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Gas-to-gas heat recovery using fluidized bed technology
Heat Recovery Systems Vol 5, No 6, pp 535-544, 1985 Pnnted m Great Britain
0198-7593/85 $3 00 + 0 00
Pergamon Press Ltd
GAS-TO-GAS HEAT RECOVERY USING FLUIDIZED BED TECHNOLOGY H. HATTORI Manufactunng Engineenng Research Center, Komatsu Ltd, 3-1-1 Ueno, Hirakata-shi, Osaka-fu, 573 Japan
and J. R. HOWARD Department of Mechanical and Production Engmeenng, Umverslty of Aston in Birmingham, Gosta Green, Birmingham, England and H.H Assocmtes, 18 Pembroke Croft, Hall Green, Birmingham B28 9EY, England
Abstract--The extraordinarily large surface area and heat eapacaty per umt volume of a bed of solid parucles makes them attractive as a heat carrier. This paper reports briefly a thcorcucal and experimental study of some of the problems if the potentaal advantages are to be exploited This revealed that the effectiveness of heat transfer from a hot gas to a flowing bed of solid particles could be estimated with suffioent accuracy, using known correlations for gas-to-pamcle heat-transfer coefficientand assuming that the parUcles flow in plug flow The work also demonstrated that this type of system has a well-defined operatmg envelope, recording that of the flowing fluidized bed used m the experiments and indicating the parameters which affect Jt Future development work required for industrial scale heat recovery systems based upon such pnnclples is discussed.
NOMENCLATURE c h H k L m Nu
specificheat at constant pressure [kJ/kgK] heat-transfer coefficient [kW/m2K] bed depth [m] thermal conductivity [kW/mK] length of bed [m] mass flow rate [kg/s] Nusselt number, (h_~/j/ks) heat-transfer rate II~Wl R thermal capaaty rate, (r/~c) [kW/K] Re Reynolds number (pxUdp/us) S surfacearea [m"] T temperature [K] x distance [m] Greek symbols r/ effecUveness,equaUon (1) p density [kg/m~J # viscosity[kg/ms] Subscripts 1 inlet conditmns 2 outlet condmons f when flmdized g gas h beater p parUcle s sohd 1. I N T R O D U C T I O N G a s - t o - h q u l d heat exchangers which exploit the a d v a n t a g e s offered by beds o f solid particles which are fluidized by the gas from which heat is to be recovered have been available commercially for several years, [1, 2]. T h e y have been used principally to generate hot water or steam. T h e solid particles, typically o f a l u m i n a or silica sand o f m e a n size a b o u t 0.5 m m are c o n t a i n e d to a shallow depth, ca 50 ram, in a vessel h a v i n g a base plate termed a d i s t r i b u t o r h a v i n g holes or slots in it t h r o u g h which the hot gas c a n pass u p w a r d s into the bed o f particles, giving up m u c h o f its heat 535
536
H_ HA'I-I'ORIand J R HOWARD
to the particles Extended-surface tubing carrying the feed water are tmmersed in the bed of particles extract the heat from the particles continuously Such heat exchangers require a significantly smaller amount of heat-transfer surface area than conventional gas to liquid heat exchangers, because the very much larger heat-transfer coefficmnt at the interface between the fluidlzed bed and the immersed surface more than compensates for the additional interface between the gas and heat-transfer surface due to the particles; they simply act as a heat carrier Further important advantages of the shallow flmdized bed heat exchangers are that the heat-transfer surfaces are prevented from becoming fouled because they are kept clean continuously by the scounng action of the particles, which appears to be gentle enough to avoid erosion, while the pressure drop across the heat exchanger is kept within acceptable bounds by the shallowness of the bed and appropriate distributor design. If however the gases contain entrained dust, attention has to be paid to avoiding blockage of the distributor passages. A gas-to-gas fluidized bed heat exchanger was described in a patent [3] and experimental work to explore its characteristics and market possibilities was reported by Newey and Howard [4] and Newey and Howard [5]. The novelty of this heat exchanger lay in the design of its distributor whmh was arranged to make both the hot gas and that to be heated emerge from the distributor at an acute angle to the plane of the dxstributor so as to impart transverse motion to the fluidized bed of particles supported on it. The containment of the fluidmed bed was shaped so that the bed of particles could circulate between the hot and cold gas streams in a s~milar manner to that of a rotary regenerator or "heat wheel" [6]. The conventional "heat wheel" is well-proven but is prone to fouling and leakage through mechanical seals at the moving surfaces, particularly at high temperatures. A flowing fluidized bed type of gas-to-gas heat exchanger could be less prone to fouling since alumina particles can withstand high temperature, corroswe atmospheres; leakage through seals separating the two gas streams or cross contamination between them can be circumvented by developing a small differentml pressure between the streams Successful application of the latter technique was reported in [4, 5]. The maximum effectiveness of the flowing fluid~zed bed type of regenerator is limited to about 50% when the thermal capacity rates, m c , of the two gas streams are equal, because the streams are in parallel flow and are only supported by a small component of cross flow. But the main advantage of this type ~s its simplicity. With the flmdmed bed type of gas-to-gas heat recovery system described m this present article however, It is possible to arrange a number of flowing fluidmed beds one above the other so that the flow of particles relative to the gas combines counter-flow w~th cross-flow, with attendant improvement in effectiveness. Such an increase in effectweness is important not only from energy conservation considerations, but also because the recovered heat is avadable at a higher temperature and thus may be more useful. The need to transfer particles to and from the hot and cold gas streams is inherent in a complete heat recovery system. T~me limited the work to investigating heat transfer from a hot gas to the parucles in a single fluidmed bed. 2. T H E O R E T I C A L C O N S I D E R A T I O N S Two alternative theoretmal models for prediction of steady state performance were developed and the adequacy of their predictions were assessed by comparing them with the measured performance of an expenmental fluidtzed bed in which hot air was cooled by the bed particles. The flowing fluidmed bed shown within the dotted system boundary in Fig. 1 was analysed for performance in the steady state. The internal thermal resistance of the particles was assumed to be negligible. The effectiveness, ~/h, of heating of the sohds may be defined as, the ratto, (actual temperature rise of the solids): (theoretmal maximum possible temperature rise); thus, using the nomenclature on Fig. 1, (T..~ - L ,) ,7~ = (T~., - L.O
(l)
Gas-to-gas heat recovery
537
CooLed gas
I
I Cord por*.|ctes
L., ~
." ,-.y...T,,~.
t~g'* • ;,.~'_
-'1 .:-"
[ T|, i HO~¢ga,t Fig 1. Flowing flmdized bed with system boundary superimposed.
The steady flow energy equation for the system is,
R,(T,.2- T,.,)= Rg(Ts.,- Ts.:).
(2)
The rate of heat transfer,~, from the gas to the particles,namely, the fight hand side of equation (2),can also be written in terms of the gas-to-particleheat-transfercoefficient,hp, the total surface area, S, of particlesin the bed and the mean temperature difference,(MTD), between the gas and particles, thus, = hpS(MTD)
(3)
The mean temperature difference ( M T D ) depends upon the distribution of particle temperature throughout the bed. This in turn depends upon how well the gas and panicles come into contact. For example, if the gas flows through preferential paths among the particles,only a fraction of the total surface area of the panicles wdl be swept by the gas so that large temperature gradients may exist in the bed. T w o cases of bed temperature distfibuUon were postulated, namely, perfect backmlxing of particles and plug flow of gas.
Perfect backmixing of particles In the case of perfect backmixing, as soon as the incoming solid particlesenter the system their temperature is assumed to rise to that of_the panicles leaving the system, see Perry and Chilton [7]. The particle temperature throughout the bed is thus uniform at T,,2.The appropriate mean temperature difference is then the Iogarithmtc mean temperature difference, (LMTD), so that,
a
/ L
Elimination of the temperatures among equations (4), (2) and (1) leads to the following equation for effecttveness, rlh, ~h = [R~{ 1 - exp k - - - - ~ )
1
(5)
Plug flow of particles With horizontal plug flow of solid particles, the particle temperature could, in general, be expected to vary in both the direction of particle flow and normal to it. For simplicity however it is assumed here that the particle temperature vanes in the direction of particle flow, but is constant along any line normal to that direction. The validity of such a simplifying assumption depends upon good mixing of the panicles m the direction normal to general particle flow. It is
538
H HA'I-IDRIand J. R. HowAav T*'l
Te'2
.
•N• \
\
Fig. 2 Diagram of flowing flmdtzed bed for modelling using assumption of plug flowof particles (perfect backmlxmg) well known that in a reasonably well-flmdized bed of parncles, all having the same density and a fairly narrow size range, the particle mixing in the vertical direction ts more vigorous than the transverse mixing. Figure 2 shows a conceptual diagram of such a flowing fluidized bed which was used as a mathematical model for the plug flow case. Consider an elemental length, Ax, of the fluidized bed. Using the nomenclature on Fig. 2, the steady flow energy for the element is,
Ax R,(AT~) = R,(T,.. - Ts,2) T '
(6)
The heat-transfer rate {), from the fluidizing gas to the particles contained within the element boundary will be,
Q = hpSa-~ In Integrating between the limits, T,
=
T~2= T g,l + ( T s l._
(r,,- r,9 1
(7)
t - T,)}
Ts. I at x = 0, and T, = T,.: at x = L, leads to, Tg.t)expI ~- Rg
_exp~,l['_-__R_Z)} h,S~
(8)
which is the equation due to McGaw [8]. Substituting this m the equation for effectiveness of heat transfer to the particles, equation (1), yields,
r / h _ _ _ l _ e x p I _ ~ R S { l _ e x p \ _].t.l. (. -~hs p S ~
(9)
Comparison of the two equations for effecuveness of heating the sohds, equations (5) and (9), for example when R,/R s = I and (hpS/R s) is large, a condition not uncommon m fluidized systems, shows that the effectiveness in plug flow to be the higher of the two. In order to achieve plug flow of the particles, McGaw [8], suggested that the bed should be as long as possible. However, a "hydraulic gradient" is required to make the flmdized bed flow, so that the upstream end of the bed is deeper than the downstream end. With a long bed this leads to non-uniform fluidization, particularly if the bed is shallow, because the shallowest part of the bed offers less resistance to the fluidizing gas flow than the deeper part.
Gas-to-gas heat recovery
539
If the distributor is inchned slightly in order to provide the necessary hydrauhc gradmnt, the variation in uniformity of fluidlzation over the length of the bed can be reduced by erecting we~rs at intervals along its length.
Gas-to-particle heat-transfer coefficient, hp Correlations for estimating the value of the gas-to-particle heat-transfer coefficient, hp in a fluidized bed having a horizontal distributor are given by Kato et al. [9] and Kunii and Levenspiel [10]. Despite the differences in uniformity of fluidization between a fluidlzed bed having a hydraulic gradient and one having no such gradmnt, ~t was considered probable that use of such correlations to calculate values of h, for insertion in equations (5) and (9) might be sufficient to allow adequate estimauon of heat transfer from the gas to the particles to be made. Notme that even with a shallow bed of particles, say 10 mm deep with particles of mean size 500/am diameter, the surface area S, of the particles is extremely large; thus the value of the exponent of ( - hpS/P~) in equations (5) and (9) will be small and an error in the value ofh, may not introduce serious error in such estimates of effectiveness. In the work reported here, the correlation due to Kato et al. [9], was used, namely,
/ d \09 Nu = 0.59 Re' ' ~ / )
(1O)
since it was claimed to be valid over the range of particle Reynolds numbers likely to be met in the subsequent experimental work, 3 < Re < 50, and also included the bed depth, HI, as a parameter. Experiments with a fluidized bed having an inclined distributor could then demonstrate which of the alternative criteria for prediction of the effectiveness, rh, (namely, perfect backmixing or plug flow), resulted in predictions which corresponded most closely to practtcal performance measurements.
3. EXPERIMENTAL WORK
Equipment The test rig for experiments is shown schemattcally m Fig. 3. It comprises two fluidized beds. One of the beds termed a "particle heater" had its containment capable of being tilted to any destred angle up to 20 ° so as to make the solids flow. Hot air could be supplied to this bed from a fan via an electric heater, the air flow_rate being measured by a rotameter. Cold silica sand particles of sine range 500-700 #m, mean size 600/~m, were fed to the "particle heater" from the lower of two hoppers via a vibratory solids feeder. After passmg through the "particle heater" the now hot particles flowed into a second bed termed a "particle cooler" where they were fluidized by cold air to cool them; the cold air flow rate was measured by a rotameter. A pneumatic transport line transported the cooled particles from the "panicle cooler" to the upper hopper. The open channel bridge between the two hoppers could be swung sideways to allow the solids to be dmcharged into a collecting vessel so that the solids flow rate could be determined by weighing the amount collected over a measured period of time. A~r temperatures were measured by a thermocouples in the plenum below the fluidized bed distributor of the "particle heater" and at the air outlet from it. The temperature of the solids was measured at the vibratory feeder and in the sloping pipe connecting the "heater" and the "cooler". Four thermocouples were also located 5 mm below the surface of the fluidized bed of the "particle heater" at intervals along the path of the particles flowing through it. Air pressures throughout the system were measured by water-filled manometers. Throughout the experiments care was taken to maintain the differential pressure between the above-bed zones of the "heater" and "cooler" to near zero so as to minimize any air flow through the pipe conveying the heated particles to the "cooler".
Test procedure Tests of the "particle heater" were conducted in the steady state with different types of
540
H HA'I'rORI and J. R HOWARD
Hoppers
Pneumatic transpert, tirm Open channel bridge
Vibratory feeder
rticte heater" "ParticLe cooLer" heater
Btowers
FIg 3. Test ng used for experiments
dtstnbutor, weir heights and angle of inclination of the distributor. The following test procedure was adopted with each assembly, 1. Set the air flows to the two fluidized beds. 2. Start the particle feeder and set the angle o f inclination of the "particle heater". 3. Select the electric heater output tO give an a~r inlet temperature to the "particle heater" in the range 120-190°C. 4. Once the steady state was reached observe all temperatures and flow rates. 5. Repeat with one of the variables changed. 4. R E S U L T S
Particle flow rate limitations For a given assembly, set to operate with a given angle of inclination and air flow rate, the particle flow rate could not be increased beyond the point at which the depth of particles m the first cell increased to such a level that air flow through that cell ceased; the air then becoming diverted to other cells. There was thus a maximum particle flow rate for each configuration. Figure 4 shows this maximum particle flow rate plotted against angle of mchnation of the distributor at various superficial fluidising air velocities for the "particle heater" having 4 cells each with a weir height 4 crn; the fluidizing air was at ambient temperature. This maximum particle flow rate constitutes one of the boundaries of the "operating envelope" of the "particle heater"[
Operating envelope Figure 5 shows such an operating envelope, ABCD, m which AB defines the maximum particle flow rate, BC the somewhat arbitrary maximum desired ratto of sohd:gas thermal capacity rates,
Gas-to-gas heat recovery
60[-
541
Ut (m/tdK)
i
A048
_o: _E
J J I ~ o
..,ore
5 IO 15 lncUned angle (dog)
20
Fig 4. Maximum parUcle flow rate vs angle of mchnaUon of distnbutor
(this is dictated by the minimum acceptable temperature of the outlet particles), R,/Rg, CD is set by excessive entrainment of particles in the air leaving the free surface of the fluidized bed and DA is the lower desired limit for R,/Rs, (this may be set by the maximum desired outlet temperature of the particles). Some experimental operating points are shown within the envelope for a "heater" having 4 cells each with a weir height of 4 cm.
Effectiveness of "particle heater" Figure 6 shows the effectiveness, %, as defined by equations (5) and (9) plotted against R,/Rg together with the measured effectiveness as defined by equation (1). Although Fig. 6 is a dimensionless plot against which all experimental data could be correlated, it is nonetheless of interest to a designer to have dimensional results of a particular experiment
J
Maximum particle flow rote through the pneumatic transl)o r t / o
:
•,,. 20 cp
Maximum i~ ¢ ~ - ~ particle ]/~o / flaw r a ~ ' - - . . ~
I
o
through
"~.a,.r" / /~
O
E u
/ F~/~
Entrainment increases ~ from this a,r fLaw rate
IC
~/~
,oc,,..,oaa°O~.(...)
O.
I
I0
I
20
o
,o
o
15
I
30
J
40
A,r mall fLow (g/sic) Fig. 5 Operating envelope of the particle heater.
542
H HATrORI and J R H O W A R D ! C
PLug sOLid flow modal
0.8
fB~L::mml~SoUd
l v
0
06
Sign OJltMbutor [ncLln(Itmn Of~l~ 0
Grote
0
Bar
D
I
&
15"
Screen laerf°r°ted
20" SO*
sheet
I
o
I0*
I
02
I
04
06
I
I
I
I0
08
12
R,/Rg(-) Fig. 6. Effectiveness of heater vs thermal capacity ratio R J R r
which shows the effect of changing the solids flow rate alone on effectiveness, %, of the "particle heater". The results of a separate experiment in which the hot air flow rate was held approximately constant, at a value slightly smaller than that giving excessive entrainment of particles, while the solids flow rate was varied is shown in Fig. 7. 5 DISCUSSION OF RESULTS The experimental data points plotted on F~g. 6 correlate more closely with the effectiveness predicted by assuming plug flow, of solids, equation (5), than with that predicted assuming perfect backmixing. Further, the changes in the type of distributor and its angle of inclination does not appear to make a radical difference to performance. CaLcuLation Air mass flow (g/sac)
-~.
08
I
1:: :oo /~3~
OE Experiments Air moss fLow
04-
~
'.%
tncLl~9.*on angle
(g Im¢)
SO* i5"
30-32 5
A
0
a
32 5 - 35
0
I
I0 Portl¢te
I
I
I
mass f L o w . M , ( g l s e c )
Fig 7 Effect of changes in sohds flow rate on effectiveness of particle heater
Gas-to-gas heat recovery
543
\
F1g 8. Flui&zatlon pattern of flmdized bed hawng an inclined distnbutor
Although the assumption of plug flow o f the solid particles allows effectiveness to be predicted with acceptable accuracy, visual observation of the pattern of fluidization of the particles indicated that the particles were flui&zed non-umformly; see the photograph Fig. 8 which shows a section of the fluidized bed having an inclined distributor. The air flowing through the shallowest region throws the particles into the above-bed zone and tends to ~mpart an anti-clockwise circulating motion to the bed. Such a phenomenon is similar to that encountered with a spouted bed [11] or whirling bed [12], reported elsewhere. Provision of weirs helped to reduce variation in distribution of fluidizing gas along the length of the bed. Clearly, a gas-to-gas heat recovery system based upon a flowing bed of fluidized particles of the type reported here is practicable. Inclining the distributor plate in order to make the solid particles flow does not seem to inhibit the overall performance.
6.
FUTURE
DEVELOPMENT
Future work includes the development of this type of heat recovery system into an industrial scale prototype, incorporating multi-stage particle heaters and coolers and alternative internal solids transport systems. This wtll allow the necessary trials to establish operational flexibihty, the consequences of prolonged thermal cycling on the size range of the particles, the extent to which contaminants in the gases can be tolerated and the reliability and life of system components.
544
H. HATTORI and J R HOWARD REFERENCES
1. D E Elhott and M J Vlrr, Proc 3rd International Conference on Fluidtzed Bed Combusuon, EPA-650/2-73-053 (December 1973)_ 2 J R_ Howard (editor), Flm&zed Beds. Combusnon and Apphcatlons, Chapter 11 Apphed Science Publishers, London (1983). 3. BnUsh Patent No 1500 231 (1978) 4_ D C Newey, PhD Thesis, Umverslty of Aston in Blnmngham (1980)_ 5 D_ C. Newey and J. R Howard, J. Heat Recovery Systems 3, 35--40 (1983) 6. D A Reay, Heat Recovery Systems, Chapter I E. & F N. Sport, London (1979) 7 R H. Perry and C H Chilton, Chemical Engineers" Handbook, 5th Edn, section 4-22. McGraw-Hill, Tokyo (1973) 8 D. R. McGaw, Int. J. Heat Mass Transfer 19, 657-663 (1976) 9 K Kato, H Ito and S Omura, J Chem Engng Japan 12, 403--404 (1979) 10 D Kunn and O_ Levenspiel, Fluidlzatwn Engineering, Chapter 7, pp. 210--219 John Wiley, New York (1969). 11 N. Epstein and K K Mathur, Spouted Reds. Academac Press, New York (1974) 12 G_ M. Rios, J L Baxerres and H Gilbert, in Fluidlzation, (edited by J. R. Grace and J M Matsen) Plenum Press, New York (1980)
0198-7593/85 $3 00 + 0 00
Pergamon Press Ltd
GAS-TO-GAS HEAT RECOVERY USING FLUIDIZED BED TECHNOLOGY H. HATTORI Manufactunng Engineenng Research Center, Komatsu Ltd, 3-1-1 Ueno, Hirakata-shi, Osaka-fu, 573 Japan
and J. R. HOWARD Department of Mechanical and Production Engmeenng, Umverslty of Aston in Birmingham, Gosta Green, Birmingham, England and H.H Assocmtes, 18 Pembroke Croft, Hall Green, Birmingham B28 9EY, England
Abstract--The extraordinarily large surface area and heat eapacaty per umt volume of a bed of solid parucles makes them attractive as a heat carrier. This paper reports briefly a thcorcucal and experimental study of some of the problems if the potentaal advantages are to be exploited This revealed that the effectiveness of heat transfer from a hot gas to a flowing bed of solid particles could be estimated with suffioent accuracy, using known correlations for gas-to-pamcle heat-transfer coefficientand assuming that the parUcles flow in plug flow The work also demonstrated that this type of system has a well-defined operatmg envelope, recording that of the flowing fluidized bed used m the experiments and indicating the parameters which affect Jt Future development work required for industrial scale heat recovery systems based upon such pnnclples is discussed.
NOMENCLATURE c h H k L m Nu
specificheat at constant pressure [kJ/kgK] heat-transfer coefficient [kW/m2K] bed depth [m] thermal conductivity [kW/mK] length of bed [m] mass flow rate [kg/s] Nusselt number, (h_~/j/ks) heat-transfer rate II~Wl R thermal capaaty rate, (r/~c) [kW/K] Re Reynolds number (pxUdp/us) S surfacearea [m"] T temperature [K] x distance [m] Greek symbols r/ effecUveness,equaUon (1) p density [kg/m~J # viscosity[kg/ms] Subscripts 1 inlet conditmns 2 outlet condmons f when flmdized g gas h beater p parUcle s sohd 1. I N T R O D U C T I O N G a s - t o - h q u l d heat exchangers which exploit the a d v a n t a g e s offered by beds o f solid particles which are fluidized by the gas from which heat is to be recovered have been available commercially for several years, [1, 2]. T h e y have been used principally to generate hot water or steam. T h e solid particles, typically o f a l u m i n a or silica sand o f m e a n size a b o u t 0.5 m m are c o n t a i n e d to a shallow depth, ca 50 ram, in a vessel h a v i n g a base plate termed a d i s t r i b u t o r h a v i n g holes or slots in it t h r o u g h which the hot gas c a n pass u p w a r d s into the bed o f particles, giving up m u c h o f its heat 535
536
H_ HA'I-I'ORIand J R HOWARD
to the particles Extended-surface tubing carrying the feed water are tmmersed in the bed of particles extract the heat from the particles continuously Such heat exchangers require a significantly smaller amount of heat-transfer surface area than conventional gas to liquid heat exchangers, because the very much larger heat-transfer coefficmnt at the interface between the fluidlzed bed and the immersed surface more than compensates for the additional interface between the gas and heat-transfer surface due to the particles; they simply act as a heat carrier Further important advantages of the shallow flmdized bed heat exchangers are that the heat-transfer surfaces are prevented from becoming fouled because they are kept clean continuously by the scounng action of the particles, which appears to be gentle enough to avoid erosion, while the pressure drop across the heat exchanger is kept within acceptable bounds by the shallowness of the bed and appropriate distributor design. If however the gases contain entrained dust, attention has to be paid to avoiding blockage of the distributor passages. A gas-to-gas fluidized bed heat exchanger was described in a patent [3] and experimental work to explore its characteristics and market possibilities was reported by Newey and Howard [4] and Newey and Howard [5]. The novelty of this heat exchanger lay in the design of its distributor whmh was arranged to make both the hot gas and that to be heated emerge from the distributor at an acute angle to the plane of the dxstributor so as to impart transverse motion to the fluidized bed of particles supported on it. The containment of the fluidmed bed was shaped so that the bed of particles could circulate between the hot and cold gas streams in a s~milar manner to that of a rotary regenerator or "heat wheel" [6]. The conventional "heat wheel" is well-proven but is prone to fouling and leakage through mechanical seals at the moving surfaces, particularly at high temperatures. A flowing fluidized bed type of gas-to-gas heat exchanger could be less prone to fouling since alumina particles can withstand high temperature, corroswe atmospheres; leakage through seals separating the two gas streams or cross contamination between them can be circumvented by developing a small differentml pressure between the streams Successful application of the latter technique was reported in [4, 5]. The maximum effectiveness of the flowing fluid~zed bed type of regenerator is limited to about 50% when the thermal capacity rates, m c , of the two gas streams are equal, because the streams are in parallel flow and are only supported by a small component of cross flow. But the main advantage of this type ~s its simplicity. With the flmdmed bed type of gas-to-gas heat recovery system described m this present article however, It is possible to arrange a number of flowing fluidmed beds one above the other so that the flow of particles relative to the gas combines counter-flow w~th cross-flow, with attendant improvement in effectiveness. Such an increase in effectweness is important not only from energy conservation considerations, but also because the recovered heat is avadable at a higher temperature and thus may be more useful. The need to transfer particles to and from the hot and cold gas streams is inherent in a complete heat recovery system. T~me limited the work to investigating heat transfer from a hot gas to the parucles in a single fluidmed bed. 2. T H E O R E T I C A L C O N S I D E R A T I O N S Two alternative theoretmal models for prediction of steady state performance were developed and the adequacy of their predictions were assessed by comparing them with the measured performance of an expenmental fluidtzed bed in which hot air was cooled by the bed particles. The flowing fluidmed bed shown within the dotted system boundary in Fig. 1 was analysed for performance in the steady state. The internal thermal resistance of the particles was assumed to be negligible. The effectiveness, ~/h, of heating of the sohds may be defined as, the ratto, (actual temperature rise of the solids): (theoretmal maximum possible temperature rise); thus, using the nomenclature on Fig. 1, (T..~ - L ,) ,7~ = (T~., - L.O
(l)
Gas-to-gas heat recovery
537
CooLed gas
I
I Cord por*.|ctes
L., ~
." ,-.y...T,,~.
t~g'* • ;,.~'_
-'1 .:-"
[ T|, i HO~¢ga,t Fig 1. Flowing flmdized bed with system boundary superimposed.
The steady flow energy equation for the system is,
R,(T,.2- T,.,)= Rg(Ts.,- Ts.:).
(2)
The rate of heat transfer,~, from the gas to the particles,namely, the fight hand side of equation (2),can also be written in terms of the gas-to-particleheat-transfercoefficient,hp, the total surface area, S, of particlesin the bed and the mean temperature difference,(MTD), between the gas and particles, thus, = hpS(MTD)
(3)
The mean temperature difference ( M T D ) depends upon the distribution of particle temperature throughout the bed. This in turn depends upon how well the gas and panicles come into contact. For example, if the gas flows through preferential paths among the particles,only a fraction of the total surface area of the panicles wdl be swept by the gas so that large temperature gradients may exist in the bed. T w o cases of bed temperature distfibuUon were postulated, namely, perfect backmlxing of particles and plug flow of gas.
Perfect backmixing of particles In the case of perfect backmixing, as soon as the incoming solid particlesenter the system their temperature is assumed to rise to that of_the panicles leaving the system, see Perry and Chilton [7]. The particle temperature throughout the bed is thus uniform at T,,2.The appropriate mean temperature difference is then the Iogarithmtc mean temperature difference, (LMTD), so that,
a
/ L
Elimination of the temperatures among equations (4), (2) and (1) leads to the following equation for effecttveness, rlh, ~h = [R~{ 1 - exp k - - - - ~ )
1
(5)
Plug flow of particles With horizontal plug flow of solid particles, the particle temperature could, in general, be expected to vary in both the direction of particle flow and normal to it. For simplicity however it is assumed here that the particle temperature vanes in the direction of particle flow, but is constant along any line normal to that direction. The validity of such a simplifying assumption depends upon good mixing of the panicles m the direction normal to general particle flow. It is
538
H HA'I-IDRIand J. R. HowAav T*'l
Te'2
.
•N• \
\
Fig. 2 Diagram of flowing flmdtzed bed for modelling using assumption of plug flowof particles (perfect backmlxmg) well known that in a reasonably well-flmdized bed of parncles, all having the same density and a fairly narrow size range, the particle mixing in the vertical direction ts more vigorous than the transverse mixing. Figure 2 shows a conceptual diagram of such a flowing fluidized bed which was used as a mathematical model for the plug flow case. Consider an elemental length, Ax, of the fluidized bed. Using the nomenclature on Fig. 2, the steady flow energy for the element is,
Ax R,(AT~) = R,(T,.. - Ts,2) T '
(6)
The heat-transfer rate {), from the fluidizing gas to the particles contained within the element boundary will be,
Q = hpSa-~ In Integrating between the limits, T,
=
T~2= T g,l + ( T s l._
(r,,- r,9 1
(7)
t - T,)}
Ts. I at x = 0, and T, = T,.: at x = L, leads to, Tg.t)expI ~- Rg
_exp~,l['_-__R_Z)} h,S~
(8)
which is the equation due to McGaw [8]. Substituting this m the equation for effectiveness of heat transfer to the particles, equation (1), yields,
r / h _ _ _ l _ e x p I _ ~ R S { l _ e x p \ _].t.l. (. -~hs p S ~
(9)
Comparison of the two equations for effecuveness of heating the sohds, equations (5) and (9), for example when R,/R s = I and (hpS/R s) is large, a condition not uncommon m fluidized systems, shows that the effectiveness in plug flow to be the higher of the two. In order to achieve plug flow of the particles, McGaw [8], suggested that the bed should be as long as possible. However, a "hydraulic gradient" is required to make the flmdized bed flow, so that the upstream end of the bed is deeper than the downstream end. With a long bed this leads to non-uniform fluidization, particularly if the bed is shallow, because the shallowest part of the bed offers less resistance to the fluidizing gas flow than the deeper part.
Gas-to-gas heat recovery
539
If the distributor is inchned slightly in order to provide the necessary hydrauhc gradmnt, the variation in uniformity of fluidlzation over the length of the bed can be reduced by erecting we~rs at intervals along its length.
Gas-to-particle heat-transfer coefficient, hp Correlations for estimating the value of the gas-to-particle heat-transfer coefficient, hp in a fluidized bed having a horizontal distributor are given by Kato et al. [9] and Kunii and Levenspiel [10]. Despite the differences in uniformity of fluidization between a fluidlzed bed having a hydraulic gradient and one having no such gradmnt, ~t was considered probable that use of such correlations to calculate values of h, for insertion in equations (5) and (9) might be sufficient to allow adequate estimauon of heat transfer from the gas to the particles to be made. Notme that even with a shallow bed of particles, say 10 mm deep with particles of mean size 500/am diameter, the surface area S, of the particles is extremely large; thus the value of the exponent of ( - hpS/P~) in equations (5) and (9) will be small and an error in the value ofh, may not introduce serious error in such estimates of effectiveness. In the work reported here, the correlation due to Kato et al. [9], was used, namely,
/ d \09 Nu = 0.59 Re' ' ~ / )
(1O)
since it was claimed to be valid over the range of particle Reynolds numbers likely to be met in the subsequent experimental work, 3 < Re < 50, and also included the bed depth, HI, as a parameter. Experiments with a fluidized bed having an inclined distributor could then demonstrate which of the alternative criteria for prediction of the effectiveness, rh, (namely, perfect backmixing or plug flow), resulted in predictions which corresponded most closely to practtcal performance measurements.
3. EXPERIMENTAL WORK
Equipment The test rig for experiments is shown schemattcally m Fig. 3. It comprises two fluidized beds. One of the beds termed a "particle heater" had its containment capable of being tilted to any destred angle up to 20 ° so as to make the solids flow. Hot air could be supplied to this bed from a fan via an electric heater, the air flow_rate being measured by a rotameter. Cold silica sand particles of sine range 500-700 #m, mean size 600/~m, were fed to the "particle heater" from the lower of two hoppers via a vibratory solids feeder. After passmg through the "particle heater" the now hot particles flowed into a second bed termed a "particle cooler" where they were fluidized by cold air to cool them; the cold air flow rate was measured by a rotameter. A pneumatic transport line transported the cooled particles from the "panicle cooler" to the upper hopper. The open channel bridge between the two hoppers could be swung sideways to allow the solids to be dmcharged into a collecting vessel so that the solids flow rate could be determined by weighing the amount collected over a measured period of time. A~r temperatures were measured by a thermocouples in the plenum below the fluidized bed distributor of the "particle heater" and at the air outlet from it. The temperature of the solids was measured at the vibratory feeder and in the sloping pipe connecting the "heater" and the "cooler". Four thermocouples were also located 5 mm below the surface of the fluidized bed of the "particle heater" at intervals along the path of the particles flowing through it. Air pressures throughout the system were measured by water-filled manometers. Throughout the experiments care was taken to maintain the differential pressure between the above-bed zones of the "heater" and "cooler" to near zero so as to minimize any air flow through the pipe conveying the heated particles to the "cooler".
Test procedure Tests of the "particle heater" were conducted in the steady state with different types of
540
H HA'I'rORI and J. R HOWARD
Hoppers
Pneumatic transpert, tirm Open channel bridge
Vibratory feeder
rticte heater" "ParticLe cooLer" heater
Btowers
FIg 3. Test ng used for experiments
dtstnbutor, weir heights and angle of inclination of the distributor. The following test procedure was adopted with each assembly, 1. Set the air flows to the two fluidized beds. 2. Start the particle feeder and set the angle o f inclination of the "particle heater". 3. Select the electric heater output tO give an a~r inlet temperature to the "particle heater" in the range 120-190°C. 4. Once the steady state was reached observe all temperatures and flow rates. 5. Repeat with one of the variables changed. 4. R E S U L T S
Particle flow rate limitations For a given assembly, set to operate with a given angle of inclination and air flow rate, the particle flow rate could not be increased beyond the point at which the depth of particles m the first cell increased to such a level that air flow through that cell ceased; the air then becoming diverted to other cells. There was thus a maximum particle flow rate for each configuration. Figure 4 shows this maximum particle flow rate plotted against angle of mchnation of the distributor at various superficial fluidising air velocities for the "particle heater" having 4 cells each with a weir height 4 crn; the fluidizing air was at ambient temperature. This maximum particle flow rate constitutes one of the boundaries of the "operating envelope" of the "particle heater"[
Operating envelope Figure 5 shows such an operating envelope, ABCD, m which AB defines the maximum particle flow rate, BC the somewhat arbitrary maximum desired ratto of sohd:gas thermal capacity rates,
Gas-to-gas heat recovery
60[-
541
Ut (m/tdK)
i
A048
_o: _E
J J I ~ o
..,ore
5 IO 15 lncUned angle (dog)
20
Fig 4. Maximum parUcle flow rate vs angle of mchnaUon of distnbutor
(this is dictated by the minimum acceptable temperature of the outlet particles), R,/Rg, CD is set by excessive entrainment of particles in the air leaving the free surface of the fluidized bed and DA is the lower desired limit for R,/Rs, (this may be set by the maximum desired outlet temperature of the particles). Some experimental operating points are shown within the envelope for a "heater" having 4 cells each with a weir height of 4 cm.
Effectiveness of "particle heater" Figure 6 shows the effectiveness, %, as defined by equations (5) and (9) plotted against R,/Rg together with the measured effectiveness as defined by equation (1). Although Fig. 6 is a dimensionless plot against which all experimental data could be correlated, it is nonetheless of interest to a designer to have dimensional results of a particular experiment
J
Maximum particle flow rote through the pneumatic transl)o r t / o
:
•,,. 20 cp
Maximum i~ ¢ ~ - ~ particle ]/~o / flaw r a ~ ' - - . . ~
I
o
through
"~.a,.r" / /~
O
E u
/ F~/~
Entrainment increases ~ from this a,r fLaw rate
IC
~/~
,oc,,..,oaa°O~.(...)
O.
I
I0
I
20
o
,o
o
15
I
30
J
40
A,r mall fLow (g/sic) Fig. 5 Operating envelope of the particle heater.
542
H HATrORI and J R H O W A R D ! C
PLug sOLid flow modal
0.8
fB~L::mml~SoUd
l v
0
06
Sign OJltMbutor [ncLln(Itmn Of~l~ 0
Grote
0
Bar
D
I
&
15"
Screen laerf°r°ted
20" SO*
sheet
I
o
I0*
I
02
I
04
06
I
I
I
I0
08
12
R,/Rg(-) Fig. 6. Effectiveness of heater vs thermal capacity ratio R J R r
which shows the effect of changing the solids flow rate alone on effectiveness, %, of the "particle heater". The results of a separate experiment in which the hot air flow rate was held approximately constant, at a value slightly smaller than that giving excessive entrainment of particles, while the solids flow rate was varied is shown in Fig. 7. 5 DISCUSSION OF RESULTS The experimental data points plotted on F~g. 6 correlate more closely with the effectiveness predicted by assuming plug flow, of solids, equation (5), than with that predicted assuming perfect backmixing. Further, the changes in the type of distributor and its angle of inclination does not appear to make a radical difference to performance. CaLcuLation Air mass flow (g/sac)
-~.
08
I
1:: :oo /~3~
OE Experiments Air moss fLow
04-
~
'.%
tncLl~9.*on angle
(g Im¢)
SO* i5"
30-32 5
A
0
a
32 5 - 35
0
I
I0 Portl¢te
I
I
I
mass f L o w . M , ( g l s e c )
Fig 7 Effect of changes in sohds flow rate on effectiveness of particle heater
Gas-to-gas heat recovery
543
\
F1g 8. Flui&zatlon pattern of flmdized bed hawng an inclined distnbutor
Although the assumption of plug flow o f the solid particles allows effectiveness to be predicted with acceptable accuracy, visual observation of the pattern of fluidization of the particles indicated that the particles were flui&zed non-umformly; see the photograph Fig. 8 which shows a section of the fluidized bed having an inclined distributor. The air flowing through the shallowest region throws the particles into the above-bed zone and tends to ~mpart an anti-clockwise circulating motion to the bed. Such a phenomenon is similar to that encountered with a spouted bed [11] or whirling bed [12], reported elsewhere. Provision of weirs helped to reduce variation in distribution of fluidizing gas along the length of the bed. Clearly, a gas-to-gas heat recovery system based upon a flowing bed of fluidized particles of the type reported here is practicable. Inclining the distributor plate in order to make the solid particles flow does not seem to inhibit the overall performance.
6.
FUTURE
DEVELOPMENT
Future work includes the development of this type of heat recovery system into an industrial scale prototype, incorporating multi-stage particle heaters and coolers and alternative internal solids transport systems. This wtll allow the necessary trials to establish operational flexibihty, the consequences of prolonged thermal cycling on the size range of the particles, the extent to which contaminants in the gases can be tolerated and the reliability and life of system components.
544
H. HATTORI and J R HOWARD REFERENCES
1. D E Elhott and M J Vlrr, Proc 3rd International Conference on Fluidtzed Bed Combusuon, EPA-650/2-73-053 (December 1973)_ 2 J R_ Howard (editor), Flm&zed Beds. Combusnon and Apphcatlons, Chapter 11 Apphed Science Publishers, London (1983). 3. BnUsh Patent No 1500 231 (1978) 4_ D C Newey, PhD Thesis, Umverslty of Aston in Blnmngham (1980)_ 5 D_ C. Newey and J. R Howard, J. Heat Recovery Systems 3, 35--40 (1983) 6. D A Reay, Heat Recovery Systems, Chapter I E. & F N. Sport, London (1979) 7 R H. Perry and C H Chilton, Chemical Engineers" Handbook, 5th Edn, section 4-22. McGraw-Hill, Tokyo (1973) 8 D. R. McGaw, Int. J. Heat Mass Transfer 19, 657-663 (1976) 9 K Kato, H Ito and S Omura, J Chem Engng Japan 12, 403--404 (1979) 10 D Kunn and O_ Levenspiel, Fluidlzatwn Engineering, Chapter 7, pp. 210--219 John Wiley, New York (1969). 11 N. Epstein and K K Mathur, Spouted Reds. Academac Press, New York (1974) 12 G_ M. Rios, J L Baxerres and H Gilbert, in Fluidlzation, (edited by J. R. Grace and J M Matsen) Plenum Press, New York (1980)