. The total time required for the particle to rise to the top of the bed is given by X/UR. The fraction of this time spent in the emulsion phase is t2(tl + t2). In the downward portion of the circulation, the time spent by the particle in the emulsion phase is X / U o . Consequently,
(X/trR)
(XlVD) + = p'hpc,u + (p - P')hpc,cl + phgc + (1 - p)hbub
(2)
G8 (1)
P=
x/go
+ X/UR
U~ + Uo
(3)
HEAT TRANSFER IN FLUIDIZED BEDS
being obtained using image analysis techniques, will be reported in due course. Thus, the time spent by the active particle during each capture in the bubble phase, tl, is equal to the coalescence time, t~, between bubbles. Using Werther's 2~ expression for t~ in a freely bubbling bed,
(tt~+t2) (X/Un) p' = x/uR + x/uo (UB - UR)Uo (UB + Uo)(UR + Uo)
919
(4)
(Us - Ua) to =
Particle Convective Components:
tl
-
-
f[1/3 U~2/3 (Us - Us) -
(6)
(uo + u~)
The particle convective heat transfer coefficients are considered to involve a contact resistance (modelled by considering conduction from particle to surface through an intervening gas film with an average thickness ~) and an emulsion phase resistance (modelled using the uniform surface renewal theory). From experimental evidence for heat transfer to fixed tubes, ~ = (dp/d~) where 6 < d~ < 10; the success of this simple representation has been analysed by Decker and Glicksman. 19 Then
where fl is the level frequency of bubbles. Since the average contact time between the particle and the emulsion phase during the downward leg of its circulation is X/Uo, dp
"
"/l'X
,o.5,-1
hpr = d~kg + 0"5(UDkePeCpv )
}
Expressions for the gas convective components of the heat transfer are obtained by using the approach described for mass transfer to large particles. 8 Thus in the emulsion phase,
(5)
ke and p~ are the effective thermal conductivity and
kg { k e (l + ReePr)l/3_ l /~ ,l/3 [ q \2/3 ) I ~ -~) ~\~mf - - R e e /I pr 1/3 hgc = ~ 2 -kg + 0.693 (ReePr)l/3
(8)
where Ree(= d~Ue/v) is the emulsion phase Reynolds number. U~ is the flow velocity through the emulsion phase; if attention is confined to Geldart Group B and D powders, then 21 Ue -~ Umf. Co~ is a porosity dependent drag coefficient and q is the tortuosity for the flow of gas through the emulsion
density (Table II), respectively, of the emulsion phase. To estimate t2, it is postulated that a bubble will capture or shed the 'active' particle when it coalesces with other bubbles. This postulate is supported qualitatively by visual observations in a twodimensional bed. Quantitative results, currently
TABLE II Parameters required in the calculation of/~ Parameter
Correlation
Ref.
ke
ke = k~ + O.lp~CvgdvUmf k~ = kg{1 + (1 - eaf)(1 - (kJk,)){(kJkp) + 0.28e~y}-1}
10, 11
-- (o.63(kp/k,) o.ls)
p.(1
p,
-- Emf) + t~mfp~
zq 2
5.3{Emf/(1 - emZ)}~ for eros < 0.5
22
q
{1 - 0.9(1 - emy)2/3 (emf - 0.25)~/3}-~
23
(24/Res)lO §
23, 24
Co, = 0.261Re ~
Co,~
- 0.105Re~; 43~ - 0.124{1 + (log~oRes)Z}-1
(24/ne,){(2z(1 = 0.261Re ~
(7)
Gas Convective Components:
~ 0.5-~ - 1
{ d p + 0 5 ( ~rt2 ~ ~ hp~ ~ = ~ 9 9 \kePefpp f J
(uo + tyR)
-
-
$'mf))/q A- (10' -- 1)}
0.105Re ~
- 0.124(1 + (log~oRe,)~)
23, 24
920
FLUIDIZED BED COMBUSTION
phase of porosity r = F.rnf; expressions for determination of these parameters are given in Table II. It may be noted that the term 2kffkg has been included in the right hand side of Eq. (8). The inclusion of this term removes the discontinuity at infinite dilution (~ ---> 1) in comparison with the approach developed earlier, s Also,
Comparison with Experimental Data: Experimental values of the heat transfer coefficients, 2 for da = 1.5 x 10-2 m, as function of superficial velocity for a wide range of bed particle sizes, are compared with model predictions Eq. (1), in Fig. 1 with the value of ~b = 8 chosen for Eqs. (5) and (7). Inspection of the results indicates that
kg{ (l+Reber)l/a-l(~) ht,~b = daa 2 + 0.693 (Reber)~/3 where Reb (= Utyda/v) is the bubble phase Reynolds number. U t f is bubble throughflow velocity; for Geldart Group B and D powders, Utf = 3Umf.~1 Coa is the isolated sphere drag coefficient based on the bubble phase Reynolds number.
Active Particle Motion and Fluidized Bed Parameters: The average rise velocity, UR, of the active particle and its penetration depth, X, in a bed with expanded height, H, were calculated from 1~ U R = 0 . 1 9 ( U 0 - Urnf) 1/2
x = 1 . 2 H ( U o - U,,,:) 1/~
(U 0
-
-
(11)
Urnf) 0"4
gU5X
9{(n + 4Aol/2)Ls - (H - X + 4Aol/Z)LS} (12) The average bubble velocity is calculated from~ U B ~- (V 0 - Umf ) d- 2 . 2 6 d 1/2
(13)
If the wake fraction associated with the bubbles is et and ~, is the bubble fraction, then 9 UD =
ac~Us Uo- Umy where ~b = 1 - ~b - et~b UB + 2Umf
(14)
The average level frequency of bubbles, fl, is obtained from integration of the correlation proposed by Werthe~ ~ as
fz =
} (Reb)z/a Pr 1/3
(9)
the model is in very good agreement with experimental data; the maximum deviation being about 15%. It is interesting to note that the model predicts that the heat transfer coefficient should keep increasing with increase in superficial velocity be~ yond the experimental range employed by Prins for all particle sizes. This trend is more evident for smaller bed particles. The rate of increase does change, and beyond a certain superficial velocity the dependence of/~ on Uo is small; however, the model does not predict a peak in the heat transfer coefficient.
(10)
The active particle circulates between heights within the bed of (H--X) and H; it is then more appropriate to use fluidized bed parameters averaged over this region. Using the expression proposed by Darton et al.Y
aB =0.3
u3
Combustion of Coke Particle The combustion of an isothermal 'active" carbonaceous particle of diameter da is assumed to proceed with the formation of a shrinking unreacted core of diameter de. Reaction is considered to occur only at the external surface of the carbonaceous core. For petroleum coke (no significant amount of ash), combustion progresses with a decrease in the diameter of the particle, that is, da = dc. For char particles, the ash layer may remain intact (da # dc); or, depending on the mechanical agitation provided by the bed particles, it may be knocked off and hence (da = tic).
Combustion Without an Ash Layer: Assuming haft-order reaction 17"18 between oxygen and carbon, the rate of consumption of carbon can be written in terms of the surface reaction or the rate of diffusion through the gas film as:
"~" CAs ~ = ~rd~Ko(CAg CAs) (16) - dmc d--T= 'rract*,c Manipulation of Eq. 16 leads to
0.0195(2H - X) + 0.57 } (0.039H + 0.57) 2 + {0.039(H - X) + 0.57}2 104
(15)
HEAT TRANSFER IN FLUIDIZED BEDS
921
800
and ~2 \da/ G
(20)
A similar expression has been obtained by Shen and Smith ~s for first-order kinetics. The particle shrinkage equation can then be solved simultaneously with the energy balance equation as in the previous case.
v
9~ 400
Surface Reaction: t-"
The surface reaction coefficient, Kc, is expressed in the Arrhenius form
Kc = ko exp(-Ea/RTp) 0.2
0.4
0.8
0.6
Uo, m/s FIG. 1. Comparison of model predictions with experimental data of Prins 2 for da = 15 mm and T~ = 573 K. O d, = 0.131 mm, 9 d r = 0.46 mm, + d~ = 1.01 mm, - model prediction.
(21)
where EA is the activation energy and ko is the preexponential factor. Following Young and Smith 17 and Rybak et al., I8 computations were performed using half-order kinetics; the parameters used are EA = 82400 kJ kmol -I and ko = 70.45 kg m -2 s -I atm 1/2 for MiUmerran char. 18
Mass Transfer: Following Field et al. 4
2
d(dc) - - -
2 0.5
{ - I ~ + (K~ + 4cAgrcKo)
}
=
Ko = 12(ShOa/da) ~/(R'Tf)
(17)
dt
(22)
peKD
The energy balance for the burning carbonaceous particle can be written as:
where ~ is the mechanism factor which takes the value of 1 for CO2 production and 2 for CO production. Tf is the film temperature, Tf = (T~ + Tb)/2. The Sherwood number for the freely moving particle was estimated from s
dTp 2 0.5 ('tr/6)d3aPaCpa ~ = 7rd~H~KcCa,
kmdo
Sh = - - ~rd~(h(Tp - Tb) § O's
- ~b))
Combustion with an Ash Layer:
= pShe + (1 - p)Shb
Shb = {2 + 0.693
In fluidizing conditions characterised by small bed particles and low fluidizing velocity, ash has been 9 27 observed to remain mtact. In such a case the overall rate of combustion reaction is influenced by the external mass transport, diffusion through the ash layer, and surface reaction resistances. Assuming steady-state diffusion of oxygen through the ash layer, it can be shown that
,t(&) -- {[(~1 q- ~2) 2 "4- 4CAg] 0"5 -- (~1 "4- 132)} dt 9 (t:C /p~)
(19)
where
R'TvKcdc
DA
(18)
1-
/C
She
(1 + RebSC)I/s - 1
RebSC)1/s
\1is
"IV)
(23a)
)
(aeb)2'3Scl'3~
(ZSb)
= ~2 DA.e + ReeSc) 1/3- 1 [ DA + 0.693(1 (ne,Sc) 1Is [ q
\2/s Scl/S}
\s
/
(23c)
where the effective mass diffusivity, DA,e, is related to the mass diffusivity, DA, according to ~ DA,e = (~my/q2)DA. The inclusion of the 2DA,e/DA term in Eq. (23e), in line with the 2ke/kg term in Eq. (8), removes the discontinuity at infinite dilution (e 1) in comparison with the approach developed earlier. s
922
FLUIDIZED BED COMBUSTION
C0/C02 Product Ratio:
soo
According to the two-film theory, 4 CO burns outside the boundary layer for small particles up to about 0.1 mm diameter and the CO/CO2 ratio at the particle surface becomes infinitely large (mechanism factor = 2). However, for particles larger than about 1 mm CO oxidation takes place close to the surface and the CO/CO2 ratio approaches zero (mechanism factor = 1). The mechanism factor, ~, is defined in terms of the CO/CO2 product ratio, f~, as:
v
"~ 200
I,m~.'
~I-Ul 100 i.)
= (1 + 2f~)/(1 + f~)
(24)
Recently, Prins 2 has determined experimentally values of CO/CO2 mole flux at the surface of single graphite spheres (3 < da < 13 mm) burning in a fluidized bed at 1110 K and 20% 02. The values ranged from 0.17 to 0.5; the recommended average value of 0.3(~ = 1.2) has been used in the present calculations. The heat generated by the reaction depends on whether CO or CO2 is produced and is expressed 4 as: Ur = 33054(2/~ - 1) + 9791(2 - 2/~)
The temperature histories of the burning particles were calculated by numerical integration of Eq. (17) and (18) for the no ash case and Eq. (18) and (19) for combustion with an ash layer. The bed was assumed to be made up of sand (dp = lxl0 -3 m, pp = 2500 kg m -3, Cpp = 0.798 kJ kg -1 K -1, kp = 0.3288 Wm -1 K -i) and fluidized with air at an operating temperature of Tb = 1123 K. The minimum fluidization velocity was calculatedz3 from
o
400 800 1200 1600 2000 Time, s
FIG. 2. Predicted temperature histories of a 10 mm petroleum coke particle using heat transfer correlations of a: Prins 2, b: This paper., e: Ross and DavidsonTM (Sh from Eq. (23a)), d: Tamarin et al, ~3 e: Baskakov et al, TM Ross and DavidsonTM (Sh = 3.5).
for all particle sizes. The correlation of Tamarin et al. 13 is not in good agreement with the other correlations towards the final stages of burn-out. The same information can be deduced, albeit qualitatively, from Fig. 3 where the calculated heat transfer coefficients are plotted as a function of the coke particle diameter. The maximum difference of about
12[
(26)
~- 1000I ~d
as 0.38 ms-i; the superficial velocity was assumed to be 1 ms -1. The specific heats of coke and char Cpa were taken as 1.7 kJ kg -1 K-1 and 1.53 kJ kg- l K-1 respectively. A wide range of carbon particle size relevant to FBC was investigated. The correlation of Ross and Davidson12 was studied using a constant Nu/Sh ratio and two different Sherwood numbers. Results for a 10 mm petroleum coke particle, in terms of the excess temperature (Tp - T#,) are plotted in Fig. 2 for heat transfer coefficients calculated using the present model and the correlations in Table I. The correlation of Parchenok and Tamarin14 was not used since the Archimedes number for the conditions simulated was out of the range of the correlation. From these plots, the correlations of Baskakov et al., z5 Prins,ZRoss and Davidsonm (Sh from Eq. (23a)), and the model yield comparable results
\
-
42.81
o
(25)
Particle Temperature Histories:
Remf = tv/(42.81) 2 + 0.061Ar
~j
~ 3=
800
1
~t~e~q
600
200
0
~0
0 ~
Coke
diometer,
20
mm
FIG. 3. Comparison of heat transfer correlations for freely moving active particle in a gas fluidized bed of sand. a: Prins 2, b: This paper, c: Ross and Davidson, 12 d: Tamarin et al, 13 e: Baskakov et al. 15
HEAT TRANSFER IN FLUIDIZED BEDS 100 W m -2 K -1 between the model, Baskakov et al. 15 and Prinsa leads to a maximum difference of 50 K in the calculated temperature of the coke particle. The Ross and Davidson correlations (Sh = 3.5 and 7.0) show that at a constant Nu/Sh ratio, maximum temperature rise is constant for a given particle size and burn-out time is influenced by the rate of mass transfer. In Fig. 4, sample calculations for a 5 mm Millmerran char particle for the case when the ash layer is stripped off (curve h) are compared with the results when the ash layer remains intact (curve a). If the ash layer is shaken off the char particle by the impact of the bed particles, the particle temperature increases gradually at first and then peaks just before burn-out. In this case, the stripped ash on bed particles may lead to agglomeration and defluidization. On the other hand, if the ash remains intact around the char particle, the oxygen concentration at the core (reaction) surface will decrease whilst heat transfer coefficient remains unchanged, leading to gradually decreasing particle temperatures. The heat transfer model predicts that the coke (or char) particle will encounter rapidly varying external heat transfer conditions. For the experimental conditions simulated, the particle circulation time is - 3 s, whereas the burn-out time is much longer. Consequently, the use of the average heat transfer coefficient in the calculation of the particle temperature is justified at least for laboratory scale experiments where individual particles are inserted within the bed. The situation will become more
9~
923
complex for continuous or batch operation where, as current evidence3~ indicates, the bubble phase is richer in oxygen in comparison with the emulsion phase. Higher combustion rates and lower heat transfer coefficients when the char particle is associated with the bubble phase may lead to much higher instantaneous particle temperatures. These results underline the necessity for careful experimentation and data interpretation in the measurement of coke particle temperatures in fluidized beds. The thermocouple technique~l may not be adequate since it may impose restrictions on particle movement. Further, ash retention on the char surface may also be effected. Fiber-optic measurement methods remove restrictions on particle movementY 'as However, monitoring the temperature history of a single particle is difficult, and frequently a batch of particles is charged into the bed. For an actual coal particle, the phenomena of drying and devolatilization may also require consideration. External heat transfer is a dominant rate limiting mechanism for these phenomena. 34-36 Drying, ignition (heterogeneous: on the char surface; or homogeneous: of the volatiles) and devolatilization occur over shorter durations in comparison with char combustion. These events, with time frames of the order of the circulation time, could be affected significantly by the variations in the heat transfer coefficient predicted by the model; further experiment and analysis are required.
Conclusions A mechanistic model for heat transfer to a freely moving active particle in a bed of smaller, denser particles has been developed. The model predictions for the average heat transfer coefficient compare well with direct measurements reported in the literature. The average heat transfer coefficient has also been used, in conjunction with a shrinking core formulation, to predict the temperature histories of burning coke and char particles in fluidized beds. The model predicts that the coke and the ashstripped char particles undergo rapid variations in the external heat transfer environment, The implications of these variations in continuous/batch operation and for drying, devolatilization and ignition need further examination.
300
200
=E t.-(/} 100
9
|
1 O0
200
i
Nomenclature
300
Time, s F]c. 4. Temperature profiles of a 5 mm Millmerran char particle using heat transfer correlation of this paper, a: particle burns with ash layer, b: particle burns without ash layer.
Ao Ar Cas
area of multi-orifice distributor per hole, m ~ (= gd~pg(pp - pg)/ix2), Archimedes number based on bed particle diameter partial pressure of diffusing species at the particle surface, atm
924 d Cd~
C&a Cp CAg
dB DA DA.e De EA
fl fr g g h~b h,o 9hinax hpc, u
h~c.d H Hr ke ko kp km Kc
KD m
mc
Mo p p'
Pr q R R'
Re~,
FLUIDIZED BED COMBUSTION particle diameter, m isolated sphere drag coefficient based on the bubble phase Reynolds number porosity dependent drag coefficient for the active particle, Table II specific heat, kJ kg-1 K-I partial pressure of diffusing species in the bulk, atm average bubble diameter, m mass diffusivity, m 2 s -1 effective mass diffusivity of the emulsion phase, m ~ s -1 effective mass diffusivity of the ash layer, m 2 s -1 activation energy, kJ kmo1-1 average level frequency of bubbles in a freely bubbling bed, m -z s -1 CO/CO2 product ratio acceleration due to gravity, m s -2 average heat transfer coefficient, W m -2 K -I heat transfer coefficient in the bubble, W m -2 K-1 gas convective heat transfer coefficient for the emulsion, W m -~ K -1 maximum average heat transfer coefficient for the emulsion, W m -~ K -1 particle convective heat transfer coefficient when the 'active' particle rises during its circulation, W m -~ K -1 particle convective heat transfer coefficient when the 'active' particle moves down during its circulation, W m -2 K -1 expanded bed height, m heat of reaction, kJ kg -1 effective thermal conductivity of the emulsion, W m -1 K -1 pre-exponential factor, kg m - 2 s- 1 atm -1/2 thermal conductivity, W m -I K -1 mass transfer coefficient, m s-1 chemical rate constant for carbon-oxygen reaction, kg m -2 s -1 atm -I/2 external mass transfer coefficient, kg m -2 S - 1 atm number of times the 'active' particle is captured or shed while it rises during one circulation mass of carbon particle, kg molecular weight of oxygen, kg kmo1-1 probability of the 'active' particle residing in the emulsion phase during one circulation probability of the 'active' particle residing in the emulsion phase while it rises during one circulation Prandtl number tortuosity Universal Gas Constant, kJ kmo1-1 K -I Universal Gas Constant, m a atm kmo1-1 K -1 (= 3Utfda/v), bubble phase Reynolds number
Ree
Ueda/v), emulsion phase Reynolds num-
(=
ber
Remf (= Umfda/v), Reynolds number at miniSc Sh t tl t2 te Tb Tf Tp UB
Uo Un Uo
Ue Umf Utf X z
mum fluidization Schmidt number (= kmda/Da), Sherwood number time, s duration of bubble capture, s duration between bubble shed and the next bubble capture, s bubble coalescence time, s bed temperature, K film temperature, K coke particle temperature, K average bubble velocity, m s -1 average descent velocity of the 'active'lpartiele with the emulsion phase, m saverage rise velocity of the 'active' particle, m s -1 superficial gas velocity, m s -1 flow velocity through the emulsion phase, m s-1 minimum fluidization velocity, m s -1 bubble throughflow velocity, m s -1 penetration depth of the 'active' particle in the bed, m cross-section factor
Greek Symbols a 8 9 9
9 9 IJ' v ~b P Or
wake fraction gas film thickness, m porosity bubble fraction voidage at minimum fluidization, voidage of the emulsion phase particle emmissivity fluid viscosity, Pa s kinematic viscosity, m 2 s -1 parameter in eq (5) and (7), dimensionless density, kg m -a Stefan-Boltzmann constant, kJ m -2 s -1 K -a mechanism factor
Subscripts a g p
'active' or coke particle fluidizing gas "inert' or bed particle
Acknowledgments This work is dedicated to the memory of Professor William E. Genetti. PKA gratefully acknowledges financial support from the Australian Research Council and the South Australian Government (through the State Energy Research Advisory Committee) for projects of which this investigation is part. TML thanks the University of Adelaide for a postgraduate scholarship. The authors also thank Dr. R.
HEAT TRANSFER IN F L U I D I Z E D BEDS D. LaNauze for continued support mad helpful discussions.
REFERENCES 1. LA NAUZE, R. D.: Chem. Eng. Res. Des. 63, 3 (1985). 2. PmNS, W. : Fluidized bed combustion of a single carbon paraticle, P h D thesis, Twente University, the Netherlands (1987). 3. MANZOORI, A. R., AGARWAL, P. K. AND LINDNER, E. R.: Tenth International Conference on Fluidized Bed Combustion, San Francisco, p. 1034, 1989. 4. FIELD, M. A., GILL, D. W., MORGAN, B. B. AND HAWKSLEY, P. G. W.: BCURA Leatherhead, 186 (1967). 5. LINJEWlLE, T. M.: P h D thesis, University of Adelaide, (Under preparation). 6. AGABWAL, P. K. AND LA NAUZE, R. D.: Chem. Eng. Res. Des. (1989, in press). 7. AGARWAL, P. K.: Chem. Engng. Sci. 42, 2481 (1987). 8. AGARWAL, P. K., MITCHELL, W. J. AND LA NAUZE, R. D.: Twenty-Second Symposium (International) on Combustion, p. 279, The Combustion Institute, 1989. 9. KUNII, D. AND LEVENSPIEL, O.: Fluidization Engineering, John Wiley, 1969. 10. GELPEmN, N. I. AND EINSTEIN, V. G.: Fluidization (J. F. Davidson and D. Harrison, Eds), p. 471, Academic Press, 1971. 11. XAVIER, A. M. AND DAVIDSON, J. F.: AIChE Symp. Ser. 208, 77, 368 (1981). 12. Ross, I. B. AND DAVIDSON, J. F.: Trans. IChemE 59, 108 (1981). 13. TAMARIN, A. I., GALERSHTEIN, D. M. AND SHUKLINA, V. M.: J. Eng. Phys. 42, 14 (1982). 14. PAL'CHENOK, G. I. AND TAMARIN, A. I.: J. Eng. Phys. 45, 427 (1983). 15. BASKAKOV,A. P., FILIPPOVSKI, N. F., MUNTS, V. A. AND ASrlIKHMIN, A. A.: J. Eng. Phys. 52, 574 (1987). 16. NIENOW, A. W., ROWE, P. N. AND CHIBA, T.: AIChE Syrup. Ser. 176, 74, 45 (1978).
925
17. YOUNG, B. C. AND SMITH, I. W.: Eighteenth Symposium (International) on Combustion, p. 1249, The Combustion Institute, 1981. 18. RYBAK, W., ZEMBRUSKI, M. AND SMITH, I. W.: Twenty-first Symposium (International) on Combustion, p. 231, The Combustion Institute, 1986. 19. DECKER, N. A. AND GLICKSMAN, L. R,: AIChE Symp. Ser. 208, 77, 341 (1981). 20. WERTHER, J.: Fluidization Technology (D. L. Keairns, Ed.), p. 215, Hemisphere, 1975. 21. VALENZUELA,J, A. AND GLICKSMAN, L. R.: Powder Tech. 44, 103 (1985). 22. ANDEBSSON, K, E. B.: Trans. R. Instn. Teeh. Stockholm No 201, (1963). 23. AGARWAL, P. K. AND O'NEILL, B. K.: Chem. Eng. Sci. 43, 2487 (1988). 24. FLEMMER, R. L. C. AND BANKS, C. L.: Powder Tech. 48, 217 (1986). 25. DARTON, R. C., LA NAUZE, R. D., DAVIDSON, J. F. AND HARRISON, D.: Trans. I Chem. E 55, 274 (1977). 26. DAVIDSON, J. F. AND HARRISON, D.: Fluidised Particles, Cambridge University Press, 1963. 27. ANDREI, M. A., SAROFIM, A. F., AND BEER, J. M.: Comb. Flame 61, 17 (1985). 28. SHEN, J. AND SMITH, J. M.: I & EC Fundamentals 4, 293 (1965). 29. EPSTEIN, N.: Chem. Eng. Sci. 44, 777 (1989). 30. MINCHENER, A. J. AND STaINGER, J.: J. Inst. Energy, 240 (1981). 31. LA NAUZE, R. D. AND JUNG, K.: Seventh In, ternational Conference on Fluidized Bed Combustion, Philadelphia, p. 1040, 1983. 32. MACEK, A. AND BUL1K, C.: Twentieth Symposium (International) on Combustion, p. 1223, The Combustion Institute, 1985. 33. LA NAUZE, R. D., JUNG, K., DENT, D. C., JOYCE, T., TAIT, P. J. AND BURGESS, J. M.: Ninth International Conference on Fluidized Bed Combustion, Boston, p. 707, 1987. 34. BOBGHI, G., SAROFIM, A. F. AND BEI~R, J. M.: Comb. Flame 61, 1 (1985). 35. AG~mWAL, P. K.: Fuel 65, 893 (1986). 36. PmNS, W., SIEMONS, R., VAN SwAMJ, W. P. M. AND RADOVANOVIC, M.: Comb. Flame 75, 57 (1989).
HEAT T R A N S F E R BEHAVIOUR A N D T E M P E R A T U R E S OF FREELY MOVING B U R N I N G C A R B O N A C E O U S PARTICLES IN F L U I D I Z E D B E D S TEMI M. LINJEWILE AND PRADEEP K. AGARWAL Department of Chemical Engineering University of Adelaide GPO Box 498, SA 5001 Australia
In fluidized bed combustion, relatively few large coal particles are fluidized along with more dense and smaller sulphur-sorbent bed particles. Predictions for drying, ignition and devolatilization, as well as particle temperatures during char combustion, require knowledge of external heat transfer coefficients. Several studies have dealt with mass transfer for freely moving large particles in fluidized beds; heat transfer to immobile tubes has also received wide research attention. Very few studies have dealt with heat transfer to freely moving large particles in fluidized beds and the correlations available are, at best, semi-empirical. In this paper a mechanistie model for heat transfer is proposed which takes into account the movement of the active particle within the bed. The average heat transfer coefficients predicted by the model are in good agreement with direct measurements reported in the literature. The average heat transfer coefficients are then used, in conjunction with a shrinking core formulation, to predict the temperature histories of burning coke and char particles. The model predicts that the coke and char particles experience rapidly changing external heat transfer conditions. In the case of the char particles the presence or absence of the ash layer will infuence the temperature history. The implication of these variations on the temperature histories in batch/continuous operation and for drying, ignition and devolatilization require further consideration, Introduction
few studies have considered heat transfer to a freely moving sphere in a fluidized bed. The empirical and semi-empirical correlations in the literature, Table I, attempt to predict only the maximum average heat transfer coefficient, hmax; neglecting the effect of superficial velocity on the average heat transfer coefficient, h. Further, the verification of most of these correlations has been indirect, that is, from measurements (with substantial scatter) of the temperatures of burning carbon particles. Clearly, such comparisons would necessitate assumptions regarding the CO/CO2 product ratio, chemical kinetics and mass transfer behaviour. In this paper, a mechanistic model for heat transfer to mobile spheres, including details Of active particle motion based on experimental observations of Nienow et al., 16 is proposed. The model predictions are compared with direct measurements of average heat transfer coefficients. 2 Using the mass transfer formulation reported at the previous Symposium, s CO/C02 product ratio from recent experimental evidence of Prins z and half-order kinetics17A8 for the carbon oxygen reaction, simplified mass and energy conservation equations are solved numerically to predict the temperature of
In fluidized bed combustion (FBC), relatively few coal particles are fluidized with denser and smaller sulphur-sorbent bed particles. The temperature of burning particles exceeds that of the bed. Prediction of the excess temperature is important not only for modelling FBC behaviour of the carbonaceous particles1"2 but also for assessing ash fusion. 3 Mathematical models for the combustion of carbonaceous particles, employing the shrinking unreacted core formulation, a are abundant in the literature. Major factors that influence particle temperature are refleeted in the estimation of the relevant heat and mass transfer coefficients, CO/CO2 product ratio and the kinetics of the carbon reaction. However, literature review reveals that existing FBC models have employed conflicting assumptions regarding Sherwood and Nusselt numbers and the CO/CO2 product ratios. 5 Several studies have now been reported on the external mass transfer behaviour for large freely moving "active' particles in fluidized beds. ~8 Heat transfer to tubes immersed in fluidized beds has also received wide research attention. 9-n However, very 917
918
FLUIDIZED BED COMBUSTION TABLE I Correlations for heat transfer to large mobile 3articles in fluidized beds Ref.
Correlation
Remarks
12
(hda)/k, = (k~d~)/(DA~f)
based on the argument that bed particles hinder mass transfer but assist heat transfer
13
(hdo)/k , = 5Ar ~176 ( d J d 2 ~
the equations apply for 1.4 x 103 < Ar < 4 x 10'; 2.3 < (d~/do) < 14
14
/~,,,~ = (kJd,){O.41ArO3 (d,/d,)O.2 (pp/po)-o.oT}
the equations apply for 1.55 x 10s < Ar < 2.2 x 10 7, 0.074 < dr/ d= < 1.21, 0.44 < Po/Pa < 2.07; for non-spherical 'active' particles, a sphericity correction factor has to be employed
15
= h, + (h2 -
h,) exp{-d,/(4do)}
h, = (kg/dp)(O.S5Ar ~
+ O.O06Ar~ Pr '/a)
the equations apply for (d,/do) > 1; additional equations were proposed for (do/do) < 1
hz = (kg/d,){lO + 0.23(ArPr) '/3} h~
= ( k J do)(3.539Ar" f r)(dJ do) -~
the equations apply for 10 < Ar < 20000 and 3 < (da/dp) < 200
n = O.105(da/do) ~176 f r = 0.844 + 0,0756(Tb/273)
freely moving carbonaceous (coke or char) particles in bubbling fluidized beds. Other implications of the heat transfer model on FBC of coal are discussed qualitatively.
Heat Transfer to a Mobile Sphere
The experimental observations of Nienow et ai.16 indicate that when flotsam (coal) particles are present in low concentrations and consist of a few large pieces, a circulation pattern is set up due to the slow sinking of the particles in the downward motion in the dense phase and a jerky upward movement provided by short rides in passing bubbles. The average contact time between the emulsion and the mobile particle during its ascent will then be different in comparison with that during its descent in the bed. Consider an 'active' particle of diameter da and density Pa moving freely in a fluidized bed of particles of diameter dp and density pp. The probability that the 'active' particle resides in the emulsion phase during one whole circulation is denoted as p; and that it is in the emulsion during its rise within the bed is denoted as p'. Then,
Emulsion Phase Residence Probabilities: The average rise velocity of the mobile particle is denoted as UR. When associated with the bubble phase, the active particle is assumed to travel upwards at the height averaged bubble velocity Us. When associated with the emulsion phase, the active particle sinks with the emulsion at a velocity Uo (Fig. 1 in Ref. 7). If there are m captures and sheddings of the active particle during its rise to the top, then m(tiUn - tzUo) = X = Un(mtl + mt2)
where X is the penetration depth of the active particle; tl and t2 are the times spent by the particle moving up with the bubble phase during each capture and moving down after being shed, respectively. The total time required for the particle to rise to the top of the bed is given by X/UR. The fraction of this time spent in the emulsion phase is t2(tl + t2). In the downward portion of the circulation, the time spent by the particle in the emulsion phase is X / U o . Consequently,
(X/trR)
(XlVD) + = p'hpc,u + (p - P')hpc,cl + phgc + (1 - p)hbub
(2)
G8 (1)
P=
x/go
+ X/UR
U~ + Uo
(3)
HEAT TRANSFER IN FLUIDIZED BEDS
being obtained using image analysis techniques, will be reported in due course. Thus, the time spent by the active particle during each capture in the bubble phase, tl, is equal to the coalescence time, t~, between bubbles. Using Werther's 2~ expression for t~ in a freely bubbling bed,
(tt~+t2) (X/Un) p' = x/uR + x/uo (UB - UR)Uo (UB + Uo)(UR + Uo)
919
(4)
(Us - Ua) to =
Particle Convective Components:
tl
-
-
f[1/3 U~2/3 (Us - Us) -
(6)
(uo + u~)
The particle convective heat transfer coefficients are considered to involve a contact resistance (modelled by considering conduction from particle to surface through an intervening gas film with an average thickness ~) and an emulsion phase resistance (modelled using the uniform surface renewal theory). From experimental evidence for heat transfer to fixed tubes, ~ = (dp/d~) where 6 < d~ < 10; the success of this simple representation has been analysed by Decker and Glicksman. 19 Then
where fl is the level frequency of bubbles. Since the average contact time between the particle and the emulsion phase during the downward leg of its circulation is X/Uo, dp
"
"/l'X
,o.5,-1
hpr = d~kg + 0"5(UDkePeCpv )
}
Expressions for the gas convective components of the heat transfer are obtained by using the approach described for mass transfer to large particles. 8 Thus in the emulsion phase,
(5)
ke and p~ are the effective thermal conductivity and
kg { k e (l + ReePr)l/3_ l /~ ,l/3 [ q \2/3 ) I ~ -~) ~\~mf - - R e e /I pr 1/3 hgc = ~ 2 -kg + 0.693 (ReePr)l/3
(8)
where Ree(= d~Ue/v) is the emulsion phase Reynolds number. U~ is the flow velocity through the emulsion phase; if attention is confined to Geldart Group B and D powders, then 21 Ue -~ Umf. Co~ is a porosity dependent drag coefficient and q is the tortuosity for the flow of gas through the emulsion
density (Table II), respectively, of the emulsion phase. To estimate t2, it is postulated that a bubble will capture or shed the 'active' particle when it coalesces with other bubbles. This postulate is supported qualitatively by visual observations in a twodimensional bed. Quantitative results, currently
TABLE II Parameters required in the calculation of/~ Parameter
Correlation
Ref.
ke
ke = k~ + O.lp~CvgdvUmf k~ = kg{1 + (1 - eaf)(1 - (kJk,)){(kJkp) + 0.28e~y}-1}
10, 11
-- (o.63(kp/k,) o.ls)
p.(1
p,
-- Emf) + t~mfp~
zq 2
5.3{Emf/(1 - emZ)}~ for eros < 0.5
22
q
{1 - 0.9(1 - emy)2/3 (emf - 0.25)~/3}-~
23
(24/Res)lO §
23, 24
Co, = 0.261Re ~
Co,~
- 0.105Re~; 43~ - 0.124{1 + (log~oRes)Z}-1
(24/ne,){(2z(1 = 0.261Re ~
(7)
Gas Convective Components:
~ 0.5-~ - 1
{ d p + 0 5 ( ~rt2 ~ ~ hp~ ~ = ~ 9 9 \kePefpp f J
(uo + tyR)
-
-
$'mf))/q A- (10' -- 1)}
0.105Re ~
- 0.124(1 + (log~oRe,)~)
23, 24
920
FLUIDIZED BED COMBUSTION
phase of porosity r = F.rnf; expressions for determination of these parameters are given in Table II. It may be noted that the term 2kffkg has been included in the right hand side of Eq. (8). The inclusion of this term removes the discontinuity at infinite dilution (~ ---> 1) in comparison with the approach developed earlier, s Also,
Comparison with Experimental Data: Experimental values of the heat transfer coefficients, 2 for da = 1.5 x 10-2 m, as function of superficial velocity for a wide range of bed particle sizes, are compared with model predictions Eq. (1), in Fig. 1 with the value of ~b = 8 chosen for Eqs. (5) and (7). Inspection of the results indicates that
kg{ (l+Reber)l/a-l(~) ht,~b = daa 2 + 0.693 (Reber)~/3 where Reb (= Utyda/v) is the bubble phase Reynolds number. U t f is bubble throughflow velocity; for Geldart Group B and D powders, Utf = 3Umf.~1 Coa is the isolated sphere drag coefficient based on the bubble phase Reynolds number.
Active Particle Motion and Fluidized Bed Parameters: The average rise velocity, UR, of the active particle and its penetration depth, X, in a bed with expanded height, H, were calculated from 1~ U R = 0 . 1 9 ( U 0 - Urnf) 1/2
x = 1 . 2 H ( U o - U,,,:) 1/~
(U 0
-
-
(11)
Urnf) 0"4
gU5X
9{(n + 4Aol/2)Ls - (H - X + 4Aol/Z)LS} (12) The average bubble velocity is calculated from~ U B ~- (V 0 - Umf ) d- 2 . 2 6 d 1/2
(13)
If the wake fraction associated with the bubbles is et and ~, is the bubble fraction, then 9 UD =
ac~Us Uo- Umy where ~b = 1 - ~b - et~b UB + 2Umf
(14)
The average level frequency of bubbles, fl, is obtained from integration of the correlation proposed by Werthe~ ~ as
fz =
} (Reb)z/a Pr 1/3
(9)
the model is in very good agreement with experimental data; the maximum deviation being about 15%. It is interesting to note that the model predicts that the heat transfer coefficient should keep increasing with increase in superficial velocity be~ yond the experimental range employed by Prins for all particle sizes. This trend is more evident for smaller bed particles. The rate of increase does change, and beyond a certain superficial velocity the dependence of/~ on Uo is small; however, the model does not predict a peak in the heat transfer coefficient.
(10)
The active particle circulates between heights within the bed of (H--X) and H; it is then more appropriate to use fluidized bed parameters averaged over this region. Using the expression proposed by Darton et al.Y
aB =0.3
u3
Combustion of Coke Particle The combustion of an isothermal 'active" carbonaceous particle of diameter da is assumed to proceed with the formation of a shrinking unreacted core of diameter de. Reaction is considered to occur only at the external surface of the carbonaceous core. For petroleum coke (no significant amount of ash), combustion progresses with a decrease in the diameter of the particle, that is, da = dc. For char particles, the ash layer may remain intact (da # dc); or, depending on the mechanical agitation provided by the bed particles, it may be knocked off and hence (da = tic).
Combustion Without an Ash Layer: Assuming haft-order reaction 17"18 between oxygen and carbon, the rate of consumption of carbon can be written in terms of the surface reaction or the rate of diffusion through the gas film as:
"~" CAs ~ = ~rd~Ko(CAg CAs) (16) - dmc d--T= 'rract*,c Manipulation of Eq. 16 leads to
0.0195(2H - X) + 0.57 } (0.039H + 0.57) 2 + {0.039(H - X) + 0.57}2 104
(15)
HEAT TRANSFER IN FLUIDIZED BEDS
921
800
and ~2 \da/ G
(20)
A similar expression has been obtained by Shen and Smith ~s for first-order kinetics. The particle shrinkage equation can then be solved simultaneously with the energy balance equation as in the previous case.
v
9~ 400
Surface Reaction: t-"
The surface reaction coefficient, Kc, is expressed in the Arrhenius form
Kc = ko exp(-Ea/RTp) 0.2
0.4
0.8
0.6
Uo, m/s FIG. 1. Comparison of model predictions with experimental data of Prins 2 for da = 15 mm and T~ = 573 K. O d, = 0.131 mm, 9 d r = 0.46 mm, + d~ = 1.01 mm, - model prediction.
(21)
where EA is the activation energy and ko is the preexponential factor. Following Young and Smith 17 and Rybak et al., I8 computations were performed using half-order kinetics; the parameters used are EA = 82400 kJ kmol -I and ko = 70.45 kg m -2 s -I atm 1/2 for MiUmerran char. 18
Mass Transfer: Following Field et al. 4
2
d(dc) - - -
2 0.5
{ - I ~ + (K~ + 4cAgrcKo)
}
=
Ko = 12(ShOa/da) ~/(R'Tf)
(17)
dt
(22)
peKD
The energy balance for the burning carbonaceous particle can be written as:
where ~ is the mechanism factor which takes the value of 1 for CO2 production and 2 for CO production. Tf is the film temperature, Tf = (T~ + Tb)/2. The Sherwood number for the freely moving particle was estimated from s
dTp 2 0.5 ('tr/6)d3aPaCpa ~ = 7rd~H~KcCa,
kmdo
Sh = - - ~rd~(h(Tp - Tb) § O's
- ~b))
Combustion with an Ash Layer:
= pShe + (1 - p)Shb
Shb = {2 + 0.693
In fluidizing conditions characterised by small bed particles and low fluidizing velocity, ash has been 9 27 observed to remain mtact. In such a case the overall rate of combustion reaction is influenced by the external mass transport, diffusion through the ash layer, and surface reaction resistances. Assuming steady-state diffusion of oxygen through the ash layer, it can be shown that
,t(&) -- {[(~1 q- ~2) 2 "4- 4CAg] 0"5 -- (~1 "4- 132)} dt 9 (t:C /p~)
(19)
where
R'TvKcdc
DA
(18)
1-
/C
She
(1 + RebSC)I/s - 1
RebSC)1/s
\1is
"IV)
(23a)
)
(aeb)2'3Scl'3~
(ZSb)
= ~2 DA.e + ReeSc) 1/3- 1 [ DA + 0.693(1 (ne,Sc) 1Is [ q
\2/s Scl/S}
\s
/
(23c)
where the effective mass diffusivity, DA,e, is related to the mass diffusivity, DA, according to ~ DA,e = (~my/q2)DA. The inclusion of the 2DA,e/DA term in Eq. (23e), in line with the 2ke/kg term in Eq. (8), removes the discontinuity at infinite dilution (e 1) in comparison with the approach developed earlier. s
922
FLUIDIZED BED COMBUSTION
C0/C02 Product Ratio:
soo
According to the two-film theory, 4 CO burns outside the boundary layer for small particles up to about 0.1 mm diameter and the CO/CO2 ratio at the particle surface becomes infinitely large (mechanism factor = 2). However, for particles larger than about 1 mm CO oxidation takes place close to the surface and the CO/CO2 ratio approaches zero (mechanism factor = 1). The mechanism factor, ~, is defined in terms of the CO/CO2 product ratio, f~, as:
v
"~ 200
I,m~.'
~I-Ul 100 i.)
= (1 + 2f~)/(1 + f~)
(24)
Recently, Prins 2 has determined experimentally values of CO/CO2 mole flux at the surface of single graphite spheres (3 < da < 13 mm) burning in a fluidized bed at 1110 K and 20% 02. The values ranged from 0.17 to 0.5; the recommended average value of 0.3(~ = 1.2) has been used in the present calculations. The heat generated by the reaction depends on whether CO or CO2 is produced and is expressed 4 as: Ur = 33054(2/~ - 1) + 9791(2 - 2/~)
The temperature histories of the burning particles were calculated by numerical integration of Eq. (17) and (18) for the no ash case and Eq. (18) and (19) for combustion with an ash layer. The bed was assumed to be made up of sand (dp = lxl0 -3 m, pp = 2500 kg m -3, Cpp = 0.798 kJ kg -1 K -1, kp = 0.3288 Wm -1 K -i) and fluidized with air at an operating temperature of Tb = 1123 K. The minimum fluidization velocity was calculatedz3 from
o
400 800 1200 1600 2000 Time, s
FIG. 2. Predicted temperature histories of a 10 mm petroleum coke particle using heat transfer correlations of a: Prins 2, b: This paper., e: Ross and DavidsonTM (Sh from Eq. (23a)), d: Tamarin et al, ~3 e: Baskakov et al, TM Ross and DavidsonTM (Sh = 3.5).
for all particle sizes. The correlation of Tamarin et al. 13 is not in good agreement with the other correlations towards the final stages of burn-out. The same information can be deduced, albeit qualitatively, from Fig. 3 where the calculated heat transfer coefficients are plotted as a function of the coke particle diameter. The maximum difference of about
12[
(26)
~- 1000I ~d
as 0.38 ms-i; the superficial velocity was assumed to be 1 ms -1. The specific heats of coke and char Cpa were taken as 1.7 kJ kg -1 K-1 and 1.53 kJ kg- l K-1 respectively. A wide range of carbon particle size relevant to FBC was investigated. The correlation of Ross and Davidson12 was studied using a constant Nu/Sh ratio and two different Sherwood numbers. Results for a 10 mm petroleum coke particle, in terms of the excess temperature (Tp - T#,) are plotted in Fig. 2 for heat transfer coefficients calculated using the present model and the correlations in Table I. The correlation of Parchenok and Tamarin14 was not used since the Archimedes number for the conditions simulated was out of the range of the correlation. From these plots, the correlations of Baskakov et al., z5 Prins,ZRoss and Davidsonm (Sh from Eq. (23a)), and the model yield comparable results
\
-
42.81
o
(25)
Particle Temperature Histories:
Remf = tv/(42.81) 2 + 0.061Ar
~j
~ 3=
800
1
~t~e~q
600
200
0
~0
0 ~
Coke
diometer,
20
mm
FIG. 3. Comparison of heat transfer correlations for freely moving active particle in a gas fluidized bed of sand. a: Prins 2, b: This paper, c: Ross and Davidson, 12 d: Tamarin et al, 13 e: Baskakov et al. 15
HEAT TRANSFER IN FLUIDIZED BEDS 100 W m -2 K -1 between the model, Baskakov et al. 15 and Prinsa leads to a maximum difference of 50 K in the calculated temperature of the coke particle. The Ross and Davidson correlations (Sh = 3.5 and 7.0) show that at a constant Nu/Sh ratio, maximum temperature rise is constant for a given particle size and burn-out time is influenced by the rate of mass transfer. In Fig. 4, sample calculations for a 5 mm Millmerran char particle for the case when the ash layer is stripped off (curve h) are compared with the results when the ash layer remains intact (curve a). If the ash layer is shaken off the char particle by the impact of the bed particles, the particle temperature increases gradually at first and then peaks just before burn-out. In this case, the stripped ash on bed particles may lead to agglomeration and defluidization. On the other hand, if the ash remains intact around the char particle, the oxygen concentration at the core (reaction) surface will decrease whilst heat transfer coefficient remains unchanged, leading to gradually decreasing particle temperatures. The heat transfer model predicts that the coke (or char) particle will encounter rapidly varying external heat transfer conditions. For the experimental conditions simulated, the particle circulation time is - 3 s, whereas the burn-out time is much longer. Consequently, the use of the average heat transfer coefficient in the calculation of the particle temperature is justified at least for laboratory scale experiments where individual particles are inserted within the bed. The situation will become more
9~
923
complex for continuous or batch operation where, as current evidence3~ indicates, the bubble phase is richer in oxygen in comparison with the emulsion phase. Higher combustion rates and lower heat transfer coefficients when the char particle is associated with the bubble phase may lead to much higher instantaneous particle temperatures. These results underline the necessity for careful experimentation and data interpretation in the measurement of coke particle temperatures in fluidized beds. The thermocouple technique~l may not be adequate since it may impose restrictions on particle movement. Further, ash retention on the char surface may also be effected. Fiber-optic measurement methods remove restrictions on particle movementY 'as However, monitoring the temperature history of a single particle is difficult, and frequently a batch of particles is charged into the bed. For an actual coal particle, the phenomena of drying and devolatilization may also require consideration. External heat transfer is a dominant rate limiting mechanism for these phenomena. 34-36 Drying, ignition (heterogeneous: on the char surface; or homogeneous: of the volatiles) and devolatilization occur over shorter durations in comparison with char combustion. These events, with time frames of the order of the circulation time, could be affected significantly by the variations in the heat transfer coefficient predicted by the model; further experiment and analysis are required.
Conclusions A mechanistic model for heat transfer to a freely moving active particle in a bed of smaller, denser particles has been developed. The model predictions for the average heat transfer coefficient compare well with direct measurements reported in the literature. The average heat transfer coefficient has also been used, in conjunction with a shrinking core formulation, to predict the temperature histories of burning coke and char particles in fluidized beds. The model predicts that the coke and the ashstripped char particles undergo rapid variations in the external heat transfer environment, The implications of these variations in continuous/batch operation and for drying, devolatilization and ignition need further examination.
300
200
=E t.-(/} 100
9
|
1 O0
200
i
Nomenclature
300
Time, s F]c. 4. Temperature profiles of a 5 mm Millmerran char particle using heat transfer correlation of this paper, a: particle burns with ash layer, b: particle burns without ash layer.
Ao Ar Cas
area of multi-orifice distributor per hole, m ~ (= gd~pg(pp - pg)/ix2), Archimedes number based on bed particle diameter partial pressure of diffusing species at the particle surface, atm
924 d Cd~
C&a Cp CAg
dB DA DA.e De EA
fl fr g g h~b h,o 9hinax hpc, u
h~c.d H Hr ke ko kp km Kc
KD m
mc
Mo p p'
Pr q R R'
Re~,
FLUIDIZED BED COMBUSTION particle diameter, m isolated sphere drag coefficient based on the bubble phase Reynolds number porosity dependent drag coefficient for the active particle, Table II specific heat, kJ kg-1 K-I partial pressure of diffusing species in the bulk, atm average bubble diameter, m mass diffusivity, m 2 s -1 effective mass diffusivity of the emulsion phase, m ~ s -1 effective mass diffusivity of the ash layer, m 2 s -1 activation energy, kJ kmo1-1 average level frequency of bubbles in a freely bubbling bed, m -z s -1 CO/CO2 product ratio acceleration due to gravity, m s -2 average heat transfer coefficient, W m -2 K -I heat transfer coefficient in the bubble, W m -2 K-1 gas convective heat transfer coefficient for the emulsion, W m -~ K -1 maximum average heat transfer coefficient for the emulsion, W m -~ K -1 particle convective heat transfer coefficient when the 'active' particle rises during its circulation, W m -~ K -1 particle convective heat transfer coefficient when the 'active' particle moves down during its circulation, W m -2 K -1 expanded bed height, m heat of reaction, kJ kg -1 effective thermal conductivity of the emulsion, W m -1 K -1 pre-exponential factor, kg m - 2 s- 1 atm -1/2 thermal conductivity, W m -I K -1 mass transfer coefficient, m s-1 chemical rate constant for carbon-oxygen reaction, kg m -2 s -1 atm -I/2 external mass transfer coefficient, kg m -2 S - 1 atm number of times the 'active' particle is captured or shed while it rises during one circulation mass of carbon particle, kg molecular weight of oxygen, kg kmo1-1 probability of the 'active' particle residing in the emulsion phase during one circulation probability of the 'active' particle residing in the emulsion phase while it rises during one circulation Prandtl number tortuosity Universal Gas Constant, kJ kmo1-1 K -I Universal Gas Constant, m a atm kmo1-1 K -1 (= 3Utfda/v), bubble phase Reynolds number
Ree
Ueda/v), emulsion phase Reynolds num-
(=
ber
Remf (= Umfda/v), Reynolds number at miniSc Sh t tl t2 te Tb Tf Tp UB
Uo Un Uo
Ue Umf Utf X z
mum fluidization Schmidt number (= kmda/Da), Sherwood number time, s duration of bubble capture, s duration between bubble shed and the next bubble capture, s bubble coalescence time, s bed temperature, K film temperature, K coke particle temperature, K average bubble velocity, m s -1 average descent velocity of the 'active'lpartiele with the emulsion phase, m saverage rise velocity of the 'active' particle, m s -1 superficial gas velocity, m s -1 flow velocity through the emulsion phase, m s-1 minimum fluidization velocity, m s -1 bubble throughflow velocity, m s -1 penetration depth of the 'active' particle in the bed, m cross-section factor
Greek Symbols a 8 9 9
9 9 IJ' v ~b P Or
wake fraction gas film thickness, m porosity bubble fraction voidage at minimum fluidization, voidage of the emulsion phase particle emmissivity fluid viscosity, Pa s kinematic viscosity, m 2 s -1 parameter in eq (5) and (7), dimensionless density, kg m -a Stefan-Boltzmann constant, kJ m -2 s -1 K -a mechanism factor
Subscripts a g p
'active' or coke particle fluidizing gas "inert' or bed particle
Acknowledgments This work is dedicated to the memory of Professor William E. Genetti. PKA gratefully acknowledges financial support from the Australian Research Council and the South Australian Government (through the State Energy Research Advisory Committee) for projects of which this investigation is part. TML thanks the University of Adelaide for a postgraduate scholarship. The authors also thank Dr. R.
HEAT TRANSFER IN F L U I D I Z E D BEDS D. LaNauze for continued support mad helpful discussions.
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