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Estimation of temperature difference between char particles and the fluidized bed in char combustion
Estimation of temperature difference between char particles and the fluidized bed in char combustion Dalkeun
Park
Korea Institute of Science and Technology, PO Box (Received 7 March 1989; revised 73 May 7989)
731, Cheongryang,
Seoul,
Korea
In fluidized bed combustion (FBC), the understanding of various phenomena associated with char combustion is very important. The temperature difference between burning char particles and the bulk of the bed can be significant (z 200 K), which makes analysis of char combustion more difficult. Using a simple model and a ratio of Nusselt number to Sherwood number (Nu/Sh) parameter, the effect of char size and oxygen concentration on the temperature difference can be estimated. Calculation of results using typical values for parameters show that the temperature difference can easily cover the range of measured values in the literature. At a constant value of Nu/Sh, the temperature difference increases with decrease of char size, then falls rapidly with further decrease in char size. Temperature increases with oxygen concentration and bed temnerature. but decreases with the value of Nu/Sh. The transient behaviour with various oxygen concentrations was also discussed. (Keywords: fluidized beds; char; particle size)
Fluidized bed combustion (FBC) is emerging as a vital technique for better utilization of coal energy, which avoids damaging the environment. As a result of extensive research and development efforts, various phenomena associated with FBC are now understood more clearly. However, the combustion efficiency of FBC is not high enough compared with pulverized combustion. The combustion efficiency is closely related to phenomena associated with the combustion of coal particles. Once fed into a hot combustor, coal particles release volatiles after a short time, because of the high heating rate. After volatiles release, the remaining char particles burn relatively slowly. As the volatiles burn more or less completely in the combustor, the combustion rate and residence time of char particles determine the combustion efficiency. Elutriation of unburned char particles is known to be the main route by which fuel is lost. Combustion of char involves the transfer of oxygen from the bulk of the bed to the surface of the char, and chemical reactions on the surface and inside pores of the char. One interesting aspect of char combustion in FBC is the temperature difference between burning char particles and the bulk of the bed. In FBC, < 1% of bed material is char and the rest is inert material such as sand, ash or limestone particles. During combustion, the temperature of the char particles is higher than that of the surroundings and the combustion rate, in turn, depends on the temperature of the char particles. The temperature rise of the char particles depends on their size, the oxygen concentration of the bulk, and the reactivity of the char. If a burning char is at a much higher temperature compared with the bulk bed, the combustion rate would be controlled by mass transfer of gases between the bulk and the char surface. However, if temperature rise is moderate, the chemical reaction is not fast enough to allow the resistance to be disregarded. Large particles at high temperatures undergo mass transfer-controlled combustion, while small particles at 0016-2361/89/10I320-05$3.00 0 1989 Butterworth & Co. (Publishers)
1320
Ltd.
FUEL, 1989, Vol 68, October
low temperatures exhibit kinetically controlled combustion, because mass transfer decreases with particle size and the chemical reaction rate increases with temperature. By viewing a hot fluidized bed combustor, one can easily recognize bright particles visible against a dull background. Many investigators have observed this, and some of the reported temperature differences between burning char and the surrounding particles have been measured up to 200K. Avedesian and Davidson’ observed that the temperature rise increases with decrease in char particle size. However, the temperature history during burnout of a single char, reported by Chakraborty and Howard’, shows a relatively constant temperature rise, except at the end when the temperature rise diminishes rapidly. Ross et ~1.~ reported that the temperature rise of tiny char particles is small, and thus the combustion rate is relatively slow. They reasoned the cause to be either higher heat transfer rate or the escape of CO from the boundary layer of tiny particles. Stubington4 compared techniques for measuring the temperature of char particles in a fluidized bed. La Nauze et a1.5 reported even larger temperature differences measured by optical methods. If the temperature rise increases with decreasing char size up to a certain critical size, the transition from mass transfer-controlled combustion to kinetically-controlled combustion would be rather abrupt around the critical size. In this paper, we will investigate the temperature rise and change of combustion rate around the critical particle size using a simple model. COMBUSTION RATE AND TEMPERATURE OF CHAR PARTICLES
RISE
Although there are still uncertainties on the reaction order in char combustion and the location of CO oxidation to CO1, we will assume char combustion is first order with respect to oxygen and that CO, is the
Temperature
difference
reaction product. Moreover, we will assume that char particles are spherical and that they shrink in size with combustion as ash is removed. With these assumptions, the combustion rate of a char based on unit external surface area can be expressed as W, = kc,
(1)
where C, is oxygen concentration, and the overall combustion rate coefficient, k, includes the effect of mass transfer, k,, and that of chemical kinetics, k,. 1
k=
(2) l/k, + Ilk,
Energy
balance
mC dT AA= 4nr2 dt
gives
W,q-h(T,-
T,)-a&(T;-
T;)
where: m is 4/3xr2 pC (mass of char); pC is heat of reaction (C + O,+CO,);
Y is radius of char; h is heat transfer coefficient; Tb is bed temperature; T, is char temperature; CJis Stefan Boltzmann constant; and 8 is emissivity. The first term on the righthand side of Equation (3) represents heat of combustion, the second is convective heat transfer, and the third is radiative heat transfer. The mass transfer coefficient and the convective heat transfer coefficient can be treated in terms of Sherwood number (Sh) and Nusselt number (Nu), respectively. Sh = k,d,/D
(4)
Nu = hd,/k,
Here, d, is diameter of char, i.e. d,=2r. For mass transfer, the choice of molecular diffusivity, D, is straightforward, as the gas molecules move through the interstices of particles. However, for heat transfer, the situation is rather complicated because heat transfer occurs through solid particles as well as gases. For this reason, an effective conductivity of emulsion phase, k,, is preferred to gas conductivity; heat transfer from a burning char immersed in a fluidized bed can be much higher than that of a char freely suspended in bulk gas. At steady state, the temperature difference between a burning char and that of bulk (i.e. bed temperature) in a fluidized bed can be given from Equations (1 t(4) as:
(5) where c( denotes contribution of radiative heat transfer, which is assumed here to be additive, and p is a measure of chemical kinetics resistance to combustion: a=&(T;p+ m
T,4)/h(T,l 1+k/Jk,
T,)
(ha) (6b)
Thus p values of zero and one correspond to chemical kinetics and mass transfer controlled combustion, respectively. p as defined in Equation (6b) is dependent on temperature, size, and reactivity of char. However, CI is not sensitive to those variables. From Equation (5), one can see that AT increases with oxygen concentration in the emulsion phase, and with ratio of Sh/Nu. Molecular diffusivity, D, is a function of temperature only, but effective thermal conductivity, k,,
between
char particles
and fluidized
bed: D. Park
depends on the properties of bulk solids as well as the thermal conductivity of gases. However, k, is largely independent of the size or combustion rate of char. One can argue Sh/Nu = s,r, voidage of the emulsion phase, because solid particles act as barriers to mass transfer, but not to heat transfer. Effective thermal conductivity, k,, takes account of solids contribution as well. La Nauze et a1.6 compared experimentally obtained values of Sherwood number and Nusselt number, and showed Sh/Nu varies with char particle size. With given heat transfer rate maximum AT corresponds to maximum combustion rate, which occurs when /I = 1, i.e. mass transfer controlled combustion. In an atmospheric fluidized bed combustor, the oxygen concentration does not exceed that of air, 21%. Using these values and those in the Appendix, we can estimate maximum AT from Equation (5) assuming Sh/Nu = 1:
ATlIX3, = &(2(?.82
X 105)(2.l)G
(1)
370 l+G( The value of a cannot be determined directly, although its estimation is straightforward. With c(=OS, AT,,, = 250 K, which is comparable to the experimental findings in the literature. CIchanges with char size because radiative heat transfer rate is unaffected by char size, while k, increases with decrease of char size if Nu is constant. Therefore c( decreases with char size, i.e. l/(1 +a) increases with decrease of char size when all other values remain constant. If this is true, AT increases with decrease of char size. However, /3 changes with char size also: 8% 1 for large char particles, but it decreases rapidly to zero with char size. Hence, AT increases with decrease of char size in char size range where /I remains close to 1. Beyond that size range, b decreases rapidly and more than compensates for an increase of l/(1 +LX). For this small size range, AT decreases rapidly with decreasing char size. The lower limit of AT is zero for an infinitely small char. From the relationship between char size and p/(1 +a), we can easily deduce that AT has a maximum, and that the char size which gives maximum AT lies where p changes rapidly from z 1 to a very low value. Some investigators3 argue that a rapid decrease of AT with decreasing char size is the result of the escape of CO without being converted to CO, near char surface, i.e. decrease of q. From the arguments given above, however, we can see that a rapid decrease in AT can occur even with constant q. In reality, a decrease in q with decreasing char size will make AT change more dramatically for small char sizes. RESULTS
AND DISCUSSION
Using Equations (1 ), (2) and (4) and values of parameters as given in the Appendix, AT was calculated under various conditions. Calculations were made for bed temperature of 1173 K and ~~~~=0.21. As shown in Figure 1, AT depends on char size and oxygen concentration. Here yoz is the mole fraction of oxygen in the bulk gas. Note that yoZ is equivalent to oxygen concentration at constant temperature and pressure. AT shows a maximum value for a certain char size. As
FUEL,
1989,
Vol 68, October
1321
Temperature
difference
between
char particles
and fluidized
~-------.
‘-..
f
.
Y02
.
.-..a21 i
I i
___
i
//
____-------_____--
0.105
,,.-
//
0.03
-
I
2
I
I
I
I
L 6 0 Diameter of char (mm)
I
12
10
Figure 1 Temperature difference between char particle and bed (AT) versus char size for various oxygen mole fractions (yO,)
i
I
dc /Imm
/
3mm
/ / ,/ / / /
,,pmm
,//Q I
/
PO.3
mm
0.05 0.10 Oxygen mole
0.15 fraction
versus
discussed earlier, AT increases slowly to a maximum value with decreasing char size and then decreases rapidly to zero with further decrease in char size. From Equation (5), AT increases with oxygen concentration, C,. The relation is non-linear (seeFigure 2). The lower oxygen concentration, the smaller AT becomes, and the AT change with char size is less pronounced. When a single char particle, or a small batch of char, is used for the measurement of ATin a fluidized bed, oxygen concentration would be close to that of incoming air, i.e. oxygen concentration variation is negligible during a run. Therefore, if a char particle shrinks in size by combustion, maintaining constant density and reactivity, AT of the particle will follow a constant yo2 line as in Figure 1 as long as Nu/Sh remains constant. If Nu/Sh changes with char size for some reason, ATversus char size will behave differently.
FUEL, 1989, Vol 68, October
Equation (5) states AT varies inversely with Nu/Sh. In Figure 3, curves for AT versus char size at various values of Nu/Sh are shown. Therefore if Nu/Sh decreases with decreasing char size, AT will rise more steeply than in the case of constant Nu/Sh, and less steeply or even fall if Nu/Sh increases with decreasing char size. The change in Nu/Sh with char size, could explain the AT versus char size, which is different from that predicted by constant Nu/Sh as shown in Figure3. Chakraborty and Howard’ reported relatively constant AT, while others reported a steadily rising AT with shrinking of char up to a certain size by combustion. As one can see in Figure3, a maximum AT occurs for relatively small chars for which insertion of a thermocouple to measure temperature is impractical. When one starts with a relatively large char (- 12 mm) as did Chakraborty and Howard’, most of the combustion time elapses before maximum AT is reached. As the combustion rate is dependent on temperature, AT affects combustion rates and the variation of combustion rate versus char size can show a maximum value similar to AT versus char size. Figure4 shows decrease in combustion rate with increase in char size for large char size, as is expected because the combustion rate of large chars is controlled by mass transfer which decreases with increase of char size. The case for Nu/Sh = 0 is also included, which represents the limiting case where only radiative heat transfer is possib1ej.e. no conduction and convection. For small particles, AT is not high, i.e. the char temperature is close to the bed temperature, thus the chemical reaction rate coefficient, k,, is smaller than that of large char particles for which AT is larger, as shown in Figures 1 and 3. The reduction in k, can outweigh any increase in k, with decrease in char size, thus resulting in a maximum combustion rate W, for a certain char size, as shown in Figure 4 for small chars. The change in AT and W, with char size is more pronounced for smaller Nu/Sh. The effect of Nu/Sh on combustion rate is due to the strong influence of the former on AT as shown in Figure3. A sharp change in AT and W, is accompanied by a sharp change from mass transfer-controlled (/I close to 1) to kinetically-controlled combustion (B close to zero)
0.20
Figure 2 Temperature difference between char particle (AT) oxygen mole fraction (y,,,) for various char sizes
1322
bed: D. Park
Diameter
of char (mm)
3 Temperature difference between char particle (AT) versus char size for various ratios of Nu/Sh
Figure
Temperature
difference
Yea= 0.21
Nu/Sh 0.0 --0.5 0.75 -----1.0 __-_____ 2.0
I
I
I
1.5 0.5 1.0 Diameter of char (mm1 Figure 4 Combustion ratios of NuiSh
nFI
I/ u
rate of char
(W,) versus char size for various
Nu/St 0.5
_________----
-_------1.0
“II
__-,/-
-
__----
./
2.0
./-‘-
/
1173K
yo,=0.21
"0
2
L
6
Diameter Figure 5 8, as defined ratios of Nu/Sh
in Equation
8
IO
between
12
I.”
bed: D. Park
I
-; 0.8 - 1.1, r
as shown in FigureS. The range of char sizes for this dramatic change in combustion rate as shown in Figure 4 is the same as those of AT and b (see Figures I and 5). Poersch’ reported similar results. Ignition/extinction hysteresis can also occur for char particles of this size range8v9. This has practical significance, as this size range also covers line particles, which can easily elutriate. Bed temperature gives effects similar to the ratio of Nu/Sh.AT decreases with bed temperature, thus lower bed temperature results not only in lower W,, but also in less pronounced maximum W, (Figure6). Bed temperature is fairly uniform in a fluidized bed combustor, although it can be lower near heat exchange surfaces such as steam tubes. However, the oxygen
and fluidized
concentration can vary widely in a fluidized bed combustor. Unlike small scale fluidized beds, which were employed in much of the literature results, the gas concentration in a large scale combustor is far from uniform. In the latter, one can visualize char particles experiencing different oxygen concentrations as they move around while burning and shrinking in the combustor. There would be high oxygen concentration near the distributor plate and low oxygen concentration near the bed surface. The burnout time of several mm of char is several hundred seconds or more, while the mixing time of particles in a large scale bed is of the order of tens of seconds or less. Hence relatively large char particles can experience many variations of oxygen concentration during their lifetime in the bed. Although a change of oxygen concentration experienced by a burning char is affected by the random nature of solids mixing in a fluidized bed, we have some insight on the transient behaviour of char particles by studying the combustion rate and AT of the char particles which are experiencing periodic changes in oxygen concentration. One extreme case of variations in oxygen concentration is step change. Although this is unlikely to happen in a real combustor, step change of oxygen concentration from zero to a maximum, corresponding to the atmosphere, can show the extremities of its effects on AT and WT. More plausibly, oxygen concentration can change abruptly when the particles move from emulsion phase to bubble phase or vice versa, if there exists a considerable concentration difference between the two phases”. To elucidate the effect of varying oxygen concentration on the history of a burning char, we set oxygen concentration to change sigmoidally. Here, frequency and magnitude of the change are two characteristic parameters. As shown in Figure 7, the transient behaviour of AT for a period of 10s is strongly dependent on the size of char: small chars follow oxygen concentration change more rapidly, owing to their small heat capacity, while larger char particles react more sluggishly, see Equation (3). AT of large char particles behaves as if the oxygen concentration changes only slightly. As the frequency increases, one can visualize that the particles
of char (mm) (7), versus char size for various
char particles
al I 3 0.6- I
’
\ ‘\
‘\ .-: I z a 2 0.L ,/----_ E / / s /
‘\ “-1. --._
---_
----‘.. ---_
473k --_J~23k
0.2/’
OO 1
1073k 2I
61
LI Diameter
Figure 6 Combustion bed temperatures
rate of char
FUEL,
8I
of
10 1
12 1
char (mm)
(W,) versus char size for various
1989, Vol 68, October
1323
Temperature
difference
between
char particles and fluidized bed: D. Park REFERENCES 1 2 3 4 5 6 7 8 9 10
Time (set) Figure 7 Transient response of AT to sigmoidal variation of oxygen concentration, C,, for various char sizes (C, = C,, [l -cos (t ?r/lO)] where C,, corresponds to y,,> =0.105)
behave as if they are immersed in a uniform environment of average oxygen concentration. The effects of step, sigmoidal, and linear change in C, show similar effects on AT and W, (results not presented here). In a real combustor, the oxygen concentration change experienced by chars is stochastic and may be much milder compared with those used for the calculations in this paper. Variation in oxygen concentration is real, and some particles may indeed experience extreme variation in oxygen concentration during their combustion in the bed. Such effects are more pronounced for intermediate sized chars.
1324
FUEL, 1989, Vol 68, October
Avedesian, M. M. and Davidson, J. F. Trans. Instn. Chem. Engrs. 1973,51, 121 Chakraborty, R. K. and Howard, J. R. J. Inst. Energy 1978, 51, 220 Ross, I. B., Patel, M. S. and Davidson, J. F. Trans. Instn. Chem. Engrs. 1981, 59, 83 Stubington, J. F. Chem. Eng. Rex Des. 1985, 63, 241 La Nauze, R. D., Jung, K., Dent, D. C., Tait, P. J. and Burgess, J. M. Proc. Ninth Int. Conf. FBC, Boston, 1987, p, 707 La Nauze, R. D., Jung, K. and Kastle, J. Chem. Eng. Sci. 1984, 39, 1623 Yagi, S. and Kunii, D. AIChE J. 1957, 3, 373 Poersch, W. W. Powder Technology 1984, 40, 331 Park, D., Levenspiel, 0. and Fitzgerald, T. J. Fuel 198 1,60,295 Agarwal, P. K., Mitchell, W. J. and La Nauze, R. D. Chem. Eng. Sci. 1988, 43, 2511
APPENDIX Combustion rate constant k, = 595 T, exp (- 149200/RT,) (ms-‘) (W, has the unit, mol carbon/external char surface) Viscosity of gas 1.09875 x 10-6~~5/(0.9183-9.08 x 10p5T) (kgm-‘s-i) Specific heat of char C, = 1.465 (J g- 1 K- ‘) Heat of combustion q =2.82 x lo5 (Jmol-‘) Heat transfer coefficient k, = k, + O.l,C,d,U,r (see Ref. 7) where k,“lk, = 10 C,= 1.13 (Jg-‘K-i) k,=6.7 (Jm-‘s-‘K-l) Voidage of emulsion phase e,, = 0.44 Gas diffusivity D= 5.2 x 10m4 T’.5/P (m’s_l) where P is pressure in Pa Emissivity of char = 0.85 Diameter of inserts d, = 800 (pm) Superficial gas velocity U,= 1.5 (m s-l) Minimum fluidizing gas velocity U,, = 0.3(ms- ‘) Density of char pc = 1500 (kg m - 3,
Park
Korea Institute of Science and Technology, PO Box (Received 7 March 1989; revised 73 May 7989)
731, Cheongryang,
Seoul,
Korea
In fluidized bed combustion (FBC), the understanding of various phenomena associated with char combustion is very important. The temperature difference between burning char particles and the bulk of the bed can be significant (z 200 K), which makes analysis of char combustion more difficult. Using a simple model and a ratio of Nusselt number to Sherwood number (Nu/Sh) parameter, the effect of char size and oxygen concentration on the temperature difference can be estimated. Calculation of results using typical values for parameters show that the temperature difference can easily cover the range of measured values in the literature. At a constant value of Nu/Sh, the temperature difference increases with decrease of char size, then falls rapidly with further decrease in char size. Temperature increases with oxygen concentration and bed temnerature. but decreases with the value of Nu/Sh. The transient behaviour with various oxygen concentrations was also discussed. (Keywords: fluidized beds; char; particle size)
Fluidized bed combustion (FBC) is emerging as a vital technique for better utilization of coal energy, which avoids damaging the environment. As a result of extensive research and development efforts, various phenomena associated with FBC are now understood more clearly. However, the combustion efficiency of FBC is not high enough compared with pulverized combustion. The combustion efficiency is closely related to phenomena associated with the combustion of coal particles. Once fed into a hot combustor, coal particles release volatiles after a short time, because of the high heating rate. After volatiles release, the remaining char particles burn relatively slowly. As the volatiles burn more or less completely in the combustor, the combustion rate and residence time of char particles determine the combustion efficiency. Elutriation of unburned char particles is known to be the main route by which fuel is lost. Combustion of char involves the transfer of oxygen from the bulk of the bed to the surface of the char, and chemical reactions on the surface and inside pores of the char. One interesting aspect of char combustion in FBC is the temperature difference between burning char particles and the bulk of the bed. In FBC, < 1% of bed material is char and the rest is inert material such as sand, ash or limestone particles. During combustion, the temperature of the char particles is higher than that of the surroundings and the combustion rate, in turn, depends on the temperature of the char particles. The temperature rise of the char particles depends on their size, the oxygen concentration of the bulk, and the reactivity of the char. If a burning char is at a much higher temperature compared with the bulk bed, the combustion rate would be controlled by mass transfer of gases between the bulk and the char surface. However, if temperature rise is moderate, the chemical reaction is not fast enough to allow the resistance to be disregarded. Large particles at high temperatures undergo mass transfer-controlled combustion, while small particles at 0016-2361/89/10I320-05$3.00 0 1989 Butterworth & Co. (Publishers)
1320
Ltd.
FUEL, 1989, Vol 68, October
low temperatures exhibit kinetically controlled combustion, because mass transfer decreases with particle size and the chemical reaction rate increases with temperature. By viewing a hot fluidized bed combustor, one can easily recognize bright particles visible against a dull background. Many investigators have observed this, and some of the reported temperature differences between burning char and the surrounding particles have been measured up to 200K. Avedesian and Davidson’ observed that the temperature rise increases with decrease in char particle size. However, the temperature history during burnout of a single char, reported by Chakraborty and Howard’, shows a relatively constant temperature rise, except at the end when the temperature rise diminishes rapidly. Ross et ~1.~ reported that the temperature rise of tiny char particles is small, and thus the combustion rate is relatively slow. They reasoned the cause to be either higher heat transfer rate or the escape of CO from the boundary layer of tiny particles. Stubington4 compared techniques for measuring the temperature of char particles in a fluidized bed. La Nauze et a1.5 reported even larger temperature differences measured by optical methods. If the temperature rise increases with decreasing char size up to a certain critical size, the transition from mass transfer-controlled combustion to kinetically-controlled combustion would be rather abrupt around the critical size. In this paper, we will investigate the temperature rise and change of combustion rate around the critical particle size using a simple model. COMBUSTION RATE AND TEMPERATURE OF CHAR PARTICLES
RISE
Although there are still uncertainties on the reaction order in char combustion and the location of CO oxidation to CO1, we will assume char combustion is first order with respect to oxygen and that CO, is the
Temperature
difference
reaction product. Moreover, we will assume that char particles are spherical and that they shrink in size with combustion as ash is removed. With these assumptions, the combustion rate of a char based on unit external surface area can be expressed as W, = kc,
(1)
where C, is oxygen concentration, and the overall combustion rate coefficient, k, includes the effect of mass transfer, k,, and that of chemical kinetics, k,. 1
k=
(2) l/k, + Ilk,
Energy
balance
mC dT AA= 4nr2 dt
gives
W,q-h(T,-
T,)-a&(T;-
T;)
where: m is 4/3xr2 pC (mass of char); pC is heat of reaction (C + O,+CO,);
Y is radius of char; h is heat transfer coefficient; Tb is bed temperature; T, is char temperature; CJis Stefan Boltzmann constant; and 8 is emissivity. The first term on the righthand side of Equation (3) represents heat of combustion, the second is convective heat transfer, and the third is radiative heat transfer. The mass transfer coefficient and the convective heat transfer coefficient can be treated in terms of Sherwood number (Sh) and Nusselt number (Nu), respectively. Sh = k,d,/D
(4)
Nu = hd,/k,
Here, d, is diameter of char, i.e. d,=2r. For mass transfer, the choice of molecular diffusivity, D, is straightforward, as the gas molecules move through the interstices of particles. However, for heat transfer, the situation is rather complicated because heat transfer occurs through solid particles as well as gases. For this reason, an effective conductivity of emulsion phase, k,, is preferred to gas conductivity; heat transfer from a burning char immersed in a fluidized bed can be much higher than that of a char freely suspended in bulk gas. At steady state, the temperature difference between a burning char and that of bulk (i.e. bed temperature) in a fluidized bed can be given from Equations (1 t(4) as:
(5) where c( denotes contribution of radiative heat transfer, which is assumed here to be additive, and p is a measure of chemical kinetics resistance to combustion: a=&(T;p+ m
T,4)/h(T,l 1+k/Jk,
T,)
(ha) (6b)
Thus p values of zero and one correspond to chemical kinetics and mass transfer controlled combustion, respectively. p as defined in Equation (6b) is dependent on temperature, size, and reactivity of char. However, CI is not sensitive to those variables. From Equation (5), one can see that AT increases with oxygen concentration in the emulsion phase, and with ratio of Sh/Nu. Molecular diffusivity, D, is a function of temperature only, but effective thermal conductivity, k,,
between
char particles
and fluidized
bed: D. Park
depends on the properties of bulk solids as well as the thermal conductivity of gases. However, k, is largely independent of the size or combustion rate of char. One can argue Sh/Nu = s,r, voidage of the emulsion phase, because solid particles act as barriers to mass transfer, but not to heat transfer. Effective thermal conductivity, k,, takes account of solids contribution as well. La Nauze et a1.6 compared experimentally obtained values of Sherwood number and Nusselt number, and showed Sh/Nu varies with char particle size. With given heat transfer rate maximum AT corresponds to maximum combustion rate, which occurs when /I = 1, i.e. mass transfer controlled combustion. In an atmospheric fluidized bed combustor, the oxygen concentration does not exceed that of air, 21%. Using these values and those in the Appendix, we can estimate maximum AT from Equation (5) assuming Sh/Nu = 1:
ATlIX3, = &(2(?.82
X 105)(2.l)G
(1)
370 l+G( The value of a cannot be determined directly, although its estimation is straightforward. With c(=OS, AT,,, = 250 K, which is comparable to the experimental findings in the literature. CIchanges with char size because radiative heat transfer rate is unaffected by char size, while k, increases with decrease of char size if Nu is constant. Therefore c( decreases with char size, i.e. l/(1 +a) increases with decrease of char size when all other values remain constant. If this is true, AT increases with decrease of char size. However, /3 changes with char size also: 8% 1 for large char particles, but it decreases rapidly to zero with char size. Hence, AT increases with decrease of char size in char size range where /I remains close to 1. Beyond that size range, b decreases rapidly and more than compensates for an increase of l/(1 +LX). For this small size range, AT decreases rapidly with decreasing char size. The lower limit of AT is zero for an infinitely small char. From the relationship between char size and p/(1 +a), we can easily deduce that AT has a maximum, and that the char size which gives maximum AT lies where p changes rapidly from z 1 to a very low value. Some investigators3 argue that a rapid decrease of AT with decreasing char size is the result of the escape of CO without being converted to CO, near char surface, i.e. decrease of q. From the arguments given above, however, we can see that a rapid decrease in AT can occur even with constant q. In reality, a decrease in q with decreasing char size will make AT change more dramatically for small char sizes. RESULTS
AND DISCUSSION
Using Equations (1 ), (2) and (4) and values of parameters as given in the Appendix, AT was calculated under various conditions. Calculations were made for bed temperature of 1173 K and ~~~~=0.21. As shown in Figure 1, AT depends on char size and oxygen concentration. Here yoz is the mole fraction of oxygen in the bulk gas. Note that yoZ is equivalent to oxygen concentration at constant temperature and pressure. AT shows a maximum value for a certain char size. As
FUEL,
1989,
Vol 68, October
1321
Temperature
difference
between
char particles
and fluidized
~-------.
‘-..
f
.
Y02
.
.-..a21 i
I i
___
i
//
____-------_____--
0.105
,,.-
//
0.03
-
I
2
I
I
I
I
L 6 0 Diameter of char (mm)
I
12
10
Figure 1 Temperature difference between char particle and bed (AT) versus char size for various oxygen mole fractions (yO,)
i
I
dc /Imm
/
3mm
/ / ,/ / / /
,,pmm
,//Q I
/
PO.3
mm
0.05 0.10 Oxygen mole
0.15 fraction
versus
discussed earlier, AT increases slowly to a maximum value with decreasing char size and then decreases rapidly to zero with further decrease in char size. From Equation (5), AT increases with oxygen concentration, C,. The relation is non-linear (seeFigure 2). The lower oxygen concentration, the smaller AT becomes, and the AT change with char size is less pronounced. When a single char particle, or a small batch of char, is used for the measurement of ATin a fluidized bed, oxygen concentration would be close to that of incoming air, i.e. oxygen concentration variation is negligible during a run. Therefore, if a char particle shrinks in size by combustion, maintaining constant density and reactivity, AT of the particle will follow a constant yo2 line as in Figure 1 as long as Nu/Sh remains constant. If Nu/Sh changes with char size for some reason, ATversus char size will behave differently.
FUEL, 1989, Vol 68, October
Equation (5) states AT varies inversely with Nu/Sh. In Figure 3, curves for AT versus char size at various values of Nu/Sh are shown. Therefore if Nu/Sh decreases with decreasing char size, AT will rise more steeply than in the case of constant Nu/Sh, and less steeply or even fall if Nu/Sh increases with decreasing char size. The change in Nu/Sh with char size, could explain the AT versus char size, which is different from that predicted by constant Nu/Sh as shown in Figure3. Chakraborty and Howard’ reported relatively constant AT, while others reported a steadily rising AT with shrinking of char up to a certain size by combustion. As one can see in Figure3, a maximum AT occurs for relatively small chars for which insertion of a thermocouple to measure temperature is impractical. When one starts with a relatively large char (- 12 mm) as did Chakraborty and Howard’, most of the combustion time elapses before maximum AT is reached. As the combustion rate is dependent on temperature, AT affects combustion rates and the variation of combustion rate versus char size can show a maximum value similar to AT versus char size. Figure4 shows decrease in combustion rate with increase in char size for large char size, as is expected because the combustion rate of large chars is controlled by mass transfer which decreases with increase of char size. The case for Nu/Sh = 0 is also included, which represents the limiting case where only radiative heat transfer is possib1ej.e. no conduction and convection. For small particles, AT is not high, i.e. the char temperature is close to the bed temperature, thus the chemical reaction rate coefficient, k,, is smaller than that of large char particles for which AT is larger, as shown in Figures 1 and 3. The reduction in k, can outweigh any increase in k, with decrease in char size, thus resulting in a maximum combustion rate W, for a certain char size, as shown in Figure 4 for small chars. The change in AT and W, with char size is more pronounced for smaller Nu/Sh. The effect of Nu/Sh on combustion rate is due to the strong influence of the former on AT as shown in Figure3. A sharp change in AT and W, is accompanied by a sharp change from mass transfer-controlled (/I close to 1) to kinetically-controlled combustion (B close to zero)
0.20
Figure 2 Temperature difference between char particle (AT) oxygen mole fraction (y,,,) for various char sizes
1322
bed: D. Park
Diameter
of char (mm)
3 Temperature difference between char particle (AT) versus char size for various ratios of Nu/Sh
Figure
Temperature
difference
Yea= 0.21
Nu/Sh 0.0 --0.5 0.75 -----1.0 __-_____ 2.0
I
I
I
1.5 0.5 1.0 Diameter of char (mm1 Figure 4 Combustion ratios of NuiSh
nFI
I/ u
rate of char
(W,) versus char size for various
Nu/St 0.5
_________----
-_------1.0
“II
__-,/-
-
__----
./
2.0
./-‘-
/
1173K
yo,=0.21
"0
2
L
6
Diameter Figure 5 8, as defined ratios of Nu/Sh
in Equation
8
IO
between
12
I.”
bed: D. Park
I
-; 0.8 - 1.1, r
as shown in FigureS. The range of char sizes for this dramatic change in combustion rate as shown in Figure 4 is the same as those of AT and b (see Figures I and 5). Poersch’ reported similar results. Ignition/extinction hysteresis can also occur for char particles of this size range8v9. This has practical significance, as this size range also covers line particles, which can easily elutriate. Bed temperature gives effects similar to the ratio of Nu/Sh.AT decreases with bed temperature, thus lower bed temperature results not only in lower W,, but also in less pronounced maximum W, (Figure6). Bed temperature is fairly uniform in a fluidized bed combustor, although it can be lower near heat exchange surfaces such as steam tubes. However, the oxygen
and fluidized
concentration can vary widely in a fluidized bed combustor. Unlike small scale fluidized beds, which were employed in much of the literature results, the gas concentration in a large scale combustor is far from uniform. In the latter, one can visualize char particles experiencing different oxygen concentrations as they move around while burning and shrinking in the combustor. There would be high oxygen concentration near the distributor plate and low oxygen concentration near the bed surface. The burnout time of several mm of char is several hundred seconds or more, while the mixing time of particles in a large scale bed is of the order of tens of seconds or less. Hence relatively large char particles can experience many variations of oxygen concentration during their lifetime in the bed. Although a change of oxygen concentration experienced by a burning char is affected by the random nature of solids mixing in a fluidized bed, we have some insight on the transient behaviour of char particles by studying the combustion rate and AT of the char particles which are experiencing periodic changes in oxygen concentration. One extreme case of variations in oxygen concentration is step change. Although this is unlikely to happen in a real combustor, step change of oxygen concentration from zero to a maximum, corresponding to the atmosphere, can show the extremities of its effects on AT and WT. More plausibly, oxygen concentration can change abruptly when the particles move from emulsion phase to bubble phase or vice versa, if there exists a considerable concentration difference between the two phases”. To elucidate the effect of varying oxygen concentration on the history of a burning char, we set oxygen concentration to change sigmoidally. Here, frequency and magnitude of the change are two characteristic parameters. As shown in Figure 7, the transient behaviour of AT for a period of 10s is strongly dependent on the size of char: small chars follow oxygen concentration change more rapidly, owing to their small heat capacity, while larger char particles react more sluggishly, see Equation (3). AT of large char particles behaves as if the oxygen concentration changes only slightly. As the frequency increases, one can visualize that the particles
of char (mm) (7), versus char size for various
char particles
al I 3 0.6- I
’
\ ‘\
‘\ .-: I z a 2 0.L ,/----_ E / / s /
‘\ “-1. --._
---_
----‘.. ---_
473k --_J~23k
0.2/’
OO 1
1073k 2I
61
LI Diameter
Figure 6 Combustion bed temperatures
rate of char
FUEL,
8I
of
10 1
12 1
char (mm)
(W,) versus char size for various
1989, Vol 68, October
1323
Temperature
difference
between
char particles and fluidized bed: D. Park REFERENCES 1 2 3 4 5 6 7 8 9 10
Time (set) Figure 7 Transient response of AT to sigmoidal variation of oxygen concentration, C,, for various char sizes (C, = C,, [l -cos (t ?r/lO)] where C,, corresponds to y,,> =0.105)
behave as if they are immersed in a uniform environment of average oxygen concentration. The effects of step, sigmoidal, and linear change in C, show similar effects on AT and W, (results not presented here). In a real combustor, the oxygen concentration change experienced by chars is stochastic and may be much milder compared with those used for the calculations in this paper. Variation in oxygen concentration is real, and some particles may indeed experience extreme variation in oxygen concentration during their combustion in the bed. Such effects are more pronounced for intermediate sized chars.
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FUEL, 1989, Vol 68, October
Avedesian, M. M. and Davidson, J. F. Trans. Instn. Chem. Engrs. 1973,51, 121 Chakraborty, R. K. and Howard, J. R. J. Inst. Energy 1978, 51, 220 Ross, I. B., Patel, M. S. and Davidson, J. F. Trans. Instn. Chem. Engrs. 1981, 59, 83 Stubington, J. F. Chem. Eng. Rex Des. 1985, 63, 241 La Nauze, R. D., Jung, K., Dent, D. C., Tait, P. J. and Burgess, J. M. Proc. Ninth Int. Conf. FBC, Boston, 1987, p, 707 La Nauze, R. D., Jung, K. and Kastle, J. Chem. Eng. Sci. 1984, 39, 1623 Yagi, S. and Kunii, D. AIChE J. 1957, 3, 373 Poersch, W. W. Powder Technology 1984, 40, 331 Park, D., Levenspiel, 0. and Fitzgerald, T. J. Fuel 198 1,60,295 Agarwal, P. K., Mitchell, W. J. and La Nauze, R. D. Chem. Eng. Sci. 1988, 43, 2511
APPENDIX Combustion rate constant k, = 595 T, exp (- 149200/RT,) (ms-‘) (W, has the unit, mol carbon/external char surface) Viscosity of gas 1.09875 x 10-6~~5/(0.9183-9.08 x 10p5T) (kgm-‘s-i) Specific heat of char C, = 1.465 (J g- 1 K- ‘) Heat of combustion q =2.82 x lo5 (Jmol-‘) Heat transfer coefficient k, = k, + O.l,C,d,U,r (see Ref. 7) where k,“lk, = 10 C,= 1.13 (Jg-‘K-i) k,=6.7 (Jm-‘s-‘K-l) Voidage of emulsion phase e,, = 0.44 Gas diffusivity D= 5.2 x 10m4 T’.5/P (m’s_l) where P is pressure in Pa Emissivity of char = 0.85 Diameter of inserts d, = 800 (pm) Superficial gas velocity U,= 1.5 (m s-l) Minimum fluidizing gas velocity U,, = 0.3(ms- ‘) Density of char pc = 1500 (kg m - 3,